Random-phase approximation correlation methods for molecules and solids

Random-phase approximation (RPA) correlation methods based on Kohn–Sham density-functional theory and Hartree–Fock are derived using the adiabatic-connection fluctuation dissipation theorem. It is shown that the correlation energy within the adiabatic-connection fluctuation-dissipation theorem is exact in a Kohn–Sham framework while for Hartree–Fock reference states this is not the case. This shows that Kohn–Sham reference states are probably better suited to describe electron correlation for use in RPA methods than Hartree–Fock reference states. Both, Kohn–Sham and Hartree–Fock RPA methods are related to each other both by comparing the underlying correlation functionals and numerically through the comparison of total energies and reaction energies for a set of small organic molecules.

[1]  M. Gell-Mann,et al.  Correlation Energy of an Electron Gas at High Density , 1957 .

[2]  Martin J. Packer,et al.  A new implementation of the second‐order polarization propagator approximation (SOPPA): The excitation spectra of benzene and naphthalene , 1996 .

[3]  K. Sawada,et al.  LINEARIZED MANY-BODY PROBLEM , 1964 .

[4]  G. Jansen,et al.  Molecular properties from coupled-cluster Brueckner orbitals , 1999 .

[5]  Andreas W. Götz,et al.  Density-Functional Theory with Orbital-Dependent Functionals: Exact-exchange Kohn-Sham and Density-Functional Response Methods , 2010 .

[6]  Georg Kresse,et al.  Making the random phase approximation to electronic correlation accurate. , 2009, The Journal of chemical physics.

[7]  Mel Levy,et al.  DFT ionization formulas and a DFT perturbation theory for exchange and correlation, through adiabatic connection , 1995 .

[8]  R. Mcweeny,et al.  Methods Of Molecular Quantum Mechanics , 1969 .

[9]  Frederick R Manby,et al.  General orbital invariant MP2-F12 theory. , 2007, The Journal of chemical physics.

[10]  M. E. Casida.  Time-Dependent Density Functional Response Theory for Molecules , 1995 .

[11]  A. D. McLachlan,et al.  Time-dependent Hartree-Fock theory , 1964 .

[12]  M. Ratner,et al.  Self-consistent polarization propagator approximation as a modified random phase method , 1972 .

[13]  T. Van Voorhis,et al.  Fluctuation-dissipation theorem density-functional theory. , 2005, The Journal of chemical physics.

[14]  David L. Freeman,et al.  Algebraic and Diagrammatic Methods in Many-Fermion Theory , 1992 .

[15]  Kenneth D. Jordan,et al.  Use of unrestricted hartree‐fock wave functions in RPA calculations , 2009 .

[16]  Poul Jo,et al.  An order analysis of the particle–hole propagator , 1977 .

[17]  Trygve Helgaker,et al.  Spin flipping in ring-coupled-cluster-doubles theory , 2011 .

[18]  Georg Kresse,et al.  Hybrid functionals including random phase approximation correlation and second-order screened exchange. , 2010, The Journal of chemical physics.

[19]  Görling,et al.  Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion. , 1993, Physical review. B, Condensed matter.

[20]  Andreas Savin,et al.  Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions. , 2014, The Journal of chemical physics.

[21]  Andreas Savin,et al.  van der Waals forces in density functional theory: Perturbational long-range electron-interaction corrections , 2005, cond-mat/0505062.

[22]  David J Rowe,et al.  EQUATIONS-OF-MOTION METHOD AND THE EXTENDED SHELL MODEL. , 1968 .

[23]  J. Ángyán,et al.  On the equivalence of ring-coupled cluster and adiabatic connection fluctuation-dissipation theorem random phase approximation correlation energy expressions. , 2010, The Journal of chemical physics.

[24]  Neil S. Ostlund,et al.  The correlation energy in the random phase approximation: Intermolecular forces between closed‐shell systems , 1977 .

[25]  Kiyoyuki Terakura,et al.  Total energy of solids: An exchange and random-phase approximation correlation study , 2002 .

[26]  K. Szalewicz,et al.  Møller–Plesset expansion of the dispersion energy in the ring approximation , 1993 .

[27]  M. Petersilka,et al.  DENSITY FUNCTIONAL THEORY OF TIME-DEPENDENT PHENOMENA , 1996 .

[28]  A. Görling,et al.  Efficient localized Hartree-Fock methods as effective exact-exchange Kohn-Sham methods for molecules , 2001 .

[29]  John P. Perdew,et al.  The exchange-correlation energy of a metallic surface , 1975 .

[30]  H. Monkhorst,et al.  Coupled-cluster method with optimized reference state , 1984 .

[31]  David B Cook,et al.  Handbook of Computational Quantum Chemistry , 1998 .

[32]  David Pines,et al.  A Collective Description of Electron Interactions. I. Magnetic Interactions , 1951 .

[33]  P. Gori-Giorgi,et al.  A short-range gradient-corrected spin density functional in combination with long-range coupled-cluster methods: Application to alkali-metal rare-gas dimers , 2006 .

