Relativistic four-component calculations of Buckingham birefringence using London atomic orbitals

Abstract

We present the first relativistic study of the electric-field-gradient induced birefringence (Buckingham birefringence), with application to the series of molecules CX 2 (X = O, S, Se, Te). A recently developed atomicorbital-driven scheme for the calculation of time-dependent molecular properties using one-, two-and four-component relativistic wave functions (Bast et al. in Chem Phys 356:177, 2009) is extended to first-order frequencydependent magnetic-field perturbations, using London atomic orbitals to ensure gauge-origin independent results and to improve basis-set convergence. Calculations are presented at the Hartree-Fock and Kohn-Sham levels of theory and results for CO 2 and CS 2 are compared with previous high-level coupled-cluster calculations. Except for the heaviest member of the series, relativistic effects are small-in particular for the temperature-independent contribution to the birefringence. By contrast, the effects of electron correlation are significant. However, the reliability of standard exchange-correlation functionals in describing Buckingham birefringence remains unclear based on the comparison with high-level coupled-cluster singles-anddoubles calculations.

Open-Ended Recursive Calculation of Single Residues of Response Functions for Perturbation-Dependent Basis Sets

“…This study is an extension of our previous work on the use of London atomic orbitals for calculating different nonlinear optical birefringences and dichroisms, 59 such as Buckingham birefringence, 60,61 the Cotton−Mouton effect, 62 Jones birefringence, 63 and magnetic circular dichroism. 64 Our present study is the second example of the use of London atomic orbitals in the calculation of single residues of a nonlinear response function, but in contrast to the case of magnetic circular dichroism (for which the magnetic field is static), the magnetic field component is frequency-dependent in the case of TPCD.…”

Recent Advances in Wave Function-Based Methods of Molecular-Property Calculations

“…Perturbative studies of spin–orbit effects have been presented in a number of works, in particular, in connection to nuclear magnetic shielding constants. , Examples of nonperturbative approaches to calculation of molecular properties is the no-pair four-component linear response theory and implementation of Visscher et al, the four-component Hartree–Fock linear response theory and implementation by Saue and Jensen, and the quadratic response theory and implementation of Norman and Jensen . More recently, the open-ended response theory of Thorvaldsen et al was extended to the two- and four-component levels of theory for calculation of arbitrary one-electron properties to any order, including London atomic orbitals to first order …”

“…A similar formulation was used in the AO-based Hartree–Fock (and Kohn–Sham) implementation by Kjærgaard et al A quasi-energy formulation of Hartree–Fock and Kohn–Sham response theories enabled the temperature-independent term of the Buckingham effect and the Cotton–Mouton effect at nonzero frequencies to be determined in a gauge-origin-independent manner. A relativistic extension of the latter formulation has recently been used to investigate the importance of relativity for the Buckingham effect of carbon dichalcogenides …”