R–8 Dispersion Interaction: Derivation and Application to the Effective Fragment Potential Method

Xu, Peng; Leonard, Samuel L.; O’Brien, William; Gordon, Mark S.

doi:10.1021/acs.jpca.3c05115

Title: R^–8 Dispersion Interaction: Derivation and Application to the Effective Fragment Potential Method

Journal Article · 27 December 2023 · Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory

DOI: https://doi.org/10.1021/acs.jpca.3c05115 · OSTI ID:2281351

Xu, Peng ^[1]; Leonard, Samuel L. ^[1]; O’Brien, William ^[2];

^[1]

Ames Lab., and Iowa State Univ., Ames, IA (United States)
Ames Laboratory (AMES), Ames, IA (United States)

The anisotropic and isotropic R^–8 dispersion contributions (disp8) are derived and implemented within the framework of the effective fragment potential (EFP) method formulated with imaginary frequency-dependent Cartesian polarizability tensors distributed at the centroids of the localized molecular orbitals (LMOs). Two forms of damping functions, intermolecular overlap-based and Tang–Toennies, are extended for disp8. To obtain LMO polarizability tensors centered at LMO centroids, an origin-shifting transformation is derived and implemented for the dipole–octopole polarizability tensor and the quadrupole–quadrupole polarizability tensor. The analytic gradient is derived and implemented for the isotropic disp8 contribution. Relative to the previously implemented empirical EFP disp8 energy, the isotropic disp8 component of the interaction energy improves the overall agreement of the EFP dispersion energies with the symmetry-adapted perturbation theory (SAPT) benchmarks, reducing the mean absolute errors (MAEs) and mean absolute percentage errors for most of the databases examined in this work. Further, while the anisotropic disp8 can further enhance the accuracy of the EFP dispersion energy and yield smaller MAEs, significantly overbound dispersion energies are predicted by the anisotropic disp8 when the maximum element in the intermolecular overlap matrix is greater than 0.1, possibly due to the breakdown of the approximations made in the EFP dispersion derivation at a short range. For potential energy scan databases, the newly developed EFP dispersion model with isotropic disp8 yields the overall correct curvature and good agreement with SAPT benchmarks around equilibrium and longer but overestimates the dispersion interactions at a short range. While the overlap-based dispersion-damping functions produce better MAEs than Tang–Toennies damping functions, further improvement is needed to better screen the large attractive dispersion energies at a short range (overlap >0.1).

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Research Organization:: Ames Laboratory (AMES), Ames, IA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-07CH11358

OSTI ID:: 2281351

Report Number(s):: IS-J-11,223

Journal Information:: Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory, Vol. 128, Issue 1; ISSN 1089-5639

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (63)

