Excited states of large open-shell molecules: an efficient, general, and spin-adapted approach based on a restricted open-shell ground state wave function.

A spin-adapted configuration interaction with singles method that is based on a restricted open-shell reference function (ROCIS) with general total spin S is presented. All excited configuration state functions (CSFs) are generated with the aid of a spin-free second quantization formalism that only leads to CSFs within the first order interacting space. By virtue of the CSF construction, the formalism involves higher than singly excited determinants but not higher than singly excited configurations. Matrix elements between CSFs are evaluated on the basis of commutator relationships using a symbolic algebra program. The final equations were, however, hand-coded in order to maximize performance. The method can be applied to fairly large systems with more than 100 atoms in reasonable wall-clock times and also parallelizes well. Test calculations demonstrate that the approach is far superior to UHF-based configuration interaction with single excitations but necessarily falls somewhat short of quantitative accuracy due to the lack of dynamic correlation contributions. In order to implicitly account for dynamic correlation in a crude way, the program optionally allows for the use of Kohn-Sham orbitals in combination with a modest downscaling of two-electron integrals (DFT/ROCIS). All two-electron integrals of Kohn-Sham orbitals that appear in the Hamiltonian matrix are reduced by a total of three scaling parameters that are suitable for a wide range of molecules. Test calculations on open-shell organic radicals as well as transition metal complexes demonstrate the wide applicability of the method and its ability to calculate the electronic spectra of large molecular systems.

[1]  M. Gouterman,et al.  Porphyrins XIV. Theory for the luminescent state in VO, Co, Cu complexes , 1969 .

[2]  Manabu Oumi,et al.  A doubles correction to electronic excited states from configuration interaction in the space of single substitutions , 1994 .

[3]  Richard R. Schrock,et al.  Catalytic Reduction of Dinitrogen to Ammonia at a Single Molybdenum Center , 2003, Science.

[4]  M. Zerner,et al.  Optical spectra of transition-metal carbonyls: chromium hexacarbonyl, iron pentacarbonyl, and nickel tetracarbonyl , 1989 .

[5]  F. Weigend.  Accurate Coulomb-fitting basis sets for H to Rn. , 2006, Physical chemistry chemical physics : PCCP.

[6]  Rodney J. Bartlett,et al.  The equation-of-motion coupled-cluster method: Excitation energies of Be and CO , 1989 .

[7]  Michael C. Zerner,et al.  An intermediate neglect of differential overlap technique for spectroscopy of transition-metal complexes. Ferrocene , 1980 .

[8]  S. Grimme,et al.  A COMBINATION OF KOHN-SHAM DENSITY FUNCTIONAL THEORY AND MULTI-REFERENCE CONFIGURATION INTERACTION METHODS , 1999 .

[9]  Frank Neese,et al.  The ORCA program system , 2012 .

[10]  Kerstin Andersson,et al.  Second-order perturbation theory with a CASSCF reference function , 1990 .

[11]  M. Atanasov,et al.  The role of the π-bonding network for trigonal level splittings of tris-bidentate Cr(acac)3 and Cr(ox)33− , 1987 .

[12]  F. Neese,et al.  Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange , 2009 .

[13]  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 .

[14]  F. Neese,et al.  Spin−Spin Contributions to the Zero-Field Splitting Tensor in Organic Triplets, Carbenes and BiradicalsA Density Functional and Ab Initio Study , 2006 .

[15]  G. Frenking,et al.  Structure and Bonding of the Transition-Metal Carbonyl Complexes M(CO)5L (M = Cr, Mo, W) and M(CO)3L (M = Ni, Pd, Pt; L = CO, SiO, CS, N2, NO+, CN-, NC-, HCCH, CCH2, CH2, CF2, H2)1 , 1996 .

[16]  F. Weigend,et al.  Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. , 2005, Physical chemistry chemical physics : PCCP.

[17]  Jean-Paul Malrieu,et al.  Specific CI calculation of energy differences: Transition energies and bond energies , 1993 .

