We propose an approach to compute the ground state properties of collections of interacting asymmetric top molecules based on the density matrix renormalization group method. Linear chains of rigid water molecules of varying sizes and density are used to illustrate the method. A primitive computational basis of asymmetric top eigenstates with nuclear spin symmetry is used, and the many-body wave function is represented as a matrix product state. We introduce a singular value decomposition approach in order to represent general interaction potentials as matrix product operators. The method can be used to describe linear chains containing up to 50 water molecules. Properties such as the ground state energy, the von-Neumann entanglement entropy, and orientational correlation functions are computed. The effect of basis set truncation on the convergence of ground state properties is assessed. It is shown that specific intermolecular distance regions can be grouped by their von-Neumann entanglement entropy, which in turn can be associated with electric dipole–dipole alignment and hydrogen bond formation. Additionally, by assuming conservation of local spin states, we present our approach to be capable of calculating chains with different arrangements of the para and ortho spin isomers of water and demonstrate that for the water dimer.
REFERENCES
1.
N. E.
Levinger
, “Water in confinement
,” Science
298
, 1722
–1723
(2002
).2.
A.
Alexiadis
and S.
Kassinos
, “Molecular simulation of water in carbon nanotubes
,” Chem. Rev.
108
, 5014
–5034
(2008
).3.
J. C.
Rasaiah
, S.
Garde
, and G.
Hummer
, “Water in nonpolar confinement: From nanotubes to proteins and beyond
,” Annu. Rev. Phys. Chem.
59
, 713
–740
(2008
).4.
G. F.
Reiter
, A.
Deb
, Y.
Sakurai
, M.
Itou
, and A. I.
Kolesnikov
, “Quantum coherence and temperature dependence of the anomalous state of nanoconfined water in carbon nanotubes
,” J. Phys. Chem. Lett.
7
, 4433
–4437
(2016
).5.
D.
Muñoz-Santiburcio
and D.
Marx
, “Chemistry in nanoconfined water
,” Chem. Sci.
8
, 3444
–3452
(2017
).6.
A. W.
Knight
, N. G.
Kalugin
, E.
Coker
, and A. G.
Ilgen
, “Water properties under nano-scale confinement
,” Sci. Rep.
9
, 8246
(2019
).7.
C. I.
Lynch
, S.
Rao
, and M. S. P.
Sansom
, “Water in nanopores and biological channels: A molecular simulation perspective
,” Chem. Rev.
120
, 10298
–10335
(2020
).8.
M. A.
Belyanchikov
, M.
Savinov
, Z. V.
Bedran
, P.
Bednyakov
, P.
Proschek
, J.
Prokleska
, V. A.
Abalmasov
, J.
Petzelt
, E. S.
Zhukova
, V. G.
Thomas
et al., “Dielectric ordering of water molecules arranged in a dipolar lattice
,” Nat. Commun.
11
, 3927
(2020
).9.
J.
Hernández-Rojas
, F.
Calvo
, J.
Bretón
, and J. M.
Gomez Llorente
, “Confinement effects on water clusters inside carbon nanotubes
,” J. Phys. Chem. C
116
, 17019
–17028
(2012
).10.
M.
Sadeghi
and G. A.
Parsafar
, “Density-induced molecular arrangements of water inside carbon nanotubes
,” Phys. Chem. Chem. Phys.
15
, 7379
–7388
(2013
).11.
S.
Li
and B.
Schmidt
, “Molecular dynamics simulations of proton-ordered water confined in low-diameter carbon nanotubes
,” Phys. Chem. Chem. Phys.
17
, 7303
–7316
(2015
).12.
X.
Ma
, S.
Cambré
, W.
Wenseleers
, S. K.
Doorn
, and H.
Htoon
, “Quasiphase transition in a single file of water molecules encapsulated in (6, 5) carbon nanotubes observed by temperature-dependent photoluminescence spectroscopy
,” Phys. Rev. Lett.
118
, 027402
(2017
).13.
C.
Beduz
, M.
Carravetta
, J. Y. C.
Chen
, M.
Concistrè
, M.
Denning
, M.
Frunzi
, A. J.
Horsewill
, O. G.
Johannessen
, R.
Lawler
, X.
Lei
et al., “Quantum rotation of ortho and para-water encapsulated in a fullerene cage
,” Proc. Natl. Acad. Sci. U. S. A.
109
, 12894
–12898
(2012
).14.
S.
Mamone
, M.
Concistrè
, E.
Carignani
, B.
Meier
, A.
Krachmalnicoff
, O. G.
Johannessen
, X.
Lei
, Y.
Li
, M.
Denning
, M.
Carravetta
et al., “Nuclear spin conversion of water inside fullerene cages detected by low-temperature nuclear magnetic resonance
,” J. Chem. Phys.
140
, 194306
(2014
).15.
P. M.
Felker
and Z.
Bačić
, “Accurate quantum calculations of translation-rotation eigenstates in electric-dipole-coupled H2O@C60 assemblies
,” Chem. Phys. Lett.
683
, 172
–178
(2017
).16.
T.
