In this paper, we have extended to the calculation of hyperfine coupling constants, the model recently proposed by some of the present authors [Giovannini et al., J. Chem. Theory Comput. 13, 4854–4870 (2017)] to include Pauli repulsion and dispersion effects in Quantum Mechanical/Molecular Mechanics (QM/MM) approaches. The peculiarity of the proposed approach stands in the fact that repulsion/dispersion contributions are explicitly introduced in the QM Hamiltonian. Therefore, such terms not only enter the evaluation of energetic properties but also propagate to molecular properties and spectra. A novel parametrization of the electrostatic fluctuating charge force field has been developed, thus allowing a quantitative reproduction of reference QM interaction energies. Such a parametrization has been then tested against the prediction of EPR parameters of prototypical nitroxide radicals in aqueous solutions.
REFERENCES
1.
J.
Tomasi
, B.
Mennucci
, and R.
Cammi
, “Quantum mechanical continuum solvation models
,” Chem. Rev.
105
, 2999
–3094
(2005
).2.
H. M.
Senn
and W.
Thiel
, “QM/MM methods for biomolecular systems
,” Angew. Chem., Int. Ed.
48
, 1198
–1229
(2009
).3.
J. R.
Cheeseman
, M. S.
Shaik
, P. L.
Popelier
, and E. W.
Blanch
, “Calculation of Raman optical activity spectra of methyl-β-d-glucose incorporating a full molecular dynamics simulation of hydration effects
,” J. Am. Chem. Soc.
133
, 4991
–4997
(2011
).4.
B.
Mennucci
, “Modeling environment effects on spectroscopies through QM/classical models
,” Phys. Chem. Chem. Phys.
15
, 6583
–6594
(2013
).5.
K. H.
Hopmann
, K.
Ruud
, M.
Pecul
, A.
Kudelski
, M.
Dračínský
, and P.
Bour
, “Explicit versus implicit solvent modeling of Raman optical activity spectra
,” J. Phys. Chem. B
115
, 4128
–4137
(2011
).6.
C.
Cappelli
, F.
Lipparini
, J.
Bloino
, and V.
Barone
, “Towards an accurate description of anharmonic infrared spectra in solution within the polarizable continuum model: Reaction field, cavity field and nonequilibrium effects
,” J. Chem. Phys.
135
, 104505
(2011
).7.
F.
Egidi
, T.
Giovannini
, M.
Piccardo
, J.
Bloino
, C.
Cappelli
, and V.
Barone
, “Stereoelectronic, vibrational, and environmental contributions to polarizabilities of large molecular systems: A feasible anharmonic protocol
,” J. Chem. Theory Comput.
10
, 2456
–2464
(2014
).8.
C.
Cappelli
, “Integrated QM/polarizable MM/continuum approaches to model chiroptical properties of strongly interacting solute-solvent systems
,” Int. J. Quantum Chem.
116
, 1532
–1542
(2016
).9.
E.
Boulanger
and J. N.
Harvey
, “QM/MM methods for free energies and photochemistry
,” Curr. Opin. Struct. Biol.
49
, 72
–76
(2018
).10.
P.
Lahiri
, K. B.
Wiberg
, P. H.
Vaccaro
, M.
Caricato
, and T. D.
Crawford
, “Large solvation effect in the optical rotatory dispersion of norbornenone
,” Angew. Chem.
126
, 1410
–1413
(2014
).11.
D.
Loco
, S.
Jurinovich
, L.
Cupellini
, M. F.
Menger
, and B.
Mennucci
, “The modeling of the absorption lineshape for embedded molecules through a polarizable QM/MM approach
,” Photochem. Photobiol. Sci.
17
, 552
–560
(2018
).12.
A.
Warshel
and M.
Levitt
, “Theoretical studies of enzymic reactions: Dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme
,” J. Mol. Biol.
103
, 227
–249
(1976
).13.
M. J.
Field
, P. A.
Bash
, and M.
Karplus
, “A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations
,” J. Comput. Chem.
11
, 700
–733
(1990
).14.
J.
Gao
, “Hybrid quantum and molecular mechanical simulations: An alternative avenue to solvent effects in organic chemistry
,” Acc. Chem. Res.
