To specify active atom regions the `active atoms`

section is required.

`selection type: [string]`

Keyword to give the type of atom selection. Required keyword.

Valid keyword values are:

`list`

A list of atoms will be given`range`

A range of atoms will be given`central atom`

A central atom and a radius will be given

`[method string]: [list, range or radius]`

Keyword to give the list, range or radius for an active space treated at the given level of theory.

Note

This keyword depends on the `selection type`

.

Valid method strings:

`hf`

`ccs`

`cc2`

`ccsd`

`cc3`

`ccsd(t)`

A list is specified using set notation: `{1,2,3}`

.

A range is specified as `[1,3]`

(equivalent to `{1,2,3}`

).

A radius is specified by a double precision real (e.g. `1.0d2`

) and is always in Angstrom units. The atoms within the radius \(r\) of the `central atom`

then define the active atoms.

Example: First three atoms in the input are chosen as HF active atoms space.

```
- active atoms
selection type: list
hf: {1,2,3}
```

`central atom: [integer]`

Specifies the central atom in the active space. Requested for `selection type: central atom`

.

Note

This keyword is necessary in case of `selection type: central atom`

.

`inactive basis: [string]`

Specifies the basis set on the inactive atoms, that is the atoms not specified in the `active atoms`

section.
Optional.

Valid keyword values are basis sets available in \(e^T\).

`[method string] basis: [string]`

Set basis for active space treated at a given level of theory. Optional.

Valid method strings:

`hf`

`ccs`

`cc2`

`ccsd`

`cc3`

`ccsd(t)`

Valid keyword values are basis sets available in \(e^T\).

Example: First three atoms in the input are chosen as CCSD active atoms space with aug-cc-pVDZ basis.

```
- active atoms
selection type: range
ccsd: [1,3]
ccsd basis: aug-cc-pVDZ
```

The `active space`

section is used to run post Hartree-Fock methods
only for an active space of orbitals.
There are three types of active spaces supported at the moment:

The frozen core approximation, where core orbitals of each atom are

*excluded*from the active space.An active space consisting of

*canonical*orbitals, as used for example in CASCI.An active space consisting of orbitals

*localized*in a specified region of the system.

`canonical: {[real], [real]}`

The first number specifies the amount of active electrons and the second number the amount of active molecular orbitals. The orbitals are selected by energy starting from the orbital with lowest energy.

`freeze atom cores: {[int], ...}`

Default: false

Enables the frozen core approximation, where the core orbital of selected atoms are frozen. The atoms are specified by integers referring to the number of the atom in the geometry section.

Note

Currently only works for second row atoms. Can be used in combination with cvs.

`freeze core: {[int], ...}`

Default: false

Enables the frozen core approximation. Selected MOs can be frozen by specifying the MO indices in a list. If no list is given the core MOs of all atoms will be frozen. Optional.

Note

Can be used in combination with cvs if the frozen core MOs are specified in a list. Note that the indices specified in core excitation refer to the MOs after freezing.

`localized`

Default: false

This enables the construction of localized Hartree-Fock orbitals after SCF is converged. Optional.

Note

The orbitals are localized for a set of `active atoms`

which needs to be defined in the active atoms section.

Warning

This keyword is currently not supported for `casci`

and `fci`

calculations.

General QED keywords.

`interaction type: [string]`

Default: photon

Specifies the type of the boson-matter interaction. Currently photon and plasmon are supported.

`modes: [integer]`

Specifies the number of boson modes.

Note

Only `modes: 1`

can be selected for SC-QED-HF.

`frequency: {[real], ...}`

Specifies the boson frequency/energy (\(\omega\)) in atomic units. Number of parameters given must be equal to the number of modes.

`boson states: {[integer], ...}`

Default: 1

Specifies the number of boson states per boson mode. Number of integers given must be equal to the number of modes.

Note

Required in post-QED-HF methods.

`coupling: {[real], ...}`

Default: 0.0

Specifies the light-matter coupling \(\lambda= \sqrt{4\pi/V_{\text{eff}}}\) in atomic units. Required in photon calculations. Number of parameters given must be equal to the number of modes.

`polarization: {[real],[real],[real]}`

Specifies the transversal polarization vector (\(\vec{\epsilon}\)). Only used in photon calculations.

`wavevector: {[real],[real],[real]}`

Specifies the direction of the wavevector (\(\vec{k}\)). Only used in photon calculations.

Note

For photon calculations, either the polarization or wavevector must be specified, but not both. The number of modes must be even when the wavevector is specified.

`coupling bilinear: {[real], ...}`

Overwrites the bilinear light-matter coupling \(\lambda \sqrt{\omega/2}\). Number of parameters given must be equal to the number of modes.

`coupling self: {[real], ...}`

Overwrites the light-matter self-coupling \(0.5 \lambda^2\). Number of couplings given must be equal to the number of modes.

`coherent state: {[real], ...}`

Specifies the coherent state / displacement for each boson mode. Number of parameters given must be equal to the number of modes.

`boson number: {[int], ...}`

Maximum number of boson occupations to be used in the strong coupling calculations for each mode.

`quadrupole oei`

Assume complete basis (\(\sum_p |p\rangle\langle p| = 1\)) to rewrite the self-interaction with quadrupole moments, removing references to the virtual density. Only used in photon calculations.

Note

Decreases accuracy in a finite basis. Without this option frozen core is disabled.

`cbo: {[real], ...}`

Specifies the displacement q of the field for each boson mode. Number of parameters given must be equal to the number of modes.

`print dipole eri construction`

Prints the transformation of the two electron integral in the basis that diagonalizes the dipole operator.

Note

Keyword only used in SC-QED-HF calculations.

General coupled cluster keywords.

`Bath orbital`

Default: false

Add a bath orbital to the calculation with zero orbital energy and zero electron repulsion integrals.

Note

This keyword is required to compute ionized states.

The `cc mean value`

section is used to obtain CC ground state expectation values.

Note

This section is required if the keyword `mean value`

is given in the `do`

section.

`dipole`

Calculation of coupled cluster ground state dipole moment.

`quadrupole`

Calculation of coupled cluster ground state quadrupole moment.

`molecular gradient`

Calculation of the coupled cluster ground state molecular gradient, if implemented. The gradient is printed to a separate output file.

Keywords related to time-dependent coupled cluster calculations go into the `cc real time`

section.

Note

One of the keywords below must be specified if you have requested `real time`

in the `do`

section.

`propagation`

Default: `false`

Perform real-time propagation of the coupled-cluster state.

`fft dipole moment`

Default: `false`

Perform complex fast Fourier transform of the dipole moment time series from an earlier real-time propagation calculation.

`fft electric field`

Default: `false`

Perform complex fast Fourier transform of the electric field time series from an earlier real-time propagation calculation.

Keywords specific to response calculations are given in the `cc response`

section.

For **EOM** transition moments from ground and excited states,
and permanent moments for excited states are implemented for CCS, CC2, CCSD and CC3.
**EOM** polarizabilities are implemented for CCS, CC2 and CCSD.

For **linear response** transition moments from the ground state
and polarizabilities are implemented for CCS, CC2, and CCSD.

Note

This section is required if the keyword `response`

is given in the `do`

section.

One of the keywords `polarizabilities`

, `permanent moments`

or `transition moments`

must be specified.

`polarizabilities: {[character], [character], ...}`

Enables the calculation of polarizabilities, and gives the option to specify cartesian componens (`xx``

, `yz`

, etc.). Specifying components is optional.

`transition moments`

Enables the calculation of transition moments.

`eom`

Properties will be calculated within the equation of motion formalism.

Either this or the `lr`

keyword must be specified.

Available for CCS, CC2, CCSD, and CC3.

`lr`

Properties will be calculated within the linear response formalism.

Either this or the `eom`

keyword must be specified.

Available for CCS, CC2, and CCSD.

`dipole length`

Compute transition dipole moments in length gauge.

`dipole velocity`

Compute transition dipole moments in length, velocity and mixed gauge.

`rotatory strength`

Compute rotatory strength in length and velocity gauge.

`frequencies: {[real], [real], ...}`

Frequencies, in Hartree, for which the polarizability shall be computed. Required for polarizabilities.

`asymmetric`

Enables the calculation of polarizabilities based on an asymmetric expression. This allows the user to avoid calculating the response of one of the two components for the polarizability. Instead both amplitude and multiplier response must be calculated for the desired component.

Asymmetric polarizabilities are only available for `eom`

and require the `response components`

keyword to be set.

`response components: {[character], [character], ...}`

The components for which to calculate amplitude and multiplier response for asymmetric polarizabilities.

`initial states: {[real], [real], ...}`

Default: `{0}`

(Only the ground state is considered.)

Numbers of the states for which the transition/permanent moments shall be computed.

`permanent moments`

Enables the calculation of permanent moments.

Note

Only implemented in the EOM formalism for excited states.

`dyson orbitals`

Enables the calculation of Dyson orbitals.

