Two‐step method for precise calculation of core properties in molecules

Abstract

Precise calculations of core properties in heavy-atom systems which are described by the operators heavily concentrated in atomic cores, like to hyperfine structure and P,T-parity nonconservation effects, usually require accounting for relativistic effects. Unfortunately, completely relativistic treatment of molecules containing heavy elements is very consuming already at the stages of calculation and transformation of two-electron integrals with a basis set of four-component spinors.In turn, the relativistic effective core potential (RECP) calculations of valence (spectroscopic, chemical etc.) properties of molecules are very popular because the RECP method allows one to treat quite satisfactory the correlation and relativistic effects for the valence electrons of a molecule and to reduce significantly the computational efforts. The valence molecular spinors are usually smoothed in atomic cores and, as a result, direct calculation of electronic densities near heavy nuclei is impossible.In the paper, the methods of nonvariational and variational one-center restoration of correct shapes of four-component spinors in atomic cores after a two-component RECP calculation of a molecule are discussed. Their efficiency is illustrated in correlation calculations of hyperfine structure and parity nonconservation effects in heavy-atom molecules YbF, BaF, TlF, and PbO.

Concept of effective states of atoms in compounds to describe properties determined by the densities of valence electrons in atomic cores

“…In practice, they are close to the last (by amplitude) maxima, R V m , of valence orbitals (thus the "large-core" pseudopotentials are generated) or, for better accuracy, to the last maxima, R OC m , of outermost core orbitals (for the "small-core" pseudopotentials). So, for the all-electron four-component case one can write Rc ≤ R V m , whereas, for the case of the pseudospinors smoothed in the atomic core, one should first restore proper four-component behavior of spinors in the core or use Rc at least not less than the largest matching radius [11]. …”

“…This method is originated from the relativistic pseudopotential theory [10,14,15] and one-center restoration approaches [11,16] to recover proper electronic structure in heavy-atom cores after the relativistic pseudopotential simulation of a chemical substance. The present research can also be considered as a generalization of our computational models utilized to study the HFS and PNC effects as well as XES chemical shifts in molecules and solids.…”

Расчет Химических Сдвигов Рентгеновских Эмиссионных Спектров Ниобия В Оксидах Ниобия(V) Относительно Металла-=sup=-*-=/Sup=-

“…Двухэтапную процедуру, примененную в данной ра-боте, можно считать обобщением описанной в рабо-тах [16][17][18]. На первом этапе выполняется молекулярный расчет в приближении релятивистского псевдопотен-циала остова [11][12][13].…”

“…атома [16,17], методика вычисления химических сдвигов рентгеновских эмиссионных спектров с использованием эффективного одночастичного оператора, описанная в работах [4,5], должна приводить к результатам, совпа-дающим с оценками химических сдвигов как разности энергий соответствующего перехода в атоме и ионе, вычисленных по теореме Купманса [24].…”

“…В настоящей работе на основе результатов расчетов иона Nb +3 и нейтрального атома Nb оценена погреш-ность в вычислении химического сдвига, возникающая из-за использования свойства пропорциональности ва-лентных спиноров в остовной области атома [5,16,17]. Показано, что для химического сдвига линии K α1 (пе-реход 2p 3/2 → 1s 1/2 ) использование свойства пропорци-ональности вносит погрешность около 20 meV, которая приемлема с точки зрения интерпретации эксперимента.…”