prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What algorithm is engaged in the PLMS-PPIC method?

Read the following text and answer briefly.

Context 1: \section{Introduction}\label{S1}

The multiple access interferences (MAI) is the root of user
limitation in CDMA systems \cite{R1,R3}  The parallel least mean
square-partial parallel interference cancelation (PLMS-PPIC) method
is a multiuser detector for code division multiple access (CDMA)
receivers which reduces the effect of MAI in bit detection  In this
method and similar to its former versions like LMS-PPIC \cite{R5}
(see also \cite{RR5}), a weighted value of the MAI of other users is
subtracted before making the decision for a specific user in
different stages \cite{cohpaper}  In both of these methods, the
normalized least mean square (NLMS) algorithm is engaged
\cite{Haykin96}  The $m^{\rm th}$ element of the weight vector in
each stage is the true transmitted binary value of the $m^{\rm th}$
user divided by its hard estimate value from the previous stage  The
magnitude of all weight elements in all stages are equal to unity 
Unlike the LMS-PPIC, the PLMS-PPIC method tries to keep this
property in each iteration by using a set of NLMS algorithms with
different step-sizes instead of one NLMS algorithm used in LMS-PPIC 
In each iteration, the parameter estimate of the NLMS algorithm is
chosen whose element magnitudes of cancelation weight estimate have
the best match with unity  In PLMS-PPIC implementation it is assumed
that the receiver knows the phases of all user channels  However in
practice, these phases are not known and should be estimated  In
this paper we improve the PLMS-PPIC procedure \cite{cohpaper} in
such a way that when there is only a partial information of the
channel phases, this modified version simultaneously estimates the
phases and the cancelation weights  The partial information is the
quarter of each channel phase in $(0,2\pi)$ 

The rest of the paper is organized as follows: In section \ref{S4}
the modified version of PLMS-PPIC with capability of channel phase
estimation is introduced  In section \ref{S5} some simulation
examples illustrate the results of the proposed method  Finally the
paper is concluded in section \ref{S6} 

\section{Multistage Parallel Interference Cancelation: Modified PLMS-PPIC Method}\label{S4}

We assume $M$ users synchronously send their symbols
$\alpha_1,\alpha_2,\cdots,\alpha_M$ via a base-band CDMA
transmission system where $\alpha_m\in\{-1,1\}$  The $m^{th}$ user
has its own code $p_m( )$ of length $N$, where $p_m(n)\in \{-1,1\}$,
for all $n$  It means that for each symbol $N$ bits are transmitted
by each user and the processing gain is equal to $N$  At the
receiver we assume that perfect power control scheme is applied 
Without loss of generality, we also assume that the power gains of
all channels are equal to unity and users' channels do not change
during each symbol transmission (it can change from one symbol
transmission to the next one) and the channel phase $\phi_m$ of
$m^{th}$ user is unknown for all $m=1,2,\cdots,M$ (see
\cite{cohpaper} for coherent transmission)  According to the above
assumptions the received signal is
\begin{equation}
\label{e1} r(n)=\sum\limits_{m=1}^{M}\alpha_m
e^{j\phi_m}p_m(n)+v(n),~~~~n=1,2,\cdots,N,
\end{equation}
where $v(n)$ is the additive white Gaussian noise with zero mean and
variance $\sigma^2$  Multistage parallel interference cancelation
method uses $\alpha^{s-1}_1,\alpha^{s-1}_2,\cdots,\alpha^{s-1}_M$,
the bit estimates outputs of the previous stage, $s-1$, to estimate
the related MAI of each user  It then subtracts it from the received
signal $r(n)$ and makes a new decision on each user variable
individually to make a new variable set
$\alpha^{s}_1,\alpha^{s}_2,\cdots,\alpha^{s}_M$ for the current
stage $s$  Usually the variable set of the first stage (stage $0$)
is the output of a conventional detector  The output of the last
stage is considered as the final estimate of transmitted bits  In
the following we explain the structure of a modified version of the
PLMS-PIC method \cite{cohpaper} with simultaneous capability of
estimating the cancelation weights and the channel phases 

Assume $\alpha_m^{(s-1)}\in\{-1,1\}$ is a given estimate of
$\alpha_m$ from stage $s-1$  Define
\begin{equation}
\label{e6} w^s_{m}=\frac{\alpha_m}{\alpha_m^{(s-1)}}e^{j\phi_m} 
\end{equation}
From (\ref{e1}) and (\ref{e6}) we have
\begin{equation}
\label{e7} r(n)=\sum\limits_{m=1}^{M}w^s_m\alpha^{(s-1)}_m
p_m(n)+v(n) 
\end{equation}
Define
\begin{subequations}
\begin{eqnarray}
\label{e8} W^s&=&[w^s_{1},w^s_{2},\cdots,w^s_{M}]^T,\\
\label{e9}
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!X^{s}(n)\!\!\!&=&\!\!\![\alpha^{(s-1)}_1p_1(n),\alpha^{(s-1)}_2p_2(n),\cdots,\alpha^{(s-1)}_Mp_M(n)]^T 
\end{eqnarray}
\end{subequations}
where $T$ stands for transposition  From equations (\ref{e7}),
(\ref{e8}) and (\ref{e9}), we have
\begin{equation}
\label{e10} r(n)=W^{s^T}X^{s}(n)+v(n) 
\end{equation}
Given the observations $\{r(n),X^{s}(n)\}^{N}_{n=1}$, in modified
PLMS-PPIC, like the PLMS-PPIC \cite{cohpaper}, a set of NLMS
adaptive algorithm are used to compute
\begin{equation}
\label{te1} W^{s}(N)=[w^{s}_1(N),w^{s}_2(N),\cdots,w^{s}_M(N)]^T,
\end{equation}
which is an estimate of $W^s$ after iteration $N$  To do so, from
(\ref{e6}), we have
\begin{equation}
\label{e13} |w^s_{m}|=1 ~~~m=1,2,\cdots,M,
\end{equation}
which is equivalent to
\begin{equation}
\label{e14} \sum\limits_{m=1}^{M}||w^s_{m}|-1|=0 
\end{equation}
We divide $\Psi=\left(0,1-\sqrt{\frac{M-1}{M}}\right]$, a sharp
range for $\mu$ (the step-size of the NLMS algorithm) given in
\cite{sg2005}, into $L$ subintervals and consider $L$ individual
step-sizes $\Theta=\{\mu_1,\mu_2,\cdots,\mu_L\}$, where
$\mu_1=\frac{1-\sqrt{\frac{M-1}{M}}}{L}, \mu_2=2\mu_1,\cdots$, and
$\mu_L=L\mu_1$  In each stage, $L$ individual NLMS algorithms are
executed ($\mu_l$ is the step-size of the $l^{th}$ algorithm)  In
stage $s$ and at iteration $n$, if
$W^{s}_k(n)=[w^s_{1,k},\cdots,w^s_{M,k}]^T$, the parameter estimate
of the $k^{\rm th}$ algorithm, minimizes our criteria, then it is
considered as the parameter estimate at time iteration $n$  In other
words if the next equation holds
\begin{equation}
\label{e17} W^s_k(n)=\arg\min\limits_{W^s_l(n)\in I_{W^s}
}\left\{\sum\limits_{m=1}^{M}||w^s_{m,l}(n)|-1|\right\},
\end{equation}
where $W^{s}_l(n)=W^{s}(n-1)+\mu_l \frac{X^s(n)}{\|X^s(n)\|^2}e(n),
~~~ l=1,2,\cdots,k,\cdots,L-1,L$ and
$I_{W^s}=\{W^s_1(n),\cdots,W^s_L(n)\}$, then we have
$W^s(n)=W^s_k(n)$, and therefore all other algorithms replace their
weight estimate by $W^{s}_k(n)$  At time instant $n=N$, this
procedure gives $W^s(N)$, the final estimate of $W^s$, as the true
parameter of stage $s$ 

Now consider $R=(0,2\pi)$ and divide it into four equal parts
$R_1=(0,\frac{\pi}{2})$, $R_2=(\frac{\pi}{2},\pi)$,
$R_3=(\pi,\frac{3\pi}{2})$ and $R_4=(\frac{3\pi}{2},2\pi)$  The
partial information of channel phases (given by the receiver) is in
a way that it shows each $\phi_m$ ($m=1,2,\cdots,M$) belongs to
which one of the four quarters $R_i,~i=1,2,3,4$  Assume
$W^{s}(N)=[w^{s}_1(N),w^{s}_2(N),\cdots,w^{s}_M(N)]^T$ is the weight
estimate of the modified algorithm PLMS-PPIC at time instant $N$ of
the stage $s$  From equation (\ref{e6}) we have
\begin{equation}
\label{tt3}
\phi_m=\angle({\frac{\alpha^{(s-1)}_m}{\alpha_m}w^s_m}) 
\end{equation}
We estimate $\phi_m$ by $\hat{\phi}^s_m$, where
\begin{equation}
\label{ee3}
\hat{\phi}^s_m=\angle{(\frac{\alpha^{(s-1)}_m}{\alpha_m}w^s_m(N))} 
\end{equation}
Because $\frac{\alpha^{(s-1)}_m}{\alpha_m}=1$ or $-1$, we have
\begin{eqnarray}
\hat{\phi}^s_m=\left\{\begin{array}{ll} \angle{w^s_m(N)} &
\mbox{if}~
\frac{\alpha^{(s-1)}_m}{\alpha_m}=1\\
\pm\pi+\angle{w^s_m(N)} & \mbox{if}~
\frac{\alpha^{(s-1)}_m}{\alpha_m}=-1\end{array}\right 
\end{eqnarray}
Hence $\hat{\phi}^s_m\in P^s=\{\angle{w^s_m(N)},
\angle{w^s_m(N)+\pi, \angle{w^s_m(N)}-\pi}\}$  If $w^s_m(N)$
sufficiently converges to its true value $w^s_m$, the same region
for $\hat{\phi}^s_m$ and $\phi_m$ is expected  In this case only one
of the three members of $P^s$ has the same region as $\phi_m$  For
example if $\phi_m \in (0,\frac{\pi}{2})$, then $\hat{\phi}^s_m \in
(0,\frac{\pi}{2})$ and therefore only $\angle{w^s_m(N)}$ or
$\angle{w^s_m(N)}+\pi$ or $\angle{w^s_m(N)}-\pi$ belongs to
$(0,\frac{\pi}{2})$  If, for example, $\angle{w^s_m(N)}+\pi$ is such
a member between all three members of $P^s$, it is the best
candidate for phase estimation  In other words,
\[\phi_m\approx\hat{\phi}^s_m=\angle{w^s_m(N)}+\pi \]
We admit that when there is a member of $P^s$ in the quarter of
$\phi_m$, then $w^s_m(N)$ converges  What would happen when non of
the members of $P^s$ has the same quarter as $\phi_m$? This
situation will happen when the absolute difference between $\angle
w^s_m(N)$ and $\phi_m$ is greater than $\pi$  It means that
$w^s_m(N)$ has not converged yet  In this case where we can not
count on $w^s_m(N)$, the expected value is the optimum choice for
the channel phase estimation, e g  if $\phi_m \in (0,\frac{\pi}{2})$
then $\frac{\pi}{4}$ is the estimation of the channel phase
$\phi_m$, or if $\phi_m \in (\frac{\pi}{2},\pi)$ then
$\frac{3\pi}{4}$ is the estimation of the channel phase $\phi_m$ 
The results of the above discussion are summarized in the next
equation
\begin{eqnarray}
\nonumber \hat{\phi}^s_m = \left\{\begin{array}{llll} \angle
{w^s_m(N)} & \mbox{if}~
\angle{w^s_m(N)}, \phi_m\in R_i,~~i=1,2,3,4\\
\angle{w^s_m(N)}+\pi & \mbox{if}~ \angle{w^s_m(N)}+\pi, \phi_m\in
R_i,~~i=1,2,3,4\\
\angle{w^n_m(N)}-\pi & \mbox{if}~ \angle{w^s_m(N)}-\pi, \phi_m\in
R_i,~~i=1,2,3,4\\
\frac{(i-1)\pi+i\pi}{4} & \mbox{if}~ \phi_m\in
R_i,~~\angle{w^s_m(N)},\angle
{w^s_m(N)}\pm\pi\notin R_i,~~i=1,2,3,4 \\
\end{array}\right 
\end{eqnarray}
Having an estimation of the channel phases, the rest of the proposed
method is given by estimating $\alpha^{s}_m$ as follows:
\begin{equation}
\label{tt4}
\alpha^{s}_m=\mbox{sign}\left\{\mbox{real}\left\{\sum\limits_{n=1}^{N}
q^s_m(n)e^{-j\hat{\phi}^s_m}p_m(n)\right\}\right\},
\end{equation}
where
\begin{equation} \label{tt5}
q^{s}_{m}(n)=r(n)-\sum\limits_{m^{'}=1,m^{'}\ne
m}^{M}w^{s}_{m^{'}}(N)\alpha^{(s-1)}_{m^{'}} p_{m^{'}}(n) 
\end{equation}
The inputs of the first stage $\{\alpha^{0}_m\}_{m=1}^M$ (needed for
computing $X^1(n)$) are given by
\begin{equation}
\label{qte5}
\alpha^{0}_m=\mbox{sign}\left\{\mbox{real}\left\{\sum\limits_{n=1}^{N}
r(n)e^{-j\hat{\phi}^0_m}p_m(n)\right\}\right\} 
\end{equation}
Assuming $\phi_m\in R_i$, then
\begin{equation}
\label{qqpp} \hat{\phi}^0_m =\frac{(i-1)\pi+i\pi}{4} 
\end{equation}
Table \ref{tab4} shows the structure of the modified PLMS-PPIC
method  It is to be notified that
\begin{itemize}
\item Equation (\ref{qte5}) shows the conventional bit detection
method when the receiver only knows the quarter of channel phase in
$(0,2\pi)$  \item With $L=1$ (i e  only one NLMS algorithm), the
modified PLMS-PPIC can be thought as a modified version of the
LMS-PPIC method 
\end{itemize}

In the following section some examples are given to illustrate the
effectiveness of the proposed method 

\section{Simulations}\label{S5}

In this section we have considered some simulation examples 
Examples \ref{ex2}-\ref{ex4} compare the conventional, the modified
