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14 Apr 2008

Volume 128, Issue 14, Articles (14xxxx)

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back to top Theoretical Methods and Algorithms

A sparse matrix based full-configuration interaction algorithm

Zoltán Rolik, Ágnes Szabados, and Péter R. Surján

J. Chem. Phys. 128, 144101 (2008); http://dx.doi.org/10.1063/1.2839304 (11 pages) | Cited 4 times

Online Publication Date: 8 April 2008

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We present an algorithm related to the full-configuration interaction (FCI) method that makes complete use of the sparse nature of the coefficient vector representing the many-electron wave function in a determinantal basis. Main achievements of the presented sparse FCI (SFCI) algorithm are (i) development of an iteration procedure that avoids the storage of FCI size vectors; (ii) development of an efficient algorithm to evaluate the effect of the Hamiltonian when both the initial and the product vectors are sparse. As a result of point (i) large disk operations can be skipped which otherwise may be a bottleneck of the procedure. At point (ii) we progress by adopting the implementation of the linear transformation by Olsen et al. [J. Chem Phys. 89, 2185 (1988) ] for the sparse case, getting the algorithm applicable to larger systems and faster at the same time. The error of a SFCI calculation depends only on the dropout thresholds for the sparse vectors, and can be tuned by controlling the amount of system memory passed to the procedure. The algorithm permits to perform FCI calculations on single node workstations for systems previously accessible only by supercomputers.
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03.65.Ge Solutions of wave equations: bound states

Single switch surface hopping for molecular dynamics with transitions

Clotilde Fermanian Kammerer and Caroline Lasser

J. Chem. Phys. 128, 144102 (2008); http://dx.doi.org/10.1063/1.2888549 (9 pages) | Cited 3 times

Online Publication Date: 8 April 2008

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A trajectory surface hopping algorithm is proposed, which stems from a mathematically rigorous analysis of propagation through conical intersections of potential energy surfaces. Since nonadiabatic transitions are only performed when a classical trajectory attains one of its local minimal surface gaps, the algorithm is called single switch surface hopping. Numerical experiments for a two mode Jahn–Teller system are presented, which illustrate the asymptotic justification of the method as well as its good performance in the physically relevant parameter range.
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03.65.Fd Algebraic methods
03.65.Ta Foundations of quantum mechanics; measurement theory
03.65.Sq Semiclassical theories and applications

The electron affinity of gallium nitride (GaN) and digallium nitride (GaNGa): The importance of the basis set superposition error in strongly bound systems

Demeter Tzeli and Athanassios A. Tsekouras

J. Chem. Phys. 128, 144103 (2008); http://dx.doi.org/10.1063/1.2883997 (7 pages) | Cited 6 times

Online Publication Date: 8 April 2008

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The electron affinity of GaN and Ga2N as well as the geometries and the dissociation energies of the ground states of gallium nitrides GaN, GaN−, Ga2N, and Ga2N− were systematically studied by employing the coupled cluster method, RCCSD(T), in conjunction with a series of basis sets, (aug-)cc-pVxZ(-PP), x = D, T, Q, and 5 and cc-pwCVxZ(-PP), x = D, T, and Q. The calculated dissociation energy and the electron affinity of GaN are 2.12 and 1.84 eV, respectively, and those of Ga2N are 6.31 and 2.53 eV. The last value is in excellent agreement with a recent experimental value for the electron affinity of Ga2N of 2.506±0.008 eV. For such quality in the results to be achieved, the Ga 3d electrons had to be included in the correlation space. Moreover, when a basis set is used, which has not been developed for the number of the electrons which are correlated in a calculation, the quantities calculated need to be corrected for the basis set superposition error.
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33.15.Ry Ionization potentials, electron affinities, molecular core binding energy
33.15.Bh General molecular conformation and symmetry; stereochemistry
31.15.bw Coupled-cluster theory

