Volume 129, Issue 3, 21 July 2008
 ARTICLES

 Theoretical Methods and Algorithms

Why are timedependent density functional theory excitations in solids equal to band structure energy gaps for semilocal functionals, and how does nonlocal Hartree–Focktype exchange introduce excitonic effects?
View Description Hide DescriptionWe examine the timedependent density functional theory (TDDFT) equations for calculating excitation energies in solids with Gaussian orbitals and analytically show that for semilocal functionals, their lowest eigenvalue collapses to the minimum band orbital energy difference. With the introduction of nonlocal Hartree–Focktype exchange (as in hybrid functionals), this result is no longer valid, and the lowest TDDFT eigenvalue reflects the appearance of excitonic effects. Previously reported “chargetransfer” problems with semilocal TDDFT excitations in molecules can be deduced from our analysis by taking the limit to infinite lattice constant.

Nonadiabatic corrections to the wave function and energy
View Description Hide DescriptionNonadiabatic corrections in molecules composed of a few atoms are considered. It is demonstrated that a systematic perturbative expansion around the adiabatic solution is possible, with the expansion parameter being the electronnucleus mass ratio to the 3/4 power. Closed form formulas for the leading corrections to the wave function and to the energy are derived. Their applicability is demonstrated by a comparison of numerical results for the hydrogen molecule with the former nonadiabatic calculations and the experimental values. Good agreement with the recent experiment is achieved for the ground statedissociation energy of both and .

A statistical analysis of the precision of reweightingbased simulations
View Description Hide DescriptionVarious advanced simulation techniques, which are used to sample the statistical ensemble of systems with complex Hamiltonians, such as those displayed in condensed matters and biomolecular systems, rely heavily on successfully reweighting the sampled configurations. The sampled points of a system from an elevated thermal environment or on a modified Hamiltonian are reused with different statistical weights to evaluate its properties at the initial desired temperature or of the original Hamiltonian. Often, the decrease of accuracy induced by this procedure is ignored and the final results can be far from what is expected. We have addressed the reasons behind such a phenomenon and have provided a quantitative method to estimate the number of sampled points required in the crucial step of reweighting of these advanced simulation methods. We also provided examples from temperature histogram reweighting and accelerated molecular dynamics reweighting to illustrate this idea, which can be generalized to the dynamic reweighting as well. The study shows that this analysis may provide a priori guidance for the strategy of setting up the parameters of advanced simulations before a lengthy one is carried out. The method can therefore provide insights for optimizing the parameters for high accuracy simulations with finite amount of computational resources.

Quantum mechanical methods applied to excitation energy transfer: A comparative analysis on excitation energies and electronic couplings
View Description Hide DescriptionWe present a comparative study on the influence of the quantum mechanical (QM) method (including basis set) on the evaluation of transition energies, transition densities and dipoles, and excitation energy transfer (EET) electronic couplings for a series of chromophores (and the corresponding pairs) typically found in organic electrooptical devices and photosynthetic systems. On these systems we have applied five different QM levels of description of increasing accuracy (ZINDO, CIS, TDDFT, CASSCF, and SACCI). In addition, we have tested the effects of a surrounding environment (either mimicking a solvent or a protein matrix) on excitation energies, transition dipoles, and electronic couplings through the polarizable continuum model (PCM) description. Overall, the results obtained suggest that the choice of the QM level of theory affects the electronic couplings much less than it affects excitation energies. We conclude that reasonable estimates can be obtained using moderate basis sets and inexpensive methods such as configuration interaction of single excitations or timedependent density functional theory when appropriately coupled to realistic solvation models such as PCM.

A hybrid recursion method to robustly ensure convergence efficiencies in the simulated scaling based free energy simulations
View Description Hide DescriptionRecently, we developed an efficient free energy simulation technique, the simulated scaling (SS) method [H. Li et al., J. Chem. Phys.126, 024106 (2007)], in the framework of generalized ensemble simulations. In the SS simulations, random walks in the scaling parameter space are realized so that both phase space overlap sampling and conformational space sampling can be simultaneously enhanced. To flatten the distribution in the scaling parameter space, in the original SS implementation, the Wang–Landau recursion was employed due to its wellknown recursion capability. In the Wang–Landau recursion based SS free energy simulation scheme, at the early stage, recursion efficiencies are high and free energy regions are quickly located, although at this stage, the errors of estimated free energy values are large; at the later stage, the errors of estimated free energy values become smaller, however, recursions become increasingly slow and free energy refinements require very long simulation time. In order to robustly resolve this efficiency problem during free energy refinements, a hybrid recursion strategy is presented in this paper. Specifically, we let the Wang–Landau update method take care of the early stage recursion: the location of target free energy regions, and let the adaptive reweighting method take care of the late stage recursion: the refinements of free energy values. As comparably studied in the model systems, among three possible recursion procedures, the adaptive reweighting recursion approach is the least favorable one because of its low recursion efficiency during free energy region locations; and compared to the original Wang–Landau recursion approach, the proposed hybrid recursion technique can be more robust to guarantee free energy simulation efficiencies.

