Abstracts of Invitedand Contributed Talks, Sep. 6157

6A1-1I  Interesting bonds formed by heavier main group elements
Shigeru Nagase1
1
Department of Theoretical and Computational Molecular Science
Institute for Molecular Science, Japan

Carbon plays a central role in many fields of chemistry and provides a wide varietyof important saturated and unsaturated compounds. It is of considerable interest to
replace the skeletal carbons of these compounds by heavier homologues such as silicon,
germanium, tin, and lead to create new compounds featured by interesting bonds andstructures, which are not expected for carbon compounds. In this talk, I present ourrecent research on the bonds and structures of hypervalent, aromatic, andmultiply-bonded compounds containing heavier main group elements (and transition
metals), which is performed in collaboration with experiment.

158

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Donor-acceptor complexes of main group elements with unusual
bonds
Gernot Frenking1
1

Fachbereich Chemie, Philipps-Universität, Hans-Meerwein-Strasse, D-35043 Marburg,
Germany

The lecture will focus on three classes of donor-acceptor complexes of main-groupelements which possess unusual bonds. One topic are divalent E(0) compounds EL2 ofgroup-14 elements E = C – Pb where L is a ı-donor ligand. The topic includes anextension to complexes (EH)L2 of group-13 atoms B – Tl and group-15 complexes(ER)L2 where E = N – Bi. The second topic concerns complexes of diatomic species
E2(NHC)2 where E = Si – Pb, P – Bi and NHC = N-heterocyclic carbene. Finally, the third
topic focuses on complexes with the formula D-C6F4-BF3 where D is a donor species Xe,
N2, CO.

159

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Accurate evaluation of very-low ionization potentials ofgroup VI metal-metal coordination compounds
I-Ya Chang,1 Jen-Shiang K. Yu,1,2
1
Department of Biological Science and Technology,
National Chiao Tung University, Taiwan
2
Institute of Bioinformatics and Systems Biology,
National Chiao Tung University, Taiwan
I. Introduction
Coordination compounds composed by two group VI metal centers (M) supported byfour hpp ligands (the anion of 1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]pyrimidne),
M2(hpp)4 [1], exhibit quadruple metal-metal bonds. The most characteristic feature ofthis series of compounds is their very-low ionization potentials. Photoionization
experiments [1] indicated that the first ionization energy (IE) corresponding to theremoval of the electron from the G orbital can be as low as 3.514 eV for W2(hpp)4. In
this work, ab initio methods were utilized to accurately evaluate the lowest four
ionization energies of Mo2(hpp)4 and W2(hpp)4.
II. Computations
The authentic structures of Mo2(hpp)4 and W2(hpp)4 were initially optimized with
BP86 density functional theory, and the performance of several basis sets of triple-]quality was compared. In the best combinations the deviations of metal-metal bondlength are less than 0.02 Å between the computed and experimental geometries.
The ionization energies were calculated first using simplified models withmulti-configuration wavefunction to assist orbital selections. Complete active space
self-consistent field (CASSCF) theory was performed followed by energy correction
with multi-reference configuration interaction (MRCI) method. The active spaceconcluded from the model study is CASSCF(8,8) and CASSCF(7,8), respectively, in theneutral singlet and cation doublet states, and then applied to the authentic molecules.
Relativistic effect was explicitly included for the tungsten system. The outcoming IE
values were also compared with other high-level ab initio methods.
III. Results• Computed IEs using the authentic structure of W2(hpp)4 are listed in Table 1.
Table 1. Vertical IEs (in eV) of W2(hpp)4 compared with experimental data.
G (Ag)
S(Au)S (Bu)V (Ag)
aExp. onset
3.514
vertical
3.76
CASSCF
2.329
4.885
5.554
4.899
b
3.594
MRCI
6.223
6.241
6.841
a
b
Reference [1]. Using second order Douglas-Kroll-Hess Hamiltonian.
[1] F.A. Cotton et al., Science 298 (2002) 1971.

160

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State-of-the-art calculation of the ground state of the Sc2 dimer
Ulises Miranda and Ilya G. Kaplan
Instituto de Invetigaciones en Materiales, Universidad Nacional Autónoma de México,
Apdo. Postal 70-360, 04510 México, D.F., México
ulimirandone@gmail.com; kaplan@iim.unam.mx
The problem of calculation of the electronic structure of transition-metal clusters stillpresents a challenge for computational chemistry. The reason is that the expansion of theground state wave function on electronic configurations does not contain a principal
configuration and a large number of reference configurations must be treated equally.
Thus, the multi-reference (MR) approaches are, in general, mandatory.
In our study of the scandium dimer we used the multi-reference configurationinteraction approach (MRCISD(+Q)) at the complete basis set (CBS) limit [1]. This is thefirst MRCISD(+Q) calculation of 3d transition-metal clusters at the CBS limit. Although
the Sc atom has only one 3d electron, its dimer presents an extremely complex system,
since it has 270 low laying almost degenerate molecular states. According to our
calculations, the ground state of Sc2 corresponds to a quintet, 5 Ȉ u with an agreementwith ESR experiment and previous precise calculations. Spin S = 2 can be realized only if
one of Sc atoms dissociates in an excited state. The employment of the C2v symmetrygroup, allowed us to obtain the Sc atoms in different states at the dissociation limit. It is
proved that in the asymptotic dissociation limit one of Sc is created in the second quartet
excited state Sc* (3d14s14p1 4F). The spectroscopic parameters of the ground potential
curve, obtained by the Dunham analysis at the MRCISD(+Q)/CBS level, Re = 5.20 bohr,
De = 50.37 kcal/mol, and Ȧe = 234.5 cm-1. The calculated value for the harmonicfrequency agrees very well with the experimental one, Ȧe = 239.9 cm-1. In respect to theexperimentally measured dissociation limit Sc (3d14s2 2Dg) + Sc (3d14s2 2Dg) De = 9.98
kcal/mol. In contrast with the Mn2 dimer, which is bonded by the weak van der Waals(dispersion) forces with De = 0.62 kcal/mol [2]. Sc2 dimer is a valence-bonded moleculestabilized by the covalent bonding on the hybrid atomic orbitals.
1. U. Miranda and I.G. Kaplan. Eur. Phys. J. D (2011); DOI: 10 1140/epjd/e2010-10607-y.
2. D. Tzeli, U. Miranda, I.G. Kaplan, and A. Mavridis, J. Chem. Phys., 129, 154310(2008).

161

6A2-1C

An Optimized Genetic Algorithm for the FunctionaIization of Fullerenes
Matthew Addicoat,1 Alister Page,2 Zoe Brain3 Lloyd Flack4 Keiji Morokuma2
Stephan Irle1
1
Institute for Advanced Research, Nagoya University, Japan
2
Fukui Institute for Fundamental Chemistry, Kyoto University, Japan3
Department of Computer Science, Australian National University, Australia
4
Department of Rheumatology,University of New South Wales, Australia
I. Introduction
The placement of n functional groups on a fullerene presents a combinatorial
explosion problem. For example, there are over 5.4 million ways to place 5 functional groups on a C60 fullerene. Adding another functional group results in over
50 million possible structures. The number of possible structures for C60 Xn scales
factorially, given by the formula 60!/[n!(60-n)!]. To locate the global minimum, we
propose a tuned, canonical Genetic Algorithm (GA). In order to ﬁnd the most eﬃcient tunings for the GA, a second GA - a meta-genetic algorithm [1] - was used totune the ﬁrst genetic algorithm to reliably ﬁnd the already known a-priori correct
answer for C20 H4 (4845 structures, 57 distinct isomers), using minimum computational resources. GA optimization was undertaken using Huckel, Density Functional
Tight Binding (DFTB) and Density Functional Theory (DFT) methods to determine whether the level of theory employed altered the optimum GA parameters.
II. Meta-Genetic Algorithm
A total of 8 parameters were simultaneously optimised by the meta-GA, being:
population size, mutation rate, crossover probability, use of elitism, mutation type,crossover type, parental selection method and scaling method. Regression analysis
was used to determine the eﬀect of each parameter on the eﬃciency of the GA.
Population size, mutation rate and selection method were found to have the greatest
eﬀect on the eﬃciency of the GA, while mutation type and selection method havethe greatest eﬀect on the reliability of the GA. These results were consistent acrossall levels of theory employed.

Figure 1: Global minimum geometry of C20 H4 .
[1] B. Friesleben and M. Hartfelder. In R. Albrecht, C. Reeves, and N. Steele, ed.
Artiﬁcial Neural Networks and Genetic Algorithms, pg 392–399. Springer-Verlag,
Heidelberg, 1993.

162

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Mechanisms of Carbon-Based Nanostructure Self-Assembly:
Insights from Density-Functional Tight-Binding Molecular Dynamics
Alister J. Page,1 Ying Wang,2 K.R.S. Chandrakumar,1 Stephan Irle,2 Keiji Morokuma1,3
1
Fukui Institute for Fundamental Chemistry, Kyoto University, Japan
2
Institute for Advanced Research and Department of Chemistry, Nagoya University,
Japan
3
Cherry L. Emerson Center for Scientific Computation and Department of Chemistry,
Emory University, USA
Carbon nanostructures, such as fullerenes, carbon nanotubes and graphene, are currently
at the forefront of nanoscale molecular and material sciences. Yet in many cases, aprecise, atomistic understanding of how such nanostructures form is currently lacking.
In this work, we will review our recent non-equilibrium, high-temperature QM/MD
simulations of the formation of graphene and carbon nanotubes on catalysts ranging
from transition metals [1] to main-group oxide materials [2]. The approach employed isbased upon the self-consistent-charge density-functional tight-binding approximation to
DFT (SCC-DFTB) [3]. We are therefore able to simulate these phenomena with anaccuracy approaching that of conventional DFT, but at a cost that is comparable toclassical force-field-based methods. The simulations reviewed here have recently
furnished a detailed understanding of mechanisms of the nucleation and growth of thesenanostructures over timescales ranging from picoseconds to nanoseconds. They havetherefore served to complement, and, in some cases, predate experimental
understanding
g of such pphenomena.