Note

Only implemented in the EOM formalism for ionized and core-ionized states.
For ionizations a bath orbital has to be requested in the cc section
and the `ionization`

keyword has to be specified solver cc es

`full-space transition moments`

Enables the calculation of full-space transition moments after band Lanczos calculations. This comes in addition to the reduced-space initial-final state transition moments calculated in the band Lanczos solver.

`damping: [real]`

Default: `0`

(No damping.)

Damping to be used in the damped response solver.

The `ci mean value`

section is used to obtain expectation values
of operators for the CI ground state.

`dipole`

Calculation of the CI ground state dipole moment.

`quadrupole`

Calculation of the CI ground state quadrupole moment.

The `ci transition property`

section is used to obtain transition matrix elements
of operators for specified CI states.

`dipole`

Calculation of the CI transition dipole moment.

`quadrupole`

Calculation of the CI transition quadrupole moment.

`initial states: {[real], [real], ...}`

Default: `{0}`

(Only the ground state is considered.)

Numbers of the states from which the CI transition/permanent moments shall be computed.

`final states: {[real], [real], ...}`

Default: `{0}`

(Only the ground state is considered.)

Numbers of the states to which the CI transition/permanent moments shall be computed.

Keywords related to the exchange-correlation functionals used in DFT calculations.

`functional: [string]`

Specifies the DFT XC functional as defined in LibXC: https://www.tddft.org/programs/libxc/functionals/

Some common functionals can be defined by:

`lda`

: lda_x + lda_c_vwn_rpa`lsda`

: lda_x + lda_c_vwn_rpa`pbe`

: gga_x_pbe + gga_c_pbe`blyp`

: gga_x_b88 + gga_c_lyp`pbe0`

: hyb_gga_xc_pbeh`b3lyp`

: hyb_gga_xc_b3lyp`bhandhlyp`

: hyb_gga_xc_bhandhlyp`sogga11x`

: hyb_gga_x_sogga11_x + gga_c_sogga11_x

`exchange: [string]`

Specifies the DFT Exchange functional as defined in LibXC: https://www.tddft.org/programs/libxc/functionals/

`correlation: [string]`

Specifies the DFT Correlation functional as defined in LibXC: https://www.tddft.org/programs/libxc/functionals/

`hf percentage: [real]`

Specifies the HF Exchange percentage for Hybrid DFT Functionals

The `do`

section is where the type of calculation is specified. It will determine the \(e^T\) engine used in the calculation.

Note

Only one of the keywords below has to be specified.
For example for the calculation of excited states only the keyword `excited state`

is required
even though the ground state equations have to be solved as well to obtain excited states.

`cholesky eri`

Keyword to run a Cholesky decomposition of the two-electron integrals. Note that this is done automatically for any coupled cluster calculation, the keyword should only be given if only Cholesky decomposition is to be performed.

`ground state`

Keyword to run a ground state calculation at the level of theory given in the `method`

section.
Enables the ground state or reference engine.

`geometry optimization`

Keyword to run a geometry optimization. Enables the geometry optimization engine. Only ground state optimizations are available for HF, while excited state optimized structures are also available at the CC level of theory. Depending on the availability, the optimization will be performed with analytical gradients (available for HF and CCSD) or numerical gradients (if analytical is not available).

`harmonic frequencies`

Keyword to determine vibrational frequencies and normal modes for HF and CC methods. Recommended to use for methods that have analytical gradients (HF and CCSD). A default calculation determines the frequencies and the normal modes. See `harmonic frequencies`

section for additional calculations (such as Wigner sampling).

`mean value`

Keyword to calculate *coupled cluster* expectation values. Enables the mean value engine, which determines the coupled cluster ground state amplitudes and multipliers, and calculates the requested expectation value. Which mean value(s) to calculate are specified in the `cc mean value`

section.

Note

For Hartree-Fock calculations, one must write `ground state`

in `do`

and specify the mean value(s) to calculate in the `hf mean value`

section.

`excited state`

Keyword to run a coupled cluster excited state calculation. Enables the excited state engine, which calculates the ground and excited state amplitudes.

Note

The `cc es solver`

section is required for excited state calculations.

`response`

Keyword to enable the coupled cluster response engine. Implemented features are EOM transition moments and polarizabilities for CCS, CC2, CCSD and CC3, and LR transition moments and polarizabilities for CCS. The response engine drives the calculation of ground state amplitudes and multipliers, excited state vectors (left and right eigenvectors of the Jacobian matrix) and the requested property.

Note

The `cc response`

section is required for coupled cluster response calculations.

`restart`

Global restart keyword to activate restart where possible.

Note

eT will first check if restart is possible and use the default start guess if not.

`real time`

Keyword to run coupled cluster time propagation. Enables the time-dependent engine.

Note

The `cc real time`

section is required for coupled cluster time propagation.

`shielding`

Keyword to run CPHF nuclear shielding tensors.

`tdhf excited state`

Keyword to run TDHF excitation energies (Tamm-Dancoff or RPA).

Note

The `solver tdhf es`

section is required for TDHF excited state calculations.

`tdhf response`

Keyword to run TDHF response calculation (polarizabilities).

To calculate the CCSD ground and four excited states, specify

```
- do
excited state
```

together with

```
- method
hf
ccsd
```

and

```
- solver cc es
singlet states: 4
```

Keywords related to the specification of electric field pulses for real-time calculations.

`envelope: {[integer], [integer],...}`

Envelope of electric field pulse \(1,2,\ldots\).

Valid keyword values are:

`1`

Use Gaussian envelope.`2`

Use sine squared envelope.

`x polarization: {[real], [real], ...}`

\(x\) polarization component of electric field pulse \(1,2,\ldots\).

`y polarization: {[real], [real], ...}`

\(y\) polarization component of electric field pulse \(1,2,\ldots\).

`z polarization: {[real], [real], ...}`

\(z\) polarization component of electric field pulse \(1,2,\ldots\).

`central time: {[real], [real], ...}`

Central time of the envelope of electric field pulse \(1,2,\ldots\).

`width: {[real], [real], ...}`

Temporal width of the envelope of electric field pulse \(1,2,\ldots\) in atomic units. The width corresponds to the Gaussian root-mean-squared width of a pulse with a Gaussian envelope and the period of a pulse with a sine squared envelope.

`carrier angular frequency: {[real], [real], ...}`

Angular frequency of the carrier wave of electric field pulse \(1,2,\ldots\) in atomic units.

`peak strength: {[real], [real], ...}`

Amplitude of the carrier wave of electric field pulse \(1,2,\ldots\) in atomic units.

`phase shift: {[real], [real], ...}`

Carrier-envelope phase shift of electric field pulse \(1,2,\ldots\). The shift corresponds to the difference between the maxima of the envelope and the carrier wave.

`repetition: {[real], [real], ...}`

Default: `{1, 1, ...}`

(a single instance of each pulse)

Number of instances of electric field pulse \(1,2,\ldots\).

`separation: {[real], [real], ...}`

The temporal separation between repetitions of electric field pulse \(1,2,\ldots\).

Note

Should only be specified if the `repetition`

keyword has been specified.

The geometry must be given as xyz coordinates either with Angstrom or Bohr units. The default units are Angstrom. The basis set is also given in the geometry section.

Minimal example for the geometry section

```
- geometry
basis: aug-cc-pVDZ
H 0.86681 0.60144 5.00000
H -0.86681 0.60144 5.00000
O 0.00000 -0.07579 5.00000
```

If other units than `Angstrom`

are desired,
this must be specified at the top of the geometry section with the `units`

keyword.
Possible values are `Angstrom`

and `Bohr`

.

```
- geometry
units: Bohr
basis: aug-cc-pVDZ
H 1.63803 1.13655 9.44863
H -1.63803 1.13655 9.44863
O 0.00000 -0.14322 9.44863
```

Different basis sets may be placed on the atoms using the `basis`

keyword.
An atom is given the last basis set specified above it,
e.g. in the following example the oxygen has the d-aug-cc-pVDZ basis
and the hydrogens have the aug-cc-pVDZ basis.
See here for a list of included basis sets.

```
- geometry
basis: aug-cc-pVDZ
H 0.86681 0.60144 5.00000
H -0.86681 0.60144 5.00000
basis: d-aug-cc-pVDZ
O 0.00000 -0.07579 5.00000
```

Basis functions can be placed without the corresponding atom by using the keyword
`ghost`

. Every atom specified after the keyword will have zero charge, which corresponds
to only placing the basis functions at the specified location. An H2 calculation run with the
same basis functions as H2O can be done using this geometry:

```
- geometry
basis: aug-cc-pVDZ
H 0.86681 0.60144 5.00000
H -0.86681 0.60144 5.00000
ghost
O 0.00000 -0.07579 5.00000
```

In case of QM/MM calculations,
the QM and MM portions have to be separated by a line containing `--`

.
The parameters for QM/MM calculations are placed after the XYZ coordinates.
In case of electrostatic QM/MM embedding (see molecular mechanics section),
the charge of each atom needs to be provided:

```
- geometry
basis: cc-pVDZ
O 0.87273600 0.00000000 -1.24675400
H 0.28827300 0.00000000 -2.01085300
H 0.28827300 0.00000000 -0.48265500
--
O [IMol= 1] -0.77880300 0.00000000 1.13268300 [q=-0.834]
H [IMol= 1] -0.66668200 0.76409900 1.70629100 [q=+0.417]
H [IMol= 1] -0.66668200 -0.76409900 1.70629000 [q=+0.417]
```

In case of polarizable QM/FQ (see molecular mechanics section), the electronegativities (chi) and chemical hardnesses (eta) are needed for each atom:

```
- geometry
basis: cc-pVDZ
O 0.87273600 0.00000000 -1.24675400
H 0.28827300 0.00000000 -2.01085300
H 0.28827300 0.00000000 -0.48265500
--
O [IMol= 1] -0.77880300 0.00000000 1.13268300 [chi=0.11685879436,eta=0.58485173233]
H [IMol= 1] -0.66668200 0.76409900 1.70629100 [chi=0.00000000000,eta=0.62501048888]
H [IMol= 1] -0.66668200 -0.76409900 1.70629000 [chi=0.00000000000,eta=0.62501048888]
```

Keywords related to the grid construction.

