[en] The quantum Drude oscillator (QDO) model has been widely used as an efficient surrogate to describe the electric response properties of matter as well as long-range interactions in molecules and materials. Most commonly, QDOs are coupled within the dipole approximation so that the Hamiltonian can be exactly diagonalized, which forms the basis for the many-body dispersion method [Phys. Rev. Lett. 108, 236402 (2012)]. The dipole coupling is efficient and allows us to study non-covalent many-body effects in systems with thousands of atoms. However, there are two limitations: (i) the need to regularize the interaction at short distances with empirical damping functions and (ii) the lack of multipolar effects in the coupling potential. In this work, we convincingly address both limitations of the dipole-coupled QDO model by presenting a numerically exact solution of the Coulomb-coupled QDO model by means of quantum Monte Carlo methods. We calculate the potential-energy surfaces of homogeneous QDO dimers, analyzing their properties as a function of the three tunable parameters: frequency, reduced mass, and charge. We study the coupled-QDO model behavior at short distances and show how to parameterize this model to enable an effective description of chemical bonds, such as the covalent bond in the H2 molecule.
Research center :
ULHPC - University of Luxembourg: High Performance Computing
Disciplines :
Physics
Author, co-author :
DITTE, Matej ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
BARBORINI, Matteo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > HPC Platform
TKATCHENKO, Alexandre ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
External co-authors :
no
Language :
English
Title :
Quantum Drude oscillators coupled with Coulomb potential as an efficient model for bonded and non-covalent interactions in atomic dimers
F. London, “ The general theory of molecular forces,” Trans. Faraday Soc. 33, 8b- 26b ( 1937). 10.1039/tf937330008b
P. Drude, “ Zur elektronentheorie der metalle,” Ann. Phys. 306, 566- 613 ( 1900). 10.1002/andp.19003060312
P. Drude, The Theory of Optics ( Dover Publications, New York, 1959), pp. 382- 417.
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, The Molecular Theory of Gases and Liquids ( John Wiley & Sons, New York, 1954), pp. 956- 960, 877-890.
W. L. Bade, “ Drude-model calculation of dispersion forces. I. General theory,” J. Chem. Phys. 27, 1280- 1284 ( 1957). 10.1063/1.1743991
F. Wang and K. D. Jordan, “ A Drude-model approach to dispersion interactions in dipole-bound anions,” J. Chem. Phys. 114, 10717- 10724 ( 2001). 10.1063/1.1376630
T. Sommerfeld and K. D. Jordan, “ Quantum Drude oscillator model for describing the interaction of excess electrons with water clusters: An application to (H2O)13−,” J. Phys. Chem. A 109, 11531- 11538 ( 2005). 10.1021/jp053768k
G. Lamoureux and B. Roux, “ Modeling induced polarization with classical Drude oscillators: Theory and molecular dynamics simulation algorithm,” J. Chem. Phys. 119, 3025- 3039 ( 2003). 10.1063/1.1589749
J. A. Crosse and S. Scheel, “ Atomic multipole relaxation rates near surfaces,” Phys. Rev. A 79, 062902 ( 2009). 10.1103/physreva.79.062902
J. A. Lemkul, J. Huang, B. Roux, and A. D. J. MacKerell, “ An empirical polarizable force field based on the classical Drude oscillator model: Development history and recent applications,” Chem. Rev. 116, 4983- 5013 ( 2016). 10.1021/acs.chemrev.5b00505
J. Hermann, R. A. DiStasio, and A. Tkatchenko, “ First-principles models for van der Waals interactions in molecules and materials: Concepts, theory, and applications,” Chem. Rev. 117, 4714- 4758 ( 2017). 10.1021/acs.chemrev.6b00446
T. Odbadrakh, V. Voora, and K. Jordan, “ Application of electronic structure methods to coupled Drude oscillators,” Chem. Phys. Lett. 630, 76- 79 ( 2015). 10.1016/j.cplett.2015.04.031
T. T. Odbadrakh and K. D. Jordan, “ Dispersion dipoles for coupled Drude oscillators,” J. Chem. Phys. 144, 034111 ( 2016). 10.1063/1.4940217