29
, 298
–305
(1996
).15.
R. A.
Friesner
and V.
Guallar
, “Ab initio quantum chemical and mixed quantum mechanics/molecular mechanics (QM/MM) methods for studying enzymatic catalysis
,” Annu. Rev. Phys. Chem.
56
, 389
–427
(2005
).16.
H.
Lin
and D. G.
Truhlar
, “QM/MM: What have we learned, where are we, and where do we go from here?
,” Theor. Chem. Acc.
117
, 185
–199
(2007
).17.
A.
Monari
, J.-L.
Rivail
, and X.
Assfeld
, “Theoretical modeling of large molecular systems. Advances in the local self consistent field method for mixed quantum mechanics/molecular mechanics calculations
,” Acc. Chem. Res.
46
, 596
–603
(2012
).18.
A.
Monari
, T.
Very
, J.-L.
Rivail
, and X.
Assfeld
, “A QM/MM study on the spinach plastocyanin: Redox properties and absorption spectra
,” Comput. Theor. Chem.
990
, 119
–125
(2012
).19.
P. N.
Day
, J. H.
Jensen
, M. S.
Gordon
, S. P.
Webb
, W. J.
Stevens
, M.
Krauss
, D.
Garmer
, H.
Basch
, and D.
Cohen
, “An effective fragment method for modeling solvent effects in quantum mechanical calculations
,” J. Chem. Phys.
105
, 1968
–1986
(1996
).20.
V.
Kairys
and J. H.
Jensen
, “QM/MM boundaries across covalent bonds: A frozen localized molecular orbital-based approach for the effective fragment potential method
,” J. Phys. Chem. A
104
, 6656
–6665
(2000
).21.
Y.
Mao
, O.
Demerdash
, M.
Head-Gordon
, and T.
Head-Gordon
, “Assessing ion–water interactions in the amoeba force field using energy decomposition analysis of electronic structure calculations
,” J. Chem. Theory Comput.
12
, 5422
–5437
(2016
).22.
D.
Loco
, É.
Polack
, S.
Caprasecca
, L.
Lagardere
, F.
Lipparini
, J.-P.
Piquemal
, and B.
Mennucci
, “A QM/MM approach using the amoeba polarizable embedding: From ground state energies to electronic excitations
,” J. Chem. Theory Comput.
12
, 3654
–3661
(2016
).23.
D.
Loco
and L.
Cupellini
, “Modeling the absorption lineshape of embedded systems from molecular dynamics: A tutorial review
,” Int. J. Quantum Chem.
119
, e25726
(2019
).24.
B. T.
Thole
, “Molecular polarizabilities calculated with a modified dipole interaction
,” Chem. Phys.
59
, 341
–350
(1981
).25.
A. H.
Steindal
, K.
Ruud
, L.
Frediani
, K.
Aidas
, and J.
Kongsted
, “Excitation energies in solution: The fully polarizable QM/MM/PCM method
,” J. Phys. Chem. B
115
, 3027
–3037
(2011
).26.
S.
Jurinovich
, C.
Curutchet
, and B.
Mennucci
, “The Fenna–Matthews–Olson protein revisited: A fully polarizable (TD) DFT/MM description
,” ChemPhysChem
15
, 3194
–3204
(2014
).27.
E.
Boulanger
and W.
Thiel
, “Solvent boundary potentials for hybrid QM/MM computations using classical drude oscillators: A fully polarizable model
,” J. Chem. Theory Comput.
8
, 4527
–4538
(2012
).28.
S. W.
Rick
, S. J.
Stuart
, and B. J.
Berne
, “Dynamical fluctuating charge force fields: Application to liquid water
,” J. Chem. Phys.
101
, 6141
–6156
(1994
).29.
S. W.
Rick
and B. J.
Berne
, “Dynamical fluctuating charge force fields: The aqueous solvation of amides
,” J. Am. Chem. Soc.
118
, 672
–679
(1996
).30.
T.
Giovannini
, M.
Olszòwka
, F.
Egidi
, J. R.
Cheeseman
, G.
Scalmani
, and C.