`maximum angular order: [int]`

Default: `30`

Maximum angular order of Lebedev quadrature

`minimum angular order: [int]`

Default: `15`

Minimum angular order of Lebedev quadrature

`partitioning: [string]`

Default: `Becke partitioning`

Partitioning applied to the the atoms.

`quadrature: [string]`

Default: `Gauss-Chebyshev`

Radial quadrature. Possible values:

`Gauss-Chebyshev`

`Treutler-Ahlrics`

`radial threshold: [real]`

Default: `1.0E-6`

Threshold of the radial quadrature. Lower values increase the quality (and numbers of points) of the grid.

`cube side: [real]`

If present, build a grid using the specified quantity as side of the discretization cubes (for debug porpuses only)

`cube offset: [real]`

If present, offset applied to the minimum/maximum atomic cartesian coordinates along each direction to construct the grid (for debug porpuses only)

The `harmonic frequencies`

section is used to specify settings for vibrational frequency calculations.
A default calculation will determine the vibrational frequencies and the normal modes for the ground state at the specified input geometry. For additional calculations and excited states, see the keywords below.

Note

This section is used if the keyword `harmonic frequencies`

is given in the `do`

section.

`gradient displacement: [real]`

Default: \(10^{-3}\) (or 1.0d-3)

Displacement for numerical differentiation used to evaluate gradients which are used to evaluate the Hessian.

`gradient method: [string]`

Default: analytical

Specifies whether to evaluate gradients using analytical calculation or numerical.

Valid keyword values are:

`analytical`

Analytical gradient evaluation.`central difference`

Numerical differentiation with central differences (recommended for numerical differentiation).`forward difference`

Numerical differentiation with forward differences.

`hessian displacement: [real]`

Default: \(10^{-4}\) (or 1.0d-4)

Displacement for numerical differentiation used to evaluate Hessian. Method used is central differences based on either analytical or numerical gradients.

`run geometry optimization`

If specified, the geometry will first be optimized before the frequency calculation. Otherwise the frequency calculation will be performed at the input geometry.

`state: [integer]`

Default: \(0\)

Specifies the state to calculate the Hessian for. State = 0 corresponds to the ground state, state = 1 to the first excited state, and so on.

`wigner samples: [integer]`

Perform 0 K Wigner sampling. This will produce the number of samples specified, sampled from a normal mode Wigner distribution at T = 0 K. The created samples are stored as wigner_sample_0.dat, wigner_sample_1.dat, and so on, where each .dat file contains first the sampled geometry and then the sampled momentum (FMS90 format).

`wigner seed: [integer]`

Default: \(0\)

Seed used in random number generator for the Wigner sampling. If not specified, eT will use the default seed (obtained from wigner seed: 0). The seed will produce reproducable Wigner samples for a given integer type (either 32 or 64).

The `hf mean value`

section is used to obtain HF expectation values.

`dipole`

Calculation of the HF dipole moment.

`quadrupole`

Calculation of the HF quadrupole moment.

`molecular gradient`

Calculation of the HF molecular gradient, if implemented. The gradient is printed to a separate output file.

In the integrals section you can specify settings for the handling of Cholesky vectors and electron repulsion integrals in coupled cluster calculations.

`cholesky storage: [string]`

Default: `memory`

if they take up less than 20% of the total memory; `disk`

otherwise

Specify how to store the Cholesky vectors. Optional.

Valid options are:

`memory`

Store Cholesky vectors in memory.`disk`

Store Cholesky vectors on file.

`eri storage: [string]`

Default: `memory`

if the entire matrix is needed in the calculation and they take up less than 20% of the total memory; `none`

otherwise

Specify how to store the electron repulsion integrals. Optional.

Valid options are:

`memory`

Store full electron repulsion matrix in memory.`none`

Always construct the integrals from Cholesky vectors.

Warning

`memory`

can slow down calculations for which the full integral matrix is not needed. This is the case for CCS and CC2 calculations. We recommend to use defaults.

`mo eri in memory`

Default: `false`

Override defaults and store full MO ERI matrix in memory if true. Recommended for time-dependent CC.

`t1 eri in memory`

Default: `false`

Override defaults and store full T1 ERI matrix in memory if true.

`ri: [string]`

Default: `None`

Enables the RI approximation for the integrals and provides the auxiliary basis set.

Valid options are any available auxiliary basis set.

Keywords related to the use of asymmetric Lanczos algorithms for solving the excited state coupled cluster equations and calculating transition properties go into the `lanczos`

section.

`biorthogonalize last: [integer]`

Default: The maximum number of iterations given by the `singlet states`

keyword.

The number of last generated Lanczos vectors that the band Lanczos algorithm should orthogonalize the vector generated at the current iteration against.

`chain length: [integer]`

Specifies the dimension of the reduced (Krylov sub-) space for the asymmetric Lanczos algorithm.
Required for `algorithm: asymmetric lanczos`

.

`deflation threshold: [real]`

Default: \(10^{-12}\) (or 1.0d-12)

Minimum value of the norm of the right or left Lanczos vector generated at any iteration. The right or left band Lanczos space is deflated if the norm goes below this threshold.

`lanczos normalization: [integer]`

Default: `asymmetric`

Specifies the type of biorthonormalization for the asymmetric Lanczos algorithm. Optional.

Valid keyword values are:

`asymmetric`

Which enables \(\tilde{p} = p\) and \(\tilde{q} = \frac{q}{p\cdot q}\)`symmetric`

Which enables \(\tilde{p} = \frac{p}{\sqrt{|p\cdot q|}}\) and \(\tilde{q} = \text{sgn}(p\cdot q)\frac{q}{\sqrt{|p\cdot q|}}\)

`max energy: [real]`

Default: 1000

Maximum energy of the states checked for convergence and/or stored in the band Lanczos algorithm, in Hartree.

`min energy: [real]`

Default: -1000

Minimum energy of the states checked for convergence and/or stored in the band Lanczos algorithm, in Hartree.

`min transition strength: [real]`

Default: 0.0

Minimum transition strength of the states checked for convergence and/or stored in the band Lanczos algorithm, to any of the initial states specified with the `restart states`

keyword, in Hartree.

`operators: {integer, integer, ... }`

List of operators used for starting vectors based on operators and initial states.
Each number in the list corresponds to a number at the same position in the `restart states`

list.
The integer `0`

specifies the unit operator, and cannot be given together with the number `0`

in the `restart states`

list (cannot use the ground state as a starting vector).
The numbers `1`

, `2`

and `3`

give the `X`

, `Y`

and `Z`

dipole operators, respectively.
The numbers `4`

, `5`

, `6`

, `7`

, `8`

and `9`

give the `XX`

, `XY`

, `XZ`

, `YY`

, `YZ`

and `ZZ`

quadrupole operators, respectively.

`overlap threshold: [real]`

Default: \(10^{-14}\) (or 1.0d-14)

Specifies the minimum value of the dot product of the right and left Lanczos vector generated at an iteration. The algorithm breaks down, and the iteration loop is exited, if the overlap goes below this threshold.

`restart states: { integer, integer, ... }`

Default: List of integers from `1`

to the integer specified with the `singlet states`

keyword.

List of precomputed initial states used for restart and operator starting vectors.
Each number in the list corresponds to a number at the same position in the `operators`

list.
The integer `0`

specifies the ground state, and must be given together with a number greater than `0`

in the `operators`

list (cannot use the ground state as a starting vector).
An integer greater than `0`

specifies the precomputed excited state with the given number, and can be used together with all operator numbers.
If the excited state does not exist on file, a default start vector will be used instead.

`skip convergence`

Skips testing the convergence of the states calculated using the band Lanczos algorithm, implying that all the calculated states are stored on file.

