A polarizable continuum model for molecules at spherical diffuse interfaces.

We present an extension of the Polarizable Continuum Model (PCM) to simulate solvent effects at diffuse interfaces with spherical symmetry, such as nanodroplets and micelles. We derive the form of the Green's function for a spatially varying dielectric permittivity with spherical symmetry and exploit the integral equation formalism of the PCM for general dielectric environments to recast the solvation problem into a continuum solvation framework. This allows the investigation of the solvation of ions and molecules in nonuniform dielectric environments, such as liquid droplets, micelles or membranes, while maintaining the computationally appealing characteristics of continuum solvation models. We describe in detail our implementation, both for the calculation of the Green's function and for its subsequent use in the PCM electrostatic problem. The model is then applied on a few test systems, mainly to analyze the effect of interface curvature on solvation energetics.

Wavelet formulation of the polarizable continuum model.

The first implementation of a wavelet discretization of the Integral Equation Formalism (IEF) for the Polarizable Continuum Model (PCM) is presented here. The method is based on the application of a general purpose wavelet solver on the cavity boundary to solve the integral equations of the IEF-PCM problem. Wavelet methods provide attractive properties for the solution of the electrostatic problem at the cavity boundary: the system matrix is highly sparse and iterative solution schemes can be applied efficiently; the accuracy of the solver can be increased systematically and arbitrarily; for a given system, discretization error accuracy is achieved at a computational expense that scales linearly with the number of unknowns. The scaling of the computational time with the number of atoms N is formally quadratic but a N(1.5) scaling has been observed in practice. The current bottleneck is the evaluation of the potential integrals at the cavity boundary which scales linearly with the system size. To reduce this overhead, interpolation of the potential integrals on the cavity surface has been successfully used.

Toward a General Formulation of Dispersion Effects for Solvation Continuum Models.

We revised the quantum model of Amovilli and Mennucci (J. Phys. Chem. B 1997, 101, 1051) to include the dispersion contribution to the solvation free energy within the framework of continuum models. Our revised formulation makes use of a single adjustable solvent-dependent parameter, and it can be readily generalized to different quantum mechanical descriptions. In particular, we made use of DFT and applied the model to investigate dispersion effects on vertical excitation energies within a time-dependent DFT framework. Our findings show that dispersion effects constitute a significant component of the absolute solvent effect but when relative solvent-solvent shifts are considered a cancellation effect is observed.

An efficient algorithm for solving nonlinear equations with a minimal number of trial vectors: applications to atomic-orbital based coupled-cluster theory.

The conjugate residual with optimal trial vectors (CROP) algorithm is developed. In this algorithm, the optimal trial vectors of the iterations are used as basis vectors in the iterative subspace. For linear equations and nonlinear equations with a small-to-medium nonlinearity, the iterative subspace may be truncated to a three-dimensional subspace with no or little loss of convergence rate, and the norm of the residual decreases in each iteration. The efficiency of the algorithm is demonstrated by solving the equations of coupled-cluster theory with single and double excitations in the atomic orbital basis. By performing calculations on H(2)O with various bond lengths, the algorithm is tested for varying degrees of nonlinearity. In general, the CROP algorithm with a three-dimensional subspace exhibits fast and stable convergence and outperforms the standard direct inversion in iterative subspace method.

General biorthogonal projected bases as applied to second-order Møller-Plesset perturbation theory.

With low-order scaling correlated wave function theories in mind, we present second quantization formalism as well as biorthonormalization procedures for general--singular or nonsingular--bases. Of particular interest are the so-called projected atomic orbital bases, which are obtained from a set of atom-centered functions and feature a separation of occupied and virtual spaces. We demonstrate the formalism by deriving and implementing second-order Møller-Plesset perturbation theory in it, and discuss the convergence and preconditioning of the iterative amplitude equations in detail.

Methodological aspects in the calculation of parity-violating effects in nuclear magnetic resonance parameters.

We examine the quantum chemical calculation of parity-violating (PV) electroweak contributions to the spectral parameters of nuclear magnetic resonance (NMR) from a methodological point of view. Nuclear magnetic shielding and indirect spin-spin coupling constants are considered and evaluated for three chiral molecules, H2O2, H2S2, and H2Se2. The effects of the choice of a one-particle basis set and the treatment of electron correlation, as well as the effects of special relativity, are studied. All of them are found to be relevant. The basis-set dependence is very pronounced, especially at the electron correlated ab initio levels of theory. Coupled-cluster and density-functional theory (DFT) results for PV contributions differ significantly from the Hartree-Fock data. DFT overestimates the PV effects, particularly with nonhybrid exchange-correlation functionals. Beginning from third-row elements, special relativity is of importance for the PV NMR properties, shown here by comparing perturbational one-component and various four-component calculations. In contrast to what is found for nuclear magnetic shielding, the choice of the model for nuclear charge distribution--point charge or extended (Gaussian)--has a significant impact on the PV contribution to the spin-spin coupling constants.

Perturbational calculations of parity-violating effects in nuclear-magnetic-resonance parameters.

We investigate the effects of the parity-violating electroweak interaction in the spectral parameters of nuclear magnetic resonance. Perturbational theory of parity-violating effects in the nuclear magnetic shielding is presented to the order of G(F)alpha, and in the indirect spin-spin coupling, to the order of G(F)alpha3. These leading-order parity-violating corrections are evaluated using analytical linear-response theory methods based on Hartree-Fock and density-functional theory reference states. Parity-violating contributions to spin-spin couplings are evaluated for the first time at the first-principles level. Calculations are carried out for two chiral halomethanes, bromochlorofluoromethane and bromofluoroiodomethane.