Modern semiempirical electronic structure methods have considerable promise in drug discovery as universal “force fields” that can reliably model biological and drug-like molecules, including alternative tautomers and protonation states. Herein, we compare the performance of several neglect of diatomic differential overlap-based semiempirical (MNDO/d, AM1, PM6, PM6-D3H4X, PM7, and ODM2), density-functional tight-binding based (DFTB3, DFTB/ChIMES, GFN1-xTB, and GFN2-xTB) models with pure machine learning potentials (ANI-1x and ANI-2x) and hybrid quantum mechanical/machine learning potentials (AIQM1 and QDπ) for a wide range of data computed at a consistent ωB97X/6-31G* level of theory (as in the ANI-1x database). This data includes conformational energies, intermolecular interactions, tautomers, and protonation states. Additional comparisons are made to a set of natural and synthetic nucleic acids from the artificially expanded genetic information system that has important implications for the design of new biotechnology and therapeutics. Finally, we examine the acid/base chemistry relevant for RNA cleavage reactions catalyzed by small nucleolytic ribozymes, DNAzymes, and ribonucleases. Overall, the hybrid quantum mechanical/machine learning potentials appear to be the most robust for these datasets, and the recently developed QDπ model performs exceptionally well, having especially high accuracy for tautomers and protonation states relevant to drug discovery.

1.
T.-S.
Lee
,
B. K.
Allen
,
T. J.
Giese
,
Z.
Guo
,
P.
Li
,
C.
Lin
,
T. D.
McGee
, Jr.
,
D. A.
Pearlman
,
B. K.
Radak
,
Y.
Tao
,
H.-C.
Tsai
,
H.
Xu
,
W.
Sherman
, and
D. M.
York
, “
Alchemical binding free energy calculations in AMBER20: Advances and best practices for drug discovery
,”
J. Chem. Inf. Model.
60
,
5595
5623
(
2020
).
2.
W. L.
Jorgensen
, “
Efficient drug lead discovery and optimization
,”
Acc. Chem. Res.
42
,
724
733
(
2009
).
3.
D. J.
Cole
,
J. T.
Horton
,
L.
Nelson
, and
V.
Kurdekar
, “
The future of force fields in computer-aided drug design
,”
Future Med. Chem.
11
,
2359
2363
(
2019
).
4.
A. D.
MacKerell
, Jr.
, “
Empirical force fields for biological macromolecules: Overview and issues
,”
J. Comput. Chem.
25
,
1584
1604
(
2004
).
5.
K.
Lindorff-Larsen
,
P.
Maragakis
,
S.
Piana
,
M. P.
Eastwood
,
R. O.
Dror
, and
D. E.
Shaw
, “
Systematic validation of protein force fields against experimental data
,”
PLoS One
7
,
e32131
(
2012
).
6.
S.
Piana
,
J. L.
Klepeis
, and
D. E.
Shaw
, “
Assessing the accuracy of physical models used in protein-folding simulations: Quantitative evidence from long molecular dynamics simulations
,”
Curr. Opin. Struct. Biol.
24
,
98
105
(
2014
).
7.
W. L.
Jorgensen
,
J.
Chandrasekhar
,
J. D.
Madura
,
R. W.
Impey
, and
M. L.
Klein
, “
Comparison of simple potential functions for simulating liquid water
,”
J. Chem. Phys.
79
,
926
935
(
1983
).
8.
H. W.
Horn
,
W. C.
Swope
,
J. W.
Pitera
,
J. D.
Madura
,
T. J.
Dick
,
G. L.
Hura
, and
T.
Head-Gordon
, “
Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew
,”
J. Chem. Phys.
120
,
9665
9678
(
2004
).
9.
Y.
Wu
,
H. L.
Tepper
, and
G. A.
Voth
, “
Flexible simple point-charge water model with improved liquid-state properties
,”
J. Chem. Phys.
124
,
024503
(
2006
).
10.
S.
Izadi
,
R.
Anandakrishnan
, and
A. V.
Onufriev
, “
Building water models: A different approach
,”
J. Phys. Chem. Lett.
5
,
3863
3871
(
2014
).
11.
S.
Izadi
and
A. V.
Onufriev
, “
Accuracy limit of rigid 3-point water models
,”
J. Chem. Phys.
145
,
074501
074510
(
2016
).
12.
I. S.
Joung
and
T. E.
Cheatham
 III
, “
Molecular dynamics simulations of the dynamic and energetic properties of alkali and halide ions using water-model-specific ion parameters
,”
J. Phys. Chem. B
113
,
13279
13290
(
2009
).
13.
P.
Li
,
B. P.
Roberts
,
D. K.
Chakravorty
, and
K. M.
Merz
, Jr.
, “
Rational design of particle mesh Ewald compatible Lennard-Jones parameters for +2 metal cations in explicit solvent
,”
J. Chem. Theory Comput.
9
,
2733
2748
(
2013
).
14.
P.
Li
and
K. M.
Merz
, Jr.
, “
Taking into account the ion-induced dipole interaction in the nonbonded model of ions
,”
J. Chem. Theory Comput.
10
,
289
297
(
2014
).
15.
P.
Li
and
K. M.
Merz
, “
Metal ion modeling using classical mechanics
,”
Chem. Rev.
