Abstracts of Invitedand Contributed Talks, Sep. 349

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From Density Functional Theory
to Density Matrix Functional Theory
Evert Jan Baerends,1,2 O. V. Gritsenko,1,2 K. J. H. Giesbertz1,2
1
WCU program, Pohang Univ. of Science and Technologyg,Pohang, South-Korea
2
VU university, Amsterdam, The Netherlands

Although DFT has been very successful, it also meets with important problems. The
dissociation of electron pair bonds, and their weakening towards transition states, areproblematic cases for (approximate) DFT. In the calculation of response properties withTDDFT, there are grave errors when one tries to construct excited state potential energy
surfaces: upon stretching of bonds the excitation energy becomes totally wrong [1] the
TDDFT method fails to describe doubly excited character [2], and fails for chargetransfer transitions.
All these problems stem from the difficulty that functionals working with the local
density and its derivatives have in recognizing the correlation of electrons along alengthening bond [3]. The exact position of the other nucleus, and the onset of strong
correlation effects, are however manifest in orbital information: the shape and energy
for occupied and virtual Kohn-Sham orbitals, and the occupation numbers for thenatural orbitals. We will discuss how orbital dependent functionals can be used todescribe the strong correlation in the indicated cases, both in the DFT context (withvirtual orbital dependent functionals [4]) and in density matrix functional theory [5,6,7].
1. K. J. H. Giesbertz, E. J. Baerends, Chem. Phys. Lett. 461 (2008) 338
2. K. J. H. Giesbertz, E. J. Baerends, O. V. Gritsenko, Phys. Rev. Lett. 101 (2008)
033004
3. E. J. Baerends, Phys. Rev. Lett. 87 (2001) 133004
4. M. Grüning, O. V. Gritsenko and E. J. Baerends, J. Chem. Phys. 118 (2003) 7183
5. D. Rohr, K. Pernal, O. Gritsenko, E. J. Baerends, J. Chem. Phys. 129 (2008) 164105
6. K. J. H. Giesbertz, K. Pernal, O. V. Gritsenko, E. J. Baerends, J. Chem. Phys. 130(2009) 114104
7. K. J. H. Giesbertz, O. V. Gritsenko, E. J. Baerends, J. Chem. Phys. 133 (2010)
17411950

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Two-Point Weighted Density Approximations for the Kinetic Energy
and Exchange-Correlation Energy
Paul Ayers1
1
Department of Chemistry & Chemical Biology; McMaster University; Canada
Many of the problems in density-functional theory can be mitigated by carefully
designing an exchange-correlation hole with the proper mathematical properties. This
leads to generalized and extended versions of the venerable weighted density
approximation (WDA). In this talk, I will show how well WDA can work for the kinetic
energy, exchange energy, and exchange-correlation energy. One advantageous featureof the WDA is that it allows one to deal with fractionally occupied sites in a better way
than conventional functionals. (For example, the H2 dissociation problem is entirely
solved.) The traditional criticism of WDA has been its high computational cost. These
costs are mitigated by new algorithms using a new limited-memory quasi-Newton
method that was designed especially for this application.

51

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Linearity condition for orbital energy in density functional theory:
Construction of orbital-specific hybrid functionals
Yutaka Imamura,1 Rie Kobayashi,1 Hiromi Nakai1,2
1School of Advanced Science and Engineering, Waseda University, Japan
2
Research Institute for Science and Engineering, Waseda University, Japan
Introduction The recent development of more advanced hybrid functionals in density
functional theory (DFT) overcome the several long-standing difficulties: dissociation
curves; charge-transfer, Rydberg, and core excitations. Our group has also developed theorbital-specific (OS) hybrid functional that owns Hartree-Fock exchange (HFx) portions
depending on orbital natures: core-valence-Rydberg (CVR)-B3LYP hybrid functional.
However, these functionals often determined parameters by numerical assessment and,as a result, narrowed their applicability. This study attempts to determine the parameters
so as to satisfy the physical constraint.
Theory The parameters included in hybrid functional, i.e., the HFx portions can be
determined by the physical constraint: linearity condition for orbital energy (LCOE) [1]:w2E
wf i 2

wH i
wf i

0

(0 d f i d 1)

(1)

where E , H i , and f i represent the total energy, orbital energy and occupation numberof the ith orbital. The LCOE enables to determine OS parameters based on a physicalfoundation and construct OS functionals.
Result & Discussion We calculate potential curves and bonding energies of He2+ using
the cc-pCVTZ basis set for conventional and OS functionals. As shown in Fig. 1, theOS functionals, LC-BLYP and HF offer a reasonable description of bond dissociation
although BLYP and B3LYP fail. The corresponding bonding energies are listed in Table
1. The deviations are shown in parentheses. The
BLYP, B3LYP, and LC-BLYP functionals
overestimate by more than 18 kcal/mol and HF
underestimates by 11.7 kcal/mol. On the other
hand, the OS LC-BLYP and OS BLYP
functionals accurately estimate bonding energies
within 0.8 kcal/mol. Table 1 He + bonding energies
2
This
numerical in kcal/mol.
81.6 (27.0)
assessment on He2+ BLYP
B3LYP
75.4
(20.8)
revealsthat
the
LC-BLYP
72.6 (18.0)
LCOE can play an HF
42.9 (-11.7)
essential role in the OS LC-BLYP 55.3 (0.7)
55.4 (0.8)
construction of DFT OS BLYP
Fig. 1 He2+ potential curves
Exact
54.6 -hybrid functionals.
[1] Y. Imamura, R. Kobayashi, and H. Nakai, J. Chem. Phys. 134, 124113 (2011).

52

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Density functional theory with fractional occupations
Jeng-Da Chai1
1
Department of Physics, National Taiwan University, Taipei 10617, Taiwan
We propose a density functional theory (DFT) with fractional occupations of
the Kohn-Sham (KS) orbitals for the study of ground states of many-electron systems. This DFT, containing a free parameter which controls the orbital occupation
numbers, can be reduced to KS-DFT with some ﬁxed parameter. Utilizing the local spin density approximation (LSDA) to this DFT, improved results are obtained
for systems dominated by either single-reference characters (e.g. reaction energies,
equilibrium geometries) or multi-reference characters (e.g. bond-breaking processesof H2 and N2 , twisted ethylene), when compared with KS-LSDA. Because of itsvery cheap computational cost (similar to KS-LSDA), this DFT is applied to thestudy of singlet-triplet energy gaps (ST gaps) of linear acenes (up to 74-acene). Our
results are in good agreement with the available experimental results, and suggestthat the decay of ST gaps with the acene length be monotonic, and the ST gap
for the inﬁnite chain be vanishingly small (smaller than 1 kcal/mol). Both physicalarguments and numerical results for the choice of optimal parameter used in thisDFT are presented.

53

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3A2-3I

Linear- and Sub-Linear Scaling Quantum-Chemical Methods
Christian Ochsenfeld
Theoretical Chemistry, University of Munich (LMU),
Butenandtstr. 7, D-81377 Munich, Germany
www.cup.uni-muenchen.de/pc/ochsenfeld/
The usefulness of the Laplace transformation for the formulation of linear-scaling
methods is discussed for both response theories at Hartree-Fock (HF) and DensityFunctional Theory (DFT) levels [1], and for the calculation of energies and energy
gradients at the Møller-Plesset (MP2) level [2-4]. The transformation allows to entirely avoid the delocalized, canonical molecular orbital (MO) representation, whichis crucial for the formulation of linear-scaling methods. In this way, only density or
pseudo-density matrix-based quantities enter the formulations, so that sparsity canbe exploited for electronically local molecular systems and linear scaling is attained.
The largest system computed at the MP2 level is an RNA system comprising 1664
atoms and 19 182 basis functions [5].
Furthermore, we introduce a sub-linear scaling NMR method [6], that allows tocompute NMR shieldings for selected nuclei only. This has important implications
not only for the study of large molecules, but also for the simulation of solvent eﬀects
and molecular dynamics, since often just a few shieldings are of interest. Our theory
relies on two major aspects both necessary to provide a sublinear scaling behavior:First, an alternative expression for the shielding tensor is derived, which involves
the response density matrix with respect to the nuclear magnetic moment insteadof the response to the external magnetic ﬁeld. Second, as unphysical long-range
contributions occur within the description of distributed gauge origin methods that
do not inﬂuence the ﬁnal expectation value, we present a reformulation suitable fortruncation, so that an early onset of the sublinear-scaling behavior can be achieved.
Applications to molecular systems with more than 1000 atoms will be shown.
[1] M. Beer, C. Ochsenfeld; J. Chem. Phys. 128, 221102 (2008)[2] B. Doser, D. S. Lambrecht, J. Kussmann, C. Ochsenfeld;
J. Chem. Phys. 130, 064107 (2009)[3] S. Schweizer, B. Doser, C. Ochsenfeld; J. Chem. Phys. 128, 154101 (2008)[4] J. Zienau, L. Clin, B. Doser, C. Ochsenfeld; J. Chem. Phys. 130, 204112 (2009)[5] B. Doser, J. Zienau, L. Clin, D. S. Lambrecht, C. Ochsenfeld;
Z. Phys. Chem. 224, 397 (2010); Special Issue ’SPP 1145’[6] M. Beer, J. Kussmann, C. Ochsenfeld; J. Chem. Phys. 134, 074102 (2011)55

3A2-5I

New developments and applications of the generalized energy-based
fragmentation approach
Shuhua Li
School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic
Chemistry of Ministry of Education, Institute of Theoretical and Computational
Chemistry, Nanjing University, Nanjing, 210093, Peoples Republic of China
In this talk, I will present our recent developments and applications of the generalized energy-based fragmentation (GEBF) approach, which provide a fast and reliable theoretical tool for approximate ab initio calculations of very large molecules.[13] The essence of this method is to divide a large molecule into many fragments andobtain the approximate ground-state energy or properties of this molecule from thecorresponding quantities of various “electronically embedded” subsystems. Veryrecently, an automatic algorithm for partitioning a large system has been accomplished,[4] which allows the applications of the GEBF approach to be available bynon-expert users. With the newly implemented GEBF approach, one can compute energies, optimized structures, vibrational spectra, and some molecular properties of very large systems at various ab initio levels on ordinary PC workstations.
The GEBF approach has been applied to investigate several interesting chemical
problems in large systems, such as the driving forces of molecular self-assemblingprocesses,[5] low-lying structures and stabilities of large water clusters,[6] and thestructures, energies and enthalpies of helical structures for capped polyalanines withup to 40 residues.[7][1] W. Li, S. Li, and Y. Jiang, J. Phys. Chem. A 2007, 111, 2193.
[2] W. Hua, T. Fang, W. Li, J.-G. Yu, and S. Li, J. Phys. Chem. A 2008, 112,10864.
[3] S. Li and W. Li, Annu. Rep. Prog. Chem., Sect. C 2008, 104, 256.
[4] S. Hua, W. Hua, and S. Li, J. Phys. Chem. A 2010, 114, 8126.
[5] H. Dong, S. Hua, and S. Li, J. Phys. Chem. A 2009, 113, 1335.
[6] Z. Yang, S. Hua, W. Hua, and S. Li, J. Phys. Chem. A 2010, 114, 9253.
[7] S. Hua, L. Xu, W. Li, and S. Li, J. Phys. Chem. B 2011, submitted.

56

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Cost-Eﬀective Treatment of Relativistic Eﬀects
Stella Stopkowicz, Lan Cheng, Werner Schwalbach, Jürgen Gauss
Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz, Germany
Relativistic eﬀects need to be considered in quantum-chemical calculations when
dealing with heavy-element compounds or when aiming at high accuracy. In the latter case these eﬀects are even important for systems containing only light elements.
In order to allow a routine treatment of relativistic eﬀects, cost-eﬀective as well as
accurate schemes are needed which in particular are also applicable in the context ofelectron-correlation calculations. Two approaches will be pursued for this purposein the following:• direct perturbation theory (DPT) with a special emphasis on higher-order
treatments;• spin-free approaches based on a non-perturbative treatment of the scalarrelativistic eﬀects. Spin-orbit coupling is here treated afterwards using perturbation theory.
In the lecture, the theoretical background of these schemes is discussed, and resultsfor energies and molecular properties are given to judge the accuracy of the presented
schemes.

