Kapusta K. S., Okovytyy S. I., Voronkov E. O., Posudievska O. R.

*
Oles Honchar Dnipropetrovsk National University *

**
ACCURATE CALCULATIONS OF DYNAMIC FIRST HYPERPOLARIZABILITY: CONSTRUCTION OF PHYSICALLY JUSTIFIED SLATER-TYPE BASIS SETS **

The first hyperpolarizability is a frequency-dependent challenging nonlinear optical property of chemical compounds, which can be measured experimentally only indirectly.Substantial progress in the development of laser technology, as well as growing demand for new materials with specific nonlinear optical properties, has been observed in the last decades. For the exact theoretical measurement of the first hyperpolarizability, it is necessary to use approaches with an attentively balanced treatment of all important contributions, to avoid subtle cancellations of various considerable contributions. Therefore, the selection of basis sets, being optimal in size, and at the same time physically adapted for large molecules where computational cost plays a critical role, is a serious task.

The widely-accepted solution of this problem is the «extension» of the initial basis set of atomic orbitals (AOs). A standard way of such «extension» involves the increase in the number of original AOs by means of adding the so-called polarization and diffuses functions to the initial set of AOs, but, in this case, the size of the obtained basis set exceeds considerably the size of the initial basis set. Besides, neither the required number of additional functions, nor the functional form of such functions is determined by any physically justified ways. Our proposal is based on the application of the closed representation of the Green’s function during the solution of the nonhomogeneous Schrödinger equation for the model problem of «one-electron atom in the external uniform field». Efficiency of such approach has been confirmed earlier at the construction of basis sets for calculations of spin–spin coupling constants, as well as of vibrational frequencies, magnetic susceptibility, nuclear magnetic shielding and polarizability. The dynamic hyperpolarizability of some inorganic and organic molecules has been calculated; therefore the performance of the obtained basis sets has been tested. As the initial basis set we have chosen the *
STO *
set. Using Green’s function method, we have obtained analytical expressions of the target first-order correction functions for Slater-type AO in the electric field. The *
STO##(II)-3Gel *
basis set includes the basis set *
STO##-3Gel, *
all additional orbital sets from the valence AO of nonhydrogen atoms, and the basis set for hydrogen atoms. The basis set *
STO##(IIS)-3Gel *
consists of *
STO##-3Gel *
basis set, one set of additions of s- and p- orbitals with the same symmetry as unperturbed valence orbitals of non-hydrogen atoms, as well as of one set of additional s-orbitals of hydrogen. It should be noted that we have taken into account only the correction functions for valence orbitals, as perturbation operator in this case represents an operator of dipole moment, which contributes mainly into the far regions of configuration space. The results of the test calculations of the first dynamic hyperpolarizability tensors for HF, H2O, NH3, CO, CH3CN, CH3F, and NO molecules with a certain number of DFT functionals illustrate the efficiency of performance of the constructed *
STO##(II)-3Gel *
and *
STO##(IIS)-3Gel *
basis sets in comparison with *
d-aug-cc-pVTZ *
and *
LPOL-n (n=FL,FS) *
basis sets. Our basis sets provide good correspondence of the calculated data as well as the experimental ones. *
LPOL *
basis sets have better correlation with the experimental data than *
d-aug-cc *
and practically coincide with *
STO##(II)-3Gel / STO##(IIS)-3Gel *
, but they are larger than the basis sets, proposed in our research. The small-sized *
STO##(IIS)-3Gel *
basis set could be considered as an accurate and cost-effective choice for the calculations of dynamic hyperpolarizability of aromatic compounds. This conclusion is supported by the results of calculations performed for certain aromatic compounds.

Thus, an augmentation of Slater-type basis sets by the second-order correction functions is proposed in this work. Such approach allows construct physically adapted basis sets *
STO##(II)-3Gel *
and *
STO##(IIS)-3Gel *
. New basis sets, in combination with DFT approach, provide a useful, efficient tool for the theoretical study of dynamic hyperpolarizability.