[1] A. J. Page et al., Acc. Chem. Res., 43, (2010), 175.
[2] A. J. Page et al., J. Am. Chem. Soc., 133, (2011), 621.
[3] M. Elstner et al., Phys. Rev. B, 58, (1998), 7260.

163

6A2-3C

New Insights from Quantum Chemical Molecular Dynamics
Simulations on the Formation Mechanism of Metallofullerenes
Stephan Irle,1 Yoshio Nishimoto,1 Benjamin Finck,2 Zhi Wang,2 Keiji Morokuma2,3
1
Department of Chemistry, Graduate School of Science, Nagoya University, Japan
2
Cherry L. Emerson Center for Scientific Computation and Department of Chemistry,
Emory University, USA
3
Fukui Institute for Fundamental Chemistry, Kyoto University, Japan
Since the discovery of fullerenes and metallofullerenes, theoreticians andexperimentalists alike have been eager to reveal their formation mechanisms. Many
hypotheses were put forward, but none has been directly verified by experimentobservations.
In this contribution we present QM/MD simulations aimed at
elucidating the formation mechanism of endohedral metallofullerenes (EMFs) andendohedral metal carbide fullerenes (EMCFs). As transition metal elements weselected Sc, Ti, and Fe atoms embedded in ensembles of randomly placed C2 molecules.
The self-consistent-charge density-functional tight-binding (abbreviated as SCC-DFTB)
method [1] in conjunction with electronic temperature was used as quantum chemical
potential for the direct MD simulations. The MD simulations were performed using
the Nose-Hoover-chain thermostat at an environmental temperature of 2000 K for up to
about two hundred picoseconds. Each system was replicated 10 times.
In the beginning of the trajectories, metal atoms become incorporated in thegrowing sp2 carbon network. Around the 60 picosecond mark, we could observe
fullerene formation similar to the previous carbon-only simulations [2], but here somemetal atoms became incorporated into the cage network. The probability of the cageformation was comparable to carbon-only simulations.
However, the cage metal
atoms became occasionally “pushed in” by outer carbon structures, with theconsequence that the metal atoms become endohedrally trapped, most often with small
carbon fragments attached. Thus, ScxCy formation was observed frequently, while
ScxC0 was not so common. Our results therefore suggest that EMCF formation
dominates the early stage of endohedral metal GF formation. This finding seems
unexpected at first sight but can be reconciled by our observation that Cy fragments can
re-attach to the cage walls during GF shrinking to produce the familiar EMFs as well as
EMCFs.
[1] M. Elstner, D. Porezag, G. Jungnickel, J. Elstner, M. Haugk, Th. Frauenheim, S.
Suhai, G. Seifert, Phys. Rev. B, 58, 7260 (1998).
[2] S. Irle, G. Zheng, Z. Wang, K. Morokuma, J. Phys. Chem. B, 110, 14531 (2006).

164

6A3-1I

Multi-Paradigm Simulations at the Nanoscale: Methodology andApplications to Functional Carbon Materials
Haibin SU1
1
Division of Materials Science, Nanyang Technological University, Singapore

Abstract
Multiparadigm methods to span the scales from quantum mechanics to practical issues offunctional nanoassembly and nanofabrication are enabling first principles predictions toguide and complement the experimental developments by designing and optimizing
computationally the materials compositions and structures to assemble nanoscale systems
with the requisite properties. In this talk, we employ multi-paradigm approaches toinvestigate functional carbon materials with versatile character, including fullerene,carbon nanotube (CNT), graphene, and related hybrid structures, which have alreadycreated an enormous impact on next generation nano devices. The topics will cover thereaction dynamics of C60 dimerization and the more challenging complex formation
dynamics in the nano carbon structures; the predicted magnetic state in NanoBuds; andopto-electronic properties of graphene nanoribbons.

165

6A3-3C

Stone-Wales Rearrangement in Pyrene via the S1 State
Kaoru Yamazaki, Naoyuki Niitsu, Hirohiko Kono
Graduate School of Science, Tohoku University, Japan
Stone-Wales rearrangement (SWR, Figure 1) is a major mechanism for defect formation in nanocarbons such as graphene and carbon nanotubes (CNTs) [1]. SWR is regarded as a key step of fullerene formation from graphite [2]. This reaction changes theelectronic and magnetic properties of nanocarbon drastically [1]. Recent experimental[3] and theoretical studies [4, 5] suggest that there is some reaction path via electronic
excited state (EES). However, the detailed mechanism of the EES paths remains unknown. What kind of EES paths of SWR exist in graphene? The EES processes of SWR
via EES can be controlled photochemically, e.g., by optimal control of femtosecond laser
pulses. This provides a new way䈃of tuning the EMPs of nanocarΔ 㻱䈃bons optically.
We have investigated the
SWR paths of graphene and
CNT via EES quantum chemically by using pyrene as a model
Figure 1: The Stone-Wales rearrangement in pyrene
system (Figure 1). By potential
energy surface scan on the IRC Table 1: Relation between the activation energy ofof the T1 state at the
SWR in pyrene (ΔE‡) and the excitation energy (verMS-CASPT2//UB3LYP level
tical: ΔEve, adiabatic: ΔEad) in pyrene at theof theory we found that elecMS-CASPT2//IRC-UB3LYP level of theory (in eV).
tronic excitation reduces theactivation energy ΔE‡(Table 1)
State
ΔEve
ΔEad
ΔE‡optΔE‡scan[6]. We also found an avoided
crossing point between the S1
S0
0.00
0.00
8.88
9.52
and the S2 state due to the disT1
2.17
1.95
8.02
8.05
tortion of the carbon frame.
This suggests that SWR can
S1
2.93
2.77
̿
7.97
have a few EES paths
branched by nonadiabatic transitions. The detailed mechanism at the MS-CASPT2//SA-CASSCF level of theory will
be reported.
Reference: [1] Neto, C. et al., Rev. Mod.Phys. 2009, 81, 109-162. [2] Chuvilin, A. et al.,Nat. Chem. 2010, 2, 450-452. [3] Mayer, J. et al., Nano. Lett. 2008, 8 (11), 3582-3586. [4]Valencia, F. et al., Phys. Rev. B. 2006, 74, 075409. [5] Romero, H. et al., Nano. Lett. 2005,
5 (7), 1361-1365. [6] Yamazaki, K. et al., in preparation.

166

6A3-4C

Symmetry Broken Edge States of Linear Acenes:
Artifact or Reality?
Balázs Hajgató,1 Michael S. Deleuze,2 Frank De Proft,1 and Paul Geerlings1
1
Eenheid Algemene Chemie (ALGC), Member of the QCMM Research Group –Alliance Ghent-Brussels, Vrije Universiteit Brussel (VUB), Brussels, Belgium
2
Universiteit Hasselt, Research Group of Theoretical Chemistry and Molecular
Modeling, Diepenbeek, Belgium
Half-metallicity has been recently predicted for graphene nanoribbons on the ground of
Density Functional Theory (DFT) [1]. Peculiar states localize at the edges of the nanoribbon
and form a twofold degenerate flat band at the Fermi energy within one third of the first
Brillouin zone when the single graphite layer is terminated by zig-zag edges (polyacetylenic
strands) on both sides [2]. These edge states have been observed in monoatomic graphitic stepedges using scanning tunneling microscopy [3]. According to DFT calculations, they are
believed to relate to ferromagnetically ordered states with opposite spin orientation across the
ribbon, yielding a total spin equal to zero [4]. DFT calculations of linear acenes confirmed thesinglet biradical or multiradical ground state of long linear acenes [5]. Unfortunately, adetailed investigation of the wave function reveals that the symmetry-broken spin-densities inunrestricted calculations are numerical artifacts, yielding an unphysical energy lowering of theelectronic wave function into an open shell singlet ground state. A benchmark theoretical
study (1 kcal/mol or 0.04 eV accuracy) of the electronic ground state and of the vertical andadiabatic ionization energies [6], electron affinities [7], and singlet-triplet (S0-T1) excitationenergies [8] of benzene (n=1) and n-acenes (C4n+2H2n+4) ranging from naphthalene (n=2) tohexacene (n=6) or heptacene (n=7) is presented. Many different criteria demonstrate that all
investigated systems exhibit a 1Ag singlet closed-shell electronic ground state. In line with theabsence of Peierls distortions, extrapolations of results indicate a vanishingly small S0-T1
energy gap of ~–1 to ~1.5 kcal/mol in the limit of an infinitely long polyacene.
[1] Y-W. Son, M. L. Cohen, S. G. Louie, Nature, 444, 347 (2006); [2] L. Nakada et. al,. Phys.
Rev. B, 54, 17954 (1996); K. Wakabayashi et. al., Phys. Rev. B, 59, 8271 (1999); Y.
Miyamoto et. al., Phys. Rev. B, 59, 9858 (1999); [3] Y. Kobayashi et. al., Phys. Rev. B, 71,
193406 (2005); T. Enoki, Y. Kobayashi, J. Mat. Chem., 15, 3999 (2005); Y. Niimi et. al.,Phys. Rev. B, 73, 085421 (2006); [4] S. Okada et. al., Phys. Rev. Lett., 87, 146803 (2001);
H. Lee et. al., Phys. Rev. B, 72, 174431 (2005); [5] M. Bendikov et. al., J. Am. Chem. Soc.,
126, 7416 (2004); J. Hachmann et. al., J. Chem. Phys. 127, 134309 (2007); M. C. dos
Santos et. al., Phys. Rev. B, 74, 045426 (2006); D-E. Jiang, S. Dai, J. Phys. Chem. A, 112,332 (2008); Z. Qu et. al., J. Phys. Chem. A, 113, 7909 (2009); [6] M. S. Deleuze, L. Claes,
E. S. Kryachko and J. -P. François, J. Chem. Phys., 119, 3106 (2003); [7] B. Hajgató, M. S.
Deleuze, D. J. Tozer, F. De Proft, J. Chem. Phys., 129, 084308 (2008); [8] B. Hajgató, M. S.
Deleuze, D. Szieberth, F. De Proft, and P. Geerlings, J. Chem. Phys., 131, 224321 (2009).

