Abstracts of Invitedand Contributed Talks, Sep. 5139

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Structure and spectroscopy of the hydrated electron: Polarizable
QM/MM simulations
John M. Herbert,1 Leif D. Jacobson
1
The Ohio State University, Columbus, OH, USA
A new one-electron model for ﬁnite water cluster anions, (H2 O)−
n , and the bulk−
aqueous electron, eaq , has been developed, based upon a reconsideration of theelectron–water pseudopotential using ab initio quantum chemistry. The new model
employs a polarizable force ﬁeld for water, and both water–water polarization andelectron–water polarization interactions are treated in a fully self-consistent manner.
Although not ﬁt directly to any observables, the model is quite accurate (as compared to various ab initio benchmarks) for small and medium-size (H2 O)−
n clusters,
and also aﬀords reasonable estimates of known experimental observables for e−aq inbulk water. We consider this to be the ﬁrst hydrated-electron model that achieves
at least semi-quantitative accuracy all the way from n = 2 to n = ∞. In the bulk,
we ﬁnd that self-consistent treatment of many-body polarization is qualitatively
necessary in order to explain the gross features of the optical absorption spectrumof e−
aq . In particular, the new model predicts the existence of polarization-bound,
quasi-continuum states that are absent in non-polarizable models. These states are
responsible for the “blue tails” that are consistently observed in optical spectraof e−aq , but which have not previously been seen in simulations. The implicationsof these results will be discussed, both in terms of our understanding of hydrated
electrons and also in terms of future development of QM/MM methodology.

140

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Effects of intermolecular electron density modulations
on the Terahertz spectral intensity of liquid water
Hajime Torii
Department of Chemistry, School of Education, Shizuoka University, Japan
I. Introduction
The vibrational spectra of liquid water have been measured in a wide frequency
range, and their band assignments (with regard to the frequency positions) are wellknown. However, understanding on the whole spectral profiles (especially with regard
to the intensities) is rather far from complete, although it is essential for detecting
structural and dynamical properties of water and aqueous solutions.
One problem concerning this is the intensity of the far-IR band observed at ~200
-1
cm (~6 THz). This band is known to arise from the molecular translation mode, butmolecular translations of a neutral molecule do not give rise to IR intensity without
intermolecular interactions. It has been pointed out that the IR intensity arising fromintramolecular polarizations induced by intermolecular electrostatic (such as
dipole-induced dipole) interactions is not sufficiently strong.
In a recent study [1], it has been demonstrated that the IR intensity enhancement of
the OH stretching mode upon hydrogen-bond formation is mainly arising from theintermolecular electron density modulation (called intermolecular charge flux). A
similar analysis is carried out here for the molecular translation mode, to show that inthis case also the intermolecular charge flux is the main source of the IR intensity.
II. Computational Procedure, Results, and Discussion
The electron density derivatives wU(el) r /wX][m], where X][m] (] = x, y, or z) stands forthe translation motion of the mth molecule in the x, y, or z direction, were analyzed for thewater molecules in the (water)28 and (water)30 clusters calculated at the B3LYP/
6-31+G(2df,p) level. The result shows that significant amplitude of intermolecularcharge flux is induced between the hydrogen-bonded water molecules by a moleculartranslation mode, and the amplitude is about 0.4 times of that induced by the OH
stretching mode.
The effect of the charge flux is included in the spectral simulations of liquid water
based on classical MD by using a formula based on dipole derivatives rather than dipole
moments themselves. It is shown that, by including four intensity parameters [wPx/wXx =1.91 D Å-1, wPy/wXy = –1.76 D Å-1, and wPy/w:x = –wPx/w:y = 1.57 D (rad-1)] per molecule,the presence of the band at ~200 cm-1 is well reproduced.
These results mean that the molecular translational and electronic motions arestrongly coupled, and this coupling is observable through the ~200 cm-1 far-IR band.
[1] H. Torii, J. Phys. Chem. B 114 (2010) 13403.