Improved transition path sampling methods for simulation of rare events

Manan Chopra, Rohit Malshe, Allam S. Reddy, and J. J. de Pablo

J. Chem. Phys. 128, 144104 (2008); http://dx.doi.org/10.1063/1.2889943 (5 pages) | Cited 5 times

Online Publication Date: 9 April 2008

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The free energy surfaces of a wide variety of systems encountered in physics, chemistry, and biology are characterized by the existence of deep minima separated by numerous barriers. One of the central aims of recent research in computational chemistry and physics has been to determine how transitions occur between deep local minima on rugged free energy landscapes, and transition path sampling (TPS) Monte-Carlo methods have emerged as an effective means for numerical investigation of such transitions. Many of the shortcomings of TPS-like approaches generally stem from their high computational demands. Two new algorithms are presented in this work that improve the efficiency of TPS simulations. The first algorithm uses biased shooting moves to render the sampling of reactive trajectories more efficient. The second algorithm is shown to substantially improve the accuracy of the transition state ensemble by introducing a subset of local transition path simulations in the transition state. The system considered in this work consists of a two-dimensional rough energy surface that is representative of numerous systems encountered in applications. When taken together, these algorithms provide gains in efficiency of over two orders of magnitude when compared to traditional TPS simulations.
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82.20.Db Transition state theory and statistical theories of rate constants
82.20.Fd Collision theories; trajectory models
82.20.Wt Computational modeling; simulation
82.60.-s Chemical thermodynamics

Application of magnetically perturbed time-dependent density functional theory to magnetic circular dichroism: Calculation of B terms

Michael Seth, Mykhaylo Krykunov, Tom Ziegler, Jochen Autschbach, and Arup Banerjee

J. Chem. Phys. 128, 144105 (2008); http://dx.doi.org/10.1063/1.2901967 (17 pages) | Cited 5 times

Online Publication Date: 9 April 2008

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Magnetically perturbed time-dependent density functional theory is applied to the calculation of the magnetic circular dichroism (MCD) B terms of closed shell molecules. Two approaches to evaluating B term parameters are described: a sum-over-states–type approach and an approach based on the direct solution of the matrix equations. The advantages and disadvantages and technical challenges of each approach are described. The interpretation of the parameters in terms of ground and excited state perturbations are discussed. Several applications of the methodology are described. Calculations of the MCD of ethene are used to compare the sum-over-states and direct solution approaches and to illustrate the potential for analysis. The other applications involving azabenzes, sulfur-nitrogen heterocycles and quinone molecules are compared with experiment and other theoretical calculations. For the most part, all important features of the observed spectra are reproduced.
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33.55.+b Optical activity and dichroism
33.57.+c Magneto-optical and electro-optical spectra and effects
31.15.ee Time-dependent density functional theory
31.15.xp Perturbation theory

Correlation regions within a localized molecular orbital approach

Ricardo A. Mata, Hans-Joachim Werner, and Martin Schütz

J. Chem. Phys. 128, 144106 (2008); http://dx.doi.org/10.1063/1.2884725 (8 pages) | Cited 8 times

Online Publication Date: 9 April 2008

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A hybrid scheme for the computation of reaction energies in large molecular systems is proposed. The approach is based on localized orbitals and allows for the treatment of different parts of a molecule at different computational levels. The localized orbitals are assigned to regions, and then different local correlation methods, such as local MP2 or local CCSD(T), can be applied to different regions. In contrast to previous hybrid schemes, the molecule does not have to be split into parts and, therefore, it is not necessary to saturate dangling bonds using link atoms. For fixed region sizes, the cost of the high-level calculation becomes independent of the molecular size, and it is demonstrated that O(1) scaling can be achieved. Illustrative applications are presented and the convergence of the results with respect to the size of the regions is investigated for reaction energies, barrier heights, and weakly bound complexes.
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82.20.Pm Rate constants, reaction cross sections, and activation energies
82.20.Wt Computational modeling; simulation
31.15.xp Perturbation theory
31.15.bw Coupled-cluster theory
31.15.V- Electron correlation calculations for atoms, ions and molecules

Dispersion energy from density-fitted density susceptibilities of singles and doubles coupled cluster theory

Tatiana Korona and Bogumil Jeziorski

J. Chem. Phys. 128, 144107 (2008); http://dx.doi.org/10.1063/1.2889006 (10 pages) | Cited 9 times

Online Publication Date: 10 April 2008

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A new method of calculation of the second-order dispersion energy is proposed. It is based on the Longuet-Higgins formula [ Faraday Discuss. Chem. Soc. 40, 7 (1965) ], which describes the dispersion interaction in terms of frequency-dependent density susceptibilities of monomers. In this study, the density susceptibilities are obtained from the coupled cluster theory at the singles and doubles level. Density fitting is applied in order to reduce the computational effort for the evaluation of density susceptibilities. It is shown that density fitting improves the scaling of the computational resources with molecular size by one order of magnitude without affecting the accuracy of the resulting dispersion energy. Numerical results are presented for several van der Waals molecules to illustrate the performance of the new approach.
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31.15.bw Coupled-cluster theory
31.15.E- Density-functional theory

Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem

David Asturiol, Miquel Duran, and Pedro Salvador

J. Chem. Phys. 128, 144108 (2008); http://dx.doi.org/10.1063/1.2902974 (5 pages) | Cited 9 times

Online Publication Date: 10 April 2008

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Recently, the surprising result that ab initio calculations on benzene and other planar arenes at correlated MP2, MP3, configuration interaction with singles and doubles (CISD), and coupled cluster with singles and doubles levels of theory using standard Pople’s basis sets yield nonplanar minima has been reported. The planar optimized structures turn out to be transition states presenting one or more large imaginary frequencies, whereas single-determinant-based methods lead to the expected planar minima and no imaginary frequencies. It has been suggested that such anomalous behavior can be originated by two-electron basis set incompleteness error. In this work, we show that the reported pitfalls can be interpreted in terms of intramolecular basis set superposition error (BSSE) effects, mostly between the C–H moieties constituting the arenes. We have carried out counterpoise-corrected optimizations and frequency calculations at the Hartree–Fock, B3LYP, MP2, and CISD levels of theory with several basis sets for a number of arenes. In all cases, correcting for intramolecular BSSE fixes the anomalous behavior of the correlated methods, whereas no significant differences are observed in the single-determinant case. Consequently, all systems studied are planar at all levels of theory. The effect of different intramolecular fragment definitions and the particular case of charged species, namely, cyclopentadienyl and indenyl anions, respectively, are also discussed.
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31.15.am Relativistic configuration interaction (CI) and many-body perturbation calculations
31.15.V- Electron correlation calculations for atoms, ions and molecules
33.15.Bh General molecular conformation and symmetry; stereochemistry

Multiconfiguration optimized effective potential method for a density-functional treatment of static correlation

Martin Weimer, Fabio Della Sala, and Andreas Görling

J. Chem. Phys. 128, 144109 (2008); http://dx.doi.org/10.1063/1.2868755 (18 pages) | Cited 9 times

Online Publication Date: 10 April 2008

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An approach to treat static correlation within a density-functional framework is presented. To that end, a multiconfiguration optimized effective potential (MCOEP) method is derived. In contrast to standard multiconfiguration self-consistent field (MCSCF) methods and previous combinations of MCSCF procedures with density-functional theory, the MCOEP method yields well-defined physically meaningful orbital and eigenvalue spectra. In addition to the electronic ground state also excited electronic states can be described. The MCOEP method is implemented invoking the localized Hartree–Fock approximation, leading to a multiconfiguration localized Hartree–Fock approach. Applications of the new method to the dissociation of the hydrogen molecule and the isomerization of ethene and cyclobutadiene show that it is capable of describing situations that are characterized by strong static correlation
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31.15.E- Density-functional theory
31.15.xr Self-consistent-field methods
82.30.Lp Decomposition reactions (pyrolysis, dissociation, and fragmentation)

Origin and control of superlinear polarizability scaling in chemical potential equalization methods

G. Lee Warren, Joseph E. Davis, and Sandeep Patel

J. Chem. Phys. 128, 144110 (2008); http://dx.doi.org/10.1063/1.2872603 (14 pages) | Cited 13 times

Online Publication Date: 10 April 2008

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Many common chemical potential equalization (μEq) methods are known to suffer from a superlinear scaling of the polarizability with increasing molecular size that interferes with model transferability and prevents the straightforward application of these methods to large, biochemically relevant molecules. In the present work, we systematically investigate the origins of this scaling and the mechanisms whereby some existing methods successfully temper the scaling. We demonstrate several types of topological charge constraints distinct from the usual single molecular charge constraint that can successfully achieve linear polarizability scaling in atomic charge based equilibration models. We find the use of recently employed charge conservation constraints tied to small molecular units to be an effective and practical approach for modulating the polarizability scaling in atomic μEq schemes. We also analyze the scaling behavior of several μEq schemes in the bond representation and derive closed-form expressions for the polarizability scaling in a linear atomic chain model; for a single molecular charge constraint these expressions demonstrate a cubic dependence of the polarizability on molecular size compared with linear scaling obtainable in the case of the atom-atom charge transfer (AACT) and split-charge equilibration (SQE) schemes. Application of our results to the trans N-alkane series reveals that in certain situations, the AACT and SQE schemes can become unstable due to an indefinite Hessian matrix. Consequently, we discuss sufficient criteria for ensuring stability within these schemes.
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87.15.R- Reactions and kinetics
33.15.Kr Electric and magnetic moments (and derivatives), polarizability, and magnetic susceptibility

