Dipole properties of atoms and molecules in the random phase approximation

Abstract

A random phase approximation (RP A) calculation and a direct sum over states is used to calculate second-order optical properties and van der Waals coefficients. A basis set expansion technique is used and no continuumlike functions are included in the basis. However, unlike other methods we do not force the basis functions to satisfy any sum-rule constraints but rather the formalism (RP A) is such that the Thomas-Reiche--Kuhn sum rule is satisfied exactly. Central attention is paid to the dynamic polarizability from which most of the other properties are derived. Application is made to helium and molecular hydrogen. In addition to the polarizability and van der Waals coefficients, results are given for the molecular anisotropy of H 2 , Rayleigh scattering cross sections, and Verdet constants as a function of frequency. Agreement with experiment and other theories is good. Other energy weighted sum rules are calculated and compare very well with previous estimates. The practicality of our method suggests its applications to larger molecular systems and other properties.

Relativistic quantum defect calculations on the copper isoelectronic sequence

“…The quantum defect orbital (QDO) method [5] and its relativistic generalization (RQDO) [6] belong to simple and reliable methods of estimation of the oscillator strengths. Their reliability has been tested in several cases [7,8].…”

Mean excitation energies of singly charged atomic anions with Z ≤ 18

“…However, in a finite basis set calculation one obtains a finite number of pseudostates placed in the continuum and we use these states to calculate the continuum contributions to the mean excitation energy. This kind of approach has with success been used for the calculation of sum over-states properties for years (Dalgarno and Epstein 1969, Martin et al 1975, McCurdy et al 1977. More recently Oddershede et al (2017) have reconfirmed that the stick spectrum representation of the continuum also gives a good representation of the continuum contributions to the mean excitation, provided large and flexible basis sets are used and all states are included in the sum over-states expressions for sum rule in equation (2).…”

“…where n is the number of electrons in the system. Thus, the fulfillment of the TRK sum rule in the length, mixed and velocity formulation is a necessary condition for basis set completeness of an RPA calculation, a criterion that was first used by Martin et al (1975) to test the reliability of finite basis set RPA calculation of molecular second order properties. We shall apply this criterion to test the reliability of our calculations.…”

Algebraic-diagrammatic construction propagator approach to molecular response properties

“…Being the only method initially available, the RPA method has been widely used to calculate frequency-dependent response properties (see for example Refs. [10,11]). But the overall accuracy afforded by the RPA method is hardly satisfactory, as the error in the excitation energies and transition moments is of second-order in the electron repulsion [12].…”