Halverson
, D.
Iouchtchenko
, and P.-N.
Roy
, “Quantifying entanglement of rotor chains using basis truncation: Application to dipolar endofullerene peapods
,” J. Chem. Phys.
148
, 074112
(2018
).17.
A.
Sarsa
, K. E.
Schmidt
, and W. R.
Magro
, “A path integral ground state method
,” J. Chem. Phys.
113
, 1366
–1371
(2000
).18.
Y.
Yan
and D.
Blume
, “Path integral Monte Carlo ground state approach: Formalism, implementation, and applications
,” J. Phys. B: At., Mol. Opt. Phys.
50
, 223001
(2017
).19.
T.
Sahoo
, D.
Iouchtchenko
, C. M.
Herdman
, and P.-N.
Roy
, “A path integral ground state replica trick approach for the computation of entanglement entropy of dipolar linear rotors
,” J. Chem. Phys.
152
, 184113
(2020
).20.
T.
Sahoo
, T.
Serwatka
, and P.-N.
Roy
, “A path integral ground state approach for asymmetric top rotors with nuclear spin symmetry: Application to water chains
,” J. Chem. Phys.
154
, 244305
(2021
).21.
T.
Zeng
, H.
Li
, and P.-N.
Roy
, “Simulating asymmetric top impurities in superfluid clusters: A para-water dopant in para-hydrogen
,” J. Phys. Chem. Lett.
4
, 18
(2013
).22.
T.
Zeng
, G.
Guillon
, J. T.
Cantin
, and P.-N.
Roy
, “Probing the superfluid response of para-hydrogen with a sulfur dioxide dopant
,” J. Phys. Chem. Lett.
4
, 2391
(2013
).23.
U.
Schollwöck
, “The density-matrix renormalization group in the age of matrix product states
,” Ann. Phys.
326
, 96
–192
(2011
).24.
D.
Iouchtchenko
and P.-N.
Roy
, “Ground states of linear rotor chains via the density matrix renormalization group
,” J. Chem. Phys.
148
, 134115
(2018
).25.
S. R.
White
, “Density matrix formulation for quantum renormalization groups
,” Phys. Rev. Lett.
69
, 2863
(1992
).26.
S. R.
White
, “Density-matrix algorithms for quantum renormalization groups
,” Phys. Rev. B
48
, 10345
(1993
).27.
U.
Schollwöck
, “The density-matrix renormalization group
,” Rev. Mod. Phys.
77
, 259
(2005
).28.
I. P.
McCulloch
, “From density-matrix renormalization group to matrix product states
,” J. Stat. Mech.: Theory Exp.
2007
, P10014
.29.
G. K.-L.
Chan
, A.
Keselman
, N.
Nakatani
, Z.
Li
, and S. R.
White
, “Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms
,” J. Chem. Phys.
145
, 014102
(2016
).30.
A.
Rényi
, “On measures of entropy and information
,” in Volume 1: Contributions to the Theory of Statistics
(University of California Press
, 1961
), pp. 547
–561
, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability.31.
P. R.
Bunker
and P.
Jensen
, Fundamentals of Molecular Symmetry
(IOP Publishing
, Bristol
, 2005
).32.
L. C.
Biedenharn
, J. D.
Louck
, and P. A.
Carruthers
, Angular Momentum in Quantum Physics: Theory and Application
(Addison-Wesley
, Reading, MA
, 1981
), Vol. 8.33.
T.
Zeng
and P.-N.
Roy
, “Microscopic molecular superfluid response: Theory and simulations
,” Rep. Prog. Phys.
77
, 046601
(2014
).34.
C.
Hubig
, I.
McCulloch
, and U.
Schollwöck
, “Generic construction of efficient matrix product operators
,” Phys. Rev. B
95
, 035129
(2017
).35.
D. E.
Parker
, X.
Cao
, and M. P.
Zaletel
, “Local matrix product operators: Canonical form, compression, and control theory
,” Phys. Rev. B
102
, 035147
(2020
).36.
D.
Peláez
and H.-D.
Meyer
, “The multigrid POTFIT (MGPF) method: Grid representations of potentials for quantum dynamics of large systems
,” J. Chem. Phys.
138
, 014108
(2013
).37.
C.
Leforestier
, “Grid method for the Wigner functions. Application to the van der Waals system Ar–H2O
,” J. Chem. Phys.
101
, 7357
–7363
(1994
).38.
T.
Westermann
, R.
Brodbeck
, A. B.
Rozhenko
, W.
Schoeller
, and U.
Manthe
, “Photodissociation of methyl iodide embedded in a host-guest complex: A full dimensional (189D) quantum dynamics study of CH3I@resorc[4]arene
,” J. Chem. Phys.
135
, 184102
(2011
).39.
J.
Schulze
, M. F.
Shibl
, M. J.
Al-Marri
, and O.
Kühn
, “Multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach to the correlated exciton-vibrational dynamics in the FMO complex
,” J. Chem. Phys.
144
, 185101
(2016
).40.
D.
Mendive-Tapia
, E.
Mangaud
, T.
