The electronic excited states of molecules and larger clusters are of great technological importance. One would like to be able to predict the optical absorption/emission spectra of any given molecular structure, but excitation energies have historically proved to be much more difficult to calculate than ground state energies.

Many computational methods have been used to study excited states. Density-functional theory (DFT) and Hartree-Fock (HF) theory are very successful for calculating ground-state properties, but they often provide a poor description of excited states. Many powerful quantum chemistry techniques such as configuration interaction (CI) and coupled cluster methods are applicable to excited states. Although these methods can produce very accurate results, the computational cost increases very rapidly with the system size and they are therefore limited to small molecules. An alternative approach is that of many-body perturbation theory. For one-body excitations such as ionization energies, techniques based on Hedin's GW approximation have proved successful. In optical absorption the electron-hole interaction can be included by solving the Bethe-Salpeter equation (BSE) which involves the two-particle Green's function. Another technique which is gaining in popularity for studying excited states is time-dependent density functional theory (TD-DFT).

Diffusion Monte Carlo presents an attractive approach for studying electronic systems because of its potentially high accuracy and the favorable scaling of the computational cost with system size. Very accurate calculations of ground-state energies have already been demonstrated and in principle such performance can also be attained for excited states. The accuracy of a DMC calculation is determined by the quality of the nodal surface of the guiding wave function. Therefore, we require an affordable and reasonably accurate method for generating excited-state guiding wave functions.

Grimes et al. used multi-configuration self-consistent field calculations (MCSCF) to generate a guiding wave function for an excited state of H₂ and more recently, Grossman have used a similar approach for the silane and methane molecules. The drawback of this approach is that MCSCF calculations are themselves expensive and cannot be applied to large systems. We have examined the usefulness of singles-only CI (CIS) and time-dependent density-functional theory as cheaper methods of generating excited-state guiding wave functions.

We have also spent some time examining excited states in solids such as diamond and silicon, and an expanded discussion of this will appear here very soon.

• Excitons in small hydrogenated silicon clusters , A.R. Porter, M.D. Towler and R.J. Needs, (submitted to Phys. Rev. B). [Preprint: postscript].
• Electronic excited-state wave functions for quantum Monte Carlo: application to silane and methane, A.R. Porter, O.K. Al-Mushadani, M.D. Towler and R.J. Needs, (submitted to J. Chem. Phys.). [Preprint: postscript].
• Minimum principles and level splitting in quantum Monte Carlo excitation spectra: application to diamond , M.D. Towler, R.Q. Hood and R.J. Needs Phys. Rev. B, 62, 2330-2337 (2000) [PDF].
• Symmetry constraints and variational principles in diffusion quantum Monte Carlo calculations of excited-state energies , W.M.C. Foulkes, R.Q. Hood and R.J. Needs, Phys. Rev. B 60, 4558 (1999) [PDF].
• Quantum Monte Carlo calculations of the one-body density matrix and excitation energies of silicon , P.R.C. Kent, R.Q. Hood, M.D. Towler, R.J. Needs and G. Rajagopal, Phys. Rev. B, 57, 15293 (1998) [PDF].
• Diffusion quantum Monte Carlo calculations of excitation energies in silicon , A.J. Williamson, R.Q. Hood, R.J. Needs and G. Rajagopal, Phys. Rev. B, 57, 12140 (1998) [PDF].