LMS-PPIC and the modified PLMS-PPIC methods in three cases: balanced
channels, unbalanced channels and time varying channels  In all
examples, the receivers have only the quarter of each channel phase 
Example \ref{ex2} is given to compare the modified LMS-PPIC and the
PLMS-PPIC in the case of balanced channels 

\begin{example}{\it Balanced channels}:
\label{ex2}
\begin{table}
\caption{Channel phase estimate of the first user (example
\ref{ex2})} \label{tabex5} \centerline{{
\begin{tabular}{|c|c|c|c|c|}
\hline
\multirow{6}{*}{\rotatebox{90}{$\phi_m=\frac{3\pi}{8},M=15~~$}} & N(Iteration) & Stage Number& NLMS & PNLMS  \\
&&&&\\
\cline{2-5} & \multirow{2}{*}{64}& s = 2 &  $\hat{\phi}^s_m=\frac{3 24\pi}{8}$ & $\hat{\phi}^s_m=\frac{3 18\pi}{8}$ \\
\cline{3-5} & & s = 3 & $\hat{\phi}^s_m=\frac{3 24\pi}{8}$ & $\hat{\phi}^s_m=\frac{3 18\pi}{8}$ \\
\cline{2-5} & \multirow{2}{*}{256}& s = 2 &  $\hat{\phi}^s_m=\frac{2 85\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 88\pi}{8}$ \\
\cline{3-5} & & s = 3 & $\hat{\phi}^s_m=\frac{2 85\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 88\pi}{8}$ \\
\cline{2-5} \hline
\end{tabular} }}
\end{table}
Consider the system model (\ref{e7}) in which $M$ users
synchronously send their bits to the receiver through their
channels  It is assumed that each user's information consists of
codes of length $N$  It is also assumd that the signal to noise
ratio (SNR) is 0dB  In this example there is no power-unbalanced or
channel loss is assumed  The step-size of the NLMS algorithm in
modified LMS-PPIC method is $\mu=0 1(1-\sqrt{\frac{M-1}{M}})$ and
the set of step-sizes of the parallel NLMS algorithms in modified
PLMS-PPIC method are
$\Theta=\{0 01,0 05,0 1,0 2,\cdots,1\}(1-\sqrt{\frac{M-1}{M}})$,
i e  $\mu_1=0 01(1-\sqrt{\frac{M-1}{M}}),\cdots,
\mu_4=0 2(1-\sqrt{\frac{M-1}{M}}),\cdots,
\mu_{12}=(1-\sqrt{\frac{M-1}{M}})$  Figure~\ref{Figexp1NonCoh}
illustrates the bit error rate (BER) for the case of two stages and
for $N=64$ and $N=256$  Simulations also show that there is no
remarkable difference between results in two stage and three stage
scenarios  Table~\ref{tabex5} compares the average channel phase
estimate of the first user in each stage and over $10$ runs of
modified LMS-PPIC and PLMS-PPIC, when the the number of users is
$M=15$ 
\end{example}

Although LMS-PPIC and PLMS-PPIC, as well as their modified versions,
are structured based on the assumption of no near-far problem
(examples \ref{ex3} and \ref{ex4}), these methods and especially the
second one have remarkable performance in the cases of unbalanced
and/or time varying channels 

\begin{example}{\it Unbalanced channels}:
\label{ex3}
\begin{table}
\caption{Channel phase estimate of the first user (example
\ref{ex3})} \label{tabex6} \centerline{{
\begin{tabular}{|c|c|c|c|c|}
\hline
\multirow{6}{*}{\rotatebox{90}{$\phi_m=\frac{3\pi}{8},M=15~~$}} & N(Iteration) & Stage Number& NLMS & PNLMS  \\
&&&&\\
\cline{2-5} & \multirow{2}{*}{64}& s=2 &  $\hat{\phi}^s_m=\frac{2 45\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 36\pi}{8}$ \\
\cline{3-5} & & s=3 & $\hat{\phi}^s_m=\frac{2 71\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 80\pi}{8}$ \\
\cline{2-5} & \multirow{2}{*}{256}& s=2 &  $\hat{\phi}^s_m=\frac{3 09\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 86\pi}{8}$ \\
\cline{3-5} & & s=3 & $\hat{\phi}^s_m=\frac{2 93\pi}{8}$ & $\hat{\phi}^s_m=\frac{3 01\pi}{8}$ \\
\cline{2-5} \hline
\end{tabular} }}
\end{table}
Consider example \ref{ex2} with power unbalanced and/or channel loss
in transmission system, i e  the true model at stage $s$ is
\begin{equation}
\label{ve7} r(n)=\sum\limits_{m=1}^{M}\beta_m
w^s_m\alpha^{(s-1)}_m c_m(n)+v(n),
\end{equation}
where $0<\beta_m\leq 1$ for all $1\leq m \leq M$  Both the LMS-PPIC
and the PLMS-PPIC methods assume the model (\ref{e7}), and their
estimations are based on observations $\{r(n),X^s(n)\}$, instead of
$\{r(n),\mathbf{G}X^s(n)\}$, where the channel gain matrix is
$\mathbf{G}=\mbox{diag}(\beta_1,\beta_2,\cdots,\beta_m)$  In this
case we repeat example \ref{ex2}  We randomly get each element of
$G$ from $[0,0 3]$  Figure~\ref{Figexp2NonCoh} illustrates the BER
versus the number of users  Table~\ref{tabex6} compares the channel
phase estimate of the first user in each stage and over $10$ runs of
modified LMS-PPIC and modified PLMS-PPIC for $M=15$ 
\end{example}

\begin{example}
\label{ex4} {\it Time varying channels}: Consider example \ref{ex2}
with time varying Rayleigh fading channels  In this case we assume
the maximum Doppler shift of $40$HZ, the three-tap
frequency-selective channel with delay vector of $\{2\times
10^{-6},2 5\times 10^{-6},3\times 10^{-6}\}$sec and gain vector of
$\{-5,-3,-10\}$dB  Figure~\ref{Figexp3NonCoh} shows the average BER
over all users versus $M$ and using two stages 
\end{example}


\section{Conclusion}\label{S6}

In this paper, parallel interference cancelation using adaptive
multistage structure and employing a set of NLMS algorithms with
different step-sizes is proposed, when just the quarter of the
channel phase of each user is known  In fact, the algorithm has been
proposed for coherent transmission with full information on channel
phases in \cite{cohpaper}  This paper is a modification on the
previously proposed algorithm  Simulation results show that the new
method has a remarkable performance for different scenarios
including Rayleigh fading channels even if the channel is
unbalanced 


Context 2: Paper Info

Title: Bistability between π-diradical open-shell and closed-shell states in indeno[1,2-a]fluorene
Publish Date: Unkown
Author List: Shantanu Mishra (from IBM Research Europe -Zurich), Manuel Vilas-Varela (from Department of Organic Chemistry, Center for Research in Biological Chemistry and Molecular Materials (CiQUS), University of Santiago de Compostela), Leonard-Alexander Lieske (from IBM Research Europe -Zurich), Ricardo Ortiz (from Donostia International Physics Center (DIPC)), Igor Rončević (from Department of Chemistry, University of Oxford), Florian Albrecht (from IBM Research Europe -Zurich), Diego Peña (from Department of Organic Chemistry, Center for Research in Biological Chemistry and Molecular Materials (CiQUS), University of Santiago de Compostela), Leo Gross (from IBM Research Europe -Zurich)

Figure

Fig  1 | Non-benzenoid non-alternant polycyclic conjugated hydrocarbons a, Classical nonbenzenoid non-alternant polycyclic conjugated hydrocarbons: pentalene, azulene and heptalene b, Generation of indacenes and indenoindenes through benzinterposition and benzannelation of pentalene, respectively Gray filled rings represent Clar sextets c, Closed-shell Kekulé (left) and openshell non-Kekulé (right) resonance structures of QDMs Note that meta-QDM is a non-Kekulé molecule All indenofluorene isomers, being derived through benzannelation of indacenes, contain a central QDM moiety d, Closed-shell Kekulé (top) and open-shell non-Kekulé (bottom) resonance structures of indenofluorenes Compared to their closed-shell structures, 1 and 5 gain two Clar sextets in the openshell structure, while 2-4 gain only one Clar sextet in the open-shell structure Colored bonds in d highlight the ortho-and para-QDM moieties in the two closed-shell Kekulé structures of 5  e, Scheme of on-surface generation of 5 by voltage pulse-induced dehydrogenation of 6 (C20H14) Structures 7 and 8 represent the two monoradical species (C20H13) 
Fig  2 | Characterization of open-shell indeno[1,2-a]fluorene on bilayer NaCl/Au(111) a, DFTcalculated wave functions of the frontier orbitals of 5OS in the triplet configuration for the spin up (occupied) level (isovalue: 0 002 e -Å -3 ) Blue and red colors represent opposite phases of the wave function b, Corresponding DFT-calculated spin density of 5OS (isovalue: 0 01 e -Å -3) Blue and orange colors represent spin up and spin down densities, respectively c, Probability density of the SOMOs of 5OS (isovalue: 0 001 e -Å -3 ) d, DFT-calculated bond lengths of 5OS e, Constant-height I(V) spectra acquired on a species of 5 assigned as 5OS, along with the corresponding dI/dV(V) spectra Open feedback parameters: V = -2 V, I = 0 17 pA (negative bias side) and V = 2 V, I = 0 17 pA (positive bias side) Acquisition position of the spectra is shown in Supplementary Fig 7 f, Scheme of many-body transitions associated to the measured ionic resonances of 5OS Also shown are STM images of assigned 5OS at biases where the corresponding transitions become accessible Scanning parameters: I = 0 3 pA (V = -1 2V and -1 5 V) and 0 2 pA (V = 1 3 V and 1 6 V)  g, Laplace-filtered AFM image of assigned 5OS STM set point: V = 0 2 V, I = 0 5 pA on bilayer NaCl, Δz = -0 3Å The tip-height offset Δz for each panel is provided with respect to the STM setpoint, and positive (negative) values of Δz denote tip approach (retraction) from the STM setpoint f and g show the same molecule at the same adsorption site, which is next to a trilayer NaCl island The bright and dark features in the trilayer NaCl island in g correspond to Cl -and Na + ions, respectively Scale bars: 10 Å (f) and 5 Å (g) 
Fig  3 | Characterization of closed-shell indeno[1,2-a]fluorene on bilayer NaCl/Au(111) a, DFTcalculated wave functions of the frontier orbitals of closed-shell 5 0 (isovalue: 0 002 e -Å -3 ) The wave functions shown here are calculated for the 5para geometry b, DFT-calculated bond lengths of 5ortho (top) and 5para (bottom) c, Constant-height I(V) spectra acquired on a species of 5 assigned as 5para, along with the corresponding dI/dV(V) spectra Open feedback parameters: V = -2 V, I = 0 15 pA (negative bias side) and V = 2 2 V, I = 0 15 pA (positive bias side) Acquisition position of the spectra is shown in Supplementary Fig  7  d, Scheme of many-body transitions associated to the measured ionic resonances of 5para Also shown are STM images of assigned 5para at biases where the corresponding transitions become accessible Scanning parameters: I = 0 15 pA (V = -1 5 V) and 0 2 pA (V = 1 7 V)  e, Laplace-filtered AFM image of assigned 5para STM set point: V = 0 2 V, I = 0 5 pA on bilayer NaCl, Δz = -0 7 Å  f, Selected bonds labeled for highlighting bond order differences between 5para and 5ortho For the bond pairs a/b, c/d and e/f, the bonds labeled in bold exhibit a higher bond order than their neighboring labeled bonds in 5para g, Laplace-filtered AFM images of 5 on bilayer NaCl/Cu(111) showing switching between 5OS and 5para as the molecule changes its adsorption position The faint protrusion adjacent to 5 is a defect that stabilizes the adsorption of 5  STM set point: V = 0 2 V, I = 0 5 pA on bilayer NaCl, Δz = -0 3Å  STM and STS data in c and d are acquired on the same species, while the AFM data in e is acquired on a different species Scale bars: 10 Å (d) and 5 Å (e,g) 
NMR (300 MHz, CDCl3) δ: 7 51 (m, 2H), 7 40 -7 28 (m, 5H), 7 27 -7 20 (m, 2H), 7 13 (d, J = 7 7 Hz, 1H), 2 07 (s, 3H), 1 77 (s, 3H) ppm  13C NMR-DEPT (75 MHz, CDCl3, 1:1 mixture of atropisomers) δ: 141 2 (C), 141 1 (C), 140 0 (C), 139 4 (2C), 137 5 (C), 137 4 (C), 136 0 (3C), 134 8 (C), 134 5 (C), 134 1 (C), 134 0 (C), 133 7 (C), 133 6 (C), 131 6 (CH), 131 2 (CH), 131 1 (CH), 130 7 (CH), 129 8 (CH), 129 7 (CH), 129 5 (CH), 129 4 (CH), 129 0 (CH), 128 9 (CH), 128 7 (2CH), 128 6 (2CH), 127 2 (CH), 127 1 (CH), 127 0 (CH), 126 9 (CH), 126 7 (CH), 126 6 (CH), 20 6 (CH3), 20 5 (CH3), 17 7 (CH3), 17 5 (CH3) ppm MS (APCI) m/z (%): 327 (M+1, 100) HRMS: C20H16Cl2; calculated: 327 0702, found: 327 0709 