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Alkali Halides Nanotubes: Structure and Stability
Francisco Alberto Fernandez-Lima1 , Enio Frota da Silveira2 ,Marco Antonio Chaer Nascimento3
1
Chemistry Department, Texas A&M University, College Station, TX, USA
2
Physics Department, Pontifı́cia Universidade Católica, Rio de Janeiro, Brazil
3
Chemistry Institute, Universidade Federal do Rio de Janeiro, Rio de Janeiro,
BrazilIn this talk we report the results of accurate quantum mechanical calculations
on some alkali halide (LiF, NaCl, KBr) neutral clusters. The relative stabilityof (MX)n=2−28 structural isomers was studied using DFT (B3LYP/LAVCV3P**).
For the members of the cubic and nanotube series Coupled Cluster calculations
at the CCSD/SDD level were also performed. Møller-Plesset perturbation theory
at the MP2/LAVCV3P** level of calculation was also used to check for possible
inconsistencies in the DFT results for the (MX)n=1−10 clusters. Quantum dynamics
calculations, at room temperature and atmospheric pressure, were also performed
for the (LiF)28 octagon nanotube. A variety of structures has been found but inthis talk we limit the discussion on the tube-like ones. Structural properties andpossible mechanisms of formation will be discussed.
The alkali halide nanotubes present much smaller diameters, ranging from 0.241
nm to 0.67 nm (LiF, tetragonal-KBr hexagonal) when compared to the more traditional covalent nanotubes of C (1-2 nm), BN (1-3 nm) or GaN (30-200 nm). Thisis a consequence of the fact that the interactions are dominantly electrostatic and,
therefore, much less strain is involved in making ring-type structures than in thecovalent ones.
The results obtained for the (LiF)n clusters show that overall the cubic series
is highly stable as expected from structures which are debris of a crystalline bulk.
Surprisingly, however, nanotube clusters with hexagonal and octagonal cross section
present similar or higher stability than the corresponding cubic clusters. This result
represents a new paradigm for 3D macro assembly of alkali halide clusters. This
work was funded by CNPq, FAPERJ and Instituto Nacional de Materiais Complexos
Funcionais. F.A.F-L acknowledges support from the National Institute of Health(Grant No. 1K99RR030188-01).

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Favorable confinement of water inside the carbon nanotubes isdriven by hydrogen bond and entropy
Yousung Jung
Graduate School of EEWS, KAIST, Korea
Nanofluidics and nanofiltration have emerged quite recently as an intriguinginterdisciplinary science, with applications to sensing, desalination and efficient energy
storage and conversion technologies. Water confined in carbon nanotubes (CNTs)
exhibits unexpected properties such as fast conduction rates and a variety of structuraland phase transitions. Future progress would undoubtedly depend on obtaining a basic
understanding of the fundamental driving forces in these systems. In particular, bothexperimental and theoretical studies have revealed that CNTs spontaneously fill withwater, a counter-intuitive proposition since hydrophobic confinement is generally
expected to decrease both entropy and bonding due to the breaking of water-waterhydrogen bonds upon creating a surface. While there has been some speculation as to thereasons for this remarkable phenomenon, it has not yet been explained.

In this talk, I present the first thermodynamic analysis of the favorable confinementof water in hydrophobic CNTs over the range of CNT diameters from 0.8 to 2.7 nm bymolecular dynamics simulations and the Two-Phase Thermodynamics method of
extracting absolute entropies and quantum corrections to the internal energy. We find forall sizes that water inside the CNTs has lower free energies than bulk water, but the natureand stability of the confined water changes dramatically with CNT sizes: fromentropy-dominated vapor-like phase of water for small CNTs, to enthalpy-dominatedice-like phase for medium sized CNTs, and to a bulk-like liquid phase for larger tubes
stabilized by the increased translational entropy. We find it to arise from the tetrahedral
H-bonded structure of liquid water.
[1] T. Pascal, W. Goddard, Y. Jung, Submitted169

6A4-1I

The structure of the water oxidizing complex in photosystem II
Per E. M. Siegbahn1
1Department of Physics, ALBA NOVA and Department of Biochemistry andBiophysics, Arrhenius Laboratory, Stockholm University, SE-106 91, Stockholm,
Sweden. Email: ps@physto.se
Hybrid density functional theory has been used for the past decade to study themechanisms of a large number of transition metal containing enzymes. The present
strategy for treating these systems using larger and larger clusters, entirely treatedquantum mechanically, will be brieﬂy outlined. DFT studies on the mechanism fordioxygen formation in photosystem II are then described, and it will be concluded
that these studies have now reached a level of convergence. After the ﬁrst X-ray
structures of PSII appeared a few years ago, the understanding of this fundamental
reaction has improved signiﬁcantly. A detailed mechanistic proposal will be presented including a complete energy diagram. During the past years major progresshas also been made concerning the structure of the oxygen evolving complex. I havepreviously argued that the theoretical prediction of the structure was more accurate than, and even qualitatively diﬀerent from, what had been obtained by X-ray
crystallography or EXAFS. It was also quite diﬀerent from what had been obtainedwith other theoretical approaches. Very recently (Shen et al, Nature, 2011), a new
X-ray structure with much higher resolution than before (1.9 Å) has been described.
The structure is very similar to the one predicted by theory.

170

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Exciton coupling and energy transfer: From prototypicalbichromophores to photosynthetic proteins
Lyudmila V. Slipchenko1
1
Department of Chemistry, Purdue University, West Lafayette, IN 47907, US
We investigate exciton coupling in several prototypical bichromophores, such as
benzene dimer, diphenylmethane (DPM), and chlorophyll dimers, as well as inphotosynthetic proteins such as the Fenna-Matthews-Olson (FMO) complex. Accurate
description of interactions between the electronic states is challenging for theory. For
instance, in flexible diphenylmethane, a small splitting between the exciton states and asensitivity of the transition dipole moment to the relative orientation of the aromaticrings leads to curious shapes and crossings of the potential energy surfaces of theexciton states. Exciton couplings are evaluated by using a perturbative approach, inwhich the coupling strength is estimated by using transition densities of the individual
chromophores. By using the effective fragment potential (EFP) and fragment molecularorbital (FMO) methods, we explicitly include and characterize the effect of the protein
environment on interactions between the electronic states of chromophores inphotosynthetic complexes.

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Electronic Coherence Effects in Photosynthetic
Light Harvesting
Yuan-Chung Cheng
Address: Department of Chemistry, National Taiwan University,
Taipei City 106, Taiwan

Highly efficient energy harvesting and trapping performed by photosynthetic systems
are critical to the success of photosynthesis; however, the physical mechanisms thatare responsible for the remarkable efficiency remain largely unclear. Recent
experimental and theoretical investigations into the mechanisms of excitation energy
transfer in photosynthetic complexes have provided evidences that quantum
coherence effects can contribute to optimize the efficiency of photosynthetic lightharvesting. In this work, we investigate quantum coherence effects in photosynthetic
complexes, including electronic coherences manifested in delocalized electronic
exciton states and excitonic coherences manifested in superposition between
electronic excitons. We show how quantum mechanical rules play important roles inthe speedup of excitation energy transfer, the stabilization of electronic excitations,and the robustness of light harvesting. In addition, we present the results of our recent
work using a simple model to investigate quantum coherence effects in inter-complex
excitation energy transfer in natural photosynthesis, with a focus on the likelihoods ofgenerating excitonic coherences during the process. Finally, the implications of allthese combined experimental and theoretical works to important open questions thatremain to be answered will be discussed in this work.

172

6B1-1I

Coherent Quantum Processes in Thermal and Nonequilibrium
Environments
Craig C. Martens
Department of Chemistry
University of California, Irvine
Irvine, CA 92697-2025
USA
In this talk, we describe recent work on investigating the role of the environment in
influencing coherent quantum dynamics. We describe numerical methodology for
simulating quantum coherent processes using classical-like molecular dynamics
simulation and ensemble averaging, and apply the approach to simulating vibrational
dephasing of I2 in cryogenic rare gas matrices and the quantum vibrations of OH
stretches of HOD in D2O. We then describe simple analytic and numerical models thathighlight novel behavior that can be exhibited by quantum coherent processes in thepresence of an environment that is not at thermal equilibrium. We finish with some
speculations on the role of nonequilibrium bath effects in quantum biological processes.