Finding important anharmonic terms in the sixth-order potential energy function by the scaled hypersphere search method: An application to vibrational analyses of molecules and clusters

Satoshi Maeda, Yu Watanabe, and Koichi Ohno

J. Chem. Phys. 128, 144111 (2008); http://dx.doi.org/10.1063/1.2884348 (11 pages) | Cited 17 times

Online Publication Date: 11 April 2008

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A fitting method of the sixth-order potential energy function is proposed, where ab initio potential energy data for the fitting are sampled in directions containing maximal anharmonic downward distortions detected by the scaled hypersphere search (SHS) method. This technique has been applied to H2O, HCHO, HCOOH, C2H4, CH3OH, CH3CHO, CH3NH2, B2H6, (H2O)2, and (H2O)3, where, without using the symmetry, 176, 904, 1432, 2992, 2520, 2760, 3608, 6232, 768, and 1456 times single-point energy calculations, respectively, were required for obtaining anharmonic terms. Experimental IR peak positions of not only fundamentals but also overtones and combinations in the excitation energy range of 1000–4000 cm−1 could be reproduced very accurately by the post-vibrational self-consistent field theory employing potential functions obtained by the present SHS based polynomial fitting method.
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34.20.-b Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions
31.15.A- Ab initio calculations
33.15.Mt Rotation, vibration, and vibration-rotation constants
33.20.Tp Vibrational analysis
33.20.Ea Infrared spectra
31.15.xr Self-consistent-field methods

Improved supermolecular second order Møller–Plesset intermolecular interaction energies using time-dependent density functional response theory

Andreas Heßelmann

J. Chem. Phys. 128, 144112 (2008); http://dx.doi.org/10.1063/1.2905808 (9 pages) | Cited 22 times

Online Publication Date: 11 April 2008

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The supermolecular second order Møller-Plesset (MP2) intermolecular interaction energy is corrected by employing time-dependent density functional (TDDFT) response theory. This is done by replacing the uncoupled second order dispersion contribution contained in the supermolecular MP2 energy with the coupled dispersion energy obtained from the TDDFT approach. Preliminary results for the rare gas dimers He2, Ne2, and Ar2 and a few structures of the (HF)2 and (H2O)2 dimers show that the conventional MP2 interaction energies are considerably improved by this procedure if compared to coupled cluster singles doubles with perturbative triples [CCSD(T)] interaction energies. However, the quality of the interaction energies obtained in this way strongly depends on the exchange-correlation potential employed in the monomer calculations: It is shown that an exact exchange-only potential surprisingly often performs better than an asymptotically corrected hybrid exchange-correlation potential. Therefore the method proposed in this work is similar to the method by Cybulski and Lytle [J. Chem. Phys., 127, 141102 (2007)] which corrects the supermolecular MP2 energies with a scaled dispersion energy from time-dependent Hartree–Fock. The results in this work are also compared to the combination of density functional theory and intermolecular perturbation theory.
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34.20.Gj Intermolecular and atom-molecule potentials and forces
31.15.ee Time-dependent density functional theory
31.15.eg Exchange-correlation functionals (in current density functional theory)
33.15.Bh General molecular conformation and symmetry; stereochemistry
31.15.xr Self-consistent-field methods

Semiempirical evaluation of post-Hartree–Fock diagonal-Born–Oppenheimer corrections for organic molecules

José R. Mohallem

J. Chem. Phys. 128, 144113 (2008); http://dx.doi.org/10.1063/1.2902286 (4 pages) | Cited 2 times

Online Publication Date: 11 April 2008

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Recent post-Hartree–Fock calculations of the diagonal-Born-Oppenheimer correction empirically show that it behaves quite similar to atomic nuclear mass corrections. An almost constant contribution per electron is identified, which converges with system size for specific series of organic molecules. This feature permits pocket-calculator evaluation of the corrections within thermochemical accuracy (10−1 mhartree or kcal/mol).
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31.15.xr Self-consistent-field methods

