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Molecular Simulations with in-deMon2k QM/MM, a Tutorial-Review^{ †}

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## Abstract

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## 1. Introduction

## 2. The in-deMon2k Implementation of Quantum Mechanical/Molecular Mechanical (QM/MM)

#### 2.1. General Framework for Additive QM/MM

#### 2.1.1. Hybrid QM/MM with Non-Polarizable Force Fields

#### 2.1.2. Hybrid QM/MMpol with Polarizable Force Fields

#### 2.1.3. Long-Range Interactions

#### 2.1.4. Frontier Interactions

#### 2.2. Density Functional Theory with deMon2k

#### 2.2.1. DFT with Variational Density Fitting

#### 2.2.2. Auxiliary Density Functional Theory (DFT)

#### 2.3. Available Methodologies

#### 2.3.1. Born–Oppenheimer Molecular Dynamics Simulations

^{−7}Ha on the elements of the XC potential matrix). Simulations have been performed on Bull

^{®}[email protected] GHz processors on the OCCIGEN machine hosted at the CINES computer center (Montpellier, France). Each node has 64 Go of Random Memory Access (RAM) which enabled the use the MIXED scheme to store all near-field electron repulsion integrals in RAM [61]. It can be seen that noticeable gains can be obtained with up to 100 processors for this medium sized QM system. The most time consuming parts are XC contributions, density fitting operations, linear algebra (matrix diagonalization) and energy gradients calculations. We stress that evaluations of electron repulsion integrals are almost negligible when using MIXED ERIS scheme (ca. 3%). The right panel shows the energy evolution along QM/MM BOMD simulation in the microcanonical ensemble (after pre-equiibration at 300 K). We see that the average energy is stable after around 10 ps.

#### 2.3.2. Biasing Born–Oppenheimer Molecular Dynamics (BOMD) Trajectories

**R**represents the atomic coordinates of the system. The dimensionality of $V\left(\mathit{X},t\right)$ is reduced by selecting a few collective variables (CVs), ${s}_{i}$:

**S**,t) can then be expressed as a time-dependent sum of Gaussian functions:

_{i}is the width of the Gaussian function associated with the ith CV, the summation runs up to the total number of CVs (n) and S

_{i}(

**R**) is the value of the i

^{th}CV that is expressed as a function of the atomic coordinates

**R**. Finally, ω is an energy rate defined by ω = W/τ

_{G}, where W and τ

_{G}are the Gaussian height and the deposition stride, respectively. Biasing forces applied to atomic nuclei are obtained as derivatives of V(

**S**,t) by application using the chain rule:

#### 2.3.3. Electron Dynamics Simulations

#### 2.3.4. Ehrenfest Molecular Dynamics Simulations

#### 2.4. How to Prepare a QM/MM Input for deMon2k?

## 3. Applications

#### 3.1. Organic Reactions ‘on Water’

^{−6}Ha·bohr

^{−1}and 1.5 × 10

^{−6}Ha·bohr

^{−1}, respectively. In order to ensure that the obtained reactants and products structures are minima on the potential energy surface, the optimized structures were characterized by frequency analysis. For this purpose, the harmonic frequencies were obtained by diagonalizing the mass-weighted Cartesian force-constant matrix.

_{b}) and reaction energies (Erxn) of the reaction of quadricyclane with dimethyl azodicarboxylate are reported in kcal·mol

^{−1}.

_{b}in the liquid phase is lower by 7 kcal·mol

^{−1}with respect to the potential energy barrier calculated for the same reaction in the gas phase. This result indeed indicates, in agreement with the experiment, that this kind of reaction occurs faster in liquid phase than gas phase. On the other hand, the calculated Erxn are in both cases very close to each other, as can be seen from Table 3. The energy profile is shown in Figure 6.

#### 3.2. Umbrella Sampling for a Chemical Reaction

_{N}2 mechanism:

^{−}+ CH

_{3}–Cl → CH

_{3}–Nu + Cl

^{−}

^{−}molecules: OH

^{−}and SH

^{−}.

_{3}Cl, and the TIP3P water model is chosen for the solvent. Periodic boundary conditions and the particle mesh Ewald method with a cutoff of 9 $\u212b$ for the computation of non-bonded interactions are used. During the equilibration, one water molecule is kept close to CH

_{3}Cl, in a position adapted for the subsequent S

_{N}2 reaction. The final structure of the system is then used to prepare QM/MM simulations. We removed one proton from the water facing the carbon atom of CH

_{3}Cl to create the OH

^{−}nucleophile (for the second S

_{N}reaction, we also changed the oxygen atom by a sulfur atom). We also kept only the water molecules within a sphere of radius 30 $\u212b$ around the solute. The QM part is composed of the OH

^{−}(or SH

^{−}) anion and the CH

_{3}Cl molecule, while all the water molecules are considered at the MM level, using the TIP3P force field. The QM part is treated with the PBE functional and a DZVP-GGA basis set. Lennard–Jones potential parameters for the QM atoms are taken from the GAFF FF for CH

_{3}Cl, from TIP3P [95] FF for OH

^{−}, and from the AMBER FF of cysteine for SH

^{−}. For all the following MD simulations, a time step of 1fs is used and harmonic restraints (with a force constant of 10 kJ·mol

^{−1}·Å

^{−2}) on water-molecule atoms located further than 25 Å from the solutes are employed to prevent evaporation of the solvent. Moreover, we added a harmonic restraint to keep the alignment of the three atoms ((O or S), C and Cl) involved in the S

_{N}2 reaction.

