Semi-empirical quantum models such as Density Functional Tight Binding (DFTB) are attractive methods for obtaining quantum simulation data at longer time and length scales than possible with standard approaches. However, application of these models can require lengthy effort due to the lack of a systematic approach for their development. In this work, we discuss the use of the Chebyshev Interaction Model for Efficient Simulation (ChIMES) to create rapidly parameterized DFTB models, which exhibit strong transferability due to the inclusion of many-body interactions that might otherwise be inaccurate. We apply our modeling approach to silicon polymorphs and review previous work on titanium hydride. We also review the creation of a general purpose DFTB/ChIMES model for organic molecules and compounds that approaches hybrid functional and coupled cluster accuracy with two orders of magnitude fewer parameters than similar neural network approaches. In all cases, DFTB/ChIMES yields similar accuracy to the underlying quantum method with orders of magnitude improvement in computational cost. Our developments provide a way to create computationally efficient and highly accurate simulations over varying extreme thermodynamic conditions, where physical and chemical properties can be difficult to interrogate directly, and there is historically a significant reliance on theoretical approaches for interpretation and validation of experimental results.
REFERENCES
1.
K. R. S.
Chandrakumar
, A. J.
Page
, S.
Irle
, and K.
Morokuma
, “Carbon coating precedes SWCNT nucleation on silicon nanoparticles: Insights from QM/MD simulations
,” J. Phys. Chem. C
117
, 4238
–4244
(2013
).2.
A.
Sharma
, G. D.
Cody
, and R. J.
Hemley
, “In situ diamond-anvil cell observations of methanogenesis at high pressures and temperatures
,” Energy Fuels
23
, 5571
(2009
).3.
W.
Peiman
, I. L.
Pioro
, K.
Gabriel
, and M.
Hosseiny
, “Thermal aspects of conventional and alternative fuels
,” in Handbook of Generation IV Nuclear Reactors
, Woodhead Publishing Series in Energy, edited by I. L.
Pioro
(Woodhead Publishing
, 2016
) Chap. 18, pp. 583
–635
.4.
B. A.
Steele
, N.
Goldman
, I.-F. W.
Kuo
, and M. P.
Kroonblawd
, “Mechanochemical synthesis of glycine oligomers in a virtual rotational diamond anvil cell
,” Chem. Sci.
11
, 7760
–7771
(2020
).5.
E.
Schwegler
, M.
Sharma
, F.
Gygi
, and G.
Galli
, “Melting of ice under pressure
,” Proc. Natl. Acad. Sci. U. S. A.
105
, 14779
(2008
).6.
A. A.
Correa
, S. A.
Bonev
, and G.
Galli
, “Carbon under extreme conditions: Phase boundaries and electronic properties from first-principles theory
,” Proc. Natl. Acad. Sci. U. S. A.
103
, 1204
–1208
(2006
).7.
M. P.
Kroonblawd
and N.
Goldman
, “Mechanochemical formation of heterogeneous diamond structures during rapid uniaxial compression in graphite
,” Phys. Rev. B
97
, 184106
(2018
).8.
M. R.
Manaa
, E. J.
Reed
, L. E.
Fried
, and N.
Goldman
, “Nitrogen-rich heterocycles as reactivity retardants in shocked insensitive explosives
,” J. Am. Chem. Soc.
131
, 5483
–5487
(2009
).9.
R. G.
Mullen
and N.
Goldman
, “Quantum accurate prediction of plutonium-plutonium dihydride phase equilibrium using a lattice gas model
,” J. Phys. Chem. C
124
, 20881
–20888
(2020
).10.
M. P.
Kroonblawd
, R. K.
Lindsey
, and N.
Goldman
, “Synthesis of nitrogen-containing polycyclic aromatic hydrocarbons in impacting glycine solutions
,” Chem. Sci.
10
, 6091
(2019
).11.
T.
Sours
, A.
Patel
, J.
Nørskov
, S.
Siahrostami
, and A.
Kulkarni
, “Circumventing scaling relations in oxygen electrochemistry using metal-organic frameworks
,” J. Phys. Chem. Lett.