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Energy relaxation pathways in liquid water
Rossend Rey,1 James T. Hynes2,31
Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya,
Barcelona, Spain
2
Department of Chemistry and Biochemistry, University of Colorado, Boulder, CO, USA
3
Department of Chemistry, Ecole Normale Supérieure, Paris, France
The mechanisms of vibrational (bend) and rotational relaxation in liquid water are
examined via a detailed analysis of energy fluxes between molecular modes [1,2,3].
Classical nonequilibrium MD runs are conducted for neat liquid water (SPC/E
model) at different temperatures. Results are averaged for sets of trajectories in which at
the initial time either: (a) the bend mode of a single flexible water molecule is excited or,(b) a purely rotational excitation is created for a single rigid molecule.
Analysis of energy fluxes is possible through the computation of the various
contributions to the power and the work. In this way one can determine, for instance,
which percentage of vibrational energy flows into self-rotation through centrifugal
coupling, and to which particular axis this flow is maximal [1,2]. Moreover the spatial
extent of energy flow into other water molecules can be ascertained as well, together
with the specific molecular modes (translational, rotational) to which excess energy istransferred.
Bend relaxation is found to be dominated by energy flow to the hindered rotation(libration) of the bend excited water molecule, due to a 2:1 Fermi resonance for thecentrifugal coupling between the water bend and rotation. The remaining energy flowfrom the excited water bend is dominated by transfer to the first hydration shell. A
slowdown of vibrational relaxation with increasing temperature is observed [3],compatible with recent experimental findings [4].
The energy flow from (the ensuing) rotational excitation of the central watermolecule is less local in character, with slightly more than half of the energy being
directly transferred to molecules in the first hydration shell of the initially excited water,
and almost half of it being transferred to molecules beyond that shell.
Finally, it is observed that, following an initial increase in interaction energy,transfer to hindered rotational (librational) modes of neighbours is substantially more
important than that to translational motions [3].
[1] F. Ingrosso, R. Rey, T. Elsaesser, J.T. Hynes, J. Phys. Chem A 113, 6657 (2009).
[2] R. Rey, F. Ingrosso, T. Elsaesser, J.T. Hynes, J. Phys. Chem A 113, 8949 (2009).
[3] R. Rey, J.T. Hynes., in preparation.
[4] S. Ashihara, S. Fujioka, K. Shibuya, Chem. Phys. Lett. 502, 57 (2011).

174

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175

6B1-6C
Interpolated potential energy surfaces for condensed phase molecular dynamics

Jae Woo Park and Young Min Rhee*

Institute of Theoretical and Computational Chemistry
Department of Chemistry
Pohang University of Science and Technology (POSTECH)
Pohang 790-784, Korea

In this talk, we will present an extension of the interpolation scheme for constructing
intramolecular potential energy surfaces for conducting molecular dynamics simulations incondensed phase. We show that our scheme can be feasibly used for the purpose when it issupplemented with additional terms for describing intermolecular interactions, and that themethod can be used for reliably building the “force field” of any arbitrary molecule without
any a priori-defined potential shape. We then apply the approach for studying the resolvation
process of coumarin 153 in a number of polar solvents. We find that the interpolated surface
actually reproduces experimental features much better than the conventional force field based
potential in terms of both solvent relaxation and solute vibrational coherence. This shows thatthe solute vibrational effect is actually important along the solvent relaxation and should bemodeled properly for accurate description of the related dynamics. Implication toward thesimulations of biological systems is also discussed.

176

6B2-1I

Incorporation of nuclear quantum effects toab initio molecular dynamics approach
Tetsuya Taketsugu, Yusuke Ootani, Akira Nakayama, and Takeshi Noro
Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo, 060-0810, Japan
E-mail: take@sci.hokudai.ac.jp
We developed an AIMD code for excited-state reactions, which takes into account nonadiabatic
transitions between adiabatic electronic states explicitly by the fewest switches algorithm [1].

Thesurface-hopping AIMD method has been applied to several dissociative recombination (DR) reactions,
HCNH+ + e- [2], H3O+ + e- [3], and HD2O+ + e- [4], as well as a photoisomerization reaction of azobenzene [5],to examine the tendency in the branching ratio of the products and to give insight to dynamical processes
accompanying non-adiabatic transitions. Very recently, we also implemented the semiclassical tunnelingmethod [6] to our AIMD code, and performed test calculations for the tunneling splitting in the umbrella
inversion of ammonia and the intramolecular hydrogen transfer in malonaldehyde [7]. In the application tomalonaldehyde, effects of multi-dimensionality were examined by assigning quantum zero-point energies only
to significant vibrational modes and changing the amount of energy given to bath modes. In this talk, ourextension of the AIMD approach to excited-state reactions and tunneling reactions is introduced anddiscussed.
References[1] J. C. Tully, J. Chem. Phys. 93, 1061 (1990).
[2] T. Taketsugu, A. Tajima, K. Ishii, and T. Hirano, Astrophys. J. 608, 323 (2004).
[3] M. Kayanuma, T. Taketsugu, and K. Ishii, Chem. Phys. Lett. 418, 511(2006).
[4] M. Kayanuma, T. Taketsugu, and K. Ishii, Theo. Chem. Acc. 120, 191 (2008).
[5] Y. Ootani, K. Satoh, A. Nakayama, T. Noro, and T. Taketsugu, J. Chem. Phys. 131, 194306 (2009).
[6] N. Makri and W. H. Miller, J. Chem. Phys. 91, 4026 (1989).
[7] Y. Ootani and T. Taketsugu, submitted.

177

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The role of Rydberg state in the photochemistry of ethylene
Toshifumi Mori1, Todd J. Martínez1
1
Department of Chemistry, Stanford University, USA
Photoinduced cis-trans isomerization is one of the fundamental topics inphotochemistry because of the way it converts photon energy into mechanical motion.
Ethylene is considered to be the simplest model for this purpose, and it has been studied
extensively to understand the mechanism and dynamics. While the overall mechanism
has been well described, the role of the low-lying Rydberg state is still not clear.
Especially, there is little knowledge about how this state contributes to the dynamics.
In this work, we investigated the role of the 3s Rydberg state in the dynamics froman ab initio molecular dynamics simulation. Describing both the Valence and Rydberg
states require a balanced electronic structure method that can include both static anddynamic electron correlation effects. For this purpose, we used the multistate
second-order perturbation theory (MSPT2), and to study the nonadiabatic events, wedeveloped a method to calculate the MSPT2 nonadiabatic coupling analytically.
φ IMSPT2

CAS−1∂ MSPT2∂H MN CAS I J CAS ∂ CAS
φJ= ∑ EJMSPT2 − EIMSPT2 u MI u NJ
+ ∑ uM uN φM
φN
∂R a
∂R a
∂R a
M ,N
M ,N

(

)

The MSPT2 method has been combined with the ab initio multiple spawning (AIMS)
method. The time resolved photoelectron spectrum (TRPES) was also calculated.
Our result shows that roughly 20% of the initial population transfers from the ππ*to the 3s Rydberg state within the first 10 fs, but it returns rapidly to the ππ* state within
50 fs (Fig. 1). The overall excited state lifetime was about 82 fs, which is slightly longer
than those calculated without the Rydberg state, thus the present result is consistent withprevious experiments. On the other hand, when the trajectories were initially excited tothe 3s Rydberg state, a fairly longer excited state lifetime was observed (~122 fs),
implying an existence of a different path. Finally, the calculated TRPES shows a brightline as an excitation from the Rydberg state, suggesting a way to further investigate therole of Rydberg states in the dynamics from both experiments and theory.
1.0

[eV]
Valence

4

S0
0.5

2
Rydberg

0

0

0.005
0.004
0.003
0.002
0.001
0

40

80

0
120

0

160 [fs]

Figure 1: Rate of populations with
Valence and Rydberg characters

50

100

150

[fs]

Fig. 2: Calculated TRPES spectrumwith a probe energy of 7.7 eV

178

6B3-1I

Composite particles in quantum chemistry: from two-electron bonds tocold atoms
Péter R. Surján and Péter Jeszenszki
Eötvös University, Institute of Chemistry, Laboratory of Theoretical Chemistry,
H-1518 Budapest, POB. 32
Ab initio quantum chemistry usually treats electrons as elementary particles,
thus the theory of composite particles is absent from most textbooks. However, we
do deal with composite particles implicitly, e.g., when considering nuclei as pointlike, structureless objects. This is a trivial limiting case, as the internal interactions
between hadrons gluing together the nuclei are so strong that no chemical process iscomparable. Consequently, the only point where the composite nature of a nucleus
enters is the counting of its total spin.
Forming composite particles from electrons is a much less trivial problem, since
the binding forces between them may easily be aﬀected by external interactions.
Such composites form the basis of certain models, among which the BCS theoryof Cooper pairs is perhaps the most successful. Another example is to consider
a localized two-electron chemical bond as a composite particle, which is clearly afragile object. In the latter case the term composite quasi-particle seems to be more
adequate.
Distinguishing between true elementary particles and composite quasi-particles
can be done most thoroughly by studying the commutation properties of their creation and annihilation operators. Quasi-particles always exhibit a complicated algebra, in contrast to elementary particles which commute or anticommute to unity inthe case of bosons or fermions, respectively. A challenge here is to make predictions
on the validity of the quasi-particle approximation based on the mathematical formof commutators. Another important issue is to develop correction schemes which
describe the eﬀect of the internal structure of quasi-particles on their interactions.
Going to larger composites, some applications permit one to treat a whole atom
as a single particle. Approximating an atom as an elementary particle may also be
permitted sometimes. The success of the Bose-Hubbard model of cold, dilute atomic
gases represents such an example. Solution of the Bose-Hubbard model is anotherchallenging ﬁeld where quantum chemical techniques may ﬁnd applications.
This work has been supported by the grants OTKA, K-81588 and the EU/European
Social Fund TÁMOP 4.2.1./B-09/1/KMR-2010-0003.

