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Relativistic Effects

Relativistic quantum chemistry

K.G. Dyall and K. Faegri Jr., Introduction to Relativistic Quantum Chemistry (Oxford Univ. Press, 2007)

Reviews

W. Kutzelnigg, in Relativistic Electronic Structure Theory Part I. Fundamentals edited by P. Schwerdtfeger (Elsevier, Amsterdam, 2002) p. 664

L. Cheng, S. Stopkowicz, and J. Gauss, Int. J. Quant. Chem. 114, 1108 (2014); review on analytic derivatives in relativistic quantum chemsitry

Single-point energy calculations

perturbation theory based on mass-velocity and Darwin terms (MVD1 and MVD2)

R.D. Cowan and D.C. Griffin, J. Opt. Soc. Am. 66, 1010 (1976)

W. Klopper, J. Comp. Chem. 18, 20 (1997)

Direct perturbation theory (DPT)

W. Kutzelnigg, E. Ottschofski, and R. Franke, J. Chem. Phys. 102, 1740 (1995); general theory at HF level

E. Ottschofski and W. Kutzelnigg, J. Chem. Phys. 102, 1752 (1995); results using STOs for rare gas atoms

W. Klopper, J. Comp. Chem. 18, 20 (1997); use of analytic gradients in DPT

S. Stopkowicz and J. Gauss, J. Chem. Phys. 134, 064114 (2011); DPT4 at HF level including SO corrections

W. Schwalbach, S. Stopkowicz, L. Cheng, and J. Gauss, J. Chem. Phys. 135, 194114 (2011); SF-DPT6 at HF level

Spin-free (SF) four-compononent (SF-Dirac Coulomb) approaches

K. Dyall, J. Chem. Phys. 100, 2118 (1994); spin separation, can be also found in earlier work of Kutzelnigg

L. Cheng and J. Gauss, J. Chem. Phys. 134, 244112 (2011); implementation for HF, MP2, and CC. Note that this implementation is different from the one in DIRAC

(Spin-free) X2C-1e calculations

K. G. Dyall, J. Chem. Phys. 106, 9618 (1997); here named normalized elimination of the small component (NESC)
W. Kutzelnigg and W. Liu, J. Chem. Phys. 123, 241102 (2005); general X2C strategy 
W. Liu and D. Peng, J. Chem. Phys. 125, 044102 (2006); X2C-mf variant
M. Ilias and T. Saue, J. Chem. Phys. 126, 064102 (2007); one-electron variant of X2C
J. Sikkema, L. Visscher, T. Saue, and M. Ilias, J. Chem. Phys. 131, 124116 (2009); X2C-mf variant
W. Liu and D. Peng, J. Chem. Phys. 131, 031104 (2009); proper choice of R matrix

Geometry optimizations

using perturbation theory based on mass-velocity and Darwin terms (MVD1 and MVD2)

C. Michauk and J. Gauss, J. Chem. Phys. 127, 044106 (2007)

using direct perturbation theory (DPT)

C. Michauk and J. Gauss, unpublished; see C. Michauk, Ph.D. thesis, University of Mainz, 2008

using SFX2c-1e

L. Cheng and J. Gauss, J. Chem. Phys. 135, 084114 (2011)
see also, W. Zou, M. Filatov, and D. Cremer, J. Chem. Phys. 134, 244117 (2011)

First-order properties

using direct perturbation theory (DPT)

S. Stopkowicz and J. Gauss, J. Chem. Phys. 129, 164119 (2008); DPT2

S. Stopkowicz and J. Gauss, J. Chem. Phys. 134, 204106 (2011); numerical differentiation at DPT4 level including SO effects

using a spin-free Dirac-Coloumb approach

L. Cheng and J. Gauss, J. Chem. Phys. 134, 244112 (2011)

using SFX2c-1e

L. Cheng and J. Gauss, J. Chem. Phys. 135, 084114 (2011)

Second-order properties

using direct perturbation theory (DPT)

S. Stopkowicz, D.P. O'Neill, and J. Gauss, unpublished; see S. Stopkowicz, diploma thesis, University of Mainz, 2008

using SFX2c-1e

L. Cheng and J. Gauss, J. Chem. Phys. 135, 244104 (2011)

Perturbative treatments of spin-orbit effects

within DPT

S. Stopkowicz and J. Gauss, J. Chem. Phys. 134, 064114 (2011)

on top of a SFDC calculation

L. Cheng, S. Stopkowicz, and J. Gauss, J. Chem. Phys. 139, 214114 (2013)

on top of a SFX2c-1e calculation

L. Cheng and J. Gauss, J. Chem. Phys. 141, 164107 (2014)

Spin-orbit splittings

using EOM-CC theory

K. Klein and J. Gauss, J. Chem. Phys. 129, 194106 (2008); first implementation for EOMIP-CC
E. Epifanovsky, K. Klein, S. Stopkowicz, J. Gauss, and A.I. Krylov, J. Chem. Phys. 143, 064102 (2015); generalization to EOMEA-, EOMEE-, and EOMSF-CC

using Mk-MRCC theory

L.A. Mück and J. Gauss, J. Chem. Phys. 136, 111103 (2012)

Two-component methods

two-component CCSD and CCSD(T) approaches using ECPs with SO couplings

F. Wang, J. Gauss, and C. van Wüllen, J. Chem. Phys. 129, 064113 (2008)

gradients for two-component CCSD and CCSD(T) approaches with SO couplings

F. Wang and J. Gauss, J. Chem. Phys. 129, 174110 (2008)

second derivatives for two-component CCSD and CCSD(T) approaches with SO couplings

F. Wang and J. Gauss, J. Chem. Phys. 131, 164113 (2009)

two-component EOMIP-CCSD approach

Z. Tu, F. Wang, and X. Li, J. Chem. Phys. 136, 174102 (2012)

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CFOUR is partially supported by the U.S. National Science Foundation.