57

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Four-component relativistic multireference perturbation theory
Ryo Ebisuzaki, Satoshi Suzuki, Yukio Kawashima, Yoshihiro Watanabe,and Haruyuki Nakano,Department of Chemistry, Graduate School of Sciences, Kyushu University, Japan
Multireference perturbation theory (MRPT) based on multiconfiguration (MC) referencefunctions has become a basic and practical tool for studying the electronic structures ofmolecules and the potential energy surfaces of chemical reactions. MRPT takes accountof both static and dynamic electron correlations and thus can obtain accurate relative
energies, including reaction, activation, and excitation energies, within a chemical
accuracy (i.e., a few kcal/mol).
We have developed an MRPT using MC functions that we call “multiconfigurational
quasidegenerate PT (MC-QDPT)”.[1] It is a multiconfiguration basis multi-referencestate method based on van Vleck PT and includes multireference Møller–Plesset PT, asingle-reference-state method based on Rayleigh–Schrödinger PT, as a special case. In
particular, a version of MC-QDPT proposed later uses general multiconfigurationreference functions (GMC-QDPT or GMC-PT).[2] GMC-QDPT imposes no restriction
on the reference space, so it is much more compact than complete active space(CAS)-based MRPT. In addition, since it can avoid unphysical multiple excitations, it isnumerically stable.
Several years ago, we extended GMC-QDPT to a relativistic version with
four-component general MC reference functions and applied it to the potential energy
curves of I2 and Sb2, and the excitation energies of CH3I, etc.[3,4] These were theinitial application of relativistic MRPT to molecular systems to the best of ourknowledge.
In the presentation in ISTCP7, we present some applications to the excited states ofseveral heavy-element complexes. The calculated excitation energies for [PtCl4]2í,[PtBr4]2í, and [PtCl6]2í, for example, were in very good agreement with available
experimental data. The maximum and average deviations were 0.18 and 0.08 eV,
respectively, which were better than time-dependent density functional theory results.
We also present an efficient simplified form of GMC-QDPT and a Kramers unrestricted
simplified MCSCF method.
[1] H. Nakano, J. of Chem. Phys. 99, 7983–7992 (1993); H. Nakano, Chem. Phys. Lett.
207, 372–378 (1993).
[2] H. Nakano, R. Uchiyama, and K. Hirao, J. Comp. Chem. 23, 1166–1175 (2002).
[3] M. Miyajima, Y. Watanabe, and H. Nakano, J. Chem. Phys. 124, 044101 (2006);
R. Ebisuzaki, Y. Watanabe, and H. Nakano, Chem. Phys. Lett. 442, 164–169 (2007);
R. Ebisuzaki, Y. Kawashima, Y. Watanabe, and H. Nakano, J. Chem. Theory Comp. 7,
998–1005 (2011).
[4] H. Moriyama, Y. Watanabe, H. Nakano, S. Yamamoto, and H. Tatewaki, J. Chem.
Phys. 132, 124310 (2010) and references therein.

58

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IDEAS OF RELATIVISTIC QUANTUM CHEMISTRY
Wenjian Liu
Institute of Theoretical and Computational Chemistry, College of Chemistry and MolecularEngineering, Peking University, Beijing 100871, P. R. China (liuwj@pku.edu.cn)
Fundamental breakthroughs have recently been achieved in relativistic quantum chemistry forboth electronic structure and magnetic properties:(1) Electronic structure
For any quantum mechanical calculation one has to first choose an electronic Hamiltonian,
the best of which must be something between the Dirac and Schrödinger equations. Here we
propose an exact two-component (X2C) equation[1-6], which is conceptually simple,
numerically accurate, and computationally efficient. In addition, it serves a seamless bridge
between the Dirac and Schrödinger equations, in the sense that it allows for relativistic
treatment of the heavy atoms and non-relativistic treatment of the light atoms in the moleculein a natural manner.
(2) Magnetic properties
Four-component relativistic theory of magnetic properties such as NMR shielding tensor isformally very simple: It consists only of a single term, the paramagnetism. Yet, it is plaguedby two fundamental issues. Conceptually, the diamagnetism known from non-relativistic
theory is “missing”. Computationally, such a standard formulation is very demanding on basis
functions of high angular momenta. Herewith we propose several strictly equivalentapproaches [7-9] based on the generic ansatz of orbital decomposition [10, 11]. Not only does
the diamagnetism arise naturally, but also is the computation simplified greatly. The X2C
counterparts have also been formulated in a most general way [12].
The X2C Hamiltonian can be combined with know-how correlation methods so as to generatea new generation of relativistic many-body theories for the whole Periodic Table of elements.
Bibliography:
1.

W. Kutzelnigg and W. Liu, J. Chem. Phys. 123, 241102 (2005).

2.

W. Liu and D. Peng, J. Chem. Phys. 125, 044102 (2006).

3.

D. Peng, W. Liu, Y. Xiao, and L. Cheng, J. Chem. Phys. 127, 104106 (2007).

4.

W. Liu and W. Kutzelnigg, J. Chem. Phys. 124, 114107 (2007).

5.

W. Liu and D. Peng, J. Chem. Phys. 131, 031104 (2009).

6.

W. Liu, Mol. Phys. 108, 1679-1706 (2010).

7.

Y. Xiao, W. Liu, L. Cheng, and D. Peng, J. Chem. Phys. 126, 214101 (2007).

8.

L. Cheng, Y. Xiao, and W. Liu, J. Chem. Phys. 130, 144102 (2009).

9.

L. Cheng, Y. Xiao, and W. Liu, J. Chem. Phys. 131, 244113 (2009).

10. Y. Xiao, D. Peng, and W. Liu, J. Chem. Phys. 126, 081101 (2007).
11. W. Kutzelnigg and W. Liu, J. Chem. Phys. 131, 044129 (2009).
12. Q. Sun, W. Liu, Y. Xiao, and L. Cheng, J. Chem. Phys. 131, 081101 (2009).

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Recent development of the fragment molecular orbital method
Dmitri G. Fedorov
NRI, AIST, JapanThe fragment molecular orbital (FMO) method [1] enables large scale quantummechanical calculations of systems containing thousands of atoms, using conventional
methods such as RHF, DFT or MP2. In FMO, the system is divided into fragments, andthe total properties are computed from those of fragments and their pairs. Recent
progress in the method development will be reviewed, including the fast geometry
optimisation method FMO/FD [2], followed by a summary of recent applications [3].
More information about FMO including freely distributed software can be found in [4].
In FMO with frozen domain (FD), only the
essential part of the system, polarizablebuffer B including the active site A, is
recomputed at each point in a geometry
optimisation. The rest of the system,domain F, is computed only at the initialgeometry. The complex of prostaglandinH(2) synthase-1 and ibuprofen, containing
19471 atoms at the B3LYP-D/6-31G* levelfor domain A and RHF/STO-3G for F was
optimised in 32 h on 6 dual CPU quad-core
2.83 GHz Xeon nodes using GAMESS.
References[1] T. Nagata, D. G. Fedorov, K. Kitaura. Mathematical Formulation of the fragment molecularorbital method. In Linear-Scaling Techniques in Computational Chemistry and Physics. R.
Zalesny, M. G. Papadopoulos, P. G. Mezey, J. Leszczynski (Eds.), Springer, New York, 2011.
[2] D. G. Fedorov, Y. Alexeev, K. Kitaura. Geometry optimization of the active site of a large
system with the fragment molecular orbital method. J. Phys. Chem. Lett. 2 (2011) 282-288.
[3] T. Sawada, D. G. Fedorov, K. Kitaura. Role of the key mutation in the selective binding of
avian and human influenza hemagglutinin to sialosides revealed by quantum-mechanicalcalculations. J. Am. Chem. Soc. 132 (2010) 16862-16872.
[4] http://staff.aist.go.jp/d.g.fedorov/60

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3A4-5I

Linear-Expansion Shooting Techniques for Accelerating
Self-Consistent Field Convergence
Yan Alexander Wang
Department of Chemistry, University of British Columbia, Vancouver, Canada
Based on the corrected Hohenberg-Kohn-Sham energy functional (cHKS) [1,2], we
present a new method to accelerate self-consistent field (SCF) convergence by utilizing
the shooting method in numerical analysis [3]. We have developed several different
linear-expansion shooting techniques (LIST) by imposing different conditions [4]. Casestudies show that overall our LIST methods are robust and efficient algorithms foraccelerating SCF convergence. More importantly, the LIST methods outperform Pulay’s
DIIS [5,6] and its recent improvements, including EDIIS [7] and ADIIS [8].
[1] B. Zhou and Y. A. Wang, J. Chem. Phys. 128, 084101 (2008).
[2] Y. A. Zhang and Y. A. Wang, J. Chem. Phys. 130, 144116 (2009).
[3] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical
Recipes in Fortran (Cambridge University Press, Cambridge, 1992).
[4] Y. A. Wang, C. Y. Yam, Y. K. Chen, and G. H. Chen, Phys. Rev.. Lett. (submitted).
[5] P. Pulay, Chem. Phys. Lett. 73, 393 (1980).
[6] P. Pulay, J. Comput. Chem. 3, 556 (1982).
[7] K. N. Kudin, G. E. Scuseria, and E. Cances, J. Chem. Phys. 116, 8255 (2002).
[8] X. Hu and W. Yang, J. Chem. Phys. 132, 054109 (2010).

62

3B1-1I

Chiral Spectroscopy:
Towards a Reliable Comparison Between Theory and Experiment
T. Daniel Crawford
107 Davidson Hall, Department of Chemistry, Virginia TechBlacksburg, Virginia, U.S.A.
Chiral enantiomers — pairs of dissymmetric molecules that are merely mirror images of one another — often exhibit dramatically diﬀerent chemical behavior whenreacting in chiral environments, and the need to distinguish between such enantiomers drives much of the multibillion-dollar research eﬀorts of the pharmaceuticalindustry. Enantiomeric pairs also exhibit mirror-image responses to circularly polarized electromagnetic ﬁelds in absorption (dichroism), refraction (birefringence),and scattering: if the left-hand enantiomer of a chiral compound preferentially absorbs right-circularly-polarized light, the right-hand enantiomer will preferentiallyabsorb the left-handed light, and vice versa. However, such responses are useful forthe identiﬁcation of the handedness of a chiral sample only if a reliable reference isavailable. This lecture will focus on our recent work to establish high-level quantum
chemical methods such as coupled cluster theory as just such a reference.[1, 2] In particular, we will discuss the impact of various physical factors — electron correlation,basis-set completeness, gauge invariance, molecular vibrations, and solvent — on thepredictive capabilities of the coupled cluster model in comparison to both gas- andsolution-phase measurements of optical rotation, electronic circular dichroism, andvibrational Raman optical activity. In addition, we will discuss approaches for reducing the computational scaling of coupled cluster methods in order to extend theirrange of applicability to large chiral molecules and explicit solvent conﬁgurations.[3][1] T.D. Crawford, “High-Accuracy Quantum Chemistry and Chiroptical Properties,” in Comprehensive Chiroptical Spectroscopy, Vol. 1, N. Berova, K. Nakanishi,
R. Woody, and P. Polavarapu, eds., Wiley and Sons, 2011[2] T.D. Crawford and P.J. Stephens, “A Comparison of Time-Dependent DensityFunctional Theory and Coupled Cluster Theory for the Calculation of the Optical
Rotations of Chiral Molecules,” J. Phys. Chem. A 112, 1339-1345 (2008).
[3] T.D. Crawford, “Reduced-Scaling Coupled-Cluster Theory for Response Properties of Large Molecules,” in Recent Progress in Coupled Cluster Methods: Theory
and Applications, P. Carsky, J. Pittner, and J. Paldus, eds., Springer, pp. 37-55,
2010.

