^{1,a)}and Carlo U. Perotto

^{1}

### Abstract

Full-dimensional variational calculations are reported for the isomerising disilyne molecule, Si2H2. Large-scale calculations using coordinates based on orthogonal satellite vectors permitted the computation of excited vibrational state energies and wavefunctions for all four isomeric forms: dibridged Si(H2)Si, monobridged Si(H)SiH, disilavinylidene H2SiSi, and trans-bent HSiSiH. Energies and wavefunctions have been determined for the lowest 2400 totally symmetric vibrational states; this set includes highly excited states above all three chemically relevant isomerisation barriers – up to about 8300 cm−1 above the (dibridged) ground state. States strongly localised in the dibridged, monobridged, and disilavinylidene regions of the potential energy surface have been found as well as many partially or fully delocalised states. For the trans-bent form, only partially localised states have been identified. Comparisons are made with similar literature calculations on the isovalent acetylene-vinylidene system HCCH/H2CC.

We are grateful to Igor N. Kozin for valuable help and advice and many stimulating conversations on this work and to David Cable for his support in using the Distributed Computing Group cluster facility of the Computational Science and Engineering Department at Daresbury laboratory. We thank the EPSRC-funded CCP6 consortium for partial financial support for this work. We also thank the reviewers for their comments on the manuscript.

This paper is dedicated to the memory of Vicki S. Harris (1967–2008).

I. INTRODUCTION

II. METHODOLOGY

A. Variational calculations

B. Assignment of vibrational states

III. CALCULATIONS

IV. RESULTS AND DISCUSSION

V. CONCLUSIONS

### Key Topics

- Vibrational states
- 20.0
- Ground states
- 16.0
- Basis sets
- 10.0
- Probability theory
- 10.0
- Wave functions
- 10.0

## Figures

Orthogonal satellite vectors. The position of the point M is as defined by Mladenović. 36

The lowest 401 totally symmetric computed energy levels of Si2H2 relative to the dibridged ground state. (State number 401 is the trans ground state.) The states are separated by isomer: (left to right) dibridged, monobridged, vinyl, and trans.

The lowest 401 totally symmetric computed energy levels of Si2H2 relative to the dibridged ground state. (State number 401 is the trans ground state.) The states are separated by isomer: (left to right) dibridged, monobridged, vinyl, and trans.

From left to right: ground vibrational state probability densities (as functions of the angles θ1 and θ2) of the dibridged, monobridged, and disilavinylidene isomers of Si2H2 (totally symmetric states 1, 33, and 89, respectively); the computed energies of these states relative to the dibridged ground state are 0.0, 3163.6, and 4210.9 cm−1.

From left to right: ground vibrational state probability densities (as functions of the angles θ1 and θ2) of the dibridged, monobridged, and disilavinylidene isomers of Si2H2 (totally symmetric states 1, 33, and 89, respectively); the computed energies of these states relative to the dibridged ground state are 0.0, 3163.6, and 4210.9 cm−1.

Probability densities (as functions of the angles θ1 and θ2) for low lying totally symmetric excited vibrational states of the dibridged, monobridged, and disilavinylidene isomers of Si2H2: (left to right) state 10, dibridged 2ν4; state 44, monobridged 2ν6; and state 136, disilavinylidene 2ν6. The computed energies of these states relative to the dibridged ground state are 2006.3, 3488.9, and 4692.0 cm−1, respectively – see Table III for mode numbering.

Probability densities (as functions of the angles θ1 and θ2) for low lying totally symmetric excited vibrational states of the dibridged, monobridged, and disilavinylidene isomers of Si2H2: (left to right) state 10, dibridged 2ν4; state 44, monobridged 2ν6; and state 136, disilavinylidene 2ν6. The computed energies of these states relative to the dibridged ground state are 2006.3, 3488.9, and 4692.0 cm−1, respectively – see Table III for mode numbering.

States with probability densities delocalised along the reaction paths dibridged-monobridged [left and centre] and disilavinylidene-monobridged [right] (totally symmetric states 169, 185, and 218, respectively with computed energies relative to the dibridged ground state of 4900.3, 5012.2, and 5218.7 cm−1).

States with probability densities delocalised along the reaction paths dibridged-monobridged [left and centre] and disilavinylidene-monobridged [right] (totally symmetric states 169, 185, and 218, respectively with computed energies relative to the dibridged ground state of 4900.3, 5012.2, and 5218.7 cm−1).

Nearest neighbour distribution of Si2H2 totally symmetric vibrational energy levels.

Nearest neighbour distribution of Si2H2 totally symmetric vibrational energy levels.

States with a high degree of localisation in the trans-bent configuration: trans ground state [left]; trans 2ν6 [centre]; and with delocalisation along the trans-monobridged reaction path [right]. These are totally symmetric states 401, 633, and 944 with computed energies of 5900.8, 6454.4, and 6969.9 cm−1, respectively.

States with a high degree of localisation in the trans-bent configuration: trans ground state [left]; trans 2ν6 [centre]; and with delocalisation along the trans-monobridged reaction path [right]. These are totally symmetric states 401, 633, and 944 with computed energies of 5900.8, 6454.4, and 6969.9 cm−1, respectively.

## Tables

Energies (in cm−1) of the Si2H2 critical points a relative to the dibridged global minimum.

Energies (in cm−1) of the Si2H2 critical points a relative to the dibridged global minimum.

Vibrational mode numbering for Si2H2 isomers. a

Vibrational mode numbering for Si2H2 isomers. a

Calculated vibrational energies and assignments of Si2H2.

Calculated vibrational energies and assignments of Si2H2.

Observed and calculated Si2H2 dibridged fundamentals and inversion splittings for the ground state, fundamentals, and first and second overtones of the ν2 inversion mode.

Observed and calculated Si2H2 dibridged fundamentals and inversion splittings for the ground state, fundamentals, and first and second overtones of the ν2 inversion mode.

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