141

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Theoretical Analysis on the Effect of Intramolecular Hydrogen
Bonding on the Overtone Spectra in Simple 1-n Alkanediols
Kaito Takahashi1
1
Institute of Atomic and Molecular Sciences, Academia Sinica Taipei, Taiwan
I. Introduction
For the OH stretching vibration of a hydrogen bonded OH bond, it is well known thatthe fundamental peak shifts to lower energy, gains intensity and broadens compared to thefree OH bond. Several studies have been performed on fundamental spectrums tounderstand the relationship between the hydrogen bonding strength versus the peak shift,intensity as well as the broadening. However studies for overtones are scarce. Recently,
Kjaergaared et al. have reported the OH stretching overtone spectra of three simple 1-nalkanediols: ethylene glycol (EG), propanediol (PD), and butanediol (BD). In thesemolecules, the most stable conformer consists of an intramolecular hydrogen bond inwhich one OH donates a hydrogen while the other OH accepts it.[1,2] Interestingly at
the v=4 excitation, while the OH peak corresponding the hydrogen bonded donor OH for
EG was observed, the one for BD was not. This disappearance was attributed to thedifference in intramolecular vibrational energy relaxation, but a clear explanation was notpresented.
II. Results and Discussion
In this presentation we present calculated peak positions, intensities and peak widths
for the OH stretching vibration of the donor (hydrogen bonded) and acceptor (free) OH in
three 1-n alkanediols reported by Kjaergaard et al. We performed vibrational
calculations using the potential energy surface and dipole moment function calculated by
the B3LYP, MPW1BK91, MP2, and CCSD(T) methods. To understand the energy flowfrom the vibrationally excited state, we performed B3LYP/6-31+G(d,p) based direct
dynamics trajectory calculations to obtain the classical survival probability in the excited
OH bonds. It was found that as Kjaergaard et al. had predicted, the OH energy of thedonor OH bond decayed at a rate ten times faster in BD than in EG. This difference will
result in a peak that is ten times broader for the BD donor OH, thereby making it hard to
experimentally observe. Interestingly, it was calculated that the decay rate of the excited
acceptor OH bond decreased when increasing the carbon chain. This feature is incontradiction with the basic assumption that the larger the molecule the faster the decayof the vibrationally excited state. Analysis on the energy flow and the intramolecularvibrational energy dynamics in these diol systems will also be presented.
[1] D. L. Howard, P. Jorgensen, and H. G. Kjaergaard, J. Am. Chem. Soc. 127, 17096(2005).
[2] D. L. Howard, H. G. Kjaergaard J Phys Chem A 11-, 10245- (2006).

142

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Revealing mysteries of the water hexamer
Urszula Góra,1,2 Wojciech Cencek,2 Rafał Podeszwa,1,2 Krzysztof Szalewicz2
1
Institute of Chemistry, University of Silesia, Katowice, Poland
2
Department of Physics and Astronomy, University of Delaware,
Newark, DE, USA
Water has been known for its untypical behavior for centuries, as the result of thatknowledge it has been extensively studied. Scientists still have an incomplete understanding of its properties. The difﬁculty in obtaining a good description of water structure
is caused by the hydrogen bond based structure existing in this liquid. Experiments andtheory are rather convincing that the water trimer, tetramer and pentamer have cyclic minimum energy structures. For larger clusters, the structure is expected to be different andthe hexamer minimum structure is at the spotlight of the water research.
After numerous experiments and theoretical modeling, the “cage” and “prism” structures of the water hexamer are found to be the lowest energy minimum conﬁgurations.
But there is still no deﬁnitive answer which of the two is the global minimum. The reason
for this uncertainty are very small energy differences between the structures and, hence,a very high accuracy is required for modeling. Several effects has to be accounted for,including high-level electronic correlation, many-body effects, monomer ﬂexibilities, andzero-point energies.
We present extensive theoretical results for water hexamer clusters. The accurate energies were obtained with many-body expansion, i.e., by calculating various many-bodycomponents separately. With such an approach, very signiﬁcant computational savings
can be achieved that allow for applying higher level of theory than the standard supermolecular approach. We have also developed a model for calculating other effects present
in the hexamer structures. These two approaches enable us to provide an answer to thewater hexamer global minimum mystery.

