## This content will become publicly available on March 20, 2020

## Vibrational theory for monatomic liquids

## Abstract

The construction of the vibration-transit theory of liquid dynamics is being presented in three sequential research reports. The first is on the entire condensed-matter collection of *N*-atom potential energy valleys and identification of the random valleys as the liquid domain. The present (second) report defines the vibrational Hamiltonian and describes its application to statistical mechanics. The following is a brief list of the major topics treated here. The vibrational Hamiltonian is universal, in that its potential energy is a single 3 *N*-dimensional harmonic valley. The anharmonic contribution is also treated. The Hamiltonian is calibrated from first-principles calculations of the structural potential and the vibrational frequencies and eigenvectors. Exact quantum-statistical-mechanical functions are expressed in universal equations and are evaluated exactly from vibrational data. Exact classical-statistical-mechanical functions are also expressed in universal equations and are evaluated exactly from a few moments of the vibrational frequency distribution. The complete condensed-matter distributions of these moments are graphically displayed, and their use in statistical mechanics is clarified. In conclusion, the third report will present transit theory, which treats the motion of atoms between the *N*-atom potential energy valleys.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1532717

- Alternate Identifier(s):
- OSTI ID: 1546355

- Report Number(s):
- LA-UR-19-20181

Journal ID: ISSN 2469-9950; PRBMDO

- Grant/Contract Number:
- 89233218CNA000001

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 10; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Wallace, Duane C., Rudin, Sven Peter, De Lorenzi-Venneri, Giulia, and Sjostrom, Travis. Vibrational theory for monatomic liquids. United States: N. p., 2019.
Web. doi:10.1103/PhysRevB.99.104204.
```

```
Wallace, Duane C., Rudin, Sven Peter, De Lorenzi-Venneri, Giulia, & Sjostrom, Travis. Vibrational theory for monatomic liquids. United States. doi:10.1103/PhysRevB.99.104204.
```

```
Wallace, Duane C., Rudin, Sven Peter, De Lorenzi-Venneri, Giulia, and Sjostrom, Travis. Wed .
"Vibrational theory for monatomic liquids". United States. doi:10.1103/PhysRevB.99.104204.
```

```
@article{osti_1532717,
```

title = {Vibrational theory for monatomic liquids},

author = {Wallace, Duane C. and Rudin, Sven Peter and De Lorenzi-Venneri, Giulia and Sjostrom, Travis},

abstractNote = {The construction of the vibration-transit theory of liquid dynamics is being presented in three sequential research reports. The first is on the entire condensed-matter collection of N-atom potential energy valleys and identification of the random valleys as the liquid domain. The present (second) report defines the vibrational Hamiltonian and describes its application to statistical mechanics. The following is a brief list of the major topics treated here. The vibrational Hamiltonian is universal, in that its potential energy is a single 3N-dimensional harmonic valley. The anharmonic contribution is also treated. The Hamiltonian is calibrated from first-principles calculations of the structural potential and the vibrational frequencies and eigenvectors. Exact quantum-statistical-mechanical functions are expressed in universal equations and are evaluated exactly from vibrational data. Exact classical-statistical-mechanical functions are also expressed in universal equations and are evaluated exactly from a few moments of the vibrational frequency distribution. The complete condensed-matter distributions of these moments are graphically displayed, and their use in statistical mechanics is clarified. In conclusion, the third report will present transit theory, which treats the motion of atoms between the N-atom potential energy valleys.},

doi = {10.1103/PhysRevB.99.104204},

journal = {Physical Review B},

number = 10,

volume = 99,

place = {United States},

year = {2019},

month = {3}

}