Analytic derivatives for the Cholesky representation of the twoelectron integrals
View Description Hide DescriptionWe propose a formalism for calculating analytic derivatives of the electronic energy with respect to nuclear coordinates using Cholesky decomposition of the twoelectron integrals. The formalism is derived by exploiting the equivalence of Cholesky decomposition and density fitting when a suitable auxiliary basis set is used for expanding atomic orbital product densities in the latter. An implementation of gradients at the nonhybrid density functional theory level is presented, and sample calculations demonstrate that the errors in equilibrium geometries due to the Cholesky representation of the integrals can be controlled by adjusting the decomposition threshold.

Simultaneous benchmarking of ground and excitedstate properties with longrangecorrected density functional theory
View Description Hide DescriptionWe present benchmark calculations using several longrangecorrected (LRC) density functionals, in which Hartree–Fock exchange is incorporated asymptotically using a rangeseparated Coulomb operator, while local exchange is attenuated using an ansatz introduced by Iikura et al. [J. Chem. Phys.115, 3540 (2001)]. We calculate groundstate atomization energies, reaction barriers, ionizationenergies, and electron affinities, each as a function of the rangeseparation parameter . In addition, we calculate excitation energies of small and mediumsized molecules, again as a function of , by applying the LRC to timedependent density functional theory. Representative examples of both pure and hybrid density functionals are tested. On the basis of these results, there does not appear to be a single rangeseparation parameter that is reasonable for both groundstateproperties and vertical excitation energies. Reasonable errors in atomization energies and barrier heights are achieved only at the expense of excessively high excitation energies, at least for the mediumsized molecules, whereas values of that afford reasonable excitation energies yield some of the largest errors for groundstate atomization energies and barrier heights in small molecules. Notably, this conclusion is obscured if the database of excitation energies includes only small molecules, as has been the case in previous benchmark studies of LRC functionals.

Stochastic surrogate Hamiltonian
View Description Hide DescriptionThe surrogate Hamiltonian is a general scheme to simulate the many body quantum dynamics composed of a primary system coupled to a bath. The method has been based on a representative bath Hamiltonian composed of twolevel systems that is able to mimic the true systembath dynamics up to a prespecified time. The original surrogate Hamiltonian method is limited to short time dynamics since the size of the Hilbert space required to obtain convergence grows exponentially with time. By randomly swapping bath modes with a secondary thermal reservoir, the method can simulate quantum dynamics of the primary system from short times to thermal equilibrium. By averaging a small number of realizations converged values of the system observables are obtained avoiding the exponential increase in resources. The method is demonstrated for the equilibration of a molecular oscillator with a thermal bath.

A direct relativistic fourcomponent multiconfiguration selfconsistentfield method for molecules
View Description Hide DescriptionA new direct relativistic fourcomponent Kramersrestricted multiconfiguration selfconsistentfield (KRMCSCF) code for molecules has been implemented. The program is based upon Kramerspaired spinors and a full implementation of the binary double groups ( and subgroups). The underlying quaternion algebra for oneelectron operators was extended to treat twoelectron integrals and density matrices in an efficient and nonredundant way. The iterative procedure is direct with respect to both configurational and spinor variational parameters; this permits the use of large configuration expansions and many basis functions. The relativistic minimummaximum principle is implemented in a secondorder restrictedstep optimization algorithm, which provides sharp and wellcontrolled convergence. This paper focuses on the necessary modifications of nonrelativistic MCSCF methodology to obtain a fully variational KRMCSCF implementation. The general implementation also allows for the use of molecular integrals from a twocomponent relativistic Hamiltonian as, for example, the Douglas–Kroll–Hess variants. Several sample applications concern the determination of spectroscopic properties of heavyelement atoms and molecules, demonstrating the influence of spinorbit coupling in MCSCF approaches to such systems and showing the potential of the new method.

