Computation of Second Harmonic Generation for Crystalline Urea and KDP. An ab Initio Approach through the Coupled Perturbed Hartree-Fock/Kohn-Sham Scheme

The electronic second harmonic generation (SHG) tensor, d, of crystalline urea, and potassium dihydrogen phosphate (KDP) is evaluated as a function of frequency using a Gaussian type basis set and the Coupled Perturbed Hartree-Fock (CPHF) and Kohn-Sham (CPKS) schemes as implemented in the CRYSTAL code. The results of various functionals, including LDA, GGA (PBE), and global and range-separated hybrids (B3LYP, PBEO, LC-BLYP), as well as Hartree-Fock, are compared. It is found that the calculated SHG intensity always decreases as the percentage of exact exchange increases. The hybrid functionals turn out to provide results that agree well with experiment. For urea and KDP the percentage of exact exchange determined by the inverse dielectric constant is too large. At 1064 nm the vibrational contribution for urea is found to be less than 5% of the total value. To the authors' knowledge, this is the first coupled (self-consistent) calculation of SHG for any periodic system.