117
,
1564
1686
(
2017
).
16.
P. E. M.
Lopes
,
O.
Guvench
, and
A. D.
MacKerell
, Jr.
, “
Current status of protein force fields for molecular dynamics simulations
,”
Methods Mol. Biol.
1215
,
47
71
(
2015
).
17.
C.
Tian
,
K.
Kasavajhala
,
K. A. A.
Belfon
,
L.
Raguette
,
H.
Huang
,
A. N.
Migues
,
J.
Bickel
,
Y.
Wang
,
J.
Pincay
,
Q.
Wu
, and
C.
Simmerling
, “
ff19SB: Amino-acid-specific protein backbone parameters trained against quantum mechanics energy surfaces in solution
,”
J. Chem. Theory Comput.
16
,
528
552
(
2020
).
18.
Y. C.
Martin
, “
Experimental and pKa prediction aspects of tautomerism of drug-like molecules
,”
Drug Discovery Today: Technol.
27
,
59
64
(
2018
).
19.
F.
Milletti
and
A.
Vulpetti
, “
Tautomer preference in PDB complexes and its impact on structure-based drug discovery
,”
J. Chem. Inf. Model.
50
,
1062
1074
(
2010
).
20.
J. I.
Wells
,
Pharmaceutical Preformulation: The Physicochemical Properties of Drug Substances
(
E. Horwood
,
Chichester, UK
,
1988
).
21.
C. D.
Navo
and
G.
Jiménez-Osés
, “
Computer prediction of pKa values in small molecules and proteins
,”
ACS Med. Chem. Lett.
12
,
1624
1628
(
2021
).
22.
W.
Thiel
, “
Semiempirical quantum–chemical methods
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
4
,
145
157
(
2014
).
23.
K.
Kříž
and
J.
Řezáč
, “
Benchmarking of semiempirical quantum-mechanical methods on systems relevant to computer-aided drug design
,”
J. Chem. Inf. Model.
60
,
1453
1460
(
2020
).
24.
V.
Khanna
and
S.
Ranganathan
, “
Physicochemical property space distribution among human metabolites, drugs and toxins
,”
BMC Bioinf.
10
,
S10
(
2009
).
25.
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
).
26.
K.
Nam
,
J.
Gao
, and
D. M.
York
, “
An efficient linear-scaling Ewald method for long-range electrostatic interactions in combined QM/MM calculations
,”
J. Chem. Theory Comput.
1
,
2
13
(
2005
).
27.
T. J.
Giese
,
M. T.
Panteva
,
H.
Chen
, and
D. M.
York
, “
Multipolar Ewald methods, 2: Applications using a quantum mechanical force field
,”
J. Chem. Theory Comput.
11
,
451
461
(
2015
).
28.
T. J.
Giese
and
D. M.
York
, “
Ambient-potential composite Ewald method for ab initio quantum mechanical/molecular mechanical molecular dynamics simulation
,”
J. Chem. Theory Comput.
12
,
2611
2632
(
2016
).
29.
J. T.
Margraf
,
M.
Hennemann
, and
T.
Clark
, “
EMPIRE: A highly parallel semiempirical molecular orbital program: 3: Born-Oppenheimer molecular dynamics
,”
J. Mol. Model.
26
,
43
(
2020
).
30.
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.
Řezáč
,
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
).
31.
T. J.
Giese
and
D. M.
York
, “
Development of a robust indirect approach for MM → QM free energy calculations that combines force-matched reference potential and Bennett’s acceptance ratio methods
,”
J. Chem. Theory Comput.
15
,
5543
5562
(
2019
).
32.
F. L.
Kearns
,
P. S.
Hudson
,
H. L.
Woodcock
, and
S.
Boresch
, “
Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities
,”
J. Comput. Chem.
38
,
1376
1388
(
2017
).
33.
S.
Boresch
and
H. L.
Woodcock
, “
Convergence of single-step free energy perturbation
,”
Mol. Phys.
115
,
1200
1213
(
2017
).
34.
P. S.
Hudson
,
F.
Aviat
,
R.
Meana-Pañeda
,
L.
Warrensford
,
B. C.
Pollard
,
S.
Prasad
,
M. R.
Jones
,
H. L.
Woodcock
, and
B. R.
Brooks
, “
Obtaining QM/MM binding free energies in the SAMPL8 drugs of abuse challenge: Indirect approaches
,”
J. Comput.-Aided Mol. Des.
36
,
263
277
(
2022
).
35.
A.
Schöller
,
F.
Kearns
,
H. L.
Woodcock
, and
S.
Boresch
, “
Optimizing the calculation of free energy differences in nonequilibrium work SQM/MM switching simulations
,”
J. Phys. Chem. B
126
,
2798
2811
(
2022
).
36.
G.
Arya
, “
Models for recovering the energy landscape of conformational transitions from single-molecule pulling experiments
,”
Mol. Simul.
42
,
1102
1115
(
2016
).
37.
A. N.
Naganathan
,
U.
Doshi
, and
V.
Muñoz
, “
Protein folding kinetics: Barrier effects in chemical and thermal denaturation experiments
,”
J. Am. Chem. Soc.
129
,
5673
5682
(
2007
).
38.
J.
Basran
,
S.