Nonnormal Lanczos methods for quantum scattering
View Description Hide DescriptionThis article presents a new complex absorbing potential (CAP) block Lanczos method for computing scattering eigenfunctions and reaction probabilities. The method reduces the problem of computing energy eigenfunctions to solving two energy dependent systems of equations. An energy independent block Lanczos factorization casts the system into a block tridiagonal form, which can be solved very efficiently for all energies. We show that CAPLanczos methods exhibit instability due to the nonnormality of CAP Hamiltonians and may break down for some systems. The instability is not due to loss of orthogonality but to nonnormality of the Hamiltonian matrix. While use of a Woods–Saxon exponential CAP—as opposed to a polynomial CAP—reduced nonnormality, it did not always ensure convergence. Our results indicate that the Arnoldi algorithm is more robust for nonnormal systems and less prone to break down. An Arnoldi version of our method is applied to a nonadiabatictunneling Hamiltonian with excellent results, while the Lanczos algorithm breaks down for this system.

Basis set limit Hartree–Fock and density functional theory response property evaluation by multiresolution multiwavelet basis
View Description Hide DescriptionWe describe the evaluation of response properties using multiresolution multiwavelet (MRMW) basis sets. The algorithm uses direct projection of the perturbed density operator onto the zeroth order density operator on the real space spanned by the MRMW basis set and is applied for evaluating the polarizability of small molecules using Hartree–Fock and Kohn–Sham density functional theory. The computed polarizabilities can be considered to be converged to effectively complete space within the requested precision. The efficiency of the method against the ordinary Gaussian basis computation is discussed.

Quantum theory of chemical reactions in the presence of electromagnetic fields
View Description Hide DescriptionWe present a theory for rigorous quantum scattering calculations of probabilities for chemical reactions of atoms with diatomic molecules in the presence of an external electric field. The approach is based on the fully uncoupled basis set representation of the total wave function in the spacefixed coordinate frame, the Fock–Delves hyperspherical coordinates, and the adiabatic partitioning of the total Hamiltonian of the reactive system. The adiabatic channel wave functions are expanded in basis sets of hyperangular functions corresponding to different reaction arrangements, and the interactions with external fields are included in each chemical arrangement separately. We apply the theory to examine the effects of electric fields on the chemical reactions of LiF molecules with H atoms and HF molecules with Li atoms at low temperatures and show that electric fields may enhance the probability of chemical reactions and modify reactive scattering resonances by coupling the rotational states of the reactants. Our preliminary results suggest that chemical reactions of polar molecules at temperatures below 1 K can be selectively manipulated with dc electric fields and microwave laser radiation.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

The 2naphthol cluster: Two competing types of hydrogenbonding arrangements
View Description Hide DescriptionThe potential energy surfaces of the and states of the 2naphthol, clusters were explored at the level of coupled cluster (CC2) response theory. In the electronic ground state two different types of hydrogenbonding networks coexist for , (i) a cyclic one [similar to those of the water trimer and phenol] where the hydroxy group of the aryl alcohol acts simultaneously as H donor for the first, and as H acceptor for the second water molecule, and (ii) a hydrogenbonding arrangement where the aromatic system is taking over the role as H acceptor. In the state, on the other hand, the cyclic conformers are unstable. Consequently, the first group of cyclic ground state conformers gives rise to broad unstructured band shapes in the absorptionspectrum, whereas the second group of conformers involving the aromatic system gives rise to nicely structured band shapes. Based on these results the puzzling absorptionspectrum of the cluster can properly be interpreted.

Single switch surface hopping for a model of pyrazine
View Description Hide DescriptionThe single switch trajectory surface hopping algorithm is tested for numerical simulations of a twostate threemode model for the internal conversion of pyrazine through a conical intersection of potential energy surfaces. The algorithm is compared to two other surface hopping approaches, namely, Tully’s method of the fewest switches [J. Chem. Phys.93, 1061 (1990)] and the method by Voronin et al. [J. Phys. Chem. A102, 6057 (1998)]. The single switch algorithm achieves the most accurate results. Replacing its deterministic nonadiabatic branching condition by a probabilistic acceptreject criterion, one obtains the method of Voronin et al. without momentum adjustment. This probabilistic version of the single switch approach outperforms the considered algorithms in terms of accuracy, memory requirement, and runtime.

: What do we know about it?
View Description Hide DescriptionThe potential energy surface of has been analyzed and stationary points and minima of intersections characterized by benchmark multireference configuration interaction calculations with basis sets as large as augmented septuble zeta. No evidence for minima other than those of the well established stable configuration has been found. Some of the results obtained previously at a lower level of ab initiotheory had to be revised.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Sitedirected electronic tunneling in a dissipative molecular environment
View Description Hide DescriptionThe ability to control electronic tunneling in complex molecular networks of multiple donor/acceptor sites is studied theoretically. Our past analysis, demonstrating the phenomenon of sitedirected transport, was limited to the coherent tunneling regime. In this work we consider electronic coupling to a dissipative molecular environment including the effect of decoherence. The nuclear modes are classified into two categories. The first kind corresponds to the internal molecular modes, which are coupled to the electronic propagation along the molecular bridges. The second kind corresponds to the external solvent modes, which are coupled to the electronic transport between different segments of the molecular network. The electronic dynamics is simulated within the effective single electron picture in the framework of the tight binding approximation. The nuclear degrees of freedom are represented as harmonic modes and the electronicnuclear coupling is treated within the timedependent Redfield approximation. Our results demonstrate that sitedirected tunneling prevails in the presence of dissipation, provided that the decoherence time is longer than the time period for tunneling oscillations (e.g., at low temperatures). Moreover, it is demonstrated that the strength of electronic coupling to the external nuclear modes (the solvent reorganization energy) controls the coherent intramolecular tunnelingdynamics at short times and may be utilized for the experimental control of sitedirected tunneling in a complex network.