63

3B1-3I

Molecules in strong magnetic ﬁelds
Trygve Helgaker,1 M. R. Hoﬀman,2 K. K. Lange1 E. I. Tellgren1
1
CTCC, Department of Chemistry, University of Oslo, Norway
2
Department of Chemistry, University of North Dakota, USA
In strong magnetic ﬁelds, chemistry changes: electronic states change character,molecules change their shape, and their interactions with radiation are aﬀected, often
in a dramatic manner. Such magnetic-ﬁeld induced changes are not only fascinating
as a contrast to the chemistry observed on the earth, they are also relevant toastrophysics, where molecules in stellar atmospheres are subject to strong magnetic
ﬁelds.
We have undertaken a quantum-mechanical study of molecules in strong magnetic ﬁelds, using a recently developed computer code for the calculation of manyelectron molecules at the Hartree–Fock, Kohn–Sham, full-conﬁguration-interaction(FCI) and complete-active-space multiconﬁgurational self-consistent-ﬁeld (CASSCF)
levels of theory. Moreover, implementations of molecular gradients and linearresponse theory allow molecular structures and excitation energies to be studiedin strong ﬁelds. Gauge-origin invariance is ensured by the use of London atomic
orbitals.
Our calculations on molecular systems in strong magnetic ﬁelds have revealed
and highlighted many interesting phenomena, such as the transition to diamagnetismof paramagnetic molecules in strong ﬁelds, changes in molecular structure such as
the squeezing and ﬂattening of ammonia, and large changes in excitation energies
and oscillator strengths in strong ﬁelds. Typically, the most dramatic changes areobserved at ﬁeld strengths of about one atomic unit; in weaker ﬁelds, chemistry isdominated by electrostatics; in stronger ﬁelds, by magnetic interactions.
In the present talk, we concentrate on the role of electron correlation in magnetic
ﬁelds, as described at the FCI and CASSCF level of theories, for small molecules.
In particular, we shall study how the electronic states of small molecules change
character with increasing magnetic ﬁeld—resulting, for example, in a strongly boundHe2 molecule in the electronic ground state. In the future, our FCI and CASSCF
code will be used to elucidate the role of the current dependence in the exchange–
correlation functional of Kohn–Sham theory; our plans for such studies are outlined.

64

3B1-5C

Near-Edge X-ray Absorption Fine Structure from Coupled Cluster
Damped Response Theory using an Asymmetric Lanczos-chain
driven algorithm
Sonia Coriani1,2,3
1
Dipartimento di Scienze Chimiche e Farmaceutiche,
Università degli Studi di Trieste, Trieste, I-34127, Italy2
3

Department of Chemistry, Aarhus University, Aarhus, DK-8000, Denmark,Centre for Theoretical and Computational Chemistry, Department of Chemistry,
University of Oslo, N-0315, Norway

Abstract
Coupled cluster methods are considered among the most accurate tools in electronic
structure theory. Nonetheless relatively limited attempt seems to have been made toextend their applicability to the description of the core-excitation phenomena that arebehind largely used spectroscopic techniques like x-ray absorption spectroscopy andx-ray circular dichroism.
As a first step to redeem for such situation, we present an implementation of damped
response theory (aka complex polarization propagator approach) based on an
asymmetric Lanczos algorithm for the CCS, CC2 and CCSD hierarchy of coupledcluster methods, and apply it to the simulation of the K-edge x-ray absorption spectra ofvarious closed-shell systems, including Neon, CH4, H2O, HF and CO [1]. Triple
excitation effects on the excitation energies are estimated by means of the CCSDR(3)approximation, and relativistic effects are accounted for using the Douglas-Kroll
approach. Results are compared with experiment as well as results obtained with othercomputational methods.
[1] S. Coriani, T. Fransson, O. Christiansen, P. Norman, P. Decleva. Work in progress.

65

3B1-6C

A study into the low-lying excited states of small and medium-sizedmolecules using the (unrestricted) ADC(2) scheme: a closecomparison with experiment
Stefan Knippenberg,1 Andreas Dreuw2
1
Service Chimie des Materiaux Nouveaux, Université de Mons, Place du Parc 20,
7000 Mons, Belgium
2
Chair of Theoretical and Computational Chemistry, Interdisciplinary Center for Scientific
Computing, University of Heidelberg, Im Neuenheimer Feld 368,
69120 Heidelberg, Germany
The algebraic diagrammatic construction (ADC) scheme is one of the scarce excitedstate methods [1] allowing for a direct comparison with experiment without a priori
knowledge of the system under investigation. At the employed level, the ground andprimary excited states are both calculated consistently up to second order of perturbation
theory according to the well-known Møller-Plesset partitioning of the Hamilton operator.
Strict and extended schemes [ADC(2)-s and ADC(2)-x] exist [2], in which the 2p–2h
block is calculated within zeroth and first order, respectively.
In a study of the vertical excited electronic states of linearly fused polyacenes (PACs),
it is shown that a combined application of both versions nicely reveals the importance of
doubly excited configurations in the description of the excited state spectrum of neutral
PACs. In contrast to general expectation, our calculations of the radical cations of the
PACs employing unrestricted ADC(2)-s and ADC(2)-x identified one B1g electronictransition whose excitation energy increases with increasing molecular size.
Since experimental gas-phase data for medium-sized radical molecules are generally
only scarcely available in the literature, use has been made of photo-electron spectra (PES)of neutral molecules to further test the recently developed unrestricted ADC(2) methods.
Indeed, adding the first ionization energy to the excitation spectrum of the radical
compound gives rise to the PES of the neutral species. As a proof of principle, theionization spectra of ethane, formaldehyde, formic acid and difluoromethane are simulatedusing the UADC(2)-s and UADC(2)-x schemes, applied to the radical cations at thesinglet ground state equilibrium geometries. Since it is impossible within this theoretical
approach to calculate partial overlaps between the neutral ground state and the cation, thereflection principle is used to compute intensities [3]. Comparison is made withexperimental spectra as well as those obtained by the reflection principle using
TDDFT/B3LYP data and by the established ionization-ADC(3) scheme.
[1] S. Grimme, Rev. Comp. Chem. 20, 153 (2004); A. Dreuw, Chem. Phys. Chem. 7, 2259
(2006).
[2] J. H. Starcke, M. Wormit, A. Dreuw, J. Chem. Phys. 130, 024104 (2009).
[3] E. A. Gislason, J. Chem. Phys. 58, 3702 (1973); S. Barth, M. Oncak, V. Ulrich, M.
Mucke, T. Lischke, P. Slavicek, U. Hergenhahn, J. Phys. Chem. A 113, 13519 (2009).

66

3B2-1I

Quantum fluctuations can promote or
inhibit glass formation
Eran Rabani
School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel

Understanding the transformation of liquid into glass is one of the outstanding
problems in the physical sciences. The major difficulty in understanding the glasstransition is the fact that glass itself is an ill-defined state of matter: unlike a crystal, aglass is not a thermodynamic phase. Quantum mechanical systems ranging fromelectron liquids to superfluid helium appear to form glasses, but as yet no unifying
framework exists connecting classical and quantum regimes.
Here we present new insights from theory and simulation into the impact ofquantum fluctuations on glass formation. As intuition may suggest, we observe thatlarge quantum fluctuations serve toinhibit glass formation as tunnelingand zero-point energy allow particles
to traverse barriers facilitating
movement. However, as the classicallimit is approached a regime isobserved in which quantum effects
slow down relaxation making thequantum system glassier than theclassical system. This dynamical‘reentrance’ occurs in the absence ofobvious structural changes and has no
Dynamic phase diagram calculated from a quantum
counterpart in the phenomenology ofclassical glass-forming systems.
mode-coupling theory for a hard-sphere fluid

T. E. Markland, J. A. Morrone, B. J. Berne, K. Miyazaki, E. Rabani and D. R. Reichman,"Quantum Fluctuations Can Promote or Inhibit Glass Formation", Nature Physics 7,
134-137 (2011).

67

3B2-3I

Extended Concept of Solvation toward Unified Analysis of Molecular
Binding in Weakly Ordered Systems
Nobuyuki Matubayasi
Institute for Chemical Research, Kyoto University, Japan
A key function of such weakly ordered systems as lipid membrane, micelle, andprotein is their ability of acting as a host and binding other molecules. In the present
work, a diverse class of binding is treated in unified manner as the solvation in an
extended sense. The basic idea is view a solution system with host structure (membrane,
micelle or protein) as a mixed solvent. The host is described not as solute species, but aspart of the mixed solvent system, and the guest molecule is the only species regarded as
the solute. A unified treatment is then implemented as the solvation in a mixed-solvent
system, which often involves nano- or mesoscale inhomogeneity.
The key quantity governing the binding ability is the standard change of free energy.
Within the (extended) notion of solvation, the quantity of interest is the solvation freeenergy, the reversible work to introduce the solute-solvent interaction. The free energy isnotorious, however, for its heavy computational demand. A fast and accurate computationof free energy is a major challenge of theoretical/computational chemistry at present. We
approach the free-energy computation by combing the molecular simulation with astatistical-mechanical theory of solutions.
Since the notion of solvation is not only extended to abovementioned
nano-organized systems, but is also strongly desired to handle such emerging systems asionic liquid, supercritical fluid, and quantum-classical coupled system, the theory ofsolutions needs to be (re-)formulated to treat these frontline subjects. To meet thisnecessity, we present a new type of solution theory called the method of energy
representation. In this method, the solute-solvent distribution is expressed over the
one-dimensional coordinate of solute-solvent pair interaction energy, and the energy
distribution functions in the solution and reference solvent systems constitute an
approximate but accurate functional for the solvation free energy. The method achieves ahigh computational efficiency compared to the standard free-energy perturbation method,while no deterioration is observed in terms of the agreement with experiment.
Two types of application are discussed. One is the molecular binding into lipid
membrane and micelle. The distribution of hydrophobic solutes is investigated in DMPC
bilayer and SDS micelle. Water is shown to delocalize the spatial distribution ofhydrophobic solutes within DMPC membrane. The interaction of transmembrane proteinwith lipid membrane is also examined and the driving force of binding is discussed.
The other is the cosolvent effect on protein stability in aqueous system. Water andthe cosolvent such as urea are viewed as mixed solvent, and all-atom analysis of protein
solvation is conducted. The “direct” and “indirect” effect of cosolvent is examined bydecomposing the solvation free energy into the water and cosolvent contributions.