Patel
,
M. J.
Sutcliffe
, and
N. S.
Scrutton
, “
Importance of barrier shape in enzyme-catalyzed reactions
,”
J. Biol. Chem.
276
,
6234
6242
(
2001
).
39.
J.
Behler
, “
Perspective: Machine learning potentials for atomistic simulations
,”
J. Chem. Phys.
145
,
170901
(
2016
).
40.
K. T.
Butler
,
D. W.
Davies
,
H.
Cartwright
,
O.
Isayev
, and
A.
Walsh
, “
Machine learning for molecular and materials science
,”
Nature
559
,
547
555
(
2018
).
41.
F.
Noé
,
A.
Tkatchenko
,
K.-R.
Müller
, and
C.
Clementi
, “
Machine learning for molecular simulation
,”
Annu. Rev. Phys. Chem.
71
,
361
390
(
2020
).
42.
M.
Pinheiro
, Jr.
,
F.
Ge
,
N.
Ferré
,
P. O.
Dral
, and
M.
Barbatti
, “
Choosing the right molecular machine learning potential
,”
Chem. Sci.
12
,
14396
14413
(
2021
).
43.
S.
Manzhos
and
T.
Carrington
, Jr.
, “
Neural network potential energy surfaces for small molecules and reactions
,”
Chem. Rev.
121
,
10187
10217
(
2021
).
44.
J.
Zeng
,
L.
Cao
, and
T.
Zhu
, “
Neural network potentials
,” in
Quantum Chemistry in the Age of Machine Learning
, edited by
P. O.
Dral
(
Elsevier
,
2022
) Chap. 12, pp.
279
294
.
45.
X.
Pan
,
J.
Yang
,
R.
Van
,
E.
Epifanovsky
,
J.
Ho
,
J.
Huang
,
J.
Pu
,
Y.
Mei
,
K.
Nam
, and
Y.
Shao
, “
Machine-learning-assisted free energy simulation of solution-phase and enzyme reactions
,”
J. Chem. Theory Comput.
17
,
5745
5758
(
2021
).
46.
P.
Zheng
,
R.
Zubatyuk
,
W.
Wu
,
O.
Isayev
, and
P. O.
Dral
, “
Artificial intelligence-enhanced quantum chemical method with broad applicability
,”
Nat. Commun.
12
,
7022
(
2021
).
47.
J.
Zeng
,
T. J.
Giese
,
Ş.
Ekesan
, and
D. M.
York
, “
Development of range-corrected deep learning potentials for fast, accurate quantum mechanical/molecular mechanical simulations of chemical reactions in solution
,”
J. Chem. Theory Comput.
17
,
6993
7009
(
2021
).
48.
T. J.
Giese
,
J.
Zeng
,
Ş.
Ekesan
, and
D. M.
York
, “
Combined QM/MM, machine learning path integral approach to compute free energy profiles and kinetic isotope effects in RNA cleavage reactions
,”
J. Chem. Theory Comput.
18
,
4304
4317
(
2022
).
49.
C. L.
Gómez-Flores
,
D.
Maag
,
M.
Kansari
,
V.-Q.
Vuong
,
S.
Irle
,
F.
Gräter
,
T.
Kubař
, and
M.
Elstner
, “
Accurate free energies for complex condensed-phase reactions using an artificial neural network corrected DFTB/MM methodology
,”
J. Chem. Theory Comput.
18
,
1213
1226
(
2022
).
50.
J.
Böser
,
T.
Kubař
,
M.
Elstner
, and
D.
Maag
, “
Reduction pathway of glutaredoxin 1 investigated with QM/MM molecular dynamics using a neural network correction
,”
J. Chem. Phys.
157
,
154104
(
2022
).
51.
P. O.
Dral
,
T.
Zubatiuk
, and
B.-X.
Xue
, “
Learning from multiple quantum chemical methods: Δ-learning, transfer learning, co-kriging, and beyond
,” in
Quantum Chemistry in the Age of Machine Learning
, edited by
P. O.
Dral
(
Elsevier
,
2022
) Chap. 21, pp.
491
507
.
52.
J.
Behler
and
M.
Parrinello
, “
Generalized neural-network representation of high-dimensional potential-energy surfaces
,”
Phys. Rev. Lett.
98
,
146401
146404
(
2007
).
53.
A. P.
Bartók
,
M. C.
Payne
,
R.
Kondor
, and
G.
Csányi
, “
Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons
,”
Phys. Rev. Lett.
104
,
136403
(
2010
).
54.
J.
Behler
, “
Atom-centered symmetry functions for constructing high-dimensional neural network potentials
,”
J. Chem. Phys.
134
,
074106
(
2011
).
55.
M.
Gastegger
,
L.
Schwiedrzik
,
M.
Bittermann
,
F.
Berzsenyi
, and
P.
Marquetand
, “
wACSF—Weighted atom-centered symmetry functions as descriptors in machine learning potentials
,”
J. Chem. Phys.
148
,
241709
(
2018
).
56.
S.
Chmiela
,
A.
Tkatchenko
,
H. E.
Sauceda
,
I.
Poltavsky
,
K. T.
Schütt
, and
K.-R.
Müller
, “
Machine learning of accurate energy-conserving molecular force fields
,”
Sci. Adv.
3
,
1603015
(
2017
).