^{−1}·$\u212b$

^{−2}for the biasing potential to bring $X$ close to the target value. Production US-MD simulations were then performed over a period of 15 ps. In order to improve the sampling, we used a ${k}_{bias}$ force constant of 1000 kJ·mol

^{−1}·$\u212b$

^{−2}for $X$ values between −1.2 and 1.2 $\u212b$ and added 14 intermediate windows within this range. A WHAM analysis of the simulations was performed using as input the RC values extracted every 10 fs over the last 10 ps for each window. Statistical uncertainties on the free energy values are obtained from a bootstrap error analysis using 50 samples. For the calculation of uncertainty, we have made the hypothesis that the correlation time for the reaction coordinate is 10 fs. This vale may be underestimated for some of the windows leading to error bars slightly underestimated as well. A precise evaluation of the uncertainty would require a more careful analysis of the autocorrelation function of the reaction coordinate and a longer sampling, which is beyond the scope of this methodological illustration. We used the 2.0.9.1 version of the freely available WHAM program of A. Grossfield to perform the WHAM analysis [96]. WHAM is freely available on Internet.

_{N}2 reactions with OH

^{−}(in black) and SH

^{−}(in red) respectively (note that positive values of the reaction coordinate correspond to [Nu

^{−}+ CH

_{3}Cl] configurations whereas negative values correspond to [Cl

^{−}+ CH

_{3}Nu]). For the sake of clarity, we have chosen not to represent error bars, which are smaller than 1 kJ·mol

^{−1}for each curve over the full range of the reaction coordinate. The nucleophilic substitution of Cl

^{−}by OH

^{−}or SH

^{−}is thermodynamically favored, with ${\mathsf{\Delta}}_{\mathrm{r}}G$ values roughly equal to −105 and −75 kJ·mol

^{−1}respectively. The transition state for the reaction with OH

^{−}is found for a reaction coordinate close to 0 and corresponds, as expected, to a structure where the 3 hydrogen atoms are within the same plane as the carbon atom. In the case of the reaction with SH

^{−}, ${X}^{\ne}$ is positive, around 0.35 $\u212b,$ because of the bigger size of S with respect to O. For the forward reaction (Cl

^{−}as leaving group), activation-free energies are very close for the two nucleophiles, roughly 65 kJ·mol

^{-1}. These results would point towards very similar nucleophilicity of OH

^{−}and SH

^{−}. This is to be compared with gas-phase results where OH

^{−}is found to be a better nucleophile than SH

^{−}in similar S

_{N}2 reactions (see for example Gonzales et al. [97]). This may be explained by the stronger solvation in water of OH

^{−}with respect to SH

^{−}. Looking at the backward reaction, one clearly sees that SH

^{−}is a much better leaving group than OH

^{−}, which is in agreement with common knowledge in organic chemistry. These interpretations should however be taken with great care because many parameters could be improved in the simulations shown here (functionals, size of the water surrounding, addition of an implicit Onsager continuum, inclusion of few water molecules in the QM part, length of the sampling), that are only intended to exemplify the capabilities of deMon2k to build free energy profiles from QM/MM simulations.

#### 3.3. Two-Dimensional Free Energy Surfaces

^{−1}. The integration time-step was set equal to 1 fs. The linear and the angular momenta were conserved with a threshold of 10

^{−8}and, therefore, the rotational and translational degrees of freedom of the molecule were frozen. The MetaD simulations were performed using Gaussian functions defined by height and width of 0.4 kcal·mol

^{−1}and 0.15 radian, respectively. They were added each 100 MD steps. The well-tempered formulation of MetaD with a bias factor of 10 was carried out for 370 ps trajectory length which corresponds to the deposition of 3700 Gaussian functions along the FES.

_{R}and β/C

_{7eq}, separated by 2–2.5 kcal/mol energy barrier. The α

_{R}conformer appears only in the water phase owing its stabilization to the hydrogen bonds formed with the water molecules, described here only at the MM level. The stabilization of α

_{R}conformer, demonstrates the good performance of the in-deMon2k electrostatic embedding QM/MM scheme (see Equations 6 and 7) in reproducing H-bond electrostatic character between the MM-water and QM-dialanine O, N and H atoms. Two high free-energy regions has ϕ coordinate in the intervals (−50°, 50°) and (100°, 180°) and is known to be constituted predominantly of less stable conformations. In the region around ϕ = 70 ± 20°, a second low-energy region is observed, although the corresponding free energies are higher compared to these in the ϕ = −100 ± 30° region. A quantitative sampling of the FES would necessitate a significantly longer simulation time. Nevertheless, although the present QM/MM simulations of alanine dipeptide in water are relatively short, only 370 ps, the landscape features of the FES resemble qualitatively those obtained previously with SCC-DFTB (Self-Consistent-Charge DFT Tight Binding) for 3.5 ns trajectory length [27] and other approaches [98,99].

