We derive and implement an alternative formulation of the Stochastic Lanczos algorithm to be employed in connection with the Many-Body Dispersion model (MBD). Indeed, this formulation, which is only possible due to the Stochastic Lanczos’ reliance on matrix-vector products, introduces generalized dipoles and fields. These key quantities allow for a state-of-the-art treatment of periodic boundary conditions via the Smooth Particle Mesh Ewald (SPME) approach which uses efficient fast Fourier transforms. This SPME-Lanczos algorithm drastically outperforms the standard replica method which is affected by a slow and conditionally convergence rate that limits an efficient and reliable inclusion of long-range periodic boundary conditions interactions in many-body dispersion modelling. The proposed algorithm inherits the embarrassingly parallelism of the original Stochastic Lanczos scheme, thus opening up for a fully converged and efficient periodic boundary conditions treatment of MBD approaches.
REFERENCES
1.
T.
Helgaker
, P.
Jørgensen
, and J.
Olsen
, Molecular Electronic Structure Theory
(John Wiley & Sons, Ltd.
, Chichester
, 2000
).2.
F.
Jensen
, Introduction to Computational Chemistry
, 3rd ed.
(Wiley
, Chichester, UK
, 2017
).3.
S.
Grimme
, A.
Hansen
, J. G.
Brandenburg
, and C.
Bannwarth
, “Dispersion-corrected mean-field electronic structure methods
,” Chem. Rev.
116
, 5105
–5154
(2016
).4.
A. G.
Donchev
, “Many-body effects of dispersion interaction
,” J. Chem. Phys.
125
, 074713
(2006
).5.
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
).6.
T.
Gould
, S.
Lebègue
, J. G.
Ángyán
, and T.
Bučko
, “A fractionally ionic approach to polarizability and van der Waals many-body dispersion calculations
,” J. Chem. Theory Comput.
12
, 5920
–5930
(2016
).7.
K.
Carter-Fenk
, K. U.
Lao
, K.-Y.
Liu
, and J. M.
Herbert
, “Accurate and efficient ab initio calculations for supramolecular complexes: Symmetry-adapted perturbation theory with many-body dispersion
,” J. Phys. Chem. Lett.
10
, 2706
–2714
(2019
).8.
P. P.
Poier
, T.
Jaffrelot Inizan
, O.
Adjoua
, L.
Lagardère
, and J.-P.
Piquemal
, “Accurate deep learning-aided density-free strategy for many-body dispersion-corrected density functional theory
,” J. Phys. Chem. Lett.
13
, 4381
–4388
(2022
).9.
P. P.
Poier
, O.
Adjoua
, L.
Lagardère
, and J.-P.
Piquemal
, “Generalized many-body dispersion correction through random-phase approximation for chemically accurate density functional theory
,” J. Phys. Chem. Lett.
14
, 1609
–1617
(2023
).10.
S.
Ubaru
, J.
Chen
, and Y.
Saad
, “Fast estimation of tr(f(A)) via stochastic Lanczos quadrature
,” SIAM J. Matrix Anal. Appl.
38
, 1075
–1099
(2017
).11.
P. P.
Poier
, L.
Lagardère
, and J.-P.
Piquemal
, “O(N) stochastic evaluation of many-body van der Waals energies in large complex systems
,” J. Chem. Theory Comput.
18
, 1633
–1645
(2022
).12.
M.
Stöhr
and A.
Tkatchenko
, “Quantum mechanics of proteins in explicit water: The role of plasmon-like solute–solvent interactions
,” Sci. Adv.
5
, eaax0024
(2019
).13.
T.
Bučko
, S.
Lebègue
, T.
Gould
, and J. G.
Ángyán
, “Many-body dispersion corrections for periodic systems: An efficient reciprocal space implementation
,” J. Phys.: Condens. Matter
28
, 045201
(2016
).14.
T.
Darden
, D.
York
, and L.
Pedersen
, “Particle mesh Ewald: An N·log(N) method for Ewald sums in large systems
,” J. Chem. Phys.
98
, 10089
–10092
(1993
).15.
U.
Essmann
, L.
Perera
, M. L.
Berkowitz
, T.
Darden
, H.
Lee
, and L. G.
Pedersen
, “A smooth particle mesh Ewald method
,” J. Chem. Phys.
103
, 8577
–8593
(1995
).16.
T. J.
Giese
, M. T.
Panteva
, H.
Chen
, and D. M.
York
, “Multipolar Ewald methods, 1: Theory, accuracy, and performance
,” J. Chem. Theory Comput.
