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7 Nov 2010

Volume 133, Issue 17, Articles (17xxxx)

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J. Chem. Phys. 133, 174502 (2010); http://dx.doi.org/10.1063/1.3493456 (7 pages)

Måns Elenius, Tomas Oppelstrup, and Mikhail Dzugutov
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Communication: Rotational g-factor and spin-rotation constant of CH+

Stephan P. A. Sauer

J. Chem. Phys. 133, 171101 (2010); http://dx.doi.org/10.1063/1.3497309 (4 pages) | Cited 2 times

Online Publication Date: 5 November 2010

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The rotational g-factor and spin-rotation constants of the methylidynium ion CH+ have been calculated for the first time with a large multiconfigurational self-consistent field wave function and at the coupled-cluster singles and doubles level augmented by a perturbative triples correction. The results for an equilibrium internuclear distance as well as for the v = 0, J = 1 vibration-rotational state are presented.
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33.20.Wr Vibronic, rovibronic, and rotation-electron-spin interactions
33.20.Vq Vibration-rotation analysis
31.15.bw Coupled-cluster theory
31.15.xr Self-consistent-field methods
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On Koopmans’ theorem in density functional theory

Takao Tsuneda, Jong-Won Song, Satoshi Suzuki, and Kimihiko Hirao

J. Chem. Phys. 133, 174101 (2010); http://dx.doi.org/10.1063/1.3491272 (9 pages) | Cited 13 times

Online Publication Date: 1 November 2010

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This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms.
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31.15.ec Hohenberg-Kohn theorem and formal mathematical properties, completeness theorems
32.50.+d Fluorescence, phosphorescence (including quenching)
34.20.Cf Interatomic potentials and forces
31.15.eg Exchange-correlation functionals (in current density functional theory)
31.15.V- Electron correlation calculations for atoms, ions and molecules
31.15.bw Coupled-cluster theory

Segmented contracted basis sets for one- and two-component Dirac–Fock effective core potentials

Florian Weigend and Alexander Baldes

J. Chem. Phys. 133, 174102 (2010); http://dx.doi.org/10.1063/1.3495681 (10 pages) | Cited 5 times

Online Publication Date: 1 November 2010

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Segmented contracted basis sets for 4d, 5d, 5s, and 6s elements of split (double zeta) valence to quadruple zeta valence quality optimized for Dirac–Fock effective core potentials (ECPs) are presented. They were obtained from previous bases optimized for Wood–Boring ECPs by comparably small modifications and reoptimizations. Additionally extensions for two-component self-consistent-field treatments accounting for spin-orbit (SO) coupling were designed and optimized. Reliability for chemical applications was assessed by comparing results to those obtained with a very large (19s16p17d7f6g) reference basis for a set of more than 80 representatively chosen 5s-5d compounds. Moreover, the effect of different types of ECPs and that of the SO-coupling at the basis set limit of density functional theory is documented for the above set of molecules extended by 40 5p-6p compounds.
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31.30.J- Relativistic and quantum electrodynamic (QED) effects in atoms, molecules, and ions
31.15.es Applications of density-functional theory (e.g., to electronic structure and stability; defect formation; dielectric properties, susceptibilities; viscoelastic coefficients; Rydberg transition frequencies)
31.15.xr Self-consistent-field methods

Design of an infrared laser pulse to control the multiphoton dissociation of the Fe–CO bond in CO-heme compounds

