A QED-Hartree-Fock (HF) calculation is performed by specifying a QED-HF (`qed-hf`

) wave function
in the method section of the input file. To start a ground state
QED-HF we specify

```
- method
qed-hf
- do
ground state
```

A minimal working example for a QED-HF single-point calculation on water with wavevector \(\vec{k}=(0,0,1)\), frequency \(\omega=0.5\) au and coupling \(\lambda=0.05\) au:

```
- system
charge: 0
- do
ground state
- method
qed-hf
- boson
interaction type: photon
modes: 2
frequency: {0.5, 0.5}
wavevector: {0.0, 0.0, 1.0}
coupling: {0.05, 0.05}
- geometry
basis: cc-pVDZ
H 0.86681 0.60144 0.00000
H -0.86681 0.60144 0.00000
O 0.00000 -0.07579 0.00000
```

Save this as `h2o.inp`

and invoke the launch script.

```
path/to/eT_launch.py h2o.inp
```

After the calculation finished you should find `h2o.out`

and `h2o.timing.out`

in your working directory. If the calculation exited successfully
(look for `eT terminated successfully!`

at the bottom of the file),
a summary of the calculation should be printed at the end.

The wave function has a coherent state parameter per each orbital in the basis that
diagonalizes the dipole operator. This way electron photon correlation is naturally
included in the methodology.
A Strong Coupling QED-Hartree-Fock (SC-QED-HF) calculation is performed by specifying a
SC-QED-HF (`sc-qed-hf`

) wave function in the method section
of the input file. To start a ground state SC-QED-HF we specify

```
- method
sc-qed-hf
- do
ground state
```

A minimal working example for a SC-QED-HF single-point calculation on water with polarization \(\vec{\epsilon}=(0,0,1)\), frequency \(\omega=0.5\) au and coupling \(\lambda=0.05\) au:

```
- system
charge: 0
- do
ground state
- method
sc-qed-hf
- boson
interaction type: photon
modes: 1
frequency: {0.5}
polarization: {0.0, 0.0, 1.0}
coupling: {0.05}
- geometry
basis: cc-pVDZ
H 0.86681 0.60144 0.00000
H -0.86681 0.60144 0.00000
O 0.00000 -0.07579 0.00000
```

Save this as `h2o.inp`

and invoke the launch script.

```
path/to/eT_launch.py h2o.inp
```

After the calculation finished you should find `h2o.out`

and `h2o.timing.out`

in your working directory. If the calculation exited successfully
(look for `eT terminated successfully!`

at the bottom of the file),
a summary of the calculation should be printed at the end.

A QED Full Configuration Interaction (FCI) calculation is performed by specifying a `qed-hf`

/`hf`

/`sc-qed-hf`

(for closed-shell systems) or a `rohf`

/`uhf`

wave function (for open-shell systems)
and the QED-FCI wave function (`qed-fci`

) in the method section of the input file.
E.g., for a QED-HF calculation we write

```
- method
qed-hf
qed-fci
```

To perform a single-point QED-FCI calculation it is necessary to specify `ground state`

do section:

```
- do
ground state
```

As in standard FCI the calculations require the solver ci section in which it is necessary to specify the number of states you want to compute in your calculation, for instance:

```
- solver fci
states: 5
```

A minimal working example for a QED-FCI single-point calculation on water with polarization \(\vec{\epsilon}=(0,0,1)\), frequency \(\omega=0.5\) au and coupling \(\lambda=0.05\) au:

```
- do
ground state
- memory
available: 16
- method
hf
fci
- boson
interaction type: photon
modes: 1
boson states: {1}
coupling: {0.05}
frequency: {0.5}
polarization: {0, 0, 1}
- solver fci
states: 5
- geometry
basis: sto-3g
H 0.86681 0.60144 0.00000
H -0.86681 0.60144 0.00000
O 0.00000 -0.07579 0.00000
```

Note

For open-shell calculations you might want to specify the multiplicity
in the system section. The default multiplicity is `1`

.

Save this as `h2o.inp`

and invoke the launch script.

```
path/to/eT_launch.py h2o.inp
```

After the calculation finished you should find `h2o.out`

and `h2o.timing.out`

in your working directory. If the calculation exited successfully
(look for `eT terminated successfully!`

at the bottom of the file),
a summary of the calculation should be printed at the end.