# A Review on Combination of Ab Initio Molecular Dynamics and NMR Parameters Calculations

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Ab Initio Molecular Dynamics Theory

#### 2.1. Molecular Dynamics Simulations

#### 2.2. Ab Initio Molecular Dynamics (aiMD)

#### 2.3. Combining the aiMD and NMR Parameters Calculations

## 3. Summary of the Chosen Studies Applying Both aiMD and NMR Parameters Calculation

#### 3.1. Studies in Liquid State

#### 3.1.1. Analysis of Pure Solvents

#### 3.1.2. Implicit Solvent

^{15}N NMR experimental analysis. In order to convert the calculated chemical shielding into experimentally observed chemical shifts for a studied compound, the information on those parameters for a reference compound is essential. For a long time, in order to do such a conversion, a gas state nitromethane was modeled, which caused some inaccuracies due to the inability to model the intermolecular interactions. In the study of Gerber and Joliboi [41], thanks to compilation of computational methods including the aiMD and the implicit solvent model, the accurate theoretical

^{15}N spectrum of liquid nitromethane was obtained.

^{1}H NMR spectra based on the BOMD trajectories were simulated. The results confirmed the correctness of the proposed theoretical mechanism. It suggests that for protonated H

_{3}PO

_{4}clusters, structural diffusion can proceed without the reorientation of H

_{3}PO

_{4}molecules.

^{1}H NMR chemical shifts of iridium polyhydride complexes revealed that in the experiment, two NMR hydride signals were inversely assigned [39]. The reason was probably the high complexity of the analyzed [Ir

_{6}(IMe)

_{8}(CO)

_{2}H

_{14}]

^{2+}system. The authors concluded their work with a statement that with aiMD at hand, there exists a reliable tool to check the correctness of a traditional NMR signals assignment.

^{23}Na shielding constants in the methylamine solution of [Na

^{+}[2.2.2]cryptand Na

^{−}] [38], in combination with other experiments, raises up the topic of the signals’ shape in the NMR spectra, electric field gradient values (see: Section 3.1.4) and ion’s core valence shell. In this case, such an approach delivers, as the authors stated, “a complete picture of the NMR of Na

^{-}in the cryptand—methylamine system”.

#### 3.1.3. Explicit vs. Implicit Solvent Model

^{7}Li NMR chemical shielding of hydrated Li

^{+}was calculated in very different environments: in a gas state, with a static method in liquid with implicit solvation model (PCM), and with a quantum-based dynamic method (BOMD) in liquid with explicit solvation model performed on big clusters. In the article, it is plainly stated that the implicit PCM solvent model is insufficient to correctly simulate Li shielding. Out of the three analyzed approaches, only the aiMD-cluster explicit one combined with the DFT-NMR calculations delivered spectra that were well-comparable with the experiment.

^{1}J(Pt···H

_{water}) coupling between the complexes and the coordinating water molecule.

#### 3.1.4. Calculation of the Quadrupolar NMR Spin Relaxation Rates and Coupling Constant from QM Calculations of an Electric Field Gradient (EFG) with Explicit Solvent

^{7}Li

^{+},

^{23}Na

^{+},

^{35}Cl

^{−},

^{81}Br

^{−},

^{127}I

^{−}) in an aqueous solution.

^{127}I

^{−},

^{131}Xe, and

^{133}Cs

^{+}[40]. High accuracy of aiMD ensured the correctness of further calculations in this study, which were based on the extracted ion-solvent clusters. The key question of this particular work was which factor contributes more to the EFG tensor value: the solvent or the polarization of a solute.

#### 3.2. Studies of Glassy Systems

_{2}O−0.7 B

_{2}O

_{3}glass system, it has been proven that the complex network of this alkali-borate glass cannot be sufficiently described solely by the GIPAW-derived NMR parameters calculated on static, geometrically-optimized structure [52]. This particular system consists of various structural units which, in terms of the computational approach, can be identified precisely enough only when the aiMD is implemented. In this case, due to the rigidness of the system, 764 snapshots must have been derived from the BOMD simulations. Each of them were transformed into a separate structural model for which the GIPAW calculations of the NMR properties were done subsequently.

_{3}system [31]. In this case, not only the network polymerization and formation in the melted glass are defined but also the electrical conductivity in the molten state are computed. The latter is based on the statistical calculations from the ionic BOMD trajectories. One of the aims of the cited work was to prove that a system that was generated via aiMD and validated through the agreement of quantum-based calculated NMR properties with the corresponding experimental data can be successfully used for a reliable calculation of the physicochemical properties, such as density and electrical conductivity. This approach is especially helpful when those data cannot be easily measured experimentally.

#### 3.3. Studies in Solid State

#### 3.3.1. Early Works

^{1}H,

^{13}C,

^{14}N,

^{17}O, and

^{35}Cl, aiMD significantly improves the accuracy of the post-simulation calculated quadrupolar couplings. This conclusion is even more appealing if one takes into account the diversity of the structures used in this particular study. Among the chosen examples there were both the simplest amino acids, glycine and alanine, as well as other small organics with aromatic or pyrimidine ring (nucleic acid basis). Such wide variety of the studied solid-state compounds enable the authors to draw some general conclusions on the differences between the NMR parameters obtained using static and aiMD-derived structures, presented in Table 2.