Keywords to specify the available memory is given in the `memory`

section.

Note

The amount specified is the total memory eT is allowed to use,
i.e. **not** the memory per thread.

`available: [integer]`

Default: 8

Specifies the available memory, default units are gigabytes. Optional.

`unit: [string]`

Default: GB

Specifies the units for the specified available memory. Optional.

Valid keyword values are:

B

KB

MB

GB

In the method section, the wave function method is specified. In the case of a post-HF calculation, both the reference wave function method and the post-HF method must be specified.

At the Self-Consistent Field level of theory the following keywords may be specified:

`hf`

for restricted Hartree-Fock (RHF)`mlhf`

for multilevel Hartree-Fock`uhf`

for unrestricted Hartree-Fock`rohf`

for restricted open-shell Hartree-Fock`cuhf`

for constrained unrestricted Hartree-Fock`qed-hf`

for quantum electrodynamics Hartree-Fock (QED-HF)`sc-qed-hf`

for strong coupling quantum electrodynamics Hartree-Fock (SC-QED-HF)`dft`

for density functional theory (DFT)

In coupled cluster calculations, either RHF or MLHF must be specified, in addition to the coupled cluster method.

The available coupled cluster methods are:

`ccs`

`cc2`

`lowmem-cc2`

`ccsd`

`ccsd(t)`

`cc3`

`ccsdt`

`mlcc2`

`mlccsd`

`qed-ccsd`

`mp2`

`fci`

`casci`

`fci`

`qed-fci`

For a Hartree-Fock calculation, specify the type of wave function (`hf`

, `mlhf`

, or `uhf`

) in the method section.

```
- method
hf
```

To perform a coupled cluster calculation, both the coupled cluster method and the type of reference wave function must be specified.

```
- method
hf
ccsd
```

Keywords specific to multilevel coupled cluster enter into the `mlcc`

section.

`levels: [string], [string], ...`

Specifies the level of theory for the different active spaces. Required keyword.

Valid keyword values are:

`ccs`

`cc2`

`ccsd`

Note

Necessary for MLCCSD calculation.

`cc2 orbitals: [string]`

Specifies the type of orbitals used for orbital partitioning in MLCC2. Required keyword.

Valid keyword values are:

`cnto-approx`

Approximated correlated natural transition orbitals`cholesky`

Cholesky orbitals (occupied and virtual)`cholesky-pao`

Cholesky occupied orbitals and projected atomic orbitals for the virtuals.`nto-canonical`

Natural transition orbitals for occupied and canonical for virtuals.

Warning

`nto-canonical`

and `cholesky`

orbitals are not generally recommended.

`ccsd orbitals: [string]`

Specifies the type of orbitals used for orbital partitioning in MLCCSD. Required keyword.

Valid keyword values are:

`cnto-approx`

Approximated correlated natural transition orbitals`cholesky`

Cholesky orbitals (occupied and virtual)`cholesky-pao`

Cholesky occupied orbitals and projected atomic orbitals for the virtuals.`nto-canonical`

Natural transition orbitals for occupied and canonical for virtuals.

Warning

`nto-canonical`

and `cholesky`

orbitals are not generally recommended.

`cholesky threshold: [real]`

Default: \(1.0\cdot 10^{-2}\) (or 1.0d-2)

Threshold for the Cholesky decomposition of the density. Only used with `cc2 orbitals: cholesky`

or `cc2 orbitals: cholesky-pao`

`cnto occupied cc2: [integer]`

Determines the number of occupied orbitals in the CC2 orbital space for the MLCC2 calculation.

Note

Necessary if `cc2 orbitals: cnto-approx`

is given.

`cnto virtual cc2: [integer]`

Default: \(n_v^{\text{CC2}} = n_o^{\text{CC2}}\cdot\frac{n_v}{n_o}\)

Sets the number of virtual orbitals in the CC2 orbital space for the MLCC2 calculation. Optional.

Note

Only used if `cc2 orbitals: cnto-approx`

is given.

`cnto occupied ccsd: [integer]`

Determines the number of occupied orbitals in the CCSD orbital space for the MLCCSD calculation.

Note

Necessary if `ccsd orbitals: cnto-approx`

is given.

`cnto virtual ccsd: [integer]`

Default: \(n_v^{\text{CCSD}} = n_o^{\text{CCSD}}\cdot\frac{n_v}{n_o}\)

Sets the number of virtual orbitals in the CCSD orbital space for the MLCCSD calculation. Optional.

Note

Only used if `ccsd orbitals: cnto-approx`

is given.

`cnto states: {[integer], [integer], ...}`

Determines which CCS excited states are used to construct the approximated CNTOs.

Note

Necessary if `cc2 orbitals: cnto-approx`

or `ccsd orbitals: cnto-approx`

is given.

`print ccs calculation`

Default: false

Enables the printing of the CCS calculation in the case of `cc2 orbitals: cnto-approx`

or `ccsd orbitals: cnto-approx`

. Optional.

`print cc2 calculation`

Default: false

Enables the printing of the CC2 calculation in the case of `ccsd orbitals: cnto`

. Optional.

`nto occupied cc2: [integer]`

Determines the number of occupied orbitals in the CC2 orbital space for the MLCC2 calculation.

Note

Necessary if `cc2 orbitals: nto-canonical`

is given.

`nto occupied ccsd: [integer]`

Determines the number of occupied orbitals in the CCSD orbital space for the MLCCSD calculation.

Note

Necessary if `ccsd orbitals: nto-canonical`

is given.

`canonical virtual cc2: [integer]`

Default: \(n_v^{\text{CC2}} = n_o^{\text{CC2}}\cdot\frac{n_v}{n_o}\)

Sets the number of virtual orbitals in the CC2 orbital space for the MLCC2 calculation. Optional.

Note

Only used if `cc2 orbitals: nto-canonical`

is given.

`canonical virtual ccsd: [integer]`

Default: \(n_v^{\text{CCSD}} = n_o^{\text{CCSD}}\cdot\frac{n_v}{n_o}\)

Sets the number of virtual orbitals in the CCSD orbital space for the MLCCSD calculation. Optional.

Note

Only used if `ccsd orbitals: nto-canonical`

is given.

`nto states: {[integer], [integer], ...}`

Determines which CCS excited states are used to construct the NTOs.

Note

Necessary if `cc2 orbitals: nto-canonical`

is given.

`cnto restart`

Default: false

If specified, the solver will attempt to restart from previously determined CNTO matrices (M and N). Optional.

`nto restart`

Default: false

If specified, eT will attempt to restart from previously determined NTO matrices (M and N). Optional.

`orbital restart`

Default: false

If specified, orbital partitioning is skipped and MLCC orbitals (and sizes of orbital sets) are read from file. Optional.

MM specific keywords enter into the `molecular mechanics`

section.

`forcefield: [string]`

Default: `non-polarizable`

Specifies the forcefield to be used for the MM portion.

Valid keyword values are:

`non-polarizable`

Electrostatic QM/MM EmbeddingNote

The charge has to be provided for each atom in the geometry section.

`fq`

Fluctuating Charge force field.Note

The electronegativity and chemical hardness has to be provided for each atom in the geometry section.

`algorithm: [string]`

Default: `mat_inversion`

Selects the algorithm to be used to solve the FQ equation. So far only the inversion algorithm is implemented. Optional.

Keywords specific to multilevel Hartree-Fock enter into the `multilevel hf`

section.

`initial hf optimization`

Default: `false`

Enables an initial optimization of the full density through a standard HF calculation to a low threshold.

`initial hf threshold: [real]`

Default: \(1.0\cdot10^{-1}\) (or 1.0d-1)

Threshold for the initial HF optimization. Should only be specified if `initial hf optimization`

is also specified.

`print initial hf`

Default: false

Enables the printing of the initial HF optimization in the case that `initial hf optimization`

is given. Optional.

`cholesky virtuals`

Default: `false`

Enable the use of Cholesky decomposition of the virtual AO density to construct the active virtual orbitals. The default is to use projected atomic orbitals.

`cholesky threshold: [real]`

Default: \(1.0\cdot10^{-2}\) or (1.0d-2)

Threshold for the Cholesky decomposition of the AO density to construct an active space.

`project on minimal basis`

Default: `false`

First diagonalization of the AO fock matrix will be performed in a minimal basis.

`no mo screening`

Default:

`false`

Disables screening based on the MO-coefficients in MLHF.

Note

Active space screening is recommended to reduce the cost of the calculation.

Keywords to enable localization of Hartree-Fock orbitals

`type: [string]`

Default: None

Determines the type of functional to use for orbital localization.

Valid keyword values are:

`edmiston-ruedenberg`

`foster-boys`

Note

This keyword is required to obtain localized Hartree-Fock orbitals

`orbitals: [string]`

Default: None

Determines which orbital sets to localize. Either occupied, virtual, or both. In the latter case, the orbitals are localized separately to obtain new Hartree-Fock orbitals (i.e., there is no occupied-virtual mixing).

