## Calculating excited states in solids

One very important aspect of practical applications and theoretical
developments in solids is the accurate study of excited electronic states. We
are interested in accurately treating systems like colour centers in solids and
excited state potential energy surfaces in chemical reactions.

In our group we aim to do this in the framework of the *Equation of Motion*
coupled cluster theory.

Similar to the usual coupled cluster exponential ansatz, i.e.,

where $ \left | 0 \right \rangle $ is a single reference starting state
such as *Hartree-Fock*, the Equation of Motion Ansatz also involves an
operator $ \hat{R} ^{(i)} $ to create the $ i$-th excited state on top of the Coupled Cluster
ground state

The operator $ \hat{R} ^{(i)} $ is very similar to the $ \hat{T} $ cluster
operator,

with $ r ^{ab\ldots} _{ij\ldots}$ being the amplitudes. These amplitudes are
obtained by diagonalizing the similarity transformed Hamiltonian $ \bar{H} $:

Of course since $ \hat{T} $ is not an hermitian operator, also
$ \bar{H} $ is not hermitian, which means that left and right eigenvectors
must be obtained, which even further increases the computational cost of the
problem.

Our task is to develop further this method and to propose more cost effective
implementations to diagonalize $ \bar{H} $.