143

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On the Development of A First-Principle Based Multi-model Method
to Study Aqueous Systems: from Clusters, Interfaces to Condensed
Phases
Jer-Lai Kuo
Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
Water is an important substance for life and many of its intriguing properties (magic
number water clusters, low temperature amorphous phases and high-pressure phases ofice) are related to the flexibility of hydrogen bonding (H-bonding) to form various
structural features. One of the common themes for the above-mentioned subjects is therough energy landscape of aqueous systems that hinder a straightforward way for astructural determination from first-principle methods. Our recent effort in developing afirst-principle based multi-model methods1 is to integrate the efficiency of empiricalmodels and the accuracy of first-principle methods to study various aqueous systems
ranging from large-sized water clusters (n ~ 100), water interfaces, to various condensed
phases (low temperature amorphous phases and proton ordering process). For clusters,
we can benchmark the commonly used DFT methods against other high-level quantum
chemistry methods and in condensed phases, we also seek for comparisons withquantum Monte Carlo methods. In this talk, we will discuss some of the successes andfailures2 we have encounter and how we utilize the information learnt to move toward a
consistent picture in simulating aqueous systems.
[1] Q. C. Nguyen, Y-S Ong, and J-L Kuo, “A multi-scale approach to study thermal
behavior of protonated water clusters”, J. Chem. Theory and Comp. 5, 2629 (2009)[2] X. F. Fan, D. Bing, J. Zhang, Z. X. Shen, and J-L Kuo, “Predicting the hydrogenbond ordered structures of ice Ih, II, III, VI and ice VII: DFT methods with localizedbased set”, Comp. Mater. Sci. 49, S170 (2010)144

5A2-1I

Nucleation and growth of calcium carbonate: how non-classical is it?
Raffaella Demichelis,1 Paolo Raiteri,1 Julian D. Gale,1, David Quigley,2 Denis Gebauer3
1
Department of Chemistry, Curtin University, Perth, Australia
2
Centre for Scientific Computing/Department of Physics, University of Warwick, UK
3
Department of Chemistry, Universität Konstanz, Germany
The interface between calcium carbonate and water is one of the most fascinating“hard-soft” interfaces, being of significance to mineralogy and biomineralization
processes. CaCO3 is known to form an amorphous precursor (ACC) that cansubsequently evolve to produce crystalline polymorphs. To add to the complexity, theACC precursor is not a single well-defined material as it can vary in water content andhave polyamorphic characteristics [1]. Furthermore, it has been demonstrated that stablepre-nucleation species also exist [2], but their relationship to ACC remains unknown.
In this presentation we will explore the use of computer simulation methods to try
to unravel the complexities of the nucleation and growth processes for calcium
carbonate. Central to this is the development of a force field that is accurately calibrated
against experimental free energies [3] since failure to do so can result in qualitative
errors for interfacial properties. Based on this we have explored the stability of ACC
versus crystalline nanoparticles while accounting for the variable water content in theamorphous structure [4]. In the light of this, and new experimental results, we propose amodel to explain the non-classical aspects of the nucleation mechanisms of calcium
carbonate, the origins for which can be traced back to the interfacial properties.

