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The fulfillment of the Hellmann–Feynman electrostatic theorem is examined for the sequences of cc-pVxZ and cc-pCVxZ Gaussian basis sets as well as for the VBx and CVBx basis sets of Slater-type orbitals. The difference between the energy gradient and electrostatic forces is large in small Gaussian basis sets of the two types, but decreases quickly as the basis sets improve. In VBx Slater basis sets these differences are small but the improvement is irregular, whereas in CVBx basis sets the fulfillment of the electrostatic theorem is very satisfactory. For the high-quality basis sets (cc-pV5Z, cc-pCVQZ, cc-pCV5Z, CVB2, and CVB3) the energy gradient can be replaced by the electrostatic force in most practical applications. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Results are presented from linear combination of Gaussian type orbitals–model core potential–local spin density calculations on equilibrium geometries and harmonic frequencies of several small main group and organometallic molecules. The equilibrium geometries were obtained by minimizing the norm of an approximate analytical energy gradient while the frequencies were obtained by numerical differentiation of these gradients. Comparison with experimental data indicates that the approximate gradients yield accurate results which typically agree better with experiment than those of the Hartree–Fock method and compare favorably with commonly used correlated techniques.

The theory of MCSCF and CI energy derivatives with respect to geometrical variations is briefly reviewed with special attention given to the MCSCF and MRCI energy gradients. A computational procedure is proposed for MRCI energy gradients that does not require the solution to any “coupled-perturbed MCSCF” equations, it does not require any expensive direct-CI matrix-vector products involving derivative integrals, and it does not require any derivative integrals to be transformed from the AO basis to the MO basis. An additional feature is that it does not require any changes to existing MCSCF gradient evaluation programs in order to compute MRCI gradients. The only difference in the two cases is the exact nature of the data passed to the gradient evaluation program from the previous steps in the computational procedure. The additional effort required to compute the entire MRCI energy gradient vector is approximately that required for one additional iteration of the MRCI diagonalization procedure and for one additional MCSCF iteration. For large scale MRCI wave functions, the MRCI energy gradient evaluation should only require about 10% of the effort of computing the wave function itself. This computational procedure removes a major computational botleneck of potential energy surface evaluation.