NMR (500 MHz, CDCl3) δ: 7 93 (d, J = 7 6 Hz, 1H), 7 85 (d, J = 7 5 Hz, 1H), 7 78 (d, J = 7 7 Hz, 1H), 7 65 (d, J = 7 4 Hz, 1H), 7 61 (d, J = 7 5 Hz, 1H), 7 59 (d, J = 7 7 Hz, 1H), 7 47 (ddd, J = 8 4, 7 2, 1 1 Hz, 1H), 7 42 (dd, J = 8 1, 7 0 Hz, 1H), 7 35 (m, 2H), 4 22 (s, 3H), 4 02 (s, 3H) ppm  13C NMR-DEPT (125 MHz, CDCl3) δ: 144 1 (C), 143 3 (C), 142 3 (C), 141 9 (C), 141 8 (C), 141 2 (C), 138 2 (C), 136 5 (C), 127 0 (CH), 126 9 (CH), 126 7 (CH), 126 6 (CH), 125 3 (CH), 125 2 (CH), 123 6 (CH), 122 2 (CH), 119 9 (CH), 118 4 (CH), 37 4 (CH2), 36 3 (CH2) ppm MS (APCI) m/z (%): 254 (M+, 88) HRMS: C20H14; calculated: 254 1090, found: 254 1090 

abstract

Indenofluorenes are non-benzenoid conjugated hydrocarbons that have received great interest owing to their unusual electronic structure and potential applications in nonlinear optics and photovoltaics  Here, we report the generation of unsubstituted indeno[1,2-a]fluorene, the final and yet unreported parent indenofluorene regioisomer, on various surfaces by cleavage of two C-H bonds in 7,12-dihydro indeno[1,2-a]fluorene through voltage pulses applied by the tip of a combined scanning tunneling microscope and atomic force microscope 
On bilayer NaCl on Au(111), indeno[1,2a]fluorene is in the neutral charge state, while it exhibits charge bistability between neutral and anionic states on the lower work function surfaces of bilayer NaCl on Ag(111) and Cu(111)  In the neutral state, indeno[1,2-a]fluorene exhibits either of two ground states: an open-shell π-diradical state, predicted to be a triplet by density functional and multireference many-body perturbation theory calculations, or a closedshell state with a para-quinodimethane moiety in the as-indacene core 
Switching between open-and closed-shell states of a single molecule is observed by changing its adsorption site on NaCl  The inclusion of non-benzenoid carbocyclic rings is a viable route to tune the physicochemical properties of polycyclic conjugated hydrocarbons (PCHs)   Non-benzenoid polycycles may lead to local changes in strain, conjugation, aromaticity, and, relevant to the context of the present work, induce an open-shell ground state of the corresponding PCHs  
Many nonbenzenoid PCHs are also non-alternant, where the presence of odd-membered polycycles breaks the bipartite symmetry of the molecular network   Figure shows classical examples of non-benzenoid non-alternant PCHs, namely, pentalene, azulene and heptalene  Whereas azulene is a stable PCH exhibiting Hückel aromaticity ([4n+2] π-electrons, n = 2), pentalene and heptalene are unstable Hückel antiaromatic compounds with [4n] π-electrons, n = 2 (pentalene) and n = 3 (heptalene) 
Benzinterposition of pentalene generates indacenes, consisting of two isomers s-indacene and as-indacene (Fig  )  Apart from being antiaromatic, indacenes also contain proaromatic quinodimethane (QDM) moieties (Fig  ) , which endows them with potential open-shell character  While the parent s-indacene and asindacene have never been isolated, stable derivatives of s-indacene bearing bulky substituents have been synthesized  
A feasible strategy to isolate congeners of otherwise unstable non-benzenoid non-alternant PCHs is through fusion of benzenoid rings at the ends of the π-system, that is, benzannelation  For example, while the parent pentalene is unstable, the benzannelated congener indeno[2,1-a]indene is stable under ambient conditions (Fig  )  
However, the position of benzannelation is crucial for stability: although indeno[2,1a]indene is stable, its regioisomer indeno[1,2-a]indene (Fig  ) oxidizes under ambient conditions   Similarly, benzannelation of indacenes gives rise to the family of PCHs known as indenofluorenes (Fig  ), which constitute the topic of the present work 
Depending on the benzannelation position and the indacene core, five regioisomers can be constructed, namely, indeno [ Practical interest in indenofluorenes stems from their low frontier orbital gap and excellent electrochemical characteristics that render them as useful components in organic electronic devices  
The potential open-shell character of indenofluorenes has led to several theoretical studies on their use as non-linear optical materials and as candidates for singlet fission in organic photovoltaics   Recent theoretical work has also shown that indenofluorene-based ladder polymers may exhibit fractionalized excitations 
Fundamentally, indenofluorenes represent model systems to study the interplay between aromaticity and magnetism at the molecular scale   Motivated by many of these prospects, the last decade has witnessed intensive synthetic efforts toward the realization of indenofluorenes  Derivatives of 1-4 have been realized in solution , while 1-3 have also been synthesized on surfaces and characterized using scanning tunneling microscopy (STM) and atomic force microscopy (AFM), which provide information on molecular orbital densities , molecular structure and oxidation state  
With regards to the open-shell character of indenofluorenes, 2-4 are theoretically and experimentally interpreted to be closed-shell, while calculations indicate that 1 and 5 should exhibit open-shell ground states   Bulk characterization of mesitylsubstituted 1, including X-ray crystallography, temperature-dependent NMR, and electron spin resonance spectroscopy, provided indications of its open-shell ground state  
Electronic characterization of 1 on Au(111) surface using scanning tunneling spectroscopy (STS) revealed a low electronic gap of 0 4 eV (ref  )  However, no experimental proof of an openshell ground state of 1 on Au(111), such as detection of singly occupied molecular orbitals (SOMOs) or spin excitations and correlations due to unpaired electrons , was shown 
In this work, we report the generation and characterization of unsubstituted 5  Our research is motivated by theoretical calculations that indicate 5 to exhibit the largest diradical character among all indenofluorene isomers   The same calculations also predict that 5 should possess a triplet ground state 
Therefore, 5 would qualify as a Kekulé triplet, of which only a handful of examples exist   However, definitive synthesis of 5 has never been reported so far  Previously, Dressler et al  reported transient isolation of mesityl-substituted 5, where it decomposed both in the solution and in solid state , and only the structural proof of the corresponding dianion was obtained 
On-surface generation of a derivative of 5, starting from truxene as a precursor, was recently reported   STM data on this compound, containing the indeno[1,2-a]fluorene moiety as part of a larger PCH, was interpreted to indicate its open-shell ground state  However, the results did not imply the ground state of unsubstituted 5  Here, we show that on insulating surfaces 5 can exhibit either of two ground states: an open-shell or a closed-shell 
We infer the existence of these two ground states based on high-resolution AFM imaging with bond-order discrimination and STM imaging of molecular orbital densities   AFM imaging reveals molecules with two different geometries  Characteristic bond-order differences in the two geometries concur with the geometry of either an open-or a closed-shell state 
Concurrently, STM images at ionic resonances show molecular orbital densities corresponding to SOMOs for the open-shell geometry, but orbital densities of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for the closed-shell geometry  Our experimental results are in good agreement with density functional theory (DFT) and multireference perturbation theory calculations 
Finally, we observe switching between open-and closed-shell states of a single molecule by changing its adsorption site on the surface  Synthetic strategy toward indeno[1,2-a]fluorene  The generation of 5 relies on the solution-phase synthesis of the precursor 7,12-dihydro indeno[1,2-a]fluorene (6)  Details on synthesis and characterization of 6 are reported in Supplementary Figs 
  Single molecules of 6 are deposited on coinage metal (Au(111), Ag(111) and Cu(111)) or insulator surfaces  In our work, insulating surfaces correspond to two monolayer-thick (denoted as bilayer) NaCl on coinage metal surfaces
Context 3: CNN com - Transcripts
Tensions Boil Over possible government shutdown; New trouble targeting Gadhafi; Libyan Rebels in Panicked Retreat; Should U S  Recognize the Rebels?; Meeting With Gadhafi; Washington, D C  to Feel Burden of Shutdown; Religious Leaders Fast to Protests Cuts for Poor
WOLF BLITZER, HOST: Don, thanks very much 
Happening now, the top U S  general in charge of the military mission in Libya now expressing doubts that the opposition has the manpower to topple Moammar Gadhafi, as deadly new air strikes force rebel fighters into another retreat  This hour, I'll speak with a former Republican Congressman who's in Tripoli right now trying to get Gadhafi to step down 
Also, growing outrage across the United States, amidst new signs tomorrow's potential government shutdown may -- repeat may be unavoidable  Why one lawmaker is telling Congress -- and I'm quoting right now -- "go straight to hell "
And possible presidential hopeful, Donald Trump, on a mission to tell President Obama, "you're fired " We're fact checking his controversial investigation into the president's birth 
Up first, the political showdown over the budget, as tensions reach a boiling point about 31 hours until impending government shutdown  Just hours from now, President Obama will meet with Republican House speaker, John Boehner, and the Democratic Senate majority leader, Harry Reid, for further negotiations  Those talks scheduled to begin 7:00 p m  Eastern 
Hundreds of thousands of people across the country will be impacted by the shutdown  And we'll be bringing you examples throughout the next two hours 
One place it would be felt heavily is right here in Congress' backyard, the city of Washington  Washington, DC -- its spending is tied to the federal budget  And this major metropolitan area could lose millions of dollars while a number of critical services, like trash collection, for example, would be suspended for at least a week 
Today, an enraged Eleanor Holmes, the delegate representing Washington, DC, lit into Congress over the stalemate 
(BEGIN VIDEO CLIP) ELEANOR HOLMES NORTON (D), D C  DELEGATE: It's one thing to beat up on the District of Columbia  It's another thing drop a bomb on the city  And that's what this Congressional -- C R  does  It takes the route of authoritarian governments and dictatorships by dictating to a local government how it may spend its local funds  And it may force the District of Columbia government to shut down, although our government had a balanced budget 
BLITZER: And get this -- the members of Congress charged with reaching a deal, they'll still be receiving a paycheck if there's a shutdown, despite the hundreds of thousands of government employees who won't be receiving any paychecks  The current Congressional salary, by the way, $174,000 a year 
Our CNN senior Congressional correspondent, Dana Bash, is up on Capitol Hill with the latest developments -- Dana, specifically, where are the sticking points right now?