57.
K. T.
Schütt
,
F.
Arbabzadah
,
S.
Chmiela
,
K. R.
Müller
, and
A.
Tkatchenko
, “
Quantum-chemical insights from deep tensor neural networks
,”
Nat. Commun.
8
,
13890
(
2017
).
58.
K. T.
Schütt
,
H. E.
Sauceda
,
P.-J.
Kindermans
,
A.
Tkatchenko
, and
K.-R.
Müller
, “
SchNet – A deep learning architecture for molecules and materials
,”
J. Chem. Phys.
148
,
241722
(
2018
).
59.
X.
Chen
,
M. S.
Jørgensen
,
J.
Li
, and
B.
Hammer
, “
Atomic energies from a convolutional neural network
,”
J. Chem. Theory Comput.
14
,
3933
3942
(
2018
).
60.
L.
Zhang
,
J.
Han
,
H.
Wang
,
R.
Car
, and
W.
E
, “
Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics
,”
Phys. Rev. Lett.
120
,
143001
(
2018
).
61.
L.
Zhang
,
J.
Han
,
H.
Wang
,
W.
Saidi
,
R.
Car
, and
W.
E
, “
End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems
,” in
Advances in Neural Information Processing Systems 31
, edited by
S.
Bengio
,
H.
Wallach
,
H.
Larochelle
,
K.
Grauman
,
N.
Cesa-Bianchi
, and
R.
Garnett
(
Curran Associates, Inc.
,
2018
), pp.
4436
4446
.
62.
Y.
Zhang
,
C.
Hu
, and
B.
Jiang
, “
Embedded atom neural network potentials: Efficient and accurate machine learning with a physically inspired representation
,”
J. Phys. Chem. Lett.
10
,
4962
4967
(
2019
).
63.
J. S.
Smith
,
O.
Isayev
, and
A. E.
Roitberg
, “
ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost
,”
Chem. Sci.
8
,
3192
3203
(
2017
).
64.
O.
Unke
and
M.
Meuwly
, “
PhysNet: A neural network for predicting energies, forces, dipole moments, and partial charges
,”
J. Chem. Theory Comput.
15
,
3678
3693
(
2019
).
65.
Z. L.
Glick
,
D. P.
Metcalf
,
A.
Koutsoukas
,
S. A.
Spronk
,
D. L.
Cheney
, and
C. D.
Sherrill
, “
AP-Net: An atomic-pairwise neural network for smooth and transferable interaction potentials
,”
J. Chem. Phys.
153
,
044112
(
2020
).
66.
T.
Zubatiuk
and
O.
Isayev
, “
Development of multimodal machine learning potentials: Toward a physics-aware artificial intelligence
,”
Acc. Chem. Res.
54
,
1575
1585
(
2021
).
67.
E. R.
Khajehpasha
,
J. A.
Finkler
,
T. D.
Kühne
, and
S. A.
Ghasemi
, “
CENT2: Improved charge equilibration via neural network technique
,”
Phys. Rev. B
105
,
144106
(
2022
).
68.
Y.
Hirano
,
N.
Okimoto
,
S.
Fujita
, and
M.
Taiji
, “
Molecular dynamics study of conformational changes of tankyrase 2 binding subsites upon ligand binding
,”
ACS Omega
6
,
17609
17620
(
2021
).
69.
P. W.
Kenny
, “
Hydrogen-bond donors in drug design
,”
J. Med. Chem.
65
,
14261
14275
(
2022
).
70.
H.
Yuki
,
Y.
Tanaka
,
M.
Hata
,
H.
Ishikawa
,
S.
Neya
, and
T.
Hoshino
, “
Implementation of π–π interactions in molecular dynamics simulation
,”
J. Comput. Chem.
28
,
1091
1099
(
2007
).
71.
T.
Chen
,
M.
Li
, and
J.
Liu
, “
π–π Stacking interaction: A nondestructive and facile means in material engineering for bioapplications
,”
Cryst. Growth Des.
18
,
2765
2783
(
2018
).
72.
M.
Mohebifar
,
E. R.
Johnson
, and
C. N.
Rowley
, “
Evaluating force-field London dispersion coefficients using the exchange-hole dipole moment model
,”
J. Chem. Theory Comput.
13
,
6146
6157
(
2017
).
73.
L. I.
Vazquez-Salazar
,
E. D.
Boittier
,
O. T.
Unke
, and
M.
Meuwly
, “
Impact of the characteristics of quantum chemical databases on machine learning prediction of tautomerization energies
,”
J. Chem. Theory Comput.
17
,
4769
4785
(
2021
).
74.
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
241743
(
2018
).
75.
J.
Smith
,
B.
Nebgen
,
R.
Zubatyuk
,
N.
Lubbers
,
C.
Devereux
,
K.
Barros
,
S.
Tretiak
,
O.
Isayev
, and
A.
Roitberg
, “
Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning
,”
Nat. Commun.
10
,
2903
(
2019
).
76.
C.
Devereux
,
J. S.
Smith
,
K. K.
Huddleston
,
K.
Barros
,
R.
Zubatyuk
,
O.
Isayev
, and
A. E.
Roitberg
, “
Extending the applicability of the ANI deep learning molecular potential to sulfur and halogens
,”
J. Chem. Theory Comput.
16
,
4192
4202
(
2020
).
