Hartree–Fock second derivatives and electric field properties in a solvent reaction field: Theory and application

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Abstract
A compact formalism for the second and third derivatives of the Hartree–Fock energy in the presence of an Onsager solvent reaction field is presented. All three standard algorithms (MO, AO, and direct) are extended to include the reaction field in a unified way. Predictions of the infrared spectrum of formaldehyde in a variety of solvents and of solvent‐induced shifts in carbonyl stretching frequencies are presented along with the results of new measurements. As for the gas‐phase case, analytical second derivatives are far more efficient than numerical ones. The reaction field provides very good predictions of solvent effects at negligible computational cost.