Quantum theory of (femtosecond) time-resolved stimulated Raman scattering

Zhigang Sun, J. Lu, Dong H. Zhang, and Soo-Y. Lee

J. Chem. Phys. 128, 144114 (2008); http://dx.doi.org/10.1063/1.2888551 (13 pages) | Cited 15 times

Online Publication Date: 11 April 2008

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We present a complete perturbation theory of stimulated Raman scattering (SRS), which includes the new experimental technique of femtosecond stimulated Raman scattering (FSRS), where a picosecond Raman pump pulse and a femtosecond probe pulse simultaneously act on a stationary or nonstationary vibrational state. It is shown that eight terms in perturbation theory are required to account for SRS, with observation along the probe pulse direction, and they can be grouped into four nonlinear processes which are labeled as stimulated Raman scattering or inverse Raman scattering (IRS): SRS(I), SRS(II), IRS(I), and IRS(II). Previous FSRS theories have used only the SRS(I) process or only the “resonance Raman scattering” term in SRS(I). Each process can be represented by an overlap between a wave packet in the initial electronic state and a wave packet in the excited Raman electronic state. Calculations were performed with Gaussian Raman pump and probe pulses on displaced harmonic potentials to illustrate various features of FSRS, such as high time and frequency resolution; Raman gain for the Stokes line, Raman loss for the anti-Stokes line, and absence of the Rayleigh line in off-resonance FSRS from a stationary or decaying v = 0 state; dispersive line shapes in resonance FSRS; and the possibility of observing vibrational wave packet motion with off-resonance FSRS.
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42.65.Dr Stimulated Raman scattering; CARS
42.65.Es Stimulated Brillouin and Rayleigh scattering
42.65.Re Ultrafast processes; optical pulse generation and pulse compression
33.15.Mt Rotation, vibration, and vibration-rotation constants
33.80.Rv Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states)
33.70.Jg Line and band widths, shapes, and shifts

Obtaining the two-body density matrix in the density matrix renormalization group method

Dominika Zgid and Marcel Nooijen

J. Chem. Phys. 128, 144115 (2008); http://dx.doi.org/10.1063/1.2883980 (13 pages) | Cited 20 times

Online Publication Date: 11 April 2008

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We present an approach that allows to produce the two-body density matrix during the density matrix renormalization group (DMRG) run without an additional increase in the current disk and memory requirements. The computational cost of producing the two-body density matrix is proportional to O(M3k2+M2k4). The method is based on the assumption that different elements of the two-body density matrix can be calculated during different steps of a sweep. Hence, it is desirable that the wave function at the convergence does not change during a sweep. We discuss the theoretical structure of the wave function ansatz used in DMRG, concluding that during the one-site DMRG procedure, the energy and the wave function are converging monotonically at every step of the sweep. Thus, the one-site algorithm provides an opportunity to obtain the two-body density matrix free from the N-representability problem. We explain the problem of local minima that may be encountered in the DMRG calculations. We discuss theoretically why and when the one- and two-site DMRG procedures may get stuck in a metastable solution, and we list practical solutions helping the minimization to avoid the local minima.
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31.15.E- Density-functional theory
02.20.-a Group theory

The density matrix renormalization group self-consistent field method: Orbital optimization with the density matrix renormalization group method in the active space

Dominika Zgid and Marcel Nooijen

J. Chem. Phys. 128, 144116 (2008); http://dx.doi.org/10.1063/1.2883981 (11 pages) | Cited 9 times

Online Publication Date: 11 April 2008

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We present the density matrix renormalization group self-consistent field (DMRG-SCF) approach that is analogous to the complete active space self-consisted field (CASSCF) method but instead of using for the description of the active space the full configuration interaction (FCI) method, the DMRG-SCF uses the density matrix renormalization group (DMRG) method. The DMRG-SCF approach, similarly to CASSCF, properly describes the multiconfigurational character of the wave function but avoids the exponential scaling of the FCI method and replaces it with a polynomial scaling. Hence, calculations for a larger number of orbitals and electrons in the active space are possible since the DMRG method provides an efficient tool to automatically select from the full Hilbert space the many-body contracted basis states that are the most important for the description of the wave function.
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31.15.E- Density-functional theory
31.15.xr Self-consistent-field methods
31.15.am Relativistic configuration interaction (CI) and many-body perturbation calculations

Orbital optimization in the density matrix renormalization group, with applications to polyenes and β-carotene

Debashree Ghosh, Johannes Hachmann, Takeshi Yanai, and Garnet Kin-Lic Chan

J. Chem. Phys. 128, 144117 (2008); http://dx.doi.org/10.1063/1.2883976 (14 pages) | Cited 35 times

Online Publication Date: 11 April 2008

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In previous work we have shown that the density matrix renormalization group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional complete active space algorithms. Here, we implement orbital optimization with the DMRG to further allow the self-consistent improvement of the active orbitals, as is done in the complete active space self-consistent field (CASSCF) method. We use our resulting DMRG-CASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as β-carotene, correlating with near-exact accuracy the optimized complete π-valence space with up to 24 active electrons and orbitals, and analyze our results in the light of the recent discovery from resonance Raman experiments of new optically dark states in the spectrum.
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31.15.xr Self-consistent-field methods
33.80.Rv Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states)