77.
J. Z.
amd Yujun Tao
,
T. J.
Giese
, and
D. M.
York
, “
QDπ: A quantum deep potential interaction model for drug discovery
,”
J. Chem. Theory Comput.
19
,
1261
1275
(
2023
).
78.
P. O.
Dral
,
X.
Wu
, and
W.
Thiel
, “
Semiempirical quantum-chemical methods with orthogonalization and dispersion corrections
,”
J. Chem. Theory Comput.
15
,
1743
1760
(
2019
).
79.
Y.
Chen
,
Y.
Ou
,
P.
Zheng
,
Y.
Huang
,
F.
Ge
, and
P. O.
Dral
, “
Benchmark of general-purpose machine learning-based quantum mechanical method AIQM1 on reaction barrier heights
,”
J. Chem. Phys.
158
,
074103
(
2023
).
80.
Y.
Yang
,
H.
Yu
,
D. M.
York
,
Q.
Cui
, and
M.
Elstner
, “
Extension of the self-consistent-charge density-functional tight-binding method: Third-order expansion of the density functional theory total energy and introduction of a modified effective coulomb interaction
,”
J. Phys. Chem. A
111
,
10861
10873
(
2007
).
81.
M.
Gaus
,
X.
Lu
,
M.
Elstner
, and
Q.
Cui
, “
Parameterization of DFTB3/3OB for sulfur and phosphorus for chemical and biological applications
,”
J. Chem. Theory Comput.
10
,
1518
1537
(
2014
).
82.
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
).
83.
W.
Liang
,
J.
Zeng
,
D. M.
York
,
L.
Zhang
, and
H.
Wang
, “
Learning DeePMD-kit: A guide to building deep potential models
,” in
A Practical Guide to Recent Advances in Multiscale Modeling and Simulation of Biomolecules
, edited by
Y.
Wang
and
R.
Zhou
(
AIP Publishing
,
2023
), Chap. 6, pp.
6–1
6–20
.
84.
Z.
Yang
,
D.
Hutter
,
P.
Sheng
,
A. M.
Sismour
, and
S. A.
Benner
, “
Artificially expanded genetic information system: A new base pair with an alternative hydrogen bonding pattern
,”
Nucleic Acids Res.
34
,
6095
6101
(
2006
).
85.
L.
Eberlein
,
F. R.
Beierlein
,
N. J. R.
van Eikema Hommes
,
A.
Radadiya
,
J.
Heil
,
S. A.
Benner
,
T.
Clark
,
S. M.
Kast
, and
N. G. J.
Richards
, “
Tautomeric equilibria of nucleobases in the hachimoji expanded genetic alphabet
,”
J. Chem. Theory Comput.
16
,
2766
2777
(
2020
).
86.
E.
Biondi
and
S. A.
Benner
, “
Artificially expanded genetic information systems for new aptamer technologies
,”
Biomedicines
6
,
53
(
2018
).
87.
B.
Behera
,
P.
Das
, and
N. R.
Jena
, “
Accurate base pair energies of artificially expanded genetic information systems (AEGIS): Clues for their mutagenic characteristics
,”
J. Phys. Chem. B
123
,
6728
6739
(
2019
).
88.
C. A.
Jerome
,
S.
Hoshika
,
K. M.
Bradley
,
S. A.
Benner
, and
E.
Biondi
, “
In vitro evolution of ribonucleases from expanded genetic alphabets
,”
Proc. Natl. Acad. Sci. U. S. A.
119
,
e2208261119
(
2022
).
89.
M. J. S.
Dewar
and
W.
Thiel
, “
A semiempirical model for the two-Center repulsion integrals in the NDDO approximation
,”
Theor. Chim. Acta
46
,
89
104
(
1977
).
90.
M. J. S.
Dewar
,
E.
Zoebisch
,
E. F.
Healy
, and
J. J. P.
Stewart
, “
Development and use of quantum mechanical molecular models. 76. AM1: A new general purpose quantum mechanical molecular model
.”
J. Am. Chem. Soc.
107
,
3902
3909
(
1985
).
91.
J. J. P.
Stewart
, “
Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements
,”
J. Mol. Model.
13
,
1173
1213
(
2007
).
92.
J.
R̆ezác̆
and
P.
Hobza
, “
Advanced corrections of hydrogen bonding and dispersion for semiempirical quantum mechanical methods
,”
J. Chem. Theory Comput.
8
,
141
151
(
2012
).
93.
J.
Řezáč
and
P.
Hobza
, “
A halogen-bonding correction for the semiempirical PM6 method
,”
Chem. Phys. Lett.
506
,
286
289
(
2011
).
94.
J. J. P.
Stewart
, “
Optimization of parameters for semiempirical methods VI: More modifications to the NDDO approximations and re-optimization of parameters
,”
J. Mol. Model.
19
,
1
32
(
2013
).
95.
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
948
(
2011
).
96.
S.
Grimme
,
C.
Bannwarth
, and
P.
Shushkov
, “
A robust and accurate tight-binding quantum chemical method for structures, vibrational frequencies, and noncovalent interactions of large molecular systems parametrized for all spd-block elements (Z = 1–86)
,”
J. Chem. Theory Comput.
13
,
1989
2009
(
2017
).
