We present a Δ-machine learning model for obtaining Kohn–Sham accuracy from orbital-free density functional theory (DFT) calculations. In particular, we employ a machine-learned force field (MLFF) scheme based on the kernel method to capture the difference between Kohn–Sham and orbital-free DFT energies/forces. We implement this model in the context of on-the-fly molecular dynamics simulations and study its accuracy, performance, and sensitivity to parameters for representative systems. We find that the formalism not only improves the accuracy of Thomas–Fermi–von Weizsäcker orbital-free energies and forces by more than two orders of magnitude but is also more accurate than MLFFs based solely on Kohn–Sham DFT while being more efficient and less sensitive to model parameters. We apply the framework to study the structure of molten Al0.88Si0.12, the results suggesting no aggregation of Si atoms, in agreement with a previous Kohn–Sham study performed at an order of magnitude smaller length and time scales.
REFERENCES
1.
W.
Kohn
and L. J.
Sham
, Phys. Rev.
140
, A1133
(1965
).2.
P.
Hohenberg
and W.
Kohn
, Phys. Rev.
136
, B864
(1964
).3.
K.
Burke
, J. Chem. Phys.
136
, 150901
(2012
).4.
V. L.
Lignères
and E. A.
Carter
, Handbook of Materials Modeling: Methods
(Springer
, 2005
), pp. 137
–148
.5.
M.
Levy
, J. P.
Perdew
, and V.
Sahni
, Phys. Rev. A
30
, 2745
(1984
).6.
K.
Jiang
and M.
Pavanello
, Phys. Rev. B
103
, 245102
(2021
).7.
L. H.
Thomas
, Mathematical Proceedings of the Cambridge Philosophical Society
(Cambridge University Press
, 1927
), Vol. 23
, pp. 542
–548
.8.
E.
Fermi
, Z. Phys.
48
, 73
(1928
).9.
C. V.
Weizsäcker
, Z. Phys.
96
, 431
(1935
).10.
L. A.
Constantin
, E.
Fabiano
, and F.
Della Sala
, J. Chem. Theory Comput.
15
, 3044
(2019
).11.
K.
Luo
, V. V.
Karasiev
, and S.
Trickey
, Phys. Rev. B
98
, 041111
(2018
).12.
L. A.
Constantin
, E.
Fabiano
, and F.
Della Sala
, J. Phys. Chem. Lett.
9
, 4385
(2018
).13.
H. I.
Francisco
, J.
Carmona-Espíndola
, and J. L.
Gázquez
, J. Chem. Phys.
154
, 084107
(2021
).14.
J. P.
Perdew
and L. A.
Constantin
, Phys. Rev. B
75
, 155109
(2007
).15.
L. A.
Constantin
, E.
Fabiano
, and F.
Della Sala
, J. Chem. Theory Comput.
13
, 4228
(2017
).16.
C.
Huang
and E. A.
Carter
, Phys. Rev. B
81
, 045206
(2010
).17.
L. A.
Constantin
, E.
Fabiano
, and F.
Della Sala
, Phys. Rev. B
97
, 205137
(2018
).18.
G. S.
Ho
, V. L.
Lignères
, and E. A.
Carter
, Phys. Rev. B
78
, 045105
(2008
).19.
V. V.
Karasiev
and S. B.
Trickey
, Comput. Phys. Commun.
183
, 2519
(2012
).20.
E.
Chacón
, J.
Alvarellos
, and P.
Tarazona
, Phys. Rev. B
32
, 7868
(1985
).21.
I.
Mazin
, “Soviet physics—Lebedev Institute reports (english translation of Sbornik Kratkie Soobshcheniya po Fizike. AN SSSR
,” arXiv:2209.02807 (Fizicheskii Institut im. P.N. Lebedeva
, 1988
), p. 17
.22.
L.-W.
Wang
and M. P.
Teter
, Phys. Rev. B
45
, 13196
(1992
).23.
