In Z-dependent perturbation theory, the lowest-order wave functions for a polyatomic molecule are

not only independent of the nuclear charges, but also of the total number of nuclear centers and

electrons in the molecule. The complexity of the problem is then determined by the highest order

retained in the calculation. Choosing the simplest possible unperturbed Hamiltonian, we describe an

n-electron, m-center polyatomic molecule as n ‘‘hydrogenic’’ electrons on a single center perturbed

by electron–electron and electron–nucleus Coulomb interactions. With this H0 , the first-order wave

function for any polyatomic molecule will be a sum of products of hydrogenic orbitals with either

two-electron, one-center or one-electron, two-center first-order wave functions. These first-order

wave functions are obtained from calculations on He-like and H2

1-like systems. Similarly, the

nth-order wave function decouples so that the most complex terms are just the nth-order wave

functions of all the p-electron, q-center subsystems (p1q5n12) contained in the molecule. We

illustrate applications of this method with some results, complete through third order in the energy,

for H3

1-like molecules. These are compared with accurate variational results available in the

literature. We conclude that, through this order, this perturbation approach is capable of yielding

results comparable in accuracy to variational calculations of moderate complexity. The ease and

efficiency with which such results can be obtained suggests that this method would be useful for

generating detailed potential energy surfaces for polyatomic molecules. © 1995 American Institute

of Physics.

J. Chem. Phys. ,Vol. 102 ,No. 12 ,  22 March 1995