Sitansh Sharma, Harjinder Singh, Jeremy N. Harvey, and Gabriel G. Balint-Kurti

J. Chem. Phys. 133, 174103 (2010); http://dx.doi.org/10.1063/1.3494543 (11 pages) | Cited 2 times

Online Publication Date: 1 November 2010

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Optimal control theory is used to design a laser pulse for the multiphoton dissociation of the Fe–CO bond in the CO-heme compounds. The study uses a hexacoordinated iron–porphyrin–imidazole–CO complex in its ground electronic state as a model for CO liganded to the heme group. The potential energy and dipole moment surfaces for the interaction of the CO ligand with the heme group are calculated using density functional theory. Optimal control theory, combined with a time-dependent quantum dynamical treatment of the laser-molecule interaction, is then used to design a laser pulse capable of efficiently dissociating the CO-heme complex model. The genetic algorithm method is used within the mathematical framework of optimal control theory to perform the optimization process. This method provides good control over the parameters of the laser pulse, allowing optimized pulses with simple time and frequency structures to be designed. The dependence of photodissociation yield on the choice of initial vibrational state and of initial laser field parameters is also investigated. The current work uses a reduced dimensionality model in which only the Fe–C and C–O stretching coordinates are explicitly taken into account in the time-dependent quantum dynamical calculations. The limitations arising from this are discussed in Sec. 4.
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33.80.Gj Diffuse spectra; predissociation, photodissociation
33.80.Wz Other multiphoton processes
33.15.Kr Electric and magnetic moments (and derivatives), polarizability, and magnetic susceptibility
33.15.Fm Bond strengths, dissociation energies
31.15.es Applications of density-functional theory (e.g., to electronic structure and stability; defect formation; dielectric properties, susceptibilities; viscoelastic coefficients; Rydberg transition frequencies)
31.50.Bc Potential energy surfaces for ground electronic states

Structure of poly(ethylene glycol)–water mixture studied by polymer reference interaction site model theory

Qinzhi Xu, Jianguo Mi, and Chongli Zhong

J. Chem. Phys. 133, 174104 (2010); http://dx.doi.org/10.1063/1.3502108 (8 pages)

Online Publication Date: 1 November 2010

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In this work, the polymer reference interaction site model is applied to investigate the structure of poly(ethylene glycol) (PEG) aqueous solution with the strong hydrogen-bond interactions. In the theoretical model, the renormalized technique of electrostatic potentials is combined with our recently proposed multisite semiflexible chain model to describe the inter- and intramolecular correlations. To test the model for the description of hydrogen bonding, the intermolecular correlation functions of water, ethylene glycol (EG), and EG-water binary mixture are calculated. The results are in good agreement with the corresponding simulation or experimental data. The validated model is then employed to predict the intermolecular correlation functions of different sites of the PEG and its aqueous solution. Another priority of the model is that it can obtain the corresponding direct correlation functions directly.
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61.25.he Polymer solutions
61.25.Em Molecular liquids
64.75.Bc Solubility
61.50.Lt Crystal binding; cohesive energy

Simulations of high-dielectric Stockmayer fluids in hyperspherical geometry

Martin Trulsson

J. Chem. Phys. 133, 174105 (2010); http://dx.doi.org/10.1063/1.3495975 (12 pages) | Cited 1 time

Online Publication Date: 1 November 2010

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The static dielectric properties of Stockmayer fluids are investigated in the hyperspherical geometry, S3. Different methods of obtaining the static dielectric constant εr are compared. Tested methods include the evaluation of the Kirkwood factor, fluctuations of the total dipole moment, and a two-center potential correlation formula to obtain the dielectric constant through effective interactions. With no coupling to the “surrounding,” the different methods give consistent estimates of the dielectric constant. Adding a coupling to the surrounding gives large size dependencies and the two-center potential correlation formula breaks down. For low dipole moments, there is a good agreement in the dielectric constant with previous studies.
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61.20.Ja Computer simulation of liquid structure
02.70.Uu Applications of Monte Carlo methods
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
77.84.Nh Liquids, emulsions, and suspensions; liquid crystals

State-dependent biasing method for importance sampling in the weighted stochastic simulation algorithm

Min K. Roh, Dan T. Gillespie, and Linda R. Petzold

J. Chem. Phys. 133, 174106 (2010); http://dx.doi.org/10.1063/1.3493460 (9 pages) | Cited 3 times

Online Publication Date: 1 November 2010

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The weighted stochastic simulation algorithm (wSSA) was developed by Kuwahara and Mura [J. Chem. Phys. 129, 165101 (2008)] to efficiently estimate the probabilities of rare events in discrete stochastic systems. The wSSA uses importance sampling to enhance the statistical accuracy in the estimation of the probability of the rare event. The original algorithm biases the reaction selection step with a fixed importance sampling parameter. In this paper, we introduce a novel method where the biasing parameter is state-dependent. The new method features improved accuracy, efficiency, and robustness.
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82.20.Fd Collision theories; trajectory models
82.20.Bc State selected dynamics and product distribution

Computation of nucleation at a nonequilibrium first-order phase transition using a rare-event algorithm

