Density functional method including weak interactions: Dispersion coefficients based on the local response approximation.

A new method to calculate the atom-atom dispersion coefficients in a molecule is proposed for the use in density functional theory with dispersion (DFT-D) correction. The method is based on the local response approximation due to Dobson and Dinte [Phys. Rev. Lett. 76, 1780 (1996)], with modified dielectric model recently proposed by Vydrov and van Voorhis [J. Chem. Phys. 130, 104105 (2009)]. The local response model is used to calculate the distributed multipole polarizabilities of atoms in a molecule, from which the dispersion coefficients are obtained by an explicit frequency integral of the Casimir-Polder type. Thus obtained atomic polarizabilities are also used in the damping function for the short-range singularity. Unlike empirical DFT-D methods, the local response dispersion (LRD) method is able to calculate the dispersion energy from the ground-state electron density only. It is applicable to any geometry, free from physical constants such as van der Waals radii or atomic polarizabilities, and computationally very efficient. The LRD method combined with the long-range corrected DFT functional (LC-BOP) is applied to calculations of S22 weakly bound complex set [Phys. Chem. Chem. Phys. 8, 1985 (2006)]. Binding energies obtained by the LC-BOP+LRD agree remarkably well with ab initio references.

[1]  Henry Margenau,et al.  Theory of intermolecular forces , 1969 .

[2]  Pier Luigi Silvestrelli,et al.  Van der Waals interactions in DFT made easy by Wannier functions. , 2007, Physical review letters.

[3]  B. A. Hess,et al.  Intermolecular interaction energies by topologically partitioned electric properties II. Dispersion energies in one-centre and multicentre multipole expansions , 1997 .

[4]  P. Geerlings,et al.  Accurate interaction energies at density functional theory level by means of an efficient dispersion correction. , 2009, The Journal of chemical physics.

[5]  K. Tang,et al.  Erratum: A simple theoretical model for the van der Waals potential at intermediate distances. I. Spherically symmetric potentials , 1977 .

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

[7]  Ashok Kumar,et al.  Pseudo-spectral dipole oscillator strengths and dipole-dipole and triple-dipole dispersion energy coefficients for HF, HCl, HBr, He, Ne, Ar, Kr and Xe , 1985 .

[8]  A. Becke,et al.  A post-Hartree-Fock model of intermolecular interactions: inclusion of higher-order corrections. , 2006, The Journal of chemical physics.

[9]  J. Soler,et al.  Efficient implementation of a van der Waals density functional: application to double-wall carbon nanotubes. , 2008, Physical review letters.

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

[11]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[12]  G. Scuseria,et al.  Assessment of a long-range corrected hybrid functional. , 2006, The Journal of chemical physics.

[13]  O. A. von Lilienfeld,et al.  Performance of optimized atom-centered potentials for weakly bonded systems using density functional theory , 2005 .

[14]  A. Daniel Boese,et al.  New exchange-correlation density functionals: The role of the kinetic-energy density , 2002 .

[15]  Axel D. Becke,et al.  A new inhomogeneity parameter in density-functional theory , 1998 .

[16]  Stefan Grimme,et al.  Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction , 2006, J. Comput. Chem..

[17]  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.

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

[19]  P. Geerlings,et al.  The use of atomic intrinsic polarizabilities in the evaluation of the dispersion energy. , 2007, The Journal of chemical physics.

[20]  D. Langreth,et al.  An application of the van der Waals density functional: Hydrogen bonding and stacking interactions between nucleobases. , 2008, The Journal of chemical physics.

[21]  T. Van Voorhis,et al.  Improving the accuracy of the nonlocal van der Waals density functional with minimal empiricism. , 2009, The Journal of chemical physics.

[22]  D. Salahub,et al.  Reparameterization of a meta-generalized gradient approximation functional by combining TPSS exchange with τ1 correlation , 2007 .

[23]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[24]  D. York,et al.  Examination of the correlation energy and second virial coefficients from accurate ab initio calculations of rare-gas dimers , 2003 .

[25]  Thomas R. Furlani,et al.  Efficient computation of the dispersion interaction with density-functional theory , 2009 .

[26]  Kimihiko Hirao,et al.  Long-range corrected density functional calculations of chemical reactions: redetermination of parameter. , 2007, The Journal of chemical physics.

[27]  Jacques Weber,et al.  Comparative Study of Benzene···X (X = O2, N2, CO) Complexes Using Density Functional Theory: The Importance of an Accurate Exchange−Correlation Energy Density at High Reduced Density Gradients , 1997 .

[28]  D. Langreth,et al.  Van Der Waals Interactions In Density Functional Theory , 2007 .

[29]  J. Perdew,et al.  Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation. , 1986, Physical review. B, Condensed matter.

[30]  K. Tang,et al.  A simple theoretical model for the van der Waals potential at intermediate distances. III. Anisotropic potentials of Ar–H2, Kr–H2, and Xe–H2 , 1978 .