179

6B3-3I

Theoretical Aspects on the Evaluation and Interpretation of theThird-Order Nonlinear Optical Properties of Diradical CompoundsBenoît Champagne,1 Edith Botek,1 Raphaël Carion,1 Akihiro Shimizu,2 Takashi Kubo,2Kenji Kamada,3 Koji Ohta,3 Ryohei Kishi,4 Hitoshi Fukui,4 Yasuteru Shigeta,4 andMasayoshi Nakano4
1

Laboratoire de Chimie Théorique, UCPTS, Facultés Universitaires Notre-Dame de laPaix, Rue de Bruxelles, 61, B-5000 Namur, BELGIUM, benoit.champagne@fundp.ac.be2

Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka,
Osaka 560-0043, JAPAN; 3 Photonics Research Institute, National Institute ofAdvanced Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, JAPAN;
4
Department of Materials Engineering Science, Graduate School of Engineering
Science, Osaka University, Toyonaka, Osaka 560-8531, JAPANI. Introduction
Over the last decades, scientists have designed molecules and materials with uniquenonlinear optical (NLO) properties targeting the realization of all-optical computing andsignal processing. For many reasons (large response, short response time) organic
compounds are of considerable interest. However, suitable materials for practicalapplications are still missing because the third-order NLO responses and the related
molecular second hyperpolarizability () are still too small. Increasing the conjugation
length was a first strategy to maximize  while in subsequent approaches appropriate
substituents with specific donor and acceptor strengths were selected. More recent
strategies consist in varying the shape and dimensionality of the chromophore and of
charging it, for instance by chemical doping.
II. Diradicals and multiradicals as third-order NLO compounds
Although most of these systems are closed-shell molecules, recent studies havedemonstrated that open-shell species show potential as materials with high NLO
efficiency and, in particular, singlet diradical systems with intermediate diradical
character.
For instance, ab initio molecular orbital and DFT calculations performedon the p-quinodimethane model showed that  attains a maximum in the intermediate
diradical character region and subsequently that -conjugated diradical systems
involving imidazole rings and compounds of the family of thermally stable diphenalenyl
diradical systems display significant enhancements of  with respect to their analogous
closed-shell systems. Then, the dependence of  on the spin states makes thesecompounds further attractive for designing multifunctional materials. In thispresentation, theoretical aspects on the evaluation and interpretation of  of diradical
and multiradical species will be discussed.

180

6B3-5C

Tautomeric equilibria and thermal decomposition of nitrogen-richheterocycles: new insights from high-level ab initio calculations
V.G. Kiselev,1,2 N.P. Gritsan1,2
U

1U

Institute of Chemical Kinetics and Combustion, 3, Institutskaya str.,
630090 Novosibirsk, Russia
2

Novosibirsk State University, 2, Pirogova Str.,
630090 Novosibirsk, Russia

Nitrogen-rich heterocycles and their derivatives have recently attracted considerable
attention as promising environmental friendly energetic compounds. Among them,tetrazole (TZ) and 5-aminotetrazole (5-ATZ) are widely used building blocks for a hugefamily of novel high-energy species [1-3].
NH2

H
C

C
NH

NH N

N
N

N
TZ

N

N

5-ATZ

The mutual interconversion and decomposition reactions of various tautomers of TZ and
5-ATZ have been studied theoretically using the W1 and G3 high-level procedures. The
concerted double H atom transfer reactions in the H-bonded complexes led to fastequilibration between various tautomeric forms of the both TZ and 5-ATZ. The carbene
isomer of TZ have never been considered before, however, it was predicted to be a key
intermediate in the mechanism of thermal decomposition of TZ. In the case of 5-ATZ,
new bimolecular reactions have been proposed to describe the experimentally detected
formation of HN3. High-level computations allowed us to reveal the role of tautomericequilibria in thermal decomposition of TZ and 5-ATZ. The existing discrepancies in themechanism and key intermediates of thermolysis have also been resolved. The calculated
values of effective activation energy of TZ decomposition are in perfect agreement withthe experimental data.
ACKNOWLEDGEMENTS. The authors are grateful to the Russian Ministry of
Education and Science (project No. P1475) and SB RAS (the Lavrentiev grant
programme) for financial support.
[1] R.P. Singh, H. Gao et al. Struct. Bond. 2007, 125, 35.
[2] T.M. Klapotke Struct. Bond. 2007, 125, 85.
[3] T.M. Klapotke, J. Stierstorfer J. Am. Chem. Soc. 2009, 131, 1122

181

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182

6B4-1I

Theoretical studies of photophysical events in π-stacked dimers of
nucleobases
Spiridoula Matsika,
Department of Chemistry, Temple University, Philadelphia, USA
The excited states of DNA and their fate after UV absorption are of extreme importance because of their biological relevance. Quantum chemistry can help addressthese problems but one has to limit the size of the system. Dimers of nucleobases are
the smallest models one can use to look into the eﬀect of π-stacking and hydrogenbonding on the excited states. We have studied the eﬀect of π-stacking on the photophysical properties of π-stacked dimers of natural nucleobases or their ﬂuorescentanalogues. Fluorescent analogues of nucleobases are very useful as probes to study
DNA dynamics, since natural DNA does not ﬂuoresce signiﬁcantly. In many of theseanalogues, such as 2-aminopurine (2AP), the ﬂuorescence is quenched when incorporated into DNA through processes that are not well understood. So 2AP presents
a case where π-stacking changes signiﬁcantly the photophysical behavior of a base,making it an interesting system to focus on. We will present theoretical studies ofthe excited states of π-staked dimers and focus on features of the potential energy
surfaces that can describe the fate of the excited state populations. Computed relaxation pathways along the excited state surfaces reveal novel mechanisms that canlead to ﬂuorescence quenching and radiationless decay in the π-stacked dimers [1].
The importance of charge transfer and exciton states will also be discussed.
[1] JX Liang and S. Matsika, J. Am. Chem. Soc., 133, 6799 - 6808, (2011)183

6B4-3C

Quantum chemistry calculations in helium clusters dopedwith diatomic molecules
G. Delgado-Barrio,1 R. Pérez de Tudela,1 D. López-Durán,1 R. Prosmiti,1P. de Lara-Castells,1 P. Villarreal1
1
Instituto Física Fundamental (CSIC), Spain
Spectroscopic studies of simple molecules surrounded by He atoms show a drastic
difference depending on the fermionic or bosonic character of the solvent atoms [1]. A
quantum chemistry-like approach has been recently developed in our group to deal with
HeN –BC doped helium clusters, where the BC dopant is a conventional di-atomic
molecule. The central idea is to consider the He atoms as “electrons” while the B and C
atoms play the role of the nuclei in standard electronic structure calculations. The
procedure provides spectral simulations and, hence, making feasible to do propercomparisons with current experiments [1]. However, due to the big difference of massesof He and electrons, and also to the replacement of Coulomb potentials by molecularinteractions, it is worthy to asses at what extent the approximations involved(decoupling of orbital angular momenta of the He atoms from the BC rotation andadiabaticity of the BC stretch versus de He motions) lead to accurate results [2-10].
Here, we consider several diatomic molecules as dopants. The model provides theenergy levels of the cluster and the intensities of the main lines of the spectrum at low
temperatures.
Up to now, Hartree/Hartree-Fock approaches involving their own limitations havebeen used. It is therefore desirable to implement more accurate ab initio methodologies.
Encouraging “full interaction configuration” results, based on a Jacobi-Davidson
diagonalization procedure, have been already obtained for small doped fermion clusters[10].
[1] S. Grebenev, J. P. Toennies, and A. F. Vilesov, Science 279, 2083 (1998).
[2] D. López-Durán, M. P. de Lara-Castells, G. Delgado-Barrio, P. Villarreal, Di Paola, F. A. Gianturco,
and J. Jellinek, Phys. Rev. Lett. 93, 053401 (2004); J. Chem. Phys. 121, 2975 (2004).
[3] M.P. de Lara-Castells, D. López-Durán, G. Delgado-Barrio, P. Villarreal, C. Di Paola,
F.A.Gianturco, and J. Jellinek, Phys. Rev. A 71, 033203 (2005).
[4] M.P. de Lara-Castells, R. Prosmiti, G. Delgado-Barrio, D. López-Durán, P.Villarreal,
F.A.Gianturco, and J. Jellinek, Phys. Rev. A 74, 053201 (2006).
[5] M.P. de Lara-Castells, R. Prosmiti, D. López-Durán, G. Delgado-Barrio, P. Villarreal, F.A.
Gianturco, and J. Jellinek, Int. J. Quant. Chem. 107, 2902 (2007).
[6] O.Roncero, R.PérezdeTudela, M.P.deLara-Castells, R.Prosmiti, G. Delgado-Barrio, and P.
Villarreal, Int. J. Quant. Chem. 107, 2756 (2007); J. Chem. Phys. 128, 164313 (2008).
[7] R. Pérez de Tudela et al., J. Chem. Phys. 132, 244303 (2010).
[8] M. Márquez-Mijares et al., J. Chem. Phys. 130, 154301 (2009).
[9] R. Prosmiti et al., J. Phys. Chem. A 113, 1478 (2009).
[10] M.P. De Lara-Castells et al., Few Body Syst. 45, 233 (2009).

