ALGEBRAIC-METHOD FOR THE EVOLUTION OPERATOR APPROXIMATION

The approximation of a short-time evolution operator for a molecular s ystem with the Hamiltonian H-o + V is constructed in terms of the evol ution operator of an unperturbed system, a perturbative potential V an d commutators of H-o and V. A description of a powerful method for suc h a construction based on the Lie-algebra technique is given. It is de monstrated that efficient representation for the evolution operator ca n be obtained using approximations like exp (-i/(h) over bar (H-o + V) t) = exp (-i/3 (h) over bar H(o)t) exp (-3i/4((h) over bar Vt) exp (-2 i/3 (h) over bar H(o)t) exp (-i/4 (h) over bar Vt) exp(S) where S = -i t(3)/48 (h) over bar(3)[[H-o, V], V]. This relation is accurate up to the third order in time. The simplest approximations of this type are listed.