Firmino
, A.
de la Lande
, M.
Desouter-Lecomte
, H.-D.
Meyer
, and F.
Gatti
, “Multidimensional quantum mechanical modeling of electron transfer and electronic coherence in plant cryptochromes: The role of initial bath conditions
,” J. Phys. Chem. B
122
, 126
–136
(2018
).41.
H. R.
Larsson
, “Computing vibrational eigenstates with tree tensor network states (TTNS)
,” J. Chem. Phys.
151
, 204102
(2019
).42.
S.
Mainali
, F.
Gatti
, D.
Iouchtchenko
, P.-N.
Roy
, and H.-D.
Meyer
, “Comparison of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method and the density matrix renormalization group (DMRG) for ground state properties of linear rotor chains
,” J. Chem. Phys.
154
, 174106
(2021
).43.
J. L. F.
Abascal
and C.
Vega
, “A general purpose model for the condensed phases of water: TIP4P/2005
,” J. Chem. Phys.
123
, 234505
(2005
).44.
S.
Habershon
, T. E.
Markland
, and D. E.
Manolopoulos
, “Competing quantum effects in the dynamics of a flexible water model
,” J. Chem. Phys.
131
, 024501
(2009
).45.
V.
Babin
, C.
Leforestier
, and F.
Paesani
, “Development of a ‘first principles’ water potential with flexible monomers: Dimer potential energy surface, VRT spectrum, and second virial coefficient
,” J. Chem. Theory Comput.
9
, 5395
–5403
(2013
).46.
V.
Babin
, G. R.
Medders
, and F.
Paesani
, “Development of a ‘first principles’ water potential with flexible monomers. II: Trimer potential energy surface, third virial coefficient, and small clusters
,” J. Chem. Theory Comput.
10
, 1599
–1607
(2014
).47.
R. T.
Hall
and J. M.
Dowling
, “Pure rotational spectrum of water vapor
,” J. Chem. Phys.
47
, 2454
–2461
(1967
).48.
M.
Fishman
, S. R.
White
, and E. M.
Stoudenmire
, “The ITensor software library for tensor network calculations
,” arXiv:2007.14822 (2020
).49.
J.
Biskupek
, S. T.
Skowron
, C. T.
Stoppiello
, G. A.
Rance
, S.
Alom
, K. L. Y.
Fung
, R. J.
Whitby
, M. H.
Levitt
, Q. M.
Ramasse
, U.
Kaiser
et al., “Bond dissociation and reactivity of HF and H2O in a nano test tube
,” ACS Nano
14
, 11178
–11189
(2020
).50.
51.
J. K.
Holt
, “Methods for probing water at the nanoscale
,” Microfluid. Nanofluid.
5
, 425
–442
(2008
).52.
G.
Pérez-Hernández
and B.
Schmidt
, “Anisotropy of the water–carbon interaction: Molecular simulations of water in low-diameter carbon nanotubes
,” Phys. Chem. Chem. Phys.
15
, 4995
–5006
(2013
).53.
S.
Dalla Bernardina
, E.
Paineau
, J.-B.
Brubach
, P.
Judeinstein
, S.
Rouzière
, P.
Launois
, and P.
Roy
, “Water in carbon nanotubes: The peculiar hydrogen bond network revealed by infrared spectroscopy
,” J. Am. Chem. Soc.
138
, 10437
–10443
(2016
).54.
J.
Liu
, L.
Feng
, X.
Wang
, and M.
Zhao
, “Exploring the effect of confinement on water clusters in carbon nanotubes
,” J. Mol. Model.
23
, 133
(2017
).55.
M.
Schmidt
and P.-N.
Roy
, “Path integral molecular dynamic simulation of flexible molecular systems in their ground state: Application to the water dimer
,” J. Chem. Phys.
148
, 124116
(2018
).56.
M.
Motta
, D. M.
Ceperley
, G.
Kin-Lic Chan
, J. A.
Gomez
, E.
Gull
, S.
Guo
, C. A.
Jiménez-Hoyos
, T.
Nguyen Lan
, J.
Li
, F.
Ma
, A. J.
Millis
, N. V.
Prokofev
, U.
Ray
, G. E.
Scuseria
, S.
Sorella
, E. M.
Stoudenmire
, Q.
Sun
, I. S.
Tupitsyn
, S. R.
White
, D.
Zgid
, and S.
Zhang
, “Towards the solution of the many-electron problem in real materials: Equation of state of the hydrogen chain with state-of-the-art many-body methods
,” Phys. Rev. X
7
, 031059
(2017
).57.
G. K.-L.
Chan
and S.
Sharma
, “The density matrix renormalization group in quantum chemistry
,” Annu. Rev. Phys. Chem.
62
, 465
–481
(2011
).58.
A.
Baiardi
and M.
Reiher
, “The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges
,” J. Chem. Phys.
152
, 040903
(2020
).59.
A.
Baiardi
, A. K.
Kelemen
, and M.
Reiher
, “Excited-state DMRG made simple with FEAST
,” J. Chem. Theory Comput.
18
, 415
–430
(2022
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