David A. Adams, Robert M. Ziff, and Leonard M. Sander

J. Chem. Phys. 133, 174107 (2010); http://dx.doi.org/10.1063/1.3499321 (9 pages)

Online Publication Date: 1 November 2010

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We introduce a new forward flux sampling in time algorithm to efficiently measure transition times in rare-event processes in nonequilibrium systems and apply it to study the first-order (discontinuous) kinetic transition in the Ziff–Gulari–Barshad model of catalytic surface reaction. The average time for the transition to take place, as well as both the spinodal and transition points, is efficiently found by this method.
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64.60.qe General theory and computer simulations of nucleation
68.35.Rh Phase transitions and critical phenomena
82.65.+r Surface and interface chemistry; heterogeneous catalysis at surfaces

Classical photodissociation dynamics with Bohr quantization

L. Bonnet

J. Chem. Phys. 133, 174108 (2010); http://dx.doi.org/10.1063/1.3502492 (5 pages) | Cited 2 times

Online Publication Date: 1 November 2010

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The standard classical expression of the state-resolved photodissociation cross section is not consistent with an efficient Bohr quantization of product internal motions. A new and strictly equivalent expression not suffering from this drawback is proposed. This expression opens the way to more realistic classical simulations of direct polyatomic photodissociations in the quantum regime where only a few states are available to the products.
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33.80.Gj Diffuse spectra; predissociation, photodissociation
31.15.-p Calculations and mathematical techniques in atomic and molecular physics

The reweighted path ensemble

Jutta Rogal, Wolfgang Lechner, Jarek Juraszek, Bernd Ensing, and Peter G. Bolhuis

J. Chem. Phys. 133, 174109 (2010); http://dx.doi.org/10.1063/1.3491817 (12 pages) | Cited 2 times

Online Publication Date: 1 November 2010

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We introduce a reweighting scheme for the path ensembles in the transition interface sampling framework. The reweighting allows for the analysis of free energy landscapes and committor projections in any collective variable space. We illustrate the reweighting scheme on a two dimensional potential with a nonlinear reaction coordinate and on a more realistic simulation of the Trp-cage folding process. We suggest that the reweighted path ensemble can be used to optimize possible nonlinear reaction coordinates.
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82.20.Wt Computational modeling; simulation
05.45.-a Nonlinear dynamics and chaos

Nonlinear reaction coordinate analysis in the reweighted path ensemble

Wolfgang Lechner, Jutta Rogal, Jarek Juraszek, Bernd Ensing, and Peter G. Bolhuis

J. Chem. Phys. 133, 174110 (2010); http://dx.doi.org/10.1063/1.3491818 (12 pages) | Cited 7 times

Online Publication Date: 1 November 2010

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We present a flexible nonlinear reaction coordinate analysis method for the transition path ensemble based on the likelihood maximization approach developed by Peters and Trout [J. Chem. Phys. 125, 054108 (2006)] . By parametrizing the reaction coordinate by a string of images in a collective variable space, we can optimize the likelihood that the string correctly models the committor data obtained from a path sampling simulation. The collective variable space with the maximum likelihood is considered to contain the best description of the reaction. The use of the reweighted path ensemble [ J. Rogal et al., J. Chem. Phys. 133, 174109 (2010) ] allows a complete reaction coordinate description from the initial to the final state. We illustrate the method on a z-shaped two-dimensional potential. While developed for use with path sampling, this analysis method can also be applied to regular molecular dynamics trajectories.
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82.20.Db Transition state theory and statistical theories of rate constants
82.20.Wt Computational modeling; simulation
82.20.Kh Potential energy surfaces for chemical reactions

Time-dependent density functional approach for the calculation of inelastic x-ray scattering spectra of molecules

Arto Sakko, Angel Rubio, Mikko Hakala, and Keijo Hämäläinen

J. Chem. Phys. 133, 174111 (2010); http://dx.doi.org/10.1063/1.3503594 (6 pages) | Cited 2 times

Online Publication Date: 2 November 2010

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We apply time-dependent density functional theory to study the valence electron excitations of molecules and generalize the typically used time-propagation scheme and Casida’s method to calculate the full wavevector dependent response function. This allows the computational study of dipole-forbidden valence electron transitions and the dispersion of spectral weight as a function of the wavevector. The method provides a novel analysis tool for spectroscopic methods such as inelastic x-ray scattering and electron energy loss spectroscopy. We present results for benzene and CF3Cl and make a comparison with experimental results.
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31.15.ee Time-dependent density functional theory
34.80.Gs Molecular excitation and ionization
34.50.Fa Electronic excitation and ionization of atoms (including beam-foil excitation and ionization)
33.20.Rm X-ray spectra