683B2-5C

Computation of reaction free energies by the QM/MM-ER approach- Exact treatment of the many-body interactions Hideaki Takahashi∗ , Akihiro Morita
Department of Chemistry, Graduate School of Science, Tohoku University, Japan
I. Introduction
Reaction pathway in a condensed phase with thermal ﬂuctuation is governedby the free energy change associated with the reaction. It is, therefore, a matterof great signiﬁcance to develop an eﬃcient methodology to compute free energychange. For this purpose we recently proposed a novel method, termed QM/MMER[1], by combining the QM/MM approach with the theory of energy representation(ER)[2]. In formulating QM/MM-ER, however, a diﬃculty arises from the fact that
the QM-MM interaction is not pairwise additive. Here, we report a simple and exact
approach to compute free energy contributions due to the many-body interactions.
II. Methodology
The point of the QM/MM-ER method is to split the total solvation free energy
Δμ into two contributions, that is, the free energy Δμ̄ due to the two-body interaction and the others δ μ̃. We show that the free energy δ μ̃ originating from many-bodyinteraction can be formulated by introducing an energy coordinate η which contains
the solute-solvent interaction energy due to the electronic polarization of the QM
solute. In terms of the distribution functions Q(η) and Q0 (η), respectively, for solution and reference systems, the free energy δ μ̃ corresponding to the electron density
ﬂuctuation around an arbitrary ﬁxed electron density ñ can be evaluated exactly
without any approximate functional. Thus, the total solvation free energy Δμ attemperature T can be simply expressed as





Q(η)
+ η Q(η)(1)Δμ = Δμ̄ + δ μ̃ = Δμ̄ + dη kB T Q(η) ln
Q0 (η)In Eq.(1) Δμ̄ is the solvation free energy of a QM solute with the electron density
ﬁxed at ñ, which can be computed with the standard version of the method of energy
representation.
III. Benchmark test calculation
To test the performance of Eq.(1), we computed solvation free energy of a QM water molecule into MM water solvent. The QM solute is described by DFT with BLYP
functional, while the MM solvent is represented by 499 SPC/E water molecules. The
thermodynamic condition of the solution was set at T = 300 K, and ρ = 1.0 g/cm3 .
Then, the solvation free energy Δμ was obtained by Eq.(1) as -6.5 kcal/mol, whichshows excellent agreement with the experimental value of -6.3 kcal/mol. This resultclearly suggests the eﬃciency of the new approach.
[1] H. Takahashi, N. Matubayasi et al. J. Chem. Phys., 121, 3989 (2004).
[2] N. Matubayasi and M. Nakahara, J. Chem. Phys., 113, 6070 (2000).

69

3B2-6CClassical Cumulant Dynamics
Y. Shigeta1, T. Inui1, K. Okuno1, T. Baba2, R. Kishi1, and M. Nakano1
1
School of Engineering Science, Osaka University, Japan
2
Graduate School of Life Science, University of Hyogo, Japan
We have proposed a quantal cumulant dynamics (QCD) method for theinvestigation of weak quantum effects on model and molecular systems including
proton transfer reactions [1-3]. The essence of this method is to treat with an extended
dynamics of distribution characterized as expectation values generating from the
distribution. Within this scheme, not only the position and momentum but also the
cumulant variables, which are functions of mixed position and momentum moment
operators plays central role in its propagation. In the present study we utilized the sameprocedures to treat problems appearing in classical statistical mechanics. We referred toit as classical cumulant dynamics (CCD). The same kind of methodology was proposedby Prezhdo and co-workers. In their method, the expectation value of the total energy isdirectly substituted into the Boltzmann factor that results in introduction of anadditional prefactor for rescaling the inverse temperature in order to apply their theory
to the exactly soluble models such as the free-particle and the harmonic oscillator [4].
For the harmonic oscillator, the Boltzmann factor substituting the expectation value ofthe total energy H is expressed as( ((Qc = exp − β 12 p 2 + λ0,2 + ω 2 q 2 + ω 2 λ2,0))) ,where β is the inverse temperature and λm,n is the m-th and n-th order cumulant
variables with respect to the coordinate and momentum. With our 2nd-order cumulant
variables approximation to the expectation values, we demonstrate that the expectation
value of the Boltzmann operator Q = exp(− β H ) has quite different structure as

(

(

))
= ω (1 + βλ ) , and τ = τ τ

Q = τ −1/2 exp − 12 βτ −1 τ 0,2 q 2 − 2τ 1,1 pq + τ 2,0 p 2 ,2where τ 2,0 = 1 ω + ωβλ2,0 , τ 1,1 = βωλ1,1 , τ 0,20,22,0 0,2 − τ 1,1 areeffective cumulant variables. The former approximation is derived from anapproximation of the expectation value of the Boltzmann operator asexp(− β H ) = exp(− β H ) . The latter has pq and λ1,1 dependence, but the former
does not. Integration of the latter Boltzmann factor within phase space gives exact
distribution function Z HO = 1 β ω . On the other hand, the later still has additional term
to be cancelled. With these Boltzmann factors, the statistical average of the energy canbe derived. We found that in the high temperature limit both Boltzmann factors result ingiving the same energy.

[1] Y. Shigeta, H. Miyachi, K. Hirao, JCP 125, 244102 (2006). [2] Y. Shigeta, JCP 128,
161103(2008). [3] Y. Shigeta, T. Matsui, H. Miyachi, K. Hirao, BCSJ 81, 1230 (2008).
[4] E. Heatwole, O. Prezhdo, JCP 121, 10967 (2004).

70

3B3-1I

Molecular modeling of the dynamics and structure of molecularaggregates in liquid solution and their spectroscopic signature
Eitan Geva
Chemistry Department, University of Michigan, Ann Arbor, MI USA

In this talk, I will present three examples of our ongoing attempts towards developing atheoretical and computational framework for modeling the dynamics and structure
molecular aggregates in liquid solution and its spectroscopic signature
In the first example, I will discuss our attempts to model the recently observed signaturesof coherence transfer in the 2DIR spectra of dimanganese decacarbonyl in liquid
cyclohexane. To this end, we describe the system in terms of a vibrational excitonic
Hamiltonian and the dynamics in terms of a quantum master equation that can account for
population
relaxation,dephasing,coherence-to-coherencetransfer
andcoherence-to-population transfer. A unique feature of our approach is that, in principle, itdoes not rely on any adjustable fitting parameters. More specifically, the anharmonic
vibrational Hamiltonian is derived from ab-initio electronic structure theory and thesystem-bath coupling is expressed explicitly in terms of liquid degrees of freedom whose
dynamics can be obtained via molecular dynamics simulations.
In the second example, I will discuss our attempts to model the unique spectroscopic
signature of nonequilibrium dynamics in the case of hydrogen-bonded methanol
oligomers in methanol/carbon-tetrachloride liquid mixtures. To this end, we employed amixed-quantum classical approach where the hydroxyl stretch of one of the methanol
molecules is treated quantum mechanically, while the remaining degrees of freedom aretreated classically. The ability of different force fields to reproduce the experimental
absorption, emission and pump-probe infrared spectra of the hydroxyl stretch was
examined as well as the insights it gives regarding hydrogen-bonding structure, dynamics
and photochemistry. I will also show how nonlinear mapping relations between thehydroxyl transition frequency and bond length and the electric field along the hydroxyl
bond axis can be used in order to reduce the computational cost of the mixed
quantum-classical treatment to that of a purely classical molecular dynamics simulation.
In the third example, I will discuss our attempts to understand the photochemistry ofelectronically photoexcited silsesquioxanes octa-functionalized by organic dyes. I will
present evidence from DFT calculations that employ range-separated hybrid functionals
and from continuum and mixed quantum-classical solvation models for the emergence ofdark states involving charge transfer between dyes. I will argue that these charge transfer
states are responsible for the unusually large Stokes shift between the electronic
absorption and emission spectra of these systems in comparison to the individual dyes,
and that these systems can be thought of as dye aggregates held together by the otherwise
inert silsesquioxane cage.

71

3B3-3I

Multi-Exciton Dynamics in Molecular Aggregates
1David Ambrosek, Sergey Polyutov, Yun-an Yan, Oliver Kühn
Institute of Physics, University of Rostock, D-18051 Rostock, Germany

Excitation energy transfer in supramolecular architectures covers a broad rangeof dynamical regimes, depending on the electronic properties of the constituent dyebuilding blocks, their mutual Coulomb interaction, and the coupling to vibrational
degrees of freedom and to some solvent environment. In view of the size of thesecomplexes quantitative insight can be provided only by combination of ﬁrst principles simulations of parametrized models yielding spectroscopic observables.[1]In the ﬁrst part of this presentation,
electronic structure theory is utilized
to construct a Frenkel exciton Hamiltonian for a J-aggregate-forming perylene
bisimide dye (see ﬁgure). In particular
it will be shown that the optical properties are strongly dependent on the aggregate size. In accord with experimental ﬂuorescence studies, the J-aggregate
turns into an H-aggregate with decreasing number of monomers.
On the basis of this Frenkel exciton
Hamiltonian quantum dynamical simulations are performed putting emphasis on the interplay between laser-driven
multi-exciton generation, exciton-vibrational coupling, and exciton-exciton annihilation.
[1] V. May, O. Kühn. Charge and Energy Transfer Dynamics in Molecular Systems,
3rd Edition, Wiley-VCH, Weinheim, 2011.

72

3B3-5C

Mixed Quantum-Classical Description of Excitation Energy Transfer in a
Model Fenna-Matthews-Olsen Complex
Aaron Kelly,1 Young Min Rhee,11Pohang University of Science and Technology, South Korea
The Fenna-Matthews-Olsen (FMO) complex has recently become a paradigmatic
model system in terms of understanding the long-lived electronic quantum coherence that has been experimentally observed in photosynthetic systems. We offer an investigation of the quantum dynamics of an FMO model within a mixed
quantum-classical dynamics approach known as the Poisson bracket mapping equation (PBME), and explore the consequences of adopting this approximate description
by simulating population transfer and electronic coherence. The results obtained via
the Poisson bracket mapping formalism are explicitly compared with a selection ofrecent results on the FMO complex. The PBME is shown to be in excellent agreement with benchmark computational results at physiological temperature, and thus
provides a computationally eﬃcient and physically consistent algorithm that may
be easily integrated in all-atom molecular dynamics simulations.

73

3B3-6I

Reduced Hierarchy equations of motion approach tomultidimensional spectroscopies of biological systems
Yoshitaka Tanimura
Department of Chemistry, Kyoto University

In complex media such as molecular liquids and biological systems,
multidimensional spectroscopy has been shown to be variable tools due to thesensitivity of nonlinear response functions. In this talk, we first give an overview of
reduced hierarchy equations of motion approach focusing on its theoretical backgroundand applications to multidimensional spectroscopies. We then apply this methodology
to see a possibility to explore a role of dissipation and fluctuation on quantum dynamics
of biochemical systems. As the observables of linear and two-dimensional (2D)
spectroscopies, the first- and third-order response functions of polarization arecalculated for different physical conditions. The profiles of the 2D spectra reflect varietyof heat-bath effects including dissipation, fluctuation, dephasing and inhomogeneous
broadening.
[1] Y. Tanimura and A. Ishizaki, Acc. Chem. Res. 42, 1270 (2009).
http://pubs.acs.org/doi/abs/10.1021/ar9000444[2] Y. Tanimura: J. Phys. Soc. Jpn. 75 (2006) 082001.
http://jpsj.ipap.jp/link?JPSJ/75/082001/

74

3B3-8C

Bridge-mediated electronic coupling between two excited states,
calculating based on the localized Slater determinant
Tsutomu Kawatsu1, Jun-ya Hasegawa1, Kenji Matsuda1
1
Department of Synthetic Chemistry and Biological Chemistry, Graduate School ofEngineering, Kyoto University, Japan
I. Introduction
The excited energy transfer (EET) is a fundamental reaction in various
energy-exchange processes between photons and others. The EET rate is proportional to
the square of the electronic coupling between the initial and final electronic states inweak coupling regime. The electronic coupling can be influenced by the bridge fragment
connecting between the donor and acceptor. The Green’s function technique with theperturbation of the donor-bridge/ acceptor-bridge interactions is often employed to
calculate the bridge-mediated electronic coupling.
II. The electronic coupling
We improved a computational method to calculate the electronic coupling including
effects of surrounding bridge fragments. The donor, acceptor and bridge groups aredefined using the localized excited-state configurations constructed by the localized
molecular orbitals (LMO) [1]. The electronic coupling calculation is generalized from theatomic orbital (AO) based to Slater determinant based. The approach has an advantage toreduce the approximation level of the Green’s function technique from the perturbation ofchemical-bond interaction (between AOs) to the perturbation of the configurationinteraction (between Slater determinants). The method is applied to the EET reaction
concerning to the pair of an electron and hole.
III. EET pathways in model systems
The LMO determinant makes convenient view for the pathway analysis of theelectronic coupling on the bridge area. We categorized indirect pathways into three typesof mediating bridge configurations as in Figure 1. In these pathways, thethrough-exciton is long-range andcharge transfer (CT) is short-range
terms. The through-direct CT can bein the direct-term category driven by
the Dexter mechanism. We applied
the method to EET model systems
with the donor, bridge and acceptor
fragments
andcalculated theelectronic coupling as well as the
direct and through-bridge terms. We
analyzedhoweach
localized
excited-state configuration contributes
to the whole electronic coupling.
Fig.1 Types of direct and indirect pathways of EETs.