Table 1. ISTCPCP ccongressCP
ongrres
ess ssites.
ites
it
es.
Figure 1: Montage showing from left to right, the free energy of ion pairing, thehydration of ACC and the consequences for nucleation and growth.
[1] D. Gebauer et al., Angew. Chem. Int. Ed., 49, 8889 (2010)[2] D. Gebauer et al., Science, 322, 1819 (2008)[3] P. Raiteri et al., J. Phys. Chem. C, 114, 5997 (2010)[4] P. Raiteri and J.D. Gale, J. Am. Chem. Soc., 132, 17623 (2010)145

5A2-3C

Novel ZIFs material as molecular separator studied bycomputer-aided modeling approaches
Oraphan Saengsawang,1 Tatiya Chokbunpiam,1,2 Suntharee Phuangjuumpee,1,2Siegfried Fritzsche,3 Supot Hannongbua1
1
Computational Chemistry Unit Cell (CCUC), Chulalongkorn University, Thailand
2
Petrochemical Science Program, Chulalongkorn University, Thailand
3
Institut für Theoretische Physik, Universität Leipzig, Germany
Zeolite imidazolate frameworks (ZIFs), a new class of porous crystalline material,
have recently been gained the attention of the scientists from various fields. Besides theunique properties such as high thermal and chemical stabilities, one most benefit is thatthe large variety of ZIFs can be achieved by virtue of flexibility with the various linker
and the metal types. As a result, during 5 years, over 90 new ZIFs structures [1,2] havebeen reported and in which
they were found to be thepotential materials in gas
adsorption and separation
applications. However, theinformation on atomic levelin terms of gas binding sites,
adsorption and diffusion
mechanisms describing the
Figure 1. Schematic of building units in ZIF-8 and ZIF-78.
basic
properties
ofadsorbate/adsorbent system are still unclear. This becomes the main goal of this work
aimed to better understanding of the above mentioned properties using computermodeling approaches. Such kind of computer aided structural design is commonly used
to seek for the future promising materials in gas adsorption and separation processes.
Using the DFT calculations together with MD simulations, the adsorption sites of
the three gases, i.e., H2, CO2 and CH4 were investigated in which the imidazolate (IM)linker group was found to be the favorable adsorption site of the three gases. Moreover,the dynamic properties such as the adsorption isotherm and self-diffusivities (DS) were
calculated. Consequently, the membrane selectivity was calculated and compared to thatobtained experimentally [2]. The obtained DS of H2 in ZIF-8 is in the order of 10-8 m2 s-1
while those of the CO2 and CH4 are 10-10 and 10-11, respectively. This indicates theselectivity of ZIF-8 in separation process. In addition, the calculated data for the ZIF-78
also indicate its ability as a promising candidate in separation of CO2 in gas mixture.
[1] Phan, A.; Doonan, C.J.; Uribe-Romo, F.J.; Knobler, C.B.; O’Keeffe, M.; Yaghi, O.M. Acc.
Chem. Res. 2010, 43, 58.
[2] Banerjee, R.; Furukawa, H.; Britt, D.; Knobler, C.; O’Keeffe, M.; Yaghi, O.M. J. Am. Chem.
Soc. 2009, 131, 3875.

146

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Quantum dynamics of photoprocesses in extended molecularsystems: coherence and correlations at the nanoscale
I. Burghardt1, E. R. Bittner2 and H. Tamura3
1

Institute of Physical and Theoretical Chemistry, Frankfurt University, Germany
2
Department of Chemistry, University of Houston, Houston, Texas, USA
3
Advanced Institute for Materials Research, Tohoku University, Sendai, Japan