#### 3.4. Absorption Spectra of a Biological Chromophore

#### 3.5. Electron Transfer Free-Energy Profile

#### 3.6. Non-Adiabatic Chemistry Induced by Ionizing Radiation

_{3}radical and the remaining side chain (Figure 13). The length of the hydrogen bond between sulfur and surrounding water increases too as a consequence of ionization of the side chain. Overall on this time scale, the energy deposited upon collision doesn’t have time to spread out within surrounding nuclear modes but before covalent bond breaking has time to take place.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Warshel, A.; Levitt, M. Theoretical studies of enzymic reactions: Dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J. Mol. Biol.
**1976**, 103, 227–249. [Google Scholar] [CrossRef] - Field, M.J.; Bash, P.A.; Karplus, M. A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J. Comput. Chem.
**1990**, 11, 700–733. [Google Scholar] [CrossRef] - Warshel, A.; Karplus, M. Calculation of ground and excited state potential surfaces of conjugated molecules. I. Formulation and parametrization. J. Am. Chem. Soc.
**1972**, 94, 5612–5625. [Google Scholar] [CrossRef] - Senn, H.M.; Thiel, W. QM/MM methods for biomolecular systems. Angew. Chem. Int. Ed.
**2009**, 48, 1198–1229. [Google Scholar] - Brunk, E.; Rothlisberger, U. Mixed quantum mechanical/molecular mechanical molecular dynamics simulations of biological systems in ground and electronically excited states. Chem. Rev.
**2015**, 115, 6217–6263. [Google Scholar] [CrossRef] [PubMed] - Řezáč, J. Cuby: An integrative framework for computational chemistry. J. Comput. Chem.
**2016**, 37, 1230–1237. [Google Scholar] - Torras, J.; Roberts, B.P.; Seabra, G.M.; Trickey, S.B. Chapter One—PUPIL: A software integration system for multi-scale qm/mm-md simulations and its application to biomolecular systems. In Advances in Protein Chemistry and Structural Biology; Karabencheva-Christova, T., Ed.; Academic Press: Oxford, UK, 2015; Volume 100, p. 1. [Google Scholar]
- Metz, S.; Kästner, J.; Sokol, A.A.; Keal, T.W.; Sherwood, P. ChemShell—A modular software package for QM/MM simulations. Wiley Interdiscip. Rev. Comput. Mol. Sci.
**2014**, 4, 101–110. [Google Scholar] [CrossRef] - Lin, H.; Zhang, Y.; Pezeshki, S.; Wang, B.; Wu, X.-P.; Gagliardi, L.; Truhlar, D. QMMM 2018; University of Minnesota: Minneapolis, MN, USA, 2018. [Google Scholar]
- Kratz, E.G.; Walker, A.R.; Lagardère, L.; Lipparini, F.; Piquemal, J.-P.; Andrés, C.G. LICHEM: A QM/MM program for simulations with multipolar and polarizable force fields. J. Comput. Chem.
**2016**, 37, 1019–1029. [Google Scholar] [CrossRef] - Salomon-Ferrer, R.; Case, D.A.; Walker, R.C. An overview of the Amber biomolecular simulation package. Wiley Interdiscip. Rev. Comput. Mol. Sci.
**2013**, 3, 198–210. [Google Scholar] - Valiev, M.; Bylaska, E.J.; Govind, N.; Kowalski, K.; Straatsma, T.P.; Van Dam, H.J.J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T.L.; et al. NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations. Comput. Phys. Commun.
**2010**, 181, 1477–1489. [Google Scholar] [CrossRef] - Shao, Y.; Gan, Z.; Epifanovsky, E.; Gilbert, A.T.B.; Wormit, M.; Kussmann, J.; Lange, A.W.; Behn, A.; Deng, J.; Feng, X.; et al. Advances in molecular quantum chemistry contained in the Q-Chem 4 program package. Mol. Phys.
**2015**, 113, 184–215. [Google Scholar] [CrossRef] - Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G.A.; et al. Gaussian 09; Gaussian, Inc.: Wallingford, CT, USA, 2009. [Google Scholar]
- Köster, A.M.; Geudtner, G.; Alvarez-Ibarra, A.; Calaminici, P.; Casida, M.E.; Carmona-Espindola, J.; Dominguez, V.; Flores-Moreno, R.; Gamboa, G.U.; Goursot, A.; et al. deMon2k Version 5, Mexico City. 2018. Available online: http://demon-software.com/public_html/program.html (accessed on 22 April 2019).
- Kohn, W.; Sham, L.J. Self-consistent equations including exchange and correlation effects. Phys. Rev.
**1965**, 140, A1133. [Google Scholar] [CrossRef] - Mintmire, J.W.; Dunlap, B.I. Fitting the Coulomb potential variationally in linear-combination-of-atomic-orbitals density-functional calculations. Phys. Rev. A
**1982**, 25, 88. [Google Scholar] [CrossRef] - Gerald, G.; Florian, J.; Köster, A.M.; Alberto, V.; Patrizia, C. Parallelization of the deMon2k code. J. Comput. Chem.
**2006**, 27, 483–490. [Google Scholar] - Salahub, D.; Noskov, S.; Lev, B.; Zhang, R.; Ngo, V.; Goursot, A.; Calaminici, P.; Köster, A.; Alvarez-Ibarra, A.; Mejía-Rodríguez, D.; et al. QM/MM Calculations with deMon2k. Molecules
**2015**, 20, 4780–4812. [Google Scholar] [CrossRef] - Amara, P.; Field, M.J. Evaluation of an ab initio quantum mechanical/molecular mechanical hybrid-potential link-atom method. Theor. Chem. Acc.
**2003**, 109, 43–52. [Google Scholar] [CrossRef] - Gamboa, G.U.; Calaminici, P.; Geudtner, G.; Köster, A.M. How important are temperature effects for cluster polarizabilities? J. Phys. Chem. A
**2008**, 112, 11969–11971. [Google Scholar] [CrossRef] - Vásquez-Pérez, J.M.; Martínez, G.U.G.; Köster, A.M.; Calaminici, P. The discovery of unexpected isomers in sodium heptamers by Born–Oppenheimer molecular dynamics. J. Chem. Phys.
**2009**, 131, 124126. [Google Scholar] [CrossRef] [PubMed] - Alvarez-Ibarra, A.; Calaminici, P.; Goursot, A.; Gómez-Castro, C.Z.; Grande-Aztatzi, R.; Mineva, T.; Salahub, D.R.; Vásquez-Pérez, J.M.; Vela, A.; Zuniga-Gutierrez, B.; et al. Chapter 7—First Principles Computational Biochemistry with deMon2k A2 - Ul-Haq, Zaheer. In Frontiers in Computational Chemistry; Madura, J.D., Ed.; Bentham Science Publishers: Sharjah, UAE, 2015; p. 281. [Google Scholar]
- Wu, X.; Teuler, J.-M.; Cailliez, F.; Clavaguéra, C.; Salahub, D.R.; de la Lande, A. Simulating electron dynamics in polarizable environments. J. Chem. Theor. Comput.