Cappelli
, “Polarizable embedding approach for the analytical calculation of Raman and Raman optical activity spectra of solvated systems
,” J. Chem. Theory Comput.
13
, 4421
–4435
(2017
).31.
F.
Lipparini
, F.
Egidi
, C.
Cappelli
, and V.
Barone
, “The optical rotation of methyloxirane in aqueous solution: A never ending story?
,” J. Chem. Theory Comput.
9
, 1880
–1884
(2013
).32.
D.
Loco
, F.
Buda
, J.
Lugtenburg
, and B.
Mennucci
, “The dynamic origin of color tuning in proteins revealed by a carotenoid pigment
,” J. Phys. Chem. Lett.
9
, 2404
–2410
(2018
).33.
J. E.
Lennard-Jones
, “Cohesion
,” Proc. Phys. Soc.
43
, 461
(1931
).34.
E.
Boulanger
, L.
Huang
, C.
Rupakheti
, A. D.
MacKerell
, Jr., and B.
Roux
, “Optimized Lennard-Jones parameters for druglike small molecules
,” J. Chem. Theory Comput.
14
, 3121
–3131
(2018
).35.
M. S.
Gordon
, Q. A.
Smith
, P.
Xu
, and L. V.
Slipchenko
, “Accurate first principles model potentials for intermolecular interactions
,” Annu. Rev. Phys. Chem.
64
, 553
–578
(2013
).36.
H.
Gokcan
, E. G.
Kratz
, T. A.
Darden
, J.-P.
Piquemal
, and G. A.
Cisneros
, “QM/MM simulations with the Gaussian electrostatic model, a density-based polarizable potential
,” J. Phys. Chem. Lett.
9
, 3062
–3067
(2018
).37.
M. S.
Gordon
, L.
Slipchenko
, H.
Li
, and J. H.
Jensen
, “The effective fragment potential: A general method for predicting intermolecular interactions
,” Annu. Rep. Comput. Chem.
3
, 177
–193
(2007
).38.
M. S.
Gordon
, M. A.
Freitag
, P.
Bandyopadhyay
, J. H.
Jensen
, V.
Kairys
, and W. J.
Stevens
, “The effective fragment potential method: A QM-based MM approach to modeling environmental effects in chemistry
,” J. Phys. Chem. A
105
, 293
–307
(2001
).39.
I.
Adamovic
and M. S.
Gordon
, “Dynamic polarizability, dispersion coefficient C6 and dispersion energy in the effective fragment potential method
,” Mol. Phys.
103
, 379
–387
(2005
).40.
L. V.
Slipchenko
, “Effective fragment potential method
,” in Many-Body Effects and Electrostatics in Biomolecules
(Pan Stanford
, 2016
), pp. 147
–187
.41.
J. M. H.
Olsen
, C.
Steinmann
, K.
Ruud
, and J.
Kongsted
, “Polarizable density embedding: A new QM/QM/MM-based computational strategy
,” J. Phys. Chem. A
119
, 5344
–5355
(2015
).42.
P.
Reinholdt
, J.
Kongsted
, and J. M. H.
Olsen
, “Polarizable density embedding: A solution to the electron spill-out problem in multiscale modeling
,” J. Phys. Chem. Lett.
8
, 5949
–5958
(2017
).43.
T.
Giovannini
, P.
Lafiosca
, and C.
Cappelli
, “A general route to include Pauli repulsion and quantum dispersion effects in QM/MM approaches
,” J. Chem. Theory Comput.
13
, 4854
–4870
(2017
).44.
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
).45.
A.
Tkatchenko
, L.
Romaner
, O. T.
Hofmann
, E.
Zojer
, C.
Ambrosch-Draxl
, and M.
Scheffler
, “Van der Waals interactions between organic adsorbates and at organic/inorganic interfaces
,” MRS Bull.
35
, 435
–442
(2010
).46.
A.
Tkatchenko
, R. A.
DiStasio
, Jr., R.
Car
, and M.
Scheffler
, “Accurate and efficient method for many-body van der Waals interactions
,” Phys. Rev. Lett.
108
, 236402
(2012
).47.
J.
Hermann
, R. A.
DiStasio
, and A.