97.
C.
Bannwarth
,
S.
Ehlert
, and
S.
Grimme
, “
GFN2-xTB—An accurate and broadly parametrized self-consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions
,”
J. Chem. Theory Comput.
15
,
1652
1671
(
2019
).
98.
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
).
99.
J.-D.
Chai
and
M.
Head-Gordon
, “
Systematic optimization of long-range corrected hybrid density functionals
,”
J. Chem. Phys.
128
,
084106
(
2008
).
100.
P. C.
Bevilacqua
,
M. E.
Harris
,
J. A.
Piccirilli
,
C.
Gaines
,
A.
Ganguly
,
K.
Kostenbader
,
Ş.
Ekesan
, and
D. M.
York
, “
An ontology for facilitating discussion of catalytic strategies of RNA-cleaving enzymes
,”
ACS Chem. Biol.
14
,
1068
1076
(
2019
).
101.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
,
G. E.
Scuseria
,
M. A.
Robb
,
J. R.
Cheeseman
,
G.
Scalmani
,
V.
Barone
,
G. A.
Petersson
,
H.
Nakatsuji
,
X.
Li
,
M.
Caricato
,
A. V.
Marenich
,
J.
Bloino
,
B. G.
Janesko
,
R.
Gomperts
,
B.
Mennucci
,
H. P.
Hratchian
,
J. V.
Ortiz
,
A. F.
Izmaylov
,
J. L.
Sonnenberg
,
D.
Williams-Young
,
F.
Ding
,
F.
Lipparini
,
F.
Egidi
,
J.
Goings
,
B.
Peng
,
A.
Petrone
,
T.
Henderson
,
D.
Ranasinghe
,
V. G.
Zakrzewski
,
J.
Gao
,
N.
Rega
,
G.
Zheng
,
W.
Liang
,
M.
Hada
,
M.
Ehara
,
K.
Toyota
,
R.
Fukuda
,
J.
Hasegawa
,
M.
Ishida
,
T.
Nakajima
,
Y.
Honda
,
O.
Kitao
,
H.
Nakai
,
T.
Vreven
,
K.
Throssell
,
J. A.
Montgomery
, Jr.
,
J. E.
Peralta
,
F.
Ogliaro
,
M. J.
Bearpark
,
J. J.
Heyd
,
E. N.
Brothers
,
K. N.
Kudin
,
V. N.
Staroverov
,
T. A.
Keith
,
R.
Kobayashi
,
J.
Normand
,
K.
Raghavachari
,
A. P.
Rendell
,
J. C.
Burant
,
S. S.
Iyengar
,
J.
Tomasi
,
M.
Cossi
,
J. M.
Millam
,
M.
Klene
,
C.
Adamo
,
R.
Cammi
,
J. W.
Ochterski
,
R. L.
Martin
,
K.
Morokuma
,
O.
Farkas
,
J. B.
Foresman
, and
D. J.
Fox
, Gaussian 16 Revision A.03,
Gaussian, Inc.
,
Wallingford CT
,
2016
.
102.
D. L.
Beveridge
,
Approximate Molecular Orbital Theory of Nuclear and Electron Magnetic Resonance Parameters
(
Springer
,
Boston
,
1977
).
103.
T.
Tuttle
and
W.
Thiel
, “
OMx-D: Semiempirical methods with orthogonalization and dispersion corrections. Implementation and biochemical application
,”
Phys. Chem. Chem. Phys.
10
,
2159
2166
(
2008
).
104.
D.
Tuna
,
Y.
Lu
,
A.
Koslowski
, and
W.
Thiel
, “
Semiempirical quantum-chemical orthogonalization-corrected methods: Benchmarks of electronically excited states
,”
J. Chem. Theory Comput.
12
,
4400
4422
(
2016
).
105.
P. O.
Dral
,
X.
Wu
,
L.
Spörkel
,
A.
Koslowski
,
W.
Weber
,
R.
Steiger
,
M.
Scholten
, and
W.
Thiel
, “
Semiempirical quantum-chemical orthogonalization-corrected methods: Theory, implementation, and parameters
,”
J. Chem. Theory Comput.
12
,
1082
1096
(
2016
).
106.
P. O.
Dral
,
X.
Wu
,
L.
Spörkel
,
A.
Koslowski
, and
W.
Thiel
, “
Semiempirical quantum-chemical orthogonalization-corrected methods: Benchmarks for ground-state properties
,”
J. Chem. Theory Comput.
12
,
1097
1120
(
2016
).
107.
D. A.
Case
,
K.
Belfon
,
I. Y.
Ben-Shalom
,
S. R.
Brozell
,
D. S.
Cerutti
,
T. E.
Cheatham
 III
,
V. W. D.
Cruzeiro
,
T. A.
Darden
,
R. E.
Duke
,
G.
Giambasu
, ,
M. K.
Gilson
,
H.
Gohlke
,
A. W.
Goetz
,
R.
Harris
,
S.
Izadi
,
S. A.
Izmailov
,
K.
Kasavajhala
,
K.
Kovalenko
,
R.
Krasny
,
T.
Kurtzman
,
T.
Lee
,
S.
Le-Grand
,
P.
Li
,
C.
Lin
,
J.
Liu
,
T.