11
, 10029
–10036
(2020
).12.
M.
Sliwa
, D.
McGonegle
, C.
Wehrenberg
, C. A.
Bolme
, P. G.
Heighway
, A.
Higginbotham
, A.
Lazicki
, H. J.
Lee
, B.
Nagler
, H. S.
Park
, R. E.
Rudd
, M. J.
Suggit
, D.
Swift
, F.
Tavella
, L.
Zepeda-Ruiz
, B. A.
Remington
, and J. S.
Wark
, “Femtosecond x-ray diffraction studies of the reversal of the microstructural effects of plastic deformation during shock release of tantalum
,” Phys. Rev. Lett.
120
, 265502
(2018
).13.
H.
Wang
, L.
Zhang
, J.
Han
, and W.
E
, “DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics
,” Comput. Phys. Commun.
228
, 178
–184
(2018
).14.
B.
Cheng
, E. A.
Engel
, J.
Behler
, C.
Dellago
, and M.
Ceriotti
, “Ab initio thermodynamics of liquid and solid water
,” Proc. Natl. Acad. Sci. U. S. A.
116
, 1110
–1115
(2019
).15.
R.
Rana
, F. D.
Vila
, A. R.
Kulkarni
, and S. R.
Bare
, “Bridging the gap between the x-ray absorption spectroscopy and the computational catalysis communities in heterogeneous catalysis: A perspective on the current and future research directions
,” ACS Catal.
12
, 13813
–13830
(2022
).16.
C.
Oses
, M.
Esters
, D.
Hicks
, S.
Divilov
, H.
Eckert
, R.
Friedrich
, M. J.
Mehl
, A.
Smolyanyuk
, X.
Campilongo
, A.
van de Walle
, J.
Schroers
, A. G.
Kusne
, I.
Takeuchi
, E.
Zurek
, M.
Buongiorno Nardelli
, M.
Fornari
, Y.
Lederer
, O.
Levy
, C.
Toher
, and S.
Curtarolo
, “aflow++: A C++ framework for autonomous materials design
,” Comput. Mater. Sci.
217
, 111889
(2023
).17.
I.
Batatia
, D. P.
Kovacs
, G. N. C.
Simm
, C.
Ortner
, and G.
Csanyi
, “MACE: Higher order equivariant message passing neural networks for fast and accurate force fields
,” in Advances in Neural Information Processing Systems
, edited by A. H.
Oh
, A.
Agarwal
, D.
Belgrave
, and K.
Cho
(Curran Associates
, 2022
).18.
A. P.
Bartók
, J.
Kermode
, N.
Bernstein
, and G.
Csányi
, “Machine learning a general-purpose interatomic potential for silicon
,” Phys. Rev. X
8
, 041048
(2018
).19.
F. A.
Faber
, L.
Hutchison
, B.
Huang
, J.
Gilmer
, S. S.
Schoenholz
, G. E.
Dahl
, O.
Vinyals
, S.
Kearnes
, P. F.
Riley
, and O. A.
Von Lilienfeld
, “Prediction errors of molecular machine learning models lower than hybrid DFT error
,” J. Chem. Theory Comput.
13
, 5255
–5264
(2017
).20.
J. S.
Smith
, B. T.
Nebgen
, R.
Zubatyuk
, N.
Lubbers
, C.
Devereux
, K.
Barros
, S.
Tretiak
, O.
Isayev
, and A. E.
Roitberg
, “Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning
,” Nat. Commun.
10
, 2903
(2019
).21.
E. J.
Reed
, “Electron-ion coupling in shocked energetic materials
,” J. Phys. Chem. C
116
, 2205
(2012
).22.
E. J.
Reed
, A. W.
Rodriguez
, M. R.
Manaa
, L. E.
Fried
, and C. M.
Tarver
, “Ultrafast detonation of hydrazoic acid (HN3)
,” Phys. Rev. Lett.
109
, 038301
(2012
).23.
M. P.
Kroonblawd
, N.
