RESTRICTED CIS GRADIENTS VIA CPHF EQUATIONS

A detailed derivation of excited-state energy gradients is presented. The excited states are generated by singles-only configuration interac tion (CIS) from the Hartree-Fock ground-state wave-function with a res triction placed on the active space (RCIS). The derivative of the RCIS equation is found using the CPHF equations. However, at this point, t he RCIS gradient equation is not in its most computationally efficient form. Therefore, the so-called Z-vector method is used to eliminate t he dependence of the derivative equation on the orbital rotation matri x U'. This is done by defining a ''Z vector,'' which for our case is M e restricted one-particle density matrix. Its product with Me Q' matri x is used to substitute for the terms which involve the orbital rotati on matrix. Since the Z-vector is defined by the RCIS Lagrangian and th e Lagrangian is redefined by the restriction on the active space, it i s necessary to rederive the derivation equation in order to eliminate unnecessary terms. Once U' has been eliminated, the derivative equatio n may be written entirely in the AO basis. This avoids time-consuming AO to MO transformations. (C) 1997 John Wiley & Sons, Inc.