The first and second derivative matrices in the random phase approximation scheme by using the Lagrangian technique

We have presented the explicit formulas for first and second derivatives of A and B matrices, appearing in the random phase approximation (RPA), with the aid of Lagrangian technique. Owing to the 2n + 1 rule, the Lagrangian approach is more efficient than the conventional approach to evaluate the higher-order matrix elements. We have confirmed the validity of our formulation by demonstrating the geometry optimization of the first-excited singlet states of formaldehyde, ethylene, and 1-amino-3-propenal molecules. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005