DANA BASH, CNN SENIOR CONGRESSIONAL CORRESPONDENT:
Well, look, Wolf, this is effectively a bill to fund the government  And the sticking points certainly are about how much spending to cut  That's what this whole issue has been about 
However -- however, one of the main issues, I am told, that were just -- that was discussed at the White House meeting this afternoon with the president, the House speaker and the Senate majority leader, was over not necessarily spending measures, but over lightning rod issues like regulating greenhouse gases and abortion 
BASH (voice-over): One of the biggest disagreements is not over government spending, but policy 
REP  JOHN BOEHNER (R-OH), SPEAKER OF THE HOUSE: Some 40 or 50 policy restrictions that were attached to -- to our bill 
BASH: So-called policy riders Republicans call essential and Democrats call nonstarters  The most divisive is over abortion  A GOP plan to cut all federal funding for Planned Parenthood, which provides abortion procedures in addition other women's health services 
SEN  HARRY REID (D-NV), MAJORITY LEADER: This is a budget  This is to keep our country running  This is not a woman's health bill 
BASH: Planned Parenthood staged a rally outside the Capitol to protest 
CECILE RICHARDS, CEO, PLANNED PARENTHOOD: They don't want to allow Planned Parenthood to serve the three million women that we see every single year  Ninety-seven percent of the services Planned Parenthood provides are preventive care 
UNIDENTIFIED MALE: I certainly don't think that taxpayers should subsidize abortions  It's -- if a woman chooses to have an abortion, it's legal to do that in this country  But I don't think taxpayers should be put in a position to have to pay for those abortions 
BASH: Another major sticking point -- how much spending to cut  A Democratic source tells CNN they have finally tentative agreement on slashing $34 5 billion from the rest of this year's budget  But a Republican source says there's no deal 
BOEHNER: There is no agreement on the number  There are no agreement on the policy issues that are contained with it 
BASH: Then there's the critical issue of what programs and agencies to cut  Democrats say they're trying to find spending cuts with the least impact on those who need it most  So they're pushing for things like temporary one year cuts in programs  Some examples, cuts in wetlands protection and Pell grants for summer school and graduate students 
Republicans call that smoke and mirrors 
BOEHNER: And our goal is to make real spending cuts 
BASH: Some examples of what Republicans want to cut -- money for food inspectors, Head Start education programs and funding for housing 
BASH: This afternoon, House Republicans did pass a bill to keep the government running for one week past tomorrow's midnight deadline  It has $12 billion in cuts  It would fund the Defense Department for the rest of the year  But Democrats, including the president of the United States, call it a distraction and they say that they really want to keep the focus on what they're negotiating, which is a bill that would keep the government open -- keep the government functioning and funded for the rest of the year 
BLITZER: And the president's playing hardball  He's saying he'll veto that legislation --
BASH: He was, yes 
BLITZER: -- if it were to pass the Senate and come to his desk  I hear, Dana, that some employees already are getting furloughing notices 
BASH: It's true  This is just preventive  But all across the Capitol here today, people in offices and -- and -- well, really, everywhere -- were told whether or not, if, in fact, it does come to a government shutdown, if they're going to be here or not  And this is an example  We obtained one of the furlough notices  And I'll just read you a line  This -- imagine if this came across your desk  It says: "Because your services are not needed for the orderly suspension of operations and you're not engaged in one of the accepted functions, you're being placed on furlough effective Saturday, April 9, 2011 "
Now, again, of course, this is just protective  The government is still open  But interesting that they're already getting ready for a government shutdown and telling people who will come to work and not 
One more note  Even people who are here, who are called essential, they're not going to get paid, either 
BLITZER: All right, Dana 
Don't go too far away 
We'll be in close touch 
The impact of the potential government shutdown is even being felt on the front lines of combat in Afghanistan  And Iraq  The Defense secretary, Robert Gates, is in Iraq right now  And he's telling U S  troops they will feel a pinch 
ROBERT GATES, SECRETARY OF DEFENSE: I hope they didn't have you standing out here in the sun too long
If -- if the government shutdown starts on the 8th and goes for a week, you'd get a half a check  If it goes from the 15th to the 30th, you wouldn't get a paycheck on the 30th but you would be back paid for all of it  So that's -- that's the deal 
BLITZER: Not great deal 
Gates also told the troops this would likely be his last trip to the country as Defense secretary and he wanted to say thank you 
He's expected to retire later this year 
Now to the deadly stalemate in Libya  New signs the military operation in the region is facing some tough new challenges 
Our Pentagon correspondent, Barbara Starr is here 
She's watching the story 
She's got more 
What are you learning? BARBARA STARR, CNN PENTAGON CORRESPONDENT: Well, Wolf, there was very dramatic, very hard-nosed testimony today on Capitol Hill from the top U S  commander responsible for the U S  involvement in Libya, saying that Gadhafi forces are becoming increasingly difficult to target, as they are using civilian vehicles, mixing in with local populations, moving next to mosques, schools, hospitals -- all the same tactics we saw for years in Iraq 
And now, all of this today leading to a very dramatic exchange between General Carter Ham and one of the most vocal administration critics, Senator John McCain 
SEN  JOHN MCCAIN (R), ARIZONA: Hearing your testimony, General Ham, is almost an Orwellian experience for me  The fact is that if we had imposed the no-fly zone three weeks, four weeks ago, Gadhafi would not be in power today 
The fact is that the situation on the ground is basically a stalemate 
Would you say that the situation on the ground is a stalemate or an emerging stalemate?
GEN  CARTER HAM, COMMANDER, U S  AFRICA COMMAND: Senator, I -- I would agree with that if present on the ground 
MCCAIN: So the goal -- our policy objective of the removal of Gadhafi is further from being achieved than it was three or four weeks ago 
HAM: Senator, I -- I don't know that I would agree with that  What I -- because that, again, was not a military mission  The military mission of protecting, I think, was not wholly achieved, but achieved in large part 
STARR: General Ham also acknowledging another problem -- a key U S  aircraft, the AC-130, that flies low and slow to target on the ground, is facing what he called "a significant threat" from surface to air missiles, which he said remain effective and operational in some cases 
And, Wolf, get this  General Ham says there were about 20,000 of those surface to air missiles when the campaign started and they are concerned that an awful lot of them are still out there -- Wolf 
BLITZER: Barbara, thanks very much for that report 
Panicked rebels are once again on the retreat from Gadhafi's forces  Just today, at least three people were killed, another 10 injured, in new air strikes  And there are mounting questions about whether NATO could be responsible for the attack 
Our senior international correspondent, Ben Wedeman, is joining us now from Benghazi 
Ben's watching all of this closely 
You just heard General Ham, who is the commander of the U S  military's Africa Command  He was in charge of the mission before handing over complete control to NATO  You just heard him say there could be a stalemate out there 
What's the sense on the ground?
BEN WEDEMAN, CNN SENIOR INTERNATIONAL CORRESPONDENT: Well, the sense was a few days ago that it was, indeed, a stalemate -- sort of a seesaw battle that went back and forth between Ajdabiya and Brega 
But what we saw today was that that seesaw was tipped over  And it was a general retreat by the opposition forces from somewhere near Brega to almost the other side of Ajdabiya  This, after this air strike, which almost everybody on the ground believes to be NATO leaving not three, but four people dead  And many others are still unaccounted for 
That set off this general retreat whereby we saw all their heavy -- all of the opposition forces' heavy equipment -- multiple rocket launchers, tens and tens of these pickup trucks mounted with heavy machine guns streaming through Ajdabiya to the other side, the far side of the city  Some of them going all the way back to Benghazi, according to the head of the rebel forces in the eastern part of the country, Abdul Fatah Younis  He says that the Gadhafi forces were approaching Ajdabiya from three different directions 
I would not call that a stalemate -- Wolf 
BLITZER: Ben, you got a close-up look at some of the casualties today out on the front lines 
WEDEMAN: It's very bad, very bad  I mean it wasn't just fighters  It was also medics who had gone to the scene of this reported air strike, which then got hit again  So one of them was a doctor, one of them was a medic  And we were in the hospital  And there was real anger at NATO, anger at the fact that when they needed those air strikes on the Gadhafi forces, they weren't getting them  And now, for the second time in a week, there's been another strike  Now, of course, we must stress that NATO says that they -- because they don't have enough boots on the ground, they can neither confirm nor deny this was a NATO strike  But certainly, speaking to eyewitnesses in the hospital, it certainly sounded like an air strike  And there are no other planes in the skies of Libya other than NATO planes -- Wolf 
BLITZER: Ben Wedeman in Benghazi for us 
The U S  says Moammar Gadhafi is no longer the legitimate leader of Libya 
So why not recognize the rebels?
Why one U S  official says it raises serious concerns 
And a former U S  Congressman in Libya armed with a message for the Libyan dictator 
Will he get to meet with him face-to-face?
My interview with Curt Weldon, that Republican former Congressman -- that's coming up, as well 
BLITZER: Let's get right to Jack 
He's got some nuclear concerns on his mind with The Cafferty File -- Jack 
JACK CAFFERTY, THE CAFFERTY FILE: Well, they had another little temblor in Japan -- a 7 1 magnitude earthquake hit Northeastern Japan today, the strongest aftershock since that massive 9 0 quake and tsunami that followed devastated that nation four weeks ago  And this one today was in roughly the same area 
One of the big concerns, of course, is possible further damage to the Fukushima Daiichi nuclear power plant  The Tokyo Electric Power Company, TEPCO, which operates the plant -- or what's left of it -- said there were no serious incidents as a result of today's aftershock 
So they say  Radioactivity from that plant has poisoned the surrounding land, air and ocean  Millions of people have been exposed  Millions more could be, as radioactivity has been picked up in food and drinking water and detected in faraway places, like California 
This week, workers plugged a crack in the plant that had been gushing contaminated water into the ocean for weeks  As a result, TEPCO says now radiation levels in the ocean waters off the coast there have dropped dramatically 
Yesterday, the head of the United Nations' scientific committee on the effects of atomic radiation said the Fukushima accident is not expected to have any serious impact on the health of the Japanese people  He said, quote: "We have seen traces of iodine in the air all over the world, but they are much, much, much lower than traces we have seen at similar distances following Chernobyl," unquote 
Well, not everybody is convinced  In South Korea, more than 130 primary schools and kindergartens ordered closed today outside of Seoul  People there were worried that windy, rainy weather could be carrying radioactive material from Japan 
North Korea aired warnings on television for its people to stay indoors during that rain storm and to take a full shower if they were caught outside in the storm 
Even here in the United States, some chefs are now using sensors to test levels of radiation in the fish they plan to serve in restaurants 
Here's the question -- do you think you're being told the truth about the nuclear accident in Japan?
If your -- if your trout is he glowing, Wolf --
BLITZER: Yes?
CAFFERTY: -- you might want to send it back and get a ham sandwich 
BLITZER: You want it well done, but not necessarily that well done 
CAFFERTY: No 
BLITZER: All right, Jack 
Not a laughing matter 
BLITZER: Serious stuff 
CAFFERTY: Right 
BLITZER: See you in a few moments 
New questions this hour about the capabilities of the rebels in Libya and whether they have the power to overthrow Moammar Gadhafi 
Should the United States -- should the United States have a hand in helping arm the rebels?
Let's bring in our foreign affairs correspondent, Jill Dougherty, with this part of the story 
What are you hearing over at the State Department -- Jill  JILL DOUGHERTY, CNN FOREIGN AFFAIRS CORRESPONDENT: Well, you know, Wolf, other countries have done it, other countries like France and Italy have done it -- recognizing the opposition  And supporters say now, with the rebels in retreat, the U S  shouldn't wait 
But what would it really change anything?
DOUGHERTY (voice-over): The U S  says Moammar Gadhafi is no longer the legitimate leader of Libya 
Secretary of State Hillary Clinton is full of praise for them 
HILLARY RODHAM CLINTON, SECRETARY OF STATE: These were not soldiers  These were not trained military forces  They were doctors and lawyers and university professors and economists and, you know, young men who were students  And they are being attacked by mercenaries, by ruthless forces that Gadhafi is utilizing to show no mercy against his people  And they are courageous  They are moving as fast as they can to try to form themselves into a military operation 
DOUGHERTY: Clinton has met with the rebel leaders personally, but the administration still is cautious  The president authorized the CIA to send in agents to learn about the rebels and assess their needs  Clinton's special representative, the State Department's Christopher Stevens, seen here in 2008 in Tripoli, is on the ground in Benghazi, scoping them out 
MARK TONER, U S  STATE DEPARTMENT SPOKESMAN: We sent somebody in to get that kind of on the ground assessment of the -- of -- of their identity, of their leadership structure, to talk with them firsthand and to see what direction we think they're moving in  We've seen some positive signals 
DOUGHERTY: Recognizing the rebels, a senior official tells CNN, raises serious issues  It would acknowledge that Libya is now a divided country 
And could the U S  be sure the group represents the whole opposition movement?
