Polyatomic molecules computational chemistry

The recent progress of computational quantum chemistry has made it possible to get realistic descriptions of vibrational frequencies for polyatomic molecules in solution. The first attempt in this direction was made by Rivail el al. [1] by exploiting a semiempirical QM molecular model coupled with a continuum description of the medium to compute vibrational frequency shifts for molecular solutes. An extension to ab initio QM methods, including the treatment of electron correlation effects and electrical and mechanical anharmonicities, was then proposed [2 1] in the framework of the Polarizable Continuum Model (PCM). 

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. 

E. R. Davidson and W. T. Borden, /. Phys. Chem., 87, 4783 (1983). Symmetry Breaking in Polyatomic Molecules Real and Artifactual. See also T. Bally and W. T. Borden, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., Wiley-VCH, New York, Vol. 13, pp. 1-97. Calculations on Open-Shell Molecules A Beginner s Guide. 

A key development in quantum chemistry has been the computation of accurate self-consistent-field wave functions for many diatomic and polyatomic molecules. The principles of molecular SCF calculations are essentially the same as for atomic SCF calculations (Section 11.1). We shall restrict ourselves to closed-shell configurations. For open shells, the formulas are more complicated. 

The title indicates that this paper is about the calculation of vibrational force constants and the geometry optimization of polyatomic molecules however, its primary impact on computational chemistry comes from the methodology for calculating analytic first derivatives with respect to molecular coordinates at the Hartree-Fock (HF) level of theory. Applications of first and higher derivatives of the energies obtained by molecular orbital (MO) calculations have revolutionized computational chemistry, allowing molecular structures and properties to be computed efficiently and reliably [1-5]. Almost all electronic structure codes compute analytic first derivatives of the energy, and Pulay s paper was the first to describe a practical calculational approach. 

Wesolowski, T. A. One-electron equations for embedded electron density challenge for theory and practical payoffs in multi-scale modelling of complex polyatomic molecules. In Leszczynski, J., Ed. Computation Chemistry Reviews of Current Trends. World Scientific Singapore, 2006,1-82. 

The molecular electostatic potential (MEP) represent just one of the attempts of connecting in depth studies on molecular systems with basic and elementary concepts of chemistry. It is no mere coincidence that the first proposals of using detailed MEP values in the study of inter- and intra-molecular processes [2] has immediately followed the obtaining of effective computer codes for ab initio calculations of the electronic stucture of polyatomic molecules. 

It has currently been demonstrated in the literature that, due to the progress of computational quantum chemistry, a realistic description of vibrational frequencies for polyatomic molecules in solution is now feasible. 

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