Volume 137, Issue 20, 28 November 2012

We extended the previously reported isotropic sitesite potential for the exchange part [D. Yokogawa, Chem. Phys. Lett.515, 179 (2011)]10.1016/j.cplett.2011.08.094 and combined it with isotropic sitesite potential for the electrostatic part. To treat complex systems, such as excitedstate molecules and metal complexes, multiconfiguration selfconsistent field method was employed. The method was applied to the calculation of intermolecular interactions between and aromatic compounds, namely, pnitoroaniline, imidazolium cation, and cyclopentadienyl anion. The potential thus obtained was combined with the extended reference interaction site model and the threedimensional reference interaction site model for the calculation of the solvation structure. The present method gave reasonable intermolecular interactions and solvation structures at ground and excited states.
 COMMUNICATIONS


Communication: Oscillated band gaps of B/Ncodoped αgraphyne
View Description Hide DescriptionThe physical mechanism for the electronic structures tuning and band gap opening of αgraphyne are investigated from the first principles calculations. The pathway of using B and N atoms to codope into graphyne is proposed. After codoping, B atom plays a role of hole doping and N atom acts as electron doping. In codoped graphyne, the Fermi energy returns around the Dirac point and a gap is introduced. Interestingly, the opened gaps oscillate periodically with the increasing distances between B and N atoms with the gap from 0.07 eV to 0.50 eV, which is caused by the breaking sublattice symmetry.

Communication: Electron impact ionization of binary H_{2}O/X clusters in helium nanodroplets: An ab initio perspective
View Description Hide DescriptionIn a recent experiment (H_{2}O)_{ n }/X_{ m } binary clusters (where X = Ar, N_{2}, CO, CO_{2}, and several other molecules) were formed in superfluid heliumnanodroplets and investigated by electron impact mass spectrometry [Liu et al., Phys. Chem. Chem. Phys.13, 13920 (2011)10.1039/c1cp20653b]. The addition of dopant X was found to affect the branching ratio between H_{3}O^{+}(H_{2}O)_{ n } and (H_{2}O)^{+} _{ n } _{+2} formation. Specifically, the addition of CO increased the proportion of protonated water cluster ions, whereas dopants such as Ar, N_{2}, and CO_{2}, had the opposite effect. In this work ab initio calculations have been performed on [X(H_{2}O)_{2}]^{+} ions, where X = Ar, N_{2}, CO, and CO_{2}, to try and explain this distinct behavior. CO is found to be unique in that it forms a HOCOH_{3}O^{+} unit in the most stable cationic complexes where the binding between HO and CO is stronger than that between H_{3}O^{+} and OH. Thus, on purely energetic grounds, loss of HOCO rather than CO should be the preferred fragmentation process. No comparable chemistry occurs when X = Ar, N_{2}, or CO_{2} and so the codopant requires less energy to depart than OH. The calculations therefore account for the experimental observations and provide evidence that HOCO formation is induced in helium droplets containing (H_{2}O)_{ n } clusters and codoped with CO when subject to electron impact ionization.

Communication: Semiclassical perturbation theory for the quantum diffractive scattering of atoms on thermal surfaces
View Description Hide DescriptionInspired by the semiclassical perturbation theory of Hubbard and Miller [J. Chem. Phys.80, 5827 (1984)10.1063/1.446609], we derive explicit expressions for the angular distribution of particles scattered from thermal surfaces. At very low surface temperature, the observed experimental background scattering is proportional to the spectral density of the phonons. The angular distribution is a sum of diffraction peaks and a broad background reflecting the spectral density. The theory is applied to measured angular distributions of Ne, Ar, and Kr scattered from a Cu(111) surface.
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 ARTICLES

 Theoretical Methods and Algorithms

Development of the isotropic sitesite potential for exchange repulsion energy and combination with the isotropic sitesite potential for electrostatic part
View Description Hide DescriptionWe extended the previously reported isotropic sitesite potential for the exchange part [D. Yokogawa, Chem. Phys. Lett.515, 179 (2011)]10.1016/j.cplett.2011.08.094 and combined it with isotropic sitesite potential for the electrostatic part. To treat complex systems, such as excitedstate molecules and metal complexes, multiconfiguration selfconsistent field method was employed. The method was applied to the calculation of intermolecular interactions between and aromatic compounds, namely, pnitoroaniline, imidazolium cation, and cyclopentadienyl anion. The potential thus obtained was combined with the extended reference interaction site model and the threedimensional reference interaction site model for the calculation of the solvation structure. The present method gave reasonable intermolecular interactions and solvation structures at ground and excited states.