It's a bit early, this official says  Maybe they turn out not to be the right folks 
But Secretary Clinton knows the timing is urgent 
CLINTON: What NATO is doing is buying time, buying space 
DOUGHERTY: So far, the U S  is providing what's called non- lethal humanitarian aid  The administration hasn't yet decided to arm them or provide financial assistance 
DOUGHERTY: But a senior U S  official tells CNN there's a lot the United States could be doing right now without going so far as to recognize the rebels, pointing out that the U S  funds political groups and other organizations around the world  But this official says you want to be careful about who they are 
So, so far, caution seems to be winning out over urgency -- Wolf 
Jill is at the State Department 
The House speaker, John Boehner, may be doing double duty if the government shuts down this weekend  You're going to find out why he could be cleaning up a lot of trash in his own backyard 
And a former U S  Congressman now on a mission to meet with Moammar Gadhafi in Tripoli in person  Curt Weldon, he's here  He'll join us in THE SITUATION ROOM from Tripoli  You're going to find out who he says would be a good replacement for the embattled Libyan leader 
BLITZER: Military leaders have a message for Congress about "don't ask/don't tell "
Well, military leaders say preparations for repealing "don't ask/don't tell" are going better than they expected  They testified before a House committee today about getting rid of the policy that bars openly gay service members  They caution, though, that it will take time and training to implement the repeal  And it must still be certified by President Obama, the Defense secretary and the chairman of the Joint Chiefs of Staff 
Well, your Smartphone just got a little smarter  The FCC is requiring that wireless carriers provide access to the mobile Internet anywhere it's available, even when it's offered by a competing provider  And that could be a huge -- make a huge difference to smaller carriers, who told the FCC they just can't compete otherwise against industry heavyweights like Verizon and AT&T 
New York City school chancellor, Cathie Black, is stepping down after only three months on the job  Mayor Michael Bloomberg says her short stint just didn't work out as either of them had expected or hoped  Her approval rating has plunged to 17 percent 
Black chaired "First" magazine before overseeing the nation's largest school system  Deputy Mayor Dennis Walcott will replace her 
And a war of words is erupting between an emerging Republican star, New Jersey Governor Chris Christie, and his state's largest teachers' union  In a network TV interview, Christie called the union leaders, quote, "political thugs " He blames them for teacher lay-offs that he says could have been avoided if they had not opposed salary freezes  The New Jersey Education Association is firing back, accusing Christie of name-calling -- Wolf 
BLITZER: Sticks and stones will break many bones 
SYLVESTER: Sticks and stones may break my bones --
SYLVESTER: But words never hurt me 
A former U S  Congressman is in Tripoli, Libya right now  His goal -- to talk to Moammar Gadhafi  His message -- we'll talk about that  My interview with Curt Weldon coming up next 
Plus, we showed it to you earlier -- a member of Congress telling colleagues to, quote, "go to hell "
Now she's is joining us live here in THE SITUATION ROOM to explain 
HOLMES NORTON: -- of Columbia  It's another thing to drop a bomb on a city  And that's what this --
BLITZER: Former Congressman Curt Weldon is in a -- Weldon is on a mission to Libya right now to try to meet with the embattled leader, Moammar Gadhafi  But that may be easier said than done 
Joining us now from Tripoli, former Republican Congressman Curt Weldon of Pennsylvania  Congressman, thanks very much for coming in 
And joining us now from Tripoli, former Republican Congressman Curt Weldon of Pennsylvania 
CURT WELDON, FORMER U S  CONGRESSMAN: My pleasure, Wolf 
BLITZER: Let's talk about your meeting with Moammar Gadhafi  I take it it has not yet happened 
Do you expect to meet with the Libyan leader? WELDON: Absolutely  The invitation that was sent to me was from his chief of staff, Bashir Salah, who I've met on all three of my official visits here in 2004 and 2005  And the letter specifically says we want you to come over and meet with the leader and our senior leadership 
And I said it's worth me coming over to support the administration and to try to let the leader know face to face that this is facing -- it's very grave timing in the situation and they have to have some movement fairly quickly or they're not going to be happy with the -- with the alternatives 
BLITZER: What's taking so long?
Why haven't you been able to meet with Gadhafi yet?
WELDON: Well, it -- that's not unusual  I mean all three of the delegation trips that I led here in 2003 and 2004 -- or, actually, 2004 and 2005 -- they always make you wait until 30 minutes before the meeting and then you go  And some of those meetings were at 10:00 at night, some were at 5:00 in the afternoon 
As you know from the excellent reporting being done by your folks here, there's a lot of security concerns, and they are very concerned where Gadhafi is at any given moment  That's one of the issues, but we have been making ourselves available 
We have been doing a lot of back-channel meetings with friends and associates that I have here, and we have met with the chief of staff and one of the sons, and today with the prime minister, a very lengthy meeting for two hours  So, we're going to give them until tomorrow  We're not going to stay beyond that  And we have given them some suggestions, and we expect a response by midday tomorrow  And if we don't, we will done exit conversation with your people and let you know our feelings 
BLITZER: What's the major headline that you got out of these meetings with other leaders? I take it you met with Saif Al-Islam Gadhafi, one of the sons of Moammar Gadhafi  What are they saying to you?
WELDON: Well, we actually didn't meet with Saif  I have met with Saif probably 10 times over the past seven years, both in America and here in Libya  I have not yet met with Saif  I have offered, if he is available 
I have met with Saadi  And the general thrust is obviously that they want peace and they want to find a way out of this  But as I have explained to them, there's certain things that have to be done according to our president and our secretary of state, who I'm here to support 
We don't have a different agenda  There's no compromise on our part  Our only mission here is to talk face to face with them and say this is reality and this is a grave situation, and you need to do certain things that we suggest that we think will get our administration to respond to your actions  And again, we're not doing any negotiating 
They know me, they have seen my efforts  I have not taken anything from their country in the way of financial benefits, and I'm here only because I want to avoid war  I don't want to see American soldiers killed, and I don't want to see more innocence Libyans killed 
BLITZER: You wrote an op-ed in "The New York Times" this week saying that once you meet face to face with Moammar Gadhafi, you will tell him to step down  Is that still your intention?
WELDON: Absolutely, Wolf  I wrote the op-ed before the trip was planned  And I wrote it, Wolf, because back in 2004, when I led the first delegation of Americans to sit down with him in the tent in Tripoli, he said to me, "Congressman, why did it take 30 years for someone from your country to come and sit with me and tell me to my face that you believe that I'm a criminal and a terrorist  And then if you didn't believe me, bomb me?"
And I said, "Leader, I can't explain that " So I said now it's time for someone to sit in a tent face to face with Colonel Gadhafi and let him know how grave this situation is 
And I'm willing to do that  And I think I'm probably the best person because I have met with him three times, and because I sat in that tent in 2004 and listened to him tell me that  So, in effect, that's why I'm here 
BLITZER: You wrote also in "The New York Times" this -- you wrote, "Colonel Gadhafi's son, Saif, a powerful businessman, a politician, could play a constructive role as a member of the committee to devise a new government structure or constitution "
You know, a lot of people, including the opposition, the rebels, as they're called, they think Saif Al-Islam Gadhafi is just as much a killer or thug as his father is, and they say they have no interest in dealing with him either 
What do you say to that criticism?
WELDON: Well, what I said, I'm not endorsing anything anyone for any office here  What I am hoping for is what the president wants, which is a free and fair election to take place, hopefully sooner rather than later 
But having been involved with Libya for seven years, I was a witness to the work that Saif did in the Lockerbie case, the La Bella nightclub bombing  I personally witnessed through the Gadhafi Foundation the work that Saif did to free up the Bulgarian nurses who were sentenced to death twice, along with a Palestinian doctor 
I have seen the work that Saif and Dr  Salani (ph) at the foundation have done in dealing with chemical weapons destruction and with the elimination of landmines and humanitarian efforts worldwide  I have been out to (INAUDIBLE), the chemical weapons plant, and I have actually seen visibly how they have removed the chemical weapons production materials  He was behind all of that 
Believe me, Wolf, I'm not happy with some of the statements and the actions that he's made over the past month, and he knows I'm not happy  But I think in a fair election, up until now, he should be given the opportunity to seek office where he can run against other candidates, perhaps, for the presidency  And so I would at this time think that he should be allowed that opportunity 
That's not to say I condone anything that he said or his actions  He will have to be accountable for those on his own 
BLITZER: Because you make him sound like he's a decent guy when so many people think he is a killer, a murderer, especially given the statements that he recently made, that if he goes into Benghazi, if he finds these rebels, he will go and kill them all  You make it sound like he's a decent guy 
WELDON: Well, I -- you know, I haven't been with him on a continual basis  I have met with him a number of times, both in the U S  and here, under some very stressful situations, especially when it came to resolving the Lockerbie case and the La Bella nightclub  And despite what Sarkozy said about resolving the issues of the Bulgarian nurses when they were sentenced to death twice, it was Saif who played a very critical role against some very powerful forces in this country that wanted to kill those people 
You know, I don't know of any incidences where I, first hand, have seen evidence of him committing human rights violations, and if he did, he has to be held accountable like everyone else  And I have said that publicly and I will say that privately 
So my judgment is just based upon my experience with him, the fact that he is a knowledgeable person, he understands the need to interact and interface with the West  I think he could be a viable candidate  But ultimately, my opinion is hopefully going to be the opinion of the Libyan people 
BLITZER: Because you probably have seen all of the articles, the reports over the past month, month and a half, of mass murder, of killings, not only by Saif Al-Islam, but some of his brothers that have gone on, the atrocities that have been so widely reported  I hear what you're saying about his role over the recent years when the Bush administration, and later the Obama administration, was trying to improve relations with Libya, but over the past several weeks, based on all of the international reporting we have seen, it's been a brutal record that he has accomplished 
WELDON: Well, again, I don't have firsthand evidence of that  I just got here two days ago  And I fully support an international tribunal to look at human rights violations on everyone in this country  That's necessary  And if they find evidence that he has been involved in that, then he should suffer the consequences of his actions 
(END VIDEOTAPE) BLITZER: In our next hour, part two of the interview with former congressman Curt Weldon  There have been some questions raised about his motive  Is he in all of this for the money? You're going to find out his answer to that and more  Stand by 
Also, Washington, D C 's congressional delegate is telling colleagues -- and I'm quoting her now -- "Go to hell " She is joining us live in THE SITUATION ROOM to tell us why 
Plus, no budget deal, no food -- the extreme tens of thousands of people are going to as a government shutdown looms 
BLITZER: Let's get back to the outrage boiling over on Capitol Hill, only hours before a potential government shutdown 
Joining us now, the Democratic delegate representing the city of Washington, D C , Eleanor Holmes Norton 
ELEANOR HOLMES NORTON (D), D C  DELEGATE: Of course, Wolf 
BLITZER: I think it's fair to say that Washington, D C , a city of a population of about 600,000 people, the only major metropolitan -- the only major city in the United States that's going to foal the direct impact of a federal government shutdown so dramatically, so powerfully, because it is a federal district 
Give me an example of what's going to happen if there's a government shutdown 
NORTON: Absolutely, although your viewers will be shocked by what they are about to hear 
They know a little bit about taxation without representation -- we pay our taxes, then we have full representation in the House and the Senate  But I bet they didn't know that our local budget, without a dime of federal money in it -- and we support ourselves almost entirely -- has to be sent to the masters in the Congress to sign off on it before we can spend our own local money 
Well, listen to this, Wolf  We passed our budget in -- last spring  The appropriators signed off on it last summer 
So, why are we in a federal budget fight over their money when it is our money I am talking about? I have put forward amendments that said the district can spend its own local funds 
BLITZER: What's going to happen in the District of Columbia Saturday, Sunday, Monday, if there is a government shutdown? Give me an example or two 
NORTON: I will give you some dramatic ones  How about the shutdown of the D C  government itself? Because since the final gavel hasn't fallen on all the federal appropriations, then the district government has now prepared to shut down on Saturday morning just because the federal government is shutting down 
We are at the height of the tourist season, the Cherry Blossom Festival  That has been severely curtailed because of the federal shutdown  That's going to -- three million people come here just in one month for the cherry blossoms  Our mayor has had to put out a list of agencies that will be open and a list of agencies that won't be open 
BLITZER: Trash collection -- will there be any trash collection in the District of Columbia?
NORTON: No trash collection, and some residents have started up a Facebook page that says if they close down the District of Columbia, we're carrying our trash to Speaker Boehner's House 
BLITZER: You don't support that do you?
NORTON: I do not 
NORTON: And let me just say right here, I do not  But let me tell you, I am only expressing a little of the rage that the taxpaying residents of the District of Columbia are feeling 
BLITZER: But let me ask you this, Congresswoman, because the Democrats were in control, they had a large majority in the House all of last year; in the Senate, a significant majority  They failed to pass a budget  Don't the Democrats deserve a lot of the blame for this current impasse?
NORTON: Absolutely not, because the Democrats would never have held our budget up here 
LISA BLOOM, CNN LEGAL ANALYST: Why didn't they pass the budget?
NORTON: Well, that doesn't have anything to do with us  This is our local money 
All it would take is -- the Democrats in the Senate are ready to agree  The president is ready to sign an amendment --
BLITZER: But they could have done this any time last year 
NORTON: Wait a minute, Wolf  Wait a minute -- an amendment that said while we're fighting it out on the federal budget, we will let the district spend its own local funds 
So that's all I'm asking  I'm not in this fight, so don't ask me why the Democrats didn't pass the Democratic budget 
I passed -- we passed our budget  Our budget is balanced  The only issue before the Senate and the House is, can we spend our local money? It doesn't have anything to do with their budget 
They can go on from now until Timbuktu  Let us spend our money and don't close down our city because the federal government can't get its act together 
BLITZER: I'm with you there  This is an outrage, the fact that there is -- if there is going to be shutdown  I'm still hoping there won't be a shutdown, but it's --
NORTON: I think there may not be 
BLITZER: -- ridiculous when you think about it, when you think about how close they are  It would be a horrible, horrible tragedy, because 800,000 people directly are going to start losing their paychecks  And the District of Columbia, which is, as you point out correctly, taxation without representation, is going to suffer a great deal more than any other city in the United States 
Good luck, Congresswoman  Thanks very much 
NORTON: Thank you, Wolf 
BLITZER: I feel your pain 
Concerns within military families over a government shutdown  Also, why they are downright scared they won't be able to put food on the table 
And tens of thousands of people on a hunger strike, including some members of Congress  We'll explain why 
CAFFERTY: The question this hour is: Do you believe you're being told the truth about the nuclear accident in January?
Fred writes, "You want the truth? You can't handle the truth "
"Just how should a government balance our right to know the truth with the perceived need to not create a panic and thus a larger problem? Can you really evacuate a million people? To where? Yes, without the truth, how can anyone try to act reasonably?"
