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# Molecular spectroscopy

## Calculating molecular spectra

High resolution molecular spectroscopy probes both the basic physics of a molecule and gives information on its environment. The calculation of molecular spectra can be used to

• test potential energy surfaces
• predict and assign spectra
• Calculate transition intensities which are needed to obtain physical data from observed spectra such as number density, temperature, ortho/para ratios
• Generate bulk data like specific heats, opacities
• Establish links with reaction dynamics
• Quantum "chaology", classical dynamics of highly excited molecules is chaotic

Conventionally vibration-rotation spectra are described using the following model. Vibrational motions of the molecule are modelled with simple harmonic oscillations about the equilibrium position. Rotational energy levels are much more difficult to model. A standard treatment is the rigid-rotor model with a perturbative expansion. The molecule changes in response to the rotational motion via a centrifugal distortion. This is for example a secnnd order perturbation calculation.

An alternative method for reproducing molecular spectra is by direct solution of the underlying quantum mechanical equations of the problem. To do this completely from first principles it is necessary to consider both how the electrons and the nuclei move. A standard step in such a treatment is the Born-Oppenheimer approximation, i.e. it is assumed that the light electrons can relax instantaneously to any movement by the heavy and slow nuclei. Within these approximation the two motions can be treated separately.

For high accuracy it is usual to use procedures based on the Variational Principle. It gives much to high values for the absolute electronic energy of the system, but this energy is not important. The important question is how the bond lengths and bond angles of the molecule vary. Such calculations define a potenial (hyper-) surface on which the nuclei move. In water this potential energy surface has 3 dimensions corresponding to the 3 vibrational degrees of motion.

The method favoured by us to get accurate energy levels and wavefunctions for the vibrational and rotational motion of a triatomic molecule on a given potential energy surface is the Discrete Variable Representation (c.f.DVR3D, a program for the fully pointwise calculation of rotational-vibrational spectra of triatomic molecules by J.Tennyson, J.R. Henderson, N.G.Fulton. Since variational methods treat vibrational and rotational motion using the same potential an improvement derived from studying vibrational motions can lead to greatly improved estimates of rotational levels.

The figure shows a flow diagram for calculating an infrared spectrum using first principles quantum mechanics. The diamonds represent the steps and the rectangles the data involved in the calculation. In our work on water we use the TRIATOMOR and DVR3D program suites to perform the calculations from the potential energy and dipole surfaces onwards.

We are extending our methods to treat very highly excited states and in particular to the dissociation region. This work is computer intensive and calculations are being performed using massively parallel computers as part of the ChemReact high performance computing consortium.