Permanent and Induced Molecular Moments and Long-Range Intermolecular Forces Buckingham, A. D. Advances in Chemical Physics https://doi.org/10.1002/9780470143582.ch2	book	January 1967
Modeling Styrene−Styrene Interactions ^† Adamovic, Ivana; Li, Hui; Lamm, Monica H. The Journal of Physical Chemistry A, Vol. 110, Issue 2 https://doi.org/10.1021/jp058140o	journal	January 2006
Many‐body perturbation theory of frequency‐dependent polarizabilities and van der Waals coefficients: Application to H ₂ O–H ₂ O and Ar–NH ₃ Wormer, Paul E. S.; Hettema, Hinne The Journal of Chemical Physics, Vol. 97, Issue 8 https://doi.org/10.1063/1.463767	journal	October 1992
Exchange-hole dipole moment and the dispersion interaction revisited Becke, Axel D.; Johnson, Erin R. The Journal of Chemical Physics, Vol. 127, Issue 15 https://doi.org/10.1063/1.2795701	journal	October 2007
Exchange-hole dipole moment and the dispersion interaction Becke, Axel D.; Johnson, Erin R. The Journal of Chemical Physics, Vol. 122, Issue 15 https://doi.org/10.1063/1.1884601	journal	April 2005
Charge transfer interaction using quasiatomic minimal-basis orbitals in the effective fragment potential method Xu, Peng; Gordon, Mark S. The Journal of Chemical Physics, Vol. 139, Issue 19 https://doi.org/10.1063/1.4829509	journal	November 2013
Derivation and Implementation of the Gradient of the R ^–7 Dispersion Interaction in the Effective Fragment Potential Method Guidez, Emilie B.; Xu, Peng; Gordon, Mark S. The Journal of Physical Chemistry A, Vol. 120, Issue 4 https://doi.org/10.1021/acs.jpca.5b11042	journal	January 2016
Approximate calculation of the dynamic polarizabilities and dispersion interaction for ethylene molecules Coulon, Philippe; Luyckx, Rene; Lekkerkerker, Hendrik N. W. Journal of the Chemical Society, Faraday Transactions 2, Vol. 77, Issue 1 https://doi.org/10.1039/f29817700201	journal	January 1981
The non-empirical calculation of second-order molecular properties by means of effective states. II. Effective TDCHF spectra for NO+ CO, CO2, and C2H2 Visser, Foppe; Wormer, Paul E. S. Chemical Physics, Vol. 92, Issue 1 https://doi.org/10.1016/0301-0104(85)80012-4	journal	January 1985
An effective fragment method for modeling solvent effects in quantum mechanical calculations Day, Paul N.; Jensen, Jan H.; Gordon, Mark S. The Journal of Chemical Physics, Vol. 105, Issue 5 https://doi.org/10.1063/1.472045	journal	August 1996
Dynamic polarizability, dispersion coefficient C ₆ and dispersion energy in the effective fragment potential method Adamovic, Ivana; Gordon *, Mark S. Molecular Physics, Vol. 103, Issue 2-3 https://doi.org/10.1080/00268970512331317246	journal	January 2005
The general theory of molecular forces London, F. Transactions of the Faraday Society, Vol. 33 https://doi.org/10.1039/tf937330008b	journal	January 1937
The BioFragment Database (BFDb): An open-data platform for computational chemistry analysis of noncovalent interactions Burns, Lori A.; Faver, John C.; Zheng, Zheng The Journal of Chemical Physics, Vol. 147, Issue 16 https://doi.org/10.1063/1.5001028	journal	October 2017
A post-Hartree-Fock model of intermolecular interactions: Inclusion of higher-order corrections Johnson, Erin R.; Becke, Axel D. The Journal of Chemical Physics, Vol. 124, Issue 17 https://doi.org/10.1063/1.2190220	journal	May 2006
The dispersion interaction between quantum mechanics and effective fragment potential molecules Smith, Quentin A.; Ruedenberg, Klaus; Gordon, Mark S. The Journal of Chemical Physics, Vol. 136, Issue 24 https://doi.org/10.1063/1.4729535	journal	June 2012