[31]  Bradley P. Dinte,et al.  Prediction of Dispersion Forces: Is There a Problem? , 2001 .

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

[33]  Dennis R. Salahub,et al.  Nonlocal correlation functional involving the Laplacian of the density , 1994 .

[34]  Kimihiko Hirao,et al.  A density functional study of van der Waals interactions , 2002 .

[35]  T. Van Voorhis,et al.  Self-consistent implementation of a nonlocal van der Waals density functional with a Gaussian basis set. , 2008, The Journal of chemical physics.

[36]  J. Ángyán.  On the exchange-hole model of London dispersion forces. , 2007, The Journal of chemical physics.

[37]  José M. Pérez-Jordá,et al.  A density-functional study of van der Waals forces: rare gas diatomics. , 1995 .

[38]  A. Becke,et al.  Exchange-hole dipole moment and the dispersion interaction revisited. , 2007, The Journal of chemical physics.

[39]  D. Truhlar,et al.  The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals , 2008 .

[40]  P. Wormer,et al.  Ab initio dispersion coefficients for interactions involving rare-gas atoms , 1992 .

[41]  Kimihiko Hirao,et al.  A NEW ONE-PARAMETER PROGRESSIVE COLLE-SALVETTI-TYPE CORRELATION FUNCTIONAL , 1999 .

[42]  G. DiLabio,et al.  Interactions in large, polyaromatic hydrocarbon dimers: application of density functional theory with dispersion corrections. , 2008, The journal of physical chemistry. A.

[43]  Troy Van Voorhis,et al.  Nonlocal van der Waals density functional made simple. , 2009, Physical review letters.

[44]  M. Head‐Gordon,et al.  Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. , 2008, Physical chemistry chemical physics : PCCP.

[45]  Yingkai Zhang,et al.  Comment on “Generalized Gradient Approximation Made Simple” , 1998 .

[46]  Giacinto Scoles,et al.  Intermolecular forces in simple systems , 1977 .

[47]  Qin Wu,et al.  Empirical correction to density functional theory for van der Waals interactions , 2002 .

[48]  A. Hesselmann.  Derivation of the dispersion energy as an explicit density- and exchange-hole functional. , 2009, The Journal of chemical physics.

[49]  Stefan Grimme,et al.  Accurate description of van der Waals complexes by density functional theory including empirical corrections , 2004, J. Comput. Chem..

[50]  D. Lacks,et al.  Pair interactions of rare-gas atoms as a test of exchange-energy-density functionals in regions of large density gradients. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[51]  Yingkai Zhang,et al.  Describing van der Waals interaction in diatomic molecules with generalized gradient approximations: The role of the exchange functional , 1997 .

[52]  Edward F. Valeev,et al.  Estimates of the Ab Initio Limit for π−π Interactions: The Benzene Dimer , 2002 .

[53]  K. Hirao,et al.  A long-range correction scheme for generalized-gradient-approximation exchange functionals , 2001 .

[54]  John P. Perdew,et al.  Accurate Density Functional with Correct Formal Properties: A Step Beyond the Generalized Gradient Approximation , 1999 .

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

[56]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[57]  Binding energies in benzene dimers: Nonlocal density functional calculations. , 2005, The Journal of chemical physics.

[58]  Kevin E. Riley,et al.  Nature and magnitude of aromatic stacking of nucleic acid bases. , 2008, Physical chemistry chemical physics : PCCP.

[59]  F. Toigo,et al.  Van der Waals interactions at surfaces by density functional theory using Wannier functions. , 2008, The Journal of chemical physics.

[60]  Jirí Cerný,et al.  Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. , 2006, Physical chemistry chemical physics : PCCP.

[61]  R. Nieminen,et al.  Linear-scaling self-consistent implementation of the van der Waals density functional , 2009 .

[62]  W. Kohn,et al.  Van der Waals interaction between an atom and a solid surface , 1976 .

[63]  Peter Pulay,et al.  CAN (SEMI) LOCAL DENSITY FUNCTIONAL THEORY ACCOUNT FOR THE LONDON DISPERSION FORCES , 1994 .

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

[65]  J. F. Ogilvie,et al.  Potential-energy functions of diatomic molecules of the noble gases I. Like nuclear species , 1992 .

[66]  K. Hirao,et al.  Van der Waals interactions studied by density functional theory , 2005 .

[67]  A. Tkatchenko,et al.  Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. , 2009, Physical review letters.

[68]  Henrik Rydberg,et al.  Van der Waals Density Functional Theory with Applications , 2005 .

[69]  A. Stone,et al.  Distributed dispersion: A new approach , 2003 .

[70]  Ivano Tavernelli,et al.  Optimization of effective atom centered potentials for london dispersion forces in density functional theory. , 2004, Physical review letters.

[71]  N. Kurita,et al.  Ab initio and DFT studies for accurate description of van der Waals interaction between He atoms , 2001 .