Valid keyword values are:

`occupied`

`virtual`

`both`

Note

This keyword is required to obtain localized Hartree-Fock orbitals

`threshold: [real]`

Default: \(10^{-6}\) (or 1.0d-6)

Threshold below which the maximum element of the gradient needs to be to stop the orbital localization procedure. Optional.

Keywords specific to the polarizable continuum model enter into the `pcm`

section.

`input: [string]`

Specifies if the input parameters are given in the \(e^{T}\) input file or in an external file handled directly by the external library PCMSolver. Required.

Valid keyword values are

`external`

Note

No further input has to be given to

`pcm`

because the parameters have to be specified in an external*.pcm*-file.

`internal`

`tesserae area: [real]`

Default: 0.3

Area of the finite elements (*tesserae*) the surface is constructed from given in square Angstrom.

`solver type: [string]`

Default: `iefpcm`

Selects the type of solver to be used to solve the PCM equation.

Valid keyword values are

`iefpcm`

Integral Equation Formalism PCM`cpcm`

conductor-like PCM

In this section you can specify settings related to the main output files.

`output print level: [string]`

Specifies the print level for the main output file. Default is `normal`

. Optional.

Valid keyword values are:

`minimal`

Only banners, final results like total energies or excitation energies, solver settings, and other essential information.`normal`

In addition to minimal, print iteration information, amplitude analysis, and other non-essential information.`verbose`

In addition to normal, print all relevant information for users. This can make the output difficult to read and navigate.`debug`

In addition to verbose, prints information mostly relevant for debugging code that behaves unexpectedly.

`timing print level: [string]`

Specifies the print level for the timing file. Default is `normal`

. Optional.

Valid keyword values are:

`minimal`

Total solver timings, total program time, and other essential timings.`normal`

In addition to minimal, iteration times and details like time to calculate omega, the Fock matrix, and other expensive terms.`verbose`

In addition to normal, times for subtasks, such as micro-iteration times as well as individual contributions to the omega vector.`debug`

In addition to verbose, prints timings mostly relevant for debugging code that behaves unexpectedly.

`full references`

If specified, implementation references will be printed in APA style. Otherwise, only the DOIs are printed to the output file.

`z-matrix`

If specified, prints the z-matrix to the output file.

Keywords related to solving the excited state coupled cluster equations go into the `solver cc es`

section.
Required for calculations of excited states!

`singlet states: [integer]`

Specifies the number of singlet excited states to calculate.

Note

Either `singlet states`

or `triplet states`

must be specified unless the asymmetric Lanczos solver is requested.
For the band Lanczos solver, the number specifies the maximum number of iterations (also known as chain length).

`triplet states: [integer]`

Specifies the number of triplet excited states to calculate.

Note

Either `singlet states`

or `triplet states`

must be specified unless the asymmetric Lanczos solver is requested.
Triplet states are currently only available for CCS, CC2 and CCSD.
Both the Davidson and DIIS solver can be used.

`algorithm: [string]`

Default: `davidson`

for CCS, CC2, MLCC2, and CCSD; `non-linear davidson`

for lowmem-CC2 and CC3.

Solver to use for converging the excited state equations.

Valid keyword values are:

`davidson`

Use Davidson algorithm with residuals preconditioned with the orbital differences approximation of the Jacobian. Cannot be used for lowmem-CC2 and CC3.

`diis`

Use DIIS algorithm with update estimates obtained from the orbital differences approximation of the Jacobian. Can be used for lowmem-CC2 and CC3.

`non-linear davidson`

Use the non-linear Davidson algorithm with residuals preconditioned with the orbital differences approximation of the Jacobian. Can be used for lowmem-CC2 and CC3.

`asymmetric lanczos`

Use the asymmetric Lanczos algorithm for excitation energies. EOM oscillator strengths will be calculated as well. Cannot be used for lowmem-CC2, MLCC2, and CC3.

`asymmetric band lanczos`

Use the asymmetric band Lanczos algorithm for excitation energies and EOM-CC transition/oscillator strengths. Cannot be used for lowmem-CC2, MLCC2, and CC3.

Note

The `asymmetric lanczos`

algorithm requires the `response`

keyword in the do section.

`right eigenvectors`

Default: true

If specified, solve for the right eigenvectors of the Jacobian matrix. This keyword should only be specified for an excited state calculation. For property calculations, the program will solve for both left and right vectors. Optional.

Note

For response calculations or when using the asymmetric lanczos algorithm, this keyword is ignored.

`left eigenvectors`

Default: false

If specified, solve for the left eigenvectors of the Jacobian matrix. This keyword should only be specified for an excited state calculation. For property calculations, the program will solve for both left and right vectors. Optional.

Note

For response calculations or when using the asymmetric lanczos algorithm, this keyword is ignored.

`energy threshold: [real]`

Default: \(10^{-3}\) (or 1.0d-3)

Energy convergence threshold, as measured with respect to the previous iteration. Optional.

Note

The solvers will not check for the energy convergence, if the energy threshold is not set.

`residual threshold: [real]`

Default: \(10^{-3}\) (or 1.0d-3)

Threshold of the \(L^{2}\)-norm of the residual vector of the excited state equation. Optional

`core excitation: { integer, integer, ... }`

Default: false

Solve for core excitations within the CVS approximation. The integers specify which orbitals to excite out of. Orbitals are ordered according to orbital energy (canonical orbitals). If the keyword has been specified, CVS will be activated automatically. Optional.

`remove core: { integer, integer, ... }`

Default: false

Valence excitations, but with excitations from core MOs projected out. The integers specify which core orbitals from which one should not excite. Orbitals are ordered according to orbital energy (canonical orbitals). Optional.

Note

This is the orthogonal projection to `core excitation: { integer, integer, ... }`

Warning

Cannot be used in CVS calculations or when frozen core is enabled.

`ionization`

Default: false

Solve for ionized state. If this keyword is specified, the ionized state will be calculated using a bath orbital and projection similar to CVS. Optional.

Note

For ionizations a bath orbital has to be requested in the cc section

`max iterations: [integer]`

Default: 100

The maximum number of iterations. The solver stops if the number of iterations exceeds this number. Optional.

`diis dimension: [integer]`

Default: 20

Number of previous DIIS records to keep. Optional.

Note

Only relevant for `algorithm: diis`

.

`restart`

Default: false

If specified, the solver will attempt to restart from a previous calculation. Optional.

`storage: [string]`

Default: `disk`

Selects storage of excited state records. Optional.

Valid keyword values are:

`memory`

Stores records in memory.`disk`

Stores records on file.

`crop`

Default: false

If specified, the CROP version of DIIS will be enabled. Optional.

Note

Only relevant for `algorithm: diis`

.

`max reduced dimension: [integer]`

Default: \(\max(100, 10 n_\mathrm{s})\), where \(n_\mathrm{s}\) is the number of singlet states specified by `singlet states: [integer]`

in the `solver cc es`

section.

The maximal dimension of the reduced space of the Davidson procedure. Optional.

Note

Only relevant for `algorithm: davidson`

and `algorithm: non-linear davidson`

.

`max micro iterations: [integer]`

Default: \(100\)

Maximum number of iterations in the non-linear Davidson solver. Optional.

`rel micro threshold: [real]`

Default: \(10^{-1}\) (or 1.0d-1)

Threshold for convergence in the micro iterations of the non-linear Davidson solver. This threshold is relative to the current norm of the residuals.

`state guesses: {i=integer, a=integer}, {i=integer, a=integer}`

Specifies start guesses for excited states in terms of transitions from occupied orbital \(i\) to virtual \(a\). Optional.

Note

Start guesses are required for all excited states requested.

The LUMO is the first virtual orbital \(a=1\)

`olsen`

Enable the Olsen update in Davidson. Will use a more accurate preconditioner which may improve convergence. Optional.

Keywords related to solving the ground state coupled cluster equations go into the `solver cc gs`

section. This section is optional. If it is not given, defaults will be used for all keywords.

`algorithm: [string]`

Default: `newton-raphson`

for CC3, `diis`

for other coupled cluster methods

Solver to use for converging the amplitude equations. Optional.

Valid keyword values are:

`diis`

Quasi-Newton algorithm accelerated by DIIS. Uses the orbital differences approximation of the coupled cluster Jacobian.`newton-raphson`

. Newton algorithm accelerated by DIIS.

`energy threshold: [real]`

Default: \(10^{-5}\) (or 1.0d-5)

Energy convergence threshold, as measured with respect to the previous iteration. Optional.

Note

The solvers will not check for the energy convergence, if the energy threshold is not set.

`residual threshold: [real]`

Default: \(10^{-5}\) (or 1.0d-5)

Threshold of the \(L^{2}\)-norm of the amplitude equations vector \(\Omega_\mu = \langle \mu \vert \bar{H} \vert \text{HF} \rangle\). Optional.

`multimodel newton: [string]`

Default: `on`

for CC3, `off`

for other coupled cluster methods

If specified as `on`

, the Newton-Raphson algorithm will solve the micro-iterations using a lower-level approximation of the Jacobian matrix. Must be combined with `algorithm: newton-raphson`

. Optional.

