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A double-zeta basis set with polarization functions (DZP) is the minimum level for semiquantitative calculations. Most basis sets used in the past decade have been optimized for HartreeFock calculations on the free atoms. This is a sound approach when the basis sets are used for molecular calculations at the Hartree-Fock, or even MCSCF, level. The inadequacies of these basis sets for the description of dynamical correlation effects have recently received attention. Almlof and Taylor32 have presented large contracted Gaussian basis sets based on atomic natural orbitals (ANO's).

A number of dynamical models based on this Hamiltonian have since been proposed. Conceptually, the idea is to consider the potential as a trough or stream bed plus 37V-7 harmonic walls that are free to contract or expand as one proceeds along the trough. The PES is approx- M. PAGE AND B. H. LENGSFIELD ill 21 imated as the potential energy of the MEP [V0(s)] plus a quadratic approximation to the energy in directions perpendicular to the MEP, 37V-7 V(s, Q1 ... 7) = V0(s) + ^ ±<4Qi k= 1 (11) Here Q is the generalized normal coordinate and co the associated harmonic frequency.

The first principles calculation of bond dissociation energies is a notoriously difficult problem in QC because there is substantially more correlation energy in the molecule than there is in the separated fragments. Quantum chemical calculations that include electron correlation at a high level and employ a DZP quality basis set typically underestimate bond energies by several kcal/mole for single bonds, and even more for multiple bonds. This is an unacceptable error, particularly if several chemical bonds are broken, such as in a calculation of a molecular atomization energy.

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