#### 3.3.2. More Advanced Works

^{1}H/

^{2}H-

^{15}N bond formed within the guanine-cytosine pair analogues was used. Even if this research’s topic is different than in the previously described systems, here also the bond distance distribution probabilities were obtained thanks to the analysis of the PIMD trajectories. Consequently, this enabled the prediction of the nitrogen shieldings. This, in turn, delivered the answer for the question of the study. The drawn conclusion was that the inter-base proton transfer reaction does not take place in the investigated system. Such information was crucial for further design of the guanine-cytosine pair analogues which could potentially serve as medication.

_{3})

_{2}) was chosen [53]. Accurate temperature measurement in variable-temperature ssNMR (solid state NMR) may prove quite difficult due to the multiple factors, including MAS frequency, rotor dimensions, and air temperature shifts. It is therefore a common practice to use the reference materials that exhibit a continuous shift of resonance frequency as a function of temperature in order to indirectly measure the temperature inside a rotor. The remarkably sensitive temperature dependence, uniform over a range of at least −130 °C to +150 °C, of the

^{207}Pb chemical shift in MAS spectra of this salt provides an excellent method for thermometry in solid-state NMR. However, this phenomenon was not fully explained, which encouraged the authors to conduct research in which the quantum MD under periodic conditions was combined with GIPAW NMR calculations. In that study, multiple MD simulations at different temperatures were performed to check if the experimentally observed linear relationship of chemical shift from temperature can be as well reproduced from calculations. The applied method proved to be successful and accurate, especially if taking into consideration the large range of

^{207}Pb chemical shifts in various compounds -over 11,000 ppm (Figure 3).

^{13}C ssNMR spectrum of one of the studied forms, the splitting of some peaks suggested that there is more than one molecule in the asymmetric unit (Z′ > 1), although in the experimental crystal structure obtained from SCXRD measurements, only one molecule was present (Z′ = 1, Z = 4). Therefore, quantum MD combined with GIPAW NMR calculations were used to confirm the quality and correctness of the deposited crystal structure. The obtained computational results supported the presence of only one molecule in the asymmetric unit as the standard deviation of the values of the

^{13}C isotropic chemical shielding calculated for the four equivalent atoms were found to be negligible. Finally, the splitting was explained as resulting from exceptionally strong residual dipolar couplings between the

^{13}C and

^{14}N atoms.

#### 3.3.3. Highly Rigid Systems

^{7}Li ions in LiTi

_{2}(PO

_{4})

_{3}and LiZr

_{2}(PO

_{4})

_{3}[36]. A stimulus for this work was huge discrepancies between the results of a static NMR calculations and experimental data previously obtained for the above-mentioned systems. Moreover, the importance of a temperature factor was discussed, as the quadrupolar coupling constant associated with Li ion depends strongly on the temperature. For phases inclosing Ti, the constant grows with temperature as the local symmetry of the system decreases. Meanwhile, for the Zr-containing phases, the Li-associated quadrupolar constant decreases, as the thermal vibrations reduce the anisotropy of the interaction. Application of aiMD has not only proven the presence of a short-range Li mobility but also has delivered an explanation for the disagreement observed between the static calculation results and the experimental NMR spectra. Therefore, it has been plainly shown that in order to properly simulate the NMR spectra, thermal vibrations as well as local motions of atoms must be included. Such opportunity is offered only by aiMD.

^{3}H in BOMD is a standard procedure. It is implemented in order to avoid too large displacements of the hydrogen atoms, which could happen if both

^{1}H and a large time step were applied in one calculation.

## 4. Discussion

^{1}H,

^{13}C, or

^{15}N, but also more exotic, for example,

^{131}Xe,

^{195}Pt, and

^{207}Pb, can be found. It was also confirmed that with aiMD, it is possible to investigate relaxation phenomena as from a single or a set of computed aiMD trajectories, the relaxation times T

