# Underlying theory of a model for the Renner–Teller effect in tetra-atomic molecules: X{sup 2}Π{sub u} electronic state of C{sub 2}H{sub 2}{sup +}

## Abstract

In the present study, we prove the plausibility of a simple model for the Renner–Teller effect in tetra-atomic molecules with linear equilibrium geometry by ab initio calculations of the electronic energy surfaces and non-adiabatic matrix elements for the X{sup 2}Π{sub u} state of C{sub 2}H{sub 2}{sup +}. This phenomenon is considered as a combination of the usual Renner–Teller effect, appearing in triatomic species, and a kind of the Jahn–Teller effect, similar to the original one arising in highly symmetric molecules. Only four parameters (plus the spin–orbit constant, if the spin effects are taken into account), which can be extracted from ab initio calculations carried out at five appropriate (planar) molecular geometries, are sufficient for building up the Hamiltonian matrix whose diagonalization results in the complete low-energy (bending) vibronic spectrum. The main result of the present study is the proof that the diabatization scheme, hidden beneath the apparent simplicity of the model, can safely be carried out, at small-amplitude bending vibrations, without cumbersome computation of non-adiabatic matrix elements at large number of molecular geometries.

- Authors:

- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12, P.O. Box 47, PAK 105305, 11158 Belgrade (Serbia)

- Publication Date:

- OSTI Identifier:
- 22415742

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 17; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ACETYLENE; CALCULATION METHODS; ELECTRONIC STRUCTURE; EQUILIBRIUM; HAMILTONIANS; JAHN-TELLER EFFECT; L-S COUPLING; MATRICES; MATRIX ELEMENTS; MOLECULAR IONS; MOLECULES; ORBITS; SPIN; SURFACES; SYMMETRY

### Citation Formats

```
Perić, M., E-mail: peric@ffh.bg.ac.rs, Jerosimić, S., Mitić, M., Milovanović, M., and Ranković, R.
```*Underlying theory of a model for the Renner–Teller effect in tetra-atomic molecules: X{sup 2}Π{sub u} electronic state of C{sub 2}H{sub 2}{sup +}*. United States: N. p., 2015.
Web. doi:10.1063/1.4919285.

```
Perić, M., E-mail: peric@ffh.bg.ac.rs, Jerosimić, S., Mitić, M., Milovanović, M., & Ranković, R.
```*Underlying theory of a model for the Renner–Teller effect in tetra-atomic molecules: X{sup 2}Π{sub u} electronic state of C{sub 2}H{sub 2}{sup +}*. United States. doi:10.1063/1.4919285.

```
Perić, M., E-mail: peric@ffh.bg.ac.rs, Jerosimić, S., Mitić, M., Milovanović, M., and Ranković, R. Thu .
"Underlying theory of a model for the Renner–Teller effect in tetra-atomic molecules: X{sup 2}Π{sub u} electronic state of C{sub 2}H{sub 2}{sup +}". United States. doi:10.1063/1.4919285.
```

```
@article{osti_22415742,
```

title = {Underlying theory of a model for the Renner–Teller effect in tetra-atomic molecules: X{sup 2}Π{sub u} electronic state of C{sub 2}H{sub 2}{sup +}},

author = {Perić, M., E-mail: peric@ffh.bg.ac.rs and Jerosimić, S. and Mitić, M. and Milovanović, M. and Ranković, R.},

abstractNote = {In the present study, we prove the plausibility of a simple model for the Renner–Teller effect in tetra-atomic molecules with linear equilibrium geometry by ab initio calculations of the electronic energy surfaces and non-adiabatic matrix elements for the X{sup 2}Π{sub u} state of C{sub 2}H{sub 2}{sup +}. This phenomenon is considered as a combination of the usual Renner–Teller effect, appearing in triatomic species, and a kind of the Jahn–Teller effect, similar to the original one arising in highly symmetric molecules. Only four parameters (plus the spin–orbit constant, if the spin effects are taken into account), which can be extracted from ab initio calculations carried out at five appropriate (planar) molecular geometries, are sufficient for building up the Hamiltonian matrix whose diagonalization results in the complete low-energy (bending) vibronic spectrum. The main result of the present study is the proof that the diabatization scheme, hidden beneath the apparent simplicity of the model, can safely be carried out, at small-amplitude bending vibrations, without cumbersome computation of non-adiabatic matrix elements at large number of molecular geometries.},

doi = {10.1063/1.4919285},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 17,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}