"In the end, we do have a right to know the truth  Honesty is the best policy "
Paul in Ohio writes, "Jack, I believe they're telling what they think they know with certainty  It is most certain that they don't know everything "
Jeremy in California, "So I'm confused  Is the current California radiation level 'harmless to human health,' 'not immediately harmful to human health,' not permanently harmful to people outside the region,' or no more than an apples-to-oranges transcontinental flight?"
Craig writes, "Perspective  In Japan, they have had yet another earthquake and have lived in fear and chaos for over a month  And yet, their government hasn't shut down  Nuclear disaster, natural disaster, absolute destruction hasn't kept their elected officials from doing their duty to the people 
"Yet, in America, we get Harry Reid, John Boehner and a White House who are more concerned with the 2012 election campaign  It's times like these when we see just how far off the mark we really are "
Louis writes, "No  Just too many things going wrong  They say that the seafood will be safe  I ask this: Do fish migrate or do they set up housekeeping in one spot and then stay there? And if so, why don't I catch fish in the same place every day?"
And Jim in Colorado, "The nuclear industry telling the truth? The unicorn, garden gnome and I were talking this over just the other day, and we all agreed it could happen  Why not?"
If you want to read more about the unicorn and the garden gnome, go to CNN com/CaffertyFile 
BLITZER: We will, for sure, Jack  Thank you  See you in a few moments 
Several sticking points in the ongoing budget negotiations, but will the government shutdown come down to money or social issues?
Plus, Donald Trump, he's making allegations about President Obama's birthplace  Does Donald Trump have any grounds for any of that? We're digging deeper for answers 
BLITZER: The growing outrage over the budget crisis isn't just about Congress' failure to reach a deal, it's also about some of the cuts that are being proposed 
Lets bring in our own Lisa Sylvester once again  She has the details -- Lisa 
Well, as congressional leaders hammer away on a budget compromise, a group of religious leaders have been fasting and praying to raise awareness of cuts in the budget that they say will harm the poor 
JIM WALLIS, PRESIDENT, SOJOURNERS: Orange juice never tasted so good 
SYLVESTER (voice-over): It's been 10 days since Jim Wallis last had solid food  The president of Sojourners, a Christian group that advocates for the underprivileged, is leading the charge among faith groups on a hunger fast to protest proposed cuts in the federal budget for the poor 
WALLIS: We're saying a budget is a moral document  And whether at your kitchen table, as a family, or a church or a nation, you make choices  What's important, what's not?
SYLVESTER: Wallis said in the last 10 days, more than 30,000 people around the country have joined in the fast in their own way  He says they have become a bit like God's lobbyists for the poor, putting a theological and moral spin on the cuts  Wallis said he is all for deficit reduction but --
WALLIS: I don't think doing this at the expense of the poorest people is a good choice, or hurting those who are already hurting the most is moral or even is smart 
SYLVESTER: Fiscal conservatives have suggested cuts in food stamps, foreign aid, and preschool programs for low-income families, that private groups can and should provide for the needy  But David Beckman of Bread for the World, who used to work at the World Bank, says the private sector can't fill the gap 
DAVID BECKMAN, PRESIDENT, BREAD FOR THE WORLD: All the private charitable feeding in the country amounts to about six percent of the food that poor people get from the national programs  So if you slash food stamps, as the House Republicans are proposing to do, there is no way that churches and charities and charitable people can make up for that 
SYLVESTER: Tony Hall was a member of Congress for years  As part of the fast, he is urging his former colleagues to reconsider cuts 
TONY HALL, ALLIANCE TO END HUNGER: When you make decisions about people's lives, be careful  You don't cut the poorest of the poor, because they didn't get you here  They didn't cause this mess 
SYLVESTER: On Wednesday, members of Congress began signing up for the fast 
REP  BARBARA LEE (D), CALIFORNIA: Several members of Congress today will be joining you in this fast 
SYLVESTER: Now, Sheila Jackson Lee, Keith Ellison and Jim McGovern are among 28 congressional Democrats who have signed on so far to join the hunger fast, and they will be doing a relay, with each taking one day to fast and then passing on the fast to their colleagues 
Wallis and Hall, they're doing it a little differently  They're fasting all the way through Easter Sunday  But they say for them, this fight for the poor is larger than just the specific budget battle -- Wolf 
BLITZER: These are committed, committed people to try to help 
We're going back to Libya in just a few moments  Rebel forces, furious with NATO right now, the R-rated message they are sending through our own Ben Wedeman 



ground_truth: The normalized least mean square (NLMS) algorithm.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What are the two ground states observed for indeno[1,2-a]fluorene on NaCl surfaces?

Read the following text and answer briefly.

Context 2:  Voltage pulses ranging between 4-6 V are applied by the tip of a combined STM/AFM system, which result in cleavage of one C-H bond at each of the pentagonal apices of 6, thereby leading to the generation of 5 (Fig  ) 
In the main text, we focus on the generation and characterization of 5 on insulating surfaces  Generation and characterization of 5 on coinage metal surfaces is shown in Supplementary Fig    )  Blue and orange colors represent spin up and spin down densities, respectively  c, Probability density of the SOMOs of 5OS (isovalue: 0 001 e -Å -3 ) 
d, DFT-calculated bond lengths of 5OS  e, Constant-height I(V) spectra acquired on a species of 5 assigned as 5OS, along with the corresponding dI/dV(V) spectra  Open feedback parameters: V = -2 V, I = 0 17 pA (negative bias side) and V = 2 V, I = 0 17 pA (positive bias side)  Acquisition position of the spectra is shown in Supplementary Fig    f, Scheme of many-body transitions associated to the measured ionic resonances of 5OS 
Also shown are STM images of assigned 5OS at biases where the corresponding transitions become accessible  Scanning parameters: I = 0 3 pA (V = -1 2 V and -1 5 V) and 0 2 pA (V = 1 3 V and 1 6 V)  g, Laplace-filtered AFM image of assigned 5OS  STM set point: V = 0 2 V, I = 0 5 pA on bilayer NaCl, Δz = -0 3
Å  The tip-height offset Δz for each panel is provided with respect to the STM setpoint, and positive (negative) values of Δz denote tip approach (retraction) from the STM setpoint  f and g show the same molecule at the same adsorption site, which is next to a trilayer NaCl island  The bright and dark features in the trilayer NaCl island in g correspond to Cl -and Na + ions, respectively 
Scale bars: 10 Å (f) and 5 Å (g)  To experimentally explore the electronic structure of 5, we used bilayer NaCl films on coinage metal surfaces to electronically decouple the molecule from the metal surfaces  Before presenting the experimental findings, we summarize the results of our theoretical calculations performed on 5 in the neutral charge state (denoted as 5 0 ) 
We start by performing DFT calculations on 5 0 in the gas phase  Geometry optimization performed at the spin-unrestricted UB3LYP/6-31G level of theory leads to one local minimum, 5OS, the geometry of which corresponds to the open-shell resonance structure of 5 (Fig  , the label OS denotes open-shell) 
The triplet electronic configuration of 5OS is the lowest-energy state, with the openshell singlet configuration 90 meV higher in energy  Geometry optimization performed at the restricted closed-shell RB3LYP/6-31G level reveals two local minima, 5para and 5ortho, the geometries of which (Fig  ) exhibit bond length alternations in line with the presence of a para-or an ortho-QDM moiety, respectively, in the as-indacene core of the closed-shell resonance structures of 5 (Fig  )  
Relative to 5OS in the triplet configuration, 5para and 5ortho are 0 40 and 0 43 eV higher in energy, respectively  Additional DFT results are shown in Supplementary Fig    To gain more accurate insights into the theoretical electronic structure of 5, we performed multireference perturbation theory calculations (Supplementary Fig  ) based on quasi-degenerate second-order n-electron valence state perturbation theory (QD-NEVPT2) 
In so far as the order of the ground and excited states are concerned, the results of QD-NEVPT2 calculations qualitatively match with DFT calculations  For 5OS, the triplet configuration remains the lowest-energy state, with the open-shell singlet configuration 60 meV higher in energy  The energy differences between the open-and closed-shell states are substantially reduced in QD-NEVPT2 calculations, with 5para and 5ortho only 0 11 and 0 21 eV higher in energy, respectively, compared to 5OS in the triplet configuration 
We also performed nucleus-independent chemical shift calculations to probe local aromaticity of 5 in the openand closed-shell states  While 5OS in the triplet configuration exhibits local aromaticity at the terminal benzenoid rings, 5OS in the open-shell singlet configuration, 5para and 5ortho all display antiaromaticity (Supplementary Fig  ) 
The choice of the insulating surface determines the charge state of 5: while 5 adopts neutral charge state on the high work function bilayer NaCl/Au(111) surface (irrespective of its openor closed-shell state, Supplementary Fig  ), 5 exhibits charge bistability between 5 0 and the anionic state 5 -1 on the lower work function bilayer NaCl/Ag(111) and Cu(111) surfaces (Supplementary Figs  ) 
In the main text, we focus on the characterization of 5 on bilayer NaCl/Au(111)  Characterization of charge bistable 5 is reported in Supplementary Figs    We first describe experiments on 5 on bilayer NaCl/Au(111), where 5 exhibits a geometry corresponding to the calculated 5OS geometry, and an open-shell electronic configuration 
We compare the experimental data on this species to calculations on 5OS with a triplet configuration, as theory predicts a triplet ground state for 5OS  For 5OS, the calculated frontier orbitals correspond to the SOMOs ψ1 and ψ2 (Fig  ), whose spin up levels are occupied and the spin down levels are empty 
Figure shows the DFT-calculated bond lengths of 5OS, where the two salient features, namely, the small difference in the bond lengths within each ring and the notably longer bond lengths in the pentagonal rings, agree with the open-shell resonance structure of 5 (Fig  )  Figure shows an AFM image of 5 adsorbed on bilayer NaCl/Au(111) that we assign as 5OS, where the bond-order differences qualitatively correspond to the calculated 5OS geometry (discussed and compared to the closed-shell state below) 
Differential conductance spectra (dI/dV(V), where I and V denote the tunneling current and bias voltage, respectively) acquired on assigned 5OS exhibit two peaks centered at -1 5 V and 1 6 V (Fig  ), which we assign to the positive and negative ion resonances (PIR and NIR), respectively  Figure shows the corresponding STM images acquired at the onset (V = -1 2
V/1 3 V) and the peak (V = -1 5 V/1 6 V) of the ionic resonances  To draw a correspondence between the STM images and the molecular orbital densities, we consider tunneling events as many-body electronic transitions between different charge states of 5OS (Fig  )  Within this framework, the PIR corresponds to transitions between 5 0 and the cationic state 5  
At the onset of the PIR at -1 2 V, an electron can only be detached from the SOMO ψ1 and the corresponding STM image at -1 2 V shows the orbital density of ψ1  Increasing the bias to the peak of the PIR at -1 5 V, it becomes possible to also empty the SOMO ψ2, such that the corresponding STM image shows the superposition of ψ1 and ψ2, that is, |ψ1| 2 + |ψ2| 2 (ref 
)  Similarly, the NIR corresponds to transitions between 5 0 and 5 -1   At the NIR onset of 1 3 V, only electron attachment to ψ2 is energetically possible  At 1 6 V, electron attachment to ψ1 also becomes possible, and the corresponding STM image shows the superposition of ψ1 and ψ2  The observation of the orbital densities of SOMOs, and not the hybridized HOMO and LUMO, proves the open-shell ground state of assigned 5OS 
Measurements of the monoradical species with a doublet ground state are shown in Supplementary Fig    Unexpectedly, another species of 5 was also experimentally observed that exhibited a closedshell ground state  In contrast to 5OS, where the frontier orbitals correspond to the SOMOs ψ1 and ψ2, DFT calculations predict orbitals of different shapes and symmetries for 5para and 5ortho, denoted as α and β and shown in Fig   