[1] Hasegawa, J.; Kawatsu, T.; Toyota, K.; Matsuda, K. Chem. Phys. Lett. 2011, in press.

75

3B4-1I

Nonadiabatic theory in electron wavepacket dynamics
Kazuo Takatsuka,
Graduate School of Arts and Sciences, The University of Tokyo, Japan
Nonadiabatic transition is one of the most important and interesting quantum effects
in chemical dynamics, in which sudden change in electronic states takes place. There
have been proposed so many theoretical methods to treat such nonadiabatic transitions
ranging from the very classic theories of Landau, Zener, Stueckelberg to state-of-the-art
theories such as Zhu-Nakamura, the fewest switch surface hopping method and natural
decay of mixing, and indeed their contributions to the progress of elementary dynamical
processes of chemical reactions have been enormous. Yet, due to the rapid progress ofexperimental studies, we quite often face complicated and difficult experimental
situations that have not been studied before. For instance, we are often interested insystems of densely degenerated electronic states, in which the concept of
Born-Oppenheimer adiabatic potential energy surface (PES) can make only a weaksense due to the energy-time uncertainty relation. In those cases the nonadiabatic
theories based on an assumption of transition among a few (mostly two) PESs at a timeshould be accordingly reformulated. Furthermore, advances in laser technology now
make it possible to modify native molecular electronic states with an intenseelectromagnetic vector potential, which can induce novel nonadiabatic coupling in
addition to the native one. Such nonadiabatic chemistry in intense laser field clearly
constitutes a strong driving force to establish new theories of nonadiabatic transition.
In this talk, we report our recent theory of nonadiabatic transition from the view
point of electron wavepaket dynamics [1]. In particular, we discuss the fundamental
features of nonadiabaticity and quantum entanglement in electron-nucleus dynamics.
We also discuss the interaction of molecular nonadiabatic states with intense laser fields[2]. It is also stressed that even without laser fields the dynamical electron theory canoffer a useful tool to analyze and conceptualize chemical reactions. The present theory
may be regarded as a general theory of mixed quantum-classical dynamics in whichquantum and classical subsystems kinematically contact each other, letting the quantum
mechanical entanglement survive in the classical subsystem.

[1] “Exploring dynamical electron theory beyond the Born-Oppenheimer framework:
From chemical reactivity to non-adiabatically coupled electronic and nuclear
wavepackets on-the-fly under laser field.” Kazuo Takatsuka and Tahehiro Yonehara,
Phys. Chem. Chem. Phys. (Perspective) 13, 4987-5016.
[2] “Nonadiabatic chemical dynamics in intermediate and intense laser fields”, Kazuo
Takatsuka and Takehiro Yonehara, Adv. Chem. Phys. 144, 93-156, (2009).

76

3B4-3I

Stochastic Time-Dependent Current-DFT: a functional theory of open
quantum systems
Massimiliano Di Ventra
Department of Physics, University of California, San Diego”Standard” density-functional methods can only deal with Hamiltonian dynamics, andnot with open quantum systems, namely systems dynamically coupled to baths/reservoirs.
There is, however, a large class of physics problems where one needs to consider thisinteraction explicitly. These include energy relaxation and dephasing, non-radiative
decay, quantum measurement theory, etc. In order to address these issues, we haveintroduced a new theory we have named Stochastic TD-CDFT [1,2] and extended it to
the correlated motion of electrons and ions [3]. I will describe this theory in detail, its
range of applicability, and show some applications with and without ionic motion.
[1] M. Di Ventra and R. D'Agosta, Stochastic Time-Dependent Current-DensityFunctional Theory, Phys. Rev. Lett. 98, 226403 (2007).
[2] R. D’Agosta and M. Di Ventra, Stochastic Time-Dependent Current-DensityFunctional Theory: a functional theory of open quantum systems, 78, 165105 (2008).
[3] H. Appel and M. Di Ventra, Stochastic Quantum Molecular Dynamics, Phys. Rev. B
80, 212303 (2009).

77

3B4-5C

On the nonadiabaticity of molecular quantum dynamicsJiĜí Vaníþek1* and Tomáš Zimmermann1
1
Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie
Chimiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
We propose to measure nonadiabaticity of molecular quantum dynamics [1,2]rigorously by the quantum fidelity between the Born-Oppenheimer quantum dynamics
and the full nonadiabatic quantum dynamics. It is shown that this measure works insituations where the standard criteria (such as the magnitude of nonadiabatic couplings,
energy-gap criterion or the population transfer) fail to detect nonadiabaticity. Our
nonadiabaticity criterion is estimated efficiently with a generalization of the dephasing
representation (DR) [3,4] of quantum fidelity to several potential energy surfaces and its
computational cost is the cost of dynamics of a classical phase space distribution. It canbe implemented easily into any molecular dynamics program and also can utilize
on-the-fly ab initio electronic structure information. The methodology is tested on threemodel problems introduced by Tully, photodissociation of NaI, and the 18-dimensional
on-the-fly CASSCF nonadiabatic dynamics of the methaniminium cation. The results
show that unlike the mixed quantum-classical methods such as surface hopping or
Ehrenfest dynamics, the DR can capture more subtle quantum effects than the
population transfer between potential energy surfaces (see Figure). Hence we propose
using the DR to estimate the dynamical importance of diabatic, spin-orbit, or othercouplings between potential energy surfaces. The acquired information can help reducethe complexity of a studied system without affecting the accuracy of the quantum
simulation.
[1] T. Zimmermann and J. Vanicek, "Communications: Evaluation of the nondiabaticity
of quantum molecular dynamics with the dephasing representation of quantum fidelity,"J. Chem. Phys. 132, 241101 (2010).
[2] T. Zimmermann and J. Vanicek, "On the nonadiabaticity of molecular quantum
dynamics," submitted, J. Chem. Phys. (2011).
[3] J. Vanicek, Phys. Rev. E 70, 055201(R) (2004).
[4] J. Vanicek, Phys. Rev. E 73, 046204 (2006).
*jiri.vanicek@epfl.ch
Figure. An example of a nonadiabatic transition detected by fidelity but unnoticed by the
population transfer criterion.

78

3B4-6C

Photo-excited Non-adiabatic Dynamics in Nano Materials
Kim Hyeon-Deuk,1 Angie B. Madrid,2 Oleg V. Prezhdo3
1
Department of Chemistry, Kyoto University, Japan2
Deparment of Chemistry, University of Washington, USA
3
Department of Chemistry, University of Rochester, USA
Confinement of charge carriers in quantum dots (QDs) of sizes smaller than the Bohr
exciton radius of the corresponding bulk material determine the electronic properties of the
QD, leading to a variety of applications.[1] High cross-sections for light absorption makeQDs excellent materials for photovoltaic devices. Further advantages of QDs inphotovoltaic devices are due to the possibility of generating multiple electron-hole pairs
upon absorption of a single photon. This is called the inverse Auger process, and provides
great potential for increasing solar energy conversion efficiencies relative to those in bulk
systems. It provides new mechanisms for utilization of the excess photon energy andavoiding energy loss to heat.

We have recently developed an atomistic simulation method for studying the Auger andinverse Auger processes, where single exciton (SE) and double exciton (DE) generation
and annihilation are allowed to happen simultaneously. Our atomistic simulation is
performed by directly solving the time-dependent Schrödinger equation with the NA
couplings and energies obtained by the time-domain ab initio simulation on a Ge QD. Our
simulation elucidated a dephasing process and a new mechanism, the phonon-assisted
Auger process, which are both important for understanding the Auger and inverse Auger
processes in QDs. We also found that the DE generation dynamics starting from the SE
states depend upon the initial excitation energies and that its generation rate increases as
the initial excitation energy increases. The population relaxation of the initially excited DE
states indicated that the lowest DE state is most strongly coupled to the SE states and canbe a main gateway to the Auger process. The insights obtained from our simulations will
be important for improving the efficiency of solar energy conversion using QDs.[2][1] K. Hyeon-Deuk, A. B. Madrid and O. V. Prezhdo, Dalton Transaction Issue 45, 10069 (2009);
Dalton Transactions' Most Highly Rated Articles; Published in Special Issue of Solar Energy
Conversion[2] K. Hyeon-Deuk and Oleg V. Prezhdo, Nano Letters, Vol.11, 1845 (2011)79

3B4-7I

Simple wavepacket modeling of electron and nuclear dynamics
Koji Ando
Department of Chemistry, Graduate School of Science, Kyoto University, Japan
Introduction
The current main-stream of theoretical/computational chemistry appears to be
directed toward highly-accurate ﬁrst-principles large-scale computational technologies. As an alternative, we are developing a simple and semi-quantitative method
based on the Gaussian wavepacket (GWP). It has some similarity to the conventional
thawed GWP [1], but has an advantage that the extended Hamiltonian formalism
oﬀers a pictorial view of eﬀective quantum potential, an aspect shared with the
expectation-value approaches such as the quantized Hamilton dynamics [2] and thequantized cummulant dynamics [3].
Semiquantal time-dependent Hartree approach
We will ﬁrst brieﬂy review the approach with applications to: a system-bathmodel deriving a semiquantal generalized Langevin equation [4], the geometric isotope eﬀect of hydrogen-bond structure [5], the kinetic isotope eﬀect in the adiabatichydrogen transfer rate [6], and a realistic molecular dynamics simulation of liquidwater [7].
Valence-bond electron wavepacket approach
The theory was extended to take account of the anti-symmetry of electronic
wavefunctions by exploiting the valence-bond theory. To overcome the so-called
N !-problem steming from the non-orthogonality of the wavepacket orbitals, various
decoupling approximations to electron-pairs are examined [8]. Encouraging results
have been obtained with use of a single ﬂoating and breathing wavepacket orbital
per electron.
[1] E. J. Heller, J. Chem. Phys. 62, 1544 (1975); 64, 63 (1976).
[2] O. V. Prezhdo, J. Chem. Phys. 117, 2995 (2002).
[3] Y. Shigeta, H. Miyachi, and K. Hirao, J. Chem. Phys. 125, 244102 (2006).
[4] K. Ando, Chem. Phys. Lett. 376, 532 (2003); J. Chem. Phys. 121, 7136 (2004).
[5] K. Ando, Phys. Rev. B 72, 172104 (2005); J. Chem. Phys. 125, 014104 (2006).
[6] N. Sakumichi and K. Ando, J. Chem. Phys. 128, 164516 (2008).
[7] K. Hyeon-Deuk and K. Ando, J. Chem. Phys 131, 064501 (2009); 132, 164507 (2010).
[8] K. Ando, Bull. Chem. Soc. Jpn. 82, 975 (2009).

80

3D1-1I

Dynamics of Biomembranes in nano- to micro-meter scales
Hiroshi Noguchi
Institute for Solid State Physics, University of Tokyo, Japan
Bilayer membranes exhibit many interesting phenomena such as shape deformationinduced by phase separation or chemical reaction, membrane fusion, and membrane
fission. Since the length scale of these phenomena widely varies from nano- to micrometer scale, different types of membrane models are required to simulate each lengthscale [1]. Thus, we have developed two types of membrane models: solvent-freecoarse-grained molecular model [2,3] and meshles membrane models [4]. In thesemodels, we can widely vary membrane properties such as the fluidity, bending rigidity,
and the line tension of membrane edges. We will present self-assembly into vesicles,
membrane fusion, and vesicle rupture using these simulation models.