Partially linearized, fully size-extensive, and reduced multireference coupled-cluster methods. I. Formalism and mutual relationship

Xiangzhu Li and Josef Paldus

J. Chem. Phys. 128, 144118 (2008); http://dx.doi.org/10.1063/1.2868758 (11 pages) | Cited 11 times

Online Publication Date: 11 April 2008

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We describe a fully size-extensive alternative of the reduced multireference (RMR) coupled-cluster (CC) method with singles (S) and doubles (D) that generates a subset of higher-than-pair cluster amplitudes, using linearized CC equations from the full CC chain, projected onto the corresponding higher-than-doubly excited configurations. This approach is referred to as partially linearized (pl) MR CCSD method and characterized by the acronym plMR CCSD. In contrast to a similar CCSDT-1 method [ Y. S. Lee et al., J. Chem. Phys. 81, 5906 (1984) ] this approach also considers higher than triples (currently up to hexuples), while focusing only on a small subset of such amplitudes, referred to as the primary ones. These amplitudes are selected using similar criteria as in RMR CCSD. An extension considering secondary triples via the standard (T)-type corrections, resulting in the plMR CCSD(T) method, is also considered. The relationship of RMR and plMR CCSD and CCSD(T) approaches is discussed, and their performance and characteristics are the subject of the subsequent Part II of this paper.
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31.15.bw Coupled-cluster theory

Partially linearized, fully size-extensive, and reduced multireference coupled-cluster methods. II. Applications and performance

Xiangzhu Li and Josef Paldus

J. Chem. Phys. 128, 144119 (2008); http://dx.doi.org/10.1063/1.2868768 (13 pages) | Cited 18 times

Online Publication Date: 11 April 2008

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The partially linearized (pl), fully size-extensive multireference (MR) coupled-cluster (CC) method, fully accounting for singles (S) and doubles (D) and approximately for a subset of primary higher than doubles, referred to as plMR CCSD, as well as its plMR CCSD(T) version corrected for secondary triples, as described in Part I of this paper [ X. Li and J. Paldus, J. Chem. Phys. 128, 144118 (2008) ], are applied to the problem of bond breaking in the HF, F2, H2O, and N2 molecules, as well as to the H4 model, using basis sets of a DZ or a cc-pVDZ quality that enable a comparison with the full configuration interaction (FCI) exact energies for a given ab initio model. A comparison of the performance of the plMR CCSD/CCSD(T) approaches with those of the reduced MR (RMR) CCSD/CCSD(T) methods, as well as with the standard single reference (SR) CCSD and CCSD(T) methods, is made in each case. For the H4 model and N2 we also compare our results with the completely renormalized (CR) CC(2,3) method [ P. Piecuch and M. Włoch, J. Chem. Phys. 123, 224105 (2005) ]. An important role of a proper choice of the model space for the MR-type methods is also addressed. The advantages and shortcomings of all these methods are pointed out and discussed, as well as their size-extensivity characteristics, in which case we distinguish supersystems involving noninteracting SR and MR subsystems from those involving only MR-type subsystems. Although the plMR-type approaches render fully size-extensive results, while the RMR CCSD may slightly violate this property, the latter method yields invariably superior results to the plMR CCSD ones and is more easy to apply in highly demanding cases, such as the triple-bond breaking in the nitrogen molecule.
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36.20.Hb Configuration (bonds, dimensions)
31.15.A- Ab initio calculations