Goldman
, and J. P.
Lewicki
, “Chemical degradation pathways in siloxane polymers following phenyl excitations
,” J. Phys. Chem. B
122
, 12201
–12210
(2018
).24.
G.
Zhou
, N.
Lubbers
, K.
Barros
, S.
Tretiak
, and B.
Nebgen
, “Deep learning of dynamically responsive chemical Hamiltonians with semiempirical quantum mechanics
,” Proc. Natl. Acad. Sci. U. S. A.
119
, e2120333119
(2022
).25.
M.
Elstner
, D.
Porezag
, G.
Jungnickel
, J.
Elsner
, M.
Haugk
, T.
Frauenheim
, S.
Suhai
, and G.
Seifert
, “Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties
,” Phys. Rev. B
58
, 7260
–7268
(1998
).26.
A. S.
Christensen
, T.
Kubař
, Q.
Cui
, and M.
Elstner
, “Semiempirical quantum mechanical methods for noncovalent interactions for chemical and biochemical applications
,” Chem. Rev.
116
, 5301
–5337
(2016
).27.
J. J.
Kranz
, M.
Kubillus
, R.
Ramakrishnan
, O. A.
von Lilienfeld
, and M.
Elstner
, “Generalized density-functional tight-binding repulsive potentials from unsupervised machine learning
,” J. Chem. Theory Comput.
14
, 2341
–2352
(2018
).28.
M. R.
Manaa
, L. E.
Fried
, C. F.
Melius
, M.
Elstner
, and T.
Frauenheim
, “Decomposition of HMX at extreme conditions: A molecular dynamics simulation
,” J. Phys. Chem. A
106
, 9024
(2002
).29.
P.
Goyal
, H.-J.
Qian
, S.
Irle
, X.
Lu
, D.
Roston
, T.
Mori
, M.
Elstner
, and Q.
Cui
, “Molecular simulation of water and hydration effects in different environments: Challenges and developments for DFTB based models
,” J. Phys. Chem. B
118
, 11007
–11027
(2014
).30.
R. K.
Szilagyi
, N. P.
Stadie
, S.
Irle
, and H.
Nishihara
, “Mechanical properties of zeolite-templated carbons from approximate density functional theory calculations
,” Carbon Rep.
1
, 231
–240
(2022
).31.
N.
Goldman
, S. G.
Srinivasan
, S.
Hamel
, L. E.
Fried
, M.
Gaus
, and M.
Elstner
, “Determination of a density functional tight binding model with an extended basis set and three-body repulsion for carbon under extreme pressures and temperatures
,” J. Phys. Chem. C
117
, 7885
–7894
(2013
).32.
S. G.
Srinivasan
, N.
Goldman
, I.
Tamblyn
, S.
Hamel
, and M.
Gaus
, “Determination of a density functional tight binding model with an extended basis set and three-body repulsion for hydrogen under extreme thermodynamic conditions
,” J. Phys. Chem. A
118
, 5520
–5528
(2014
).33.
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
).34.
S.
Grimme
, J.
Antony
, S.
Ehrlich
, and H.
Krieg
, “A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
,” J. Chem. Phys.
132
, 154104
(2010
).35.
C.-P.
Chou
, Y.
Nishimura
, C.-C.
Fan
, G.
Mazur
, S.
Irle
, and H. A.
Witek
, “Automatized parameterization of DFTB using particle swarm optimization
,” J. Chem. Theory Comput.
12
, 53
–64
(2016
).36.
M.
Hellström
, K.
Jorner
, M.
Bryngelsson
, S. E.
Huber
, J.
Kullgren
, T.
Frauenheim
, and P.
Broqvist
, “An SCC-DFTB repulsive potential for various ZnO polymorphs and the zno–water system
,” J. Phys. Chem. C
117
, 17004
–17015
(2013
).37.
A. K. A.
Kandy
, E.
Wadbro
, B.
Aradi
, P.
Broqvist
, and J.
Kullgren
, “Curvature constrained splines for DFTB repulsive potential parametrization
,” J. Chem. Theory Comput.