Tetrahydrides of third-row transition elements: Spin-orbit coupling effects on the stability of rhenium tetrahydride

Shiro Koseki, Taka-aki Hisashima, Toshio Asada, Azumao Toyota, and Nikita Matsunaga

J. Chem. Phys. 133, 174112 (2010); http://dx.doi.org/10.1063/1.3495680 (9 pages) | Cited 1 time

Online Publication Date: 2 November 2010

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The potential energy surfaces of low-lying states in rhenium tetrahydride (ReH4) were explored by using the multiconfiguration self-consistent field (MCSCF) method together with the SBKJC effective core potentials and the associated basis sets augmented by a set of f functions on rhenium atom and by a set of p functions on hydrogen atoms, followed by spin-orbit coupling (SOC) calculations to incorporate nonscalar relativistic effects. The most stable structure of ReH4 was found to have a D2d symmetry and its ground state is 4A2. It is found that this is lower in energy than the dissociation limit, ReH2+H2, after dynamic correlation effects are taken into account by using second-order multireference Møller–Plesset perturbation (MRMP2) calculations. This reasonably agrees with previous results reported by Andrews et al. [J. Phys. Chem. 107, 4081 (2003)] . The present investigation further revealed that the dissociation reaction of ReH4 cannot occur without electronic transition from the lowest quartet state to the lowest sextet state. This spin-forbidden transition can easily occur because of large SOC effects among low-lying states in such heavy metal-containing compounds. The minimum-energy crossing (MEX) point between the lowest quartet and sextet states is proved to be energetically and geometrically close to the transition state for the dissociation reaction on the potential energy surface of the lowest spin-mixed state. The MEX point (C2 symmetry) was estimated to be 9184 cm−1 (26.3 kcal/mol) higher than the 4A2 state in D2d symmetry at the MRMP2 level of theory. After inclusion of SOC effects, an energy maximum on the lowest spin-mixed state appears near the MEX point and is recognized as the transition state for the dissociation reaction to ReH2+H2. The energy barrier for the dissociation, evaluated to be MEX in the adiabatic picture, was calculated to be 5643 cm−1 (16.1 kcal/mol) on the lowest spin-mixed state when SOC effects were estimated at the MCSCF level of theory.
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82.30.Lp Decomposition reactions (pyrolysis, dissociation, and fragmentation)
82.20.Kh Potential energy surfaces for chemical reactions
82.20.Db Transition state theory and statistical theories of rate constants
31.30.J- Relativistic and quantum electrodynamic (QED) effects in atoms, molecules, and ions
31.15.xp Perturbation theory
31.15.xr Self-consistent-field methods

Spin-component-scaled Møller–Plesset (SCS-MP) perturbation theory: A generalization of the MP approach with improved properties

Reinhold F. Fink

J. Chem. Phys. 133, 174113 (2010); http://dx.doi.org/10.1063/1.3503041 (12 pages) | Cited 8 times

Online Publication Date: 3 November 2010

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A rigorous perturbation theory is proposed, which has the same second order energy as the spin-component-scaled Møller–Plesset second order (SCS-MP2) method of Grimme [J. Chem. Phys. 118, 9095 (2003)] . This upgrades SCS-MP2 to a systematically improvable, true wave-function-based method. The perturbation theory is defined by an unperturbed Hamiltonian, math(0), that contains the ordinary Fock operator and spin operators math2 that act either on the occupied or the virtual orbital spaces. Two choices for math(0) are discussed and the importance of a spin-pure math(0) is underlined. Like the SCS-MP2 approach, the theory contains two parameters (cos and css) that scale the opposite-spin and the same-spin contributions to the second order perturbation energy. It is shown that these parameters can be determined from theoretical considerations by a Feenberg scaling approach or a fit of the wave functions from the perturbation theory to the exact one from a full configuration interaction calculation. The parameters cos = 1.15 and css = 0.75 are found to be optimal for a reasonable test set of molecules. The meaning of these parameters and the consequences following from a well defined improved MP method are discussed.
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31.15.xp Perturbation theory
31.15.V- Electron correlation calculations for atoms, ions and molecules

