Calculation of response properties with the normalized elimination of the small component method

Abstract

The normalized elimination of the small component method is a first principles two-component relativistic approach that leads to the Dirac-exact description of one-electron systems. Therefore, it is an ideal starting point for developing procedures, by which first-and second-order response properties can be routinely calculated. We present algorithms and methods for the calculation of molecular response properties such as geometries, dipole moments, hyperfine structure constants, vibrational frequencies and force constants, electric polarizabilities, infrared intensities and so forth. The described formalisms are applied to molecules containing mercury and other heavy elements, which require a relativistic treatment. Perspectives for the future development and application of Dirac-exact methods are outlined.

Perturbative treatment of spin-orbit coupling within spin-free exact two-component theory

“…A further advantage of the X2C scheme is that its simple block-diagonalization technique greatly facilitates the construction of analytic derivatives of the X2C Hamiltonian matrix elements. [39][40][41][42][43][44] As the exact block diagonalization of the four-component Hamiltonian matrix requires information about the four-component wave function, the construction of the X2C Hamiltonian matrix elements is as expensive as the solution of the corresponding four-component equation. Therefore, the practical computational efficiency of the X2C approach originates from using the X2C Hamiltonian matrix constructed at a lower level of theory in higher-level quantum-chemical calculations, since the computational cost is usually dominated by the level of theory used for treating the electron-electron interactions.…”

Dieter Cremer's contribution to the field of theoretical chemistry

“…Between 2009 and 2017, Dieter Cremer took the NESC program package to the next level of sophistication by adding higher derivatives, new response properties, and spin‐orbit coupling (SOC). In 2011, the computational difficulties still accompanying the solution of the NESC equations were finally solved by Zou, Filatov, and Cremer leading to a generally applicable NESC method that can be used for the routine calculation of first‐order response properties (eg, molecular geometries, electric field gradients, hyperfine structure constants, contact densities, and Mössbauer shifts) and second‐order response properties (eg, vibrational frequencies, electric polarizabilities, and infrared intensities). Special features of this new, effective NESC program are (1) the use of IORA as a convenient starting point for an iterative solution of the NESC equations, (2) a finite nucleus model based on a Gaussian charge distribution, and (3) a first‐diagonalize‐then‐contract strategy for the solution of the NESC equations .…”

Calculations of electric dipole moments and static dipole polarizabilities based on the two-component normalized elimination of the small component method

“…Combining the CPGHF method with the direct inversion in the iterative subspace (DIIS) method, 43,44 we iteratively obtain the first-order density matrix P (1) t based on Eqs. (19), (29), (30), (35), and (36)- (39).…”

“…The CPGHF and CPGKS methods have already been used in 2c-relativistic property calculations, but to the best of our knowledge the CPGKS approach for the noncollinear exchange-correlation (XC) potential [30][31][32] or the long-range corrected (LC) exchange functional 33,34 have so far not been developed. Apart from this, we install CPGHF and CPGKS into 2c-NESC to exploit the compact and efficient programming of NESC response properties in terms of products of traces of matrices 35,36 to provide the possibility of a rapid calculation of first and second order 2c-NESC response properties. Hence, we consider the presentation of the CPGHF/CPGKS equations of 2c-NESC as the basis for our future work on vibrational frequencies, infrared intensities, and other 2nd-order properties of 2c-NESC.…”