# Nuclear Motion Is Classical: Spectra of Hydrogen Chloride and Ammonia

## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Results and Discussion

#### 3.1. Ammonia

#### 3.2. Hydrogen Chloride

## 4. Conclusions

## Supplementary Materials

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AIMD | Ab Initio Molecular Dynamics |

BLYP | Becke–Lee–Yang–Parr density functional |

B3LYP | Hybrid functional based on BLYP |

B2PLYP | Double-hybrid functional based on B3LYP and MP2 |

CPMD | Car–Parrinello Molecular Dynamics |

-D3: | With dispersion correction |

DFT | Density functional theory |

MP2 | Moeller–Plesset second-order perturbation theory |

## References

- Car, R.; Parrinello, M. Unified Approach for Molecular Dynamics and Density-Functional Theory. Phys. Rev. Lett.
**1985**, 55, 2471–2474. [Google Scholar] [CrossRef] [PubMed] - Marx, D.; Hutter, J. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods; Cambridge University Press: Cambridge, UK, 2009. [Google Scholar]
- Frank, I.; Genuit, S.; Matz, F.; Oschinski, H. Ammonia, water, and hydrogen: Can nuclear motion be described classically? Int. J. Quantum Chem.
**2020**, 120, e26142. [Google Scholar] [CrossRef] - Frank, I. Classical motion of the nuclei in a molecule: A concept without alternatives. Chem. Select
**2020**, 5, 1872. [Google Scholar] [CrossRef] - Büchel, R.C.; Rudolph, D.A.; Frank, I. Deterministic quantum mechanics: The role of the Maxwell-Boltzmann distribution. Int. J. Quantum Chem.
**2021**, 121, e26555. [Google Scholar] [CrossRef] - Frank, I. Classical nuclear motion: Comparison to approaches with quantum mechanical nuclear motion. Hydrogen
**2023**, 4, 11–21. [Google Scholar] [CrossRef] - Yurchenko, S.N.; Barber, R.J.; Tennyson, J.; Thiel, W.; Jensen, P. Towards efficient refinement of molecular potential energy surfaces: Ammonia as a case study. J. Mol. Spectrosc.
**2011**, 268, 123. [Google Scholar] [CrossRef] - Marquardt, R.; Sagui, K.; Zheng, J.; Thiel, W.; Luckhaus, D.; Yurchenko, S.N.; Mariotti, F.; Quack, M. Global analytical potential energy surface for the electronic ground state of NH
_{3}from high level ab initio calculations. J. Phys. Chem. A**2013**, 117, 7502. [Google Scholar] [CrossRef] - Fabri, C.; Marquardt, R.; Csaszar, A.G.; Quack, M. Controlling tunneling in ammonia isotopomers. J. Chem. Phys.
**2019**, 150, 014102. [Google Scholar] [CrossRef] - Hutter, J.; Alavi, A.; Deutsch, T.; Bernasconi, M.; Goedecker, S.; Marx, D.; Tuckerman, M.; Parrinello, M. CPMD Version 4.3. Copyright IBM Corp 1990–2015. Copyright MPI für Festkörperforschung Stuttgart 1997–2001. Available online: https://github.com/CPMD-code/CPMD/releases/tag/4.3 (accessed on 11 May 2023).
- Grimme, S. Accurate Description of van der Waals Complexes by Density Functional Theory Including Empirical Corrections. J. Comput. Chem.
**2004**, 25, 1463. [Google Scholar] [CrossRef] [PubMed] - Troullier, N.; Martins, J.L. Efficient Pseudopotentials for Plane-Wave Calculations. Phys. Rev. B
**1991**, 43, 1993. [Google Scholar] [CrossRef] - Boero, M.; Parrinello, M.; Terakura, K.; Weiss, H. Car-Parrinello study of Ziegler-Natta heterogeneous catalysis: Stability and destabilization problems of the active site models. Mol. Phys.
**2002**, 100, 2935–2940. [Google Scholar] [CrossRef] - Brehm, M.; Kirchner, B. TRAVIS—A free analyzer and visualizer for monte carlo and molecular dynamics trajectories. J. Chem. Inf. Model.
**2011**, 51, 2007. [Google Scholar] [CrossRef] [PubMed] - Brehm, M.; Thomas, M.; Gehrke, S.; Kirchner, B. TRAVIS—A free analyzer for trajectories from molecular simulation. J. Chem. Phys.
**2020**, 152, 164105. [Google Scholar] [CrossRef] [PubMed] - Thomas, M.; Brehm, M.; Fligg, R.; Vöhringer, P.; Kirchner, B. Computing vibrational spectra from ab initio molecular dynamics. Phys. Chem. Chem. Phys.
**2013**, 15, 6608. [Google Scholar] [CrossRef] [PubMed] - Thomas, M.; Brehm, M.; Kirchner, B. Voronoi dipole moments for the simulation of bulk phase vibrational spectra. Phys. Chem. Chem. Phys.
**2015**, 17, 3207. [Google Scholar] [CrossRef] [PubMed] - Marzari, N.; Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B
**1997**, 56, 12847. [Google Scholar] [CrossRef] - Ikeda, T.; Boero, M. Role of van der Waals corrections in first principles simulations of alkali metal ions in aqueous solutions. J. Chem. Phys.
**2015**, 143, 194510. [Google Scholar] [CrossRef] [PubMed] - Silvestrelli, P.L.; Ambrosetti, A. Van der Waals interactions in DFT using Wannier functions without empirical parameters. J. Chem. Phys.
**2019**, 150, 164109. [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.; Petersson, G.A.; Nakatsuji, H.; et al. Gaussian~16 Revision A.03; Gaussian Inc.: Wallingford, CT, USA, 2016. [Google Scholar]
- Becke, A. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A
**1988**, 38, 3098. [Google Scholar] [CrossRef] [PubMed] - Becke, A. A New Mixing of Hartree-Fock and Local-Density Functional Theories. J. Chem. Phys.
**1993**, 98, 1372. [Google Scholar] [CrossRef] - Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem.
**2006**, 27, 1787. [Google Scholar] [CrossRef] [PubMed] - Grimme, S. Semiempirical hybrid density functional with perturbative second-order correlation. J. Chem. Phys.
**2006**, 124, 034108. [Google Scholar] [CrossRef] [PubMed] - NIST Chemistry WebBook. Available online: https://webbook.nist.gov/ (accessed on 30 December 2022).

