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EOM-CCSD

The EOM-CCSD method solves for excited states given a CCSD ground state. The key here is to apply a linear (CI-like) excitation operator to the CCSD ground state:1

\[\psi=R e^{T_1+T_2}|\psi_0>\]

where \(R\) is given as:

\[ R = r_0 + \sum_{ia} r_{ia} \hat a^{\dagger}_a \hat a_i + \frac{1}{2} \sum_{ijab} r_{ijab} \hat a^{\dagger}_a \hat a_i \hat a^{\dagger}_b \hat a_j \]

EOM-CCSD is often quite accurate for excitation energies of singly-excited states when the underlying CCSD method for the ground state is reasonable (i.e., when CCSD breaks down for the groundstate because of bond-breaking, the EOM-CCSD method for excited states will also become suspect). Excited states which have significant double excitation character are often treated less accurately compared to those which are primarily of single excitation character.

To run an EOM-CCSD calculation in TeraChem, one should start with a CIS calculation to obtain an initial guess for the \(R\) amplitudes. One obviously also needs to run a CCSD calculation for the ground state. A simple example would include: 

cis yes
cisnumstates 8
ccbox yes
ccbox_ccsd yes
ccbox_eomccsd_states 4
ccbox_eomccsd_guessvecs 8

in the input file. This codes for a CIS calculation with 8 excited states, a CCSD calculation for the ground state, and an EOM-CCSD calculation of 4 excited states, using the 8 CIS excited states to get an initial guess for the EOM-CCSD amplitudes.

Summary of relevant keywords

Keyword Type Default Description
ccbox_eomccsd_states integer 0 Number of EOM-CCSD excited states - setting this to a positive integer triggers an EOM-CCSD calculation
ccbox_eomccsd_maxiter integer 100 Maximum number of iterations in the EOM-CCSD equations
ccbox_eomccsd_r_convthre float 1.0e-6 Convergence threshold for EOM-CCSD amplitudes
ccbox_eomccsd_guessvecs integer 1 Number of inital guess vectors for EOM-CCSD
ccbox_eomccsd_maxsubspace integer 4*ccbox_eomccsd_states Maximum number of Davidson-like subspace vectors for EOM-CCSD
ccbox_properties bool no Compute ground state dipole moment and transition dipole moments?
ccbox_ntos bool no Compute natural transition orbitals? If yes, must also set ccbox_properties to yes

References

  1. J. F. Stanton and R. J. Bartlett, J. Chem. Phys. 98 7029 (1993) ↩