The model of level broadening in condensed phase

We study a model of non-Markovian kinetics for a harmonic oscillator embedded in a harmonic heat bath. We present a new scheme for approximately solving the quantum relaxation equation for the density matrix to find a distribution of level populations. It is found to be an extended Lorentzian with the width depending on the energy. A more convenient non-Markovian distribution called square root Fourier distribution that was implemented in the preceding paper [M. V. Basilevsky et al., J. Chem. Phys. 125, 194513 (2006)] is closely related to this extended Lorentzian model. Both distributions decay exponentially far away from their centers and reproduce well standard Lorentzian widths in the vicinity of the central region. A conventional Lorentzian model with such widths results when the Redfield approximation is applied in the frame of the present procedure.     

Localized exchange-correlation potential from second-order self-energy for accurate Kohn-Sham energy gap

A local Kohn-Sham (KS) exchange-correlation potential is derived by localizing the second-order self-energy operator, using approximations to the linear response Sham-Schlüter equation. Thanks to the use of the resolution-of-identity technique for the calculation of the self-energy matrix elements, the method is very efficient and can be applied to large systems. The authors investigate the KS energy gaps and lowest excitation energies of atoms and small- and medium-size molecules. Reference KS energy gaps (from accurate densities) of atoms and small molecules can be reproduced with great accuracy. For larger systems they found that the KS energy gap is smaller than the one obtained from the local-density approximation, showing the importance of an ab initio correlation in the Kohn-Sham potential.     

Padé spectrum decompositions of quantum distribution functions and optimal hierarchical equations of motion construction for quantum open systems

Pade? spectrum decomposition is an optimal sum-over-poles expansion scheme of Fermi function and Bose function [J. Hu, R. X. Xu, and Y. J. Yan, J. Chem. Phys. 133, 101106 (2010)]. In this work, we report two additional members to this family, from which the best among all sum-over-poles methods could be chosen for different cases of application. Methods are developed for determining these three Pade? spectrum decomposition expansions at machine precision via simple algorithms. We exemplify the applications of present development with optimal construction of hierarchical equations-of-motion formulations for nonperturbative quantum dissipation and quantum transport dynamics. Numerical demonstrations are given for two systems. One is the transient transport current to an interacting quantum-dots system, together with the involved high-order co-tunneling dynamics. Another is the non-Markovian dynamics of a spin-boson system.     

The orbital-specific-virtual local coupled cluster singles and doubles method

We extend the orbital-specific-virtual tensor factorization, introduced for local M?ller-Plesset perturbation theory in Ref. [J. Yang, Y. Kurashige, F. R. Manby and G. K. L. Chan, J. Chem. Phys. 134, 044123 (2011)], to local coupled cluster singles and doubles theory (OSV-LCCSD). The method is implemented by modifying an efficient projected-atomic-orbital local coupled cluster program (PAO-LCCSD) described recently, [H.-J. Werner and M. Schu?tz, J. Chem. Phys. 135, 144116 (2011)]. By comparison of both methods we find that the compact representation of the amplitudes in the OSV approach affords various advantages, including smaller computational time requirements (for comparable accuracy), as well as a more systematic control of the error through a single energy threshold. Overall, the OSV-LCCSD approach together with an MP2 correction yields small domain errors in practical calculations. The applicability of the OSV-LCCSD is demonstrated for molecules with up to 73 atoms and realistic basis sets (up to 2334 basis functions).     

Optimized hierarchical equations of motion theory for Drude dissipation and efficient implementation to nonlinear spectroscopies

Hierarchical equations of motion theory for Drude dissipation is optimized, with a convenient convergence criterion proposed in advance of numerical propagations. The theoretical construction is on the basis of a Pade? spectrum decomposition that has been qualified to be the best sum-over-poles scheme for quantum distribution function. The resulting hierarchical dynamics under the a priori convergence criterion are exemplified with a benchmark spin-boson system, and also the transient absorption and related coherent two-dimensional spectroscopy of a model exciton dimer system. We combine the present theory with several advanced techniques such as the block hierarchical dynamics in mixed Heisenberg-Schro?dinger picture and the on-the-fly filtering algorithm for the efficient evaluation of third-order optical response functions.     

Exploring fundamental differences between red- and blue-shifted intramolecular hydrogen bonds using FAMSEC,FALDI, IQA and QTAIM

We have discovered, using developed by us recently FALDI and FAMSEC computational techniques, fundamentally distinct mechanisms of intramolecular red- and blue-shifted H-bond formation that occurred in different conformers of the same molecule (amino-acid β-alanine) involving the same heteroatoms (O–H???N and N–H???O). Quantitative topological, geometric and energetic data of both H-bonds obtained with well-known QTAIM and IQA methodologies agree with what is known regarding H-bonding in general. However, the FALDI charge and decomposition scheme for calculating in real space 3D conformational deformation densities provided clear evidence that the process of electron density redistribution taking place on the formation of the stronger red-shifted H-bond is fundamentally distinct from the weaker blue-shifted H-bond. Contributions made by atoms of the X–H???Y–Z fragment (IUPAC notation) as well as distinct atoms on the H-bond formation were fully explored. The FAMSEC energy decomposition approach showed that the atoms involved in formation of the red-shifted H-bond interact in a fundamentally different fashion, both locally and with the remainder of the molecule, as compared with those of the blue-shifted H-bond. Excellent correlations of trends obtained with QTAIM, IQA, FAMSEC and FALDI techniques were obtained. Commentary regarding IUPAC recommended definition of an H-bond and validity of observed AILs (or bond paths) of the two H-bond kinds is also discussed.     

