We study the problem of representing the molecular charge distribution in a convenient way for practical applications and we propose, instead of a single representation, a flexible procedure for building approximations with an arbitrary level of accuracy as concerns the long-range part of the electrostatic potential. We first discuss the splitting of the total electrostatic potential into a multipolar part (long-range) and a penetration part (shortrange) in connection with the usual one-center multipole expansion: at large enough distances, this expansion precisely converges towards the multipolar part. However, this representation is not practically efficient as soon as the molecule departs from a spherical shape, and we therefore consider a so-called multicenter multipole representation. In the MO-LCAO framework, the use of a basis of Gaussian atomic orbitals {χα} generates such a representation in a natural way: indeed, each elementary distribution χ*αχβ then reduces to a one-center distribution with a finite number of multipoles, hence an exact multipolar representation (corresponding to the approximate MO-LCGO wave function) involving a finite (albeit large, in general) number of centers, each one bearing a finite (small) number of multipoles. From this representation used as a reference, we then generate simplified multicenter multipole representations through a systematic procedure of reduction of the number of centers (having chosen a reduced set of new centers, we represent the multipoles of each suppressed old center through suitable new multipoles located on a few new centers closest to the old one under consideration). The number and locations of the new centers are arbitrary, hence the great flexibility of the method. We checked the accuracy of this procedure for molecules of different polarity (water, benzene, adenine), and we noticeably found that a representation involved as centers, the atoms plus one point per chemical bond exhibited quite a satisfactory accuracy. In the conclusion, we briefly discuss the possibility of extending the method to other kinds of basis functions (e.g., Slater orbitals), in connection with the problem of representing the charge distribution associated with the exact molecular wave function, we also discuss the choice of the number centers according to the desired accuracy and we briefly describe a way of applying the method to the problem of representing a large molecule in terms of molecular fragments.

A significant effort has teen made in order to improve the continuum model used for calculation of the solvation thermodynamic quantities of a molecule embedded in a cavity formed by the intersecting van der Waals spheres of the solute in a polarizable medium. These improvements principally concern the thermodynamic quantities associated with the electrostatic part of the solvation energy. A simple method is proposed for the calculation of the fictive charge density representing the reaction potential. The calculated values obtained agree quite well with those calculated within more sophisticated methods. The improvements also principally concern the representation of solvation sites. The method is applied to the calculation of the vaporization thermodynamic quantities of nonassociated liquids, and the results obtained are discussed in relation with experimental data.

An additive procedure is derived for the computation of intermolecular interactions, in which an explicit expression for the charge-transfer energy contribution E, is implemented. In the total interaction energy, AE = E m + E,, + E , + E,, + E,, the electrostatic terms Em and E , are calculated as in our previous treatment. The dispersion contribution is calibrated by reference to variation-perturbation computations on model systems and the repulsion contribution is computed as a sum of bond-bond, bond-lone pair, and lone pair-lone pair interactions. Tests of the procedure are given for representative hydrogen-bonded systems.

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It is shown that, for systems with an arbitrary number of degrees of freedom, a necessary and sufficient condition for the Wigner function to be nonnegative is that the corresponding state wavefunction is the exponential of a quadratic form. This result generalizes the one obtained by Hudson [Rep. Math. Phys. 6, 249 (1974)] for one-dimensional systems.

This paper presents systematic developments in the previously initiated line of research concerning a quantum Monte Carlo (QMC) method based on the use of a pure diffusion process corresponding to some reference function and a generalized Feynman–Kac path integral formalism. Not only mean values of quantum observables, but also response properties are expressed using suitable path integrals involving the diffusion measure of the reference diffusion process. Moreover, by relying on the ergodic character of this process, path integrals may be evaluated as time-averages along any sample trajectory of the process. This property is of crucial importance for the computer implementation of the method. As concerns the treatment of many-fermion systems, where the Pauli principle must be taken into account, we can use the fixed-node approximation, but we also discuss the potentially exact release-node procedure, whereby some adequate symmetry is imposed on the integrand (of the generalized Feynman–Kac formula), associated with a possibly refined choice of the reference function.

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