**2017**, 13, 3985–4002. [Google Scholar] [CrossRef] - Wu, X.; Alvarez-Ibarra, A.; Salahub, D.R.; de la Lande, A. Retardation in electron dynamics simulations based on time-dependent density functional theory. Eur. Phys. J. D
**2018**, 72, 206. [Google Scholar] [CrossRef] - Tribello, G.A.; Bonomi, M.; Branduardi, D.; Camilloni, C.; Bussi, G. PLUMED 2: New feathers for an old bird. Comput. Phys. Commun.
**2014**, 185, 604–613. [Google Scholar] [CrossRef] - Cuny, J.; Korchagina, K.; Menakbi, C.; Mineva, T. Metadynamics combined with auxiliary density functional and density functional tight-binding methods: Alanine dipeptide as a case study. J. Mol. Model.
**2017**, 23, 72. [Google Scholar] [CrossRef] [PubMed] - Koster, A.M.; Alvarez-Ibarra, G.G.A.; Calaminici, P.; Casida, M.E.; Carmona-Espindola, J.; Dominguez, V.D.; Flores-Moreno, R.; Gamboa, G.U.; Goursot, A. deMon2k. Available online: http://www.demon-software.com (accessed on 26 April 2019).
- Wang, J.; Wolf, R.M.; Caldwell, J.W.; Kollman, P.A.; Case, D.A. Development and testing of a general amber force field. J. Comput. Chem.
**2005**, 26, 1157–1174. [Google Scholar] [CrossRef] [PubMed] - MacKerell, A.D.; Bashford, D.; Bellott, M.; Dunbrack, R.L.; Evanseck, J.D.; Field, M.J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; et al. All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B
**1998**, 102, 3586–3616. [Google Scholar] [CrossRef] - Foloppe, N.; MacKerell, J. Alexander D. All-atom empirical force field for nucleic acids: I. Parameter optimization based on small molecule and condensed phase macromolecular target data. J. Comput. Chem.
**2000**, 21, 86–104. [Google Scholar] [CrossRef] - MacKerell, A.D., Jr.; Banavali, N.K. All-atom empirical force field for nucleic acids: II. Application to molecular dynamics simulations of DNA and RNA in solution. J. Comput. Chem.
**2000**, 21, 105–120. [Google Scholar] [CrossRef] - Jorgensen, W.L.; Maxwell, D.S.; Tirado-Rives, J. Development and testing of the opls all-atom force field on conformational energetics and properties of organic liquids. J. Am. Chem. Soc.
**1996**, 118, 11225–11236. [Google Scholar] [CrossRef] - Piotr, C.; François-Yves, D.; Yong, D.; Junmei, W. Polarization effects in molecular mechanical force fields. J. Phys. Condens. Matter
**2009**, 21, 333102. [Google Scholar] - Caldwell, J.W.; Kollman, P.A. Structure and properties of neat liquids using nonadditive molecular dynamics: Water, methanol, and N-methylacetamide. J. Phys. Chem.
**1995**, 99, 6208–6219. [Google Scholar] [CrossRef] - Wang, Z.-X.; Zhang, W.; Wu, C.; Lei, H.; Cieplak, P.; Duan, Y. Strike a balance: Optimization of backbone torsion parameters of AMBER polarizable force field for simulations of proteins and peptides. J. Comput. Chem.
**2006**, 27, 781–790. [Google Scholar] [CrossRef] - Thole, B.T. Molecular polarizabilities calculated with a modified dipole interaction. Chem. Phys.
**1981**, 59, 341–350. [Google Scholar] [CrossRef] - van Duijnen, P.T.; Swart, M. Molecular and atomic polarizabilities: Thole’s model revisited. J. Phys. Chem. A
**1998**, 102, 2399. [Google Scholar] [CrossRef] - Mineva, T.; Russo, N. Solvent effects computed with the Gaussian density functional method. Int. J. Quantum Chem.
**1997**, 61, 665–671. [Google Scholar] [CrossRef] - Eurenius, K.P.; Chatfield, D.C.; Brooks, B.R.; Hodoscek, M. Enzyme mechanisms with hybrid quantum and molecular mechanical potentials. I. Theoretical considerations. Int. J. Quantum Chem.
**1996**, 60, 1189–1200. [Google Scholar] [CrossRef] - Eichler, U.; Kölmel, C.M.; Sauer, J. Combining ab initio techniques with analytical potential functions for structure predictions of large systems: Method and application to crystalline silica polymorphs. J. Comput. Chem.
**1997**, 18, 463–477. [Google Scholar] [CrossRef] - Hohenberg, P.; Kohn, W. Inhomogeneous electron gas. Phys. Rev.
**1964**, 136, B864. [Google Scholar] [CrossRef] - Levy, M. Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem. Proc. Natl. Acad. Soc. USA
**1979**, 76, 6062–6065. [Google Scholar] [CrossRef] - Levy, M.; Perdew, J.P. The constrained search formulation of density functional theory. In Density Functional Methods In Physics, 1st ed.; Dreizler, R.M., Providência, J.d., Eds.; Springer US: New York, NY, USA, 1985. [Google Scholar]
- Dunlap, B.I.; Connolly, J.W.D.; Sabin, J.R. On first-row diatomic molecules and local density models. J. Chem. Phys.