_{1}and T

_{2}can be determined.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Pulay, P. Foreword in Calculation of NMR and EPR Parameters: Theory and Applications; Kaupp, M., Bhl, M., Malkin, V.G., Eds.; WILEY-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2004. [Google Scholar]
- IJMS Special Issue: Combined NMR Spectroscopy and Molecular Dynamics Studies for Infectious Diseases. Available online: mdpi.com (accessed on 29 March 2021).
- Gelpi, J.; Hospital, A.; Goñi, R.; Orozco, M. Molecular dynamics simulations: Advances and applications. Adv. Appl. Bioinf. Chem.
**2015**, 8, 37–47. [Google Scholar] [CrossRef][Green Version] - Feller, S.E. Molecular dynamics simulations of lipid bilayers. Curr. Opin. Colloid Interface Sci.
**2000**, 5, 217–223. [Google Scholar] [CrossRef] - Perilla, J.R.; Goh, B.C.; Cassidy, C.K.; Liu, B.; Bernardi, R.C.; Rudack, T.; Schulten, K. Molecular dynamics simulations of large macromolecular complexes. Curr. Opin. Struct. Biol.
**2015**, 31, 64–74. [Google Scholar] [CrossRef][Green Version] - Tuckerman, M.E. Ab initio molecular dynamics: Basic concepts, current trends and novel applications. J. Phys. Condens. Matter
**2002**, 14, R1297–R1355. [Google Scholar] [CrossRef] - De Vivo, M.; Masetti, M.; Bottegoni, G.; Cavalli, A. Role of Molecular Dynamics and Related Methods in Drug Discovery. J. Med. Chem.
**2016**, 59, 4035–4061. [Google Scholar] [CrossRef] [PubMed] - Feng, J.; Chen, J.; Selvam, B.; Shukla, D. Computational microscopy: Revealing molecular mechanisms in plants using molecular dynamics simulations. Plant Cell
**2019**, 31. [Google Scholar] [CrossRef] - Ghoufi, A.; Malfreyt, P. Entropy and enthalpy calculations from perturbation and integration thermodynamics methods using molecular dynamics simulations: Applications to the calculation of hydration and association thermodynamic properties. Mol. Phys.
**2006**, 104, 2929–2943. [Google Scholar] [CrossRef] - Lazim, R.; Suh, D.; Choi, S. Advances in Molecular Dynamics Simulations and Enhanced Sampling Methods for the Study of Protein Systems. Int. J. Mol. Sci.
**2020**, 21, 6339. [Google Scholar] [CrossRef] - Guvench, O.; MacKerell, A.D. Comparison of Protein Force Fields for Molecular Dynamics Simulations. In Molecular Modeling of Proteins; Kukol, A., Ed.; Methods Molecular Biology; Humana Pressbook: Totowa, NJ, USA, 2008; Volume 443, pp. 63–88. [Google Scholar]
- Rohskopf, A.; Seyf, H.R.; Gordiz, K.; Tadano, T.; Henry, A. Empirical interatomic potentials optimized for phonon properties. Npj Comput. Mater.
**2017**, 3, 1–7. [Google Scholar] [CrossRef][Green Version] - Paquet, E.; Viktor, H.L. Computational Methods for Ab Initio Molecular Dynamics. Adv. Chem.
**2018**, 98396411-14. [Google Scholar] [CrossRef][Green Version] - Kühne, T.D. Second generation Car-Parrinello molecular dynamics. Wiley Interd. Rev. Comp. Mol. Sci.
**2014**, 4, 391–406. [Google Scholar] [CrossRef][Green Version] - Stanke, M. Adiabatic, Born-Oppenheimer, and Non-adiabatic Approaches. In Handbook of Computational Chemistry; Leszczynski, J., Ed.; Springer: Dordrecht, The Netherlands, 2015; Volume 1, pp. 1–51. [Google Scholar]
- Niklasson, A.M.N. Extended Born-Oppenheimer Molecular Dynamics. Phys. Rev. Lett.
**2008**, 100, 1–4. [Google Scholar] [CrossRef] - Marx, D.; Parrinello, M. Ab initio path integral molecular dynamics: Basic ideas. J. Chem. Phys.
**1996**, 104, 4077–4082. [Google Scholar] [CrossRef] - Ab Initio Molecular Dynamics. Available online: https://th.fhi-berlin.mpg.de/sitesub/meetings/dft-workshop-2016/uploads/Meeting/May_9_Rossi.pdf (accessed on 29 March 2021).
- Kulagina, V.V.; Eremeev, S.V.; Potekaev, A.I. The Molecular-Dynamics Method for Different Statistical Ensembles. Russ. Phys. J.
**2004**, 48, 122–130. [Google Scholar] [CrossRef] - Okumura, H.; Okamoto, Y. Molecular dynamics simulations in the multibaric–multithermal ensemble. Chem. Phys. Lett.
**2004**, 391, 248–253. [Google Scholar] [CrossRef] - Lippert, R.A.; Predescu, C.; Ierardi, D.J.; Mackenzie, K.M.; Eastwood, M.P.; Dror, R.O.; Shaw, D.E. Accurate and efficient integration for molecular dynamics simulations at constant temperature and pressure. J. Chem. Phys.
**2013**, 139, 164106. [Google Scholar] [CrossRef] - CMP. Available online: icmp.lviv.ua (accessed on 29 March 2021).
- Cheeseman, J.R.; Trucks, G.W.; Keith, T.A.; Frisch, M.J. A comparison of models for calculating nuclear magnetic resonance shielding tensors. J. Chem. Phys.