Luchko
,
R.
Luo
,
V.
Man
,
K.
Merz
,
Y.
Miao
,
O.
Mikhailovskii
,
G.
Monard
, ,
H.
Nguyen
,
A.
Onufriev
,
F.
Pan
,
S.
Pantano
,
R.
Qi
,
D. R.
Roe
,
A.
Roitberg
,
C.
Sagui
,
S.
Schott-Verdugo
,
J.
Shen
,
C. L.
Simmerling
,
N.
Skrynnikov
,
J.
Smith
,
J.
Swails
,
R. C.
Walker
,
J.
Wang
,
R. M.
Wilson
,
R. M.
Wolf
,
X.
Wu
,
Y.
Xiong
,
Y.
Xue
,
D. M.
York
, and
P. A.
Kollman
, AMBER 20,
University of California
,
San Francisco, CA
,
2020
.
108.
R. C.
Walker
,
M. F.
Crowley
, and
D. A.
Case
, “
The implementation of a fast and accurate QM/MM potential method in Amber
,”
J. Comput. Chem.
29
,
1019
1031
(
2008
).
109.
M.
Thiel
, MNDO, Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr,
2022
.
110.
J. J. P.
Stewart
, “
MOPAC: A semiempirical molecular orbital program
,”
J. Comput.-Aided Mol. Des.
4
,
1
105
(
1990
).
111.
J.
Hostaš
,
J.
Řezáč
, and
P.
Hobza
, “
On the performance of the semiempirical quantum mechanical PM6 and PM7 methods for noncovalent interactions
,”
Chem. Phys. Lett.
568
,
161
166
(
2013
).
112.
A. V.
Sulimov
,
D. C.
Kutov
,
E. V.
Katkova
,
I. S.
Ilin
, and
V. B.
Sulimov
, “
New generation of docking programs: Supercomputer validation of force fields and quantum-chemical methods for docking
,”
J. Mol. Graphics Modell.
78
,
139
147
(
2017
).
113.
T. J.
Giese
and
D. M.
York
, “
Density-functional expansion methods: Grand challenges
,”
Theor. Chem. Acc.
131
,
1145
(
2012
).
114.
M.
Gaus
,
A.
Goez
, and
M.
Elstner
, “
Parametrization and benchmark of DFTB3 for organic molecules
,”
J. Chem. Theory Comput.
9
,
338
354
(
2013
).
115.
G.
Seabra
,
R. C.
Walker
,
M.
Elstner
,
D. A.
Case
, and
A. E.
Roitberg
, “
Implementation of the SCC-DFTB method for hybrid QM/MM simulations within the amber molecular dynamics package
,”
J. Phys. Chem. A
111
,
5655
5664
(
2007
).
116.
C. H.
Pham
,
R. K.
Lindsey
,
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
).
117.
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
).
118.
H.
Li
,
C.
Collins
,
M.
Tanha
,
G. J.
Gordon
, and
D. J.
Yaron
, “
A density functional tight binding layer for deep learning of chemical Hamiltonians
,”
J. Chem. Theory Comput.
14
,
5764
5776
(
2018
).
119.
J.
Zhu
,
V. Q.
Vuong
,
B. G.
Sumpter
, and
S.
Irle
, “
Artificial neural network correction for density-functional tight-binding molecular dynamics simulations
,”
MRS Commun.
9
,
867
873
(
2019
).
120.
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
).
121.
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
).
122.
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
).
123.
X.
Gao
,
F.
Ramezanghorbani
,
O.
Isayev
,
J. S.
Smith
, and
A. E.
Roitberg
, “
TorchANI: A free and open source PyTorch-based deep learning implementation of the ANI neural network potentials
,”
J. Chem. Inf. Model.
60
,
3408
3415
(
2020
).
124.
E.
Caldeweyher
,
C.
Bannwarth
, and
S.
Grimme
, “
Extension of the D3 dispersion coefficient model
,”
J. Chem. Phys.
147
,
034112
(
2017
).
125.
D. C.
Liu
and
J.
Nocedal
, “
On the limited memory BFGS method for large scale optimization
,”
Math. Program.
45
,
503
528
(
1989
).
126.
A.
Hjorth Larsen
,
J.
Jørgen Mortensen
,
J.
Blomqvist
,
I. E.
Castelli
,
R.
Christensen
,
M.
Dułak
,
J.
Friis
,
M. N.
Groves
,
B.
Hammer
,
C.
Hargus
,
E. D.
Hermes
,
P. C.
Jennings
,
P.
Bjerre Jensen
,
J.
Kermode
,
J. R.
Kitchin
,
E.
Leonhard Kolsbjerg
,
J.
Kubal
,
K.
Kaasbjerg
,
S.
Lysgaard
,
J.
Bergmann Maronsson
,
T.
Maxson
,
T.
Olsen
,
L.
Pastewka
,
A.
Peterson
,
C.
Rostgaard
,
J.
Schiøtz
,
O.
Schütt
,
M.
Strange
,
K. S.
Thygesen
,
T.
Vegge
,
L.
Vilhelmsen
,
M.
Walter
,
Z.
Zeng
, and
K. W.
Jacobsen
, “
The atomic simulation environment—A Python library for working with atoms
,”
J. Phys.: Condens. Matter
29
,
273002
(
2017
).