Fig. 1: Sequential snapshots of vesicle rupture to worm-like micelle.

[1] H. Noguchi, J. Phys. Soc. Jpn. 78, 041007 (2009).
[2] H. Noguchi and M. Takasu, J. Chem. Phys. 115, 9547 (2001).
[3] H. Noguchi, J. Chem. Phys. 134, 055101 (2011).
[4] H. Noguchi and G. Gompper, Phys. Rev. E 73, 021903 (2006).

81

3D1-3I

Roles of Water and ATP in Functioning of ATP-Driven Proteins
Masahiro Kinoshita
Institute of Advanced Energy, Kyoto University, Japan

Upon the biological self-assembly, the number of accessible translational
configurations of water in the system increases greatly, leading to a large gain in the water
entropy. Using our theoretical methods wherein this effect is treated as the key factor,
we have succeeded in reproducing the thermodynamic data of apoplastocyanin folding[1], elucidating the pressure [2] and cold[3] denaturation of proteins, suggesting ameasure of thermal stability of proteins [4], and developing a free-energy function
which is capable of discriminating the native fold from misfolded decoys [5]. The tool iseither the three-dimensional integral equation theory [6] or the angle-dependent integral
equation theory [7] combined with the morphometric approach [8].
We believe that the water-entropy effect plays critical roles in the functioning of
ATP-driven proteins. We have recently made significant progresses in the following
subjects: (1) the unidirectional movement of a linear-motor protein along a filament [9];(2) rotational mechanism of F1-ATPase [10]; and (3) insertion of an unfoled protein andrelease of the folded one into and from the chaperonin GroEL [11]. In this talk, I will
discuss the roles of water (especially, its translational entropy) coupled with the cycle of
the ATP binding, hydrolysis, and release of the products (Pi and ADP) in the functioningof these ATP-driven proteins.
[1] T. Yoshidome, M. Kinoshita, S. Hirota, N. Baden, and M. Terazima, J. Chem. Phys.
128, 225104 (2008).
[2] Y. Harano, T. Yoshidome, and M. Kinoshita, J. Chem. Phys. 129, 145103 (2008).
[3] H. Oshima, T. Yoshidome, K. Amano, and M. Kinoshita, J. Chem. Phys. 131, 205102(2009).
[4] K. Amano, T. Yoshidome, Y. Harano, K. Oda, and M. Kinoshita, Chem. Phys. Lett.
474, 190 (2009).
[5] T. Yoshidome, K. Oda, Y. Harano, R. Roth, Y. Sugita, M. Ikeguchi, and M. Kinoshita,
Proteins 77, 950 (2009).
[6] M. Kinoshita, J. Chem. Phys. 116, 3493 (2002).
[7] M. Kinoshita, J. Chem. Phys. 128, 024507 (2008).
[8] R. Roth, Y. Harano, and M. Kinoshita, Phys. Rev. Lett. 97, 078101 (2006).
[9] K. Amano, T. Yoshidome, M. Iwaki, M. Suzuki, and M. Kinoshita, J. Chem. Phys.
133, 045103 (2010).
[10] T. Yoshidome, Y. Ito, M. Ikeguchi, and M. Kinoshita, J. Am. Chem. Soc. 133, 4030
(2011).
[11] K. Amano and M. Kinoshita, Chem. Phys. Lett. 504, 221 (2011).

82

3D1-5C
Resolving Mixed Protein Amyloid-Aggregate Distributions
Damien Hall1,21Instititue of Basic Medical Sciences, University of Tsukuba
2
JST Wakate Initiative for Young Scientists’ Independent Research
I. Introduction
Although the correlative evidence relating the presence of amyloid fibrils and certain
disease states (e.g. Alzheimer’s disease and Type 2 Diabetes) is overwhelming, a directcausative role for amyloid has proved harder to establish. Current thinking links a certain
region of the aggregate protein size distribution, the so called ‘early aggregate’ domain tocellular toxicity. Further development of this hypothesis is dependent upon theavailability of techniques capable of finely resolving amyloid protein aggregate
distributions. Size exclusion chromatography (SEC) is a powerful technique forseparating mixtures of components on the basis of their molecular dimensions. In thispaper we investigate the theoretical potential of SEC for resolving mixtures of protein
aggregates (of various sizes and shapes) produced in the generation of amyloid fibrilspresenting our findings in the form of an equilibrium model. We first discuss the generalcharacteristics of SEC and then review the physicochemical basis of the phenomena ofpreferential partition. We demonstrate a new method for estimating partition coefficientsfor the various components of aggregate mixtures on the basis of their moleculardimensions. Finally we detail procedure for relating SEC column characteristics to theirlikely resolving power for a given aggregate size range. This information should provide
a basic appreciation of the competing factors at work and allow for an informed choice tobe made, prior to commencement of experiment, for selection of the optimal SEC column
media to achieve efficient separation of a desired range of aggregate size distribution.
Fig. 1: In this talk we examine theproblems associated with physicallyresolving protein amyloid aggregatesand quantitatively interpreting theirelution profiles using the technique ofsize exclusion chromatography.

83

3D1-6C

Adding Dynamical Insight to Protein X-ray Images by Solution and
Crystal Molecular Dynamics Simulation
Osamu Miyashita
Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
Decades of investigation have confirmed the importance of protein dynamics forbiological functions. X-ray crystallography has been playing the major role in structural
biology, providing information on protein conformations. However, interpretation ofthis data is not always trivial. While proteins are flexible and adopt different
conformations, X-ray structures represent only a single snapshot of the conformational
ensemble. Some structures may represent conformations that are indeed most stable insolution environment, while some may be unrepresentative of the physiologically
relevant forms since they may be subject to artificial forces such as crystal packing. At
present, there is no general guideline for interpretations of X-ray structures.
Here we compare solution and crystal lattice molecular dynamics (MD) simulations1 to
add dynamical insight to the interpretation of X-ray images. As a model system weconsider the dimeric λ Cro transcription factor2 whose crystal structures range from aclosed DNA-free conformation to an open DNA-bound form. Here we attempt to unveil
the true solution structures of the dimer and the extent of energetically accessible
conformations using Replica Exchange Molecular Dynamics3 in explicit solvent. The
simulated conformational ensemble shows remarkable correlation with available X-ray
structures. Clustering and network analysis1 together with free energy profiles
constructed along the open/closed transitions of the dimer reveal an ensemble
dominated by open and closed dimer forms, with a modest barrier separating these twostates. Intersubunit salt bridging between Arg4 and Glu53 during simulation stabilizes
closed conformations, but open states are clearly accessible and relatively stable. Thus,
Cro-DNA binding may not entail large conformational change relative to the dominant
dimer forms in solution, supporting an extension of the “conformational selection”
model. Our results provide a robust description of Cro conformational space in solution
and reveal the functional context of available X-ray structures.4 Our methods ofperforming crystal MD simulations may also improve the interpretation of other protein
X-ray images to aid in establishing structure-function relationships.
[1] Vorontsov, I.I. and Miyashita, O. (2009) Biophys. J., 97, 2532-2540.
[2] Anderson, W. F., Ohlendorf, D. H., Takeda, Y. & Matthews, B. W. (1981). Nature
290, 754-758.
[3] Sugita, Y. & Okamoto, Y. (1999). Chem. Phys. Lett. 314, 141-151.
[4] Ahlstrom, L.S. and Miyashita, O. submitted.

84

3D2-3I

Giant enhancement of the second hyperpolarizabilities of open-shell
singlet molecular systems by an external electric field anddonor-acceptor substitution
Masayoshi Nakano,1 Takuya Minami,1 Kyohei Yoneda,1 Shabbir Muhammad,1 Ryohei
Kishi,1 Yasuteru Shigeta,1 Takashi Kubo,2 Léa Rougier,3 Benoît Champagne,3 Kenji
Kamada,4 Koji Ohta4
1
Department of Materials Engineering Science, Graduate School of Engineering
Science, Osaka University, Toyonaka, Osaka 560-8531, Japan2
Department of Chemistry, Graduate School of Science, Osaka University Toyonaka,
Osaka 560-0043, Japan
3
Laboratoire de Chimie Théorique (LCT), Facultés Universitaires Notre-Dame de la
Paix (FUNDP) Rue de Bruxelles, 61, B-5000 Namur, Belgium
4
Research Institute for Ubiquitous Energy Devices, National Institute of Advanced
Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, Japanγ [a.u.]We have theoretically found an external field (F) induced giant enhancement of thesecond hyperpolarizability γ of open-shell singlet systems with intermediate diradical
characters [1]. As realistic examples, we examine the field effects on the γ ofpolyaromatic
diradicaloid
havingintermediate
diradical
character,s-indaceno[1,2,3-cd;5,6,7-c’d’]diphenalene (IDPL), in comparison to a closed-shellanalogue of similar size composed of two pyrene moieties (PY2) by carrying out
spin-unrestricted density functional theory, LC-UBLYP, calculations (see Figure 1) [2].
For IDPL, the field-induced enhancement1011
ratio is estimated to reach 4 orders ofmagnitude for an electric field of 0.0077
IDPL
PY2
1010
a.u., whereas it is less than a factor of 2
for PY2. Moreover, an enhancement is109
also observed by substituting both-end
108
phenalenyl rings of IDPL by donor(NH2)/acceptor (NO2) groups but this107
enhancement is limited to about twoordersofmagnitude.
These
106
enhancements are associated with a105
reduction of the diradical character – and
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0-3
therefore an improved thermal stability –F [x10 a.u.]
as well as with the appearance of
Figure 1. Static electric field (F) effectsubstantial Type-I contributions to γ.
on γ [a.u.] of IDPL and PY2 calculatedby the LC-UBLYP/6-31G* method.
[1] (a) M. Nakano et al. Phys. Rev. Lett. 99, 033001 (2007); J. Chem. Phys. 133, 154302(2010). (b) K. Kamada et al. J. Phys. Chem. Lett. 1, 937 (2010) [2] M. Nakano et al. J.
Phys. Chem. Lett. 2, 1094 (2011).
85

3D2-5I

Nonlinear chiroptical properties and spectroscopies
Antonio Rizzo1
1
CNR-Consiglio Nazionale delle Ricerche, Istituto per I Processi Chimico Fisici (IPCF)
UoS di Pisa, Area della Ricerca, Via Moruzzi 1, loc. S. Cataldo, I-56124, Pisa, Italy
In this talk the speaker will review the latest developments in the theoretical andcomputational studies of nonlinear optical properties and spectroscopies involving theconcept of chirality.
The results of a combined experimental-computational analysis of the two-photon
circular dichroism of some bi-aryls (BINOL, VANOL, VAPOL) exhibiting structuralchirality will presented. The challenges faced in the ab initio calculation of nonlinear
optical properties in molecules of the size and complexity of those mentioned just above
will be discussed. They involve the careful choice of appropriate basis sets, electronic
structure and condensed phase models, besides the need to account properly for theeffect of molecular vibrations, conformationalvariety and magnetic gauge origin invariance[1].
The focus will then shift to othernonlinear spectroscopic properties, proven to
be amenable to ab initio simulation resortingto the tools of modern analytical response
theory: excited state electronic circulardichroism, circular intensity difference arising in second harmonic generation and ageneral family of birefringences and dichroisms arising in the interaction of radiation
with chiral samples [2]. Special emphasis will be on the phenomenon ofmagnetochirality, the axial birefringenceand the related dichroism observed whenan unpolarized light beam interacts withchiral sample in the presence of a magnetic
field with a component parallel to thedirection of propagation [3].