The photophysics of extended systems like conjugated polymers or molecularaggregates is characterized on the one hand by the properties of the molecular building
blocks and on the other hand by the delocalized nature of the electronic excitations, i.e.,
the formation of excitonic states. The dynamical phenomena induced by photoexcitation
therefore involve an interplay of site-site interactions entailing excitation energy transfer(EET) and charge transfer (CT), and on-site vibronic coupling and trapping effects. Dueto the prominent role of electron-phonon coupling, often accompanied by coherent
dynamical effects on ultrafast time scales, an explicit quantum dynamical treatment isgenerally required. Our approach combines parametrized Hamiltonians, based onsemiempirical and ab initio calculations, with accurate quantum dynamics simulations
using the multiconfiguration time-dependent Hartree (MCTDH) method [1]. In addition,
we employ transformation techniques [2,3] by which a relevant set of effective modes
are constructed that allow for a hierarchical description of non-adiabatic dynamics inhigh-dimensional systems. Against this background, the talk will focus on coherent
excitation transfer driven by torsional dynamics in poly-phenylene-vinylene (PPV) typesystems [4], and on ultrafast exciton dissociation at polymer heterojunctions influorene-based TFB:F8BT blends [3] as well as at oligothiophene-fullerene junctions[5]. Particular consideration is given to the role of excitonic coherence vs. static anddynamic conformational disorder.
References[1] G. A. Worth, H.-D. Meyer, H. Köppel, L. S. Cederbaum, and I. Burghardt, Int. Rev.
Phys. Chem. 27, 569 (2008).
[2] R. Martinazzo, B. Vacchini, K. H. Hughes, and I. Burghardt, J. Chem. Phys.
(Comm.) 134, 011101 (2011).
[3] H. Tamura, J. G. S. Ramon, E. R. Bittner, and I. Burghardt, Phys. Rev. Lett. 100,
107402 (2008); I. Burghardt, E. R. Bittner, H. Tamura, A. Pereverzev, and J. G. S.
Ramon, in: Energy Transfer Dynamics in Biomaterial Systems, Edited by I. Burghardt,
D. A. Micha, E. R. Bittner (Springer, Heidelberg, 2009), Chem. Phys. Ser. 93, 183.
[4] F. Sterpone, R. Martinazzo, A. N. Panda, and I. Burghardt, Z. Phys. Chem., in press.
[5] H. Tamura, I. Burghardt, and M. Tsukada, J. Phys. Chem. C, in press.

147

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Quantum dynamical treatment of systems with many degrees of
freedom using time-dependent multiconfiguration methods
Michael Thoss,1 Haobin Wang2
1
Institute of Theoretical Physics and Interdisciplinary Center for Molecular Materials,
University of Erlangen, Germany
2
Department of Chemistry and Biochemistry, MSC 3C,
New Mexico State University, Las Cruces, New Mexico 88003, USA

The accurate theoretical treatment and simulation of quantum dynamical processes
in many-body systems is a central issue in chemical and condensed matter physics. In
this talk, the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH)
method [1] is discussed as an example of an approach that allows an accurate
description of quantum dynamics in systems with many degrees of freedom. The
ML-MCTDH method is a variational basis-set approach, which uses amulticonfiguration expansion of the wavefunction employing a multilayer
representation and time-dependent basis functions. It extends the original MCTDH
method [2] to significantly larger and more complex systems. Employing the second
quantization representation of Fock space, the ML-MCTDH method has recently been
extended to allow the treatment of indistinguishable particles [3,4]. The performance ofthe ML-MCTDH method is illustrated by several application to models of charge andenergy transport in molecular systems in the condensed phase [4,5,6,7].
[1] H. Wang and M. Thoss, J. Chem. Phys. 119, 1289 (2003).
[2] H.-D. Meyer, U. Manthe, L.S. Cederbaum, Chem. Phys. Lett. 165 , 73 (1990); H.-D.
Meyer, F. Gatti. G.A. Worth (Eds.), Multidimensional Quantum Dynamics: MCTDH
Theory and Applications, Wiley-VCH, Weilheim, 2009.
[3] H. Wang and M. Thoss, J. Chem. Phys. 131, 024114 (2009).
[4] H. Wang and M. Thoss, arXiv:1103.4945 (2011).
[5] I. Craig, M.Thoss, and H. Wang, J. Chem. Phys. 127, 133503 (2007).
[6] K.A. Velizhanin, H. Wang, and M. Thoss, Chem.Phys. Lett. 460, 325 (2008).
[7] J. Li, I. Kondov, H. Wang, and M. Thoss, J. Phys. Chem. C 114, 18481 (2010).