`crop`

Default: false

If specified, the CROP version of DIIS will be enabled. Optional.

`max iterations: [integer]`

Default: 100

The maximum number of iterations. The solver stops if the number of iterations exceeds this number. Optional.

`max micro iterations: [integer]`

Default: 100

The maximum number of micro-iterations in the exact Newton solver (see `algorithm: newton-raphson`

).
The solver stops if the number of iterations exceeds this number.
Optional.

`rel micro threshold: [real]`

Default: \(10^{-2}\) (or 1.0d-2)

The relative threshold \(\tau\) used for micro-iterations by the exact Newton solver (see `algorithm: newton-raphson`

). The micro-iterations are considered converged if the \(L^{2}\)-norm of the Newton equation is less than \(\tau \vert\vert \boldsymbol{\Omega} \vert\vert\). Optional.

`storage: [string]`

Default: `disk`

Selects storage of DIIS records in coupled cluster calculations. Optional.

Valid keyword values are:

`memory`

Stores DIIS records in memory.`disk`

Stores DIIS records on file.

`micro iteration storage: [string]`

Default: value of the keyword storage

Selects storage of records in the micro iterations (if any) in ground state coupled cluster calculations. Optional.

Valid keyword values are:

`memory`

Stores records in memory.`disk`

Stores records on file.

`diis dimension: [integer]`

Default: 8

Number of previous DIIS records to keep. Optional.

`restart`

Default: false

If specified, the solver will attempt to restart from a previous calculation. Optional.

Keywords related to solving the coupled cluster multiplier equation (left coupled cluster ground state) go into this section.

`algorithm: [string]`

Default: `diis`

for `ccs`

, `lowmem-cc2`

, and `cc2`

;
`newton-raphson`

for `cc3`

;
`davidson`

for other coupled cluster models.

Solver to use for converging the multiplier equation. Not supported for MLCC2.

Valid keyword values are:

`davidson`

Use Davidson algorithm with residuals preconditioned with orbital differences approximation of the Jacobian. Cannot currently be used for lowmem-CC2, CC2, and CC3.`diis`

Use DIIS algorithm with update estimates obtained from the orbital differences approximation of the Jacobian.`newton-raphson`

. Newton algorithm accelerated by DIIS.

`threshold: [real]`

Default: \(10^{-5}\) (or 1.0d-5)

Threshold of the \(L^{2}\)-norm of the residual vector of the multiplier equation. Optional.

`max iterations: [integer]`

Default: 100

The maximum number of iterations. The solver stops if the number of iterations exceeds this number. Optional.

`diis dimension: [integer]`

Default: 20

Number of previous DIIS records to keep. Optional.

Note

Only relevant for `algorithm: diis`

.

`restart`

Default: false

If specified, the solver will attempt to restart from a previous calculation. Optional.

`storage: [string]`

Default: `disk`

Selects storage of solver subspace records. Optional.

Valid keyword values are:

`memory`

Stores records in memory.`disk`

Stores records on file.

`crop`

Default: false

If specified, the CROP version of DIIS will be enabled. Optional.

Note

Only relevant for `algorithm: diis`

.

`max reduced dimension: [integer]`

Default: 100

The maximal dimension of the reduced space of the Davidson procedure. Optional.

Note

Only relevant for `algorithm: davidson`

.

`max micro iterations: [integer]`

Default: 100

The maximum number of micro-iterations in the exact Newton solver
(see `algorithm: newton-raphson`

).
The solver stops if the number of iterations exceeds this number. Optional.

`micro iteration storage: [string]`

Default: `disk`

Selects storage of records in the micro iterations (if any). Optional.

Valid keyword values are:

`memory`

Stores records in memory.`disk`

Stores records on file.

`rel micro threshold: [real]`

Default: \(10^{-2}\) (or 1.0d-2)

The relative threshold \(\tau\)
used for micro-iterations by the exact Newton solver (see `algorithm: newton-raphson`

).
The micro-iterations are considered converged if the \(L^{2}\)-norm
of the Newton equation is less than \(\tau\). Optional.

`multimodel newton: [string]`

Default: `on`

for CC3, `off`

for other coupled cluster methods

If specified as `on`

, the Newton-Raphson algorithm will solve the micro-iterations
using a lower-level approximation of the Jacobian matrix.
Must be combined with `algorithm: newton-raphson`

. Optional.

Keywords related to time-dependent coupled cluster propagation settings.

`integrator: [string]`

Specifies the integration method used for real-time propagation. Required.

Valid keyword values are:

`rk4`

Fourth-order Runge-Kutta (RK4)`gl2`

Second-order Gauss-Legendre (GL2)`gl4`

Fourth-order Gauss-Legendre (GL4)`gl6`

Sixth-order Gauss-Legendre (GL6)`dopri5`

Dormand-Prince 5(4) (DOPRI5)`dop853`

Dormand-Prince 8(5,3) (DOP853)

`initial time: [real]`

The start time for the real-time propagation given in atomic units. Required.

`final time: [real]`

The end time for the real-time propagation given in atomic units. Required.

`time step: [real]`

Size of the time steps for the real-time propagation given in atomic units. Required.

`method: [string]`

Default: `tdcc`

Specifies the real-time coupled cluster method used for real-time propagation. Optional.

Valid keyword values are:

`tdcc`

Time-dependent coupled cluster method.`elementary td-eom-cc`

Elementary basis time-dependent equation-of-motion coupled cluster method.`diagonal td-eom-cc`

Diagonal basis time-dependent equation-of-motion coupled cluster method.

`steps between output: [integer]`

Default: \(1\)

Specifies how many time steps the solver should take between each time output (energy, dipole moment, …) is written to file. Optional.

`implicit threshold: [real]`

Default: \(10^{-11}\) (or 1.0d-11)

Specifies how tightly the Euclidian norm of the residual of implicit Runge-Kutta methods should converge before going to the next time step. Optional.

`energy output`

Default: `false`

Write energy to file every `steps between output`

. Optional.

`dipole moment output`

Default: `false`

Write dipole moment to file every `steps between output`

. Optional.

`electric field output`

Default: `false`

Write electric field to file every `steps between output`

. Optional.

`parameters output`

Default: `false`

Write time-dependent parameters to file every `steps between output`

.
The parameters are the cluster amplitudes and Lagrange multipliers for TDCC,
and the EOM-CC right and left amplitudes for TD-EOM-CC. Optional.

`mo density matrix output`

Default: `false`

Write molecular orbital (MO) density matrix to file every `steps between output`

. Optional.

`max error: [real]`

Default: `1.0e-10`

Maximum value of error estimate of embedded methods. Time step size is halved if estimate is greater than this value. Optional.

`min error: [real]`

Default: `1.0e-12`

Minimum value of error estimate of embedded methods. Time step size is doubled if estimate is smaller than this value. Optional.

`step reduction factor: [int]`

Default: `2`

Factor by which the propagation solver divides and multiplies the time step size in embedded methods,
in order to keep the error estimate between the values of `max error`

and `min error`

. Optional.

Keywords related to solving the coupled cluster response equations. Used when solving the amplitude response and multiplier response equations.

`threshold: [real]`

Default: \(10^{-3}\) (or 1.0d-3)

Residual norm threshold for convergence. Optional.

`gradient response threshold: [real]`

Default: \(10^{-5}\) (or 1.0d-5)

Residual norm threshold for convergence of amplitude response equations needed when computing CCSD level excited state gradients. Optional.

`storage: [string]`

Default: `disk`

Storage for Davidson records. Optional.

Valid options are:

`disk`

Store records on file.`memory`

Store records in memory.

`max iterations: [real]`

Default: \(100\)

Note

When running a CC excited state geometry optimization, the maximum number of iterations for solving the
amplitude response equations is set to **20**, unless otherwise specified. This is only done for analytical
gradients and will have no effect for numerical gradients.

Keywords related to the Cholesky decomposition of electron repulsion integrals go into the `solver cholesky`

section. This section is optional. If it is not given, defaults will be used for all keywords.

`threshold: [real]`

Default: \(10^{-4}\) (or 1.0d-4).

Decomposition threshold. All electron repulsion integrals will be reproduced by the Cholesky vectors to within this threshold. This threshold puts an upper limit to the accuracy of coupled cluster calculations. Optional.

`batches: [integer]`

Default: 1

Number of batches
\(n_b\)
in partitioned Cholesky decomposition. In this procedure, the Cholesky basis is chosen from a reduced set generated by decomposing diagonal blocks of the matrix (of which there are
\(n_b\)).
Introduces an error of about an order of magnitude higher than `threshold`

. Optional.

`one center`

Default: false

If specified, the Cholesky decomposition is restricted to diagonal elements
\(g_{\alpha\beta,\alpha\beta}\)
for which both atomic orbital indices,
\(\alpha\)
and
\(\beta\)
, are centered on the same atom. Introduces an error of about
\(10^{-3}\)
that cannot be reduced further by `threshold`

. Optional.

