Structure calculations polyatomic molecules

Many qualitative and semiempirical studies followed Mulliken s analysis [6], but it was not until 1960 that the first ab initio calculation on CH2 was published [7] by J. M. Foster and S. F. Boys in the famous April 1960 issue of the Reviews of Modem Physics which contained the papers from a conference on Molecular Quantum Mechanics that was held at the University of Colorado in June of 1959. This is the same Boys who in 1950 introduced the idea of using oscillator functions or as we know them now, gaussian fionctions as basis functions for calculating the electronic structure of polyatomic molecules. 

Her Herzberg, G. Molecular Spectra and Molecular Structure III. Electronic Spectra and Electronic Structure of Polyatomic Molecules, New York Van Nostrand Reinhold Company, 1966. 7OH0U Hougen, J.T. The Calculation of Rotational Energy Levels and Rotational Line Intensities in Diatomic Molecules, Natl. Bur. Stand. Monogr. 115 (1970). 

Other flexible framework calculations of methane diffusion in silicalite have been performed by Catlow et al. (64, 66). A more rigorous potential was used to simulate the motion of the zeolite lattice, developed by Vessal et al. (78), whose parameters were derived by fitting to reproduce the static structural and elastic properties of a-quartz. The guest molecule interactions were taken from the work of Kiselev et al. (79), with methane treated as a flexible polyatomic molecule. Concentrations of 1 and 2 methane molecules per 2 unit cells were considered. Simulations were done with a time step of 1 fs and ran for 120 ps. 

The generalized valence bond (GVB) method was the earliest important generalization of the Coulson—Fischer idea to polyatomic molecules (13,14). The method uses OEOs that are free to delocalize over the whole molecule during orbital optimization. Despite its general formulation, the GVB method is usually used in its restricted form, referred to as GVB SOPP, which introduces two simplifications. The first one is the perfect-pairing (PP) approximation, in which only one VB structure is generated in the calculation. The wave function may then be expressed in the simple form of Equation 9.1, as a product of so-called geminal two-electron functions ... 

There have been many attempts made to calculate the preexponential factors of bimolecular reactions from molecular constants based on the considerations of the transition-state theory. Such efforts depend on a number of educated guesses as to the vibrational properties and structure of the transition-state complex, an assumption about the transmission coefficient for the reaction, and the assumption of the validity of the normal coordinate treatment for computing the thermodynamic properties of polyatomic molecules. 

For a number of comparatively simple polyatomic molecules the moments of inertia and hence die intemuclear distances may be calculated from the rotational fine structure. In addition to the spectroscopic method, interatomic distances and valency angles may also be determined by x-ray and electron diffraction. Thus an exact quantitative picture of tlac molecule may be made whenever it has been possible to make the necessary calculations. In those cases where the same quantity, e.g, tlie interatomic distance, has been determined by more than one method the agreement between the two values is generally found to be good. 

The initial structure of the polyatom system corrresponded to the procedure described earlier by Boys and Cook and in similar work by Reeves and Harrison entitled Use of Gaussian Functions in the Calculation of Wavefunctions for Small Molecules . The use of Gaussian functions, rather than the Slater (exponential) functions favoured by Mulliken and his coworkers at that time, was to be crucial to the success of practical computational quantum chemistry and, in particular, its application to arbitrary polyatomic molecules. 

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