State-selective optimization of local excited electronic states in extended systems

Arseny Kovyrshin and Johannes Neugebauer

J. Chem. Phys. 133, 174114 (2010); http://dx.doi.org/10.1063/1.3488230 (14 pages) | Cited 2 times

Online Publication Date: 3 November 2010

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Standard implementations of time-dependent density-functional theory (TDDFT) for the calculation of excitation energies give access to a number of the lowest-lying electronic excitations of a molecule under study. For extended systems, this can become cumbersome if a particular excited state is sought-after because many electronic transitions may be present. This often means that even for systems of moderate size, a multitude of excited states needs to be calculated to cover a certain energy range. Here, we present an algorithm for the selective determination of predefined excited electronic states in an extended system. A guess transition density in terms of orbital transitions has to be provided for the excitation that shall be optimized. The approach employs root-homing techniques together with iterative subspace diagonalization methods to optimize the electronic transition. We illustrate the advantages of this method for solvated molecules, core-excitations of metal complexes, and adsorbates at cluster surfaces. In particular, we study the local π→π∗ excitation of a pyridine molecule adsorbed at a silver cluster. It is shown that the method works very efficiently even for high-lying excited states. We demonstrate that the assumption of a single, well-defined local excitation is, in general, not justified for extended systems, which can lead to root-switching during optimization. In those cases, the method can give important information about the spectral distribution of the orbital transition employed as a guess.
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31.15.ee Time-dependent density functional theory

Correcting for dispersion interaction and beyond in density functional theory through force matching

Yang Song, Omololu Akin-Ojo, and Feng Wang

J. Chem. Phys. 133, 174115 (2010); http://dx.doi.org/10.1063/1.3503656 (10 pages) | Cited 3 times

Online Publication Date: 3 November 2010

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The force matching method is used to improve density functional theory (DFT) by designing a supplemental potential to capture the difference in atomic forces between a DFT functional and a high-quality post Hartree–Fock method. The supplemental potential has two-body terms designed to correct for dispersion and hydrogen bond interactions. The potential also has one-body terms to improve the description of the intramolecular potential energy surface. Our procedure is tested by providing corrections to the Becke–Lee–Yang–Parr exchange-correlation functional for water and is found to perform significantly better than the standard DFT-D approach, giving QCISD quality predictions for relative cluster energies, atomic forces, and molecular structures. It is found that a simple Lennard-Jones term does a good job at correcting for van der Waals interactions and possibly also providing corrections to exchange repulsion. The one-body corrections, while contributing only slightly to improving relative cluster energies, significantly reduce the errors in binding energies and atomic forces for the systems studied.
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34.20.Cf Interatomic potentials and forces
33.15.Ry Ionization potentials, electron affinities, molecular core binding energy
31.15.xr Self-consistent-field methods
31.15.E- Density-functional theory

Molecular core-valence correlation effects involving the post-d elements Ga–Rn: Benchmarks and new pseudopotential-based correlation consistent basis sets