`span: [real]`

Default: \(10^{-2}\) (or 1.0d-2)

Span factor \(\sigma\) . For a given iteration of the Cholesky decomposition, this number determines the range of possible pivots to select/qualify: \(D_{\alpha\beta} \geq \sigma D_\mathrm{max}\) . Optional.

`qualified: [integer]`

Default: \(1000\)

Maximum number of qualified pivots in an iteration of the Cholesky decomposition. Optional.

`mo screening`

Perform Cholesky decomposition such that the MO electron repulsion integrals are targeted. The default screening targets the AO integrals.

Note

This keyword should always be used for CC-in-HF and CC-in-MLHF calculations, for which the the number of MOs is typically much smaller than the number of AOs.

Keywords related to solution of the CI equations

Note

These sections are relevant only if you have specified `fci`

or `casci`

in the `method`

section.

`energy threshold: [real]`

Default: \(10^{-6}\) (or 1.0d-6)

Energy convergence threshold, as measured with respect to the previous iteration. Optional.

Note

The solvers will not check for the energy convergence, if the energy threshold is not set.

`residual threshold: [real]`

Default: \(10^{-6}\) (or 1.0d-6)

Threshold of the \(L^{2}\)-norm of the residual vector of the CI equation. Optional

`max reduced dimension: [integer]`

Default: 100

The maximal dimension of the reduced space of the Davidson procedure. Optional.

`max iterations: [integer]`

Default: 100

`start guess: [string]`

Default: `single determinant`

Specifies start guesses for CI. Optional.

Valid keyword values are:

`single determinant`

Set a single element of the CI vector to one for every state. For the ground state it corresponds to the HF determinant.`random`

Gives random starting guess to the coefficient of the CI vector.

`states: [integer]`

Default: 1

Specifies the number of states to calculate. Optional.

`restart`

Default: false

If specified, the solver will attempt to restart from a previous calculation. Optional.

`storage: [string]`

Default: `disk`

Selects storage of records for the CI vectors. Optional.

Valid keyword values are:

`memory`

Stores records in memory.`disk`

Stores records on file.

Keywords related to solving the CPHF magnetic response equations go into the `solver cphf`

section.
The magnetic CPHF equations are only implemented for RHF and the only available magnetic property is the the nuclear shielding tensors.

`max iterations: [integer]`

Default: 100

`max reduced dimension: [integer]`

Default: 50

The maximal dimension of the reduced space of the Davidson procedure. Optional.

`residual threshold: [real]`

Default: \(10^{-3}\) (or 1.0d-3)

Threshold of the \(L^{2}\)-norm of the residual vector of the response equation. Optional.

`restart`

Default: false

If specified, the solver will attempt to restart from a previous calculation. Optional.

`storage: [string]`

Default: `disk`

Selects storage of solver subspace records. Optional.

Valid keyword values are:

`memory`

Stores records in memory.`disk`

Stores records on file.

Keywords related to solving the complex polarization propagator coupled cluster equations go into the `solver cpp`

section.
Required for damped response calculations!

`max iterations: [integer]`

Default: 100

`max reduced dimension: [integer]`

Default: 200

The maximal dimension of the reduced space of the CPP procedure. Optional

`residual minimization`

Specifies that residual minimization should be used to solve the reduced space equations in the damped response solver. This procedure might in some cases improve convergence. Optional.

`residual threshold: [real]`

Default: \(10^{-11}\) (or 1.0d-11)

Threshold of the \(L^{2}\)-norm of the residual vector of the excited state equation. Optional.

`restart`

Default: false

If specified, the solver will attempt to restart from a previous calculation. Optional.

`storage: [string]`

Default: `disk`

Selects storage of excited state records. Optional.

Valid keyword values are:

`memory`

Stores records in memory.`disk`

Stores records on file.

Keywords related to Fast Fourier transform (FFT) functionality for the time-dependent coupled cluster code. Below you find keywords that are valid in the two sections `solver fft dipole moment`

and `solver fft electric field`

.

Note

These sections are relevant only if you have specified `fft dipole moment`

or `fft electric field`

in the `cc real time`

section.

`initial time: [real]`

Specifies the start of the interval of interest in the time series file to Fourier transform. Required.

`final time: [real]`

Specifies the end of the interval of interest in the time series file to Fourier transform. Required.

`time step: [real]`

Specifies the time step between the data points in the time series file to Fourier transform. Required.

Warning

This must be equal to \(\text{time step} \times \text{steps between output}\) in the propagation section of the calculation that generated time series file.

`padding initial time: [real]`

Specifies the initial time that the time series will be padded from. Solver will use the value of the time series at `initial time`

for every time step between `padding initial time`

and `initial time`

. Optional.

`hann window`

Modulates the time series (including potential padding) with a Hann function. Optional.

`rectangular window`

Modulates the time series (including potential padding) with a rectangular function. This is the default. Optional.

Keywords related to the geometry optimization solver go in here.

`state: [integer]`

Default: 0

Selects state to perform geometry optimization on. Optional. State: 0 corresponds to the ground state, 1 to the first excited state, and so on.

`algorithm: [string]`

Default: `bfgs`

Selects the solver to use. Optional.

Valid keyword values are:

`bfgs`

A Broyden-Fletcher-Goldberg-Shanno (BFGS) solver using redundant internal coordinates and a rational function (RF) level shift obtained from an augmented Hessian.

`max step: [real]`

Default:
\(0.5\) (or *0.5d0*)

Maximum accepted step length in \(L^{2}\)-norm. Rescales the step to the boundary otherwise. Optional.

`energy threshold: [real]`

Default: \(10^{-6}\) (or 1.0d-6)

Energy convergence threshold, as measured with respect to the previous iteration. Optional.

`residual threshold: [real]`

Default: \(3\times 10^{-4}\) (or 3.0d-4)

Threshold checking the absolute maximal value of the energy gradient with respect to the previous iteration. Optional.

`residual rms threshold: [real]`

Default: \(1.2*10^{-4}\) (or 1.2d-4)

Threshold checking the root mean square of the energy gradient with respect to the previous iteration. Optional.

`displacement threshold: [real]`

Default: \(1.2\times 10^{-4}\) (or 1.2d-4)

Threshold checking the maximal value of the absolute displacements of the atoms with respect to the previous iteration. Optional.

`displacement rms threshold: [real]`

Default: \(1.2*10^{-4}\) (or 1.2d-4)

Threshold checking the root mean square of the displacements of the atoms with respect to the previous iteration. Optional.

`max iterations: [integer]`

Default: 100

`restart`

Default: false

If specified, the solver will attempt to restart from a previous calculation. Optional.

`gradient method: [string]`

Default: `analytical`

Selects the gradient method to use. Optional.

Valid keyword values are:

`analytical`

`forward difference`

`central difference`

`step size: [real]`

Default: `none`

Selects the step size used when calculating numerical gradients.

Note

This keyword is only read when numerical gradients are used.

Keywords related to the SCF solver go into the `solver scf`

section.
This section is optional. If it is not given, defaults will be used for all keywords.

`algorithm: [string]`

Default: `scf-diis`

Selects the solver to use.

Valid keyword values are:

`scf-diis`

AO-based self-consistent Roothan-Hall algorithm with direct inversion of the iterative subspace (DIIS) acceleration.`scf`

Self-consistent Roothan-Hall algorithm.`mo-scf-diis`

MO-based self-consistent Roothan-Hall algorithm with DIIS acceleration. Recommended for multilevel Hartree-Fock (MLHF).`level-shift-newton-raphson`

MO-based second-order trust-region step-constrained optimization procedure.

`energy threshold: [real]`

Default: \(10^{-7}\) (or 1.0d-7)

Energy convergence threshold, as measured with respect to the previous iteration.

Note

The solvers will not check for the energy convergence, if the energy threshold is not set.

`residual threshold: [real]`

Default: \(10^{-7}\) (or 1.0d-7)

residual threshold \(\tau\). The equations have converged if \(\max \mathbf{G} < \tau\).

`gradient response threshold: [real]`

Default: \(10^{-7}\) (or 1.0d-7)

Gradient response threshold \(\tau\). The orbital relaxation equations needed to compute the CC level gradient have converged if \(\max \mathbf{G} < \tau\).

`storage: [string]`

Default: `memory`

Selects storage of DIIS records.

Valid keyword values are:

`memory`

Stores DIIS records in memory.`disk`

Stores DIIS records on file.

`write orbitals`

Default: `false`

If specified, the *mo_coefficients.out file is created and copied to the working directory by `eT_launch`

.

`write molden`

Default: `false`

If specified, a molden input file called *.molden is created and copied to the working directory by `eT_launch`

.

`crop`

Default: `false`

If specified, the conjugate residual with optimal trial vectors (CROP) version of DIIS will be enabled.

