Requests an excited state calculation using the EOM-CCSD method [Koch90, Stanton93, Koch94a, Kallay04, Caricato12a, Caricato12b, Caricato13, Caricato13a, Caricato13b, Caricato14, Goings14]. EOM-CCSD is an extension of CCSD for modeling excited states. It provides CCSD-level accuracy for excited-state calculations and requires comparable computational cost (scaling as N^{6} like CCSD) and additional disk space. This method uses a preliminary CIS calculation to generate the initial guess for the states followed by an EOM-CCSD analysis.

Note: The EOM-CCSD method exploits abelian symmetry (and not higher point groups).

The various solvation methods for EOM developed by Caricato [Cammi09, Cammi10, Caricato12b] are available; see the SCRF=PTED option for details.

### State Selection and Specification

#### NStates=N

Try to solve for the lowest N states in EOM. It is a good idea to set N to be larger than the desired number of states to take account of likely state reordering between the CIS and EOM portions.

#### NStPIR=K

Number of states per symmetry type to solve for in the EOM. The default is 2. Note that the symmetry types correspond to the largest abelian subgroups. If K is less than zero, then a separate blank line-terminated input section is read specifying the number of states for each symmetry type (irreducible representation). The symmetry ordering can be determined quickly by running a preliminary job with the %KJob L301 Link 0 command. We recommend that you also specify NCISState with a reasonable number of states for the CIS (see below).

Only one of NState and NStPIR should be used to specify the desired number of states. If both are specified, then NState takes precedence. If nothing is specified, then NStPIR=2 is the default.

#### Singlets

Solve for singlet excited states. This option only affects calculations on closed-shell systems, for which it is the default.

#### Triplets

Solve for triplet excited states. This option only affects calculations on closed-shell systems. Must be combined with Singlets to solve for both kinds of states.

#### NCISState=M

Total number of states to be generated as guesses by CIS. The default with NState is N*Irr.Reps.; with NStPIR, it is (K+2)*Irr.Reps.

#### Root=N

Specifies the state of interest. The default is the first excited state (N=1).

### Procedure-Related Options

#### MaxCyc=N

Specifies the maximum number of cycles for the calculation.

#### Convergence=N

Sets the convergence calculations to 10^{-N} on the energy and 10^{-(N-2)} on the wavefunction. The default is N=7.

#### CCConvergence=N

Use 10^{-N} as the convergence on the CCSD and ground-state Z-vector iterations. CCSDConvergence is a synonym for this option. The default is N=8.

#### LRTransitionDensities

Requests linear response transition densities [Koch94a, Koch90, Kallay04] in addition to EOM-style (unrelaxed) ones. This formalism is more rigorous than the default EOM-CCSD, but it is also computationally more expensive. Note that the two formalisms are equivalent when CCSD provides the exact wavefunction (i.e., the two electron system). Applies only to singlet closed shell and open shell systems.

#### EnergyOnly

Save time by computing only right eigenvectors, which are sufficient for excitation energies but not for transition densities.

### Reading/Saving Amplitudes

Amplitudes are saved by default for use in a subsequent calculation. They may be optionally read-in from a previous calculation. The number of states can be increased in the subsequent calculation. The CIS for the guess also reads in vectors and automatically adds states if more guesses are required (provided there is no change in the basis set).

#### TWInCore

Forces the program to store amplitudes and products in memory during higher-order post-SCF calculations. The default is to do so if possible, but to run off disk if memory is insufficient. TWInCore causes the program to terminate if these can not be held in memory, while NoTWInCore prohibits in-memory storage.

#### SaveAmplitudes

Saves the converged amplitudes in the checkpoint file for use in a subsequent calculation (e.g., using a larger basis set). Using this option results in a very large checkpoint file, but also may significantly speed up later calculations.

#### ReadAmplitudes

Reads the converged amplitudes from the checkpoint file (if present). Note that the new calculation can use a different basis set, method (if applicable), etc. than the original one.

#### ReadGroundStateAmplitudes

Reads in only the ground-state (and Z-vector) amplitudes and not the excited state amplitudes. This option is useful when going from an EOM calculation on singlets to one on triplets. ReadGSAmplitudes is a synonym for this option.

#### NewCIS

Do a new CIS calculation from scratch when reading EOM amplitudes. This option is needed when reading in singlet states but calculating both singlets and triplets. It is also needed when using a different basis set than was used for a prior calculation retrieved with ReadAmplitudes.

Using EOM-CCSD. It is often useful to perform a preliminary, smaller EOM-CCSD calculation which solves for a large number of states, and then run a more accurate calculation on the states of interest. The following route sections illustrate this approach:

First calculation:
%Chk=my_eom
# EOMCCSD(NStates=10,EnergyOnly)/Aug-CC-PVDZ
Second calculation:
%Chk=my_eom
# EOMCCSD(NStates=2,ReadAmplitudes,NewCIS)/Aug-CC-PVQZ

Here is some example output from an EOM-CCSD calculation. This header introduces the results section:

==============================================
EOM-CCSD transition properties
==============================================

Next comes the transition electric dipole moment, separated into left and right sections. The dipole and oscillator strengths reported at the end of each line are identical in the two sections as the former is the product of the two:

Ground to excited state transition electric dipole moments (Au):
state X Y Z Dip. S. Osc.
1 0.0000 0.0000 -0.3969 0.1601 0.0614
2 0.0000 0.3963 0.0000 0.1638 0.0756
3 0.0000 1.3681 0.0000 1.9183 1.0604
Excited to ground state transition electric dipole moments (Au):
state X Y Z Dip. S. Osc.
1 0.0000 0.0000 -0.4034 0.1601 0.0614
2 0.0000 0.4133 0.0000 0.1638 0.0756
3 0.0000 1.4022 0.0000 1.9183 1.0604

For each state, a separate section lists the CI expansion coefficients for excitation along with the corresponding orbital abelian symmetry type, divided by left and right, and then by excitation type:

Excited State 1: Singlet-A1 15.6603 eV 79.17 nm f=0.0614
Right Eigenvector
Alpha Singles Amplitudes
I SymI A SymA Value
4 1 6 1 0.675597 Excitation from orbital 4 (occ.) to 6 (virt.).
3 4 7 4 0.122684
Beta Singles Amplitudes
I SymI A SymA Value
4 1 6 1 0.675597
3 4 7 4 0.122684
Alpha-Beta Doubles Amplitudes Similar information for a double excitation.
I SymI J SymJ A SymA B SymB Value
4 1 4 1 6 1 6 1 -0.118378
Left Eigenvector
Alpha Singles Amplitudes
I SymI A SymA Value
4 1 6 1 0.676418
3 4 7 4 0.121856
Beta Singles Amplitudes
I SymI A SymA Value
4 1 6 1 0.676418
3 4 7 4 0.121856
Alpha-Beta Doubles Amplitudes
I SymI J SymJ A SymA B SymB Value
4 1 4 1 6 1 6 1 -0.107806
Total Energy, E(EOM-CCSD) = -74.4340926881 Total energy reported for state of interest.