Tkatchenko
, “First-principles models for van der Waals interactions in molecules and materials: Concepts, theory, and applications
,” Chem. Rev.
117
, 4714
–4758
(2017
).48.
C.
Curutchet
, L.
Cupellini
, J.
Kongsted
, S.
Corni
, L.
Frediani
, A. H.
Steindal
, C. A.
Guido
, G.
Scalmani
, and B.
Mennucci
, “Density-dependent formulation of dispersion–repulsion interactions in hybrid multiscale quantum/molecular mechanics (QM/MM) models
,” J. Chem. Theory Comput.
14
, 1671
–1681
(2018
).49.
G. A.
Cisneros
, J.-P.
Piquemal
, and T. A.
Darden
, “Intermolecular electrostatic energies using density fitting
,” J. Chem. Phys.
123
, 044109
(2005
).50.
J.-P.
Piquemal
, G. A.
Cisneros
, P.
Reinhardt
, N.
Gresh
, and T. A.
Darden
, “Towards a force field based on density fitting
,” J. Chem. Phys.
124
, 104101
(2006
).51.
G. A.
Cisneros
, J.-P.
Piquemal
, and T. A.
Darden
, “Generalization of the Gaussian electrostatic model: Extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods
,” J. Chem. Phys.
125
, 184101
(2006
).52.
M.
Pavone
, P.
Cimino
, F.
De Angelis
, and V.
Barone
, “Interplay of stereoelectronic and environmental effects in tuning the structural and magnetic properties of a prototypical spin probe: Further insights from a first principle dynamical approach
,” J. Am. Chem. Soc.
128
, 4338
–4347
(2006
).53.
V.
Barone
, “Electronic, vibrational and environmental effects on the hyperfine coupling constants of nitroxide radicals. H2NO as a case study
,” Chem. Phys. Lett.
262
, 201
–206
(1996
).54.
R.
Improta
and V.
Barone
, “Interplay of electronic, environmental, and vibrational effects in determining the hyperfine coupling constants of organic free radicals
,” Chem. Rev.
104
, 1231
–1254
(2004
).55.
M.
Pavone
, P.
Cimino
, O.
Crescenzi
, A.
Sillanpaeae
, and V.
Barone
, “Interplay of intrinsic, environmental, and dynamic effects in tuning the EPR parameters of nitroxides: Further insights from an integrated computational approach
,” J. Phys. Chem. B
111
, 8928
–8939
(2007
).56.
V.
Barone
, P.
Cimino
, O.
Crescenzi
, and M.
Pavone
, “Ab initio computation of spectroscopic parameters as a tool for the structural elucidation of organic systems
,” J. Mol. Struct.: THEOCHEM
811
, 323
–335
(2007
).57.
M.
Pavone
, A.
Sillanpää
, P.
Cimino
, O.
Crescenzi
, and V.
Barone
, “Evidence of variable H-bond network for nitroxide radicals in protic solvents
,” J. Phys. Chem. B
110
, 16189
–16192
(2006
).58.
V.
Barone
, M.
Brustolon
, P.
Cimino
, A.
Polimeno
, M.
Zerbetto
, and A.
Zoleo
, “Development and validation of an integrated computational approach for the modeling of cw-ESR spectra of free radicals in solution: p-(methylthio) phenyl nitronylnitroxide in toluene as a case study
,” J. Am. Chem. Soc.
128
, 15865
–15873
(2006
).59.
E.
Stendardo
, A.
Pedone
, P.
Cimino
, M. C.
Menziani
, O.
Crescenzi
, and V.
Barone
, “Extension of the amber force-field for the study of large nitroxides in condensed phases: An ab initio parameterization
,” Phys. Chem. Chem. Phys.
12
, 11697
–11709
(2010
).60.
V.
Barone
, P.
Cimino
, and A.
Pedone
, “An integrated computational protocol for the accurate prediction of EPR and PNMR parameters of aminoxyl radicals in solution
,” Magn. Reson. Chem.
48
, S11
–S22
(2010
).61.
J. C.
Schöneboom
, F.
Neese
, and W.
Thiel
, “Toward identification of the compound I reactive intermediate in cytochrome P450 chemistry: A QM/MM study of its EPR and Mössbauer parameters
,” J. Am. Chem. Soc.