184

6B4-4C

Excited states of nucleotide bases and nucleotides: matrix isolation
spectroscopic and quantum chemical studya,bPéter G. Szalay,1,2 Gábor Bazsó,1 György Tarczay,1 Géza Fogarasi,1 Thomas
Watson,2 S. Ajith Perera,2 Victor Lotrich,2 Rod J. Bartlett 2
1
Eötvös Loránd University, Budapest, Hungary
2
Quantum Theory Project, University of Florida, Gainesville, FL, USA
Our research focuses on the spectral properties of the building blocks of DNA
and RNA, the so called nucleobases and nucleosides, in order to understand theirinteraction with light.
Our ﬁrst target was cytosine, the smallest of the nucleobases. Here we used a
combined experimental and theoretical procedure using matrix isolation (MI) spectroscopy and high level ab initio (coupled cluster) calculations. We have found that
there are three tautomers of cytosine present in the MI experiment and all threeneed to be considered to explain the observed UV spectra. Using the obtained ratios of these tautomers, very good agreement could be found between simulated andexperimental UV spectra.
The success of this ﬁrst project made us conﬁdent that very accurate information can be obtained from the high level theoretical calculations. Therefore in asecond step we have calculated at the EOM-CCSD(T)/aug-cc-pVDZ level of theory
the excited state properties for the nucleobases (cytosine, guanine) their complexes
with water and with each other (Watson-Crick base pairs and stacks) as well as corresponding nucleosides and try to answer the following questions: (1) How the orderof excited states varies in diﬀerent nucleobases? (2) How hydration inﬂuences theexcited states and their order? (3) Is there any eﬀect of the sugar substituent? (4)How do close lying other bases change the spectrum? The calculations involve overhundred correlated electrons and up to thousand basis functions. Such calculations
are now routinely available with ACESIII codec and can make use of hundreds oreven thousands of processors.

a

The Hungarian American Enterprise Scholarship Foundation (HAESF) supported the sabbatical stay of P.G.Sz. at QTP.
Contribution from TAMOP, supported by the European Union and coﬁnanced by the European Social Fund (grant agreement no.
TAMOP 4.2.1./B-09/1/KMR-2010-0003) is also acknowledged.
cV. Lotrich, N.Flocke, M. Ponton, A. Yau, A. Perera, E. Deumens, R. J. Bartlett, JCP, 2008,128,194104.
b

185

6B4-5C

Distribution and Orientation of Retinol in
Dipalmitoylphosphatidylcholine Bilayer
Warabhorn Boonyarat1,2, Witcha Treesuwan1,2,4, Patchareenart Saparpakorn1,2, Kiattawee
Choowongkomol3 , Peter Wolschann5 and Supa Hannongbua1,2
1

Department of Chemistry, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand
2

Center of Nanotechnology, Kasetsart University, Bangkok 10900, Thailand

3
4

Department of Biochemistry, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand

Institute of Food Research and Product Development, Kasetsart University, Bangkok 10900, Thailand
5
Institute of Theoretical Chemistry, University of Vienna, Austria

Abstract
Vitamin A (retinol) is called fat-soluble vitamins. They are absorbed from the small
intestine with dietary fat[1]. Moreover it is hydrophobic and absorbed similarly to otherdietary lipids[2]. The study of absorption of retinol at the molecular level is still unclear
and thus of interest[3].

In the present study, the distribution of retinol atwater/membrane interface was investigated by means of molecular dynamics (MD)simulations [4]. The study of the molecular dynamics was focused on the favorable
binding sites of retinol inside the DPPC bilayer. Three MD simulations of the retinol/dipalmitoylphosphatidylcholine (DPPC) were performed with a single-point charge
water model [5]. The retinol preferably accommodated at the head of the bilayer upper
part of the glycerol moiety. The absorption process proved that the hydrophobic aromaticpart of the retinol is located inside the more ordered region of DPPC by a gradual deeper
shift inside the hydrocarbon core of the bilayer. The retinol formed a weak hydrogenbonding to the glycerol group of DPPC bilayer.

Key words: Vitamin A, retinol, dipalmitoylphosphatidylcholine (DPPC), Molecular dynamics
simulations, Absorption

References
1. Epstein FH., and Goodman DS., 1984, New England Journal of Medicine 310 (16),1023-1031.
2. Quadro L., Gamble MV., Vogel S., Lima AAM., Piantedosi R., Moore SR., Colantuoni V.,
Gottesman ME., Guerrant RL., and Blaner WS., Journal of Infectious Diseases, 2000, 182(Supplement 1), S97-S102.
3. Asai Y., and Watanabe S., Chemistry and Physics of Lipids, 1999, 99 (1), 87-93
4. Tieleman DP., Marrink SJ., and Berendsen HJC., Biochimica et Biophysica Acta (BBA) Reviews on Biomembranes, 1997, 1331 (3), 235-270.
5. Berendsen H., Postma J., van Gunsteren W., and Hermans J., Intermolecular Forces, 1981,
331 - 342.

186

6C1-1I

Approximate Variational Coupled Cluster Theory
Bridgette Cooper,1,2 Andrew Jenkins,1 James B. Robinson,1 Peter J. Knowles1
1
School of Chemistry, Cardiﬀ University, United Kingdom
2
Department of Physics, Imperial College London, United Kingdom
A modiﬁcation is presented of the variational conﬁguration interaction functional in the ﬁrst-order interacting space for molecular electronic structure. The
modiﬁed functional is a fully-linked expression, that by construction is extensive
and invariant to transformations of the underlying orbital basis, and is exact for an
ensemble of separated 2-electron subsystems. The method is then extended by including additional terms in the functional that can be computed with O(N 6 ) work,
and which make it agree at low order with variational coupled-cluster with double excitations (VCCD). This method demonstrates accuracy that exceeds that of
the standard coupled-cluster (CCD) method, in particular in situations where thereference Slater determinant is not a good approximation.
We also discuss the inclusion of the eﬀect of single orbital excitations, either
through minimisation of the approximate VCCD functional with respect to theorbitals, or through an explicit generalisation of the functional to approximate
VCCSD.
A further extension generalises the use of the functional to a multiconﬁgurationalreference wavefunction.
[1] P. J. Knowles and B. Cooper, J. Chem. Phys., 133 (2010) 224106

187

6C1-3I

General implementation of the relativistic coupled-cluster method
Mihály Kállay,1 Huliyar S. Nataraj,2 Lucas Visscher2
1
Department of Physical Chemistry and Materials Science, Budapest University ofTechnology and Economics, Budapest P.O.Box 91, H-1521 Hungary
2Amsterdam Center for Multiscale Modeling, VU University Amsterdam, De Boelelaan
1083, 1081 HV Amsterdam, The Netherlands
We report the development of a general order relativistic coupled-cluster (CC) code.
Our implementation is based on Kramers-paired molecular spinors, utilizes double groupsymmetry, and is applicable with the full Dirac-Coulomb and several approximate relativistic Hamiltonians. The available methods include iterative and perturbative singlereference CC approaches with arbitrary excitations as well as a state-selective multireference CC ansatz. To illustrate the performance of the new code benchmark calculations have been performed for the total energies, bond lengths, and vibrational frequenciesof the monoxides of Group IVa elements. The trends due to the simultaneous inclusionof relativity as well as higher-order electron correlation effects are analyzed. The newly
developed code signiﬁcantly widens the scope of the ab initio relativistic calculations, forboth molecules and atoms alike, surpassing the accuracy and reliability of the currently
available implementations in the literature.

188

6C1-5C

Unitary perturbation theory for the electron correlation problem
Ágnes Szabados, Péter Nagy
Laboratory of Theoretical Chemistry, Loránd Eötvös University, H-1518 Budapest,
POB 32, Hungary
The scheme proposed by Mayer for a symmetrical treatment of 2×2 Jacobi rotations [1] is investigated. The technique involves an explicit construction of theunitary matrix
U = exp


i

Ai

,

where Ai ’s are anti-hermitian matrices, parametrized by the single rotation angle
aﬀecting the ground state and the i’th excited state. The idea can be exploited todevelop an eﬃcient correction scheme, applicable in electron correlation theory.
Starting from an arbitrary reference function, the ﬁrst column of matrix U provides a corrected function. Depending on the actual algorithm, the computational
price may vary between ∼N and ∼N 2 , with N denoting the dimension of the subspace interacting with the reference. The performance of this approach is exploredon the example of covalent bond breaking, based on a multideterminantal initial
function. The results are contested with related methods: Jacobi-rotations and degeneracy corrected perturbation theory [2,3]. The possibility of amending the simple
sum in the exponential by commutators of the form [[Ai , Aj ] , Aj ] is also examined.
[1] Mayer I Theor Chem Acc 104, 163 (2000).
[2] Lepetit M-B, Malrieu J-P Chem Phys Lett 208, 503 (1993).
[3] Assfeld X, Almlöf JE, Truhlar DG Chem Phys Lett 241, 438 (1995).
The Project is supported by the European Union and co-ﬁnanced by the European
Social Fund (grant agreement no. TÁMOP 4.2.1./B-09/1/KMR-2010-0003).

189

6C1-6C

Coupled cluster method in application to the double ionized and double
electron attached states
Monika MusialUniversity of Silesia, Institute of Chemistry, Katowice, Poland
The double ionization potentials (DIP) and double electron aﬃnities (DEA) canbe described within the coupled cluster (CC) theory via the multireference (MR) or
equation-of-motion (EOM) extensions. The MR approach requires inclusion of the(0,2) and (2,0) sectors of the Fock space to treat the DIP and DEA, respectively.
The current work reports development of the new computational schemes aimed at
the evaluation of the DIP and DEA quantities employing the powerful intermediate
Hamiltonian strategy of the multireference theory.
The performance of the new methods is discussed on the basis of the test calculations for several molecules. They can be applied also to study potential energy
curves (PEC) for the systems for which double positive or double negative ionsdissociate into closed-shell fragments.
The signiﬁcance of the DIP and/or DEA results can be appreciated by comparison with the experimental (AES - Auger electron spectroscopy, DCT - double chargetransfer spectroscopy, ...) data. The new methods can be particularly useful in the
studying PEC for the halogen dimers (DIP methods) or for the alkali metal dimers(DEA methods).