148

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Quantum Dynamics Simulation in Balanced Resolution
Representation in Time-Space
Hideo Sekino,1 Shinji Hamada1
1
Toyohashi University of Technology, JapanI.

Abstract

Quantum dynamics can be simulated using classical fluid formulation. First, we
present a classical fluid dynamics formulation of Schr·dinger equation on Multiwavelet
Wavelet (MW) spectral space. While the MW formalism is powerful in very accurate
evaluation of near equilibrium properties such as electric polarizability, it reveals aserious problem of instability in solving Time-dependent equations. We find that the
instability can be removed using elaborated techniques introducing Cayley algorithm
for time progression operator [1] or other types of wavelet basis functions such as
Mayer wavelet [2]. However, we need to introduce a balanced resolution representationin time domain as well as space domain for simper solution of the problem. We present
a very simple solution of time-dependent Schr·dinger equation in such balanced
representation on even grid time-space using local unitary transformation consideringinternal co-ordinate freedoms.

Solution of 2Dimensional Time Dependent Schr·dinger equation[1] Shinji Hamada and Hideo Sekino, Int. J. Quant. Chem.(Cano Issue)
111,7 (2011)1480[2] Hideo Sekino and Shinji Hamada, proceedings ICWAPR 2011149

5B1-6C

Semiclassical molecular dynamics including spin-orbit coupling andelectric ﬁelds
Philipp Marquetand,1 Martin Richter,1 Jesús González-Vázquez,1,2 Ignacio Sola,2Leticia González1
1
Friedrich-Schiller-Universität Jena, Institut für Physikalische Chemie,
Helmholtzweg 4, 07743 Jena, Germany
2
Departamento de Quı́mica Fı́sica I, Universidad Complutense, 28040 Madrid,
Spain
I. Introduction
Research in the area of chemical reaction control and analysis is attaining progressively shorter timescales. We have reached the femto- and attosecond regime,
where traditional approaches to manipulate larger and larger systems are reaching
their limits. New techniques are necessary to study the interaction of electrons andnuclei with strong laser ﬁelds in multiple molecular states including also relativistic
eﬀects.
II. The SHARC method
We have developed an ab initio molecular dynamics (MD) code including arbitrary coupling as a general tool for studying excited-state processes. Up to now, spinorbit couplings are not included in standard ab initio MD packages and the description of laser interactions in MD is in its infancy. In our new method, termed SHARC(surface-hopping-in-the-adiabatic-representation-including-arbitrary-couplings), we
treat all couplings on the same footing and incorporate them into the system’s Hamiltonian via a unitary transformation [1]. In this adiabatic representation, transitions
are treated by a variation of the surface hopping technique.
III. Numerical applications
In order to test the method, IBr is taken as a model system, where spin-orbit
coupling plays an important role for the dissociation dynamics. Additionally, theinﬂuence of laser control via the non-resonant dynamic Stark eﬀect is investigated [2].
As MD allows for the handling of many atoms, the photo-induced dynamics including
the interplay between triplet and singlet states of large molecular systems will beaccessible. Further applications of the SHARC method to complex systems include
the relaxation of DNA nucleobases via triplet states after photoexcitation.
[1] M. Richter, P. Marquetand, J. González-Vázquez, I. Sola, L. González, J. Chem.
Theory Comput., accepted.
[2] P. Marquetand, M. Richter, J. González-Vázquez, I. Sola, L. González, Faraday
Discuss., submitted.