17
, 1771
–1781
(2021
).38.
N.
Goldman
, L.
Koziol
, and L. E.
Fried
, “Using force-matched potentials to improve the accuracy of density functional tight binding for reactive conditions
,” J. Chem. Theory Comput.
11
, 4530
–4535
(2015
).39.
N.
Goldman
, K. E.
Kweon
, B.
Sadigh
, T.-W.
Heo
, R. K.
Lindsey
, C. H.
Pham
, L. E.
Fried
, B.
Aradi
, K.
Holliday
, J. R.
Jeffries
, and B. C.
Wood
, “Semi-automated creation of density functional tight binding models through leveraging Chebyshev polynomial-based force fields
,” J. Chem. Theory Comput.
17
, 4435
–4448
(2021
).40.
P.
Miró
and C. J.
Cramer
, “Water clusters to nanodrops: A tight-binding density functional study
,” Phys. Chem. Chem. Phys.
15
, 1837
–1843
(2013
).41.
V. Q.
Vuong
, J. M. L.
Madridejos
, B.
Aradi
, B. G.
Sumpter
, G. F.
Metha
, and S.
Irle
, “Density-functional tight-binding for phosphine-stabilized nanoscale gold clusters
,” Chem. Sci.
11
, 13113
–13128
(2020
).42.
R. K.
Lindsey
, S.
Bastea
, N.
Goldman
, and L. E.
Fried
, “Investigating 3,4-bis(3-nitrofurazan-4-yl)furoxan detonation with a rapidly tuned density functional tight binding model
,” J. Chem. Phys.
154
, 164115
(2021
).43.
M.
Gaus
, Q.
Cui
, and M.
Elstner
, “DFTB3: Extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB)
,” J. Chem. Theory Comput.
7
, 931
(2011
).44.
S.
Markov
, B.
Aradi
, C.-Y.
Yam
, H.
Xie
, T.
Frauenheim
, and G.
Chen
, “Atomic level modeling of extremely thin silicon-on-insulator MOSFETs including the silicon dioxide: Electronic structure
,” IEEE Trans. Electron. Devices
62
, 696
–704
(2015
).45.
J.
Kullgren
, M. J.
Wolf
, K.
Hermansson
, C.
Köhler
, B.
Aradi
, T.
Fauenheim
, and P.
Broqvist
, “Self-consistent-charge density-functional tight-binding (SCC-DFTB) parameters for ceria in 0D to 3D
,” J. Phys. Chem. C
121
, 4593
–4607
(2017
).46.
M.
Stöhr
, L.
Medrano Sandonas
, and A.
Tkatchenko
, “Accurate many-body repulsive potentials for density-functional tight binding from deep tensor neural networks
,” J. Phys. Chem. Lett.
11
, 6835
–6843
(2020
). 47.
D.
Bissuel
, T.
Albaret
, and T. A.
Niehaus
, “Critical assessment of machine-learned repulsive potentials for the density functional based tight-binding method: A case study for pure silicon
,” J. Chem. Phys.
156
, 064101
(2022
).48.
C.
Panosetti
, A.
Engelmann
, L.
Nemec
, K.
Reuter
, and J. T.
Margraf
, “Learning to use the force: Fitting repulsive potentials in density-functional tight-binding with Gaussian process regression
,” J. Chem. Theory Comput.
16
, 2181
–2191
(2020
).49.
S.
Wengert
, G.
Csányi
, K.
Reuter
, and J. T.
Margraf
, “Data-efficient machine learning for molecular crystal structure prediction
,” Chem. Sci.
12
, 4536
(2021
).50.
R. K.
Lindsey
, L. E.
Fried
, and N.
Goldman
, “ChIMES: A force matched potential with explicit three-body interactions for molten carbon
,” J. Chem. Theory Comput.
13
, 6222
–6229
(2017
).51.
R. K.
Lindsey
, L. E.
Fried
, N.
Goldman
, and S.