**1996**, 104, 5497–5509. [Google Scholar] [CrossRef] - Wolinski, K.; Hinton, J.F.; Pulay, P. Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations. J. Am. Chem. Soc.
**1990**, 112, 8251–8260. [Google Scholar] [CrossRef] - Keith, T.A.; Bader, R.F.W. Calculation of magnetic response properties using a continuous set of gauge transformations. Chem. Phys. Lett.
**1993**, 210, 223–231. [Google Scholar] [CrossRef] - Charpentier, T. The PAW/GIPAW approach for computing NMR parameters: A new dimension added to NMR study of solids. Solid State Nucl. Mag. Res.
**2011**, 40, 1–20. [Google Scholar] [CrossRef] - Pierens, G.K. 1H and 13C NMR scaling factors for the calculation of chemical shifts in commonly used solvents using density functional theory. J. Comput. Chem.
**2014**, 35, 1388–1394. [Google Scholar] [CrossRef] - Aliev, A.E.; Courtier-Murias, D.; Zhou, S. Scaling factors for carbon NMR chemical shifts obtained from DFT B3LYP calculations. J. Mol. Struct. Theochem.
**2009**, 893, 1–5. [Google Scholar] [CrossRef] - Bártová, K.; Čechová, L.; Procházková, E.; Socha, O.; Janeba, Z.; Dračínský, M. Influence of Intramolecular Charge Transfer and Nuclear Quantum Effects on Intramolecular Hydrogen Bonds in Azopyrimidines. J. Org. Chem.
**2017**, 82, 10350–10359. [Google Scholar] [CrossRef] - Strangmüller, S.; Eickhoff, H.; Müller, D.; Klein, W.; Raudaschl-Sieber, G.; Kirchhain, H.; Fässler, T.F. Fast Ionic Conductivity in the Most Lithium-Rich Phosphidosilicate Li14SiP6. J. Am. Chem. Soc.
**2019**, 141, 14200–14209. [Google Scholar] [CrossRef] [PubMed] - Rakhmatullin, A.; Machado, K.; Zanghi, D.; Polovov, I.B.; Bakirov, R.; Maksimtsev, K.V.; Bessada, C. Study of the NaF-ScF3 system as a molten bath for production of Sc alloys: A combination of NMR and molecular dynamics simulations. J. Alloys Compd.
**2019**, 786, 953–959. [Google Scholar] [CrossRef] - Dračínský, M.; Hodgkinson, P. A molecular dynamics study of the effects of fast molecular motions on solid-state NMR parameters. CrystEngComm
**2013**, 15, 8705. [Google Scholar] [CrossRef][Green Version] - Dumez, J.-N.; Pickard, C.J. Calculation of NMR chemical shifts in organic solids: Accounting for motional effects. J. Chem. Phys.
**2009**, 130, 104701. [Google Scholar] [CrossRef] - Dračínský, M.; Bouř, P. Vibrational averaging of the chemical shift in crystalline α-glycine. J. Comput. Chem.
**2012**, 33, 1080–1089. [Google Scholar] [CrossRef] [PubMed] - Dračínský, M.; Kaminský, J.; Bouř, P. Structure of the Alanine Hydration Shell as Probed by NMR Chemical Shifts and Indirect Spin−Spin Coupling. J. Phys. Chem. B
**2009**, 113, 14698–14707. [Google Scholar] [CrossRef] - Diez-Gómez, V.; Andres, P.L.; Sanz, J. Effects of Li confined motion on NMR quadrupolar interaction. A combined 7Li NMR and DFT-MD study of LiR2(PO4)3 (R = Ti and Zr) phases. ChemSusChem
**2020**, 13, 1027–1036. [Google Scholar] [CrossRef] - Pohl, R.; Socha, O.; Slavicek, P.; Sala, M.; Hodgkinson, P.; Dracinsky, M. Proton transfer in a guanine–cytosine base pair analogue studied by NMR spectroscopy and PIMD simulation. Faraday Discuss.
**2018**, 212, 331. [Google Scholar] [CrossRef][Green Version] - Abella, L.; Philip, A.; Autschbach, J. Ab initio molecular dynamics study of sodium NMR chemical shifts in the methylamine solution of [Na
^{+}[2.2.2]cryptand Na^{−}]. Phys. Chem. Chem. Phys.**2021**, 23, 339–346. [Google Scholar] [CrossRef] - Castro, A.C.; Balcells, D.; Repisky, M.; Helgaker, T.; Cascella, M. First-Principles Calculation of 1H NMR Chemical Shifts of Complex Metal Polyhydrides: The Essential Inclusion of Relativity and Dynamics. Inorg. Chem.