127.
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
).
128.
T.
Fink
,
H.
Bruggesser
, and
J.-L.
Reymond
, “
Virtual exploration of the small-molecule chemical universe below 160 daltons
,”
Angew. Chem., Int. Ed.
44
,
1504
1508
(
2005
).
129.
L. C.
Blum
and
J.-L.
Reymond
, “
970 million druglike small molecules for virtual screening in the chemical universe database GDB-13
,”
J. Am. Chem. Soc.
131
,
8732
8733
(
2009
).
130.
V.
Law
,
C.
Knox
,
Y.
Djoumbou
,
T.
Jewison
,
A. C.
Guo
,
Y.
Liu
,
A.
Maciejewski
,
D.
Arndt
,
M.
Wilson
,
V.
Neveu
,
A.
Tang
,
G.
Gabriel
,
C.
Ly
,
S.
Adamjee
,
Z. T.
Dame
,
B.
Han
,
Y.
Zhou
, and
D. S.
Wishart
, “
DrugBank 4.0: Shedding new light on drug metabolism
,”
Nucleic Acids Res.
42
,
1091
1097
(
2014
).
131.
L.
Goerigk
,
H.
Kruse
, and
S.
Grimme
, “
Benchmarking density functional methods against the S66 and S66x8 datasets for non-covalent interactions
,”
ChemPhysChem.
12
,
3421
3433
(
2011
).
132.
B.
Brauer
,
M. K.
Kesharwani
,
S.
Kozuch
, and
J. M. L.
Martin
, “
The S66x8 benchmark for noncovalent interactions revisited: Explicitly correlated ab initio methods and density functional theory
,”
Phys. Chem. Chem. Phys.
18
,
20905
20925
(
2016
).
133.
J.
Řezáč
, “
Non-covalent interactions atlas benchmark data sets: Hydrogen bonding
,”
J. Chem. Theory Comput.
16
,
2355
2368
(
2020
).
134.
O.
Wahl
and
T.
Sander
, “
Tautobase: An open tautomer database
,”
J. Chem. Inf. Model.
60
,
1085
1089
(
2020
).
135.
M.
Wieder
,
J.
Fass
, and
J. D.
Chodera
, “
Fitting quantum machine learning potentials to experimental free energy data: Predicting tautomer ratios in solution
,”
Chem. Sci.
12
,
11364
11381
(
2021
).
136.
A.
Moser
,
K.
Range
, and
D. M.
York
, “
Accurate proton affinity and gas-phase basicity values for molecules important in biocatalysis
,”
J. Phys. Chem. B
114
,
13911
13921
(
2010
).
137.
L.
Goerigk
,
A.
Hansen
,
C.
Bauer
,
S.
Ehrlich
,
A.
Najibi
, and
S.
Grimme
, “
A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions
,”
Phys. Chem. Chem. Phys.
19
,
32184
32215
(
2017
).
138.
N.
Ree
,
A. H.
Göller
, and
J. H.
Jensen
, “
RegioSQM20: Improved prediction of the regioselectivity of electrophilic aromatic substitutions
,”
J. Cheminf.
13
,
10
(
2021
).
139.
N. B.
Leontis
and
E.
Westhof
, “
Geometric nomenclature and classification of RNA base pairs
,”
RNA
7
,
499
512
(
2001
).
140.
N. B.
Leontis
,
J.
Stombaugh
, and
E.
Westhof
, “
The non-Watson–Crick base pairs and their associated isostericity matrices
,”
Nucleic Acids Res.
30
,
3497
3531
(
2002
).
141.
N. B.
Leontis
and
E.
Westhof
, “
Analysis of RNA motifs
,”
Curr. Opin. Struct. Biol.
13
,
300
308
(
2003
).
142.
I.
Singh
,
M.-J.
Kim
,
R. W.
Molt
,
S.
Hoshika
,
S. A.
Benner
, and
M. M.
Georgiadis
, “
Structure and biophysics for a six letter DNA alphabet that includes imidazo[1,2-a]-1,3,5-triazine-2(8H)-4(3H)-dione (X) and 2,4-diaminopyrimidine (K)
,”
ACS Synth. Biol.
6
,
2118
2129
(
2017
).
143.
R. T.
Raines
, “
Ribonuclease A
,”
Chem. Rev.
98
,
1045
1066
(
1998
).
144.
H.
Gu
,
S.
Zhang
,
K.-Y.
Wong
,
B. K.
Radak
,
T.
Dissanayake
,
D. L.
Kellerman
,
Q.
Dai
,
M.
Miyagi
,
V. E.
Anderson
,
D. M.
York
,
J. A.
Piccirilli
, and
M. E.
Harris
, “
Experimental and computational analysis of the transition state for ribonuclease A-catalyzed RNA 2′-O-transphosphorylation
,”
Proc. Natl. Acad. Sci. U. S. A.
110
,
13002
13007
(
2013
).
145.
M. E.
Harris
,
J. A.
Piccirilli
, and
D. M.
York
, “
Integration of kinetic isotope effect analyses to elucidate ribonuclease mechanism
,”
Biochim. Biophys. Acta, Proteins Proteomics
1854
,
1801
1808
(
2015
).

Supplementary Material

You do not currently have access to this content.