Critical analysis and extension of the Hirshfeld atoms in molecules Bultinck, Patrick; Van Alsenoy, Christian; Ayers, Paul W. The Journal of Chemical Physics, Vol. 126, Issue 14 https://doi.org/10.1063/1.2715563	journal	April 2007
Levels of symmetry adapted perturbation theory (SAPT). I. Efficiency and performance for interaction energies Parker, Trent M.; Burns, Lori A.; Parrish, Robert M. The Journal of Chemical Physics, Vol. 140, Issue 9 https://doi.org/10.1063/1.4867135	journal	March 2014
Time‐dependent coupled Hartree–Fock calculations of multipole polarizabilities and dispersion interactions in van der Waals dimers consisting of He, H ₂ , Ne, and N ₂ Visser, F.; Wormer, P. E. S.; Stam, P. The Journal of Chemical Physics, Vol. 79, Issue 10 https://doi.org/10.1063/1.445591	journal	November 1983
Benzene−Pyridine Interactions Predicted by the Effective Fragment Potential Method Smith, Quentin A.; Gordon, Mark S.; Slipchenko, Lyudmila V. The Journal of Physical Chemistry A, Vol. 115, Issue 18 https://doi.org/10.1021/jp201039b	journal	May 2011
Ab initio dispersion coefficients for interactions involving rare‐gas atoms Thakkar, Ajit J.; Hettema, Hinne; Wormer, Paul E. S. The Journal of Chemical Physics, Vol. 97, Issue 5 https://doi.org/10.1063/1.463012	journal	September 1992
Density functional method including weak interactions: Dispersion coefficients based on the local response approximation Sato, Takeshi; Nakai, Hiromi The Journal of Chemical Physics, Vol. 131, Issue 22 https://doi.org/10.1063/1.3269802	journal	December 2009
Evaluating interaction energies of weakly bonded systems using the Buckingham-Hirshfeld method Krishtal, A.; Van Alsenoy, C.; Geerlings, P. The Journal of Chemical Physics, Vol. 140, Issue 18 https://doi.org/10.1063/1.4873133	journal	May 2014
Evaluating London Dispersion Interactions in DFT: A Nonlocal Anisotropic Buckingham–Hirshfeld Model Krishtal, A.; Geldof, D.; Vanommeslaeghe, K. Journal of Chemical Theory and Computation, Vol. 8, Issue 1 https://doi.org/10.1021/ct200718y	journal	December 2011
Distributed multipole analysis: Methods and applications Stone, A. J.; Alderton, M. Molecular Physics, Vol. 56, Issue 5 https://doi.org/10.1080/00268978500102891	journal	December 1985
A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu Grimme, Stefan; Antony, Jens; Ehrlich, Stephan The Journal of Chemical Physics, Vol. 132, Issue 15 https://doi.org/10.1063/1.3382344	journal	April 2010
Charge transfer interaction in the effective fragment potential method Li, Hui; Gordon, Mark S.; Jensen, Jan H. The Journal of Chemical Physics, Vol. 124, Issue 21 https://doi.org/10.1063/1.2196884	journal	June 2006
Water−Benzene Interactions: An Effective Fragment Potential and Correlated Quantum Chemistry Study ^† Slipchenko, Lyudmila V.; Gordon, Mark S. The Journal of Physical Chemistry A, Vol. 113, Issue 10 https://doi.org/10.1021/jp808845b	journal	March 2009
Bonded-atom fragments for describing molecular charge densities Hirshfeld, F. L. Theoretica Chimica Acta, Vol. 44, Issue 2 https://doi.org/10.1007/BF00549096	journal	January 1977
Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals Lu, W. C.; Wang, C. Z.; Schmidt, M. W. The Journal of Chemical Physics, Vol. 120, Issue 6 https://doi.org/10.1063/1.1638731	journal	February 2004
Recent developments in the general atomic and molecular electronic structure system Barca, Giuseppe M. J.; Bertoni, Colleen; Carrington, Laura The Journal of Chemical Physics, Vol. 152, Issue 15 https://doi.org/10.1063/5.0005188	journal	April 2020
Interactions between halide anions and a molecular hydrophobic interface Rankin, Blake M.; Hands, Michael D.; Wilcox, David S. Faraday Discuss., Vol. 160 https://doi.org/10.1039/C2FD20082A	journal	January 2013
