## Technical Note:

Gaussian‘s Configuration Interaction with single excitations method (CI-Singles) enables it to compute excited state energies and gradients. This method may be used to predict excited state structures, UV/visible spectra, adiabatic excitation energies, 0-0 transitions, electron densities, and similar properties for a wide range of molecules. *Gaussian* includes both conventional and direct CI-Singles capabilities.

By default, when an excited state calculation is specified with the CIS keyword, Gaussian solves for the lowest three excited state of the molecule and reports on excitation energies and oscillator strengths for all three. It performs other requested operations, such as geometry optimizations, computes molecular properties (such as generalized densities, populations, and so on) for the lowest state of these three.

The Root option may be used to select a different, higher excited state for which to compute molecular properties, perform a geometry optimization, etc. For example, CIS(Root=2) is used to specify the second excited state. The value for Root defaults to 1.

In the course of its computations, Gaussian chooses twice as many vectors as the number of states in its initial guess (thus six by default) and iterates until the first three converge. For most molecular systems, normal invocation of this feature with default parameters will work fine. For highly symmetric molecules, however, special care is needed to ensure that the correct lowest energy state is calculated. Because the symmetry in the initial guess is conserved, if the molecule has very high symmetry and the number of states sought is too small, then all of the symmetry types in the molecule may not be represented in the initial guess vectors, and the program may converge to a higher energy state than desired.

The solution is to increase the number of initial vectors by increasing the number of solved for states via the NStates option. The recommended value for NStates is the number of operations in the largest abelian point group, which is output by Gaussian in the symmetry section, just preceding the standard orientation, with the normal (#) output option (but not with #T).

Here is an example for benzene:

Stoichiometry C6H6 Framework group D6H[3C2'(HC.CH)] Deg. of freedom 2 Full point group D6H NOp 24 Largest Abelian subgroup D2H NOp 8 Largest concise Abelian subgroup D2 NOp 4 Standard orientation: --------------------------------------------------------- ...

Therefore, for benzene, one would include CIS(NStates=8) in the route section.

Gaussian‘s CI-Singles methods thus make possible accurate and cost-effective calculations of the excited states for a wide range of molecules, including highly symmetric ones.

### Reference

James B. Foresman, Martin Head-Gordon, John A. Pople, and Michael J. Frisch. "Toward a Systematic Molecular Orbital Theory for Excited States," J Phys Chem. 96, 135 (1992).

Last updated on: 13 August 2016.