[34]  E. A. Sanderson,et al.  Nuclear ground states in the random phase approximation , 1965 .

[35]  B. Lundqvist,et al.  Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism , 1976 .

[36]  D. Pines,et al.  A dielectric formulation of the many body problem: Application to the free electron gas , 1958 .

[37]  Stefano de Gironcoli,et al.  Efficient calculation of exact exchange and RPA correlation energies in the adiabatic-connection fluctuation-dissipation theory , 2009, 0902.0889.

[38]  Excited states from time-dependent density functional theory , 2007, cond-mat/0703590.

[39]  Jens Oddershede,et al.  Polarization Propagator Calculations , 1978 .

[40]  A. D. McLACHLAN,et al.  Time-Dependent Hartree—Fock Theory for Molecules , 1964 .

[41]  John P. Perdew,et al.  Exchange-correlation energy of a metallic surface: Wave-vector analysis , 1977 .

[42]  V. McKoy,et al.  HIGHER RANDOM-PHASE APPROXIMATION AS AN APPROXIMATION TO THE EQUATIONS OF MOTION. , 1970 .

[43]  A. Hesselmann.  Third-order corrections to random-phase approximation correlation energies. , 2011, The Journal of chemical physics.

[44]  P. Jørgensen,et al.  Self-consistent time-dependent Hartree--Fock scheme , 1974 .

[45]  A. Görling,et al.  Comparison between optimized effective potential and Kohn–Sham methods , 2008 .

[46]  J. Linderberg.  London forces as an aspect of the correlation problem in molecular solids , 2009 .

[47]  Georg Kresse,et al.  Accurate bulk properties from approximate many-body techniques. , 2009, Physical review letters.

[48]  Editors , 1986, Brain Research Bulletin.

[49]  R. Mattuck,et al.  A guide to Feynman diagrams in the many-body problem , 1976 .

[50]  H. Callen,et al.  Irreversibility and Generalized Noise , 1951 .

[51]  Martin Schütz,et al.  Molpro: a general‐purpose quantum chemistry program package , 2012 .

[52]  Manfred Lein,et al.  Toward the description of van der Waals interactions within density functional theory , 1999, J. Comput. Chem..

[53]  David Pines,et al.  The Many-body Problem , 1971 .

[54]  D. Pines,et al.  The theory of quantum liquids , 1968 .

[55]  Georg Kresse,et al.  Assessing the quality of the random phase approximation for lattice constants and atomization energies of solids , 2010 .

[56]  Andreas Hesselmann,et al.  Numerically stable optimized effective potential method with balanced Gaussian basis sets. , 2007, The Journal of chemical physics.

[57]  A. Görling,et al.  Correct description of the bond dissociation limit without breaking spin symmetry by a random-phase-approximation correlation functional. , 2011, Physical review letters.

[58]  Exact exchange-correlation kernel for dynamic response properties and excitation energies in density-functional theory , 1998 .

[59]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[60]  J. Harris,et al.  Correlation energy and van der Waals interaction of coupled metal films , 1975 .

[61]  T. Kotani.  An optimized-effective-potential method for solids with exact exchange and random-phase approximation correlation , 1998 .

[62]  F. Furche.  Developing the random phase approximation into a practical post-Kohn-Sham correlation model. , 2008, The Journal of chemical physics.

[63]  D. Pines.  A Collective Description of Electron Interactions: II. Collective vs Individual Particle Aspects of the Interactions , 1952 .

[64]  R. Dreizler,et al.  Density-Functional Theory , 1990 .

[65]  Andreas Savin,et al.  Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation. , 2008, Physical review letters.

[66]  Thomas M Henderson,et al.  The ground state correlation energy of the random phase approximation from a ring coupled cluster doubles approach. , 2008, The Journal of chemical physics.

[67]  Josef Paldus,et al.  Stability Conditions for the Solutions of the Hartree—Fock Equations for Atomic and Molecular Systems. Application to the Pi‐Electron Model of Cyclic Polyenes , 1967 .

[68]  D. Pines.  A Collective Description of-Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas , 1953 .

[69]  Horst Weiss,et al.  A direct algorithm for self‐consistent‐field linear response theory and application to C60: Excitation energies, oscillator strengths, and frequency‐dependent polarizabilities , 1993 .

[70]  P. Jørgensen.  Molecular and Atomic Applications of Time-Dependent Hartree-Fock Theory , 1975 .

[71]  Kieron Burke,et al.  Basics of TDDFT , 2006 .

[72]  F. London,et al.  The general theory of molecular forces , 1937 .

[73]  U. V. Barth,et al.  Linear density response function within the time-dependent exact-exchange approximation , 2008, 0807.0091.

[74]  N. H. Beebe,et al.  Self‐consistent time‐dependent Hartree–Fock calculations of dynamic polarizabilities, dispersion forces, and nuclear spin–spin coupling constants for the H2 and HF molecules , 1975 .

[75]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[76]  V. McKoy,et al.  Application of a Higher RPA to a Model π‐Electron System , 1970 .

[77]  V. McKoy,et al.  Nonempirical Calculations on Excited States: The Ethylene Molecule , 1967 .