K. R. Bryenton and E. R. Johnson, “ Many-body dispersion in model systems and the sensitivity of self-consistent screening,” J. Chem. Phys. 158, 204110 ( 2023). 10.1063/5.0142465
A. Tkatchenko, R. A. DiStasio, R. Car, and M. Scheffler, “ Accurate and efficient method for many-body van der Waals interactions,” Phys. Rev. Lett. 108, 236402 ( 2012). 10.1103/physrevlett.108.236402
M. Stöhr, M. Sadhukhan, Y. Al-Hamdani, J. Hermann, and A. Tkatchenko, “ Coulomb interactions between dipolar quantum fluctuations in van der Waals bound molecules and materials,” Nat. Commun. 12, 137 ( 2021). 10.1038/s41467-020-20473-w
M. Sadhukhan and F. R. Manby, “ Quantum mechanics of Drude oscillators with full Coulomb interaction,” Phys. Rev. B 94, 115106 ( 2016). 10.1103/physrevb.94.115106
A. P. Jones, J. Crain, V. P. Sokhan, T. W. Whitfield, and G. J. Martyna, “ Quantum Drude oscillator model of atoms and molecules: Many-body polarization and dispersion interactions for atomistic simulation,” Phys. Rev. B 87, 144103 ( 2013). 10.1103/physrevb.87.144103
D. V. Fedorov, M. Sadhukhan, M. Stöhr, and A. Tkatchenko, “ Quantum-mechanical relation between atomic dipole polarizability and the van der Waals radius,” Phys. Rev. Lett. 121, 183401 ( 2018). 10.1103/physrevlett.121.183401
O. Vaccarelli, D. V. Fedorov, M. Stöhr, and A. Tkatchenko, “ Quantum-mechanical force balance between multipolar dispersion and pauli repulsion in atomic van der Waals dimers,” Phys. Rev. Res. 3, 033181 ( 2021). 10.1103/physrevresearch.3.033181
S. Góger, A. Khabibrakhmanov, O. Vaccarelli, D. V. Fedorov, and A. Tkatchenko, “ Optimized quantum Drude oscillators for atomic and molecular response properties,” J. Phys. Chem. Lett. 14, 6217- 6223 ( 2023). 10.1021/acs.jpclett.3c01221
A. Ambrosetti, P. Umari, P. L. Silvestrelli, J. Elliott, and A. Tkatchenko, “ Optical van-der-Waals forces in molecules: From electronic bethe-salpeter calculations to the many-body dispersion model,” Nat. Commun. 13, 813 ( 2022). 10.1038/s41467-022-28461-y
M. Ditte, M. Barborini, L. M. Sandonas, and A. Tkatchenko, “ Molecules in environments: Toward systematic quantum embedding of electrons and Drude oscillators,” Phys. Rev. Lett. 131, 228001 ( 2023). 10.1103/PhysRevLett.131.228001
A. Khabibrakhmanov, D. V. Fedorov, and A. Tkatchenko, “ Universal pairwise interatomic van der Waals potentials based on quantum Drude oscillators,” J. Chem. Theory Comput. 19, 7895- 7907 ( 2023). 10.1021/acs.jctc.3c00797
R. Eisenschitz and F. London, “ Über das Verhältnis der van der Waalsschen Kräfte zu den homöopolaren Bindungskräften,” Z. Phys. 60, 491- 527 ( 1930). 10.1007/bf01341258
W. L. Bade and J. G. Kirkwood, “ Drude-model calculation of dispersion forces. II. The linear lattice,” J. Chem. Phys. 27, 1284- 1288 ( 1957). 10.1063/1.1743992
W. L. Bade, “ Drude-model calculation of dispersion forces. III. The fourth-order contribution,” J. Chem. Phys. 28, 282- 284 ( 1958). 10.1063/1.1744106
D. J. Margoliash and W. J. Meath, “ Pseudospectral dipole oscillator strength distributions and some related two body interaction coefficients for H, He, Li, N, O, H2, N2, O2, No, N2O, H2O, NH3, and CH4,” J. Chem. Phys. 68, 1426- 1431 ( 1978). 10.1063/1.435963
A. Tkatchenko and M. Scheffler, “ Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data,” Phys. Rev. Lett. 102, 073005 ( 2009). 10.1103/physrevlett.102.073005
A. A. Lucas, “ Effect of many-body van der Waals forces on the lattice dynamics of rare-gas crystals,” Phys. Rev. 176, 1093- 1097 ( 1968). 10.1103/physrev.176.1093
A. Dodin and P. L. Geissler, “ Symmetrized Drude oscillator force fields improve numerical performance of polarizable molecular dynamics,” J. Chem. Theory Comput. 19, 2906- 2917 ( 2023). 10.1021/acs.jctc.3c00278
A. Ambrosetti, A. M. Reilly, R. A. DiStasio, and A. Tkatchenko, “ Long-range correlation energy calculated from coupled atomic response functions,” J. Chem. Phys. 140, 18A508 ( 2014). 10.1063/1.4865104
The exact solution of the QDO dimer in the dipole interaction limit that is described in Refs. 1 and 4 is of the form E ± ( R ) = ω 2 2 1 ± q 2 μ ω 2 R 3 + 1 ∓ 2 q 2 μ ω 2 R 3 and E0(R) = E+(R) + E−(R), with ℏ = 1.