**1979**, 71, 4993–4999. [Google Scholar] [CrossRef] - Köster, A.M. Hermite Gaussian auxiliary functions for the variational fitting of the Coulomb potential in density functional methods. J. Chem. Phys.
**2003**, 118, 9943–9951. [Google Scholar] - Köster, A.M.; Campo, J.M.d.; Janetzko, F.; Zuniga-Gutierrez, B. A MinMax self-consistent-field approach for auxiliary density functional theory. J. Chem. Phys.
**2009**, 130, 114106. [Google Scholar] - Alvarez-Ibarra, A.; Köster, A.M. Double asymptotic expansion of three-center electronic repulsion integrals. J. Chem. Phys.
**2013**, 139, 024102. [Google Scholar] [CrossRef] - Alvarez-Ibarra, A.; Köster, A.M.; Zhang, R.; Salahub, D.R. Asymptotic expansion for electrostatic embedding integrals in QM/MM calculations. J. Chem. Theor. Comput.
**2012**, 8, 4232–4238. [Google Scholar] [CrossRef] - Köster, A.M.; Reveles, J.U.; del Campo, J.M. Calculation of exchange-correlation potentials with auxiliary function densities. J. Chem. Phys.
**2004**, 121, 3417–3424. [Google Scholar] - Laikov, D.N. Fast evaluation of density functional exchange-correlation terms using the expansion of the electron density in auxiliary basis sets. Chem. Phys. Lett.
**1997**, 281, 151–156. [Google Scholar] [CrossRef] - Mejía-Rodríguez, D.; Köster, A.M. Robust and efficient variational fitting of Fock exchange. J. Chem. Phys.
**2014**, 141, 124114. [Google Scholar] [CrossRef] - Mejía-Rodríguez, D.; Huang, X.; del Campo, J.M.; Köster, A.M. Chapter Four—hybrid functionals with variationally fitted exact exchange. In Advances in Quantum Chemistry; Sabin, J.R., Cabrera-Trujillo, R., Eds.; Academic Press: Oxford, UK, 2015; Volume 71, pp. 41–67. [Google Scholar]
- Delesma, F.A.; Geudtner, G.; Mejía-Rodríguez, D.; Calaminici, P.; Köster, A.M. Range-separated hybrid functionals with variational fitted exact exchange. J. Chem. Theor. Comput.
**2018**, 14, 5608–5616. [Google Scholar] [CrossRef] [PubMed] - Calaminici, P.; Alvarez-Ibarra, A.; Cruz-Olvera, D.; Domínguez-Soria, V.-D.; Flores-Moreno, R.; Gamboa, G.U.; Geudtner, G.; Goursot, A.; Mejía-Rodríguez, D.; Salahub, D.R.; et al. Auxiliary density functional theory: from molecules to nanostructures. In Handbook of Computational Chemistry; Leszczynski, J., Ed.; Springer: Dordrecht, The Netherlands, 2016; p. 1. [Google Scholar]
- Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett.
**1996**, 77, 3865. [Google Scholar] [CrossRef] [PubMed] - Perdew, J.P.; Ernzerhof, M.; Burke, K. Rationale for mixing exact exchange with density functional approximations. J. Chem. Phys.
**1996**, 105, 9982–9985. [Google Scholar] [CrossRef] - Iikura, H.; Tsuneda, T.; Yanai, T.; Hirao, K. A long-range correction scheme for generalized-gradient-approximation exchange functionals. J. Chem. Phys.
**2001**, 115, 3540–3544. [Google Scholar] [CrossRef] - Krukau, A.V.; Vydrov, O.A.; Izmaylov, A.F.; Scuseria, G.E. Influence of the exchange screening parameter on the performance of screened hybrid functionals. J. Chem. Phys.
**2006**, 125, 224106. [Google Scholar] [CrossRef] [PubMed] - Lange, A.W.; Rohrdanz, M.A.; Herbert, J.M. Charge-transfer excited states in a π-stacked adenine dimer, as predicted using long-range-corrected time-dependent density functional theory. J. Phys. Chem. B
**2008**, 112, 6304. [Google Scholar] [CrossRef] [PubMed] - Alvarez-Ibarra, A.; Köster, A.M. A new mixed self-consistent field procedure. Mol. Phys.
**2015**, 113, 3128–3140. [Google Scholar] [CrossRef] - Torrie, G.M.; Valleau, J.P. Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling. J. Comput. Phys.
**1977**, 23, 187–199. [Google Scholar] [CrossRef] - Kästner, J. Umbrella sampling. Wiley Interdiscip. Rev. Comput. Mol. Sci.
**2011**, 1, 932–942. [Google Scholar] - Laio, A.; Gervasio, F.L. Metadynamics: A method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science. Rep. Prog. Phys.
**2008**, 71, 126601. [Google Scholar] [CrossRef] - Barducci, A.; Bonomi, M.; Parrinello, M. Metadynamics. Wiley Interdiscip. Rev. Comput. Mol. Sci.
**2011**, 1, 826–843. [Google Scholar] [CrossRef] - Runge, E.; Gross, E.K.U. Density-functional theory for time-dependent systems. Phys. Rev. Lett.
**1984**, 52, 997. [Google Scholar] [CrossRef] - Gómez Pueyo, A.; Marques, M.A.L.; Rubio, A.; Castro, A. Propagators for the time-dependent Kohn-Sham equations: Multistep, Runge-Kutta, exponential Runge-Kutta, and commutator free Magnus methods. J. Chem. Theor. Comput.
**2018**, 14, 3040–3052. [Google Scholar] - Li, X.; Tully, J.C.; Schlegel, H.B.; Frisch, M.J. Ab initio Ehrenfest dynamics. J. Chem. Phys.
**2005**, 123, 084106. [Google Scholar] [CrossRef] - Lopata, K.; Govind, N. Modeling fast electron dynamics with real-time time-dependent density functional theory: Application to small molecules and chromophores. J. Chem. Theor. Comput.
**2011**, 7, 1344–1355. [Google Scholar] [CrossRef] - Magnus, W. On the exponential solution of differential equations for a linear operator. Commun. Pure Appl. Math.
**1954**, 7, 649–673. [Google Scholar] [CrossRef] - Cheng, C.