Role of noncollinear magnetization for the first-order electric-dipole hyperpolarizability at the four-component Kohn–Sham density functional theory level

Abstract

The quadratic response function has been derived and implemented at the adiabatic four-component Kohn-Sham density functional theory level with inclusion of noncollinear spin magnetization and gradient corrections in the exchange-correlation functional-a work that is an extension of our previous report where magnetization dependencies in the exchange-correlation functional were ignored [J. Henriksson, T. Saue, and P. Norman, J. Chem. Phys. 128, 024105 (2008)]. The electric-field induced second-harmonic generation experiments on CF(3)Cl and CF(3)Br are addressed by a determination of beta(-2omega;omega, omega) for a wavelength of 694.3 nm, and the same property is also determined for CF(3)I. The relativistic effects on the static hyperpolarizability for the series of molecules amount to 1%, 5%, and 9%, respectively. At the experimental wavelength, the contributions to beta due to the magnetization dependence in the exchange-correlation functional are negligible for CF(3)Cl and CF(3)Br and small for CF(3)I. The noticeable effect of magnetization in the latter case is attributed to a near two-photon resonance with the excited state 1 (3)E (nonrelativistic notation). It is emphasized, however, that the effect of magnetization on beta for CF(3)I is negligible both in comparison to the total relativistic correction as well as to the effects of electron correlation. It is concluded that, in calculations of hyperpolarizabilities under nonresonant conditions, the magnetization dependence in the exchange-correlation functional may be ignored.

The DIRAC code for relativistic molecular calculations

“…At the closed-shell SCF level, both for Hartree-Fock and for Kohn-Sham, DIRAC allows for the calculation of molecular properties corresponding to expectation values as well as linear 5,116 and quadratic 131,132 response functions. In addition, first-and secondorder residues of the quadratic response function have been programmed, allowing for the calculation of two-photon absorption cross sections 118 and first-order properties of electronically excited states, 133 respectively.…”

“…NMR shieldings as well as magnetizabilities may be calculated using London orbitals and simple magnetic balance. 18 For KS calculations, non-collinear spin magnetization has been implemented 132 and all required derivatives of exchange-correlation functionals are provided. The implementations for obtaining density matrices for molecular properties are still under development.…”

The DIRAC code for relativistic molecular calculations

“…At the closed-shell SCF level, DIRAC allows the calculation of molecular properties corresponding to expectation values as well as linear 5,108 and quadratic 124,125 response functions.…”

“…NMR shieldings as well as magnetizabilities may be calculated using London orbitals and simple magnetic balance. 133 For KS calculations non-collinear spin magnetization has been implemented 125 and all required derivatives of exchange-correlation functionals are provided.…”

Nuclear spin-spin coupling in a van der Waals-bonded system: Xenon dimer

“…In the NR DFT calculations by the DAL-TON program, the "ULTRAFINE" integration grid 31 was further tightened in its radial part to the parameter value of 1.0 × 10 −16 in single-point calculations at r e , and further to 1.0 × 10 −17 in calculations of the J-coupling curve. In DIRAC, we used the default non-collinear 48 definition of spin density.…”