190

6C2-1I

Multireference F12 Coupled Cluster Theory
Ondřej Demel,1 Stanislav Kedžuch,2 Jozef Noga,2,3 Jiřı́ Pittner1
1
J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech
Republic, Prague, Czech Republic
2
Institute of Inorganic Chemistry, Slovak Academy of Sciences, Bratislava,
Slovakia
3
Faculty of Natural Sciences, Comenius University, Bratislava, Slovakia
We report development and implementation of explicitly correlated multireference coupled cluster methods that include conﬁgurations explicitly depending on
the correlation factor of Slater type geminal. Namely, Brillouin Wigner [1] andMukherjee’s [2] MR CC approaches with single and double excitations are extended
in this manner. Additional conﬁgurations that include pair functions with the correlation factor are generated separately for each reference determinant [3] similarly
as in CCSD-F12 [4]. The performance is shown for model systems and small polyatomic molecules using variants with full optimization of the geminal amplitudes,
partial optimization of those amplitudes, and ﬁxed amplitudes corresponding to thetheoretical cusp conditions. Like in single reference methods, results show a dramatically improved convergence of total energies towards the complete basis set limit ascompared to a conventional MR CC approach.
[1] J. Mášik, I. Hubač, Adv. Quant. Chem. 31 (1998) 75–104; J. Pittner, J. Chem.
Phys. 118 (2003) 10876.
[2] U. S. Mahapatra, B. Datta, D. Mukherjee, Chem. Phys. Lett. 299 (1999) 42–50;
J. Chem. Phys. 110 (1999) 6171–6188.
[3] S. Kedžuch, O. Demel, J. Pittner, J. Noga, in: P. Čársky, J. Paldus, J. Pittner(Eds.), Recent Progress in Coupled Cluster Methods: Theory and Applications,
Springer Science, New York, 2010, pp. 251–266; S. Kedžuch, O. Demel, J. Pittner,
S. Ten-no, Chem. Phys. Lett. (2011) in press[4] J. Noga, S. Kedžuch, J. Šimunek, S. Ten-no, J. Chem. Phys. 128 (2008) 174103.

191

6C2-3C

Multireference Explicitly Correlated F12 Theories
Toru Shiozaki and Hans-Joachim WernerInstitut für Theoretische Chemie, Universität Stuttgart, Germany
We will present the newly developed CASPT2-F12 and MRCI-F12 methods [1,2],
which achieve much improved basis-set convergence compared to the conventional
CASPT2 and MRCI methods by introducing a basis function explicitly dependent on
the electron-electron distances. The applicability of these methods are exactly the sameas the conventional CASPT2 and MRCI; they can be routinely used for systems withnear degeneracy (such as avoided crossing and conical intersections) and forcomplicated electronic structures of electronic excited states [3]. In this presentation,
numerical results for some benchmark systems, including the ozone excited states and
PES of the OH (A2Σ+) + H2 reaction, will be presented to illustrate the superior basis-set
convergence of the multireference F12 theories. They suggest that the accuracy
comparable to MRCI with a quadruple-zeta basis set can be achieved by MRCI-F12
with a double-zeta basis set with an order of magnitude smaller computational effort.
[1] T. Shiozaki and H.-J. Werner, J. Chem. Phys. (Comm.) 133, 141103 (2010).
[2] T. Shiozaki, G. Knizia, and H.-J. Werner, J. Chem. Phys. 134, 034113 (2011).
[3] T. Shiozaki and H.-J. Werner, submitted

192

6C3-1I

The divide–expand–consolidate (DEC) coupled cluster method.
A linear–scaling approach with energy–based error control
Poul Jørgensen,1 Kasper Kristensen,1 Marcin Ziólkowski,1 Branislav Jansı́k ,1Thomas Kjærgaard,1,2 Simen Reine,2
1
Lundbeck Foundation Center for Theoretical Chemistry, Department ofChemistry, Aarhus University, Denmark
2
Centre for Theoretical and Computational Chemistry, Department of Chemistry,
University of Oslo, Norway
We present the Divide-Expand-Consolidate (DEC) coupled cluster (CC) model,
where a CC calculation on a full molecular system is carried out in terms of calculations on small orbital fragments of the total molecular system. The fragmentation
does not involve non–physical bond cuts and represents only an eﬃcient way of dividing the calculation on a full molecular system into calculations on small orbital
fragments. The sizes of the orbital fragment spaces are optimized during the calculation in a black box manner to ensure that that the fragment energies are determined
to a preset threshold. This in turn deﬁnes the total correlation energy as a sum offragment energies to a preset threshold compared to a full molecular calculation.
The number of independent fragment calculations scales linearly with the systemsize, and the method is therefore linearly scaling and embarrasingly parallel.
The fragmentation of orbital spaces relies on using a set of local Hartree-Fock(HF) orbitals. We use our recently developed orbital localization strategy where
powers of the orbital variances are minimized to yield a set of local occupied andvirtual HF orbitals.
DEC calculations are presented for the energy using second order Møller-Plesset
perturbation (MP2) theory and the coupled cluster singles doubles (CCSD) models
to demonstrate the performance of the DEC model. Calculations of the molecular
gradient for MP2 will also be presented.

1936C3-3I

Local Coupled-Cluster Methods for Chemical Reaction Pathways
Involving Large Molecular Systems and their Multi-Level
Generalizations
Piotr Piecuch,1 Wei Li1,2
1
Department of Chemistry, Michigan State University, East Lansing, Michigan 48824,
U.S.A
2
School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu
210093, China
Coupled-cluster (CC) theory has become the de facto standard for high-accuracy
molecular calculations, but as all electronic structure approaches that aim at the accurate
description of many-electron correlation effects, it faces a number of challenges. Amongthem are the prohibitive costs of CC calculations for larger molecular systems. To address
this challenge, we have recently extended a number of CC methods, including thesize-extensive, left-eigenstate, completely renormalized CC method with singles, doubles,
and non-iterative connected triples, abbreviated as CR-CC(2,3), which is known toprovide an accurate description of chemical reaction profiles involving single bondbreaking and biradicals, to larger systems with hundreds of atoms through the use of thelocal correlation, cluster-in-molecule (CIM) ansatz. The resulting CIM-CR-CC(2,3) andother CIM-CC methods are characterized by (i) the linear scaling of the CPU time withthe system size when the same level of theory is applied to all CIM subsystems, (ii) theuse of orthonormal orbitals in subsystem calculations, (iii) the natural coarse-grain parallelism, which can be further enhanced by the additional fine-grain parallelism of eachsubsystem calculation, (iv) the high computational efficiency, enabling calculations forlarge molecular systems at high levels of CC theory, (v) the purely non-iterative characterof the local triples and other perturbative corrections to correlation energy, and (vi) theapplicability to the covalently and weakly bound molecular systems. In addition, one canuse the flexibility of the CIM local correlation ansatz to mix different CC or CC andnon-CC methods within a single calculation, enabling the rigorous formulation ofmulti-level local correlation theories that combine the high-level CC methods, such as
CR-CC(2,3), to treat, for example, the reactive part of a large molecular system with thelower-order ab initio (e.g., MP2) scheme(s) to handle the chemically inactive regions
without splitting it into ad hoc fragments and saturating dangling bonds. The performanceof the CIM-CR-CC(2,3) approach in applications involving chemical reaction profiles is
illustrated by examining the bond dissociation curves in normal alkanes and alkyl radicals,
the diffusion of atomic oxygen on the silicon surface, the proton transfer in the aggregatesof dithiophosphinic acids with the water molecules, and the Co-C bond dissociation inmethylcobalamin.

194

6C3-5C

Highly accurate linear scaling method -elongation method- andits applications to large systems
Yuriko Aoki1,4, Kai Liu2, and Feng Long Gu3,4
1

Department of Material Sciences, Faculty of Engineering Sciences, Kyushu University, Kasuga,
Fukuoka 816-8580, Japan2
Department of Molecular and Material Sciences, Interdisciplinary Graduate School of Engineering
Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
3
Center for Computational Quantum Chemistry, South China Normal University, Guangzhou,
Guangdong 510631, China
4
CREST, Japan Science and Technology Agency (JST), Kawaguchi, Saitama, JapanThe elongation method, developed for many years in our group[for examples Refs. 1-12], isthe method towards O(N) with high efficiency and high accuracy for any dimensional systems. Thismethod adapts the concept of ‘quantum locality’ and works on the Region Localized MolecularOrbital (RLMO) basis we proposed and has recently been extended to be applicable for threedimensional (3D) systems. As an approach toward post-Hartree-Fock, we developed the elongation
local MP2 (ELG-LMP2) method. We also confirmed that the RLMO is very useful to evaluate local
excitation around chromophore center in a large system at single excitation configuration interaction(SCI) and TDHF levels. To make sure the applicability of this method to ring-shaped peptide
systems, a pentapeptide argifin is chosen to test the 3D-Elongation. As the system is elongated, there
are more frozen units are required to be included to achieve high accuracy.

For more applications

to entangled large bio-systems, 3D-Elongation method was applied to entangled insulin peptides andalso we confirmed that the accuracy is good enough and also this method is applicable by increasing
the active region even to the systems in which the end terminal parts have strongly polar amino acids.
For any type of calculation path, the elongation method has very high accuracy, 10-8 a.u./atom error
in total energy compared to the conventional direct calculations. These results are promising for
application of our 3D-Elongation method to gigantic real bio-systems in the near future. Recently,
we also succeeded to incorporate energy gradient technique into elongation method and will show
the results in some bio-model systems for geometry optimization based on elongation method.
[1] A. Imamura, Y. Aoki, and K. Maekawa, J. Chem. Phys. 95 (1991) 5419.
[2] Y. Aoki and A. Imamura, J. Chem. Phys. 97 (1992) 8432.
[3] F. L. Gu, Y. Aoki, A. Imamura, D. M. Bishop, and B. Kirtman, Mol. Phys. 101 (2003) 1487.
[4] F. L. Gu, Y. Aoki, J. Korchowiec, A. Imamura, and B. Kirtman, J. Chem. Phys. 121 (2004) 10385.
[5] S. Ohnishi, F. L. Gu, K. Naka, A. Imamura, B. Kirtman, and Y. Aoki, J. Phys. Chem. A 108 (2004) 8478.
[6] J. Korchowiec, F. L. Gu, A. Imamura, B. Kirtman, and Y. Aoki, Int. J. Quantum Chem. 102 (2005) 785.
[7] “Elongation Method for Polymers and its Application to Nonlinear Optics, in Atoms, Molecules and Clusters inElectric Fields: Theoretical Approaches to the Calculation of Electric Polarizabilities”, Feng Long Gu, Akira
Imamura, and Yuriko Aoki, (edited by G. Maroulis, Imperial College Press), Vol. 1, Page 97-177, 2006.
[8] M. Makowski, J. Korchowiec, F. L. Gu, Y. Aoki, J. Comp. Chem. 27 (2006) 1603.
[9] Y. Orimoto, F. L. Gu, A. Imamura, and Y. Aoki, J. Chem. Phys. 126 (2007) 215104.
[10]S. Ohnishi, Y. Orimoto, F. L. Gu, and Y. Aoki, J. Chem. Phys. 127 (2007) 084702.
[11]W. Chen, G. -T. Yu, F. L. Gu, and Y. Aoki, J. Phys. Chem. C 113 (2009) 8447.
[12]J. Korchowiec, P. D. Silva, M. Makowski, F. L. Gu, and Y. Aoki, Int. J. Quantum Chem. 110 (2010) 2130.

