The calculation of the static first and second susceptibilities of crystalline urea: A comparison of Hartree–Fock and density functional theory results obtained with the periodic coupled perturbed Hartree–Fock/Kohn–Sham scheme
Résumé
The static polarizability αα and first hyperpolarizability ββ tensors of crystalline urea and the corresponding first-(χ(1))(χ(1)) and second-(χ(2))(χ(2)) susceptibilities are calculated and compared to the same quantities obtained for the molecule by using the same code (a development version of CRYSTAL), basis set, and level of theory. In order to separate geometrical and solid state effects, two geometries are considered for the molecule in its planar conformation: (i) as cut out from the bulk structure and (ii) fully optimized. First, the effect of basis sets on computed properties is explored at the B3LYP level by employing basis sets of increasing complexity, from 6-31G(d,p) to 6-311G(2df,2pd) (Pople’s family) and from DZP to QZVPPP (Thakkar/Ahlrichs/Dunning’s family) on αα and ββ for both the molecule and the bulk. Then, five different levels of theory, namely, SVWN (local density approximation), PBE (generalized gradient approximation), PBE0 and B3LYP (hybrid), and Hartree–Fock are compared in combination with a TZPP basis set. Present results show that hybrid methods, in particular, B3LYP, are remarkably successful in predicting correctly both the first and second susceptibilities of urea bulk when combined at least with a triple-zeta quality basis set containing a double set of polarization functions. It is also shown that diffuse functions that are needed for molecular calculations are less crucial for the crystalline structure, as expected. Indeed, B3LYP/TZPP computed χ(1)χ(1) and χ(2)χ(2) tensor components (χ(1)aa=1.107χaa(1)=1.107, χ(1)cc=1.459χcc(1)=1.459, and χ(2)=−0.93 a.u.χ(2)=−0.93 a.u.) are in very good agreement with experimental values. At variance with respect to previous periodic ab initio calculations, but in agreement with recent supermolecular results, the negative sign of χ(2)χ(2) is confirmed. Overall, static linear and nonlinear optical properties such as dielectric constants, refractive, and birefringence indices and second-harmonic generation coefficient of crystalline urea are very well reproduced by present calculations.