**2020**, 59, 17509–17518. [Google Scholar] [CrossRef] - Philips, A.; Autschbach, J. Quadrupolar NMR relaxation of aqueous 127I–, 131Xe, and 133Cs+: A first-principles approach from dynamics to properties. J. Chem. Theory Comput.
**2020**, 16, 5835–5844. [Google Scholar] [CrossRef] [PubMed] - Gerber, I.C.; Jolibois, F. Theoretical gas to liquid shift of 15N isotropic nuclear magnetic shielding in nitromethane using ab initio molecular dynamics and GIAO/GIPAW calculations. Phys. Chem. Chem. Phys.
**2015**, 17, 12222–12227. [Google Scholar] [CrossRef] [PubMed][Green Version] - Badu, S.; Truflandier, L.; Autschbach, J. Quadrupolar NMR Spin Relaxation Calculated Using Ab Initio Molecular Dynamics: Group 1 and Group 17 Ions in Aqueous Solution. J. Chem. Theory Comput.
**2013**, 9, 4074–4086. [Google Scholar] [CrossRef] [PubMed] - Dračínský, M.; Möller, H.M.; Exner, T.E. Conformational Sampling by Ab Initio Molecular Dynamics Simulations Improves NMR Chemical Shift Predictions. J. Chem. Theory Comput.
**2013**, 9, 3806–3815. [Google Scholar] [CrossRef] [PubMed] - Folliet, N.; Roiland, C.; Bégu, S.; Aubert, A.; Mineva, T.; Goursot, A.; Azaïs, T. Investigation of the Interface in Silica-Encapsulated Liposomes by Combining Solid State NMR and First Principles Calculations. J. Am. Chem. Soc.
**2011**, 133, 16815–16827. [Google Scholar] [CrossRef] [PubMed] - Alam, T.M.; Hart, D.; Rempe, S.L.B. Computing the 7Li NMR chemical shielding of hydrated Li+ using cluster calculations and time-averaged configurations from ab initio molecular dynamics simulations. Phys. Chem. Chem. Phys.
**2011**, 13, 13629. [Google Scholar] [CrossRef] - Sutter, K.; Truflandier, L.A.; Autschbach, J. NMR J-Coupling Constants in Cisplatin Derivatives Studied by Molecular Dynamics and Relativistic DFT. ChemPhysChem
**2011**, 12, 1448–1455. [Google Scholar] [CrossRef] - Zheng, S.; Autschbach, J. Modeling of Heavy-Atom-Ligand NMR Spin-Spin Coupling in Solution: Molecular Dynamics Study and Natural Bond Orbital Analysis of Hg—C Coupling Constants. Chem. A Eur. J.
**2010**, 17, 161–173. [Google Scholar] [CrossRef] [PubMed] - Banyai, D.R.; Murakhtina, T.; Sebastiani, D. NMR chemical shifts as a tool to analyze first principles molecular dynamics simulations in condensed phases: The case of liquid water. Magn. Res. Chem.
**2010**, 48, S56–S60. [Google Scholar] [CrossRef] [PubMed] - Andersen, A.; Rajput, N.N.; Han, K.S.; Pan, H.; Govind, N.; Persson, K.A.; Murugesan, V. Structure and Dynamics of Polysulfide Clusters in a Nonaqueous Solvent Mixture of 1,3-dioxolane and 1,2-dimethoxyethane. Chem. Mater.
**2019**, 31, 2308–2319. [Google Scholar] [CrossRef] - Philips, A.; Marchenko, A.; Ducati, L.C.; Autschbach, J. Quadrupolar 14N NMR Relaxation from Force-Field and Ab Initio Molecular Dynamics in Different Solvents. Chem. Theory Comput.
**2019**, 15, 509–519. [Google Scholar] [CrossRef] [PubMed] - Suwannakham, P.; Sagarik, K. Dynamics of structural diffusion in phosphoric acid hydrogen-bond clusters. RSC Adv.
**2017**, 7, 21492–21506. [Google Scholar] [CrossRef][Green Version] - Ohkubo, T.; Tsuchida, E.; Takahashi, T.; Iwadate, Y. Ab Initio Molecular Dynamics Simulations and GIPAW NMR Calculations of a Lithium Borate Glass Melt. J. Phys. Chem. B
**2016**, 120, 3582–3590. [Google Scholar] [CrossRef] - Szeleszczuk, Ł.; Pisklak, D.M.; Gubica, T.; Matjakowska, K.; Kaźmierski, S.; Zielińska-Pisklak, M. Application of combined solid state NMR and DFT calculations for the study of piracetam polymorphism. Solid State Nucl. Magn. Reason.
**2019**, 97, 17–24. [Google Scholar] [CrossRef] - Szeleszczuk, Ł.; Pisklak, D.M.; Zielińska-Pisklak, M. How does the NMR thermometer work? Application of combined quantum molecular dynamics and GIPAW calculations into the study of lead nitrate. J. Comput. Chem.
**2019**, 40, 811–819. [Google Scholar] - Marchenko, A.; Truflandier, L.A.; Autschbach, J. Uranyl Carbonate Complexes in Aqueous Solution and Their Ligand NMR Chemical Shifts and 17O Quadrupolar Relaxation Studied by ab Initio Molecular Dynamics. Inorg. Chem.
**2017**, 56, 7384–7396. [Google Scholar] [CrossRef] - Piana, S.; Sebastiani, D.; Carloni, P.; Parrinello, M. Ab Initio Molecular Dynamics-Based Assignment of the Protonation State of Pepstatin A/HIV-1 Protease Cleavage Site. J. Am. Chem. Soc.
**2001**, 123, 8730–8737. [Google Scholar] [CrossRef] - Onufriev, A. Chapter 7—Implicit Solvent Models in Molecular Dynamics Simulations: A Brief Overview. Ann. Rep. Compt. Chem.