[72]  Benny G. Johnson,et al.  A standard grid for density functional calculations , 1993 .

[73]  Ola Engkvist,et al.  Structure and vibrational dynamics of the benzene dimer , 1999 .

[74]  An Overview of Molecular Quantum Mechanics , 1992 .

[75]  Axel D. Becke,et al.  Density‐functional thermochemistry. IV. A new dynamical correlation functional and implications for exact‐exchange mixing , 1996 .

[76]  N. Marzari,et al.  Maximally localized generalized Wannier functions for composite energy bands , 1997, cond-mat/9707145.

[77]  Donald G Truhlar,et al.  Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions. , 2006, Journal of chemical theory and computation.

[78]  Saroj K. Nayak,et al.  Towards extending the applicability of density functional theory to weakly bound systems , 2001 .

[79]  Takao Tsuneda,et al.  Long-range corrected density functional study on weakly bound systems: balanced descriptions of various types of molecular interactions. , 2007, The Journal of chemical physics.

[80]  H. C. Longuet-Higgins.  Spiers Memorial Lecture. Intermolecular forces , 1965 .

[81]  Gustavo E. Scuseria,et al.  A novel form for the exchange-correlation energy functional , 1998 .

[82]  S. F. Boys,et al.  The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors , 1970 .

[83]  Yan Zhao,et al.  Density Functionals for Noncovalent Interaction Energies of Biological Importance. , 2007, Journal of chemical theory and computation.

[84]  Jirí Cerný,et al.  Density functional theory augmented with an empirical dispersion term. Interaction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations , 2007, J. Comput. Chem..

[85]  Bradley P. Dinte,et al.  Constraint satisfaction in local and gradient susceptibility approximations: Application to a van der Waals density functional. , 1996, Physical review letters.

[86]  Xin Xu,et al.  From The Cover: The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and thermochemical properties. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[87]  M. Dion,et al.  van der Waals density functional for general geometries. , 2004, Physical review letters.

[88]  G. Scuseria,et al.  Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. , 2003, Physical review letters.

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

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

[91]  O. A. von Lilienfeld,et al.  Library of dispersion-corrected atom-centered potentials for generalized gradient approximation functionals: Elements H, C, N, O, He, Ne, Ar, and Kr , 2007 .

[92]  Vincenzo Barone,et al.  Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: The mPW and mPW1PW models , 1998 .

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

[94]  Pier Luigi Silvestrelli,et al.  Van der Waals interactions in density functional theory using Wannier functions. , 2009, The journal of physical chemistry. A.

[95]  G. DiLabio,et al.  Accurate treatment of van der Waals interactions using standard density functional theory methods with effective core-type potentials: Application to carbon-containing dimers , 2008 .

[96]  A. Stone,et al.  Local and non-local dispersion models , 1989 .

[97]  Ashcroft,et al.  Fluctuation attraction in condensed matter: A nonlocal functional approach. , 1991, Physical review. B, Condensed matter.

[98]  W. Thiel,et al.  Exchange-correlation density functional beyond the gradient approximation , 1998 .

[99]  A. Becke.  A multicenter numerical integration scheme for polyatomic molecules , 1988 .

[100]  K. Tang,et al.  An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients , 1984 .

[101]  A. Becke,et al.  Exchange-hole dipole moment and the dispersion interaction. , 2005, The Journal of chemical physics.

[102]  J. F. Ogilvie,et al.  Potential-energy functions of diatomic molecules of the noble gases , 1993 .

[103]  Kimihiko Hirao,et al.  A density-functional study on pi-aromatic interaction: benzene dimer and naphthalene dimer. , 2005, The Journal of chemical physics.

[104]  Elsebeth Schröder,et al.  Application of van der Waals density functional to an extended system: adsorption of benzene and naphthalene on graphite. , 2006, Physical review letters.

[105]  A. Becke,et al.  Van der Waals Interactions in Density-Functional Theory: Rare-Gas Diatomics. , 2009, Journal of chemical theory and computation.

[106]  A. Becke,et al.  Exchange-hole dipole moment and the dispersion interaction: high-order dispersion coefficients. , 2006, The Journal of chemical physics.

[107]  John W. Hepburn,et al.  A simple but reliable method for the prediction of intermolecular potentials , 1975 .

[108]  A. Becke,et al.  A density-functional model of the dispersion interaction. , 2005, The Journal of chemical physics.

[109]  D. Cremer,et al.  An efficient algorithm for the density-functional theory treatment of dispersion interactions. , 2009, The Journal of chemical physics.

[110]  S. Tsuzuki,et al.  Origin of attraction and directionality of the pi/pi interaction: model chemistry calculations of benzene dimer interaction. , 2002, Journal of the American Chemical Society.

[111]  U. Rothlisberger,et al.  Accurate DFT Descriptions for Weak Interactions of Molecules Containing Sulfur. , 2009, Journal of chemical theory and computation.

[112]  J. Murray,et al.  Polarizability and volume , 1993 .