For 5ortho, α and β correspond to HOMO and LUMO, respectively  The orbitals are inverted in energy and occupation for 5para, where β is the HOMO and α is the LUMO  Fig  shows an AFM image of 5 that we assign as 5para  We experimentally infer its closed-shell state first by using qualitative bond order discrimination by AFM 
In high-resolution AFM imaging, chemical bonds with higher bond order are imaged brighter (that is, with higher frequency shift Δf) due to stronger repulsive forces, and they appear shorter   In Fig  , we label seven bonds whose bond orders show significant qualitative differences in the calculated 5ortho, 5para (Fig  ) and 5OS (Fig  ) geometries 
In 5para, the bonds b and d exhibit a higher bond order than a and c, respectively  This pattern is reversed for 5ortho, while the bond orders of the bonds a-d are all similar and small for 5OS  Furthermore, in 5para bond f exhibits a higher bond order than e, while in 5ortho and 5OS bonds e and f exhibit similar bond order (because they belong to Clar sextets) 
Finally, the bond labeled g shows a higher bond order in 5para than in 5ortho and 5OS  The AFM image of assigned 5para shown in Fig  indicates higher bond orders of the bonds b, d and f compared to a, c and e, respectively  In addition, the bond g appears almost point-like and with enhanced Δf contrast compared to its neighboring bonds, indicative of a high bond order (see Supplementary Fig  for height-dependent measurements) 
These observations concur with the calculated 5para geometry (Fig  )  Importantly, all these distinguishing bond-order differences are distinctly different in the AFM image of 5OS shown in Fig  , which is consistent with the calculated 5OS geometry (Fig  )  In the AFM images of 5OS (Fig  and Supplementary Fig  ), the bonds a-d at the pentagon apices appear with similar contrast and apparent bond length 
The bonds e and f at one of the terminal benzenoid rings also exhibit similar contrast and apparent bond length, while the central bond g appears longer compared to assigned 5para  Further compelling evidence for the closed-shell state of assigned 5para is obtained by STM and STS  dI/dV(V) spectra acquired on an assigned 5para species exhibit two peaks centered at -1 4 V (PIR) and 1 6 V (NIR) (Fig  ) 
STM images acquired at these biases (Fig  ) show the orbital densities of β (-1 4 V) and α (1 6 V)  First, the observation of α and β as the frontier orbitals of this species, and not the SOMOs, strongly indicates its closed-shell state  Second, consistent with AFM measurements that indicate good correspondence to the calculated 5para geometry, we observe β as the HOMO and α as the LUMO 
For 5ortho, α should be observed as the HOMO and β as the LUMO  We did not observe molecules with the signatures of 5ortho in our experiments  We observed molecules in open-(5OS, Fig  ) and closed-shell (5para, Fig  ) states in similar occurrence after their generation from 6 on the surface  We could also switch individual molecules between open-and closed-shell states as shown in Fig  and Supplementary Fig   
To this end, a change in the adsorption site of a molecule was induced by STM imaging at ionic resonances, which often resulted in movement of the molecule  The example presented in Fig  shows a molecule that was switched from 5para to 5OS and back to 5para  The switching is not directed, that is, we cannot choose which of the two species will be formed when changing the adsorption site, and we observed 5OS and 5para in approximately equal yields upon changing the adsorption site 
The molecule in Fig  is adsorbed on top of a defect that stabilizes its adsorption geometry on bilayer NaCl  At defect-free adsorption sites on bilayer NaCl, that is, without a third layer NaCl island or atomic defects in the vicinity of the molecule, 5 could be stably imaged neither by AFM nor by STM at ionic resonances (Supplementary Fig  ) 
Without changing the adsorption site, the state of 5 (open-or closedshell) never changed, including the experiments on bilayer NaCl/Ag(111) and Cu(111), on which the charge state of 5 could be switched (Supplementary Figs  )  Also on these lower work function surfaces, both open-and closed-shell species were observed for 5 0 and both showed charge bistability between 5 0 (5OS or 5para) and 5 -1 (Supplementary Figs  ) 
The geometrical structure of 5 -1 probed by AFM, and its electronic structure probed by STM imaging at the NIR (corresponding to transitions between 5 -1 and the dianionic state 5 -2 ), are identical within the measurement accuracy for the charged species of both 5OS and 5para  When cycling the charge state of 5 between 5 0 and 5 -1 several times, we always observed the same state (5OS or 5para) when returning to 5 0 , provided the molecule did not move during the charging/discharging process 
Based on our experimental observations we conclude that indeno[1,2-a]fluorene (5), the last unknown indenofluorene isomer, can be stabilized in and switched between an open-shell (5OS) and a closed-shell (5para) state on NaCl  For the former, both DFT and QD-NEVPT2 calculations predict a triplet electronic configuration 
Therefore, 5 can be considered to exhibit the spin-crossover effect, involving magnetic switching between high-spin (5OS) and low-spin (5para) states, coupled with a reversible structural transformation  So far, the spin-crossover effect has mainly only been observed in transition-metal-based coordination compounds with a near-octahedral geometry  
The observation that the switching between open-and closedshell states is related to changes in the adsorption site but is not achieved by charge-state cycling alone, indicates that the NaCl surface and local defects facilitate different electronic configurations of 5 depending on the adsorption site 
Gas-phase QD-NEVPT2 calculations predict that 5OS is the ground state, and the closed-shell 5para and 5ortho states are 0 11 and 0 21 eV higher in energy  The experiments, showing bidirectional switching between 5OS and 5para, indicate that a change in the adsorption site can induce sufficient change in the geometry of 5 (leading to a corresponding change in the ground state electronic configuration) and thus induce switching 
Switching between open-and closed-shell states in 5 does not require the breaking or formation of covalent bonds , but a change of adsorption site on NaCl where the molecule is physisorbed  Our results should have implications for single-molecule devices, capitalizing on the altered electronic and chemical properties of a system in π-diradical open-shell and closed-shell states such as frontier orbital and singlet-triplet gaps, and chemical reactivity 
For possible future applications as a single-molecule switch, it might be possible to also switch between open-and closed-shell states by changing the local electric field, such as by using chargeable adsorbates   Scanning probe microscopy measurements and sample preparation  STM and AFM measurements were performed in a home-built system operating at base pressures below 1×10 -10 mbar and a base temperature of 5 K  Bias voltages are provided with respect to the sample 
All STM, AFM and spectroscopy measurements were performed with carbon monoxide (CO) functionalized tips  AFM measurements were performed in non-contact mode with a qPlus sensor   The sensor was operated in frequency modulation mode with a constant oscillation amplitude of 0 5 Å  STM measurements were performed in constantcurrent mode, AFM measurements were performed in constant-height mode with V = 0 V, and I(V) and Δf(V) spectra were acquired in constant-height mode 
Positive (negative) values of the tip-height offset Δz represent tip approach (retraction) from the STM setpoint  All dI/dV(V) spectra are obtained by numerical differentiation of the corresponding I(V) spectra  STM and AFM images, and spectroscopy curves, were post-processed using Gaussian low-pass filters 
Au(111), Ag(111) and Cu(111) surfaces were cleaned by iterative cycles of sputtering with Ne + ions and annealing up to 800 K  NaCl was thermally evaporated on Au(111), Ag(111) and Cu(111) surfaces held at 323 K, 303 K and 283 K, respectively  This protocol results in the growth of predominantly bilayer (100)-terminated islands, with a minority of trilayer islands 
Sub-monolayer coverage of 6 on surfaces was obtained by flashing an oxidized silicon wafer containing the precursor molecules in front of the cold sample in the microscope  CO molecules for tip functionalization were dosed from the gas phase on the cold sample  Density functional theory calculations  DFT was employed using the PSI4 program package  
All molecules with different charge (neutral and anionic) and electronic (open-and closed-shell) states were independently investigated in the gas phase  The B3LYP exchangecorrelation functional with 6-31G basis set was employed for structural relaxation and singlepoint energy calculations  The convergence criteria were set to 10 −4 eV Å −1 for the total forces and 10 −6 eV for the total energies 
Multireference calculations  Multireference calculations were performed on the DFToptimized geometries using the QD-NEVPT2 level of theory , with three singlet roots and one triplet root included in the state-averaged calculation  A (10,10) active space (that is, 10 electrons in 10 orbitals) was used along with the def2-TZVP basis set  
Increasing either the active space size or expanding the basis set resulted in changes of about 50 meV for relative energies of the singlet and triplet states  These calculations were performed using the ORCA program package   Nucleus-independent chemical shift (NICS) calculations  Isotropic nucleus-independent chemical shift values were evaluated at the centre of each ring using the B3LYP exchangecorrelation functional with def2-TZVP basis set using the Gaussian 16 software package  
Starting materials (reagent grade) were purchased from TCI and Sigma-Aldrich and used without further purification  Reactions were carried out in flame-dried glassware and under an inert atmosphere of purified Ar using Schlenk techniques  Thin-layer chromatography (TLC) was performed on Silica Gel 60 F-254 plates (Merck) 
Column chromatography was performed on silica gel (40-60 µm)  Nuclear magnetic resonance (NMR) spectra were recorded on a Bruker Varian Mercury 300 or Bruker Varian Inova 500 spectrometers  Mass spectrometry (MS) data were recorded in a Bruker Micro-TOF spectrometer  The synthesis of compound 6 was developed following the two-step synthetic route shown in Supplementary Fig  , which is based on the preparation of methylene-bridge polyarenes by means of Pd-catalyzed activation of benzylic C-H bonds  
Supplementary Figure | Synthetic route to obtain compound 6  The complex Pd2(dba)3 (20 mg, 0 02 mmol) was added over a deoxygenated mixture of 1,3-dibromo-2,4-dimethylbenzene (9, 100 mg, 0 38 mmol), boronic acid 10 (178 mg, 1 14 mmol), K2CO3 (314 mg, 2 28 mmol) and XPhos (35 mg, 0 08 mmol) in toluene (1:1, 10 mL), and the resulting mixture was heated at 90 °C for 2 h 
After cooling to room temperature, the solvents were evaporated under reduced pressure  The reaction crude was purified by column chromatography (SiO2; hexane:CH2Cl2 9:1) affording 11 (94 mg, 76%) as a colorless oil  The complex Pd(OAc)2 (7 mg, 0 03 mmol) was added over a deoxygenated mixture of terphenyl 11 (90 mg, 0 27 mmol), K2CO3 (114 mg, 0 83 mmol) and ligand L (26 mg, 0 06 mmol) in NMP (2 mL) 
The resulting mixture was heated at 160 °C for 4 h  After cooling to room temperature, H2O (30 mL) was added, and the mixture was extracted with EtOAc (3x15 mL)  The combined organic extracts were dried over anhydrous Na2SO4, filtered, and evaporated under reduced pressure  The reaction crude was purified by column chromatography (SiO2; hexane:CH2Cl2 9:1) affording compound 6 (8 mg, 11%) as a white solid  in AFM imaging due to their reduced adsorption height compared to the rest of the carbon atoms 
We attribute this observation to the significantly different lattice parameter of Cu(111) (2 57 Å) compared to Au(111) and Ag(111) (2 95 Å and 2 94 Å, respectively) , such that the apical carbon atoms of the pentagonal rings of 5 adsorb on the on-top atomic sites on Au(111) and Ag(111), but not on Cu(111) 
Our speculation is based on a previous study of polymers of 1 on Au(111) by Di Giovannantonio et al  , where both tilted and planar individual units of 1 were observed depending on whether the apical carbon atoms of the pentagonal rings in 1 adsorbed on the on-top or hollow sites of the surface, respectively 
Given the strong molecule-metal interaction, we found no electronic state signatures of 5 on all three metal surfaces  STM set point for AFM images: V = 0  e, Frontier orbital spectrum of 5 -1   In the anionic state, ψ2 becomes doubly occupied and ψ1 is the SOMO  Filled and empty circles denote occupied and empty orbitals, respectively 
For each panel, zero of the energy axis has been aligned to the respective highest-energy occupied orbital 



ground_truth: Open-shell π-diradical state and closed-shell state with a para-quinodimethane moiety.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the sticking point in the political showdown over the budget?

Read the following text and answer briefly.

