Perturbation intermolecular forces/interactions

Quantum mechanical calculations of intermolecular forces generally start from wave functions of the isolated particles. With regard to the actual treatment of the interaction, however, there is some competition between perturbation theory and MO methods. 

Before we tarn to MO theory of molecular interactions a short discussion on the reliability of semiempirical calculations of the CNDO type by means of perturbation theory would be useful. For a better understanding of the possibilities and limitations of semiempirical MO approaches to intermolecular forces we calculated first-order perturbation energies for very simple complexes with and... 

In order to leam more about the nature of the intermolecular forces we will start with partitioning of the total molecular energy, AE, into individual contri butions, which are as close as possible to those we defined in intermolecular perturbation theory. Attempts to split AE into suitable parts were undertaken independently by several groups 83-85>. The most detailed scheme of energy partitioning within the framework of MO theory was proposed by Morokuma 85> and his definitions are discussed here ). This analysis starts from antisymmetrized wave functions of the isolated molecules, a and 3, as well as from the complete Hamiltonian of the interacting complex AB. Four different approximative wave functions are used to describe the whole system ... 

Rigorous perturbational treatments of the interaction between two molecules belong to the field of intermolecular forces, and I shall not attempt a comprehensive review, since the topic has been reviewed by Stamper129 in the previous volume in this series. However, several authors have devised perturbation schemes with a view to their application in problems of reactivity, which is a departure from conventional theory of intermolecular forces, where the possibility of making and breaking of bonds is usually excluded, on the reasonable grounds that the problem is quite hard enough anyway. 

The form of this equation makes explicit the fact that intermolecular forces do depend upon their vibrational states as well as on their electronic states. Due to the antisymmetrization of the global electronic wave function, Vaia2(R R12) contains Coulomb exchange terms and a direct term formed by the Coulomb multipole interactions and the infinite order perturbation electrostatic effects embodied in the reaction field potential [21, 22],... 

G. Chalasinski, M. Szczesniak. On the connection between the supermolecular M0ller-Plesset treatment of the interaction energy and the perturbation theory of intermolecular forces. Mol. Phys. 63, 205-224 (1988)... 

In principle, however, the intermolecular force problem has a compensating advantage. Because of the very small changes introduced by the interaction, at least until the repulsive part of the potential surface is reached, this is an ideal situation for the application of perturbation theory which has not, in general, been a particularly powerful tool in valence problems. Even so, except at large distance where the overlap of the wavefunctions of the two molecules is negligible, the application of perturbation theory raises some problems. In the main these were sorted out in the years around 1970, but work in this area continues and some of it is discussed in Section 2. 

As a second model potential we shall briefly discuss the PES for the water dimer. Analytical potentials developed from ab initio calculations have been available since the mid seventies, when Clementi and collaborators proposed their MCY potential [49], More recent calculations by dementi s group led to the development of the NCC surface, which also included many-body induction effects (see below) [50]. Both potentials were fitted to the total energy and therefore their individual energy components are not faithfully represented. For the purposes of the present discussion we will focus on another ab initio potential, which was designed primarily with the interaction energy components in mind by Millot and Stone [51]. This PES was obtained by applying the same philosophy as in the case of ArCC>2, i.e., both the template and calibration originate from the quantum chemical calculations, and are rooted in the perturbation theory of intermolecular forces. 

Rigorous perturbational treatments of the interaction between two molecules belong to the field of intermolecular forces, and I shall not attempt a comprehensive review, since the topic has been reviewed by Stamper in the previous volume in this... 

All the important contributions to the forces between molecules arise ultimately from the electrostatic interactions between the particles that make up the two molecules. Thus our main theoretical insight into the nature of intermolecular forces comes from perturbation theory, using these interactions as the perturbation operator H = Z e, /(4jtSor/y), where is the charge on particle i in one molecule, is the distance between particles i and / in different molecules, and 8q is permittivity of a vacuum. The definitions of the contributions, such as the repulsion, dispersion, and electrostatic terms, which are normally included in model potentials, correspond to different terms in the perturbation series expansion. 

Recently, a new theoretical method of calculating potential energy and dipole/polarizability surfaces for van der Waals molecules based on symmetry-adapted perturbation theory (sapt) of intermolecular forces (12)— (15) has been developed (16)-(24). In this method, referred to as many-body symmetry-adapted perturbation theory, all physically important contributions to the potential and the interaction-induced properties, such as electrostatics, exchange, induction, and dispersion are identified and computed separately. By making a perturbation expansion in the intermolecular interaction as well as in the intramolecular electronic correlation, it is possible to sum the correlation contributions to the different physical... 

As we mentioned in the opening paragraph, thermodynamic perturbation theory has been used in two contexts in applications to interaction site fluids. In this section, we will describe efforts to treat the thermodynamics and structure of interaction site fluids in terms of a perturbation expansion where the reference system is a fluid in which the intermolecular forces are spherically symmetric. In developing thermodynamic perturbation theories, it is generally necessary to choose both a reference system and a function for describing the path between the reference fluid and the fluid of interest. The latter choice is usually made between the pair potential and its Boltzmann factor. Thus one writes either... 

As we stated at the beginning of this section, most of the work in this area has focused upon the study of molecular orientation at the liquid-vapor interface and how this is affected by details of the intermolecular forces. Thompson and Gubbins have carried out molecular dynamics simulations of the vapor-liquid interface for homonuclear 12-6 diatomic molecules and for such molecules with point-charge quadrupoles. They find that in the case of the nonpolar molecules, there is a tendency for molecules in the liquid to align perpendicular to the surface and those in the vapor to align parallel to the surface. The addition of a quadrupole to the 12-6 diatomic " reverses this effect. A study of the vapor-liquid interface for an interaction site model of -octance leads to similar conclusions as for the nonpolar diatomic. These effects are reproduced qualitatively by all the theoretical approximations, with the exception of the influence of the quadrupole, which can only be predicted at first order within the context of the perturbation theory based upon division of the Mayer function Eq. (3.5.2). 

G. Chalasinski and M. M. Szczesniak,. Mol. Phys., 63, 205 (1988). On the Connection Between the Supermolecular Mpller-Plesset Treatment of the Interaction Energy and the Perturbation Theory of Intermolecular Forces. 

In a typical molecular solid, the intermolecular interaction is much weaker than the intramolecular bonding energy, so the bulk properties of a molecular solid can usually be analyzed as the sum of individual molecular contributions, with small perturbations from the intermolecular forces. Such weak intermolecular interactions rarely extend beyond the nearest neighbors. In such cases, the electronic properties of a molecular crystal are independent of the size of the crystal. 

Perturbation theory is a natural tool for the description of intermolecular forces because they are relatively weak. If the interacting molecules (A and B) are far enough apart, then the theory becomes relatively simple because the overlap between the wavefunctions of the two molecules can be neglected. This is called the polarization approximation. Such a theory was first formulated by London [3, 4], and then reformulated by several others [5, 6 and 7]. 

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