The Use of Pseudopotentials in Molecular Calculations

During the past few years there has been a rapid increase in the range of molecules for which the methods of quantum chemistry have proved useful. Improvements in computer power and developments in theory have both contributed to these advances, so that ab initio methods are now routine for molecules which could only have been the subjects of semi-empirical calculations a few years ago. One area of this extension has been to molecules containing atoms of high atomic number, and it is this area which is the subject of this Report. 

The theoretical difficulty of making this separation derives from the indistinguish-ability of electrons and the requirement that the total wavefunction be antisymmetric with respect to permutations of the electronic co-ordinates. One approach has been to abandon a full quantum mechanical description in favour of a simplified model hamiltonian which can be conveniently parameterized in terms of experimental quantities. This is the rationale behind Huckel theory, CNDO, and other more sophisticated methods such as MINDO. These techniques have been well documented and reviewed elsewhere (Dewar,1 Pariser, Parr, and Pople,2 Murrell and Hargett,3 etc.) and will not be pursued further here. 

From the computational point of view any treatment which reduces the number of orbitals which are explicitly taken into account is very attractive. In the normal LCAO MO method the number of integrals to be calculated, stored, and read for each SCF cycle is roughly proportional to the fourth power of the number of basis functions, and for a Cl calculation the integral transformation process depends on the number of basis functions to the fifth power. The basis set required for a good 

Murrell and A. J. Hargett, Semi-empirical SCF-MO Theory of Molecules, Wiley, London and New York, 1972. 

The scheme for achieving the core-valence separation which we wish to discuss in this Report is embodied in the idea of a pseudopotential . The hamiltonian for the electronic part of the wavefunction can be symbolically expressed within the Bom-Oppenheimer ( clamped nucleus ) approximation as 

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The Use of Pseudopotentials in Molecular Calculations arbitrary non-local potential ... 

Hinchliffe and Bounds review in detail the calculation of the electric and magnetic properties of molecules. Finally, the use of pseudopotentials in molecular calculations is extending the range of ab initio calculation to molecules containing heavy atoms, and Dixon and Robertson survey this rapidly growing field. 

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