Bastea
, “Active learning for robust, high-complexity reactive atomistic simulations
,” J. Chem. Phys.
153
, 134117
(2020
).52.
L.
Koziol
, L. E.
Fried
, and N.
Goldman
, “Using force matching to determine reactive force fields for water under extreme thermodynamic conditions
,” J. Chem. Theory Comput.
13
, 135
–146
(2017
).53.
R. K.
Lindsey
, L. E.
Fried
, and N.
Goldman
, “Application of the chimes force field to nonreactive molecular systems: Water at ambient conditions
,” J. Chem. Theory Comput.
15
, 436
–447
(2019
).54.
M. R.
Armstrong
, R. K.
Lindsey
, N.
Goldman
, M. H.
Nielsen
, E.
Stavrou
, L. E.
Fried
, J. M.
Zaug
, and S.
Bastea
, “Ultrafast shock synthesis of nanocarbon from a liquid precursor
,” Nat. Commun.
11
, 353
(2020
).55.
R. K.
Lindsey
, N.
Goldman
, L. E.
Fried
, and S.
Bastea
, “Many-body reactive force field development for carbon condensation in C/O systems under extreme conditions
,” J. Chem. Phys.
153
, 054103
(2020
).56.
C. H.
Pham
, R. K.
Lindsey
, L. E.
Fried
, and N.
Goldman
, “Calculation of the detonation state of HN3 with quantum accuracy
,” J. Chem. Phys.
153
, 224102
(2021
).57.
N.
Goldman
, B.
Aradi
, R. K.
Lindsey
, and L. E.
Fried
, “Development of a multicenter density functional tight binding model for plutonium surface hydriding
,” J. Chem. Theory Comput.
14
, 2652
–2660
(2018
).58.
N.
Goldman
, L.
Zepeda-Ruiz
, R. G.
Mullen
, R. K.
Lindsey
, C. H.
Pham
, L. E.
Fried
, and J. L.
Belof
, “Estimates of quantum tunneling effects for hydrogen diffusion in PuO2
,” Appl. Sci.
12
, 11005
(2022
).59.
C. H.
Pham
, R. K.
Lindsel
, L. E.
Fried
, and N.
Goldman
, “High-accuracy semiempirical quantum models based on a minimal training set
,” J. Phys. Chem. Lett.
13
, 2934
–2942
(2022
).60.
B.
Aradi
, B.
Hourahine
, and T.
Frauenheim
, “DFTB+, a sparse matrix-based implementation of the DFTB method
,” J. Phys. Chem. A
111
, 5678
–5684
(2007
).61.
B.
Hourahine
, B.
Aradi
, V.
Blum
, F.
Bonafé
, A.
Buccheri
, C.
Camacho
, C.
Cevallos
, M. Y.
Deshaye
, T.
Dumitrică
, A.
Dominguez
, S.
Ehlert
, M.
Elstner
, T.
van der Heide
, J.
Hermann
, S.
Irle
, J. J.
Kranz
, C.
Köhler
, T.
Kowalczyk
, T.
Kubař
, I. S.
Lee
, V.
Lutsker
, R. J.
Maurer
, S. K.
Min
, I.
Mitchell
, C.
Negre
, T. A.
Niehaus
, A. M. N.
Niklasson
, A. J.
Page
, A.
Pecchia
, G.
Penazzi
, M. P.
Persson
, J.
Řeziáč
, C. G.
Sánchez
, M.
Sternberg
, M.
Stöhr
, F.
Stuckenberg
, A.
Tkatchenko
, V. W.-z.
Yu
, and T.
Frauenheim
, “DFTB+, a software package for efficient approximate density functional theory based atomistic simulations
,” J. Chem. Phys.
152
, 124101
(2020
).62.
Y.
Wang
, B. C.
Shepler
, B. J.
Braams
, and J. M.
Bowman
, “Full-dimensional, ab initio potential energy and dipole moment surfaces for water
,” J. Chem. Phys.
131
, 054511
(2009
).63.
Y.
Wang
, X.
Huang
, B. C.
Shepler
, B. J.