An asymptotically consistent approximant method with application to soft and hardsphere fluids
View Description Hide DescriptionA modified Padé approximant is used to construct an equation of state, which has the same largedensity asymptotic behavior as the model fluid being described, while still retaining the lowdensity behavior of the virial equation of state (virial series). Within this framework, all sequences of rational functions that are analytic in the physical domain converge to the correct behavior at the same rate, eliminating the ambiguity of choosing the correct form of Padé approximant. The method is applied to fluids composed of “soft” spherical particles with separation distance r interacting through an inversepower pair potential, ϕ = ε(σ/r)^{ n }, where ε and σ are model parameters and n is the “hardness” of the spheres. For n < 9, the approximants provide a significant improvement over the 8term virial series, when compared against molecular simulation data. For n ⩾ 9, both the approximants and the 8term virial series give an accurate description of the fluid behavior, when compared with simulation data. When taking the limit as n → ∞, an equation of state for hard spheres is obtained, which is closer to simulation data than the 10term virial series for hard spheres, and is comparable in accuracy to other recently proposed equations of state. By applying a least square fit to the approximants, we obtain a general and accurate softsphere equation of state as a function of n, valid over the full range of density in the fluid phase.

The Nleap method for stochastic simulation of coupled chemical reactions
View Description Hide DescriptionNumerical simulation of the time evolution of a spatially homogeneous chemical system is always of great interest. Gillespie first developed the exact stochastic simulation algorithm (SSA), which is accurate but timeconsuming. Recently, many approximate schemes of the SSA are proposed to speed up simulation. Presented here is the Nleap method, which guarantees the validity of the leap condition and at the same time keeps the efficiency. In many cases, Nleap has better performance than the widelyused τleap method. The details of the Nleap method are described and several examples are presented to show its validity.

Evaluation of the pressure tensor and surface tension for molecular fluids with discontinuous potentials using the volume perturbation method
View Description Hide DescriptionIn this article we apply the volumeperturbation method to systems of particles interacting via discontinuous potentials. We have found that an accurate Monte Carlo simulation protocol can be used in order to study properties of very general nonspherical systems with discontinuous potentials, such as chain molecules and spherocylinders with squarewell interactions, and chain molecules with squarewell and squareshoulder interactions. From the simulation results obtained for these systems we verify that: (1) the method reproduces the pressure as used in NPT simulations; (2) discontinuous infinite repulsive interactions give asymmetric contributions to the pressure when compression and expansion movements are used; however for finite interactions these contributions are symmetric; and (3) the pressure contributions preserve the additivity of the potential interactions. Density profiles and surface tension for subcritical conditions are accurately predicted.

Incorporating configurationalbias Monte Carlo into the WangLandau algorithm for continuous molecular systems
View Description Hide DescriptionConfigurationalbias Monte Carlo has been incorporated into the WangLandau method. Although the WangLandau algorithm enables the calculation of the complete density of states, its applicability to continuous molecular systems has been limited to simple models. With the inclusion of more advanced sampling techniques, such as configurationalbias, the WangLandau method can be used to simulate complex chemical systems. The accuracy and efficiency of the method is assessed using as a test case systems of linear alkanes represented by a unitedatom model. With strict convergence criteria, the density of states derived from the WangLandau algorithm yields the correct heat capacity when compared to conventional Boltzmann sampling simulations.

Originindependent calculation of quadrupole intensities in Xray spectroscopy
View Description Hide DescriptionFor electronic excitations in the ultraviolet and visible range of the electromagnetic spectrum, the intensities are usually calculated within the dipole approximation, which assumes that the oscillating electric field is constant over the length scale of the transition. For the short wavelengths used in hard Xray spectroscopy, the dipole approximation may not be adequate. In particular, for metal Kedge Xray absorption spectroscopy(XAS), it becomes necessary to include higherorder contributions. In quantumchemical approaches to Xray spectroscopy, these socalled quadrupole intensities have so far been calculated by including contributions depending on the square of the electricquadrupole and magneticdipole transition moments. However, the resulting quadrupole intensities depend on the choice of the origin of the coordinate system. Here, we show that for obtaining an originindependent theory, one has to include all contributions that are of the same order in the wave vector consistently. This leads to two additional contributions depending on products of the electricdipole and electricoctupole and of the electricdipole and magneticquadrupole transition moments, respectively. We have implemented such an originindependent calculation of quadrupole intensities in XAS within timedependent densityfunctional theory, and demonstrate its usefulness for the calculation of metal and ligand Kedge XASspectra of transition metal complexes.

