Paired orbitals for different spins equations

Eigenvalue‐type equations for Löwdin–Amos–Hall spin‐paired (corresponding) orbitals are developed to provide an alternative to the standard spin‐polarized Hartree–Fock or Kohn–Sham equations in dealing with broken‐symmetry (BS) states. To derive paired orbitals for different spins (PODS) equations there has been applied Adams–Gilbert “localizing” operator approach. The PODS equations contain different operators for different spins the eigenvectors of which are paired orbitals associated with the same eigenvalue for each pair. Preliminary applications to simple systems show viability of this approach. Although the spectrum of possible applications of the PODS equations seems to be quite wide, they would be especially useful for obtaining and analyzing the Sz = 0 BS solutions for the systems with antiferromagnetic structure. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010

[1]  M. Head‐Gordon,et al.  Locating multiple self-consistent field solutions: an approach inspired by metadynamics. , 2008, Physical review letters.

[2]  G. Forsythe,et al.  Computer solution of linear algebraic systems , 1969 .

[3]  M. Reiher.  On the definition of local spin in relativistic and nonrelativistic quantum chemistry. , 2007, Faraday discussions.

[4]  Förster.  Molecular Orbitals in Chemistry Physics and Biology , 1965 .

[5]  W. Adams,et al.  Orbital Theories of Electronic Structure , 1962 .

[6]  Nicolai Lehnert,et al.  Electronic structure of iron(II)–porphyrin nitroxyl complexes: Molecular mechanism of fungal nitric oxide reductase (P450nor) , 2006, J. Comput. Chem..

[7]  K. Hirao.  How to resolve the orbital ambiguity to obtain the orbital set which is stable to an excitation , 1974 .

[8]  I. Mayer.  Simple theorems, proofs, and derivations in quantum chemistry , 2003 .

[9]  K. Hirao.  On the coupling operator method , 1974 .

[10]  G. M. Zhidomirov,et al.  Unrestricted density functional theory of the bonding between NO radical and ferrous ion , 2004 .

[11]  M. Kaupp,et al.  Where is the spin? Understanding electronic structure and g-tensors for ruthenium complexes with redox-active quinonoid ligands. , 2005, Journal of the American Chemical Society.

[12]  E. Baerends,et al.  The spin-unrestricted molecular Kohn-Sham solution and the analogue of Koopmans's theorem for open-shell molecules. , 2004, The Journal of chemical physics.

[13]  S. Yamanaka,et al.  CAS-DFT based on odd-electron density and radical density , 2002 .

[14]  Josef Paldus,et al.  Hartree–Fock stability and symmetry breaking: oxygen doubly negative ion , 1985 .

[15]  I. Mayer.  Simple proof of the pairing theorem , 1997 .

[16]  F. Sasaki,et al.  Spin-Component Analysis of Single-Determinant Wavefunctions , 1963 .

[17]  A. Stuchebrukhov.  Long-distance electron tunneling in proteins , 2003 .

[18]  I. Mayer,et al.  Spin projected extended Hartree--Fock equations , 1973 .

[19]  E. Baerends,et al.  The analog of Koopmans' theorem in spin-density functional theory , 2002 .

[20]  P. Pulay,et al.  Direct inversion in the iterative subspace (DIIS) optimization of open‐shell, excited‐state, and small multiconfiguration SCF wave functions , 1986 .

[21]  K. C. Mundim,et al.  GSA algorithm applied to electronic structure II: UHF‐GSA method , 2006 .

[22]  T. Van Voorhis,et al.  Accurate magnetic exchange couplings in transition-metal complexes from constrained density-functional theory. , 2006, The Journal of chemical physics.

[23]  P. Karadakov.  An extension of the pairing theorem , 1985 .

[24]  Louis Noodleman,et al.  Valence bond description of antiferromagnetic coupling in transition metal dimers , 1981 .

[25]  G. G. Hall,et al.  Single determinant wave functions , 1961, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[26]  I. Mayer.  The Spin-Projected Extended Hartree-Fock Method , 1980 .

[27]  P. Löwdin.  Band Theory, Valence Bond, and Tight‐Binding Calculations , 1962 .

[28]  G. Forsythe,et al.  Computer solution of linear algebraic systems , 1969 .

[29]  P. Löwdin.  Quantum Theory of Many-Particle Systems. III. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects , 1955 .

[30]  H. Gray.  Molecular orbitals in chemistry, physics, and biology (Lowdin, Per-Olov; Pullman, Bernard; eds.) , 1965 .

[31]  M. Urban,et al.  Hartree-fock stability and broken symmetry solutions of O2- and S2-anions in external confinement , 2007 .

[32]  I. Zilberberg,et al.  Expansion of the unrestricted determinant in the basis of paired orbitals , 2004 .