Intermolecular potentials based on symmetry-adapted perturbation theory with dispersion energies from time-dependent density-functional calculations.

Recently, three of us have proposed a method [Phys. Rev. Lett. 91, 33201 (2003)] for an accurate calculation of the dispersion energy utilizing frequency-dependent density susceptibilities of monomers obtained from time-dependent density-functional theory (DFT). In the present paper, we report numerical calculations for the helium, neon, water, and carbon dioxide dimers and show that for a wide range of intermonomer separations, including the van der Waals and short-range repulsion regions, the method provides dispersion energies with accuracies comparable to those that can be achieved using the current most sophisticated wave-function methods. If the dispersion energy is combined with (i) the electrostatic and first-order exchange interaction energies as defined in symmetry-adapted perturbation theory (SAPT) but computed using monomer Kohn-Sham (KS) determinants, and (ii) the induction energy computed using the coupled KS static response theory, (iii) the exchange-induction and exchange-dispersion energies computed using KS orbitals and orbital energies, the resulting method, denoted by SAPT(DFT), produces very accurate total interaction potentials. For the helium dimer, the only system with nearly exact benchmark values, SAPT(DFT) reproduces the interaction energy to within about 2% at the minimum and to a similar accuracy for all other distances ranging from the strongly repulsive to the asymptotic region. For the remaining systems investigated by us, the quality of the SAPT(DFT) interaction energies is so high that these energies may actually be more accurate than the best available results obtained with wave-function techniques. At the same time, SAPT(DFT) is much more computationally efficient than any method previously used for calculating the dispersion and other interaction energy components at this level of accuracy.

[1]  W. J. Meath,et al.  Dipole oscillator strength distributions, sums, and dispersion energy coefficients for CO and CO2☆ , 1982 .

[2]  Fred A. Hamprecht,et al.  Development and assessment of new exchange-correlation functionals , 1998 .

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

[4]  K. Szalewicz,et al.  Pair potential for water from symmetry-adapted perturbation theory , 1997 .

[5]  Krzysztof Szalewicz,et al.  Dispersion energy from density-functional theory description of monomers. , 2003, Physical review letters.

[6]  K. Szalewicz,et al.  Intermolecular potential energy surfaces and spectra of Ne-HCN complex from ab initio calculations , 2001 .

[7]  Georg Jansen,et al.  Intermolecular dispersion energies from time-dependent density functional theory , 2003 .

[8]  K. Szalewicz,et al.  Unified treatment of chemical and van der Waals forces via symmetry-adapted perturbation expansion. , 2004, The Journal of chemical physics.

[9]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[10]  Hans Peter Lüthi,et al.  Interaction energies of van der Waals and hydrogen bonded systems calculated using density functional theory: Assessing the PW91 model , 2001 .

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

[12]  K. Szalewicz,et al.  Helium dimer potential from symmetry-adapted perturbation theory calculations using large Gaussian geminal and orbital basis sets , 1997 .

[13]  Georg Jansen,et al.  First-order intermolecular interaction energies from Kohn–Sham orbitals , 2002 .

[14]  P. Wormer,et al.  Many‐body perturbation theory of frequency‐dependent polarizabilities and van der Waals coefficients: Application to H2O–H2O and Ar–NH3 , 1992 .

[15]  Jiří Čížek,et al.  Direct calculation of the Hartree–Fock interaction energy via exchange–perturbation expansion. The He … He interaction , 1987 .

[16]  Georg Jansen,et al.  Intermolecular induction and exchange-induction energies from coupled-perturbed Kohn–Sham density functional theory , 2002 .

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

[18]  C. Chabalowski,et al.  AB INITIO INTERACTION POTENTIALS FOR SIMULATIONS OF DIMETHYLNITRAMINE SOLUTIONS IN SUPERCRITICAL CARBON DIOXIDE WITH COSOLVENTS , 1999 .

[19]  Krzysztof Szalewicz,et al.  Intraatomic correlation effects for the He–He dispersion and exchange–dispersion energies using explicitly correlated Gaussian geminals , 1987 .

[20]  Dennis R. Salahub,et al.  Dynamic polarizabilities and excitation spectra from a molecular implementation of time‐dependent density‐functional response theory: N2 as a case study , 1996 .

[21]  F. Weigend,et al.  Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations , 2002 .

[22]  C. Chabalowski,et al.  Using Kohn−Sham Orbitals in Symmetry-Adapted Perturbation Theory to Investigate Intermolecular Interactions , 2001 .

[23]  K. Szalewicz,et al.  On the effectiveness of monomer‐, dimer‐, and bond‐centered basis functions in calculations of intermolecular interaction energies , 1995 .

[24]  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 .

[25]  Krzysztof Szalewicz,et al.  Intermolecular forces from asymptotically corrected density functional description of monomers , 2002 .

