Survey of exact N-body decompositions of stochastic scalar-Jastrow–Hartree form

The quantum N-body dynamics problem with pairwise interactions can be exactly decomposed into the average of N stochastically evolving 1-body problems, thereby eliminating the usual exponential scaling of computational costs. Unfortunately, the variance in such averages can be large leading to slow Monte Carlo convergence. In addition, norm preserving decompositions are available only for identical fermions or bosons. Here we introduce a family of decompositions of scalar-Jastrow–Hartree form which can be applied to electronic structure and many molecular dynamics problems. We also discuss their convergence properties and test a few such methods on the vibrational stretching mode dynamics of CH₄. Finally, we explain how the Monte Carlo convergence problem can be completely eliminated via the introduction of a perfect control variate.     

Surface Corrugation in Rotational and Diffractive Scattering of O2 from LiF （001）

A quantum dynamic calculation on a five-dimensional O2/LiF （001） model system is performed using the multi-configuration time-dependent Hartree method. The obtained results show that the mechanism of rotational and diffractive excitation in details： Comparison with the rotational excited state, the initially non-rotational state is seen to favor the inelastic scattering in the rotational excitation process. The surface corrugation can damp the quantum interferences and produce a greater amount of rotational inelastic scattering at the expense of the elastic process in the rotational excitation process. The diffraction process and the average energy transferred into the rotational and diffractive mode are also discussed.     

Proton-coupled electron transfer of the phenoxyl/phenol couple: effect of Hartree-Fock exchange on transition structures

Proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) reactions of the phenoxyl/phenol couple are studied theoretically by using wave function theory (WFT) as well as DFT methods. At the complete active space self-consistent field (CASSCF) level, geometry optimization is found to give two transition states (TSs); one is the PCET type with two benzene rings being nearly coplanar, and the other is the HAT type with two benzene rings taking a stacking structure. Geometry optimization at the (semilocal) DFT level, on the other hand, is found to give only one transition state (i.e., the PCET-type one) and fail to obtain the stacking TS structure. By comparing various levels of theories (including long-range corrected DFT functionals), we demonstrate that the Hartree-Fock exchange at long range plays a critical role in obtaining the sufficient stacking stabilization of the present open-shell system, and that the sole addition of empirical dispersion correction to semilocal DFT functionals may not be adequate for describing such a stacking interaction. Next, we investigate the solvent effect on the PCET and HAT TS thus obtained using the reference interaction site model self-consistent field (RISM-SCF) method. The results suggest that the free energy barrier increases with increasing polarity of the solvent, and that the solvent effects are stronger for the PCET TS than the stacking HAT TS pathway. The reason for this is discussed based on the dipole moment of different TS structures in solution.     

Semiclassical spectral series of a Hartree-type operator corresponding to a rest point of the classical Hamilton-Ehrenfest system

We consider the classical equations of motion in quantum means, i.e., the Hamilton-Ehrenfest system. In the semiclassical approximation in the framework of the covariant approach based on these equations, we construct the spectral series of a nonlinear Hartree-type operator corresponding to a rest point. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 26–40, January, 2007.     

Molecular properties in the Tamm–Dancoff approximation: indirect nuclear spin–spin coupling constants

The Tamm–Dancoff approximation (TDA) can be applied to the computation of excitation energies using time-dependent Hartree–Fock (TD-HF) and time-dependent density-functional theory (TD-DFT). In addition to simplifying the resulting response equations, the TDA has been shown to significantly improve the calculation of triplet excitation energies in these theories, largely overcoming issues associated with triplet instabilities of the underlying reference wave functions. Here, we examine the application of the TDA to the calculation of another response property involving triplet perturbations, namely the indirect nuclear spin–spin coupling constant. Particular attention is paid to the accuracy of the triplet spin–dipole and Fermi-contact components. The application of the TDA in HF calculations leads to vastly improved results. For DFT calculations, the TDA delivers improved stability with respect to geometrical variations but does not deliver higher accuracy close to equilibrium geometries. These observations are rationalised in terms of the ground- and excited-state potential energy surfaces and, in particular, the severity of the triplet instabilities associated with each method. A notable feature of the DFT results within the TDA is their similarity across a wide range of different functionals. The uniformity of the TDA results suggests that some conventional evaluations may exploit error cancellations between approximations in the functional forms and those arising from triplet instabilities. The importance of an accurate treatment of correlation for evaluating spin–spin coupling constants is highlighted by this comparison.     