Multireference equationofmotion coupled cluster theory
View Description Hide DescriptionA generalization of the equationofmotion coupled clustertheory is proposed, which is built upon a multireference parent state. This method is suitable for a number of electronic states of a system that can be described by similar active spaces, i.e., different linear combinations of the same set of active space determinants. One of the suitable states is chosen as the parent state and the dominant dynamical correlation is optimized for this state using an internally contracted multireference coupled cluster ansatz. The remaining correlation and orbital relaxation effects are obtained via an uncontracted diagonalization of the transformed Hamiltonian, , in a compact multireference configuration interaction space, which involves configurations with at most single virtual orbital substitution. The latter effects are thus statespecific and this allows us to obtain multiple electronic states in the spirit of the equationofmotion coupled cluster approach. A crucial aspect of this formulation is the use of the amplitudes of the generalized normalordered transformed Hamiltonian as the residual equations for determining the internally contracted cluster amplitudes without any projection onto the excited configurations. These residuals have been termed as the manybody residuals. These equations are formally nonsingular and thus allow us to solve for all amplitudes without discarding any, in contrast to other internally contracted approaches. This is desirable to ensure transferability of dynamical correlation from the parent state to the target states. Preliminary results involving the lowlying electronic states of C_{2}, O_{2}, and the excitation spectra of three transition metal atoms, e.g., Fe, Cr, and Mn, including hundreds of excited states, illustrate the potential of our approach.

Development of Monte Carlo configuration interaction: Natural orbitals and secondorder perturbation theory
View Description Hide DescriptionApproximate natural orbitals are investigated as a way to improve a Monte Carlo configuration interaction (MCCI) calculation. We introduce a way to approximate the natural orbitals in MCCI and test these and approximate natural orbitals from MøllerPlesset perturbation theory and quadratic configuration interaction with single and double substitutions in MCCI calculations of singlepoint energies. The efficiency and accuracy of approximate natural orbitals in MCCI potential curve calculations for the double hydrogen dissociation of water, the dissociation of carbon monoxide, and the dissociation of the nitrogen molecule are then considered in comparison with standard MCCI when using full configuration interaction as a benchmark. We also use the method to produce a potential curve for water in an augccpVTZ basis. A new way to quantify the accuracy of a potential curve is put forward that takes into account all of the points and that the curve can be shifted by a constant. We adapt a secondorder perturbation scheme to work with MCCI (MCCIPT2) and improve the efficiency of the removal of duplicate states in the method. MCCIPT2 is tested in the calculation of a potential curve for the dissociation of nitrogen using both Slater determinants and configuration state functions.

Excitation energies from extended random phase approximation employed with approximate one and twoelectron reduced density matrices
View Description Hide DescriptionStarting from Rowe's equation of motion we derive extended random phase approximation (ERPA) equations for excitation energies. The ERPA matrix elements are expressed in terms of the correlated ground state one and twoelectron reduced density matrices, 1 and 2RDM, respectively. Three ways of obtaining approximate 2RDM are considered: linearization of the ERPA equations, obtaining 2RDM from density matrix functionals, and employing 2RDM corresponding to an antisymmetrized product of strongly orthogonal geminals (APSG) ansatz. Applying the ERPA equations with the exact 2RDM to a hydrogen molecule reveals that the resulting excitation energies are not exact. A correction to the ERPA excitation operator involving some double excitations is proposed leading to the ERPA2 approach, which employs the APSG one and twoelectron reduced density matrices. For twoelectron systems ERPA2 satisfies a consistency condition and yields exact singlet excitations. It is shown that 2RDM corresponding to the APSG theory employed in the ERPA2 equations yields excellent singlet excitation energies for Be and LiH systems, and for the N_{2} molecule the quality of the potential energy curves is at the coupled cluster singles and doubles level. ERPA2 nearly satisfies the consistency condition for small molecules that partially explains its good performance.

Accounting for intramolecular vibrational modes in open quantum system description of molecular systems
View Description Hide DescriptionElectronicvibrational dynamics in molecular systems that interact with an environment involve a large number of degrees of freedom and are therefore often described by means of open quantum system approaches. A popular approach is to include only the electronic degrees of freedom into the system part and to couple these to a nonMarkovian bath of harmonic vibrational modes that is characterized by a spectral density. Since this bath represents both intramolecular and external vibrations, it is important to understand how to construct a spectral density that accounts for intramolecular vibrational modes that couple further to other modes. Here, we address this problem by explicitly incorporating an intramolecular vibrational mode together with the electronic degrees of freedom into the system part and using the Fano theory for a resonance coupled to a continuum to derive an “effective” bath spectral density, which describes the contribution of intramolecular modes. We compare this effective model for the intramolecular mode with the method of pseudomodes, a widely used approach in simulation of nonMarkovian dynamics. We clarify the difference between these two approaches and demonstrate that the respective resulting dynamics and optical spectra can be very different.

Modeling plasmonics: A Huygens subgridding scheme for Lorentz media
View Description Hide DescriptionHuygens subgridding for the gridbased solution of the Maxwell equations is a new and promising technique that enables accurate computation of mixed systems, by efficiently reducing the computational cost for simulating structures where increased spatial resolution is required in part of space. The Huygens subgridding approach has previously been derived and tested for perfect electric conductors and Debye media. This work introduces a Huygens subgridding method that is applicable to Lorentz media, thus opening a range of new applications in the field of plasmonics.