Kirk A. Peterson and Kazim E. Yousaf

J. Chem. Phys. 133, 174116 (2010); http://dx.doi.org/10.1063/1.3503659 (8 pages) | Cited 12 times

Online Publication Date: 3 November 2010

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Correlation consistent basis sets that are suitable for the correlation of the outer-core (n−1)spd electrons of the post-d elements Ga–Rn have been developed. These new sets, denoted by cc-pwCVXZ-PP (X = D,T,Q,5), are based on the previously reported cc-pVXZ-PP sets that were built in conjunction with accurate small-core relativistic pseudopotentials (PPs) and designed only for valence nsp correlation. These new basis sets have been utilized in benchmark coupled cluster calculations of the core-valence correlation effects on the dissociation energies and spectroscopic properties of several small molecules. As expected, the most important contribution is the correlation of the (n−1)d electrons. For example, in the case of the group 13 homonuclear diatomics (Ga2,In2,Tl2), this leads to a dissociation energy increase compared to a valence-only treatment from 1.5 to 3.2 kcal/mol, bond length shortenings from −0.076 to −0.125 Å, and harmonic frequency increases of 7–8 cm−1. Even in the group 15 cases (As2,Sb2,Bi2), the analogous effects of (n−1)d electron correlation are certainly not insignificant, the largest values being +4.4 kcal/mol, −0.049 Å, and +9.6 cm−1 for the effects on De, re, and ωe, respectively. In general, the effects increase in magnitude down a group from 4p to 6p. Correlation of the outer-core (n−1)p electrons is about an order of magnitude less important than (n−1)d but larger than that of the (n−1)s. The effect of additional tight functions for Hartree–Fock and valence sp correlation was found to be surprisingly large, especially for the post-4d and post-5d elements. The pseudopotential results for the molecules containing post-3d elements are also compared to the analogous all-electron calculations employing the Douglas–Kroll–Hess Hamiltonian. The errors attributed to the PP approximation are found to be very small.
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31.15.vn Electron correlation calculations for diatomic molecules
31.15.bw Coupled-cluster theory
31.15.xr Self-consistent-field methods
33.15.Fm Bond strengths, dissociation energies
33.15.Dj Interatomic distances and angles

Explicitly correlated coupled-cluster theory using cusp conditions. I. Perturbation analysis of coupled-cluster singles and doubles (CCSD-F12)

Andreas Köhn and David P. Tew

J. Chem. Phys. 133, 174117 (2010); http://dx.doi.org/10.1063/1.3496372 (18 pages) | Cited 7 times

Online Publication Date: 3 November 2010

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Geminal functions based on Slater-type correlation factors and fixed expansion coefficients, determined by cusp conditions, have in recent years been forwarded as an efficient and numerically stable method for introducing explicit electron correlation into coupled-cluster theory. In this work, we analyze the equations of explicitly correlated coupled-cluster singles and doubles (CCSD-F12) theory and introduce an ordering scheme based on perturbation theory which can be used to characterize and understand the various approximations found in the literature. Numerical results for a test set of 29 molecules support our analysis and give additional insight. In particular, our results help rationalize the success of the CCSD(F12) approximation which is based on a very systematic cancellation of the neglected, otherwise individually large third-order geminal-geminal coupling terms. Further approximations to CCSD(F12) can be introduced without sacrificing the accuracy if the entire set of third-order coupling terms between the conventional doubles cluster amplitudes and the geminal doubles amplitudes is retained, leading to the recently proposed CCSD[F12] and CCSD(F12∗) models, which have negligible overhead compared to conventional CCSD calculations. Particularly, the importance of the ring-term type contribution is pointed out which may be used to improve on other existing approximations such as CCSD-F12b. For small basis sets, it might be advantageous to keep certain higher-order terms leading to CCSD-F12∗, which, for the case of the SP ansatz, merely involves a noniterative correction to CCSD(F12∗).
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31.15.bw Coupled-cluster theory
31.15.V- Electron correlation calculations for atoms, ions and molecules
31.15.xp Perturbation theory

Explicitly correlated coupled-cluster theory using cusp conditions. II. Treatment of connected triple excitations

Andreas Köhn

J. Chem. Phys. 133, 174118 (2010); http://dx.doi.org/10.1063/1.3496373 (15 pages) | Cited 7 times

Online Publication Date: 3 November 2010

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The coupled-cluster singles and doubles method augmented with single Slater-type correlation factors (CCSD-F12) determined by the cusp conditions (also denoted as SP ansatz) yields results close to the basis set limit with only small overhead compared to conventional CCSD. Quantitative calculations on many-electron systems, however, require to include the effect of connected triple excitations at least. In this contribution, the recently proposed [ A. Köhn, J. Chem. Phys. 130, 131101 (2009) ] extended SP ansatz and its application to the noniterative triples correction CCSD(T) is reviewed. The approach allows to include explicit correlation into connected triple excitations without introducing additional unknown parameters. The explicit expressions are presented and analyzed, and possible simplifications to arrive at a computationally efficient scheme are suggested. Numerical tests based on an implementation obtained by an automated approach are presented. Using a partial wave expansion for the neon atom, we can show that the proposed ansatz indeed leads to the expected (Lmax+1)−7 convergence of the noniterative triples correction, where Lmax is the maximum angular momentum in the orbital expansion. Further results are reported for a test set of 29 molecules, employing Peterson’s F12-optimized basis sets. We find that the customary approach of using the conventional noniterative triples correction on top of a CCSD-F12 calculation leads to significant basis set errors. This, however, is not always directly visible for total CCSD(T) energies due to fortuitous error compensation. The new approach offers a thoroughly explicitly correlated CCSD(T)-F12 method with improved basis set convergence of the triples contributions to both total and relative energies.
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31.15.bw Coupled-cluster theory
31.15.vj Electron correlation calculations for atoms and ions: excited states

