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## Back Matter - Relativistic Theory of Atoms and Molecules III

### Relativistic Theory of Atoms and Molecules III (2000-01-01): 76 , January 01, 2000

## Relativistic Pseudopotentials

### Relativistic Methods for Chemists (2010-01-01) 10: 215-277 , January 01, 2010

A brief overview over the foundations and modern variants of the relativistic effective core potential method, i.e., energy-consistent and shape-consistent ab initio pseudopotentials as well as ab initio model potentials, is given. The energy-consistent ab initio pseudopotential approach is discussed in more detail, focussing on the uranium atom as an example. The selection of appropriate relativistic reference data, the choice of the core and the fitting procedure are discussed. Results of atomic and molecular test calculations, e.g., for the low-lying electronic states of uranium hydride, are summarized. Whereas the 5f-in-core large-core approximation provides an efficient approximate treatment of larger actinide systems without having to struggle with complexities arising from the open 5f shell, the 5f-in-valence small-core approach allows to reach a similar accuracy as the best available relativistic all-electron calculations.

## Improved valence basis sets for divalent lanthanide 4f-in-core pseudopotentials

### Theoretical Chemistry Accounts (2010-11-26): 1-13 , November 26, 2010

Improved energy-optimized (6s5p4d) and (7s6p5d) primitive valence basis sets have been derived for energy-consistent scalar-relativistic 4f-in-core pseudopotentials of the Stuttgart-Cologne variety modeling divalent lanthanides with a
$$4\hbox{f}^{n+1}$$
occupation (*n* = 0–13 for La–Yb). Segmented contracted basis sets covering the range of polarized double-, triple-, and quadruple-zeta quality, augmented by 2f1g correlation sets, were created for use in molecular calculations. The basis sets contain smaller (4s4p3d) and (5s5p4d) primitive subsets, which are designed in particular for solid state calculations of crystals containing divalent lanthanide ions. Hartree–Fock, density functional theory and coupled cluster results obtained with the new basis sets for lanthanide atomic ionization potentials as well as of geometry optimizations of various test molecules, i.e. selected lanthanide mono- and dihydrides, mono- and difluorides, and monooxides, show a satisfactory agreement with experimental data as well as with corresponding scalar-relativistic all-electron results. Core-polarization potentials are found to improve the results, especially for the atomic first and second ionization potentials.

## Quasirelativistic f-in-core pseudopotentials and core-polarization potentials for trivalent actinides and lanthanides: molecular test for trifluorides

### Theoretical Chemistry Accounts (2010-06-04) 126: 117-127 , June 04, 2010

Calibration studies of actinide and lanthanide trifluorides are reported for actinide and lanthanide scalar-relativistic energy-consistent f-in-core pseudopotentials, respectively, accompanying valence basis sets as well as core-polarization potentials. Results from Hartree–Fock and coupled-cluster singles, doubles, and perturbative triples f-in-core pseudopotential calculations are compared to corresponding data from f-in-valence pseudopotential and all-electron calculations as well as to experimental data. In general, good agreement is observed between the f-in-core and f-in-valence pseudopotential results, whereas due to the lack of experimental data for the actinides only a good agreement of the calculated and experimentally determined bond lengths of the lanthanide systems can be established. Nevertheless, the results indicate that the core-polarization potentials devised here for actinides improve the f-in-core results.

## Quasirelativistic energy-consistent 5f-in-core pseudopotentials for trivalent actinide elements

### Theoretical Chemistry Accounts (2007-03-14) 117: 473-481 , March 14, 2007

Quasirelativistic energy-consistent 5f-in-core pseudopotentials modelling trivalent actinides, corresponding to a near-integral 5f^{n} occupation (*n* = 0–14 for Ac–Lr), have been generated. Energy-optimized (6s5p4d), (7s6p5d), and (8s7p6d) primitive valence basis sets contracted to polarized double to quadruple zeta quality as well as 2f1g correlation functions have been derived. Corresponding smaller basis sets (4s4p3d), (5s5p4d), and (6s6p5d) suitable for calculations on actinide(III) ions in crystalline solids form subsets of these basis sets designed for calculations on neutral molecules. Results of Hartree–Fock test calculations for actinide(III) monohydrates and actinide trifluorides show a satisfactory agreement with corresponding calculations using 5f-in-valence pseudopotentials. Even in the beginning of the actinide series, where the 5f shell is relatively diffuse, only quite acceptable small deviations occur as long as the 5f-shell does not participate significantly in covalent bonding.