Adaptive biasing force method for scalar and vector free energy calculations

Eric Darve, David Rodríguez-Gómez, and Andrew Pohorille

J. Chem. Phys. 128, 144120 (2008); http://dx.doi.org/10.1063/1.2829861 (13 pages) | Cited 29 times

Online Publication Date: 11 April 2008

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In free energy calculations based on thermodynamic integration, it is necessary to compute the derivatives of the free energy as a function of one (scalar case) or several (vector case) order parameters. We derive in a compact way a general formulation for evaluating these derivatives as the average of a mean force acting on the order parameters, which involves first derivatives with respect to both Cartesian coordinates and time. This is in contrast with the previously derived formulas, which require first and second derivatives of the order parameter with respect to Cartesian coordinates. As illustrated in a concrete example, the main advantage of this new formulation is the simplicity of its use, especially for complicated order parameters. It is also straightforward to implement in a molecular dynamics code, as can be seen from the pseudocode given at the end. We further discuss how the approach based on time derivatives can be combined with the adaptive biasing force method, an enhanced sampling technique that rapidly yields uniform sampling of the order parameters, and by doing so greatly improves the efficiency of free energy calculations. Using the backbone dihedral angles Φ and Ψ in N-acetylalanyl-N′-methylamide as a numerical example, we present a technique to reconstruct the free energy from its derivatives, a calculation that presents some difficulties in the vector case because of the statistical errors affecting the derivatives.
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05.70.Ce Thermodynamic functions and equations of state
02.70.Ns Molecular dynamics and particle methods

Hamiltonian replica exchange molecular dynamics using soft-core interactions

Jozef Hritz and Chris Oostenbrink

J. Chem. Phys. 128, 144121 (2008); http://dx.doi.org/10.1063/1.2888998 (10 pages) | Cited 9 times

Online Publication Date: 14 April 2008

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To overcome the problem of insufficient conformational sampling within biomolecular simulations, we have developed a novel Hamiltonian replica exchange molecular dynamics (H-REMD) scheme that uses soft-core interactions between those parts of the system that contribute most to high energy barriers. The advantage of this approach over other H-REMD schemes is the possibility to use a relatively small number of replicas with locally larger differences between the individual Hamiltonians. Because soft-core potentials are almost the same as regular ones at longer distances, most of the interactions between atoms of perturbed parts will only be slightly changed. Rather, the strong repulsion between atoms that are close in space, which in many cases results in high energy barriers, is weakened within higher replicas of our proposed scheme. In addition to the soft-core interactions, we proposed to include multiple replicas using the same Hamiltonian/level of softness. We have tested the new protocol on the GTP and 8-Br-GTP molecules, which are known to have high energy barriers between the anti and syn conformation of the base with respect to the sugar moiety. During two 25 ns MD simulations of both systems the transition from the more stable to the less stable (but still experimentally observed) conformation is not seen at all. Also temperature REMD over 50 replicas for 1 ns did not show any transition at room temperature. On the other hand, more than 20 of such transitions are observed in H-REMD using six replicas (at three different Hamiltonians) during 6.8 ns per replica for GTP and 12 replicas (at six different Hamiltonians) during 8.7 ns per replica for 8-Br-GTP. The large increase in sampling efficiency was obtained from an optimized H-REMD scheme involving soft-core potentials, with multiple simulations using the same level of softness. The optimization of the scheme was performed by fast mimicking [ J. Hritz and C. Oostenbrink, J. Chem. Phys. 127, 204104 (2007) ].
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87.15.ap Molecular dynamics simulation
87.15.B- Structure of biomolecules
87.15.hg Dynamics of intermolecular interactions
87.15.hp Conformational changes

Toward accurate thermochemical models for transition metals: G3Large basis sets for atoms Sc–Zn

Nicholas J. Mayhall, Krishnan Raghavachari, Paul C. Redfern, Larry A. Curtiss, and Vitaly Rassolov

J. Chem. Phys. 128, 144122 (2008); http://dx.doi.org/10.1063/1.2896084 (9 pages) | Cited 3 times

Online Publication Date: 14 April 2008

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An augmented valence triple-zeta basis set, referred to as G3Large, is reported for the first-row transition metal elements Sc through Zn. The basis set is constructed in a manner similar to the G3Large basis set developed previously for other elements (H–Ar, K, Ca, Ga–Kr) and used as a key component in Gaussian-3 theory. It is based on a contraction of a set of 15s13p5d Gaussian primitives to 8s7p3d, and also includes sets of f and g polarization functions, diffuse spd functions, and core df polarization functions. The basis set is evaluated with triples-augmented coupled cluster [CCSD(T)] and Brueckner orbital [BD(T)] methods for a small test set involving energies of atoms, atomic ions, and diatomic hydrides. It performs well for the low-lying s→d excitation energies of atoms, atomic ionization energies, and the dissociation energies of the diatomic hydrides. The Brueckner orbital-based BD(T) method performs substantially better than Hartree–Fock–based CCSD(T) for molecules such as NiH, where the starting unrestricted Hartree–Fock wavefunction suffers from a high degree of spin contamination. Comparison with available data for geometries of transition metal hydrides also shows good agreement. A smaller basis set without core polarization functions, G3MP2Large, is also defined.
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31.15.bw Coupled-cluster theory
33.15.Ry Ionization potentials, electron affinities, molecular core binding energy
31.15.xr Self-consistent-field methods
32.50.+d Fluorescence, phosphorescence (including quenching)
back to top Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Computed lifetimes of metastable states of the NO2+ dication