150

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151

5C1-1I

The MP2-F12 method in the Turbomole program package
Rafal A. Bachorz,1 Florian A. Bischoﬀ,2 Andreas Glöß,3 Christof Hättig,4Sebastian Höfener,5 Wim Klopper,1 David P. Tew6
1
Theoretical Chemistry Group, Karlsruhe Institute of Technology, Germany
2
Department of Chemistry, Virginia Tech, Blacksburg, U.S.A.
3
Laboratory of Physical Chemistry, ETH Hönggerberg, Zurich, Switzerland
4
Chair of Theoretical Chemistry, Ruhr-University Bochum, Germany
5
Division of Theoretical Chemistry, VU University Amsterdam, The Netherlands
6
School of Chemisry, University of Bristol, United Kingdom
I. Introduction
The implementation of the explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12) method [1,2] in the Turbomole program package [2,3] ispresented and discussed. A brief introduction to explicitly correlated coupled-cluster
methods, as implemented in Turbomole, is also given [4].
II. MP2-F12 theory
Turbomole’s MP2-F12 implementation makes use of density ﬁtting, which greatly
reduces the prefactor for integral evaluation. Methods are available for the treatmentof ground states of open- and closed-shell atoms and molecules, using unrestricted
as well as restricted (open-shell) Hartree–Fock reference determinants [5]. The implementation has been parallelized.
III. Performance assessment
The performance of the Turbomole implementation is assessed by performing
calculations on the molecule ethylenedioxytetrafulvalene, on a cluster model for theadsorption of methanol on the zeolite H-ZSM-5, and on the (antirheumatic) drugs
leﬂunomide, prednisone, and methotrexate.
Basis sets of varying size (from aug-cc-pVDZ to aug-cc-pV5Z) are used, including
correlation-consistent basis sets optimized for explicitly correlated calculations. The
largest calculation was performed in a basis set with 3652 basis functions.
[1] W. Klopper, F.R. Manby, S. Ten-no, and E.F. Valeev, Int. Rev. Phys. Chem.
2006, 25, 427–468.
[2] R.A. Bachorz, F.A. Bischoﬀ, A. Glöß, C. Hättig, S. Höfener, W. Klopper, and
D.P. Tew, J. Comput. Chem. 2011 (in press).
[3] Turbomole V6.3, a development of Universität Karlsruhe (TH) and Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, since 2007.
See http://www.turbomole.com. For information on license schemes, prices, andhow to order the Turbomole program package, please contact COSMOlogic GmbH& Co. KG in Leverkusen, Germany, via turbomole@cosmologic.de.
[4] C. Hättig, W. Klopper, A. Köhn, and D.P. Tew, Chem. Rev. (in preparation).
[5] D.P. Tew and W. Klopper, Mol. Phys. 2010, 108, 315–325.

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5C1-3I

Local explicitly correlated MP2 theory using pair natural orbitals
David P. Tew
School of Chemistry, University of Bristol,
Bristol BS8 1TS, United Kingdom
Benjamin Helmich and Christof Hättig
Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany

Abstract
Localization in the framework of pair natural orbitals is explored at the explicitly correlated
MP2-F12 level of theory. Our results demonstrate that very small virtual active spaces, 20-50
orbitals per signiﬁcant pair, return more than 98% of the basis set limit correlation energy. The
extension of pair natural orbital ideas to the complementary auxiliary basis set for the RI also
aﬀords enormous truncation of the auxiliary orbital space without signiﬁcant loss of accuracy.

153

5C1-5C

Resolving Coulomb operator
A new approach toward faster QM methods
Taweetham Limpanuparb and Peter M. W. Gill
Research School of Chemistry, Australian National University, Australia
Two-particle interaction described by Coulomb operators
rij−1 ≡ |ri − rj |−1(1)

is the most diﬃcult part of non-relativistic Schrödinger equation for chemical systems. We replace these troublesome terms by products of one-particle function
rij−1 ≈K
φk (ri )φk (rj )

(2)

k=1

and obtain the reduced-rank Schrödinger equation (RRSE). In analogous to resolution of the identity and Cholesky decomposition, this new approach allows us toexpand Coulomb matrix elements into products of auxiliary integrals.
−1|b) ≈(a|r12K
(a|φk )(φk |b).