Modeling Solvent Effects on Electronic Excited States DeFusco, Albert; Minezawa, Noriyuki; Slipchenko, Lyudmila V. The Journal of Physical Chemistry Letters, Vol. 2, Issue 17 https://doi.org/10.1021/jz200947j	journal	August 2011
Density Functional Theory of Time-Dependent Systems Gross, E. K. U.; Ullrich, C. A.; Gossmann, U. J. NATO ASI Series https://doi.org/10.1007/978-1-4757-9975-0_7	book	January 1995
Dispersion forces between noble gas atoms Luyckx, R.; Coulon, Ph.; Lekkerkerker, H. N. W. The Journal of Chemical Physics, Vol. 69, Issue 6 https://doi.org/10.1063/1.436927	journal	September 1978
General atomic and molecular electronic structure system Schmidt, Michael W.; Baldridge, Kim K.; Boatz, Jerry A. Journal of Computational Chemistry, Vol. 14, Issue 11, p. 1347-1363 https://doi.org/10.1002/jcc.540141112	journal	November 1993
The Role of Quadrupole Forces in Van Der Waals Attractions Margenau, Henry Physical Review, Vol. 38, Issue 4 https://doi.org/10.1103/PhysRev.38.747	journal	August 1931
Effective Fragment Potential Study of the Interaction of DNA Bases Smith, Quentin A.; Gordon, Mark S.; Slipchenko, Lyudmila V. The Journal of Physical Chemistry A, Vol. 115, Issue 41 https://doi.org/10.1021/jp2047954	journal	October 2011
Anisotropy of long range interactions between linear molecules: H₂-H₂ and H₂-He Mulder, Fred; van der Avoird, Ad; Wormer, Paul E. S. Molecular Physics, Vol. 37, Issue 1 https://doi.org/10.1080/00268977900100131	journal	January 1979
Gradients of the Exchange-repulsion Energy in the General Effective Fragment Potential Method Li, Hui; Gordon, Mark S. Theoretical Chemistry Accounts, Vol. 115, Issue 5 https://doi.org/10.1007/s00214-006-0080-x	journal	February 2006
Intermolecular Interactions in Complex Liquids: Effective Fragment Potential Investigation of Water– tert -Butanol Mixtures Hands, Michael D.; Slipchenko, Lyudmila V. The Journal of Physical Chemistry B, Vol. 116, Issue 9 https://doi.org/10.1021/jp2077566	journal	February 2012
ISA-Pol: distributed polarizabilities and dispersion models from a basis-space implementation of the iterated stockholder atoms procedure Misquitta, Alston J.; Stone, Anthony J. Theoretical Chemistry Accounts, Vol. 137, Issue 11 https://doi.org/10.1007/s00214-018-2371-4	journal	October 2018
Accurate and Efficient Method for Many-Body van der Waals Interactions Tkatchenko, Alexandre; DiStasio, Robert A.; Car, Roberto Physical Review Letters, Vol. 108, Issue 23 https://doi.org/10.1103/PhysRevLett.108.236402	journal	June 2012
An approximate formula for the intermolecular Pauli repulsion between closed shell molecules Jensen, Jan; Gordon, Mark Molecular Physics, Vol. 89, Issue 5 https://doi.org/10.1080/00268979609482543	journal	December 1996
Dispersion forces between linear molecules Coulon, Ph.; Luyckx, R.; Lekkerkerker, H. N. W. The Journal of Chemical Physics, Vol. 71, Issue 8 https://doi.org/10.1063/1.438735	journal	October 1979
Dispersion energies for small organic molecules: first row atoms Misquitta, Alston; Stone, Anthony Molecular Physics, Vol. 106, Issue 12 https://doi.org/10.1080/00268970802258617	journal	June 2008
A Hirshfeld partitioning of polarizabilities of water clusters Krishtal, A.; Senet, P.; Yang, M. The Journal of Chemical Physics, Vol. 125, Issue 3 https://doi.org/10.1063/1.2210937	journal	July 2006
The R ^–7 Dispersion Interaction in the General Effective Fragment Potential Method Xu, Peng; Zahariev, Federico; Gordon, Mark S. Journal of Chemical Theory and Computation, Vol. 10, Issue 4 https://doi.org/10.1021/ct500017n	journal	March 2014
