A new tuned range-separated density functional for the accurate calculation of second hyperpolarizabilities

The calculation of nonlinear optical properties (NLOPs) using density functional theory (DFT) remains a challenge in computational chemistry. Although the existing range-separated functionals display the best performance for the calculation of this type of properties, their errors strongly depend on the family of molecules studied. Herein, we have explored a new strategy to empirically tune the range-separated LC-BLYP method to improve the accuracy of the calculation of the second hyperpolarizabilities ( γ ), which are poorly described by current density functional approximations. First, we benchmarked nine of the most accurate commonly used range-separated hybrid and optimally tuned functionals ( i.e. B3LYP, PBE0, BH&HLYP, M06-2X, MN15, ω B97X-D, CAM-B3LYP, LC-BLYP and OT-LC-BLYP) for the calculation of γ using as a reference the CCSD(T) values of a chemically diverse set of 60 molecules. Among these nine functionals, LC-BLYP gives the lowest average errors. We determined the value of the range-separation parameter ω required to reproduce the CCSD(T) second hyperpolarizabilities with the LC-BLYP functional ( ω CC ) for the set of 60 molecules. Our new tuned range-separated functional, Tα-LC-BLYP, uses a quadratic correlation between ω CC and a molecular descriptor in terms of the linear polarizability and the number of electrons in the molecule. The average error of the γ values obtained with Tα-LC-BLYP is reduced by half or more as compared with the most accurate among the nine density functional approximations benchmarked. Among the nine functionals benchmarked, the most accurate γ are obtained by Tα-LC-BLYP, reducing about half the errors of LC-BLYP.