The adiabatic approximation in time-dependent density matrix functional theory: Response properties from dynamics of phase-including natural orbitals

K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends

J. Chem. Phys. 133, 174119 (2010); http://dx.doi.org/10.1063/1.3499601 (13 pages) | Cited 3 times

Online Publication Date: 4 November 2010

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The adiabatic approximation is problematic in time-dependent density matrix functional theory. With pure density matrix functionals (invariant under phase change of the natural orbitals) it leads to lack of response in the occupation numbers, hence wrong frequency dependent responses, in particular α(ω→0) ≠ α0 (the static polarizability). We propose to relinquish the requirement that the functional must be a pure one-body reduced density matrix (1RDM) functional, and to introduce additional variables which can be interpreted as phases of the one-particle states of the independent particle reference system formed with the natural orbitals, thus obtaining so-called phase-including natural orbital (PINO) functionals. We also stress the importance of the correct choice of the complex conjugation in the two-electron integrals in the commonly used functionals (they should not be of exchange type). We demonstrate with the Löwdin–Shull energy expression for two-electron systems, which is an example of a PINO functional, that for two-electron systems exact responses (polarizabilities, excitation energies) are obtained, while writing this energy expression in the usual way as a 1RDM functional yields erroneous responses.
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31.15.E- Density-functional theory

Optimum and efficient sampling for variational quantum Monte Carlo

J. R. Trail and Ryo Maezono

J. Chem. Phys. 133, 174120 (2010); http://dx.doi.org/10.1063/1.3488651 (16 pages) | Cited 1 time

Online Publication Date: 4 November 2010

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Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial wave functions, that is to variational quantum Monte Carlo. Almost all previous implementations employ samples distributed as the physical probability density of the trial wave function, and assume the central limit theorem to be valid. In this paper we provide an analysis of random error in estimation and optimization that leads naturally to new sampling strategies with improved computational and statistical properties. A rigorous lower limit to the random error is derived, and an efficient sampling strategy presented that significantly increases computational efficiency. In addition the infinite variance heavy tailed random errors of optimum parameters in conventional methods are replaced with a Normal random error, strengthening the theoretical basis of optimization. The method is applied to a number of first row systems and compared with previously published results.
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31.15.xt Variational techniques
05.30.-d Quantum statistical mechanics
02.70.Ss Quantum Monte Carlo methods
02.50.Cw Probability theory
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Effective Floquet Hamiltonians for dipolar and quadrupolar coupled N-spin systems in solid state nuclear magnetic resonance under magic angle spinning

Manoj Kumar Pandey and Mangala Sunder Krishnan

J. Chem. Phys. 133, 174121 (2010); http://dx.doi.org/10.1063/1.3496407 (10 pages) | Cited 1 time

Online Publication Date: 4 November 2010

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Spin dynamics under magic angle spinning has been studied using different theoretical approaches and also by extensive numerical simulation programs. In this article we present a general theoretical approach that leads to analytic forms for effective Hamiltonians for an N-spin dipolar and quadrupolar coupled system under magic angle spinning (MAS) conditions, using a combination of Floquet theory and van Vleck (contact) transformation. The analytic forms presented are shown to be useful for the study of MAS spin dynamics in solids with the help of a number of simulations in two, three, and four coupled, spin-1/2 systems as well as spins in which quadrupolar interactions are also present.
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76.60.-k Nuclear magnetic resonance and relaxation
75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.)
75.40.Mg Numerical simulation studies
75.10.Dg Crystal-field theory and spin Hamiltonians

Density cumulant functional theory: First implementation and benchmark results for the DCFT-06 model