-L.; Evans, J.S.; Van Voorhis, T. Simulating molecular conductance using real-time density functional theory. Phys. Rev. B
**2006**, 74, 155112. [Google Scholar] [CrossRef] - Castro, A.; Marques, M.A.L.; Rubio, A. Propagators for the time-dependent Kohn–Sham equations. J. Chem. Phys.
**2004**, 121, 3425–3433. [Google Scholar] [CrossRef] - Gilmore, R. Baker-Campbell-Hausdorff formulas. J. Math. Phys.
**1974**, 15, 2090–2092. [Google Scholar] [CrossRef] - Choi, J.; Dongarra, J.J.; Pozo, R.; Walker, D.W. ScaLAPACK: A scalable linear algebra library for distributed memory concurrent computers. In Proceedings of the Fourth Symposium on the Frontiers of Massively Parallel Computation, Washington, DC, USA, 19–21 October 1992; p. 120. [Google Scholar]
- Choi, J.; Demmel, J.; Dhillon, I.; Dongarra, J.; Ostrouchov, S.; Petitet, A.; Stanley, K.; Walker, D.; Whaley, R.C. ScaLAPACK: A portable linear algebra library for distributed memory computers—Design Issues and performance. Comput. Phys. Commun.
**1996**, 97, 1–15. [Google Scholar] [CrossRef] - Morzan, U.N.; Ramírez, F.F.; Oviedo, M.B.; Sánchez, C.G.; Scherlis, D.A.; Lebrero, M.C.G. Electron dynamics in complex environments with real-time time dependent density functional theory in a QM-MM framework. J. Chem. Phys.
**2014**, 140, 164105. [Google Scholar] [CrossRef] [PubMed] - Donati, G.; Wildman, A.; Caprasecca, S.; Lingerfelt, D.B.; Lipparini, F.; Mennucci, B.; Li, X. Coupling real-time time-dependent density functional theory with polarizable force field. J. Phys. Chem. Lett.
**2017**, 8, 5283–5289. [Google Scholar] [CrossRef] - Wildman, A.; Donati, G.; Lipparini, F.; Mennucci, B.; Li, X. Nonequilibrium environment dynamics in a frequency-dependent polarizable embedding model. J. Chem. Theor. Comput.
**2019**, 15, 43–51. [Google Scholar] [CrossRef] - Tully, J.C. Mixed quantum-classical dynamics. Faraday Discuss.
**1998**, 110, 407–419. [Google Scholar] [CrossRef] - Curchod, B.F.E.; Rothlisberger, U.; Tavernelli, I. Trajectory-based nonadiabatic dynamics with time-dependent density functional theory. ChemPhysChem
**2013**, 14, 1314–1340. [Google Scholar] [CrossRef] - Brooks, B.R.; Brooks, C.L., III; Mackerell, A.D., Jr.; Nilsson, L.; Petrella, R.J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S.; et al. CHARMM: The biomolecular simulation program. J. Comput. Chem.
**2009**, 30, 1545–1614. [Google Scholar] [PubMed] - Phillips, J.C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R.D.; Kalé, L.; Schulten, K. Scalable molecular dynamics with NAMD. J. Comput. Chem.
**2005**, 26, 1781–1802. [Google Scholar] [CrossRef] [PubMed] - Ponder, J. Tinker 8—software tools for molecular design. J. Chem. Theory Comput.
**2018**, 14, 5273–5289. [Google Scholar] - Lagardere, L.; Jolly, L.-H.; Lipparini, F.; Aviat, F.; Stamm, B.; Jing, Z.F.; Harger, M.; Torabifard, H.; Cisneros, G.A.; Schnieders, M.J.; et al. Tinker-HP: A massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields. Chem. Sci.
**2018**, 9, 956–972. [Google Scholar] [CrossRef] - Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys.
**1999**, 110, 6158. [Google Scholar] [CrossRef] - Calaminici, P.; Janetzko, F.; Köster, A.M.; Mejia-Olvera, R.; Zuniga-Gutierrez, B. Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems. J. Chem. Phys.
**2007**, 126, 044108. [Google Scholar] [CrossRef] - Berweger, C.D.; van Gunsteren, W.F.; Müller-Plathe, F. Force field parametrization by weak coupling. Re-engineering SPC water. Chem. Phys. Lett.
**1995**, 232, 429–436. [Google Scholar] [CrossRef] - Reveles, J.U.; Köster, A.M. Geometry optimization in density functional methods. J. Comput. Chem.
**2004**, 25, 1109–1116. [Google Scholar] [CrossRef] [PubMed] - Campo, J.M.d.; Köster, A.M. A hierarchical transition state search algorithm. J. Chem. Phys.
**2008**, 129, 024107. [Google Scholar] [CrossRef] - Gonzalez, C.; Schlegel, H.B. An improved algorithm for reaction path following. J. Chem. Phys.
**1989**, 90, 2154. [Google Scholar] [CrossRef] - Kumar, S.; Rosenberg, J.M.; Bouzida, D.; Swendsen, R.H.; Kollman, P.A. Multidimensional free-energy calculations using the weighted histogram analysis method. J. Comput. Chem.
**1995**, 16, 1339–1350. [Google Scholar] [CrossRef] - Kästner, J. Umbrella integration in two or more reaction coordinates. J. Chem. Phys.
**2009**, 131, 034109. [Google Scholar] [CrossRef] [PubMed] - Wang, J.; Wang, W.; Kollman, P.A.; Case, D.A. Automatic atom type and bond type perception in molecular mechanical calculations. J. Mol. Gr. Modell.
**2006**, 25, 247–260. [Google Scholar] [CrossRef] [PubMed] - Wang, J.; Wolf, R.M.; Caldwell, J.W.; Kollman, P.A.; Case, D.A. Development and testing of a general amber force field. J. Comput. Chem
**2004**, 25, 1157–1174. [Google Scholar] [CrossRef] - Jorgensen, W.L.; Chandrasekhar, J.; Madura, J.D.; Impey, R.W.; Klein, M.L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys.
**1983**, 79, 926. [Google Scholar] [CrossRef] - Grossfield, A. WHAM: The Weighted Histogram Analysis Method; 2.0.9; University of Rochester: Rochester, NY, USA, 2013. [Google Scholar]
- Gonzales, J.M.; Cox, R.S.; Brown, S.T.; Allen, W.D.; Schaefer, H.F. Assessment of density functional theory for model SN2 reactions: CH3X + F- (X = F, Cl, CN, OH, SH, NH2, PH2). J. Phys. Chem. A