11
, 436
–450
(2015
).17.
T.
Brinck
, J. S.
Murray
, and P.
Politzer
, “Polarizability and volume
,” J. Chem. Phys.
98
, 4305
–4306
(1993
).18.
A. D.
Becke
and E. R.
Johnson
, “Exchange-hole dipole moment and the dispersion interaction: High-order dispersion coefficients
,” J. Chem. Phys.
124
, 014104
(2006
).19.
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
).20.
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
).21.
D.
Massa
, A.
Ambrosetti
, and P. L.
Silvestrelli
, “Many-body van der Waals interactions beyond the dipole approximation
,” J. Chem. Phys.
154
, 224115
(2021
).22.
M.
Hutchinson
, “A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines
,” Commun. Stat. Simul. Comput.
19
, 433
–450
(1990
).23.
G. H.
Golub
and G.
Meurant
, Matrices, Moments and Quadrature with Applications
(Princeton University Press
, 2009
).24.
M. A.
Blood-Forsythe
, T.
Markovich
, R. A.
DiStasio
, R.
Car
, and A.
Aspuru-Guzik
, “Analytical nuclear gradients for the range-separated many-body dispersion model of noncovalent interactions
,” Chem. Sci.
7
, 1712
–1728
(2016
).25.
S. W.
de Leeuw
, J. W.
Ewald
, and E. R.
Smith
, “Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants
,” Proc. R. Soc. London, Ser. A
373
, 27
–56
(1980
).26.
P. P.
Poier
and J.
Frank
, “Including implicit solvation in the bond capacity polarization model
,” J. Chem. Phys.
151
, 114118
(2019
).27.
P. P.
Poier
and F.
Jensen
, “Polarizable charges in a generalized Born reaction potential
,” J. Chem. Phys.
153
, 024111
(2020
).28.
B.
Stamm
, L.
Lagardère
, E.
Polack
, Y.
Maday
, and J.-P.
Piquemal
, “A coherent derivation of the Ewald summation for arbitrary orders of multipoles: The self-terms
,” J. Chem. Phys.
149
, 124103
(2018
).29.
A.
Redlack
and J.
Grindlay
, “Coulombic potential lattice sums
,” J. Phys. Chem. Solids
36
, 73
–82
(1975
).30.
T. R. C.
Kenny
, B.
Lipkowitz
, and D. B.
Boyd
, Reviews in Computational Chemistry
(Wiley
, 2007
), Vol. 24
.31.
M. P.
Allen
and D. J.
Tildesley
, Computer Simulation of Liquids
(Clarendon Press
, New York
, 1989
).32.
C.
Sagui
, L. G.
Pedersen
, and T. A.
Darden
, “Towards an accurate representation of electrostatics in classical force fields: Efficient implementation of multipolar interactions in biomolecular simulations
,” J. Chem. Phys.
120
, 73
–87
(2004
).33.
L.
Lagardère
, L.-H.
Jolly
, F.
Lipparini
, F.
Aviat
, B.
Stamm
, Z. F.
Jing
, M.
Harger
, H.
Torabifard
, G. A.
Cisneros
, M. J.
Schnieders
, N.
Gresh
, Y.
Maday
, P. Y.
Ren
, J. W.
Ponder
, and J.-P.
Piquemal
, “Tinker-HP: A massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields
,” Chem. Sci.
9
, 956
–972
(2018
).34.
O.
Adjoua
, L.
Lagardère
, L.-H.
Jolly
, A.
Durocher
, T.
Very
, I.
Dupays
, Z.
Wang
, T. J.
Inizan
, F.
Célerse
, P.
Ren
, J. W.
Ponder
, and J. P.
Piquemal
, “Tinker-HP: Accelerating molecular dynamics simulations of large complex systems with advanced point dipole polarizable force fields using GPUs and multi-GPU systems
,” J. Chem. Theory Comput.
17
, 2034
–2053
(2021
).35.
C.
Lanczos
, “An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
,” J. Res. Natl. Bur. Stand.
45
, 255
–282
(1950
).36.
C.
Brezinski
, M.
Zaglia
, and H.
Sadok
, “A review of formal orthogonality in Lanczos-based methods
,” J. Comput. Appl. Math.
140
, 81
–98
(2002
), Int. Congress on Computational and Applied Mathematics 2000.37.
I.
Chollet
, L.
Lagardère
, and J.-P.
Piquemal
, “ANKH: A generalized O(N) interpolated Ewald strategy for molecular dynamics simulations
,” J. Chem. Theory Comput.
19
, 2887
–2905
(2023
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
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