Analytic energy derivatives in many-body methods. I. First derivatives

The theory of analytic energy derivatives is developed for the coupled cluster (CC) model using diagrammatic techniques. Explicit expressions for the derivative energy and response density for the full coupled-cluster singles, doubles and triples (CCSDT) model are presented. Analytic derivatives for the finite-order MBPT models through MBPT(4) and the recently proposed ‘‘quadratic’’ CI models are derived as special cases of the theory. First derivatives of the energy correspond to first-order response properties and molecular gradients; the analytic expressions for the derivative energy are given in terms of the response (or ‘‘relaxed’’) density for efficient evaluation. The theory of analytic second derivatives of the CC/MBPT energy is presented in part II.