R. Baková, J. Fišer, T. Šedivcová-Uhlíková, and V. Špirko

J. Chem. Phys. 128, 144301 (2008); http://dx.doi.org/10.1063/1.2898495 (7 pages) | Cited 6 times

Online Publication Date: 8 April 2008

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Based on the ab initio potential energy, spin-orbit coupling, electronic transition dipole moment, and radial nonadiabatic coupling functions, the energy level positions, lifetimes, and radiative transition probabilities (Einstein A coefficients) have been determined for the lowest electronic states of NO2+ using the log-amplitude-phase, stabilization, and complex-scaling methods. The calculated characteristics are in reasonable agreement to the available experimental data, thus, evidencing the reliability of the theoretical predictions for the characteristics unobserved to date. With the exception of the v ⩽ 2 vibrational states of the B 2Σ+ electronic state, the calculated radiative lifetimes of the excited electronic states are longer than their predissociation lifetimes, hence, accounting for the failure of the attempts which have been made so far to observe any emission from the latter states.
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31.15.aj Relativistic corrections, spin-orbit effects, fine structure; hyperfine structure
33.70.Ca Oscillator and band strengths, lifetimes, transition moments, and Franck-Condon factors
33.15.Mt Rotation, vibration, and vibration-rotation constants
33.20.Tp Vibrational analysis
33.80.Gj Diffuse spectra; predissociation, photodissociation
31.50.Df Potential energy surfaces for excited electronic states

Quantum dynamics study of the K+HF(v = 0–2,j = 0)→KF+H reaction and comparison with quasiclassical trajectory results

Jordi Mayneris, Rodrigo Martínez, Jordi Hernando, Stephen K. Gray, and Miguel González

J. Chem. Phys. 128, 144302 (2008); http://dx.doi.org/10.1063/1.2850887 (7 pages) | Cited 2 times

Online Publication Date: 8 April 2008

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Extensive quantum real wave packet calculations within the helicity decoupling approximation are used to analyze the influence of the HF vibrational excitation on the K+HF(v = 0–2,j = 0)→KF+H reaction. Quantum reaction probabilities P and reaction cross sections σ are compared with corresponding quasiclassical trajectory (QCT) results. Disregarding threshold regions for v = 0 and 1 (v = 2 has no threshold), both approaches lead to remarkably similar results, particularly for σ, validating the use of the QCT method for this system. When moving from v = 0 to v = 1 there is a large increase in P and σ, as expected for a late barrier system. For v = 2 the reaction becomes exoergic and P ≈ 0.95 (with the exception of large total angular momenta where centrifugal barriers play a role). While substantial vibrational enhancement of the reactivity is thus seen, it is still quite less than that inferred from experimental data in the intermediate and high collision energy ranges. The origin of this discrepancy is unclear.
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82.30.Hk Chemical exchanges (substitution, atom transfer, abstraction, disproportionation, and group exchange)
82.20.Pm Rate constants, reaction cross sections, and activation energies
82.20.Ej Quantum theory of reaction cross section
82.20.Fd Collision theories; trajectory models

Excitation levels and magic numbers of small parahydrogen clusters (N ⩽ 40)

Rafael Guardiola and Jesús Navarro

J. Chem. Phys. 128, 144303 (2008); http://dx.doi.org/10.1063/1.2903462 (7 pages) | Cited 8 times

Online Publication Date: 9 April 2008

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The excitation energies of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of 1 molecule from 3 to 40 molecules. These clusters possess a very rich spectra, with angular momentum excitations arriving up to L = 13 for the heavier ones. No regular pattern can be guessed in terms of the angular momenta and the size of the cluster. Clusters with N = 13 and 36 are characterized by a peak in the chemical potential and a large energy gap of the first excited level, which indicate the magical character of these clusters. From the calculated excitation energies, the partition function has been obtained, thus allowing for an estimate of thermal effects. An enhanced production is predicted for cluster sizes of N = 13, 31, and 36, which is in agreement with the experiment.
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36.40.Mr Spectroscopy and geometrical structure of clusters
33.80.Rv Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states)
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