[18]  Michael C. Zerner,et al.  Calculated spectra of hydrated ions of the first transition-metal series , 1986 .

[19]  L. A. Duncanson,et al.  586. Olefin co-ordination compounds. Part III. Infra-red spectra and structure: attempted preparation of acetylene complexes , 1953 .

[20]  Bernard Philippe,et al.  The Davidson Method , 1994, SIAM J. Sci. Comput..

[21]  J. Meyer,et al.  Classification and phylogeny of hydrogenases. , 2001, FEMS microbiology reviews.

[22]  Michael C. Zerner,et al.  An intermediate neglect of differential overlap technique for spectroscopy: Pyrrole and the azines , 1973 .

[23]  E. Gross,et al.  Density-Functional Theory for Time-Dependent Systems , 1984 .

[24]  Poul Jørgensen,et al.  The second-order approximate coupled cluster singles and doubles model CC2 , 1995 .

[25]  P. Löwdin.  On the Non‐Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals , 1950 .

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

[27]  Björn O. Roos,et al.  Second-order perturbation theory with a complete active space self-consistent field reference function , 1992 .

[28]  Roald Hoffmann,et al.  Bonding capabilities of transition metal carbonyl fragments , 1975 .

[29]  Hideo Sekino,et al.  A linear response, coupled‐cluster theory for excitation energy , 1984 .

[30]  Evert Jan Baerends,et al.  Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure , 1973 .

[31]  M. Zerner,et al.  Calculating ESR G tensors of doublet radicals by the semiempirical INDO/S method , 1999 .

[32]  Robert J. Buenker,et al.  Individualized configuration selection in CI calculations with subsequent energy extrapolation , 1974 .

[33]  R. Caballol,et al.  Variational calculation of small energy differences. The singlet-triplet gap in [Cu2Cl6]2− , 1992 .

[34]  Frank Neese,et al.  Vibrational markers for the open-shell character of transition metal bis-dithiolenes: an infrared, resonance raman, and quantum chemical study. , 2006, Journal of the American Chemical Society.

[35]  Luis Serrano-Andrés,et al.  Does density functional theory contribute to the understanding of excited states of unsaturated organic compounds , 1999 .

[36]  Evert Jan Baerends,et al.  Relativistic regular two‐component Hamiltonians , 1993 .

[37]  Frank Neese,et al.  All-Electron Scalar Relativistic Basis Sets for Third-Row Transition Metal Atoms. , 2008, Journal of chemical theory and computation.

[38]  Stefan Grimme,et al.  Substantial errors from time-dependent density functional theory for the calculation of excited states of large pi systems. , 2003, Chemphyschem : a European journal of chemical physics and physical chemistry.

[39]  Manabu Oumi,et al.  A perturbative correction to restricted open shell configuration interaction with single substitutions for excited states of radicals , 1995 .

[40]  Marco Häser,et al.  Auxiliary basis sets to approximate Coulomb potentials , 1995 .

[41]  F. Neese,et al.  The electronic structure of the isoelectronic, square-planar complexes [FeII(L)2]2- and [CoIII(L Bu)2]- (L2- and (L Bu)2-=benzene-1,2-dithiolates): an experimental and density functional theoretical study. , 2005, Journal of the American Chemical Society.

[42]  Stefan Grimme,et al.  The Vibronic Structure of Electronic Absorption Spectra of Large Molecules: A Time-Dependent Density Functional Study on the Influence of “Exact” Hartree−Fock Exchange , 2004 .

[43]  Christof Hättig,et al.  CC2 excitation energy calculations on large molecules using the resolution of the identity approximation , 2000 .

[44]  John R. Sabin,et al.  On some approximations in applications of Xα theory , 1979 .

[45]  A. Köhn,et al.  First-order properties for triplet excited states in the approximated coupled cluster model CC2 using an explicitly spin coupled basis , 2002 .

[46]  M. Head‐Gordon,et al.  On the Nature of Electronic Transitions in Radicals: An Extended Single Excitation Configuration Interaction Method , 1996 .

[47]  J. Almlöf,et al.  Integral approximations for LCAO-SCF calculations , 1993 .