Physically based molecular device model in a transient circuit simulator

Two efficient, physically based models for the real-time simulation of molecular device characteristics of single molecules are developed. These models assume that through-molecule tunnelling creates a steady-state Lorentzian distribution of excess electron density on the molecule and provides for smooth transitions for the electronic degrees of freedom between the tunnelling, molecular-excitation, and charge-hopping transport regimes. They are implemented in the fREEDA™ transient circuit simulator to allow for the full integration of nanoscopic molecular devices in standard packages that simulate entire devices including CMOS circuitry. Methods are presented to estimate the parameters used in the models via either direct experimental measurement or density-functional calculations. The models require 6–8 orders of magnitude less computer time than do full a priori simulations of the properties of molecular components. Consequently, molecular components can be efficiently implemented in circuit simulators. The molecular-component models are tested by comparison with experimental results reported for 1,4-benzenedithiol.     

Using simultaneous diagonalization and trace minimization to make an efficient and simple multidimensional basis for solving the vibrational Schrodinger equation

In this paper we improve the product simultaneous diagonalization (SD) basis method we previously proposed [J. Chem. Phys. 122, 134101 (2005)] and applied to solve the Schrodinger equation for the motion of nuclei on a potential surface. The improved method is tested using coupled complicated Hamiltonians with as many as 16 coordinates for which we can easily find numerically exact solutions. In a basis of sorted products of one-dimensional (1D) SD functions the Hamiltonian matrix is nearly diagonal. The localization of the 1D SD functions for coordinate qc depends on a parameter we denote alphac. In this paper we present a trace minimization scheme for choosing alphac to nearly block diagonalize the Hamiltonian matrix. Near-block diagonality makes it possible to truncate the matrix without degrading the accuracy of the lowest energy levels. We show that in the sorted product SD basis perturbation theory works extremely well. The trace minimization scheme is general and easy to implement.     

Approximate density matrices and wigner distribution functions from density,kinetic energy density,and idempotency constraints

The Wigner distribution function and the corresponding density matrix are calculated using a form for the distribution function suggested by maximization of the entropy. Wigner functions and density matrices are determined by imposing conditions of idempotency on the density matrix. Exchange energies and Compton profiles calculated from density matrices obtained by imposing the idempotency constraints are compared with the results of calculations using the Hartree–Fock density matrix and a Gaussian approximation for the density matrix for H and the noble gases He through Xe. Compton profiles from Wigner functions with idempotency constraints show improvements over the Gaussian approximation for the lighter atoms, but do not show significant changes for the heavier atoms. Exchange energies from density matrices with idempotency constraints show improvements over the Gaussian approximation except for the heavier atoms Kr and Xe.     

Finite-difference solution of the Poisson–Boltzmann equation: Complete elimination of self-energy

A new procedure to solve the Poisson–Boltzmann equation is proposed and shown to be efficient. The electrostatic potential due to the reaction field is calculated directly. Self-interactions among the charges are completely eliminated. Therefore, the reference calculation to cancel out the self-energy is not needed. © 1996 by John Wiley & Sons, Inc.     

Efficient particle labeling in atomistic simulations

The authors develop an efficient particle labeling procedure based on a linked cell algorithm which is shown to reduce the computing time for a molecular dynamics simulation by a factor of 3. They prove that the improvement of performance is due to the efficient fulfillment of both spatial and temporal locality principles, as implemented by the contiguity of labels corresponding to interacting atoms. Finally, they show that the present label reordering procedure can be used to devise an efficient parallel one-dimensional domain decomposition molecular dynamics scheme.     

Symmetry-adapted formulation of the G-particle-hole hypervirial equation method

Highly accurate 2-body reduced density matrices of atoms and molecules have been directly determined without calculation of their wave functions with the use of the G-particle-hole hypervirial (GHV) equation method (Alcoba et?al. in Int. J. Quantum Chem. 109:3178, 2009). Very recently, the computational efficiency of the GHV method has been significantly enhanced through the use of sum factorization and matrix-matrix multiplication (Alcoba et?al. in Int. J. Quantum Chem 111:937, 2011). In this paper, a detailed analysis of the matrix contractions involved in GHV calculations is carried out. The analysis leads to a convenient strategy for exploiting point group symmetry, by which the computational efficiency of the GHV method is further improved. Implementation of the symmetry-adapted formulation of the method is reported. Computer timings and hardware requirements are illustrated for several representative chemical systems. Finally, the method is applied to the well-known challenging calculation of the torsional potential in ethylene.     

