Intermolecular potentials induction energy

Since intermolecular forces are repulsive at short range and attractive at large distances, there must be at least two contributions of opposite sign to the total force and hence to the intermolecular potential. The attractive contributions are due to the coulombic energies of first and second order (electrostatic, induction, dispersion), the repulsive contribution to the requirement of antisymmetry of the total wf due to the Pauli principle, which for closed shells results in a reduction of the electron density in the region of overlap between the molecules and hence in an increased repulsion. 

Most popular in the ab initio calculation of intermolecular potentials is the so-called supermolecule method, because it allows the use of standard computer programs for electronic structure calculations. This method automatically includes all the electrostatic, penetration and exchange effects. If the calculations are performed at the SCF (self-consistent field) level the induction effects are included, too, but the dispersion energy is not. The latter, which is an intermolecular electron correlation effect, can be obtained by configuration interaction (Cl), coupled cluster (CC) calculations or many-body perturbation theory (MBPT). These calculations are all plagued... 

Now the expression (19) is an uncoupled formulation of the polarizability. We can replace it by a polarizability derived from coupled Hartree-Fock perturbation theory, which is more accurate, because it takes account of the reorganisation of the electron distribution in a self-consistent manner. Better still would be to evaluate the monomer polarizability by a method that takes account of electron correlation as well . But whatever the level of calculation, we can once again perform a much better calculation of the monomer property than is possible for the dimer. In this way we arrive at a description of the induction energy that is far more accurate than we can obtain through either intermolecular perturbation theory, where the perturbation is treated in an uncoupled fashion, or from a supermolecule calculation, where the size of the basis is limited by the need to perform calculations at a large number of points on the potential energy surface. 

It can be useful to know the approximate magnitude of the various contributions to the intermolecular potential. The relative importance of each varies from system to system. Thus electrostatic and induction energies are zero in the inert gases, in which the dispersion force is the sole source of attraction between these atoms, whereas in hydrogen-bonded systems the electrostatic energy is predominant. 

Other expressions for these so-called asymptotic intermolecular potentials are available for dipole pole cases, etc., including explicit orientation-dependent terms. A simple example is the interaction of an ion with a molecule that has a permanent dipole moment fj,. In this case, the induction energy (2.17) has an extra term, /z E, where E is the field of the ion, which is in the direction of the relative position vector R and the dot represents the scalar product of two vectors. Using the angle y between the permanent dipole and the relative separation ... 

The vast majority of CSP has been limited to using intermolecular potentials that lack explicit inclusion of polarization,although its importance has become a topic of interest.Nonpolarizable force fields, based on fixed partial charges or fixed atomic multipoles, must implicitly account for the 20-40% of the lattice energy attributable induction. " On the contrary, polarizable models such as the AMOEBA force field for organic molecules... 

Dipole-dipole, induction, and dispersion forces are collectively referred to as van der Waals forces. The intermolecular potential energy for each of these interactions falls off as the sixth power of position. Thus, all three van der Waals interactions are of the form ... 

In a solution of a solute in a solvent there can exist noncovalent intermolecular interactions of solvent-solvent, solvent-solute, and solute—solute pairs. The noncovalent attractive forces are of three types, namely, electrostatic, induction, and dispersion forces. We speak of forces, but physical theories make use of intermolecular energies. Let V(r) be the potential energy of interaction of two particles and F(r) be the force of interaction, where r is the interparticle distance of separation. Then these quantities are related by... 

Straight self-consistent field calculations have been carried out on the interaction of water with neon and argon.30 Here it is possible to obtain some of the attractive contribution to the intermolecular force since there will be an inductive second-order interaction caused by the large dipole of the water molecule. Such interactions appear at the SCF level and the authors find a minimum in the potential at an O -Ne distance of 3.63 A, with a binding energy of 0.71 kJ mol-1. There is a shallower minimum in the case of argon. Calculations at a similar level of sophistication have been carried out on the H2----He system,31 primarily, however, from the... 

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. 

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