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 interaction (CIS) from the Hartree-Fock ground-state wave-function with a restriction placed on the active space (RCIS). The derivative of the RCIS equation is found using the CPHF equations. However, at this point, the RCIS gradient equation is not in its most computationally efficient form. Therefore, the so-called Z-vector method is used to eliminate the dependence of the derivative equation on the orbital rotation matrix U'. This is done by defining a ''Z vector,'' which for our case is Me restricted one-particle density matrix. Its product with Me Q' matrix is used to substitute for the terms which involve the orbital rotation matrix. Since the Z-vector is defined by the RCIS Lagrangian and the Lagrangian is redefined by the restriction on the active space, it is necessary to rederive the derivation equation in order to eliminate unnecessary terms. Once U' has been eliminated, the derivative equation may be written entirely in the AO basis. This avoids time-consuming AO to MO transformations. (C) 1997 John Wiley & Sons, Inc.