### Abstract

The analytical expression for the matrix elements between Morse's wavefunctions is shown and a modified temperature-dependent Morse potential was developed and validated. The developed formulae indicate that anharmonicity is responsible for a non-null displacement with respect to the equilibrium position at 0 K, that we call Zero Point Position. With their advantage of being computationally inexpensive and fast, the present model can be used to provide highly accurate theoretical estimation in the internuclear distance at vibrational ground state as well as their temperature dependence for not only diatomic but also polyatomic molecules. The present theoretical model was implemented to the development of a simple atomic-level model for the estimation of temperature-dependent thermal expansion coefficients of bulk metals, and was proved to be an efficient and rapid way for the evaluation of material mechanic properties. These models are analytical and are successfully tested on a series of metals.

Original language | English |
---|---|

Pages (from-to) | 323-335 |

Number of pages | 13 |

Journal | Chemical Physics |

Volume | 515 |

DOIs | |

Publication status | Published - 14 Nov 2018 |

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### Keywords

- Hypervirial theorem
- Morse potential
- Second quantisation
- Thermal expansion coefficient
- Zero Point Position

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

**The Zero Point Position in Morse's potential and accurate prediction of thermal expansion in metals.** / Benassi, Enrico.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The Zero Point Position in Morse's potential and accurate prediction of thermal expansion in metals

AU - Benassi, Enrico

PY - 2018/11/14

Y1 - 2018/11/14

N2 - The analytical expression for the matrix elements between Morse's wavefunctions is shown and a modified temperature-dependent Morse potential was developed and validated. The developed formulae indicate that anharmonicity is responsible for a non-null displacement with respect to the equilibrium position at 0 K, that we call Zero Point Position. With their advantage of being computationally inexpensive and fast, the present model can be used to provide highly accurate theoretical estimation in the internuclear distance at vibrational ground state as well as their temperature dependence for not only diatomic but also polyatomic molecules. The present theoretical model was implemented to the development of a simple atomic-level model for the estimation of temperature-dependent thermal expansion coefficients of bulk metals, and was proved to be an efficient and rapid way for the evaluation of material mechanic properties. These models are analytical and are successfully tested on a series of metals.

AB - The analytical expression for the matrix elements between Morse's wavefunctions is shown and a modified temperature-dependent Morse potential was developed and validated. The developed formulae indicate that anharmonicity is responsible for a non-null displacement with respect to the equilibrium position at 0 K, that we call Zero Point Position. With their advantage of being computationally inexpensive and fast, the present model can be used to provide highly accurate theoretical estimation in the internuclear distance at vibrational ground state as well as their temperature dependence for not only diatomic but also polyatomic molecules. The present theoretical model was implemented to the development of a simple atomic-level model for the estimation of temperature-dependent thermal expansion coefficients of bulk metals, and was proved to be an efficient and rapid way for the evaluation of material mechanic properties. These models are analytical and are successfully tested on a series of metals.

KW - Hypervirial theorem

KW - Morse potential

KW - Second quantisation

KW - Thermal expansion coefficient

KW - Zero Point Position

UR - http://www.scopus.com/inward/record.url?scp=85053698405&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053698405&partnerID=8YFLogxK

U2 - 10.1016/j.chemphys.2018.09.005

DO - 10.1016/j.chemphys.2018.09.005

M3 - Article

VL - 515

SP - 323

EP - 335

JO - Chemical Physics

JF - Chemical Physics

SN - 0301-0104

ER -