**2008**, 4, 125–137. [Google Scholar] - Mennucci, B.; Tomasi, J.; Cammi, R.; Cheeseman, J.R.; Frisch, M.J.; Devlin, F.J.; Gabriel, S.; Stephens, P.J. Polarizable Continuum Model (PCM) Calculations of Solvent Effects on Optical Rotations of Chiral Molecules. J. Phys. Chem. A
**2002**, 106, 6102–6113. [Google Scholar] [CrossRef] - York, D.M.; Karplus, M. A smooth solvation potential based on the conductor-like screening model. J. Phys. Chem. A
**1999**, 103, 11060–11079. [Google Scholar] [CrossRef] - Laury, M.L.; Wang, L.-P.; Pande, V.S.; Head-Gordon, T.; Ponder, J.W. Revised Parameters for the AMOEBA Polarizable Atomic Multipole Water Model. J. Phys. Chem. B
**2002**, 119, 9423–9437. [Google Scholar] [CrossRef] [PubMed][Green Version] - Da Silva, E.F.; Svendsen, H.F.; Merz, K.M. Explicitly Representing the Solvation Shell in Continuum Solvent Calculations. J. Phys. Chem. A
**2009**, 113, 6404–6409. [Google Scholar] [CrossRef] [PubMed][Green Version] - Jindal, A.; Vasudevan, S. Molecular Conformation and Hydrogen Bond Formation in Liquid Ethylene Glycol. J. Phys. Chem. B
**2020**, 124, 9136–9143. [Google Scholar] [CrossRef] [PubMed] - Philips, A.; Marchenko, A.; Truflandier, L.A.; Autschbach, J. Quadrupolar NMR relaxation from ab-initio molecular dynamics: Improved sampling and cluster models vs. periodic calculations. J. Chem. Theory Comput.
**2017**, 13, 4397–4409. [Google Scholar] [CrossRef] - Jaszunski, M.; Mikkelsen, K.V.; Rizzo, A.; Witanowski, M.A. Study of the Nitrogen NMR Spectra of Azoles and their Solvent Dependence. J. Phys. Chem. A
**2000**, 104, 1466–1473. [Google Scholar] [CrossRef] - Socha, O.; Hodgkinson, P.; Widdifield, C.M.; Yates, J.R.; Dračínský, M. Exploring Systematic Discrepancies in DFT Calculations of Chlorine Nuclear Quadrupole Couplings. J. Phys. Chem. A
**2017**, 121, 4103–4113. [Google Scholar] [CrossRef][Green Version] - Shen, S.; Kendall, E.; Oliver, A.; Ngassam, V.; Hu, D.; Parikh, A.N. N. Liposil-supported lipid bilayers as a hybrid platform for drug delivery. Soft Matter
**2011**, 7, 1001–1005. [Google Scholar] [CrossRef] - Clark, S.C.; Segall, M.D.; Pickard, C.J.; Hasnip, P.J.; Probert, M.I.J.; Refson, K.; Payne, M.C. First principles methods using CASTEP. Z. Kristallogr.
**2004**, 220, 567–570. [Google Scholar] [CrossRef][Green Version] - CASTEP. Available online: www.castep.org (accessed on 29 March 2021).
- Kühne, T.D.; Iannuzzi, M.; Del Ben, M.; Rybkin, V.V.; Seewald, P.; Stein, F.; Golze, D. CP2K: An Electronic Structure and Molecular Dynamics Software Package—Quickstep: Efficient and Accurate Electronic Structure Calculations. arXiv
**2020**, arXiv:2003.03868. [Google Scholar] [CrossRef] [PubMed] - CP2K Open Source Molecular Dynamics. Available online: www.cp2k.org (accessed on 29 March 2021).
- Andreoni, W.; Curioni, A. New advances in chemistry and material science with CPMD and parallel computing. Parallel Comput.
**2000**, 26, 819–842. [Google Scholar] [CrossRef] - CPMD. Available online: www.cpmd.org/wordpress (accessed on 29 March 2021).
- Balasubramani, S.G.; Chen, G.P.; Coriani, S.; Diedenhofen, M.; Frank, M.S.; Franzke, Y.J.; Yu, J.M. TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations. J. Chem. Phys.
**2020**, 152, 184107. [Google Scholar] [CrossRef] [PubMed] - Turbomole. Available online: www.turbomole.org (accessed on 29 March 2021).
- Giannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Nardelli, M.B.; Calandra, M.; Colonna, N. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys. Condens. Matter
**2017**, 29, 465901. [Google Scholar] [CrossRef] [PubMed][Green Version] - Quantum Espresso. Available online: www.quantum-espresso.org (accessed on 29 March 2021).
- Sun, G.; Kürti, J.; Rajczy, P.; Kertesz, M.; Hafner, J.; Kresse, G. Performance of the Vienna ab initio simulation package (VASP) In chemical applications. J. Mol. Struct. Theochem.
**2003**, 624, 37–45. [Google Scholar] [CrossRef] - VASP. Available online: www.vasp.at (accessed on 29 March 2021).
- Blanc, F.; Middlemiss, D.S.; Buannic, L.; Palumbo, J.L.; Farnan, I.; Grey, C.P. Thermal phase transformations in LaGaO
_{3}and LaAlO_{3}perovskites: An experimental and computational solid-state NMR study. Solid State Nucl. Magn. Res.**2012**, 42, 87–97. [Google Scholar] [CrossRef]

