Pseudopotential Energy-Consistent

Figgen, D., Rauhut, G., Dolg, M. and StoD, H. (2005) Energy-consistent pseudopotentials for group 11 and 12 atoms adjustment to multi-configuration Dirac-Hartree-Fock data. Chemical Physics, 311, 227-244. 

M. Burkatzki, C. Filippi, M. Dolg, Energy-consistent pseudopotentials for quantum Monte Carlo calculations. J. Chem. Phys. 126, 234105 (2007) (and references contained therein)... 

Stoll H, Metz B, Dolg M. Relativistic energy-consistent pseudopotentials—recent developments. J Comput Chem 2002 23 767-778. 

In the most recent version of the energy-consistent pseudopotential approach the reference data is derived from finite-dilference all-electron multi-configuration Dirac-Hartree-Fock calculations based on the Dirac-Coulomb or Dirac-Coulomb-Breit Hamiltonian. As an example the first parametrization of such a potential,... 

It may be asked how accurate energy-consistent pseudopotentials will reproduce the shape of the valence orbitals/spinors and their energies. Often radial expectation values < r > are used as a convenient measure for the radial shape of orbitals/spinors. Due to the pseudo-valence orbital transformation and the simplified nodal structure it is clear that values n < 0 are not suitable, since the resulting operator samples the orbitals mainly in the core region. Table 2 lists orbital energies, < r > and < > expectation values for the Db [Rn] 5f 6d ... 

The formalism described here to derive energy-consistent pseudopotentials can be used for one-, two- and also four-component pseudopotentials at any desired level of relativity (nonrelativistic Schrbdinger, or relativistic Wood-Boring, Douglas-Kroll-Hess, Dirac-Coulomb or Dirac-Coulomb-Breit Hamiltonian implicit or explicit treatment of relativity in the valence shell) and electron correlation (single- or multi-configurational wavefunctions. The freedom... 

The functional form of energy-consistent pseudopotentials is identical to the one of shape-consistent pseudopotentials, both types of pseudopotentials can be used in standard quantum chemical program packages (e.g., COLUMBUS, GAUSSIAN, GAMESS, MOLPRO, TURBOMOLE) as well as polymer or solid state codes using Gaussian basis sets (e.g., CRYSTAL). 

Bond lengths R (A), binding energies D. (eV) and vibrational constants a>e (cm ) of the homonuclear halogen dimers from dl-electron (AE) Douglas-Kroll-HeB (DKH) and valence-only energy-consistent pseudopotential (EC-PP) Hartree-Fock self-consistent field (SCF) calculations. The effects of static and dynamic core-polarization at the valence-only level are modelled by a core-polarization potential (CPP). 

Bond lengths (A), vibrational constants (Og (cm ) and binding energies D (eV) of ThO in the ground state from energy-consistent pseudopotential (EC-PP) [198,243], model potential (MP) [269] and ab initio model potentiM (AIMP) [115] calculations in comparison to experimentd data. The values are without/with counter poise correction of the basis set superposition error. 

The author is grateful to H. Stoll (Stuttgart) and P. Schwerdtfeger (Auckland) many years of cooperation on the field of energy-consistent pseudopotentials. Financial support of the Deutsche Forschungsgemeinschaft (DFG) and the Fonds der Chemischen Industrie (FCI) is gratefully acknowledged. 

Recently, Stoll et al [94] used a very similar approach to EPCISO. One minor difference is the use of the DGCI Pitzer s code which works with CSFs basis functions instead of determinants. Apparently another difference here is the absence of a selection process of the spin-orbit matrix elements. In this study small-core and large-core energy-consistent pseudopotentials were combined for the calculation of spectroscopic constants of lead and bismuth compounds (BiH, BiO, PbX, BiX, (X=F, Cl, Br, I)). 

Let us first consider ground state spectroscopic properties. Schwerdtfeger et al tested relativistic and correlation effects using a large-core (seven valence electrons) energy-consistent pseudopotential, with or without U )... 

StoU, H., Metz, B., Dolg, M. Relativistic energy-consistent pseudopotentials— recent developments, J. Comp. Chem. 2002,23,767. 

M. Dolg. Improved relativistic energy-consistent pseudopotentials for 3d-transition metals. Theor. Chem. Acc., 114(4-5) (2005) 297- 04. 

T. Hangele, M. Dolg. Accuracy of relativistic energy-consistent pseudopotentials for superheavy elements 111-118 Molecular calibration calculations. /. Chem. Phys., 138 (2013) 044104. 

Hangle, T., Dolg, M., Hanrath, M., Cao, X., Stoll, H., Schwerdtfeger, P. Accurate relativistic energy-consistent pseudopotentials for the superheavy elements 111 to 118 including quantum electrodynamic effects. J. Chem. Phys. 136, 214105 (1-10) (2012)... 

Stuttgart-Cologne energy-consistent pseudopotentials [Internet]. Available from http //www.tc. uni-koeln.de/PP/index.en.html. 

A. Weigand, X. Cao, V. Vallet, J.-P. Flament, and M. Dolg, Multi-configuration Dirac-Hartree-Fock adjusted energy-consistent pseudopotential for uranium spin-orbit configuration interaction and Fock-space coupled-cluster study of U and J. Phys. Chem. A, 113, 11509-11516(2009). 

Peterson KA, Figgen D, Dolg M, and Stoll H. 2007. Energy-consistent relativistic pseudopotentials and correlation consistent basis sets for the 4d elements Y-Pd. J. Chem. Phys. 126, 124101 b) Figgen D, Peterson KA, Dolg M, StoU H. 2009. Energy-consistent pseudopotentials and correlation consistent basis sets for the 5d elements Hf-Pt. J. Chem. Phys. 130, 164108. 

There have been a number of basis sets for lanthanide and actinide elements previously reported in the literature that are based on relativistic effective core (ECP) potentials, or pseudopotentials (PP). These can be most easily categorized by the type of underlying ECP used (a) shape consistent pseudopotentials, (b) energy consistent pseudopotentials, and (c) model potentials. 

Figgen D, Peterson KA, Dolg M, Stoll H. Energy-consistent pseudopotentials and correlation consistent basis sets for the 5d elements Hf-Pt. J Chem Phys. 2009 130 164108. 

Weigand A, Cao X, Vallet V, Flament JP, Dolg M. Multi-configuration Diract-Hartree-Fock Adjusted Energy-consistent Pseudopotential for Uranium Spin-orbit Configuration Interaction and Fock-Space Coupled-Cluster Study of U + and U + J Phys Chem A 2009 1 IJ-llSOO-llSlb. 

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