Y. A.
Wang
, N.
Govind
, and E. A.
Carter
, Phys. Rev. B
60
, 16350
(1999
).24.
K. M.
Carling
and E. A.
Carter
, Modell. Simul. Mater. Sci. Eng.
11
, 339
(2003
).25.
B.
Zhou
, V. L.
Ligneres
, and E. A.
Carter
, J. Chem. Phys.
122
, 044103
(2005
).26.
G.
Ho
, M. T.
Ong
, K. J.
Caspersen
, and E. A.
Carter
, Phys. Chem. Chem. Phys.
9
, 4951
(2007
).27.
I.
Mazin
and D.
Singh
, Phys. Rev. B
57
, 6879
(1998
).28.
X.
Shao
, W.
Mi
, and M.
Pavanello
, Phys. Rev. B
104
, 045118
(2021
).29.
W.
Mi
, A.
Genova
, and M.
Pavanello
, J. Chem. Phys.
148
, 184107
(2018
).30.
Q.
Xu
, C.
Ma
, W.
Mi
, Y.
Wang
, and Y.
Ma
, Nat. Commun.
13
, 1385
(2022
).31.
I.
Shin
and E. A.
Carter
, J. Chem. Phys.
140
, 18A531
(2014
).32.
P.
Golub
and S.
Manzhos
, Phys. Chem. Chem. Phys.
21
, 378
(2019
).33.
M.
Alghadeer
, A.
Al-Aswad
, and F. H.
Alharbi
, Phys. Lett. A
414
, 127621
(2021
).34.
M.
Fujinami
, R.
Kageyama
, J.
Seino
, Y.
Ikabata
, and H.
Nakai
, Chem. Phys. Lett.
748
, 137358
(2020
).35.
36.
37.
K.
Ryczko
, S. J.
Wetzel
, R. G.
Melko
, and I.
Tamblyn
, J. Chem. Theory Comput.
18
, 1122
(2022
).38.
S.
Kumar
, B.
Sadigh
, S.
Zhu
, P.
Suryanarayana
, S.
Hamel
, B.
Gallagher
, V.
Bulatov
, J.
Klepeis
, and A.
Samanta
, J. Chem. Phys.
156
, 024107
(2022
).39.
R.
Meyer
, M.
Weichselbaum
, and A. W.
Hauser
, J. Chem. Theory Comput.
16
, 5685
(2020
).40.
J. C.
Snyder
, M.
Rupp
, K.
Hansen
, L.
Blooston
, K.-R.
Müller
, and K.
Burke
, J. Chem. Phys.
139
, 224104
(2013
).41.
G. R.
Schleder
, A. C.
Padilha
, C. M.
Acosta
, M.
Costa
, and A.
Fazzio
, J. Phys.: Mater.
2
, 032001
(2019
).42.
I.
Poltavsky
and A.
Tkatchenko
, J. Phys. Chem. Lett.
12
, 6551
(2021
).43.
O. T.
Unke
, S.
Chmiela
, H. E.
Sauceda
, M.
Gastegger
, I.
Poltavsky
, K. T.
Schütt
, A.
Tkatchenko
, and K.-R.
Müller
, Chem. Rev.
121
, 10142
(2021
).44.
J. M.
Bowman
, C.
Qu
, R.
Conte
, A.
Nandi
, P. L.
Houston
, and Q.
Yu
, J. Chem. Theory Comput.
19
, 1
(2022
).45.
M.
Bogojeski
, L.
Vogt-Maranto
, M. E.
Tuckerman
, K.-R.
Müller
, and K.
Burke
, Nat. Commun.
11
, 5223
(2020
).46.
A.
Nandi
, C.
Qu
, P. L.
Houston
, R.
Conte
, and J. M.
Bowman
, J. Chem. Phys.
154
, 051102
(2021
).47.
C.
Qu
, P. L.
Houston
, R.
Conte
, A.