An interaction site model integral equation study of molecular fluids explicitly considering the molecular orientation

We implemented an interaction site model integral equation for rigid molecules based on a density-functional theory where the molecular orientation is explicitly considered. In this implementation of the integral equation, multiple integral of the degree of freedom of the molecular orientation is performed using efficient quadrature methods, so that the site-site pair correlation functions are evaluated exactly in the limit of low density. We apply this method to Cl(2), HCl, and H(2)O molecular fluids that have been investigated by several integral equation studies using various models. The site-site pair correlation functions obtained from the integral equation are in good agreement with the one from a simulation of these molecules. Rotational invariant coefficients, which characterize the microscopic structure of molecular fluids, are determined from the integral equation and the simulation in order to investigate the accuracy of the integral equation.     

Comparison of two genres for linear scaling in density functional theory: purification and density matrix minimization methods

Two classes of linear-scaling methods to replace diagonalization of the one-particle Hamiltonian matrix in density functional theory are compared to each other. Purification takes a density matrix with the correct eigenfunctions and corrects the occupation numbers; density matrix minimization takes a density matrix with correct occupation numbers and corrects the eigenfunctions by rotating the orbitals. Computational comparisons are performed through modification of the MondoSCF program on water clusters and the protein endothelin. A purification scheme and a density matrix minimization scheme, based on the 1,2-contracted Schrodinger equation [D. A. Mazziotti, J. Chem. Phys. 115, 8305 (2001)] are implemented in large systems.     

Direct energy functional minimization under orthogonality constraints

The direct energy functional minimization problem in electronic structure theory, where the single-particle orbitals are optimized under the constraint of orthogonality, is explored. We present an orbital transformation based on an efficient expansion of the inverse factorization of the overlap matrix that keeps orbitals orthonormal. The orbital transformation maps the orthogonality constrained energy functional to an approximate unconstrained functional, which is correct to some order in a neighborhood of an orthogonal but approximate solution. A conjugate gradient scheme can then be used to find the ground state orbitals from the minimization of a sequence of transformed unconstrained electronic energy functionals. The technique provides an efficient, robust, and numerically stable approach to direct total energy minimization in first principles electronic structure theory based on tight-binding, Hartree-Fock, or density functional theory. For sparse problems, where both the orbitals and the effective single-particle Hamiltonians have sparse matrix representations, the effort scales linearly with the number of basis functions N in each iteration. For problems where only the overlap and Hamiltonian matrices are sparse the computational cost scales as O(M2N), where M is the number of occupied orbitals. We report a single point density functional energy calculation of a DNA decamer hydrated with 4003 water molecules under periodic boundary conditions. The DNA fragment containing a cis-syn thymine dimer is composed of 634 atoms and the whole system contains a total of 12,661 atoms and 103,333 spherical Gaussian basis functions.     

Simultaneous integration of mixed quantum-classical systems by density matrix evolution equations using interaction representation and adaptive time step integrator

A density matrix evolution method [H. J. C. Berendsen and J. Mavri, J. Phys. Chem., 97, 13464 (1993)] to simulate the dynamics of quantum systems embedded in a classical environment is applied to study the inelastic collisions of a classical particle with a five-level quantum harmonic oscillator. We improved the numerical performance by rewriting the Liouville–von Neumann equation in the interaction representation and so eliminated the frequencies of the unperturbed oscillator. Furthermore, replacement of the fixed time step fourth-order Runge–Kutta integrator with an adaptive step size control fourth-order Runge–Kutta resulted in significantly lower computational effort at the same desired accuracy. © 1996 by John Wiley & Sons, Inc.     

An ab initio study of the relationship between the O?H bond length and the harmonic and anharmonic stretching force constants for planar molecules containing C?OH,N?OH,and O?OH groups

The O? H bond length and the quadratic, cubic, and quartic stretching force constants, calculated ab initio using the unscaled 4-31G basis set with full geometry optimization, are reported for 30 planar conformers of ten molecules contaning either the C? OH, N? OH, or O? OH group. The data are analyzed in terms of the general form of Clark's equation, and the power functions and exponential functions proposed by Herschbach and Laurie. In the case of the quadratic constants, significant trends are found in the values of the parameters depending on whether the O? H group is bonded to carbon, nitrogen, or oxygen, and whether it is non-hydrogen-bonded or involved in intramolecular hydrogen bond formation in four-, five-, or six-membered rings. Using data for diatomic molecules, O? H, and C? H bonds, and the C?O and C? C bonds in planar monosubstituted carbonyl compounds, the parameter d_ij in the power function equation for quadratic constants, which can be regarded as the distance of closest approach of the two nuclei, is shown to increase progressively along the series (i) diatomic molecule; (ii) similar bond in a polyatomic environment with one of the two atoms covalently bonded to a neighboring atom; (iii) as in (ii) but with the second atom hydrogen bonded; and (iv) with both atoms covalently bonded to neighboring atoms.