## Scalar-relativistic 5f-in-core pseudopotentials and core-polarization potentials for trivalent actinides: calibration calculations for Ac3+, Cm3+ and Lr3+ complexes

### Theoretical Chemistry Accounts (2012-03-03) 131: 1-11 , March 03, 2012

The performance of recently proposed 5f-in-core pseudopotentials for the trivalent actinides was investigated in calculations for model complexes An^{3+}L^{n−} for three selected actinides (An^{3+} = Ac^{3+}, Cm^{3+}, Lr^{3+}) and eight simple ligands with atoms from the first three periods of the table of elements (L^{n−} = F^{−}, Cl^{−}, OH^{−}, SH^{−}, CO, NH
_{2}^{−}
, H_{2}O, H_{2}S, NH_{3}). Results of Hartree-Fock and Coupled Cluster with singles, doubles and perturbative triples calculations using basis sets of quadruple-zeta quality are compared to corresponding reference data obtained with scalar-relativistic energy-adjusted 5f-in-valence small-core pseudopotentials. The inclusion of core-polarization potentials in the 5f-in-core pseudopotential calculations and corrections of the basis set superposition error by the counterpoise correction leads to very good agreement between the 5f-in-valence and 5f-in-core pseudopotential results for bond lengths, bond angles and binding energies. Results from 5f-in-core pseudopotential calculations using different density functionals also show reasonable agreement with the more rigorous Coupled Cluster results. It is argued that the An 5f rather than the An f population is a useful criterion for the applicability of a specific An 5f-in-core pseudopotential.

## Quasirelativistic energy-consistent 5f-in-core pseudopotentials for divalent and tetravalent actinide elements

### Theoretical Chemistry Accounts (2007-11-16) 118: 845-854 , November 16, 2007

Quasirelativistic energy-consistent 5f-in-core pseudopotentials modeling divalent (5f^{n+1} occupation with *n* = 5–13 for Pu–No) respectively tetravalent (5f^{n-1} occupation with *n* = 1–9 for Th–Cf) actinides together with corresponding core-polarization potentials have been generated. Energy-optimized (6s5p4d) and (7s6p5d) valence basis sets as well as 2f1g correlation functions have been derived and contracted to polarized double, triple, and quadruple zeta quality. Corresponding smaller (4s4p) and (5s5p) respectively (4s4p3d) and (5s5p4d) basis sets suitable for calculations on actinide(II) respectively actinide(IV) ions in crystalline solids form subsets of these basis sets designed for calculations on molecules. Results of Hartree–Fock test calculations for actinide di- and tetrafluorides show a satisfactory agreement with calculations using 5f-in-valence pseudopotentials.

## A combination of quasirelativistic pseudopotential and ligand field calculations for lanthanoid compounds

### Theoretica Chimica Acta (1993-06-01) 85: 441-450 , June 01, 1993

### Summary

Improved energy-adjusted quasirelativistic pseudopotentials for lanthanoid atoms with fixed valency are presented and tested in molecular calculations for CeO, CeF, EuO, GdO, YbO, and YbF. The pseudopotential calculations treat the lanthanoid 4*f* shell as part of the core and yield accurate estimates for average bond lengths, vibrational frequencies and dissociation energies of all states belonging to a superconfiguration. Information for each individual state of the considered superconfiguration may be obtained from subsequent ligand field model calculations. The results of this combined pseudo-potential and ligand field approach (PPLFT) are compared to more accurate calculations with ab initio pseudopotentials that include the lanthanoid 4*f* orbitals explicitly in the valence shell and to available experimental data.

## Relativistic Pseudopotentials

### Theoretical Chemistry and Physics of Heavy and Superheavy Elements (2003-01-01) 11: 399-438 , January 01, 2003

The pseudopotential approximation is reviewed in detail for heavy and superheavy elements. It is shown that pseudopotentials are an effective and accurate way to treat relativistic effects in heavy element containing systems.

## Improved relativistic energy-consistent pseudopotentials for 3d-transition metals

### Theoretical Chemistry Accounts (2005-10-01) 114: 297-304 , October 01, 2005

Energy-consistent relativistic pseudopotentials for 3*d*-transition metals Sc to Ni based on modified valence energies are proposed. The pseudopotentials are adjusted at the finite difference level within the intermediate coupling scheme with respect to multi-configuration Dirac–Hartree–Fock data based on the Dirac–Coulomb Hamiltonian with an estimate of the Breit contributions in quasidegenerate perturbation theory. Typically a few hundred to thousand J levels arising from about 35 to 40 configurations ranging from the anion down to the highly charged cation are considered as references. It is shown that introducing a small common energetic shift of all valence energies reduces the errors in the parameter adjustment considerably. Results of highly correlated atomic and molecular test calculations using large basis sets and basis set extrapolation techniques are presented.