[1] N. Lin, F. Santoro, X. Zhao, C. Toro, L. De Boni, F. E. Hernández, A. Rizzo, J. Phys.
Chem B (2011), 115, 211.
[2] A. Baranowska, A. Rizzo, B, Jansik, S. Coriani, J. Chem. Phys. (2006), 125, 054107.
[3] B. Jansík, A. Rizzo, L. Frediani, K. Ruud, S. Coriani J. Chem. Phys. (2006), 125,23410586

3D3-1I

Theoretical Study of Gas-Adsorption to Metal-Organic-Framework (MOF)
Shigeyoshi Sakaki,1* Milind Deshmukh,1 Hideo Ando,2 Yoshihide Nakao,2Hirofumi Sato2
Fukui Institute for Fundamental Chemistry, Kyoto University, Japan
Department of Molecular Engineering, Graduate School of Engineering, Kyoto Univeristy, Kyoto,
Japan
Metal-organic framework (MOF) attracts a lot of recent interests as separate absorption
material, functional material, and catalyst.

For instance, the Hoffmann type MOF induces the highspin (HS) to low spin transition (LS) by CS2 adsorption.1 Theoretical evaluation of interaction
between gas molecule and MOF is necessary for well understanding of such functions of MOF andfurther development of the MOF chemistry. However, the evaluation of the interaction is not easy
because of its very large size. Here, we wish to report highly reliable approximate method toevaluate binding energy of molecular cluster and its application to the interaction between gas
molecule and MOF. Also, we wish to report the high-spin to low-spin transition of the Hoffmann
type MOF by CS2 adsorption.
In our new method, the binding energy of molecular cluster/complex is provided by eq 1,2
BE = BE(HF) + 6 [BE(Mi-Mj)MP2.5 – BE(Mi-Mj)HF](1)

where HF represents the Hartree-Fock method, and Mi etc. represents a molecule involved in themolecular complex. This equation can be derived based on the MP2 and MP3 energies.
We applied this method to evaluate the binding energy ofCS2 and CO2 molecules with the Hoffmann type MOF{Fe(Pz)Pt(CN)4}n (Pz = pyrazine); see Scheme 1.1 In this MOF,
CS2 is sandwiched by two Pz molecules. The binding energy is
not different very much between CS2 and CO2 when two Pz
molecules are considered, but very different between them whentotal MOF framework is considered. Detailed discussion of thebinding energy and the mechanism of the high-spin to low-spintransition will be presented in the talk.

Scheme 1

1) Ohba, M.; Yoneda, K.; Agustí, G.; Muñoz, M.C.; Gaspar, A.B.; Real, J. A.; Yamasaki, M., Ando,
H.; Nakao, Y.; Sakaki, S.; Kitagawa, S. Angew Chem Int Ed, 2009, 48, 4767.
2) Deshmukh, M.; Sakaki, S. to be published.
3) Ando, H.; Nakao, Y.; Sato, H.; Ohba, M.; Sakaki, S. to be published.

87

3D3-3I

Dehydrogenation Mechanism of Chemical Hydrogen Storage
Materials: Catalytic Role of Metal
Ming Wah Wong and Viet Cuong Vu
Department of Chemistry, National University of Singapore, 3 Science Drive 3,
Singapore 117543

Hydrogen is a promising choice of clean energy carrier for both transportation andstationary applications. Hydrogen storage materials via chemical approach have attracted
intense interest nowadays. Varieties of promising materials, for instance metal-hydrideand metal-N-H systems, have been developed in recent years with high hydrogen %wt
and promising reversible hydrogen storage capacity. Molecular-level, mechanistic
understanding of the hydrogenation and dehrogenation mechanisms of these hydrogenstorage materials is critical for optimizing existing materials and rational development ofnovel hydrogen storage materials. In general, limited mechanistic information isavailable in experimental studies. Theory provides a powerful and insightfulcomplementary approach to map out the detailed mechanism and understand thegoverning factors of the thermodynamics and kinetics of requirements of a particularhydrogenation/dehydrogenation reaction. In this presentation, we report our
computational studies of the dehydrogenation mechanisms of several boron-based
metal-N-H systems. We found that the various stages of H2 release of these hydrogenstorage materials are characterized by a common two-step mechanism: hydride transfer
followed by H2 release. The metal atom plays an important and crucial catalytic role inbringing two hydrogen atoms (HG+ and HG-) in close proximity and lowering the activation
barrier of hydrogen release. A similar catalytic role is found for metal-doped hydrogenstorage materials.
H
B

G
Step 1hydridetransfer

N

G

HH
H

Li
Li

N

B

88

Step 2hydrogenrelease3D3-5I

Computational Molecular Electrocatalysis:
The Role of Proton Relays in H2 Oxidation and Evolution Catalysts
M. Dupuis, S. Chen, M.H. Ho, R. Rousseau, S. Raugei,
D. L. DuBois, R. M. Bullock, and J. M. Yang,
EFRC Center for Molecular Electrocatalysis,
Pacific Northwest National Laboratory, Richland WA, USA

The rational design of improved molecular electrocatalysts for small molecule
activation (for example H2, O2, N2, H2O, CO2) requires a detailed molecular level
understanding of the energetic and mechanistic factors controlling the movement ofprotons and electrons during the catalytic cycle. Ni(P2N2)22+ complexes are a family ofmononuclear nickel complexes with cyclic diphosphine ligands that incorporate aminebases, in a mimic of enzyme functionalities. The presence and positioning of the aminebases near the metal center is the critical, enzyme-mimicking structural feature for theactivity1 and the efficiency of these catalysts, as these bases facilitate the heterolytic
cleavage or formation of the H-H bond while acting as proton relays in the managementof the proton and electron movement during the catalytic cycle.
We will highlights computational studies (electronic structure and ab initio
meta-dynamics calculations) of the catalytic cycles in Ni(P2N2)22+ catalysts.
Proton-hydride species are key intermediates.
H2 oxidation and evolution proceed via
heterolytic bond cleavage or formation of the
H-H bond. We will discuss what we havelearned about these catalysts, the importanceof the proton relays, their number, their active
and inactive states, and the role of solvent andwater molecules in giving rise to fast turnoverTypical Potential Energy Maps for Ni(P N )rates. The concept of proton relays is being
Complexes Depicting the Role ofPendant Amine Relays in H Oxidation or Evolution
extended to O2 and N2 reductions reactions as
VKRZQKHUHEDVHGRQǻ*
well as H2O oxidation.
2

2+
2 2

2

Acknowledgements:
This research was carried out in the Center for Molecular Electrocatalysis, an Energy Frontier Research Center fundedby the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. Pacific Northwest National
Laboratory is operated for the U.S. Department of Energy by Battelle.
References:
1. DuBois D. L. and Bullock R. M., Eur. J. Inorg. Chem. 2011, 1017; Yang, J. Y.; Bullock, R. M.; Shaw, W. J.;
Twamley, B.; Fraze, K.; DuBois, M. R.; DuBois, D. L. J. Am. Chem. Soc. 2009, 131, 5935; Yang, J. Y.; Chen, S.;
Dougherty, W. G.; Kassel, W. S.; Bullock, R. M.; DuBois, D. L.; Raugei, S.; Rousseau, R.; Dupuis, M.; Rakowski
DuBois, M. Chem. Comm. 2010, 46, 8618.
2. Chen, S.; Raugei, S.; Rousseau, R.; Dupuis, M.; Bullock, R. M. J. Phys. Chem. A 2010, 114, 12716.

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Theoretical study of counter anion displacement in phenoxyimine-based
catalysts of ethylene polymerization activated withperﬂuorophenylborate
Zygmunt Flisak
Faculty of Chemistry, University of Opole, Oleska 48, 45-052 Opole, Poland
I. Introduction
The search for new catalysts of oleﬁn polymerization focuses on the modiﬁcationof both ligands [1] and counter anions [2]. At the same time, theoretical calculations
accompanying experimental works help reveal intricate details of the polymerization
mechanism. Knowledge acquired in this way will make it possible to design new
catalytic systems in silico.
II. Results and Discussion
Certain phenoxyimine-based catalysts turned out to be exceptionally active in
ethylene polymerization [3]. The energetic proﬁles of the polymerization process
calculated by DFT for selected titanium bis(phenoxyimine) complexes activatedwith perﬂuorophenylborate indicate that the counter anion is very weakly boundto the cationic active site [4], unlike in metallocenes and numerous postmetallocene
catalytic systems [5,6]. We believe that this fact might rationalize unprecedented
activities of certain bis(phenoxyimine) catalysts.
We have also noticed signiﬁcant structural ﬂexibility of the cationic active sites
formed after the activation and counter anion separation.
Table 1. Energetic barriers, kcal/mol.
Catalytic system Separation Insertion
Salan
14.9
a
Phenoyimine
8.4
6.9
b
Phenoxyimine
0.7
Substituents at the imine N atom:amethyl; b phenyl.
[1] Kawai K., Fujita T., Top. Organomet. Chem. 2009, 26, 3.
[2] Bochmann M., Organometallics 2010, 29, 4711.
[3] Matsui S., Mitani M., Saito J., Tohi Y., Makio H., Matsukawa N., Takagi Y.,
Tsuru K., Nitabaru M., Nakano T., Tanaka H., Kashiwa N., Fujita T., J. Am. Chem.
Soc. 2001, 123, 6847.
[4] Flisak Z., Suchorska P., Organometallics, 2010, 29, 6196.
[5] Vanka K., Xu Z., Ziegler T., Organometallics 2004, 23, 2900.
[6] Flisak Z., Ziegler T., Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 15338.

90

3D3-8C

Why the silica surface is negatively charged at pH=7?
Mia Ledyastuti, Yunfeng Liang and Toshifumi Matsuoka

Department of Urban Management, Kyoto University, Kyoto 615-8540, Japan

Silica surface is known to be negatively charged when the pH value is higher than 2-3. Anaverage surface density of Si-OH of amorphous is suggested to be 4.6 Si-OH/nm2, which
is much lower than those of the "ideal surface" ~ 9.57 Si-OH/nm2, assuming the geminal
Si-(OH)2, on quartz (0001) surface. Here, by using first-principles molecular dynamics
simulations, we have found that water molecules dissociate into H+ and OH-, when
new-cleaved quartz (0001) surface is immersed in the water. And the OH- immediatelybind chemically with Si and H+ bind chemically with Si-O* radicals at the surface, theresulting Si-OH density is 5.72 Si-OH/nm2 in average for different starting configurations
and thermal conditions. The rest of Si-O* radicals, presumably negatively charged, is at
sub-surface regime and protected by new-formed Si-OH. This may be the fundamental
reason that the silica surface is negatively charged.

91

3D4-1I

Toward Coherent Control in the Nanoscale
Tamar Seideman
Department of Chemistry and Department of Physics,
Northwestern University, 2145 Sheridan Road, Evanston 60208-3113
Inelastic electron tunneling via molecular-scale junctions can induce a variety offascinating dynamical processes in the molecular moiety. These include vibration,
rotation, inter-mode energy flow and reaction. Potential applications of current-driven
dynamics in heterojunctions range from new forms of molecular machines and newmodes of conduction, to new directions in surface nanochemistry and nanolithography.
In the first part of the talk, I will discuss the qualitative physics underlying currentdriven dynamics in molecular-scale devices, briefly outline the theory we developed to
explore these dynamics, describe the results of ongoing research on surface
nanochemistry and molecular machines, and sketch several of our dreams and plans inthese areas.
The application of light to control molecular motions and electronic transport injunctions is intriguing, since photonic (by contrast to electronic) sources offer(sub)femtosecond time resolution and tunable phase and polarization properties. One ofseveral challenges, however, is the requirement of coherent light sources that are tightly
localized in space. It is here that plasmonics offer an opportunity.
In the second part of the talk, we will combine plasmonics physics with concepts andtools borrowed from coherent control of molecular dynamics with two goals in mind.
One is to introduce new function into nanoplasmonics, including ultrafast elements andbroken symmetry elements. The second is to develop coherent nanoscale sources andapply them to coherent control of both molecular dynamics and electric transport in thenanoscale.
Several simple elements in what we envision developing
into coherently controlled nanoplasmonics areschematically illustrated in Fig. 1. The T-junction of Fig.
1A guides electromagnetic energy traveling down the leg
into one or the other of the two symmetry-equivalent armsof the junction. Figure 1B depicts a hybrid construct,which combines elements that provide local enhancementwith elements that provide long distance propagation inorder to minimize losses. The structural parameters of theconstruct are optimized using a genetic algorithm. Fig. 1C
depicts a plasmonic nanocrystal, developed to separate anincident plane wave into two frequency components and funnel each component in adifferent direction normal to the direction of incidence. To conclude the talk, we will
return to nanoelectronics, and illustrate the application of plasmonics to control oftransport in the nanoscale, with a view to ultrafast electric switches.