**Figure 1.**Upper panel: Spectrum of ammonia as computed for a single molecule at different kinetic energies without dispersion correction using CPMD/BLYP. Medium panel: With dispersion correction. Lower panel: Experimental spectrum.

**Figure 2.**Upper panel: Spectrum of ammonia as computed for a single molecule at different kinetic energies without dispersion correction using CPMD/BLYP. The rotational degrees of freedom are frozen. Medium panel: With dispersion correction. Lower panel: Spectrum of ammonia as computed for a single NH${}_{3}$ molecule with Gaussian. Black: BLYP, red: B3LYP, green: BLYP-D3, blue: B3LYP-D3, yellow: B2PLYP, brown: B2PLYP-D3. The choice of the functional has little influence on the result. In particular the dispersion correction makes hardly a difference.

**Figure 3.**Upper panel: Spectrum of hydrogen chloride as computed for a single molecule at different kinetic energies without dispersion correction using CPMD/BLYP. Medium panel: With dispersion correction. Lower panel: Experimental spectrum. Red: Sum over computed peaks, respectively, average of the experimental spectrum.

**Figure 4.**Upper panel: Spectrum of hydrogen chloride as computed for a single molecule at different kinetic energies without dispersion correction using CPMD/BLYP. The rotational degrees of freedom are frozen. Medium panel: With dispersion correction. Lower panel: Spectrum of ammonia as computed for a single NH${}_{3}$ molecule with Gaussian. Black: BLYP, red: BLYP-D3, green: B3LYP, blue: B3LYP-D3, yellow: B2PLYP, brown: B2PLYP-D3. The choice of the functional has little influence on the result. In particular, the dispersion correction makes hardly a difference; hence, the graphs without dispersion correction are hardly visible.

**Figure 5.**Upper panel: Resulting spectrum of two single simulations (red: 100 K, green: 900 K) for hydrogen chloride. Medium panel: Result obtained by using different time steps and electronic masses. This affects mainly the rotational structure. Blue: lowest time step (0.1 a.u resp. 0.0024 fs, corresponding to a simulation time of 2.4 ps), cyan: highest time step (4.0 a.u. resp. 0.096 fs, corresponding to a simulation time of 96.0 ps). Lower panel: Experimental spectrum. For describing the experimental spectrum, it is necessary to perform many simulations at different kinetic energies.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Frank, I.
Nuclear Motion Is Classical: Spectra of Hydrogen Chloride and Ammonia. *Hydrogen* **2023**, *4*, 287-294.
https://doi.org/10.3390/hydrogen4020020

**AMA Style**

Frank I.
Nuclear Motion Is Classical: Spectra of Hydrogen Chloride and Ammonia. *Hydrogen*. 2023; 4(2):287-294.
https://doi.org/10.3390/hydrogen4020020

**Chicago/Turabian Style**

Frank, Irmgard.
2023. "Nuclear Motion Is Classical: Spectra of Hydrogen Chloride and Ammonia" *Hydrogen* 4, no. 2: 287-294.
https://doi.org/10.3390/hydrogen4020020