# Classical Nuclear Motion: Comparison to Approaches with Quantum Mechanical Nuclear Motion

## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Results

#### 3.1. Wave Packets and Alternatives

#### 3.2. Multiple Spawning

#### 3.3. Path Integrals

#### 3.4. Full Treatment

## 4. Discussion

## Supplementary Materials

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AIMD | Ab initio molecular dynamics |

BOMD | Born–Oppenheimer molecular dynamics |

CPMD | Car–Parrinello molecular dynamics |

DFT | Density functional theory |

ESIPT | Excited-state intramolecular proton transfer |

HOMO | Highest occupied molecular orbital |

LUMO | Lowest unoccupied molecular orbital |

NEO | Nuclear-electronic orbital method |

QM/MM | Quantum mechanics/molecular mechanics |

ROKS | Restricted open-shell Kohn–Sham theory |

SCF | Self-consistent field theory |

TDDFT | Time-dependent DFT |

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**Figure 1.**HOMO of phenol during the photoreaction (ROKS simulation). Apart from a rapid change of sign between 12 and 24 fs, not much happens to the electronic structure. A hydrogen atom is expelled at the end of the simulation (at the right side of the molecule).

**Figure 2.**LUMO of phenol during the photoreaction (ROKS simulation). The motion starts from a ${\pi}^{*}$ orbital which has already an antibinding interaction concerning the O–H bond. The elongation of this bond leads to the formation of the 1s orbital of the dissociating hydrogen atom.

**Figure 3.**Photoreaction of [2,2${}^{\prime}$-bipyridyl]-3,3${}^{\prime}$-diol, ROKS simulation. Upper and lower panel: reaction of the two OH groups, respectively. The isomerization events, which are characterized by a crossing of the orange and red curves, are not exactly simultaneous, but follow closely one after the other. Color code of educt and product plots: white: hydrogen, black: carbon, green: nitrogen, red: oxygen.

**Figure 4.**HOMO and LUMO of [2,2′-bipyridyl]-3,3′-diol before and after the photoreaction. The central carbon–carbon bond is strengthened in the excited state and adopts double bond character.

**Figure 5.**(

**a**) LUMO of [2,2′-bipyridyl]-3-ol; (

**b**) LUMO of bipyridine. The LUMOs resemble the LUMO of bipyridyl-diol. Upon occupation of this orbital, the central carbon–carbon bond is strengthened. This prevents a rotation.

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**MDPI and ACS Style**

Frank, I.
Classical Nuclear Motion: Comparison to Approaches with Quantum Mechanical Nuclear Motion. *Hydrogen* **2023**, *4*, 11-21.
https://doi.org/10.3390/hydrogen4010002

**AMA Style**

Frank I.
Classical Nuclear Motion: Comparison to Approaches with Quantum Mechanical Nuclear Motion. *Hydrogen*. 2023; 4(1):11-21.
https://doi.org/10.3390/hydrogen4010002

**Chicago/Turabian Style**

Frank, Irmgard.
2023. "Classical Nuclear Motion: Comparison to Approaches with Quantum Mechanical Nuclear Motion" *Hydrogen* 4, no. 1: 11-21.
https://doi.org/10.3390/hydrogen4010002