**2001**, 105, 11327. [Google Scholar] [CrossRef] - Doshi, U.; Hamelberg, D. Improved statistical sampling and accuracy with accelerated molecular dynamics on rotatable torsions. J. Chem. Theor. Comput.
**2012**, 8, 4004–4012. [Google Scholar] [CrossRef] - Apostolakis, J.; Ferrara, P.; Caflisch, A. Calculation of conformational transitions and barriers in solvated systems: Application to the alanine dipeptide in water. J. Chem. Phys.
**1999**, 110, 2099. [Google Scholar] [CrossRef] - García-Iriepa, C.; Gosset, P.; Berraud-Pache, R.; Zemmouche, M.; Taupier, G.; Dorkenoo, K.D.; Didier, P.; Léonard, J.; Ferré, N.; Navizet, I. Simulation and analysis of the spectroscopic properties of oxyluciferin and its analogues in water. J. Chem. Theor. Comput.
**2018**, 14, 2117–2126. [Google Scholar] - de la Lande, A.; Cailliez, F.; Salahub, D.R. Electron transfer reactions in enzymes: seven things that might break down in vanilla marcus theory and how to fix them if they do. In Simulating Enzyme Reactivity: Computational Methods in Enzyme Catalysis; Moliner, V., Tunon, I., Eds.; Royal Chemical Society: London, UK, 2017; p. 89. [Google Scholar]
- Warshel, A.; Hwang, J.K. Simulation of the dynamics of electron transfer reactions in polar solvents: Semiclassical trajectories and dispersed polaron approaches. J. Chem. Phys.
**1986**, 84, 4938. [Google Scholar] [CrossRef] - King, G.; Warshel, A. Investigation of the free energy functions for electron transfer reactions. J. Chem. Phys.
**1990**, 93, 8682. [Google Scholar] [CrossRef] - Warshel, A. Dynamics of reactions in polar solvents. Semiclassical trajectory studies of electron-transfer and proton-transfer reactions. J. Phys. Chem.
**1982**, 86, 2218–2224. [Google Scholar] [CrossRef] - Dederichs, P.H.; Blügel, S.; Zeller, R.; Akai, H. Ground states of constrained systems: application to cerium impurities. Phys. Rev. Lett.
**1984**, 53, 2512. [Google Scholar] [CrossRef] - Wu, Q.; Van Voorhis, T. Direct optimization method to study constrained systems within density-functional theory. Phys. Rev. A
**2005**, 72, 024502. [Google Scholar] [CrossRef] - de la Lande, A.; Salahub, D.R. Derivation of interpretative models for long range electron transfer from constrained density functional theory. J. Mol. Struct. THEOCHEM
**2010**, 943, 115–120. [Google Scholar] [CrossRef] - Řezáč, J.; Lévy, B.; Demachy, I.; de la Lande, A. Robust and efficient constrained DFT molecular dynamics approach for biochemical modeling. J. Chem. Theor. Comput.
**2012**, 8, 418–427. [Google Scholar] - Blumberger, J. Free energies for biological electron transfer from QM/MM calculation: Method, application and critical assessment. Phys. Chem. Chem. Phys.
**2008**, 10, 5651–5667. [Google Scholar] [CrossRef] - Balabin, I.A.; Onuchic, J.N. Dynamically controlled protein tunneling paths in photosynthetic reaction centers. Science
**2000**, 290, 114–117. [Google Scholar] [CrossRef] - Mangaud, E.; de la Lande, A.; Meier, C.; Desouter-Lecomte, M. Electron transfer within a reaction path model calibrated by constrained DFT calculations: Application to mixed-valence organic compounds. Phys. Chem. Chem. Phys.
**2015**, 17, 30889–30903. [Google Scholar] [CrossRef] [PubMed] - Firmino, T.; Mangaud, E.; Cailliez, F.; Devolder, A.; Mendive-Tapia, D.; Gatti, F.; Meier, C.; Desouter-Lecomte, M.; de la Lande, A. Quantum effects in ultrafast electron transfers within cryptochromes. Phys. Chem. Chem. Phys.
**2016**, 18, 21442–21457. [Google Scholar] [CrossRef] [PubMed] - Cailliez, F.; Müller, P.; Firmino, T.; Pernot, P.; de la Lande, A. Energetics of photoinduced charge migration within the tryptophan tetrad of an animal (6–4) photolyase. J. Am. Chem. Soc.
**2016**, 138, 1904–1915. [Google Scholar] [CrossRef] [PubMed] - Dunning, T.H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys.
**1989**, 90, 1007. [Google Scholar] [CrossRef] - Krause, P.; Sonk, J.A.; Schlegel, H.B. Strong field ionization rates simulated with time-dependent configuration interaction and an absorbing potential. J. Chem. Phys.
**2014**, 140, 174113. [Google Scholar] [CrossRef] [PubMed] - Parise, A.; Alvarez-Ibarra, A.; Wu, X.; Zhao, X.; Pilmé, J.; Lande, A.d.l. Quantum chemical topology of the electron localization function in the field of attosecond electron dynamics. J. Phys. Chem. Lett.
**2018**, 9, 844–850. [Google Scholar] [CrossRef] - de la Lande, A.; Clavaguéra, C.; Köster, A. On the accuracy of population analyses based on fitted densities. J. Mol. Model.
**2017**, 23, 99. [Google Scholar] [CrossRef] [PubMed] - Niklasson, A.M.N.; Steneteg, P.; Odell, A.; Bock, N.; Challacombe, M.; Tymczak, C.J.; Holmström, E.; Zheng, G.; Weber, V. Extended Lagrangian Born–Oppenheimer molecular dynamics with dissipation. J. Chem. Phys.
**2009**, 130, 214109. [Google Scholar] [CrossRef] [PubMed] - Huang, J.; MacKerell, A.D., Jr. CHARMM36 all-atom additive protein force field: Validation based on comparison to NMR data. J. Comput. Chem.
**2013**, 34, 2135–2145. [Google Scholar] [CrossRef] [PubMed]