[26]  Nicholas C. Handy,et al.  Improving virtual Kohn-Sham orbitals and eigenvalues: Application to excitation energies and static polarizabilities , 1998 .

[27]  Sl,et al.  Many‐body theory of intermolecular induction interactions , 1994 .

[28]  Stephen Wilson,et al.  Handbook of molecular physics and quantum chemistry , 2003 .

[29]  M. Schütz,et al.  Density-functional theory-symmetry-adapted intermolecular perturbation theory with density fitting: a new efficient method to study intermolecular interaction energies. , 2005, The Journal of chemical physics.

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

[31]  Konrad Patkowski,et al.  Symmetry-forcing procedure and convergence behavior of perturbation expansions for molecular interaction energies , 2002 .

[32]  K. Szalewicz,et al.  Many‐body theory of exchange effects in intermolecular interactions. Density matrix approach and applications to He–F−, He–HF, H2–HF, and Ar–H2 dimers , 1994 .

[33]  R. Amos,et al.  The calculation of frequency-dependent polarizabilities using current density functional theory , 1997 .

[34]  Stanisl,et al.  Many‐body perturbation theory of electrostatic interactions between molecules: Comparison with full configuration interaction for four‐electron dimers , 1993 .

[35]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[36]  Robert Moszynski,et al.  Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes , 1994 .

[37]  T. Heijmen,et al.  Symmetry-adapted perturbation theory for the calculation of Hartree-Fock interaction energies , 1996 .

[38]  R. Podeszwa,et al.  Accurate interaction energies for argon, krypton, and benzene dimers from perturbation theory based on the Kohn–Sham model , 2005 .

[39]  David E. Woon,et al.  Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties , 1994 .

[40]  Pavel Hobza,et al.  On geometries of stacked and H-bonded nucleic acid base pairs determined at various DFT, MP2, and CCSD(T) levels up to the CCSD(T)/complete basis set limit level. , 2005, The Journal of chemical physics.

[41]  Krzysztof Szalewicz,et al.  Symmetry-adapted perturbation-theory calculations of intermolecular forces employing density-functional description of monomers. , 2005, The Journal of chemical physics.

[42]  N. Handy,et al.  Assessment of exchange correlation functionals , 2000 .

[43]  Distributed polarizabilities using the topological theory of atoms in molecules , 1994 .

[44]  Betsy M. Rice,et al.  Intermolecular potential of carbon dioxide dimer from symmetry-adapted perturbation theory , 1999 .

[45]  K. Szalewicz,et al.  Many‐body theory of exchange effects in intermolecular interactions. Second‐quantization approach and comparison with full configuration interaction results , 1994 .

[46]  D. M. Bishop,et al.  Dipole, quadrupole, octupole and dipole-octupole polarizabilities at real and imaginary frequencies for H, He, and H2 and the dispersion-energy coefficients for interactions between them , 1993 .

[47]  Handy,et al.  Determination of frequency-dependent polarizabilities using current density-functional theory. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[48]  David J. Tozer,et al.  Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials , 2001 .

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

[50]  Georg Jansen,et al.  The helium dimer potential from a combined density functional theory and symmetry-adapted perturbation theory approach using an exact exchange–correlation potential , 2003 .

[51]  A. Daniel Boese,et al.  A new parametrization of exchange–correlation generalized gradient approximation functionals , 2001 .

[52]  J. Connolly,et al.  On first‐row diatomic molecules and local density models , 1979 .

[53]  William J. Meath,et al.  Dispersion energy constants C 6(A, B), dipole oscillator strength sums and refractivities for Li, N, O, H2, N2, O2, NH3, H2O, NO and N2O , 1977 .

[54]  K. Szalewicz,et al.  Dispersion Energy in the Coupled Pair Approximation with Noniterative Inclusion of Single and Triple Excitations , 1995 .

[55]  V. Barone,et al.  Toward reliable density functional methods without adjustable parameters: The PBE0 model , 1999 .

[56]  Brett I. Dunlap,et al.  Robust and variational fitting , 2000 .

[57]  A. Becke.  Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals , 1997 .

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

[59]  A. McLachlan.  Retarded dispersion forces between molecules , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[60]  Krzysztof Szalewicz,et al.  Efficient calculation of coupled Kohn-Sham dynamic susceptibility functions and dispersion energies with density fitting , 2005 .

[61]  Stanisl,et al.  Many‐body symmetry‐adapted perturbation theory of intermolecular interactions. H2O and HF dimers , 1991 .

[62]  Jirí Cerný,et al.  The X3LYP extended density functional accurately describes H-bonding but fails completely for stacking. , 2005, Physical chemistry chemical physics : PCCP.

[63]  G. Peinel,et al.  Coupled perturbation theory within the antisymmetrized product of separated geminals (APSG) framework , 1981 .