Interfacing relativistic and nonrelativistic methods. III. Atomic 4-spinor expansions and integral approximations

Abstract

Two approximations to the normalized elimination of the small component are presented which enable the work of a relativistic calculation to be substantially reduced. The first involves fixing the ratio of the large and small components in atomic calculations, which corresponds to a basis set expansion in terms of positive energy atomic 4-spinors. The second involves the definition of a local, i.e., center-dependent, fine structure constant, which has the effect of making atoms with α=0 nonrelativistic. A series of test calculations on a variety of molecules and properties indicates that the errors incurred in the first approximation are negligible. In the second approximation, the errors are dependent on the property, the chemical environment and the atomic number. For the second period elements the errors in the approximation are for chemical purposes negligible. In the third period this is true for many properties, but for some, such as ligand-metal binding energies, there are discrepancies which may be a cause for concern in more accurate calculations. Beyond the third period it is usually necessary to treat atoms relativistically.

Ab initio study of bonding trends for f 0 actinide oxyfluoride species

“…1 The basis set for O was the aug-cc-pVDZ basis [56] and the basis set for U was a double-zeta-quality basis set used previously for calculations on dioxoactinide species [30]. The O atoms were treated nonrelativistically according to the model proposed by Dyall and Enevoldsen [57]. Geometries and harmonic frequencies were obtained from numerical ®ts to data obtained at a range of points.…”

“…For thermochemical estimates the aug-cc-PVTZ basis set for O and F was also tested, but the changes were minimal. QR calculations were done with the Gaussian 98 [57], Molcas-4 [52] and Turbomole [53] packages.…”

Local relativistic exact decoupling

“…However, invoking the free-particle FW transformation turns out to be not necessary for the construction of the exact-decoupling transformation in a one-step protocol. The pioneering work of this one-step transformation was provided by Dyall [28][29][30][31][32] in the form of the so-called normalized elimination of the small component (NESC) approach. Later it was generalized to the so-called exact twocomponent (X2C) method by several groups.…”

Relativistic calculations of magnetic resonance parameters: background and some recent developments

“…There have been other elimination schemes devised to construct formally exact twocomponent relativistic operators, for instance, infinite-order methods by Barysz and co-workers (BSS = Barysz-Sadlej-Snijders, IOTC = infinite-order two-component) [55][56][57][58] and normalized elimination of the small component (NESC) methods [59][60][61][62][63][64][65][66]. In its recent incarnations, the X2C technique rests on a representation of the four-component equation in an RKB basis.…”