Claudio Amovilli

Recent Advances in the Description of Solvent Effects with the Polarizable Continuum Model

Publisher Summary This chapter presents a set of methods addressed to the study of solvation problems at the quantum mechanical level with the use of polarizable continuum model (PCM). The chapter describes the evolution of continuous methods since the first proposals or the first formulation at a QM level, semiempirical, or ab initio. PCM belongs to the family of methods in which focuses on a limited portion of matter, the ‘solute’ (one or more molecules) while the remaining, and larger, portion of the solution, called here the ‘solvent’, is treated at a lower level of accuracy. PCM is a quantum mechanical (QM) method in which use is made of an effective Hamiltonian for the solute M , and the corresponding Schrodinger equation is generally (but not compulsory) treated at the ab initio level. PCM makes use of continuous solvent distributions to describe the solute-solvent interaction potential. The chapter demonstrates that PCM manages to treat not only the well known model based on a uniform isotropic dielectric description of the solvent, whose interactions are limited to the electrostatic terms, but also more complex models including interactions of different physical origin and other solvent distribution functions.

Calculation of the intermolecular energy of large molecules by a fragmentation scheme: Application to the 4-n-pentyl-4′- cyanobiphenyl (5CB) dimer

We present a method for computing intermolecular energies of large molecules based on a suitable fragmentation scheme, which allows one to express the complete interaction energy as a sum of interaction energies between pairs of fragments. The main advantage consists in the possibility of using standard ab initio quantum methods to evaluate the fragment energies. For the 4-n-pentyl-4′-cyanobiphenyl (5CB) dimer, the present results indicate that the most favorite arrangement corresponds to an antiparallel side-by-side geometry with a stabilization energy of about 16 kcal/mol. It is shown that, by the present method, the interaction energy of the 5CB dimer can be evaluated for all geometrical conformations and, in principle, it can be used for bulk simulations.

On the effect of Pauli repulsion and dispersion on static molecular polarizabilities and hyperpolarizabilities in solution

Abstract A study of the effect of repulsion and dispersion solute–solvent interactions on solute (hyper)polarizabilities is reported. The calculations have been performed within the polarizable continuum model and include the electrostatic contribution. The results show a negligible effect due to dispersion while for repulsion a substantial effect, especially on the second hyperpolarizabilities, has been found.

Effective potential in density matrix functional theory

In the previous paper it was shown that in the ground state the diagonal of the spin independent second-order density matrix n can be determined by solving a single auxiliary equation of a two-particle problem. Thus the problem of an arbitrary system with even electrons can be reduced to a two-particle problem. The effective potential of the two-particle equation contains a term v(p) of completely kinetic origin. Virial theorem and hierarchy of equations are derived for v(p) and simple approximations are proposed. A relationship between the effective potential u(p) of the shape function equation and the potential v(p) is established.

Size-Extensive Wave Functions for Quantum Monte Carlo: A Linear Scaling Generalized Valence Bond Approach.

We propose a new class of multideterminantal Jastrow-Slater wave functions constructed with localized orbitals and designed to describe complex potential energy surfaces of molecular systems for use in quantum Monte Carlo (QMC). Inspired by the generalized valence bond formalism, we elaborate a coupling scheme between electron pairs which progressively includes new classes of excitations in the determinantal component of the wave function. In this scheme, we exploit the local nature of the orbitals to construct wave functions which have increasing complexity but scale linearly. The resulting wave functions are compact, can correlate all valence electrons, and are size extensive. We assess the performance of our wave functions in QMC calculations of the homolytic fragmentation of N-N, N-O, C-O, and C-N bonds, very common in molecules of biological interest. We find excellent agreement with experiments, and, even with the simplest forms of our wave functions, we satisfy chemical accuracy and obtain dissociation energies of equivalent quality to the CCSD(T) results computed with the large cc-pV5Z basis set.

Calculation of the dispersion energy contribution to the solvation free energy

Abstract A general expression for the dispersion energy contribution to the solvation free energy is derived by exploiting the analogy between certain aspects of the theory of intermolecular forces and of the theory of solvation in the polarizable continuum model. The proposed method of calculation requires a knowledge of the solvent dielectric constant at imaginary frequencies, often efficiently approximated in terms of simple experimental data such as refractive index and ionization potential, and molecular transition densities and energies obtained by standard ab initio methods. By way of examples, the dispersion contribution is calculated for the systems CH 4 , NH 3 , H 2 O, HF and Ne in water as solvent.

A matrix partitioning approach to the calculation of intermolecular potentials. General theory and some examples

Abstract A general expression for the interaction energy of two molecules is obtained by using a matrix partitioning method. The wavefunction of the whole system is expanded in terms of antisymmetrized products of free-molecule functions and using a matrix perturbation scheme it is possible to describe the interaction energy in terms of free-molecule quantities (like frequency-dependent polarizabilities and density or spin density matrices) that, in principle, can be evaluated at any level of approximation. By way of example, the interaction potentials are calculated for (N 2 ) 2 and Ne 2 using wavefunctions of HF and TDHF form. The results are in substantial accord with those available in the literature. Application of these potentials to the calculation of macroscopic properties, however, leads to considerable errors. From the analysis of our results it appears that the dispersion energy is underestimated, probably on account of the neglect of intrasystem correlation energy in the TDHF approximation. The use of more sophisticated methods of evaluation of dynamic polarizabilities will not involve any extension of the approach presented in this work.

Perturbation calculations of molecular interaction energies: an example, HF....HF

Abstract An expression for the interaction energy of two molecules, obtained by expanding the wavefunction for the whole system in terms of antisymmetrized products of free-molecule functions and using a matrix perturbation scheme, is used in ab initio calculations on the HF dimer. The computed interaction energy is fitted with considerable accuracy by a simple analytical formula. The equilibrium geometry and hydrogen-bond energy are in satisfactory agreement with available experimental results.

Quantum Monte Carlo formulation of volume polarization in dielectric continuum theory

We present a novel formulation based on quantum Monte Carlo techniques for the treatment of volume polarization due to quantum mechanical penetration of the solute charge density in the solvent domain. The method allows to accurately solve Poissons equation of the solvation model coupled with the Schrodinger equation for the solute. We demonstrate the performance of the approach on a representative set of solutes in water solvent and give a detailed analysis of the dependence of the volume polarization on the solute cavity and the treatment of electron correlation.

Electronic Excitations in Nonpolar Solvents: Can the Polarizable Continuum Model Accurately Reproduce Solvent Effects?

In nonpolar solvents, both electrostatic and nonelectrostatic interactions play a role in tuning the electronic excitations of molecular solutes. This specificity makes the application of continuum solvation models a challenge. Here, we propose a strategy for the calculation of solvatochromic shifts on absorption spectra, using a coupling of the polarizable continuum model with a time-dependent density functional theory framework, which explicitly accounts for dispersion and repulsion, as well as for electrostatic effects. Our analysis makes a step further in the interpretation of the effects of nonpolar solvents and suggests new directions in their modeling using continuum formulations.