F. S. Cipcigan, J. Crain, V. P. Sokhan, and G. J. Martyna, “ Electronic coarse graining: Predictive atomistic modeling of condensed matter,” Rev. Mod. Phys. 91, 025003 ( 2019). 10.1103/revmodphys.91.025003
L. Shirkov and V. Sladek, “ Benchmark CCSD-SAPT study of rare gas dimers with comparison to MP-SAPT and DFT-SAPT,” J. Chem. Phys. 147, 174103 ( 2017). 10.1063/1.4997569
P. Bandyopadhyay and M. Sadhukhan, “ Modeling coarse-grained van der Waals interactions using dipole-coupled anisotropic quantum Drude oscillators,” J. Comput. Chem. 44, 1164- 1173 ( 2023). 10.1002/jcc.27073
A. Jones, A. Thompson, J. Crain, M. H. Müser, and G. J. Martyna, “ Norm-conserving diffusion Monte Carlo method and diagrammatic expansion of interacting Drude oscillators: Application to solid xenon,” Phys. Rev. B 79, 144119 ( 2009). 10.1103/physrevb.79.144119
W. Heitler and F. London, “ Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik,” Z. Phys. 44, 455- 472 ( 1927). 10.1007/bf01397394
J. C. Slater, “ The theory of complex spectra,” Phys. Rev. 34, 1293- 1322 ( 1929). 10.1103/physrev.34.1293
S. F. Boys, “ Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system,” Proc. R. Soc. A 200, 542- 554 ( 1950). 10.1098/rspa.1950.0036
T. Kato, “ On the eigenfunctions of many-particle systems in quantum mechanics,” Commun. Pure Appl. Math. 10, 151- 177 ( 1957). 10.1002/cpa.3160100201
R. Jastrow, “ Many-body problem with strong forces,” Phys. Rev. 98, 1479- 1484 ( 1955). 10.1103/physrev.98.1479
N. D. Drummond, M. D. Towler, and R. J. Needs, “ Jastrow correlation factor for atoms, molecules, and solids,” Phys. Rev. B 70, 235119 ( 2004). 10.1103/physrevb.70.235119
H. Padé, “ Sur la représentation approchée d’une fonction par des fractions rationnelles,” Ann. Sci. Éc. Norm. Supér. 9, 3- 93 ( 1892). 10.24033/asens.378
W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal, “ Quantum Monte Carlo simulations of solids,” Rev. Mod. Phys. 73, 33- 83 ( 2001). 10.1103/revmodphys.73.33
M. H. Kalos and P. A. Whitlock, “ Quantum Monte Carlo,” in Monte Carlo Methods ( John Wiley & Sons, Ltd, 2008), pp. 159- 178, Chap. 8.
F. Becca and S. Sorella, Quantum Monte Carlo Approaches for Correlated Systems ( Cambridge University Press, 2017).
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “ Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087- 1092 ( 1953). 10.1063/1.1699114
S. Sorella, “ Generalized lanczos algorithm for variational quantum Monte Carlo,” Phys. Rev. B 64, 024512 ( 2001). 10.1103/physrevb.64.024512
M. Barborini, Quantum Mecha (QMeCha) package (private repository August 2023).
P. G. Hajigeorgiou, “ An extended Lennard-Jones potential energy function for diatomic molecules: Application to ground electronic states,” J. Mol. Spectrosc. 263, 101- 110 ( 2010). 10.1016/j.jms.2010.07.003
J. P. Araújo and M. Y. Ballester, “ A comparative review of 50 analytical representation of potential energy interaction for diatomic systems: 100 years of history,” Int. J. Quantum Chem. 121, e26808 ( 2021). 10.1002/qua.26808
A. J. A. Price, K. R. Bryenton, and E. R. Johnson, “ Requirements for an accurate dispersion-corrected density functional,” J. Chem. Phys. 154, 230902 ( 2021). 10.1063/5.0050993
A. Ambrosetti, D. Alfè, R. A. J. DiStasio, and A. Tkatchenko, “ Hard numbers for large molecules: Toward exact energetics for supramolecular systems,” J. Phys. Chem. Lett. 5, 849- 855 ( 2014). 10.1021/jz402663k
S. Varrette, P. Bouvry, H. Cartiaux, and F. Georgatos, “ Management of an academic HPC cluster: The Ul experience,” in Proceedings of the 2014 International Conference on High Performance Computing & Simulation (HPCS 2014) ( IEEE, Bologna, Italy, 2014), pp. 959- 967.