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3D4-3I

Hierarchical equations of motion for quantum dissipation and quantum
transport
YiJing Yan
Department of Chemistry, Hong Kong University of Science and Technology
Hefei National Laboratory for Physical Sciences at Microscale, University of
Science and Technology of China
In the mesoscopic world the nano-structured environment is not just of quantumin nature but also often nonperturbative and non-Markovian for its inﬂuence on thesystem of primary interest. In this talk, I will discuss the hierarchical equations of
motion (HEOM) approach [1–4] that can be considered as a fundamental formalism
in quantum mechanics of dissipative and open systems.
HEOM is formally equivalent to such as the Feynman-Vernon inﬂuence functionaland nonequilibrium many-body Green’s function formalisms [5], but numericallymore implementable. It provides a uniﬁed treatment of various decoherence andquantum transport processes. It renders also a uniﬁed view on various existing approximated theories, such as the quantum master equation and stochastic Liouvilleequation [6], and consequently, often further results in some simple but important
modiﬁcations to those conventional approximations [7].
I will also discuss about two recent developments, the best/minimum stochastic
environment basis set for optimal HEOM construction [8] and the eﬃcient on-the-ﬂy
numerical ﬁltering algorithm [9], that signiﬁcantly enhance the numerical tractabilityof the exact HEOM dynamics. Numerical results on the 2D spectrum of a model lightharvesting antenna system and the quantum transport through Anderson model
quantum dots system will be presented.

[1] Y. Tanimura, Phys. Rev. A 41, 6676 (1990); J. Phys. Soc. Jpn. 75, 082001 (2006).
[2] R. X. Xu, P. Cui, X. Q. Li, Y. Mo, and Y. J. Yan, J. Chem. Phys. 122, 041103 (2005).
[3] R. X. Xu and Y. J. Yan, Phys. Rev. E 75, 031107 (2007).
[4] J. S. Jin, X. Zheng, and Y. J. Yan, J. Chem. Phys. 128, 234703 (2008).
[5] X. Zheng, G. H. Chen, Y. Mo, S. K. Koo, H. Tian, C. Y. Yam, and Y. J. Yan, J.
Chem. Phys. 133, 114101 (2010).
[6] Q. Shi, L. P. Chen, G. J. Nan, R. X. Xu, and Y. J. Yan, J. Chem. Phys. 130, 164518(2009).
[7] R. X. Xu, B. L. Tian, J. Xu, Q. Shi, and Y. J. Yan, J. Chem. Phys. 131, 214111(2009).
[8] J. Hu, R. X. Xu, and Y. J. Yan, J. Chem. Phys. 133, 101106 (2010).
[9] Q. Shi, L. P. Chen, G. J. Nan, R. X. Xu, and Y. J. Yan, J. Chem. Phys. 130, 084105(2009).

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3D4-5C

Theoretical Study for Pseudo Degenerated Multi-electron
Systems and Applications for Real Systems
Mitsutaka Okumura,1,2 S. Yamanaka,1 T. Kawakami1, Y. Kitagawa1
1
Department of Chemistry,Graduate School of Science, Osaka University, Japan
2
Core Research for Environmental Science and Technology (CREST), Japan Scienceand Technology Agency, Japan
I. Introduction
Lately, organic and inorganic pseudo degenerated multi-electron systems havereceived much attention as nano-scale magnets, conductors and catalysts. The BS hybrid
density functional theory (DFT) method has been applied to a various pseudodegenerated multi-electron systems with considerable success. Our group proposed an
Approximately spin projection (AP) method and geometry optimization procedure basedon the AP method, namely the AP-opt method. Then, we apply the AP and AP-opt
method to the organic radical and metal containing systems.
II. Calculation results
As organic and inorganic pseudo degenerated multi-electron model systems,
p-NPNN and Cu(II) ion containing artificial DNA systems are investigated.
The E-phase p-NPNN was found to be the first organic bulk ferromagnet below 0.6
K. First-principle calculations of its sign and magnitude are crucial for theoreticalelucidation and understanding of the mechanism of its organic ferromagnetism. Here, inorder to determine the effective exchange integrals for all four phase of p-NPNN
crystals, hybrid density functional theory (HDFT) calculations are carried out for
p-NPNN clusters, whose geometries are taken from the X-ray structures of the four
different phase crystal. Moreover, Monte Carlo simulations are used to estimate its
transition temperatures (Tc). the ferromagnetic transition temperatures (Tc) calculatedusing the J values calculate by UB2LYP (0.35) are 0.7 K. The obtained ferromagnetictransition temperature is in good agreement with the experimental result. Therefore, it
could be concluded that the obtained results are in qualitatively agreement with theexperimental results.
The magnetic and other physical properties between Cu2+ ions coordinated by salen
̄base pairs (Cu2+̄DNA) are examined by using DFT calculations. The total energies ofthe HS and the BS LS states are degenerated but Jab values show weakanti-ferromagnetic couplings within the examined model structures. These results agreewith Metal̄DNA based on natural B-DNA. So, we can conclude that this artificial
Metal̄DNA system shows anti-ferromagnetic interaction, which is consistent with theexperimental result. The Jab values strongly depend on the ligand structure caused by en
but not backbones.
[1]Y. Nakanishi, Y. Kitagawa, M. Okumura et al., Polyhedron 28, 1945-1949 (2009).

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3D4-6C

Zero-field splitting tensors of arylnitrenes: A theoretical study
Kenji Sugisaki,1 Kazuo Toyota,1 Kazunobu Sato,1 Daisuke Shiomi,1Masahiro Kitagawa,2 Takeji Takui1
1
Department of Chemistry, Graduate School of Science, Osaka City University, Japan2
Department of System Innovation, Graduate School of Engineering Science,
Osaka University, Japan
Zero-field splitting (ZFS) is a separation of the electron spin multiplet sublevels of
atomic/molecular systems in the absence of an external magnetic field. Its origins are
spin–spin dipolar (SS) and spin–orbit (SO) couplings. Reliable first principle
calculations of ZFS tensors (D tensors) are a long-standing issue in the field of electron
spin science from the theoretical side. Recently, we have proposed a hybrid
CASSCF/MRMP2 approach to quantitative calculations of the spin–orbit term of the D
tensor (DSO tensor) [1–3]. This approach uses spin–orbit coupling matrices computed at
the CASSCF level and MRMP2 energy difference in the sum-over-states formula, toefficiently eliminate errors in the DSO tensor arising from inaccurate CASSCF energies
in the conventional SOS-CASSCF approach. In this work the hybrid approach is applied
to spin-triplet arylnitrenes (Figure 1), focusing on the aryl ring size and topologicaleffects on the D tensor.

Figure 1. Target molecules

The equilibrium geometry is optimized at the UB3LYP/6-31G* level. The DSO tensor
calculations are carried out by the hybrid CASSCF/MRMP2 method with the cc-pVDZ
basis set. The spin–spin part of the D tensor (DSS tensor) is calculated by using
McWeeny–Mizuno’s equation with RO-HCTH/407/EPR-II spin densities [2,3].
The theoretical and experimental ZFS parameters D (D = DZZ – (DXX + DYY)/2) aresummarized in Table 1. In all nitrenes under study, the spin–orbit contribution to Damounts to about 10%. Except for 6, the DSS+SO value reproduces the experimental D
one within 10% of error. Table 1. Theoretical and experimental D values.
Errors in the calculations Molecule DSS/cm−1 DSO/cm−1 DSS+SO/cm−1 |D(Exptl.)|/cm−1
are possibly from the DSS
1+0.8820 +0.1118+0.9938
0.99782+0.6642+0.0809+0.7451
0.793
term. Origins of the errors
3+0.7925 +0.0965+0.8890
0.925
in the putative DFT-based
4+0.5254 +0.0682+0.59360.6625SS
D tensor calculation will5+0.6451 +0.0838+0.72890.7779also be discussed.
6+0.3476 +0.0487+0.39630.47[1] Sugisaki, K. et al. Chem. Phys. Lett. 2009, 477, 369–373.
[2] Sugisaki, K. et al. ChemPhysChem 2010, 11, 3146–3151.
[3] Sugisaki, K. et al. Phys. Chem. Chem. Phys. 2011, 13, 6970–6980.

95

3D4-7CInteractions with electromagnetic ﬁelds: frequency-dependent
magnetizability and electric permittivity
Marco Anelli, Dan Jonsson, Kenneth Ruud
Centre for Theoretical and Computational Chemistry, Department of Chemistry,
University of Tromsø, 9037 Tromsø, Norway
Materials with a negative index of refraction are substances in which either
one or both of the permittivity and the permeability of the medium is nega- tive.
Whereas the permittivity of the medium is well deﬁned and related to the frequencydependent polarizability, the dispersion behaviour of the permeabil- ity is not as welldeﬁned. The relation between the macroscopic permeability and the microscopic
quantity describing the interaction with the magnetic com- ponent of the electromagnetic ﬁeld, the frequency-dependent magnetizability, is in contrast poorly understood. Indeed, even the deﬁnition of the frequency- dependent magnetizability
appear unsatisfactory.
A theory for the frequency-dependent magnetizability has been presented by Raaband de Lange [1], and these authors have also considered the frequency- dependent permeability [2]. However, the expression derived for the frequency- dependent
magnetizability is based on a number of assumptions, making the theory somewhat
unsatisfactory.
A macroscopic analysis of the interaction between matter and electromagnetic ﬁelds
using multipole theory leads to origin-dependent expression of the material constants. Since material constants are observable quantities, we expect that multipole
theory, which correctly describes several optical phenomena, would provide originindependent expression of them. Thus origin-independent deﬁnitions of the material
constants, which describes the response of the matter to an external electromagnetic
perturbation, should be derived.
In this talk, we will discuss our recent analysis of the frequency-dependent magnetizability, and propose a new way of deriving the frequency-dependent permittivity,
inverse permeability and magnetizability starting from an analysis of the currentcurrent response function and of the scattering amplitude.

References[1] R. E. Raab and O. L. de Lange. Mol. Phys. 104, 1925 (2006)[2] R. E. Raab and O. L. de Lange. Proc. Royal Soc. 461, 595 (2005)

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Novel Polarization-Phase Selective (PPS) Models: Probing and Imaging Unusual Electronic Behavior
Kresimir Rupnik, Department of Chemistry, LSU, Baton Rouge LA 70803 , USA
We are developing novel PPS models with broad applications from ultrafast tunneling electron(wavefunction) probing and imaging in atoms and molecules (New J. Phys.) to the electron-protontransfer studies associated with metal clusters and substrates in proteins, enzymes and bio-hybrids(JBIC, JACS). We show that the models provide a very good insight into the drivers of the key redox
electrons. Indeed, models of spin-coupling mechanisms and energy levels clearly indicate some unusualelectronic behavior driven by the specific clusters and bio-ligands. They also provide theoreticalframework for related electron properties and image morphing. The results of PPS modeling are now
also confirmed by PPS structural characterization at NHMF Laboratory using very high magnetic fields.
We expect that the new Split-Florida helix will facilitate these efforts.

97