127
, 5840
–5853
(2005
).62.
S.
Sinnecker
and F.
Neese
, “QM/MM calculations with DFT for taking into account protein effects on the EPR and optical spectra of metalloproteins. Plastocyanin as a case study
,” J. Comput. Chem.
27
, 1463
–1475
(2006
).63.
S.
Moon
, S.
Patchkovskii
, and D. R.
Salahub
, “QM/MM calculations of EPR hyperfine coupling constants in blue copper proteins
,” J. Mol. Struct.: THEOCHEM
632
, 287
–295
(2003
).64.
H. M.
Senn
and W.
Thiel
, “QM/MM studies of enzymes
,” Curr. Opin. Chem. Biol.
11
, 182
–187
(2007
).65.
V.
Barone
, A.
Bencini
, M.
Cossi
, A. D.
Matteo
, M.
Mattesini
, and F.
Totti
, “Assessment of a combined QM/MM approach for the study of large nitroxide systems in vacuo and in condensed phases
,” J. Am. Chem. Soc.
120
, 7069
–7078
(1998
).66.
67.
N.
Kocherginsky
and H. M.
Swartz
, Nitroxide Spin Labels: Reactions in Biology and Chemistry
(CRC Press
, New York
, 1995
).68.
A. H.
Buchaklian
and C. S.
Klug
, “Characterization of the walker a motif of MsbA using site-directed spin labeling electron paramagnetic resonance spectroscopy
,” Biochemistry
44
, 5503
–5509
(2005
).69.
M.
Engström
, O.
Vahtras
, and H.
Ågren
, “MCSCF and DFT calculations of EPR parameters of sulfur centered radicals
,” Chem. Phys. Lett.
328
, 483
–491
(2000
).70.
Z.
Rinkevicius
, B.
Frecus
, N. A.
Murugan
, O.
Vahtras
, J.
Kongsted
, and H.
Ågren
, “Encapsulation influence on EPR parameters of spin-labels: 2, 2, 6, 6-tetramethyl-4-methoxypiperidine-1-oxyl in cucurbit[8]uril
,” J. Chem. Theory Comput.
8
, 257
–263
(2011
).71.
K. J.
de Almeida
, Z.
Rinkevicius
, H. W.
Hugosson
, A. C.
Ferreira
, and H.
Ågren
, “Modeling of EPR parameters of copper (ii) aqua complexes
,” Chem. Phys.
332
, 176
–187
(2007
).72.
C.
Di Valentin
, G.
Pacchioni
, A.
Selloni
, S.
Livraghi
, and E.
Giamello
, “Characterization of paramagnetic species in N-doped TiO2 powders by EPR spectroscopy and DFT calculations
,” J. Phys. Chem. B
109
, 11414
–11419
(2005
).73.
M.
Anpo
, Y.
Shioya
, H.
Yamashita
, E.
Giamello
, C.
Morterra
, M.
Che
, H. H.
Patterson
, S.
Webber
, and S.
Ouellette
, “Preparation and characterization of the Cu+/zsm-5 catalyst and its reaction with NO under UV irradiation at 275 K. In situ photoluminescence, EPR, and FT-IR investigations
,” J. Phys. Chem.
98
, 5744
–5750
(1994
).74.
J.-L.
Clément
, N.
Ferré
, D.
Siri
, H.
Karoui
, A.
Rockenbauer
, and P.
Tordo
, “Assignment of the EPR spectrum of 5, 5-dimethyl-1-pyrroline N-oxide (DMPO) superoxide spin adduct
,” J. Org. Chem.
70
, 1198
–1203
(2005
).75.
E.
Giner
, L.
Tenti
, C.
Angeli
, and N.
Ferré
, “Computation of the isotropic hyperfine coupling constant: Efficiency and insights from a new approach based on wave function theory
,” J. Chem. Theory Comput.
13
, 475
–487
(2017
).76.
C.
Amovilli
and R.
McWeeny
, “A matrix partitioning approach to the calculation of intermolecular potentials. General theory and some examples
,” Chem. Phys.
140
, 343
–361
(1990
).77.
78.
F.
