Spin densities in two-component relativistic density functional calculations: Noncollinear versus collinear approach

With present day exchange-correlation functionals, accurate results in nonrelativistic open shell density functional calculations can only be obtained if one uses functionals that do not only depend on the electron density but also on the spin density. We consider the common case where such functionals are applied in relativistic density functional calculations. In scalar-relativistic calculations, the spin density can be defined conventionally, but if spin-orbit coupling is taken into account, spin is no longer a good quantum number and it is not clear what the “spin density” is. In many applications, a fixed quantization axis is used to define the spin density (“collinear approach”), but one can also use the length of the local spin magnetization vector without any reference to an external axis (“noncollinear approach”). These two possibilities are compared in this work both by formal analysis and numerical experiments. It is shown that the (nonrelativistic) exchange-correlation functional should be invariant with respect to rotations in spin space, and this only holds for the noncollinear approach. Total energies of open shell species are higher in the collinear approach because less exchange energy is assigned to a given Kohn-Sham reference function. More importantly, the collinear approach breaks rotational symmetry, that is, in molecular calculations one may find different energies for different orientations of the molecule. Data for the first ionization potentials of Tl, Pb, element 113, and element 114, and for the orientation dependence of the total energy of I and PbF indicate that the error introduced by the collinear approximation is ∼0.1 eV for valence ionization potentials, but can be much larger if highly ionized open shell states are considered. Rotational invariance is broken by the same amount. This clearly indicates that the collinear approach should not be used, as the full treatment is easily implemented and does not introduce much more computational effort. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 779–785, 2002

[1]  E. Engel,et al.  Systematic study of the Ib diatomic molecules Cu 2 , Ag 2 , and Au 2 using advanced relativistic density functionals , 1999 .

[2]  Wenjian Liu,et al.  Spectroscopic constants of gold and eka-gold (element 111) diatomic compounds: The importance of spin–orbit coupling , 1999 .

[3]  Häberlen,et al.  Relevance of relativistic exchange-correlation functionals and of finite nuclei in molecular density-functional calculations. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[4]  Görling.  Symmetry in density-functional theory. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[5]  J. Perdew,et al.  Density-functional approximation for the correlation energy of the inhomogeneous electron gas. , 1986, Physical review. B, Condensed matter.

[6]  M. Klobukowski,et al.  Well-tempered gaussian basis set expansions of Roothaan-Hartree-Fock atomic wavefunctions for lithium through mercury , 1988 .

[7]  Lemin Li,et al.  A simplified scheme for relativistic density functional computation in the zeroth-order regular approximation , 2000 .

[8]  E. Davidson,et al.  A density functional method for degenerate spin-multiplet components , 2001 .

[9]  Evert Jan Baerends,et al.  The zero order regular approximation for relativistic effects: the effect of spin-orbit coupling in closed shell molecules. , 1996 .

[10]  Christoph van Wüllen,et al.  Molecular density functional calculations in the regular relativistic approximation: Method, application to coinage metal diatomics, hydrides, fluorides and chlorides, and comparison with first-order relativistic calculations , 1998 .

[11]  E. Baerends,et al.  Atomic reference energies for density functional calculations , 1997 .

[12]  Eberhard Engel,et al.  Four-component relativistic density functional calculations of heavy diatomic molecules , 2000 .

[13]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[14]  Keller,et al.  Generalized gradient approximation for the relativistic exchange-only energy functional. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[15]  N. Rösch,et al.  A scalar-relativistic extension of the linear combination of Gaussian-type orbitals local density functional method: application to AuH, AuCl and Au2 , 1992 .

[16]  Evert Jan Baerends,et al.  Relativistic total energy using regular approximations , 1994 .

[17]  L. Hedin,et al.  A local exchange-correlation potential for the spin polarized case. i , 1972 .

[18]  E. Gross,et al.  Spin-Density Functionals from Current-Density Functional Theory and Vice Versa: A Road towards New Approximations , 1997 .

[19]  Hans W. Horn,et al.  Fully optimized contracted Gaussian basis sets for atoms Li to Kr , 1992 .

[20]  Wenjian Liu,et al.  Spectroscopic constants of Pb and Eka-lead compounds , 2001 .

[21]  Keller,et al.  Local and nonlocal relativistic exchange-correlation energy functionals: Comparison to relativistic optimized-potential-model results. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[22]  K. Burke,et al.  Density Functionals: Where Do They Come from, Why Do They Work? , 1996 .

[23]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[24]  Helmut Eschrig,et al.  The fundamentals of density functional theory , 1996 .

[25]  Joseph Callaway,et al.  Inhomogeneous Electron Gas , 1973 .

[26]  M. S. Singh,et al.  Noncollinear intra-atomic magnetism. , 1996, Physical review letters.

[27]  H. Stoll,et al.  Correlation energies in the spin-density functional formalism , 1980 .

[28]  L. Sandratskii.  Noncollinear magnetism in itinerant-electron systems: Theory and applications , 1998 .

[29]  D. Ellis,et al.  Self‐consistent Dirac–Slater calculations for molecules and embedded clusters , 1984 .

[30]  G. Seifert,et al.  Current density functional theory of quantum electrodynamics , 1985 .

[31]  N. Rösch,et al.  A two-component variant of the Douglas–Kroll relativistic linear combination of Gaussian-type orbitals density-functional method: Spin–orbit effects in atoms and diatomics , 2001 .