Molecular Gaussian

Most contemporary schemes for designing atomic and molecular Gaussian basis sets e.g. [4]- [7]) exploit, in one form or another, the idea of even-tempered basis sets [8], [9] (see also [4]), which have exponents, (p, defined by the geometric series ... 

Hi) Gaussian statistics. Chandler [39] has discussed a model for fluids in which the probability P(N,v) of observing Y particles within a molecular size volume v is a Gaussian fimction of N. The moments of the probability distribution fimction are related to the n-particle correlation functions and... 

The assumption of Gaussian fluctuations gives the PY approximation for hard sphere fluids and tire MS approximation on addition of an attractive potential. The RISM theory for molecular fluids can also be derived from the same model. 

Braun M, Metlu H and Engel V 1998 Molecular femtosecond excitation described within the Gaussian wave packet approximation J. Chem. Phys. 108 8983-8... 

Flehre W J, Ditchfieid R and Popie J A 1972 Self-consistent molecular-orbital methods XII. Further extension of Gaussian-type basis sets for use in molecular orbital studies of organic molecules J. Chem. Phys. 56 2257-61 Flariharan P C and Popie J A 1973 The influence of polarization functions on molecular orbital hydrogenation energies Theoret. Chim. Acta. 28 213-22... 

Flelgaker T and Taylor P R 1995 Gaussian basis sets and molecular integrals Modem Electronic Structure Theory yo 2, ed D R Yarkony (Singapore World Scientific) section 5.4, pp 725-856... 

Dupuis M, Rys J and King H F 1976 Evaluation of molecular integrals over Gaussian basis functions J. Chem. Phys. 65 111-16... 

McMurchie L E and Davidson E R 1978 One-and two-electron integrals over Cartesian Gaussian functions J. Comp. Phys. 26 218-31 Gill P M W 1994 Molecular integrals over Gaussian basis functions Adv. Quantum Chem. 25 141-205... 

In modem quantum chemistry packages, one can obtain moleculai basis set at the optimized geometry, in which the wave functions of the molecular basis are expanded in terms of a set of orthogonal Gaussian basis set. Therefore, we need to derive efficient fomiulas for calculating the above-mentioned matrix elements, between Gaussian functions of the first and second derivatives of the Coulomb potential ternis, especially the second derivative term that is not available in quantum chemistry packages. Section TV is devoted to the evaluation of these matrix elements. 

A Gaussian expansion contains two parameters the coefficient and the exponent. The most flexible way to use Gaussian functions in ab initio molecular orbital calculations permits both of these parameters to vary during the calculation. Such a calculation is said to use... 

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