[48]  C. Daniel,et al.  A CASSCF/MR-CCI study of the excited states of Fe(CO)5 , 1999 .

[49]  J. L. Whitten,et al.  Coulombic potential energy integrals and approximations , 1973 .

[50]  B. Roos,et al.  A theoretical study of the chemical bonding in M(CO)x (M=Cr, Fe, and Ni) , 1994 .

[51]  Michael C. Zerner,et al.  An intermediate neglect of differential overlap theory for transition metal complexes: Fe, Co and Cu chlorides , 1979 .

[52]  Frank Neese,et al.  Time-dependent density functional calculations of ligand K-edge X-ray absorption spectra , 2008 .

[53]  E. Davidson.  The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices , 1975 .

[54]  Frank Neese,et al.  Advanced aspects of ab initio theoretical optical spectroscopy of transition metal complexes: Multiplets, spin-orbit coupling and resonance Raman intensities , 2007 .

[55]  Computational study of the electronic structure and magnetic properties of the Ni–C state in [NiFe] hydrogenases including the second coordination sphere , 2012, JBIC Journal of Biological Inorganic Chemistry.

[56]  John F. Stanton,et al.  The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties , 1993 .

[57]  A. Dreuw,et al.  Critique of the foundations of time-dependent density-functional theory , 2007 .

[58]  Benjamin T. Miller,et al.  A parallel implementation of the analytic nuclear gradient for time-dependent density functional theory within the Tamm–Dancoff approximation , 1999 .

[59]  M. Zerner,et al.  On the low-lying states and electronic spectroscopy of iron(II) porphine. , 1986, Journal of the American Chemical Society.

[60]  A. Becke.  A New Mixing of Hartree-Fock and Local Density-Functional Theories , 1993 .

[61]  Henrik Koch,et al.  Coupled cluster response functions , 1990 .

[62]  Ingvar Lindgren,et al.  Diagonalisation of the Dirac Hamiltonian as a basis for a relativistic many-body procedure , 1986 .

[63]  F. Neese,et al.  Efficient use of the resolution of the identity approximation in time-dependent density functional calculations with hybrid density functionals , 2002 .

[64]  F. Neese,et al.  Experimental and theoretical EPR study of Jahn-Teller-active [HIPTN(3)N]MoL complexes (L = N(2), CO, NH(3)). , 2010, Journal of the American Chemical Society.

[65]  Walter Thiel,et al.  Benchmarks for electronically excited states: time-dependent density functional theory and density functional theory based multireference configuration interaction. , 2008, The Journal of chemical physics.

[66]  K. Pierloot,et al.  Optical Spectra of Ni(CO)4 and Cr(CO)6 Revisited , 1996 .

[67]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[68]  Michael C. Zerner,et al.  A generalized restricted open-shell Fock operator , 1987 .

[69]  Andreas Dreuw,et al.  Single-reference ab initio methods for the calculation of excited states of large molecules. , 2005, Chemical reviews.

[70]  R. Schrock,et al.  Reduction of dinitrogen to ammonia at a well-protected reaction site in a molybdenum triamidoamine complex. , 2002, Journal of the American Chemical Society.

[71]  Frank Neese,et al.  A spectroscopy oriented configuration interaction procedure , 2003 .

[72]  P. Knowles,et al.  An efficient internally contracted multiconfiguration–reference configuration interaction method , 1988 .

[73]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[74]  Stefan Grimme,et al.  Density functional calculations with configuration interaction for the excited states of molecules , 1996 .

[75]  A. D. McLean,et al.  Classification of configurations and the determination of interacting and noninteracting spaces in configuration interaction , 1973 .

[76]  M. Adams,et al.  The structure and mechanism of iron-hydrogenases. , 1990, Biochimica et biophysica acta.

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

[78]  M. Zerner,et al.  Metal-ligand exchange coupling in transition-metal complexes , 1991 .

[79]  M. Head‐Gordon,et al.  Configuration interaction with single substitutions for excited states of open-shell molecules , 1995 .