**Figure 1.**The major differences between the methods of aiMD simulations [18]. Bolded methods have already found their application in combination with NMR parameters calculations.

**Figure 3.**The convergence of the isotropic shielding for the Pb atom in Pb(NO

_{3})

_{2}with respect to the simulation time. The calculations were performed at 295 K, and the shielding values for the four equivalent atoms in the unit cell (1–4, color circles) were averaged (mean, black disk). Source: author’s personal archive.

**Table 1.**Computational details of literature examples of aiMD combined with DFT-NMR calculations studies. The systems analyzed in a solid state are bolded.

Ref. in Article | Software (MD) | Software (NMR) | Functional (MD) | Functional (NMR) | NMR-Investigated Nuclei and Investigated System | Type of MD | Integration Time Step | Total Simulation Time | Simulation Temperature | Solvation Model |
---|---|---|---|---|---|---|---|---|---|---|

[29] | CASTEP | CASTEP | B3LYP | GGA PBE | ^{15}N in 5-azopyrimidines | PIMD | 0.5 fs | 5 ps | 300 K | PCM |

[30] | CP2K | CASTEP | Goedecker-Teter-Hutter | GGA PBE | Li in polycrystalline Li_{14}SiP_{6} | BOMD | 0.5 fs | 5 ps | 1023 K | non applicable |

[31] | VASP | CASTEP | GGA PBE | GGA PBE | ^{19}F, ^{23}Na, ^{45}Sc in melted NaF-ScF_{3} (glass) | BOMD | 1 fs | 1 ns | 900 K–1660 K | non applicable |

[32] | CASTEP | CASTEP | GGA PBE | GGA PBE | ^{1}H, ^{13}C, ^{14}N, ^{17}O, ^{35}Cl in amino acids | BOMD | 0.5 fs | 5 ps | 300 K | non applicable |

[33] | CASTEP | CASTEP | GGA PBE | GGA PBE | ^{1}H, ^{13}C in l-alanine and beta-l-aspartyl-l-alanine | BOMD | 1 fs | 3.2 ps | 293 K | non applicable |

[34] | CPMD | CASTEP | BLYP | no information provided | ^{1}H, ^{15}N, ^{13}C in glycine | BOMD | 0.29028 fs | 96ps | 300 K and 427 K | non applicable |

[35] | CPMD | Gaussian | B3LYP | B3LYP | ^{15}N, ^{13}C in alanine | BOMD | 0.09676 fs | 10 ps | 300K | PCM |

[36] | CASTEP | CASTEP | GGA PBE | GGA PBE | ^{7}Li in LiR_{2}(PO4)_{3}(R= Ti and Zr) | BOMD | 1 fs | 5 ps | 300 K and 4050 K | non applicable |

[37] | CASTEP | CASTEP | GGA PBE < B3LYP | GGA PBE | ^{15}N in guanine-cytozine dimers and isocytosine (monomer, dimer) | CPMD | 0.5 fs (monomer, solid state), 0.72 fs (liquid, dimer) | 9 ps | 300 K | non applicable |

[38] | Quantum Espresso | CASTEP | BLYP | GGA PBE | ^{23}Na in methylamine solution of [Na+ [2.2.2]cryptand Na-] † | CPMD | no information provided | 20 ps | 258 K | COSMO |

[39] | CP2K | ReSpect, ADF | GGA PBE | GGA PBE, KT2 | ^{1}H in [Ir_{6}(IMe)_{8}(CO)2H_{14}]2+ | BOMD | 0.25 fs | 30 ps (complex I), 40 ps (complex II) | 298 K | PCM, COSMO |

[40] | Quantum Espresso | ADF | GGA PBE | GGA PBE | ^{127}I, ^{131}Xe, ^{133}Cs | CPMD | 0.145 fs | 25 ps for Xe and Cs+, 50 ps for I- | 350 K | COSMO and explicit |

[41] | VASP | VASP | PBE<<B3LYP | GGA PBE | ^{15}N | BOMD | 0.5 fs | 10 ps | 298 K | implicit |

[42] | Quantum Espresso | ADF | GGA PBE | GGA PBE, PBE0 | ^{7}Li, ^{23}Na, ^{35}Cl, ^{81}Br,^{127}I | CPMD | 0.121 fs | 20 ps | 300 K | explicit |

[43] | CPMD | CASTEP | BLYP | B3LYP | ^{1}H, ^{13}C, ^{14}N, ^{17}O in N-methyl acetamide | CPMD | 0.09676 fs | 106 ps | 300 K | PCM and explicit |

[44] | VASP | PARATEC | PW | GGA PBE | ^{1}H, ^{31}P in silica-encapsulated liposomes | BOMD | 2.5 fs | 4 ps | 300 K | non applicable |

[45] | VASP | Gaussian09 | GGA PBE | B3LYP | ^{7}Li in hydrated Li | BOMD | 0.5 fs | 45.2 ps | 400 K | PCM and explicit |

[46] | Quantum Espresso | ADF | GGA PBE | GGA PBE, LDA | ^{195}Pt in cisplatin | CPMD | 5 a.u. (0.122 fs) | 5ps NVT + 12ps NVE | 300 K | COSMO and explicit |

