Approximations can be consistent with the very high accuracy associate
d with traditional quantum chemistry provided that the approximations
are variational. Variational approximations include the linear combina
tion of atomic orbitals (LCAO) approximation of Hartree-Fock-Roothaan
theory. In density functional theory, variationality usually requires
that approximations be made in the expression for the energy which var
iationally yields the Kohn-Sham-Roothaan equations. These ideas are il
lustrated in a derivation of accurate forces for quantum chemical mole
cular dynamics using the very efficient analytic Xa method. This metho
d is used to follow directly the time evolution of collisions in a col
linear (NO)(12) system and the excited-state dynamics of ICN and ICH3
photodissociation. (C) 1998 John Wiley & Sons, Inc.