The isotropic nuclear magnetic shielding constants of acetone in supercritical water: A sequential Monte Carlo/quantum mechanics study including solute polarization
View Description Hide DescriptionThe nuclear isotropic shielding constants and of the carbonyl bond of acetone in water at supercritical ( and ) and normal water conditions have been studied theoretically using Monte Carlo simulation and quantum mechanics calculations based on the method. Statistically uncorrelated configurations have been obtained from Monte Carlo simulations with unpolarized and insolution polarized solute. The results show that solvent effects on the shielding constants have a significant contribution of the electrostatic interactions and that quantitative estimates for solvent shifts of shielding constants can be obtained modeling the water molecules by point charges (electrostatic embedding). In supercritical water, there is a decrease in the magnitude of but a sizable increase in the magnitude of when compared with the results obtained in normal water. It is found that the influence of the solutepolarization is mild in the supercritical regime but it is particularly important for in normal water and its shielding effect reflects the increase in the average number of hydrogen bonds between acetone and water. Changing the solvent environment from normal to supercritical water condition, the calculations on the statistically uncorrelated configurations sampled from the Monte Carlo simulation give a chemical shift of for polarized acetone in good agreement with the experimentally inferred result of .

Refinements in the characterization of the heterogeneous dynamics of Li ions in lithium metasilicate
View Description Hide DescriptionWe have performed the molecular dynamics simulations of ionically conducting lithium metasilicate, , to get a more in depth understanding of the heterogeneous ion dynamics by separating out the partial contributions from localized and diffusive ions to the mean square displacement (MSD) , the nonGaussian parameter , and the van Hove function . Several different cage sizes have been used for the definition of localized ions. Behaviors of fast ions are obtained by the subtraction of the localized component from the of all ions, and accelerated dynamics is found in the resultant subensemble. The fractional power law of MSD is explained by the geometrical correlation between successive jumps. The waiting time distribution of jumps also plays a role in determining but does not affect the exponent of its fractional power law time dependence. Partial nonGaussian parameters are found to be instructive to learn how long lengthscale motions contribute to various quantities. As a function of time, the partial nonGaussian parameter for the localized ions exhibits a maximum at around , the onset time of the fractional power law regime of . The position of the maximum is slightly dependent on the choice of . The power law increases in the nonGaussian parameter before the maximum are attributed to the Lévy distribution of length scales of successive (long) jumps. The decreases with time, after the maximum has been reached, are due to large back correlation of motions of different length scales. The dynamics of fast ions with superlinear dependence in their MSD also start at time around the maximum. Also investigated are the changes of the characteristic times demarcating different regimes of on increasing temperatures from the glassy state to the liquid state. Relation between the activation energies for short time and long time regimes of is in accord with interpretation of ion dynamics by the coupling model.

POLIR: Polarizable, flexible, transferable water potential optimized for IR spectroscopy
View Description Hide DescriptionA polarizable, flexible and transferable potential for water, POLIR, is presented. In addition to providing a good description of the usual structural and kinetic properties, POLIR correctly describes the vibrational frequencies, absolute infrared intensities, and HOH angle in clusters, liquid water, and ice, offering the possibility of a comprehensive classical theory of vibrational spectroscopy. The high degree of transferability suggests applications to solvation and to water that is confined, interfacial, and under the extreme conditions encountered in the geological and planetary sciences.

The microscopic structure of an exactly solvable model binary solution that exhibits two closed loops in the phase diagram
View Description Hide DescriptionAn exactly solvable lattice model describing a binary solution is considered where rodlike molecules of types and cover the links of a honeycomb lattice, the neighboring molecular ends having threebody and orientationdependent bonding interactions. At phase coexistence of rich and rich phases, the average fraction of each type of triangle of neighboring molecular ends is calculated exactly. The fractions of the different types of triangles are then used to deduce the local microscopic structure of the coexisting phases for a case of the model that contains two closed loops in the phase diagram.