Sample Availability: Not available. |

**Figure 1.**A recommended partition for Quantum Mechanical/Molecular Mechanical (QM/MM)/Onsager simulations with deMon2k.

**Figure 2.**Comparison of Kohn–Sham Density Functional Theory (DFT) self-consistent field (SCF) timings (red) with corresponding auxiliary density functional theory (ADFT) QM (green) and QM/MM (light blue) SCF timings.

**Figure 3.**Computational performances for QM/MM Born–Oppenheimer molecular dynamics (BOMD) simulation. Left: speed-up as a function of number of processors. Only tasks representing more than 15% of total execution time are depicted. Middle: pie chart illustrating the most computationally demanding task (taking the job run on 48 processors). Right: energy conservation for in the microcanonical simulations.

**Figure 4.**Computational performances for QM/MM RT-TD-ADFT simulation. Left: scalability of code with size QM region. Right: Simulated system with QM and MM atoms represented with balls-and-sticks and lines respectively. The picture represents the QM/MM calculation with the largest QM systems (878 atoms).

**Figure 6.**Reaction profile of quadricyclane with dimethyl azodicarboxylate in the gas and liquid phase (respectively, left and right panels).

**Figure 7.**Free energy profiles for S

_{N}2 reactions between CH

_{3}Cl and OH

^{−}(in black) or SH

^{−}(in red).

**Figure 8.**(

**A**) A snapshot of the QM dialanine (ball and stick) and MM water (lines) model; (

**B**) the two most stable conformations of alanine dipeptide in vacuum, C7

_{ax}and C7

_{eq}, with the backbone dihedral angles φ and ψ and (

**C**) two-dimensional free energy surface (FES), projected on φ and ψ angles. The atom color is the following: C-cyan; N-blue; O-red and H- grey.

**Figure 9.**Representation of the system under study: oxyluciferin (CPK drawing method) and the water molecules mimicking water solution.

**Figure 10.**Simulated absorption spectra taking the snapshots from (

**A**) the classical MD simulation and (

**B**) the QM/MM simulations both at the low and high levels of theory. (

**C**) Experimental absorption spectrum of oxyluciferin.

**Figure 11.**Constrained DFT/MM simulation of charge transfer between tryptophane residues. Left: zoom on the peptide. The atoms with ball-and-stick representation are treated at the QM level. All other atoms are treated with force field (FF). Right: Marcus theory free energy profiles taking the vertical energy gap as reaction coordinate. Circles and triangles correspond to simulation data obtained from non-polarizable and polarizable FF respectively. The lines correspond to parabolic regressions on the simulation data (with induction in dashed lines, without induction in plain lines). The points at the bottom of each free energy curves are directly coming from the simulation data while those are obtained by applying $\Delta G\left(\epsilon \right)=\epsilon $ which derives from the ergodic hypothesis (see Reference [102] for demonstration).

**Figure 12.**Collision of terminal methionine residue by a 100 keV proton. Left: QM/MM set-up. Only methionine residue is treated as QM (balls and sticks), the rest of the system pertains to the MM region. Right: Variation of QM/MM energy of the system and charges of the carbon and sulfur atoms region.

**Figure 13.**Fragmentation of methionine side chain after collision by high energy proton. Left: snapshot at 20 fs. Right: evolution of two distances involving S atom.

**Table 1.**New features of deMon2k for quantum mechanical/molecular mechanical (QM/MM) simulations with respect to 2015 review paper [19].

Methods | References |
---|---|

Polarizable embedding | [24] |

Attosecond electron dynamics | [24,25] |

Ehrenfest non-adiabatic electron-nuclear dynamics | - |

Link atoms | this work |

Continuum solvation model for long range interactions | this work |

Tutorials | this work |

Geometrical restraints | this work |

Metadynamics via interface to plumed library [26] | [27], this work |

**Table 2.**Comparison of potential energy barrier (Eb) and reaction energy (Erxn) in gas phase and liquid. All values are in kcal·mol

^{−1}.

Gas Phase (QM) | Liquid Phase (QM/MM) | ||
---|---|---|---|

E_{b} | E_{rxn} | E_{b} | E_{rxn} |

22.8 | −59.6 | 15.7 | −60.0 |

**Table 3.**First harmonic frequency (in cm

^{−1}) of all structures reported in the mechanism of the reaction in gas phase and liquid phase.

Gas Phase (QM) | Liquid Phase (QM/MM) | ||||||
---|---|---|---|---|---|---|---|

Reactant | TS1 | Intermediary | TS2 | Product | Reactant | TS | Product |

9.2 | 61.0i | 8.3 | 504.4i | 58.8 | 15.2 | 372.8i | 13.9 |

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## Share and Cite

**MDPI and ACS Style**

de la Lande, A.; Alvarez-Ibarra, A.; Hasnaoui, K.; Cailliez, F.; Wu, X.; Mineva, T.; Cuny, J.; Calaminici, P.; López-Sosa, L.; Geudtner, G.; Navizet, I.; Garcia Iriepa, C.; Salahub, D.R.; Köster, A.M. Molecular Simulations with in-deMon2k QM/MM, a Tutorial-Review. *Molecules* **2019**, *24*, 1653.
https://doi.org/10.3390/molecules24091653

**AMA Style**

de la Lande A, Alvarez-Ibarra A, Hasnaoui K, Cailliez F, Wu X, Mineva T, Cuny J, Calaminici P, López-Sosa L, Geudtner G, Navizet I, Garcia Iriepa C, Salahub DR, Köster AM. Molecular Simulations with in-deMon2k QM/MM, a Tutorial-Review. *Molecules*. 2019; 24(9):1653.
https://doi.org/10.3390/molecules24091653

**Chicago/Turabian Style**

de la Lande, Aurélien, Aurelio Alvarez-Ibarra, Karim Hasnaoui, Fabien Cailliez, Xiaojing Wu, Tzonka Mineva, Jérôme Cuny, Patrizia Calaminici, Luis López-Sosa, Gerald Geudtner, Isabelle Navizet, Cristina Garcia Iriepa, Dennis R. Salahub, and Andreas M. Köster. 2019. "Molecular Simulations with in-deMon2k QM/MM, a Tutorial-Review" *Molecules* 24, no. 9: 1653.
https://doi.org/10.3390/molecules24091653