`cumulative fock threshold: [real]`

Default:
\(1.0\) (or *1.0d0*)

When the gradient max-norm reaches this threshold, the Fock matrix is built using the difference in the density matrix relative to the previous iteration. When the max-norm exceeds the threshold, the Fock matrix is built directly using the current density matrix.

`max iterations: [integer]`

Default: \(100\)

The maximum number of iterations. The solver stops if the number of iterations exceeds this number.

`diis dimension: [integer]`

Default: \(8\)

Number of previous DIIS records to keep.

`restart`

Default: `false`

If specified, the solver will attempt to restart from a previous calculation.

`skip`

Default: `false`

If specified, orbitals will be read from file, the convergence of the gradient will be checked, but the rest of the SCF solver will be skipped.

Note

This is used to restart from eT v1.0.x, as the orbitals will not be flipped.

`ao density guess: [string]`

Default: `sad`

Which atomic orbital density matrix to use as start guess.

Valid keyword values are:

`sad`

Use the superposition of atomic densities (SAD) guess. This is built on-the-fly by performing spherically averaged UHF calculations on each unique atom (and basis) in the specified molecular system.`core`

Use the density obtained by approximating the Fock matrix by its one-electron contribution and performing one Fock diagonalization.

`coulomb threshold: [real]`

Default: \(10^{-6}*(\text{residual threshold})\)

The threshold for neglecting Coulomb contributions to the two-electron part of the AO Fock matrix.

Default: \(\text{(coulomb threshold)}^2\)

The \(\epsilon\) value for Libint 2. Gives the precision in the electron repulsion integrals.

Note

Changes dynamically during Fock construction to give the required precision in the Fock matrix and not the integrals (small density contributions require less accuracy in the integrals).

Warning

The value does not guarantee the given precision. It is highly recommended to let the program handle the integral precision value.

`exchange threshold: [real]`

Default: \(10^{-4}*(\text{residual threshold})\)

The threshold for neglecting Exchange contributions to the two-electron part of the AO Fock matrix.

Note

Changes dynamically during Fock construction to give the required precision in the Fock matrix and not the integrals (small density contributions require less accuracy in the integrals).

Will be set equal to the coulomb threshold if the coulomb threshold is bigger than the exchange threshold.

Warning

The value does not guarantee the given precision. It is highly recommended to let the program handle the integral precision value.

`coulomb exchange terms: [string]`

Default: `collective`

Determines if the two-electron part of the Fock matrix (G(D)) is computed at once or if Coulomb and exchange contributions are calculated separately.

Valid keyword values are:

`collective`

`separated`

`population analysis: [string]`

Request calculation of population analysis and specify type of analysis.

Valid keyword values are:
- `mulliken`

- `loewdin`

- `all`

`rohf coupling parameters: [string]`

Default: `guest-saunders`

Coupling parameters \(\vec{A}, \vec{B}\) for the ROHF orbitals, see for instance J. Chem. Phys. 125, 204110 (2006).

Valid keyword values are:

`guest-saunders`

: \(\vec{A} = (1/2, 1/2, 1/2), \vec{B}=(1/2, 1/2, 1/2)\)`mcweeny-diercksen`

: \(\vec{A} = (1/3, 1/3, 2/3), \vec{B}=(2/3, 1/3, 1/3)\)`faegri-manne`

: \(\vec{A} = (1/2, 1, 1/2), \vec{B}=(1/2, 0, 1/2)\)

`diabatize orbitals`

Request diabatization of orbitals. This will try to make the current converged canonical orbitals as similar as possible as the previous orbitals stored on file. This is typically used with restart, where the goal is to make sure a consistent phase and ordering is maintained at different geometries.

Keywords related to solving the TDHF and TD-QED-HF equations go into the `solver tdhf es`

section.
Required to find TDHF excitation energies. Currently TDHF is only implemented for RHF.

`singlet states: [integer]`

Specifies the number of singlet excited states to calculate.

`energy threshold: [real]`

Default: \(10^{-3}\) (or 1.0d-3)

Energy convergence threshold, as measured with respect to the previous iteration. Optional.

Note

The solvers will not check for the energy convergence, if the energy threshold is not set.

`max iterations: [integer]`

Default: 100

`max reduced dimension: [integer]`

Default: 50

The maximal dimension of the reduced space of the Davidson procedure. Optional.

`residual threshold: [real]`

Default: \(10^{-3}\) (or 1.0d-3)

Threshold of the \(L^{2}\)-norm of the residual vector of the excited state equation. Optional.

`restart`

Default: false

If specified, the solver will attempt to restart from a previous calculation. Optional.

`storage: [string]`

Default: `memory`

Selects storage of excited state records. Optional.

Valid keyword values are:

`memory`

Stores records in memory.`disk`

Stores records on file.

`tamm-dancoff`

Default: false

Enables the Tamm-Dancoff approximation. Optional.

Keywords related to solving the TDHF response equations go into the `solver tdhf response`

section.
Currently TDHF is only implemented for RHF and the only available response property is the polarizabilities (static and frequency-dependent).

`max iterations: [integer]`

Default: 100

`max reduced dimension: [integer]`

Default: 100

The maximal dimension of the reduced space of the Davidson procedure. Optional.

`residual threshold: [real]`

Default: \(10^{-3}\) (or 1.0d-3)

Threshold of the \(L^{2}\)-norm of the residual vector of the response equation. Optional.

`frequencies: [list of reals]`

Default: None

Frequencies for frequency-dependent polarizabilities. Static polarizabilities are obtained either by specifying frequency zero, or by not giving this keyword. Optional.

`print iterations`

Default: false

Enables the printing of the iterations of the response solver. Optional.

In the system section of the input the charge and multiplicity of the system is given. Furthermore, the use of cartesian Gaussians may be specified in this section.

`charge: [integer]`

Default: \(0\)

Specifies the charge of the system.

`multiplicity: [integer]`

Default: \(1\)

Specifies the spin multiplicity of the system.

`cartesian gaussians`

Enforce cartesian Gaussians basis functions for all atoms. Default for Pople basis sets.

`pure gaussians`

Enforce spherical Gaussian basis functions for all atoms. Default for all basis sets except Pople basis sets.

`write orbitals`

Write orbital coefficients to `*mo_information.out`

files
when the orbital coefficients change,
e.g. when `frozen hf`

or `MLCC`

are used.

The `visualization`

section is used for plotting orbitals and densities.

`file format: [string]`

Default: `plt`

Specify format of the output files containing the grid data. Optional.

Valid options are:

`plt`

`cube`

`grid buffer: [real]`

Default: \(2.0\) (or 2.0d0)

Sets the distance between the edge of the grid (x, y, and z direction) and the molecule in Angstrom units. Optional.

`grid max: {[real], [real], [real]}`

Sets the maximum values of the grid in x, y and z direction in Angstrom. Optional.

Note

`grid min`

is required if `grid max`

is specified.

`grid buffer`

is not used in this case.

`grid min: {[real], [real], [real]}`

Sets the minimum values of the grid in x, y and z direction in Angstrom. Optional.

Note

`grid max`

is required if `grid min`

is specified.

`grid buffer`

is not used in this case.

`grid spacing: [real]`

Default: \(0.1\) (or 1.0d-1)

Sets the spacing between grid points for the visualization given in Angstrom units. Optional.

`plot cc density`

Plots the coupled cluster density. Optional.

Note

This keyword is only read if `cc mean value`

or `response`

is specified in the `do`

section.

`plot es densities`

Plots the coupled cluster excited state densities for the `states to plot`

. Optional.

Note

This keyword is only read if `response`

is specified in the `do`

section.

`plot hf active density`

Plots the active HF density in the case of a reduced space calculation. Optional.

Note

This keyword is only read if `hf`

is specified in the `frozen orbitals`

section.

`plot hf density`

Plots the HF density. Optional.

`plot hf orbitals: {[integer], [integer], ...}`

Plots the canonical orbitals given in the comma separated list. Optional.

`plot transition densities`

Plots the coupled cluster transition densities for the `states to plot`

. Optional.

Note

This keyword is only read if `response`

is specified in the `do`

section.

`states to plot: {[integer], [integer], ...}`

List of integers specifying which densities should be plotted.

Note

By default the densities of the states specified in `initial states`

from the response section are plotted.

`plot cc orbitals: {[integer], [integer], ...}`

Plots the orbitals given in the comma separated list from a CC wave function. Optional.

Note

This keyword is used to visualize the orbitals in `MLCC`

or after freezing of orbitals.

`plot dyson orbitals`

Plots the coupled cluster dyson orbitals for the `states to plot`

. Optional.

Note

This keyword is only read if `response`

is specified in the `do`

section
and ionized states are requested.

`plot ntos`

Request plotting of NTOs for the `states to plot`

. Optional.

`plot cntos`

Request plotting of CNTOs for the `states to plot`

. Optional.

`nto threshold: [real]`

Determines the number of NTOs to be plotted. All NTOs will be plotted whose eigenvalues sum up to at least \(1-t\), where t is the given threshold. \(\sum_i e_i \geq 1 - t\)