Lipparini
and V.
Barone
, “Polarizable force fields and polarizable continuum model: A fluctuating charges/PCM approach. 1. Theory and implementation
,” J. Chem. Theory Comput.
7
, 3711
–3724
(2011
).79.
F.
Lipparini
, C.
Cappelli
, G.
Scalmani
, N.
De Mitri
, and V.
Barone
, “Analytical first and second derivatives for a fully polarizable QM/classical Hamiltonian
,” J. Chem. Theory Comput.
8
, 4270
–4278
(2012
).80.
T.
Giovannini
, M.
Olszowka
, and C.
Cappelli
, “Effective fully polarizable QM/MM approach to model vibrational circular dichroism spectra of systems in aqueous solution
,” J. Chem. Theory Comput.
12
, 5483
–5492
(2016
).81.
T.
Giovannini
, G.
Del Frate
, P.
Lafiosca
, and C.
Cappelli
, “Effective computational route towards vibrational optical activity spectra of chiral molecules in aqueous solution
,” Phys. Chem. Chem. Phys.
20
, 9181
–9197
(2018
).82.
T.
Giovannini
, M.
Macchiagodena
, M.
Ambrosetti
, A.
Puglisi
, P.
Lafiosca
, G.
Lo Gerfo
, F.
Egidi
, and C.
Cappelli
, “Simulating vertical excitation energies of solvated dyes: From continuum to polarizable discrete modeling
,” Int. J. Quantum Chem.
119
, e25684
(2019
).83.
F.
Lipparini
, C.
Cappelli
, and V.
Barone
, “Linear response theory and electronic transition energies for a fully polarizable QM/classical Hamiltonian
,” J. Chem. Theory Comput.
8
, 4153
–4165
(2012
).84.
T.
Giovannini
, M.
Ambrosetti
, and C.
Cappelli
, “A polarizable embedding approach to second harmonic generation (SHG) of molecular systems in aqueous solutions
,” Theor. Chem. Acc.
137
, 74
(2018
).85.
C.
Amovilli
and B.
Mennucci
, “Self-consistent-field calculation of Pauli repulsion and dispersion contributions to the solvation free energy in the polarizable continuum model
,” J. Phys. Chem. B
101
, 1051
–1057
(1997
).86.
F. L.
Hirshfeld
, “Bonded-atom fragments for describing molecular charge densities
,” Theor. Chem. Acc.
44
, 129
–138
(1977
).87.
I.
Harczuk
, B.
Nagy
, F.
Jensen
, O.
Vahtras
, and H.
Ågren
, “Local decomposition of imaginary polarizabilities and dispersion coefficients
,” Phys. Chem. Chem. Phys.
19
, 20241
–20250
(2017
).88.
S.
Grimme
, “Density functional theory with London dispersion corrections
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci
1
, 211
–228
(2011
).89.
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
).90.
O. L.
Malkina
, J.
Vaara
, B.
Schimmelpfennig
, M.
Munzarová
, V. G.
Malkin
, and M.
Kaupp
, “Density functional calculations of electronic g-tensors using spin-orbit pseudopotentials and mean-field all-electron spin-orbit operators
,” J. Am. Chem. Soc.
122
, 9206
–9218
(2000
).91.
M.
Kaupp
, C.
Remenyi
, J.
Vaara
, O. L.
Malkina
, and V. G.
Malkin
, “Density functional calculations of electronic g-tensors for semiquinone radical anions. The role of hydrogen bonding and substituent effects
,” J. Am. Chem. Soc.
124
, 2709
–2722
(2002
).92.
V.
Barone
and P.
Cimino
, “Accurate and feasible computations of structural and magnetic properties of large free radicals: The PBE0/N07D model
,” Chem. Phys. Lett.
454
, 139
–143
(2008
).93.
V.
Barone
, P.
Cimino
, and E.
Stendardo
, “Development and validation of the B3LYP/N07D computational model for structural parameter and magnetic tensors of large free radicals
,” J. Chem. Theory Comput.
4
, 751
–764
(2008
).94.
V.
Barone
, “Structure, magnetic properties and reactivities of open-shell species from density functional and self-consistent hybrid methods
,” in Recent Advances in Density Functional Methods: Part I
(World Scientific
, 1995
), pp. 287
–334
.95.