195

6C3-6C

Divide-and-conquer evaluation of optical response properties
Masato Kobayashi,1,2 Tsuguki Touma,1 Hiromi Nakai1,3,4
1School of Advanced Science and Engineering, Waseda University, Japan
2
Institute for Molecular Science, Japan
3
Research Institute for Science and Engineering, Waseda University, Japan
4
CREST, Japan Science and Technology Agency, Japan
I. Introduction
For theoretical design of optical materials, we desire that (hyper)polarizability
evaluation of nano-materials becomes tractable. We have developed the linear-scaling
divide-and-conquer (DC) electronic structure method [1]. Recently, we have extended
the DC method to the TDHF dynamic polarizability calculations [2]. We will report its
brief summary and further extension to the hyperpolarizability calculations.
II. DC-TDHF method for dynamic first hyperpolarizability evaluation
In the standard calculation, the first hyperpolarizability can be evaluated from thefirst-order CPHF solution as:(1)
EK1K2K3 (Z1 ; Z2 , Z3 ) PˆK1 ,K2 ,K3 Tr ª¬ DcK1K2 (Z1 , Z2 )FK3 (Z3 )  WcK1K2K3 (Z1 , Z2 , Z3 )S º¼ ,where DcK1K2 (Z1 , Z2 ) and WcK1K2K3 (Z1 , Z2 , Z3 ) can be constructed in the same form as

the density and energy-weighted density matrices, respectively. In the present scheme,
these two matrices are calculated in the DC manner as:s
cK1K2 (Z1 , Z2 ) ¦ pPQ
DPQ(2)¦ CPK1i ,s (Z1 )CQKi2 ,s* (Z2 ) .
siFigure shows the frequency dependence of(a) polarizability D(Z), (b) Pockels coefficientE(Z;0,+Z), and (c) second-harmonic generation(SHG) coefficient E(2Z;+Z,+Z) of a normal
saturated aldehyde C60H121CHO calculated withconventional and DC-TDHF methods. The DC
results agree with the conventional results within
0.0002%, 0.06%, and 2.6% errors for (a), (b), and(c), respectively. The SHG curve has a pole at
4.89 eV, the half of C=O S-S* excitation energy(9.77 eV). The position of the pole is also
reproduced accurately in the DC scheme.
[1] M. Kobayashi and H. Nakai, in LinearScaling Techniques in Computational Chemistry
and Physics (Springer, 2011), pp.97–127.
[2] T. Touma, M. Kobayashi, and H. Nakai, Chem. Fig. (a) Polarizability, (b) Pockels
coefficient, and (c) SHG coefficient of
Phys. Lett. 485, 247 (2010).
C60H121CHO (TDHF/6-31G**).

196

6C4-1I

Correcting model energies by numerically integrating along the adiabatic
connection and a link to density functional theory
Andreas Savin,1
1
Laboratoire de Chimie Théorique, CNRS and UPMC Sorbonne Universités, Paris,
FranceModel Hamiltonians are considered for which electrons interact via long-range
forces. It is assumed that their eigenvalues can be obtained with satisfying accuracy. Extrapolation techniques using asymptotic behavior considerations provide
estimates for the energy of the physical system. Results for the uniform electron
gas and some two-electron systems show that very few quadrature points can already produce good quality results. Connections to the density functional theory
are discussed.

197

6C4-3I

Assessing the Performance of Density-Functional and Wavefunction
Quantum Chemical Methods for Noncovalent Interactions
C. David Sherrill,1 Lori A. Burns1
1
Center for Computational Molecular Science and Engineering and School ofChemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA, USA
Very high quality benchmark data, from CCSD(T) and high-order symmetryadapted perturbation theory (SAPT), has been obtained for a signiﬁcant collection of van der Waals dimers (469 high-quality single-point energies, and growing). This data is allowing for a thorough assessment of the quality of various
wavefunction-based and modiﬁed DFT methods for noncovalent interactions. We
have examined various DFT-D methods, Becke and Johnson’s exchange dipole moment (XDM) method, various double-hybrids (ωB97X-D, XYG3), the Minnesota
functionals (M05-2X, M06-2X), MP2C, and wavefunction-based methods such as
lower-order SAPT, spin-component-scaled MP2, spin-component-scaled CCSD, andMP2.5. Results are analyzed for various classes of noncovalent interactions (hydrogenbonded, dispersion-dominated, and mixed systems). Basis set eﬀects are examined.
We also explore how the quality of results is expected to behave as one moves tolarger noncovalent complexes, and we consider the nature of noncovalent interactions
in large systems.
L. A. Burns, A. Vazquez-Mayagoitia, B. G. Sumpter, and C. D. Sherrill, J. Chem.
Phys. 134, 084107 (2011).

198

6C4-5C

Dispersionless density functional theory with physically sounddispersion correction.
Rafał Podeszwa,1,2 Katarzyna Pernal,2,3 Konrad Patkowski2 ,and Krzysztof Szalewicz2
1
Institute of Chemistry, University of Silesia, Katowice, Poland
2
Department of Physics and Astronomy, University of Delaware, Newark, DE, USA
3
Institute of Physics, Technical University of Lodz, Lodz, Poland
Symmetry-adapted perturbation theory based on the density functional theory description of the monomers [SAPT(DFT)] has become the method of choice for calculating interaction energies for systems with a few dozen atoms [1]. Its accuracy has been provedin several applications for both dispersion-dominated and hydrogen-bonded systems, including successful predictions of structure of molecular crystals [2]. On the other hand, its
reasonable scaling enabled its use for systems as large as coronene dimer [3]. Additionally, the method provides a physical decomposition of the interaction energy, including
high-accuracy dispersion contribution.
The dispersion energy obtained from SAPT(DFT) has been used in developing a density functional (dlDF) designed to contain only the non-dispersion part of the interactionenergy. Such dispersionless energy contains only terms that the local and semi-local
density functionals can model. The SAPT(DFT) dispersion energy was also used in parameterization of an atom-atom dispersion (D) correction. The dispersionless functionalwith the dispersion correction (dlDF+D) approach [4] provides physically correct decomposition of the interaction energy. It is accurate for a wide range of intermolecular separations, including both the potential well and the asymptotic region. Correct modeling ofthese two regions had been particularly difficult for standard (dispersion-corrected) DFT
functionals. An alternative approach to modeling of the dispersionless energy is also presented. It uses the Hartree-Fock method corrected by low-order SAPT(DFT) terms [5].
The method does not require adjustable parameters and does not rely on error cancellations.
[1] R. Podeszwa, R. Bukowski, and K. Szalewicz, J. Chem. Theor. Comput., 2, 400(2006).
[2] R. Podeszwa, B. M. Rice, and K. Szalewicz, Phys. Rev. Lett, 101, 115503 (2008).
[3] R. Podeszwa, J. Chem. Phys., 132, 044704 (2010).
[4] K. Pernal, R. Podeszwa, K. Patkowski, and K. Szalewicz, Phys. Rev. Lett., 103,
263201 (2009).
[5] R. Podeszwa, K. Pernal, K. Patkowski, and K. Szalewicz, J. Phys. Chem. Lett., 1,
550–555 (2010).

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6C4-6C

Cubic scaling doubly hybrid density functional method close tochemical accuracy and its gradient theory
Yousung Jung
Graduate School of EEWS, KAIST, Korea
Obtaining chemical accuracy (0.04 eV) to quantify key chemical quantities (e.g.
heats of formation, bond dissociation energies, and reaction barrier heights) using
quantum mechanics has been a major focus in the development of the theory. This has led
to, for example, the Gn method that approaches to this accuracy. Because G3 is a coupledcluster based method, it scales on the order of N7, where N measures the system size,
limiting to fairly small molecules for routine use. Present-day density functional methods
are generally believed to provide a sweet spot between feasibility and accuracy, yet stilllead to significant errors for some systems. For example, current density functionals givea poor description of London dispersion, which is essential to predict the packing ofmolecules into solids, and the binding of drug molecules to proteins. They are also poor in
predicting the magnitude of reaction barriers often cases.
In this talk, I will present a new doubly
hybrid density functional we developed which
includes the perturbative correlation treatmentof opposite-spin electrons only and therefore
provides a unique combination of highaccuracy and speed, namely XYGJ-OOS.
Scaling of the method is shown to be cubic by
utilizing the local characteristics and sparsityof the electron correlations, two orders lower
than the scaling of conventional doubly hybrid
methods. The analytic gradient theory of this
opposite-spin based doubly hybrid functional
is also formulated and implemented into
Q-CHEM for geometry optimization. Someinteresting chemical applications are presented
for geometries and potential energy surfaces.

[1] I.Y. Zhang, X. Xu, Y. Jung, W. Goddard, Submitted

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