Van der Waals interactions in solids using the exchange-hole dipole moment model Otero-de-la-Roza, A.; Johnson, Erin R. The Journal of Chemical Physics, Vol. 136, Issue 17 https://doi.org/10.1063/1.4705760	journal	May 2012
Long-range interaction of two ls-hydrogen atoms expressed in terms of natural spin-orbitals Hirschfelder, J. O.; Löwdin, P. O. Molecular Physics, Vol. 2, Issue 3 https://doi.org/10.1080/00268975900100231	journal	July 1959
Quantum theoretical calculations of van der Waals interactions between molecules. Anisotropic long range interactions Wormer, Paul E. S.; Mulder, Fred; Van Der Avoird, Ad International Journal of Quantum Chemistry, Vol. 11, Issue 6 https://doi.org/10.1002/qua.560110608	journal	June 1977
Quantentheorie des Wasserstoffmolek�lions und der Born-Land�schen Absto�ungskr�fte Uns�ld, Albrecht Zeitschrift f�r Physik, Vol. 43, Issue 8 https://doi.org/10.1007/BF01397633	journal	August 1927
An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients Tang, K. T.; Toennies, J. Peter The Journal of Chemical Physics, Vol. 80, Issue 8 https://doi.org/10.1063/1.447150	journal	April 1984
Local response dispersion method. II. Generalized multicenter interactions Sato, Takeshi; Nakai, Hiromi The Journal of Chemical Physics, Vol. 133, Issue 19 https://doi.org/10.1063/1.3503040	journal	November 2010
TDHF Evaluation of the Dipole−Quadrupole Polarizability and Its Geometrical Derivatives Quinet, Olivier; Liégeois, Vincent; Champagne, Benoît Journal of Chemical Theory and Computation, Vol. 1, Issue 3 https://doi.org/10.1021/ct049888y	journal	April 2005
Erratum: Time-dependent coupled Hartree–Fock calculations of multipole polarizabilities and dispersion interactions in van der Waals dimers consisting of He, H2, Ne, and N2 [J. Chem. Phys. 7 9, 4973 (1983)] Visser, F.; Wormer, Paul E. S.; Stam, P. The Journal of Chemical Physics, Vol. 81, Issue 8 https://doi.org/10.1063/1.448203	journal	October 1984
A post-Hartree–Fock model of intermolecular interactions Johnson, Erin R.; Becke, Axel D. The Journal of Chemical Physics, Vol. 123, Issue 2 https://doi.org/10.1063/1.1949201	journal	July 2005
Theory of long-range dispersion forces Buckingham, A. D. Discussions of the Faraday Society, Vol. 40 https://doi.org/10.1039/df9654000232	journal	January 1965
Dispersion forces between closed shell atoms Lekkerkerker, H. N. W.; Coulon, Ph.; Luyckx, R. Physica A: Statistical Mechanics and its Applications, Vol. 88, Issue 2 https://doi.org/10.1016/0378-4371(77)90011-5	journal	August 1977
Local and non-local dispersion models Stone, A. J.; Tong, C. -S. Chemical Physics, Vol. 137, Issue 1-3 https://doi.org/10.1016/0301-0104(89)87098-3	journal	October 1989
Modeling intermolecular exchange integrals between nonorthogonal molecular orbitals Jensen, Jan H. The Journal of Chemical Physics, Vol. 104, Issue 19 https://doi.org/10.1063/1.471485	journal	May 1996
Many-Body Dispersion in Molecular Clusters Alkan, Melisa; Xu, Peng; Gordon, Mark S. The Journal of Physical Chemistry A, Vol. 123, Issue 39 https://doi.org/10.1021/acs.jpca.9b05977	journal	September 2019
Damping functions in the effective fragment potential method Slipchenko†, Lyudmila V.; Gordon, Mark S. Molecular Physics, Vol. 107, Issue 8-12 https://doi.org/10.1080/00268970802712449	journal	April 2009
Modeling π–π Interactions with the Effective Fragment Potential Method: The Benzene Dimer and Substituents Smith, Toni; Slipchenko, Lyudmila V.; Gordon*, Mark S. The Journal of Physical Chemistry A, Vol. 112, Issue 23 https://doi.org/10.1021/jp800107z	journal	June 2008

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