Rareevent sampling: Occupationbased performance measures for parallel tempering and infinite swapping Monte Carlo methods
View Description Hide DescriptionIn the present paper we identify a rigorous property of a number of temperingbased Monte Carlo sampling methods, including parallel tempering as well as partial and infinite swapping. Based on this property we develop a variety of performance measures for such rareevent sampling methods that are broadly applicable, informative, and straightforward to implement. We illustrate the use of these performance measures with a series of applications involving the equilibrium properties of simple LennardJones clusters, applications for which the performance levels of partial and infinite swapping approaches are found to be higher than those of conventional parallel tempering.

Ab initio analytical infrared intensities for periodic systems through a coupled perturbed HartreeFock/KohnSham method
View Description Hide DescriptionA fully analytical method for calculating Born charges and, hence, infrared intensities of periodic systems, is formulated and implemented in the CRYSTAL program, which uses a local Gaussian type basis set. Our efficient formalism combines integral gradients with firstorder coupled perturbed Hartree–Fock/Kohn Sham electronic response to an electric field. It avoids numerical differentiation with respect to wave vectors, as in some Berry phase approaches, and with respect to atomic coordinates. No perturbation equations for the atomic displacements need to be solved. Several tests are carried out to verify numerical stability, consistency in one, two, and three dimensions, and applicability to large unit cells. Future extensions to piezoelectricity and Raman intensities are noted.

An efficient solution of Liouvillevon Neumann equation that is applicable to zero and finite temperatures
View Description Hide DescriptionApplication of quantum dissipation theory to electronic dynamics has been limited to model systems with few energy levels, and its numerical solutions are mostly restricted to high temperatures. A highly accurate and efficient numerical algorithm, which is based on the Chebyshev spectral method, is developed to integrate a singleparticle Liouvillevon Neumann equation, and the two longstanding limitations of quantum dissipation theory are resolved in the context of quantum transport. Its computational time scales to with N being the number of orbitals involved, which leads to a reality for the quantum mechanical simulation of real open systems containing hundreds or thousands of atomic orbitals. More importantly, the algorithm spans both finite and zero temperatures. Numerical calculations are carried out to simulate the transient current through a metallic wire containing up to 1000 orbitals.

Towards an efficient multiscale modeling of lowdimensional reactive systems: Study of numerical closure procedures
View Description Hide DescriptionWe study a numerical closure approach for systems of chemically reacting systems on lattices with lowdimensional support, for which a meanfield approximation is insufficiently accurate because of lateral interaction on the lattice. We introduce a hierarchy of macroscopic state variables, taking particle clusters into account, whose time evolution is obtained via microscopic (kinetic Monte Carlo) simulation. The macroscopic state variables are chosen such that they can be straightforwardly conserved during reconstruction of a microscopic configuration (the socalled lifting step). We present and compare the effects of different alternatives to initialize the remaining degrees of freedom. We illustrate the strong interplay between the number of macroscopic state variables and the specifics of the lifting and that, for a given lifting operator, accuracy of the macroscopic dynamics does not necessarily improve monotonically when adding macroscopic state variables.

Diffusion of multiple species with excludedvolume effects
View Description Hide DescriptionStochastic models of diffusion with excludedvolume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the interspecies competition emerges at the population level. Each individual is described as a finitesize hard core interacting particle undergoing Brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear crossdiffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excludedvolume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and selfdiffusion. Simulations of the discrete system show good agreement with the analytic results.

On the formulation of a density matrix functional for Van der Waals interaction of like and oppositespin electrons in the helium dimer
View Description Hide DescriptionWhereas a density functional that incorporates dispersion interaction has remained elusive to date, we demonstrate that in principle the dispersion energy can be obtained from a density matrixfunctional. In density matrix functionaltheory one tries to find suitable approximations to the twoparticle reduced density matrix (2RDM) in terms of natural orbitals (NOs) and natural orbital occupation numbers (ONs). The total energy is then given as a function(al) of the NOs and ONs, i.e., as an implicit functional of the 1RDM. The leftright correlation in a (dissociating) bond, as well as various types of dynamical correlation, can be described accurately with a NO functional employing only J and K integrals (JKonly functional). We give a detailed analysis of the full CI wavefunction of the He_{2} dimer, from which the dispersion part of the twoparticle density matrix is obtained. It emerges that the entirely different physics embodied in the dispersion interaction leads to an essentially different type of exchangecorrelation orbital functional for the dispersion energy (nonJK). The distinct NO functionals for the different types of correlation imply that they can be used in conjunction without problems of double counting. Requirements on the (primitive) basis set for Van der Waals bonding appear to be more modest than for other types of correlation.