R. M.
Parrish
, L. A.
Burns
, D. G. A.
Smith
, A. C.
Simmonett
, A. E.
DePrince
, E. G.
Hohenstein
, U.
Bozkaya
, A. Y.
Sokolov
, R.
Di Remigio
, R. M.
Richard
, J. F.
Gonthier
, A. M.
James
, H. R.
McAlexander
, A.
Kumar
, M.
Saitow
, X.
Wang
, B. P.
Pritchard
, P.
Verma
, H. F.
Schaefer
, K.
Patkowski
, R. A.
King
, E. F.
Valeev
, F. A.
Evangelista
, J. M.
Turney
, T. D.
Crawford
, and C. D.
Sherrill
, “Psi4 1.1: An open-source electronic structure program emphasizing automation, advanced libraries, and interoperability
,” J. Chem. Theory Comput.
13
, 3185
–3197
(2017
).96.
P.
Mark
and L.
Nilsson
, “Structure and dynamics of the TIP3P, SPC, and SPC/E water models at 298 K
,” J. Phys. Chem. A
105
, 9954
–9960
(2001
).97.
I.
Carnimeo
, C.
Cappelli
, and V.
Barone
, “Analytical gradients for MP2, double hybrid functionals, and TD-DFT with polarizable embedding described by fluctuating charges
,” J. Comput. Chem.
36
, 2271
–2290
(2015
).98.
V.
Hornak
, R.
Abel
, A.
Okur
, B.
Strockbine
, A.
Roitberg
, and C.
Simmerling
, “Comparison of multiple amber force fields and development of improved protein backbone parameters
,” Proteins
65
, 712
–725
(2006
).99.
D. A.
Case
, T. E.
Cheatham
, T.
Darden
, H.
Gohlke
, R.
Luo
, K. M.
Merz
, A.
Onufriev
, C.
Simmerling
, B.
Wang
, and R. J.
Woods
, “The amber biomolecular simulation programs
,” J. Comput. Chem.
26
, 1668
–1688
(2005
).100.
J.-P.
Ryckaert
, G.
Ciccotti
, and H. J.
Berendsen
, “Numerical integration of the Cartesian equations of motion of a system with constraints: Molecular dynamics of n-alkanes
,” J. Comput. Phys.
23
, 327
–341
(1977
).101.
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
).102.
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
.103.
J. F.
Keana
, T. D.
Lee
, and E. M.
Bernard
, “Side-chain substituted 2, 2, 5, 5-tetramethylpyrrolidine-N-oxyl (proxyl) nitroxides. A new series of lipid spin labels showing improved properties for the study of biological membranes
,” J. Am. Chem. Soc.
98
, 3052
–3053
(1976
).104.
A.
Rockenbauer
, L.
Korecz
, and K.
Hideg
, “Ring pseudorotation in pyrrolidine N-oxyl radicals: An analysis of 13C-hyperfine structure of EPR spectra
,” J. Chem. Soc., Perkin Trans. 2
0
(11
), 2149
–2156
(1993
).105.
C.
Puzzarini
and V.
Barone
, “Diving for accurate structures in the ocean of molecular systems with the help of spectroscopy and quantum chemistry
,” Acc. Chem. Res.
51
, 548
–556
(2018
).106.
K.
Szalewicz
, “Symmetry-adapted perturbation theory of intermolecular forces
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
2
, 254
–272
(2012
).107.
E. G.
Hohenstein
and C. D.
Sherrill
, “Wavefunction methods for noncovalent interactions
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci
2
, 304
–326
(2012
).108.
T. M.
Parker
, L. A.
Burns
, R. M.
Parrish
, A. G.
Ryno
, and C. D.
Sherrill
, “Levels of symmetry adapted perturbation theory (SAPT). I. Efficiency and performance for interaction energies
,” J. Chem. Phys.
140
, 094106
(2014
).109.
S. F.
Boys
and F. d.
Bernardi
, “The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors
,” Mol. Phys.
19
, 553
–566
(1970
).© 2019 Author(s).
2019
Author(s)
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