Wave functions intermolecular forces

The dispersive force arises due to the intermolecular electron correlation between the solute and the solvent. Further, it is also important to include the changes in intramolecular and intermolecular solvent electron correlation upon insertion of the solute in the solvent continuum. Further, electron correlation affects the structure of the solute and its charge distribution. Hence, the wave function obtained from the calculation with electron correlation provides a more accurate description of reaction field. 

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. 

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 ... 

The various methods used in quantum chemistry make it possible to compute equilibrium intermolecular distances, to describe intermolecular forces and chemical reactions too. The usual way to calculate these properties is based on the independent particle model this is the Hartree-Fock method. The expansion of one-electron wave-functions (molecular orbitals) in practice requires technical work on computers. It was believed for years and years that ab initio computations will become a routine task even for large molecules. In spite of the enormous increase and development in computer technique, however, this expectation has not been fulfilled. The treatment of large, extended molecular systems still needs special theoretical background. In other words, some approximations should be used in the methods which describe the properties of molecules of large size and/or interacting systems. The further approximations are to be chosen carefully this caution is especially important when going beyond the HF level. The inclusion of the electron correlation in the calculations in a convenient way is still one of the most significant tasks of quantum chemistry. 

The SCF-MI BSSE free method does not take into account dispersion forces, connected to electronic intermolecular correlation effects. By using the SCF-MI wave function as a starting point, however, a non orthogonal BSSE free Cl procedure can be developed. This approach was applied to compute intermolecular interactions in water dimer and trimer the resulting ab initio values were used to generate a new NCC-like potential (Niesar et al, 1990). Molecular dynamics simulation of liquid water were performed and satisfactory results obtained (Raimondi et al, 1997). 

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],... 

In the MO theory, the most reliable approach for the study of reaction pathways perhaps is CASSCF [12, 13], but multi-VBSCF is essentially at the same level with CASSCF [14]. Since a VB wave function can be expanded into the combination of numerous Slater determinants that are used to define configurations in the MO theory, the VB theory provides a very compact, accurate description for chemical reactions. While both MO and VB theories have their own advantages as well as disadvantages, in our opinions, there are some areas where the VB theory is particularly superior to the MO theory 1) the refinement of molecular mechanics force field 2) the development of empirical or semi-empirical VB approaches 3) the impact of intermolecular charge transfer or intramolecular electron delocalization on the structure and properties 4) the validation of classical chemical theories and concepts at the quantitative level 5) the elucidation of chemical reactions and excited states intuitively. 

A more exact procedure is to solve the Bom-von Karman equations of motions 38) to obtain frequencies as a function of the wave vector, q, for each branch or polarization. These will depend upon unit-cell symmetry and periodicity, force constants, and masses. Thus, for a simple Bravais lattice with identical atoms per unit cell, one obtains three phase-frequency relations for the three polarizations. For crystals having two atoms per unit cell, six frequencies are obtained for each value of the phase or wave vector. When these equations have been solved for a sufficient number of wave-vectors, g hco) can, in principle, be obtained by direct count . Thus, a recent calculation (13) of g to) based upon a normal-mode calculation that included intermolecular forces gave an improved fit to the specific heat data of Wunderlich, and showed additional peaks of 140, 90 and 60 cm in the frequency distribution. Even with this procedure, care must be exercised, since it has been shown that significant features of g k(o) may be rormded out. Topological considerations have shown that significant structure in g hco) vs. ho may arise from extreme or saddle points in the phase-frequency curves (38). 

It can now be predicted with confidence that machine calculations will lead gradually toward a really fundamental quantitative understanding of the rules of valence and the exceptions to these toward a real understanding of the dimensions and detailed structures, force constants, dipole moments, ionization potentitils, and other properties of stable molecules and equally unstable radicals, anions, and cations, and chemical reaction intermediates toward a basic understanding of activated states in chemical reactions, and of triplet and other excited states which are important in combustion and explosion processes and in photochemistry and in radiation chemistry and also of intermolecular forces further, of the structure and stability of metals and other solids of those parts of molecular wave functions which are important in nuclear magnetic resonance, nuclear quadrupole coupling, and other interaction involving electrons and nuclei and of very many other aspects of the structure of matter which are now understood only qualitatively or semi-empirically. 

London forces Intermolecular forces resulting from the attraction of correlated temporary dipole moments induced in adjacent molecules, wave function (i/r) The mathematical description of an orbital. The square of the wave function is proportional to the electron density, (p. 39)... 

Third, all degrees of electron donation are possible, ranging from essentially zero in the case of weak intermolecular forces and idealized ion associations to the complete transfer of one or more electrons from the donor to the acceptor. This continuity can be represented [ 10.2.1 ] by wave functions, were the degree of donation increases as the ratio (a/b). ... 

---