Corrected small basis set Hartree‐Fock method for large systems

A quantum chemical method based on a Hartree‐Fock calculation with a small Gaussian AO basis set is presented. Its main area of application is the computation of structures, vibrational frequencies, and noncovalent interaction energies in huge molecular systems. The method is suggested as a partial replacement of semiempirical approaches or density functional theory (DFT) in particular when self‐interaction errors are acute. In order to get accurate results three physically plausible atom pair‐wise correction terms are applied for London dispersion interactions (D3 scheme), basis set superposition error (gCP scheme), and short‐ranged basis set incompleteness effects. In total nine global empirical parameters are used. This so‐called Hartee‐Fock‐3c (HF‐3c) method is tested for geometries of small organic molecules, interaction energies and geometries of noncovalently bound complexes, for supramolecular systems, and protein structures. In the majority of realistic test cases good results approaching large basis set DFT quality are obtained at a tiny fraction of computational cost. © 2013 Wiley Periodicals, Inc.     

Proton and Carbon‐13 NMR Studies of the Phencyclone Adducts of Medium Alkyl Chain‐Length N‐n‐Alkylmaleimides. Hindered Rotations and Magnetic Anisotropic Effects. Ab initio Calculations for Optimized Structures

Abstract

The Diels–Alder adducts, 3a–e, of phencyclone, 1, have been prepared from a series of N‐n‐alkylmaleimides, 2, with medium chain‐length n‐alkyl groups. The maleimides were obtained by cyclodehydration of the N‐n‐alkylmaleamic acids, 4, formed from reaction of maleic anhydride with the corresponding n‐alkylamines. The five adducts prepared included derivatives from n‐heptyl, 3a; n‐octyl, 3b; n‐nonyl, 3c; n‐decyl, 3d; and n‐dodecyl, 3e. The NMR spectra of the adducts were studied in CDCl₃ at ambient temperatures at 300 MHz for proton and 75 MHz for carbon‐13, with full proton assignments achieved by high‐resolution COSY45 spectra for the aryl and the alkyl regions. Slow exchange limit (SEL) spectra were observed for both ¹H and ¹³C spectra showing slow rotation on the NMR timescales of the unsubstituted bridgehead phenyl groups. Endo Diels–Alder adduct stereochemistry was supported by striking magnetic anisotropic shielding effects in the ¹H spectra of the alkyl groups, with the NCH₂ CH ₂ signal of each adduct appearing upfield of tetramethylsilane (TMS) at ca. ?0.32 ppm. Proton NMR spectra for precursor maleamic acids and maleimides are reported, with some solvent effects found (CDCl₃ vs. d ₆‐acetone) for the carbon‐bound HC?CH protons of 4. Ab initio molecular modeling calculations at the Hartree‐Fock level using the 6‐31G* basis set have been performed for two key conformers of the phencyclone adduct of N‐n‐octylmaleimide, as a representative structure for these hindered adducts, to estimate geometric parameters for the adduct. A syn conformer, with the alkyl chain directed into the adduct cavity, was found to be ca. 0.23 kcal/mol lower energy than an anti conformer (in which the alkyl chain was directed away from the phenanthrenoid moiety).     

Solvent effects in four-component relativistic electronic structure theory based on the reference interaction-site model

A combined method of the Dirac–Hartree–Fock (DHF) method and the reference interaction-site model (RISM) theory is reported; this is the initial implementation of the coupling of the four-component relativistic electronic structure theory and an integral equation theory of molecular liquids. In the method, the DHF and RISM equations are solved self-consistently, and therefore the electronic structure of the solute, including relativistic effects, and the solvation structure are determined simultaneously. The formulation is constructed based on the variational principle with respect to the Helmholtz energy, and analytic free energy gradients are also derived using the variational property. The method is applied to the iodine ion (I⁻), methyl iodide (CH₃I), and hydrogen chalcogenide (H₂X, where X = O–Po) in aqueous solutions, and the electronic structures of the solutes, as well as the solvation free energies and their component analysis, solvent distributions, and solute–solvent interactions, are discussed.     

Efficient electronic structure calculations for systems of one-dimensional periodicity with the restricted Hartree–Fock–linear combination of atomic orbitals method implemented in Fourier space

 Formulas are presented for restricted Hartree–Fock (RHF) calculations on systems with periodicity in one dimension using a basis set of contracted spherical Gaussians. Applying Fourier-space and Ewald-type methods, all lattice sums appearing in the formulation have been brought to forms exhibiting accelerated convergence. Calculations have been carried out for infinite chains of Li₂ molecules and a poly(oxymethylene) chain. The methods used here yield results that are far more precise than corresponding direct-space calculations and for the first time show the vanishing of the RHF density of states at the Fermi level for situations of partial band occupancy. Our initial computational implementation was about 5 times slower than the fastest direct-space RHF code, but improvements in special-function evaluations and numerical integrations over the Brillouin zone are shown to remove this disparity in computing speed. Received: 20 August 1999 / Accepted: 17 January 2000 / Published online: 5 June 2000