Braams
, and J. M.
Bowman
, “Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer
,” J. Chem. Phys.
134
, 094509
(2011
).64.
J.
Tersoff
, “Empirical interatomic potential for carbon, with application to amorphous-carbon
,” Phys. Rev. Lett.
61
, 2879
(1988
).65.
R.
Drautz
, “Atomic cluster expansion for accurate and transferable interatomic potentials
,” Phys. Rev. B
99
, 014104
(2019
).66.
D. P.
Kovács
, C.
van der Oord
, J.
Kucera
, A. E. A.
Allen
, D. J.
Cole
, C.
Ortner
, and G.
Csányi
, “Linear atomic cluster expansion force fields for organic molecules: Beyond RMSE
,” J. Chem. Theory Comput.
17
, 7696
–7711
(2021
).67.
K. A.
Fichthorn
, R. A.
Miron
, Y.
Wang
, and Y.
Tiwary
, “Accelerated molecular dynamics simulation of thin-film growth with the bond-boost method
,” J. Phys.: Condens. Matter
21
, 084212
(2009
).68.
Y.
Zuo
, C.
Chen
, X.
Li
, Z.
Deng
, Y.
Chen
, J.
Behler
, G.
Csányi
, A. V.
Shapeev
, A. P.
Thompson
, M. A.
Wood
, and S. P.
Ong
, “A performance and cost assessment of machine learning interatomic potentials
,” J. Phys. Chem. A
124
, 731
(2021
).69.
F.
Ercolessi
and J. B.
Adams
, “Interatomic potentials from first-principles calculations: The force-matching method
,” Europhys. Lett.
26
, 583
–588
(1994
).70.
W.
Press
, B. P.
Flannery
, S. A.
Teukolsky
, and W. T.
Wetterling
, Numerical Recipes
(Cambridge University Press
, Cambridge
, 1989
).71.
R.
Tibshirani
, “Regression shrinkage and selection via the lasso
,” J. R. Stat. Soc.: Ser. B (Methodol.)
58
, 267
–288
(1996
).72.
J.
Friedman
, T.
Hastie
, and R.
Tibshirani
, “Regularization paths for generalized linear models via coordinate descent
,” J. Stat. Software
33
, 1
(2010
).73.
B.
Efron
, T.
Hastie
, I.
Johnstone
, and R.
Tibshirani
, “Least angle regression
,” Ann. Stat.
32
, 407
–499
(2004
).74.
F.
Pedregosa
, G.
Varoquaux
, A.
Gramfort
, V.
Michel
, B.
Thirion
, O.
Grisel
, M.
Blondel
, P.
Prettenhofer
, R.
Weiss
, V.
Dubourg
et al, “Scikit-learn: Machine learning in python
,” J. Mach. Learn. Res.
12
, 2825
–2830
(2011
).75.
N.
Goldman
and L. E.
Fried
, “Extending the density functional tight binding method to carbon under extreme conditions
,” J. Phys. Chem. C
116
, 2198
–2204
(2012
).76.
A.
Sieck
, T.
Frauenheim
, and K. A.
Jackson
, “Shape transition of medium-sized neutral silicon clusters
,” Phys. Status Solidi B
240
, 537
(2003
).77.
G.
Kresse
and J.
Hafner
, “Ab initio molecular dynamics for liquid metals
,” Phys. Rev. B
47
, 558
–561
(1993
).78.
G.
Kresse
and J.
Hafner
, “Ab initio molecular dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium
,” Phys. Rev. B
49
, 14251
–14271
(1994
).79.
G.
Kresse
and J.
Furthmüller
, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
,” Phys. Rev. B
54
, 11169
–11186
(1996
).80.
P. E.
Blöchl
, “Projector augmented-wave method
,” Phys. Rev. B
50
, 17953
–17979
(1994
).81.
G.
Kresse
and D.
Joubert
, “From ultrasoft pseudopotentials to the projector augmented-wave method
,” Phys. Rev. B
59
, 1758
–1775
(1999
).82.
J. P.
Perdew
, K.
