Second-Order Analytic Derivatives for XYG3 Type of Doubly Hybrid Density Functionals: Theory, Implementation, and Application to Harmonic and Anharmonic Vibrational Frequency Calculations.

Analytic derivative methods in quantum chemistry are powerful tools for the calculation of molecular properties and simulation of chemical systems. While the derivatives of the well-established B2PLYP type of doubly hybrid (DH) density functionals can be generated by a straightforward combination between the Kohn-Sham density functional and the second-order perturbation theory (PT2), both of these two contributions have to be considered nonvariationally for the XYG3 type of DH functionals (xDHs). A total Lagrangian that includes both parts is therefore needed for the corresponding Z-vector equations for the first-order derivatives of xDHs. Starting from the differentiation of the Z-vector equations, a theory for the second-order derivatives for xDHs is developed here and is applied to the molecular harmonic and anharmonic vibrational frequency calculations. The results are generally of high quality, as compared to the well-established experimental and CCSD(T) counterparts. Further investigations on the fundamental frequency predictions prove the capability of the xDH functionals for an accurate calculation of spectroscopic properties for a wide range of medium-size molecules.