[47] | Turmobole | ADF | GGA PBE | GGA PBE | ^{199}Hg in [Hg(CN) _{2}], [CH_{3}HgCl] | BOMD | 40 a.u. (0.978 fs) | 9 fs (1H), 13 ps (2H) | 300 K and 305 K | COSMO and explicit |

[48] | CPMD | CPMD | BLYP, GGA PBE | BLYP, GGA PBE | ^{1}H in water | CPMD | no information provided | 10 ps | 330 K | non applicable |

[49] | CP2K | NWChem | GGA PBE | GGA PBE | ^{7}Li in Li _{2}S_{4}, Li_{2}S_{6}, Li_{2}S_{8} | BOMD | 1 fs | 5 ps | 298.15 K, NPT (1 atm) | COSMO |

[50] | Quantum Espresso | ADF | GGA PBE | GGA PBE | ^{14}N in neat acetonitrile and 1-methyl-1,3-imidazole and 1-methyl-1,3,4-triazole in different solvents | CPMD | 0.145 fs | 50 ps for water, 60 ps for benzene, 40 ps for neat acetonitrile, 20 ps for water and benzene systems | 350 K | explicit |

[51] | Turbomole | Turbomole | B3LYP, RIMP2 | B3LYP, RIMP2 | ^{1}H in phosphoric acid | BOMD | 1 fs | 20,000 fs | 298–430 K | COSMO |

[52] | FEMTECK | Quantum Espresso | GGA PBE | GGA PBE | ^{11}B, ^{17}O, ^{7}Li in molten 0.3Li_{2}O–0.7B_{2}O_{3} (glass) | BOMD | 1.2 fs | no information provided | 1250 K | non applicable |

[53] | CASTEP | CASTEP | GGA PBE | GGA PBE | ^{207}Pb in Pb(NO _{3})_{2} | BOMD | 0.5–1.0 fs | From 5 to 20 ps | various | non applicable |

[54] | CASTEP | CASTEP | GGA PBE | GGA PBE | ^{13}C in piracetam | BOMD | 1.0 fs | 5 ps | 298 K | non applicable |

[55] | Quantum Espresso | ADF | PW91 XC | B1PW91 | ^{17}O in UO _{2}^{2+}, UO_{2}(CO_{3})_{3}^{4−}, (UO_{2})_{3}(CO_{3})_{6}^{6-} | CPMD | 0.122 fs | 8.5 ps | 330 K | COSMO |

[56] | CPMD | CPMD | BLYP | BLYP | ^{13}C in Asp 25-Asp25′ dyad in pepstatin A/HIV-1 protease | CPMD | 0.0096 fs | 2 ps | no information provided | no information provided |

**Table 2.**Influence of the vibrational contribution to the analyzed NMR parameter vs. static DFT-NMR calculations [32].

Analyzed NMR Parameter | Influence of the Vibrational Contribution to the Analyzed Parameter vs. Static DFT-NMR Calculations |
---|---|

Isotropic chemical shift | Increase |

Chemical shift anisotropy | Almost no changes (close to the experimental error) |

Quadrupolar coupling | Decrease, closer to the experimental data |

**Table 3.**Software applied in aiMD combined with the DFT-based NMR calculations. “+” indicates that this is possible to request the NMR parameters calculation in that software.

N° | Software/Code | Type of aiMD | NMR Parameters Calculation | License Type | Ref. Method | Ref. in Article |
---|---|---|---|---|---|---|

1 | CASTEP | BOMD, PIMD, CPMD | + | Academic, Commercial | [67,68] | [28,31,32,35,36,52,53] |

2 | CP2K | BOMD | + | Free, General Public License (GPL) | [69,70] | [29,37,48] |

3 | CPMD | BOMD, CPMD | + | Academic | [71,72] | [33,34,42,47,56] |

4 | Turbomole | BOMD | + | Commercial | [73,74] | [46,50] |

5 | Quantum Espresso | CPMD | + | Free, General Public License (GPL) | [75,76] | [37,39,41,45,49,55] |

6 | VASP | BOMD | + | Academic, Commercial | [77,78] | [30,40,43,44] |

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**MDPI and ACS Style**

Mazurek, A.H.; Szeleszczuk, Ł.; Pisklak, D.M. A Review on Combination of Ab Initio Molecular Dynamics and NMR Parameters Calculations. *Int. J. Mol. Sci.* **2021**, *22*, 4378.
https://doi.org/10.3390/ijms22094378

**AMA Style**

Mazurek AH, Szeleszczuk Ł, Pisklak DM. A Review on Combination of Ab Initio Molecular Dynamics and NMR Parameters Calculations. *International Journal of Molecular Sciences*. 2021; 22(9):4378.
https://doi.org/10.3390/ijms22094378

**Chicago/Turabian Style**

Mazurek, Anna Helena, Łukasz Szeleszczuk, and Dariusz Maciej Pisklak. 2021. "A Review on Combination of Ab Initio Molecular Dynamics and NMR Parameters Calculations" *International Journal of Molecular Sciences* 22, no. 9: 4378.
https://doi.org/10.3390/ijms22094378