## 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.