Andrew C. Simmonett, Jeremiah J. Wilke, Henry F. Schaefer, III, and Werner Kutzelnigg

J. Chem. Phys. 133, 174122 (2010); http://dx.doi.org/10.1063/1.3503657 (5 pages) | Cited 5 times

Online Publication Date: 4 November 2010

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Density cumulant functional theory [ W. Kutzelnigg, J. Chem. Phys. 125, 171101 (2006) ] is implemented for the first time. Benchmark results are provided for atoms and diatomic molecules, demonstrating the performance of DCFT-06 for both nonbonded and bonded interactions. The results show that DCFT-06 appears to perform similarly to coupled cluster theory with single and double excitations (CCSD) in describing dispersion. For covalently bound systems, the physical properties predicted by DCFT-06 appear to be at least of CCSD quality around equilibrium geometries. The computational scaling of both DCFT-06 and CCSD is O(N6), but the former has reduced nonlinearities among the variables and a Hermitian energy functional, making it an attractive alternative.
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31.15.es Applications of density-functional theory (e.g., to electronic structure and stability; defect formation; dielectric properties, susceptibilities; viscoelastic coefficients; Rydberg transition frequencies)

The complemented system approach: A novel method for calculating the x-ray scattering from computer simulations

Andrej Lajovic, Matija Tomšič, and Andrej Jamnik

J. Chem. Phys. 133, 174123 (2010); http://dx.doi.org/10.1063/1.3502683 (6 pages)

Online Publication Date: 4 November 2010

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In this paper, we review the main problem concerning the calculation of x-ray scattering of simulated model systems, namely, their finite size. A novel method based on the Rayleigh–Debye–Gans approximation was derived, which allows sidestepping this issue by complementing the missing surroundings of each particle with an average image of the system. The method was designed to operate directly on particle configurations without an intermediate step (e.g., calculation of pair distribution functions): in this way, all information contained in the configurations was preserved. A comparison of the results against those of other known methods showed that the new method combined several favorable properties: an arbitrary q-scale, scattering curves free of truncation artifacts, and good behavior down to the theoretical lower limit of the q-scale. A test of computational efficiency was also performed to establish a relative scale between the speeds of all known methods: the reciprocal lattice approach, the brute force method, the Fourier transform approach, and the newly presented complemented system approach.
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78.70.Ck X-ray scattering
02.60.-x Numerical approximation and analysis

A transition state view on reactive scattering: Initial state-selected reaction probabilities for the H+CH4→H2+CH3 reaction studied in full dimensionality

Gerd Schiffel and Uwe Manthe

J. Chem. Phys. 133, 174124 (2010); http://dx.doi.org/10.1063/1.3489409 (17 pages) | Cited 17 times

Online Publication Date: 4 November 2010

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Initial state-selected reaction probabilities for the H+CH4→H2+CH3 reaction are computed for vanishing total angular momentum by full-dimensional calculations employing the multiconfigurational time-dependent Hartree approach. An ensemble of wave packets completely describing reactivity for total energies up to 0.58 eV is constructed in the transition state region by diagonalization of the thermal flux operator. These wave packets are then propagated into the reactant asymptotic region to obtain the initial state-selected reaction probabilities. Reaction probabilities for reactants in all rotational states of the vibrational 1A1, 1F2, and 1E levels of methane are presented. Vibrational excitation is found to decrease reactivity when reaction probabilities at equivalent total energies are compared but to increase reaction probabilities when the comparison is done at the basis of equivalent collision energies. Only a fraction of the initial vibrational energy can be utilized to promote the reaction. The effect of rotational excitation on the reactivity differs depending on the initial vibrational state of methane. For the 1A1 and 1F2 vibrational states of methane, rotational excitation decreases the reaction probability even when comparing reaction probabilities at equivalent collision energies. In contrast, rotational energy is even more efficient than translational energy in increasing the reaction probability when the reaction starts from the 1E vibrational state of methane. All findings can be explained employing a transition state based interpretation of the reaction process.
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82.30.Cf Atom and radical reactions; chain reactions; molecule-molecule reactions
82.20.Fd Collision theories; trajectory models
82.20.Db Transition state theory and statistical theories of rate constants
82.20.Bc State selected dynamics and product distribution
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