Burke
, and M.
Enzerhof
, “Generalized gradient approximation made simple
,” Phys. Rev. Lett.
77
, 3865
–3868
(1996
).83.
N. D.
Mermin
, “Thermal properties of the inhomogenous electron gas
,” Phys. Rev.
137
, 1441
–1443
(1965
).84.
H. J.
Monkhorst
and J. D.
Pack
, “Special points for Brillouin-zone integrations
,” Phys. Rev. B
13
, 5188
–5192
(1976
).85.
86.
W. G.
Hoover
, Phys. Rev. A
31
, 1695
(1985
).87.
G. J.
Martyna
, M. L.
Klein
, and M.
Tuckerman
, “Nosé-Hoover chains: The canonical ensemble via continuous dynamics
,” J. Chem. Phys.
97
, 2635
–2643
(1992
).88.
See https://pymatgen.org. for software and associated documentation.
89.
K.
Kitabayashi
, K.
Edalati
, H.-W.
Li
, E.
Akiba
, and Z.
Horita
, “Phase transformations in MgH2-TiH2 hydrogen storage system by high-pressure torsion process
,” Adv. Eng. Mater.
22
, 1900027
(2020
).90.
K. V.
Shanavas
, L.
Lindsay
, and D. S.
Parker
, “Electronic structure and electron-phonon coupling in TiH2
,” Sci. Rep.
6
, 28102
(2016
).91.
Q.
Peng
, B.
Yang
, L.
Liu
, C.
Song
, and B.
Friedrich
, “Porous TiAl alloys fabricated by sintering of TiH2 and Al powder mixtures
,” J. Alloys Compd.
656
, 530
–538
(2016
).92.
N.
Goldman
, “Multi-center semi-empirical quantum models for carbon under extreme thermodynamic conditions
,” Chem. Phys. Lett.
622
, 128
–136
(2015
).93.
R.
Podeszwa
, W.
Jankiewicz
, M.
Krzuś
, and H. A.
Witek
, “Correcting long-range electrostatics in DFTB
,” J. Chem. Phys.
150
, 234110
(2019
).94.
J. S.
Smith
, R.
Zubatyuk
, B.
Nebgen
, N.
Lubbers
, K.
Barros
, A. E.
Roitberg
, O.
Isayev
, and S.
Tretiak
, “The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules
,” Sci. Data
7
, 134
(2020
).95.
M.
Gaus
, A.
Goez
, and M.
Elstner
, “Parametrization and benchmark of DFTB3 for organic molecules
,” J. Chem. Theory Comput.
9
, 338
–354
(2013
).96.
J.-D.
Chai
and M.
Head-Gordon
, “Systematic optimization of long-range corrected hybrid density functionals
,” J. Chem. Phys.
128
, 084106
(2008
).97.
J. S.
Smith
, B.
Nebgen
, N.
Lubbers
, O.
Isayev
, and A. E.
Roitberg
, “Less is more: Sampling chemical space with active learning
,” J. Chem. Phys.
148
, 241733
(2018
).98.
S.
Grimme
, M.
Steinmetz
, and M.
Korth
, “How to compute isomerization energies of organic molecules with quantum chemical methods
,” J. Org. Chem.
72
, 2118
–2126
(2007
).99.
H. E.
Sauceda
, M.
Gastegger
, S.
Chmiela
, K.-R.
Müller
, and A.
Tkatchenko
, “Molecular force fields with gradient-domain machine learning (GDML): Comparison and synergies with classical force fields
,” J. Chem. Phys.
153
, 124109
(2020
).100.
Y. X.
Zhao
and I. L.
Spain
, “X-ray diffraction data for graphite to 20 GPa
,” Phys. Rev. B
40
, 993
(1989
).101.
T.
Bučko
, J.
Hafner
, S.
Lebègue
, and J. G.
Ángyán
, “Improved description of the structure of molecular and layered crystals: Ab initio DFT calculations with van der Waals corrections
,” J. Phys. Chem. A
114
, 11814
–11824
(2010
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.