Nandi
, and J. M.
Bowman
, J. Phys. Chem. Lett.
12
, 4902
(2021
).48.
P.
Zaspel
, B.
Huang
, H.
Harbrecht
, and O. A.
von Lilienfeld
, J. Chem. Theory Comput.
15
, 1546
(2019
).49.
R.
Ramakrishnan
, P. O.
Dral
, M.
Rupp
, and O. A.
Von Lilienfeld
, J. Chem. Theory Comput.
11
, 2087
(2015
).50.
Z.
Qiao
, M.
Welborn
, A.
Anandkumar
, F. R.
Manby
, and T. F.
Miller
, J. Chem. Phys.
153
, 124111
(2020
).51.
P.
Liu
, C.
Verdi
, F.
Karsai
, and G.
Kresse
, Phys. Rev. B
105
, L060102
(2022
).52.
C.
Verdi
, L.
Ranalli
, C.
Franchini
, and G.
Kresse
, Phys. Rev. Mater.
7
, L030801
(2023
).53.
C.
Qu
, Q.
Yu
, R.
Conte
, P. L.
Houston
, A.
Nandi
, and J. M.
Bomwan
, Digital Discovery
1
, 658
(2022
).54.
C.
Qu
, Q.
Yu
, P.
Houston
, R.
Conte
, A.
Nandi
, and J.
Bowman
, “Many-body Δ-machine learning brings the accuracy of conventional force field to coupled cluster: Application to the TTM2.1 water force field
,” Research Square
(2022
).55.
Q.
Yu
, C.
Qu
, P. L.
Houston
, A.
Nandi
, P.
Pandey
, R.
Conte
, and J. M.
Bowman
, J. Phys. Chem. Lett.
14
, 8077
(2023
).56.
M.
Levy
and H.
Ou-Yang
, Phys. Rev. A
38
, 625
(1988
).57.
A.
Holas
and N.
March
, Phys. Rev. A
44
, 5521
(1991
).58.
W.
Mi
, K.
Luo
, S.
Trickey
, and M.
Pavanello
, Chem. Rev.
123
, 12039
(2023
).59.
A.
Gangwar
, S. S.
Bulusu
, and A.
Banerjee
, J. Chem. Phys.
159
, 124114
(2023
).60.
T.
Sjostrom
and J.
Daligault
, Phys. Rev. Lett.
113
, 155006
(2014
).61.
C.
Gao
, S.
Zhang
, W.
Kang
, C.
Wang
, P.
Zhang
, and X.
He
, Phys. Rev. B
94
, 205115
(2016
).62.
J.
Danel
, L.
Kazandjian
, and R.
Piron
, Phys. Rev. E
98
, 043204
(2018
).63.
D.
Sheppard
, J. D.
Kress
, S.
Crockett
, L. A.
Collins
, and M. P.
Desjarlais
, Phys. Rev. E
90
, 063314
(2014
).64.
F.
Lambert
, J.
Clérouin
, and G.
Zérah
, Phys. Rev. E
73
, 016403
(2006
).65.
A.
Sharma
, S.
Hamel
, M.
Bethkenhagen
, J. E.
Pask
, and P.
Suryanarayana
, J. Chem. Phys.
153
, 034112
(2020
).66.
B.
Thapa
, X.
Jing
, J. E.
Pask
, P.
Suryanarayana
, and I. I.
Mazin
, J. Chem. Phys.
158
, 214112
(2023
).67.
A. P.
Bartók
, M. C.
Payne
, R.
Kondor
, and G.
Csányi
, Phys. Rev. Lett.
104
, 136403
(2010
).68.
A. P.
Bartók
, R.
Kondor
, and G.
Csányi
, Phys. Rev. B
87
, 184115
(2013
).69.
J.
Behler
and M.
Parrinello
, Phys. Rev. Lett.
98
, 146401
(2007
).70.
K.
Kaufmann
and W.