(3)

k=1

This opens possibilities to signiﬁcantly reduce time and memory complexity of many
QM methods. We ﬁnd that φk proportional to product of a spherical Bessel function
and a spherical harmonics is the one well-suited for computational purposes.
[1] S. A. Varganov, A. T. B. Gilbert, E. Deplazes, and P. M. W. Gill, J. Chem.
Phys. 128, 201104 (2008).
[2] P. M. W. Gill and A. T. B. Gilbert, Chem. Phys. 356, 86 (2009).
[3] T. Limpanuparb and P. M. W. Gill, Phys. Chem. Chem. Phys. 11, 9176 (2009).
[4] T. Limpanuparb, A. T. B. Gilbert, and P. M. W. Gil, J. Chem. Theory Comput.
7, 830 (2011)[5] T. Limpanuparb and P. M. W. Gil, J. Chem. Theory Comput. (in preparation)154

5C1-6C

New three-body correlation expression applied to solid surface
Quantum Monte Carlo simulation.
Philip E. Hoggan

LASMEA, UMR 6602 CNRS.
Pascal institute of Physics
24 avenue des Landais,
BP 80026.
63171 AUBIERE Cedex, FRANCE.
Abstract
This paper presents a near analytical expression for the two-electron and nucleus three-bodycorrelation terms that are essential, yet so time consuming to optimise in the variational stepof Quantum Monte Carlo simulations used to determine free-parameters in the Jastrow factor.
The expression is devised using co-ordinate systems in six-dimensional space, previously usedby Fano and Rao.
The quasi-exact expression obtained is applied in a series of solid state simulations ofmolecules adsorbed at solid surfaces.
The simulations are carried out with the CASINO code due to Needs et al running on a
Bluegene parallel system on more than 10000 processors.
The Fixed node error in the Diﬀusion monte carlo step is limited by expanding the trial
wave-function in a Coulomb Sturmian basis in co-ordinate space and plane waves in the ﬁrst
Brillouin zone of Fourier transform space.

Keywords: Coulomb Sturmian basis, nodal structure, Fourier Transform, ab initio quantum
chemistry.

1555C2-1I

Strong Correlations from Constrained Mean-Field Approaches
Gustavo E. Scuseria
Department of Chemistry
Rice University
Houston, Texas, USA
One of the fundamental challenges in modern quantum chemistry is the efficientincorporation of strong correlations at low computational cost. Localizing theexchange hole and using symmetry broken orbitals in DFT are standard tricks
towards achieving this goal. However, this is insufficient and unpleasant fromthe perspective that it goes hand-in-hand with the introduction of self-interaction
error in an uncontrolled manner, one that has proven extremely difficult toovercome. Our work has recently focused on incorporating strong correlations
into mean-field approaches via selective symmetry breaking followed by arestoration step. Constrained-pairing mean-field theory (CPMFT) [1] introduces
pairings between electrons in an active space and yields a two-particle density
matrix (2pdm) ansatz that exclusively describes strong correlations. The model
breaks electron number conservation which is correct only on average but
expectation values calculated from its effective 2pdm contain no particle number
fluctuations. On the other hand, Constrained Unrestricted Hartree-Fock (CUHF)
theory [2,3] limits spin symmetry breaking to an active space. Based on it, wehave developed a novel approach for obtaining high-spin ROHF wave functions.
If the active space is properly chosen, CUHF greatly benefits from a controlled
broken-symmetry effect while avoiding the massive spin contamination of
traditional UHF. Spin projection operators can be applied to restore symmetry
and obtain multireference wave functions with moderate computational cost.
Singlet-triplet energy splittings show that our scheme outperforms fully
unrestricted methods. This constrained approach can be used in spin density
functional theory with similar favorable effects.
1. T. Tsuchimochi, T. M. Henderson, G. E. Scuseria, and A. Savin, J. Chem.
Phys. 133, 134108 (2010).
2. T. Tsuchimochi and G. E. Scuseria, J. Chem. Phys. 133, 141102 (2010).
3. T. Tsuchimochi and G. E. Scuseria, J. Chem. Phys. 134, 064101 (2011).

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