Context 4:  
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\indent The exact atomic structure of the defects could in principle be determined from a comparison of $dI/dV$ spectra with simulated first-principle LDOS signatures of expected defect types  In reality, this is hampered by the large number of possible geometries to simulate, including complex multiple defect structures~\cite{Buchs_Ar}, together with the large unit cells of the semiconducting chiral SWNTs studied here 
\\
\subsection{1D piecewise constant potential model}
\label{1D}
To better understand the physical origins of the non-trivial signatures of the quantized states, we model the experimental $dI/dV$ maps by solving the time independent one-dimensional Schr\"odinger equation over a piecewise constant potential model of QD I and QD II  The scattering centers are approximated by semi-transparent rectangular tunneling barriers leading to a square confinement potential~\cite{Laird:2015}  This is supported by previous results on defect-induced confinement in metallic SWNTs using the same experimental conditions~\cite{Buchs_PRL} and is consistent with ab-initio simulations presented later in this work  The potential modulation within the QD is approximated by a potential step  The resulting potential geometries are illustrated with gray shaded areas in Fig ~\ref{exp_data_Ar} (c) and (d) and Fig ~\ref{exp_data_N}(b)  Dispersion relations $E(k)$ can be extracted experimentally from the quantized states wavefunctions by measuring the energy and corresponding momenta in the left and right sides of the QDs  The wavevectors $k$ are determined using stationary wave-like fitting functions~\cite{Buchs_PRL} displayed with dashed red curves in Figs ~\ref{exp_data_Ar}(a)-(b) and ~\ref{exp_data_N}(a))  From this procedure, the potential step height and position can be estimated (see supplementary information)  The experimental data sets $E(k)$ are plotted in the right panels of Figs ~\ref{exp_data_Ar}(a) and \ref{exp_data_N}(a) together with dispersion relations from a third-nearest neighbor tight-binding calculation closely approximating ab-initio results~\cite{Reich_TB_2002}  These chirality-dependent tight-binding dispersion relations, calculated within an extended Brillouin zone resulting from the defect-induced breaking of the translation invariance~\cite{Bercioux_prb_2011}, are used in the Hamiltonian of our one-dimensional model  Taking into account the measured chiral angle, diameter distribution~\cite{Buchs_conf} and measured bandgaps, we find the best match with chiralities $(7,6)$ for QD I and $(11,1)$ for QD II (see supplementary information)  
\\
\indent Once chiralities together with potential step heights and positions are optimized, one can fit the height and width of the rectangular tunneling barriers in order to reproduce the experimental level spacings and general LDOS patterns  On a qualitative ground, a symmetric double barrier system results in the formation of spatially symmetric discrete bound states  Increasing both barrier heights simultaneously shifts the bound state energy levels and level spacings up  This leads to sharper bound states as the confinement in the QD is made stronger thus increasing the lifetime of the confined electrons  Increasing the barrier thickness with constant inner edge separation does not affect much the level spacings but further sharpens the bound states  Any asymmetry introduced by a change in the width or height of one single barrier leads to broader bound states  The presence of a potential step modifies the LDOS in lifting the levels of the bound states, with a more pronounced effect on the lower states  In QD I and II, the center of each barrier is aligned with the center of the gap states ($d3'$-$d4$ for QD I and $d6'$-$d7$ in QD II) and the width ratio is kept proportional to the ratio of the spatial extent of the gap states  Thus, by increasing the width of the barriers, we decrease the length of the QD leading to higher level spacings, and vice versa  The experimental level spacings can then be approximated by tuning both barrier widths in the same ratio and the heights individually, knowing that the scattering strength of $d3'$ ($d7$) is larger than $d4$ ($d6'$) according to the observed asymmetry in the LDOS described above \footnote{The transmission probability through a rectangular tunneling barrier is given by $T=\left( 1+\frac{V^{2}\sinh^{2}\left( a \cdot \sqrt{2m^{*}(V-E)}/\hbar \right)}{4E(V-E)} \right)^{-1}$, where $V$ and $a$ are respectively the barrier height and width  For the argument in the $\sinh$ sufficiently small such that $\sinh(x)\simeq x$, it can be shown that $a$ and $V$ can be coupled such that the transmission probability becomes a function of the area under the barrier $A=a\cdot V$, with $T=\left( 1+ \frac{m^{*}A^{2}}{2\hbar^{2}E} \right)^{-1}$  In our case, this condition is not satisfied and thus the barrier geometries are tuned empirically to fit the experimental level spacings }  
\\
\indent For QD I, we find a good match in the conduction band for the barrier heights $V_\mathrm{d3'}=1$ eV and $V_\mathrm{d4}=0 85$ eV, widths $a_\mathrm{d3'}=a_\mathrm{d4}=$ 3 4 nm,  and potential step $V_\mathrm{L}-V_\mathrm{R}=60$ meV  With these parameters, the spatial profile of the obtained quantized states (see lower subpanels in Fig ~\ref{exp_data_Ar}(a) and (c)) reproduces the experimental modulation features remarkably well  Also, the simulated LDOS displays a pattern with curved stripes oriented from top left to bottom right, as observed experimentally, due to a left barrier with a larger scattering strength  In the valence band, although modes m-2 and lower do not show a well defined structure in the spatial direction, thinner barriers with dimensions $a_\mathrm{d3'/d4}=2 5$ nm, $V_\mathrm{d3'/d4}=-0 4$ eV, leading to a slightly longer QD length (9 6 nm compared to 8 7 nm in the conduction band) can reproduce the measured level spacings very well  
\\
\indent For QD II, we observed that the measured energy levels are overestimated by a factor $\alpha\sim1 29$, presumably due to a voltage division effect induced by the impurity layer mentioned above (see details in supplementary information)  We find a good agreement with the experimental LDOS with the parameters: $V_{d3'}=V_{d4}\simeq$ 0 47 eV, $a_\mathrm{d6'}=1 5$ nm, $a_\mathrm{d7}=2 6$ nm and $U_\mathrm{C}=V_\mathrm{L}-V_\mathrm{R}\simeq 47$ meV  Note that in Fig ~\ref{exp_data_N}(b) the barrier and potential heights are multiplied by $\alpha$ to allow a direct comparison with the experimental LDOS  The simulated LDOS shows a pattern with curved stripes oriented from bottom left to top right, as observed experimentally, due to a right barrier exhibiting a larger scattering strength  Also, the spatial profile of the obtained bound states (see lower subpanels in Fig ~\ref{exp_data_N}(a) and (b)) reproduces the experimental features quite well  Note also that one can distinguish an isolated state in the experimental LDOS at an energy level between m1 and m2, about in the middle of the QD  This state that prevented an accurate fit of the state m2 in the right QD part is attributed to a spatial feature visible in the STM topography image in Fig ~\ref{exp_data_Ar}(d) (see also supplementary information, Fig S2(f)), probably a physisorbed impurity which does not affect the LDOS significantly 
\\
\subsection{Ab-initio calculations}
\begin{figure}
  \includegraphics[width=16cm]{Figure_4 pdf}
  \caption{\label{num_data} (a)-(c) LDOS ab-initio simulations of a semiconducting $(16,0)$ SWNT with combinations of vacancies defects separated by 11 1 nm  Subpanels display QD state linecut profiles  (d) Tight-binding (black curve) and ab-initio dispersion relations (green circles) for a pristine $(16,0)$ SWNT with $E_\mathrm{n}(k_\mathrm{n})$ data sets extracted from (a)-(c)  (e)-(g) LDOS ab-initio simulations of a semiconducting $(17,0)$ SWNT with combinations of N ad-atoms and vacancies defects separated by 10 7 nm  (h) Tight-binding (black curve) and ab-initio dispersion relations (green circles) for a pristine $(17,0)$ SWNT with $E_\mathrm{n}(k_\mathrm{n})$ data sets extracted from (e)-(g) }
\end{figure}
In order to elucidate the physical nature of the electron/hole confining scattering centers, we performed ab-initio simulations based on a combination of density functional theory~\cite{pbe,paw,vasp_paw,VASP2}, maximally localized Wannier orbitals~\cite{transportwannier90} and Green's functions (see supplementary information)  Without loss of generality, we have simulated short unit cell semiconducting zigzag SWNTs with different combinations of the most probable defect structures  Results for vacancy defects likely being induced by 200 eV Ar$^{+}$ ions, separated by about 11 nm in a $(16,0)$ SWNT are shown in Fig ~\ref{num_data}(a)-(c) with DV-DV, DV-SV and SV-SV pairs, respectively  The LDOS displays midgap states at the defect positions as expected as well as defect states in the valence band~\cite{Buchs_Ar}  Most importantly, clear quantized states with a number of maxima increasing with energy are observed between the defects in the conduction band, emphasizing the ability of SVs and DVs to confine carriers  For the asymmetric configuration DV-SV, one can distinguish faint curved stripe patterns oriented from top left to bottom right, indicating a larger scattering strength for DVs compared to SVs  This is consistent with observations in transport experiments~\cite{Gomez05nm}  On the other hand, the patterns in the valence band strongly depend on the defect types  Discrete states can be distinguished for the DV-DV case, with m-2 being mixed with defect states  For the DV-SV case, clear curved stripe patterns oriented from bottom left to top right indicate again a stronger scattering strength for DV  Also, broader states are observed, indicating that the scattering strength of DVs and SVs is weaker in the valence band compared to the conduction band 
\\
\indent More insight on the energy dependent scattering strength for each defect pair configuration can be obtained by extracting the wavevector $k_\mathrm{n}(E_\mathrm{n})$ for each resonant state  This data set is plotted in Fig ~\ref{num_data}(d) for the conduction and valence bands together with the $(16,0)$ dispersion relations calculated from the third-nearest neighbor TB model and from the ab-initio calculation for the pristine nanotube  A first observation is the excellent agreement between TB and ab-initio results, further validating the method used in Figs ~\ref{exp_data_Ar}(a)-(b) and ~\ref{exp_data_N}(a)  The vertical dashed lines indicate the limiting $k_\mathrm{n,\infty}=\frac{\pi \cdot n}{L}$ values corresponding to the closed system (infinite hard walls potential) with $L=11 1$ nm being the defect-defect distance  In the conduction band, we find that $k_\mathrm{n}(E_\mathrm{n})=\frac{\pi \cdot n}{L_\mathrm{eff}(n)} < k_\mathrm{n,\infty}$, indicating that the effective lengths $L_\mathrm{eff}(n)$ of the QD are larger than $L$ ($i e $ the resonant states wavefunctions are characterized by penetrating evanescent modes inside the defect scattering potential), as expected for an open system  The shortest $L_\mathrm{eff}(n)$ are obtained for the DV-DV configuration with 12 1 nm (m1), 13 1 nm (m2) and 12 9 nm (m3), which we attribute to wider scattering potential profiles for DVs compared to SVs  In the valence band, we find that $k_\mathrm{n}(E_\mathrm{n})=\frac{\pi \cdot n}{L_\mathrm{eff}(n)} > k_\mathrm{n,\infty}$, with $L_\mathrm{eff}(n)$ values between 7 9 nm (DV-DV, m-1) and 9 66 nm (DV-SV, m-2)  We attribute this pronounced QD shortening to wider scattering potential profiles of both DVs and SVs in the valence band, probably due to mixing with wide spread defect states in the valence band 
\\
\indent Ab-initio calculations for different defect pairs combinations containing at least one N ad-atom, $i e $ N-DV, N-SV and N-N, are presented in Fig ~\ref{num_data}(e)-(h) for a $(17,0)$ SWNT, along with details on the defects geometries  Remarkably, clear QD states are generated for all three configurations, underlining the potential of N ad-atoms to confine carriers in semiconducting SWNTs and thus to generate intrananotube QDs  
\\
\indent In order to demonstrate the scattering strengths of the different defects, we calculated the energy dependent conductance in addition to the LDOS for the different combinations of the QD defining scattering defects on the $(16,0)$ and $(17,0)$ SWNTs, see supplementary information  Generally we can observe strong conductance modulation of the order of 30-40\% with regard to the pristine CNT for all three tested defects (double vacancies DV, single vacancies SV and chemisorbed C-N) with the DVs having the largest scattering strength in the CB and VB   
\\
\indent Note that the choice of the zigzag SWNT chiralities in the two different ab-initio scenarios is motivated by the different effective masses of both chiralities ($m^{*}_{(17,0)}>m^{*}_{(16,0)}$) which is typical for chirality families $(3n-1,0)$ and $(3n-2,0)$~\cite{ZZ_families}  Taking advantage of recent reports on SWNT chirality control~\cite{chirality_control_EMPA,chirality_control_chinese,chirality_chemistry}, this property could be used in practice to design QDs with different level spacings for the same QD length  From an application point of view, however, QDs generated by DVs will have far superior stability at room temperature due to their high migration barrier above 5 eV ($\sim$~1 eV for single vacancy)~\cite{Kra06vm}  This value drops down by at least 2 eV for N ad-atoms depending on their chemisorption configuration~\cite{Nitrogen_prb_07,Yma05nitr} 
\\
\indent Our ab-initio simulations do not take into account any substrate effect  In the experimental case, the carriers can decay through the substrate, thus limiting their lifetime  This leads to state broadening, measured between about 60 meV up to 120 meV in QD I and II, while the quantized states widths in ab-initio simulations vary between about 5 meV and 45 meV  This suggests that a better contrast of the experimental quantized states, especially in the valence band, could be achieved by lowering the nanotubes-substrate interaction through $e g $ the insertion of atomically thin insulating NaCl films~\cite{Ruffieux_Nature_2016}  This would allow to gain more insight on the electronic structure of the QDs as well as in the associated scattering physics at the confining defects~\cite{Buchs_PRL}  

\section{Conclusions and outlook}
In summary, using low-temperature STM/STS measurements supported by an analytical model and ab-initio simulations, we have demonstrated that intrananotube quantum dots with confined electron and hole states characterized by energy level spacings well above thermal broadening at room temperature can be generated in semiconducting SWNTs by structural defects such as vacancies and di-vacancies, as well as nitrogen ad-atoms  These results, combined with recent progresses in type and spatial control in the formation of defects~\cite{Robertson_2012,Yoon_2016,Laser_writing_2017} as well as chirality control~\cite{tunable_QD_defects}, hold a high potential for applications in the design of SWNT based quantum devices  These include $e g $ electrically driven single-photon emitters operating at room temperature and telecom wavelength  In this context, the observation of quantum confinement effects in the emitted light of cut, sub-10 nm, semiconducting SWNTs~\cite{Dai_2008} shall be seen as an additional motivation for investigating the optical properties of our "QD with leads" building-blocks  These would include $e g $ studying optical transitions selection rules for different types and configurations of defect pairs~\cite{sel_rules_2006} associated with experimental studies such as photoluminescence~\cite{Lefebvre06} combined to $g^{(2)}$ correlation measurements~\cite{Hofmann_2013} in suspended SWNT devices as well as photocurrent imaging~\cite{Buchs_Nat_comm} and spectroscopy~\cite{Gabor_2009} 

\section*{Acknowledgements}
The authors thank Ethan Minot, Lee Aspitarte, Jhon Gonzalez, Andres Ayuela, Omjoti Dutta and Arkady Krasheninnikov for fruitful discussions 
The work of DB is supported by Spanish Ministerio de Econom\'ia y Competitividad (MINECO) through the project  FIS2014-55987-P and by the (LTC) QuantumChemPhys  LM acknowledges support from the BMBF-project WireControl (FKZ16ES0294) and computing time for the supercomputers JUROPA and JURECA at the J\"ulich Supercomputer Centre (JSC) 


\clearpage

\section*{References}






ground_truth: The sticking point in the political showdown over the budget is how much spending to cut.