[78]  M. Gell-Mann,et al.  Correlation Energy of an Electron Gas at High Density , 1957 .

[79]  Giulia Galli,et al.  Power series expansion of the random phase approximation correlation energy: The role of the third- and higher-order contributions. , 2010, The Journal of chemical physics.

[80]  Alexandre Tkatchenko,et al.  Beyond the random-phase approximation for the electron correlation energy: the importance of single excitations. , 2010, Physical review letters.

[81]  Andreas Görling,et al.  Exact exchange kernel for time‐dependent density‐functional theory , 1998 .

[82]  R O Jones,et al.  The surface energy of a bounded electron gas , 1974 .

[83]  Andreas Savin,et al.  Combining long-range configuration interaction with short-range density functionals , 1997 .

[84]  M. Karplus,et al.  The self-consistent random phase approximation , 1971 .

[85]  Benjamin G. Janesko,et al.  Long-range-corrected hybrid density functionals including random phase approximation correlation: application to noncovalent interactions. , 2009, The Journal of chemical physics.

[86]  B. Lévy,et al.  Ab initio Hartree-Fock instabilities in closed-shell molecular systems , 1978 .

[87]  Huy V. Nguyen,et al.  A first-principles study of weakly bound molecules using exact exchange and the random phase approximation. , 2010, The Journal of chemical physics.

[88]  Julian Yarkony,et al.  Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration. , 2010, The Journal of chemical physics.

[89]  Andreas Görling,et al.  Charge-transfer excitation energies with a time-dependent density-functional method suitable for orbital-dependent exchange-correlation kernels , 2009 .

[90]  X. Gonze,et al.  Band-gap energy in the random-phase approximation to density-functional theory , 2004 .

[91]  Andreas Görling,et al.  Random phase approximation correlation energies with exact Kohn–Sham exchange , 2010 .

[92]  Andreas Savin,et al.  Long-range/short-range separation of the electron-electron interaction in density functional theory , 2004 .

[93]  A. Savin,et al.  Range-separated density-functional theory with the random-phase approximation: Detailed formalism and illustrative applications , 2010, 1006.2061.

[94]  H. Ehrenreich,et al.  Self-Consistent Field Approach to the Many-Electron Problem , 1959 .

[95]  P. Jørgensen,et al.  Two-particle, two-hole corrections to a self-consistent time-dependent Hartree—Fock scheme , 1975 .

[96]  M. Hellgren,et al.  Correlation energy functional and potential from time-dependent exact-exchange theory. , 2009, The Journal of chemical physics.

[97]  N. Rösch,et al.  Density- and density-matrix-based coupled Kohn–Sham methods for dynamic polarizabilities and excitation energies of molecules , 1999 .

[98]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[99]  K. Burke,et al.  Describing static correlation in bond dissociation by Kohn-Sham density functional theory. , 2004, The Journal of chemical physics.

[100]  W. Windsch,et al.  Electron nuclear double resonance of 13C nuclei with natural abundance in trissarcosine calcium chloride doped with Mn2+ ions , 1983 .

[101]  Xavier Gonze,et al.  Accurate density functionals: Approaches using the adiabatic-connection fluctuation-dissipation theorem , 2002 .

[102]  M. Hellgren,et al.  Exact-exchange kernel of time-dependent density functional theory: frequency dependence and photoabsorption spectra of atoms. , 2009, The Journal of chemical physics.

[103]  Andreas Hesselmann,et al.  Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock. , 2011, The Journal of chemical physics.

[104]  M. Karplus,et al.  Excitation operators and the extended random phase approximation: II. Applications , 1979 .

[105]  Mark Earl Casida,et al.  In Recent Advances in Density-Functional Methods , 1995 .

[106]  V. McKoy,et al.  Application of the RPA and Higher RPA to the V and T States of Ethylene , 1971 .

[107]  Andreas Görling,et al.  Molecular excitation spectra by TDDFT with the nonadiabatic exact exchange kernel , 2010 .

[108]  V. McKoy,et al.  Equations‐of‐motion method including renormalization and double‐excitation mixing , 1973 .

[109]  Filipp Furche,et al.  On the density matrix based approach to time-dependent density functional response theory , 2001 .

[110]  E. Engel,et al.  Random-phase-approximation-based correlation energy functionals: benchmark results for atoms. , 2007, The Journal of chemical physics.

[111]  P. Jørgensen,et al.  Polarization propagator methods in atomic and molecular calculations , 1984 .

[112]  Thomas M Henderson,et al.  Long-range-corrected hybrids including random phase approximation correlation. , 2009, The Journal of chemical physics.

[113]  G. Csanak.  The application of the time-dependent Hartree-Fock method to the calculation of excited state-excited state transition densities of atoms (molecules) , 1974 .

[114]  Benjamin G. Janesko,et al.  The role of the reference state in long-range random phase approximation correlation. , 2009, The Journal of chemical physics.

[115]  G. Arrighini,et al.  Some connections among dynamic polarizabilities from approximate methods , 1974 .