Baumeister
, J. Phys. B: At., Mol. Opt. Phys.
22
, 1
(1989
).71.
R.
Jinnouchi
, F.
Karsai
, and G.
Kresse
, Phys. Rev. B
100
, 014105
(2019
).72.
C. M.
Bishop
and N. M.
Nasrabadi
, Pattern Recognition and Machine Learning
(Springer
, 2006
), Vol. 4
.73.
S.
Ghosh
and P.
Suryanarayana
, Comput. Phys. Commun.
212
, 189
(2017
).74.
S.
Ghosh
and P.
Suryanarayana
, Comput. Phys. Commun.
216
, 109
(2017
).75.
Q.
Xu
, A.
Sharma
, B.
Comer
, H.
Huang
, E.
Chow
, A. J.
Medford
, J. E.
Pask
, and P.
Suryanarayana
, SoftwareX
15
, 100709
(2021
).76.
B.
Zhang
, X.
Jing
, Q.
Xu
, S.
Kumar
, A.
Sharma
, L.
Erlandson
, S. J.
Sahoo
, E.
Chow
, A. J.
Medford
, J. E.
Pask
et al, arXiv:2305.07679 (2023
).77.
78.
T. A.
Young
, T.
Johnston-Wood
, V. L.
Deringer
, and F.
Duarte
, Chem. Sci.
12
, 10944
(2021
).79.
P.
Minary
, G. J.
Martyna
, and M. E.
Tuckerman
, J. Chem. Phys.
118
, 2510
(2003
).80.
D.
Hamann
, Phys. Rev. B
88
, 085117
(2013
).81.
M. F.
Shojaei
, J. E.
Pask
, A. J.
Medford
, and P.
Suryanarayana
, Comput. Phys. Commun.
283
, 108594
(2023
).82.
J. P.
Perdew
and A.
Zunger
, Phys. Rev. B
23
, 5048
(1981
).83.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, Phys. Rev. Lett.
77
, 3865
(1996
).84.
S.
Ghosh
and P.
Suryanarayana
, J. Comput. Phys.
307
, 634
(2016
).85.
P.
Suryanarayana
and D.
Phanish
, J. Comput. Phys.
275
, 524
(2014
).86.
C. F. v.
Weizsäcker
, Z. Phys.
96
, 431
(1935
).87.
B.
Zhou
, Y.
Alexander Wang
, and E. A.
Carter
, Phys. Rev. B
69
, 125109
(2004
).88.
Y.
Tomishima
and K.
Yonei
, J. Phys. Soc. Jpn.
21
, 142
(1966
).89.
K.
Tran
, W.
Neiswanger
, J.
Yoon
, Q.
Zhang
, E.
Xing
, and Z. W.
Ulissi
, Mach. Learn.: Sci. Technol.
1
, 025006
(2020
).90.
P.
Pernot
, J. Chem. Phys.
157
, 144103
(2022
).91.
Y.
Hu
, J.
Musielewicz
, Z. W.
Ulissi
, and A. J.
Medford
, Mach. Learn.: Sci. Technol.
3
, 045028
(2022
).92.
U.
Dahlborg
, M.
Besser
, M.
Calvo-Dahlborg
, G.
Cuello
, C.
Dewhurst
, M. J.
Kramer
, J. R.
Morris
, and D.
Sordelet
, J. Non-Cryst. Solids
353
, 3005
(2007
).93.
K.
Khoo
, T.-L.
Chan
, M.
Kim
, and J. R.
Chelikowsky
, Phys. Rev. B
84
, 214203
(2011
).94.
X.
Huang
, X.
Dong
, L.
Liu
, and P.
Li
, J. Non-Cryst. Solids
503–504
, 182
(2019
).95.
A.
Sharma
, A.
Metere
, P.
Suryanarayana
, L.
Erlandson
, E.
Chow
, and J. E.
Pask
, J. Chem. Phys.
158
, 204117
(2023
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
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