# Kramers restricted Polarization Propagator in the ADC framework¶

See [Pernpointner2014] for the initial POLPRP implementation. The transition moment implementation and parallelization is described in [Pernpointner2017].

# **POLPRP¶

Specification of the overall calculation. Davidson diagonalizer (see DAVIDSON section) is automatically invoked.

## .STATES¶

Specifies the symmetries of the excited final states to be calculated. If you leave out this keyword all symmetries are checked for the occurrence of possible final states and those are calculated in the respective perturbational order. If the keyword is present, states have to be specified according to the following input example

*Input example:*

```
.STATES
4
1,3,17,19
```

This determines calculation for all eigenstates in the symmetries (irreducible representations) 1,3,17 and 19. Keep in mind that the numbering scheme for the double group ireps is a bit unconventional and depends on the type of Hamiltonian used.

## .DOEXTE¶

Presence of this keyword triggers an extended ADC(2) calculation in the sense that first-order contributions are included in the 2p2h (satellite) block. This often helps to localize states having a sizeable amount of double excitation character because those will alter their energy considerably when calculated in the extended scheme.

## .WRITET¶

Determines the threshold for writing matrix elements into the ADC matrix (default = 0.0). Can save considerable numerical effort with negligible loss of accuracy. Thresholds of 1.0E-06 are in order but it also depends a bit on the system. Value follows the keyword.

## .NODIAG¶

Diagonalization is skipped if keyword is present and only the eigenvectors of the particle-hole block are written to disk. This is mainly for test purposes since getting full eigenvectors is required for the calculation of transition moments.

## .DOTRMO¶

Transition moments are calculated if keyword is present, otherwise no TMs are calculated.

## .PRINT¶

Printlevel (default = 0) number follows the keyword. More output is produced if print level > 0.

# **DAVIDSON¶

Specifications for the Davidson diagonalizer. Holds for POLPRP and for other propagators if activated. POLPRP relies on Davidson exclusively and does not address other diagonalizers such as Lanczos.

## .DVROOTS¶

Number of desired roots. Remember that Davidson is an iterative diagonalizer that will not be able to generate thousands of roots. Normally one asks for 10 to 50 roots at the spectral boundary that will be well converged. This is a typical situation occurring for the valence excitation spectra.

## .DVMAXSP¶

This is the maximum size of the Krylov space generated internally and where the full Hamiltonian is projected on, in other words, this is the dimension of your trial space. If the dimension is reached during the iterations one macroiteration cycle is finalized and the subspace will be collapsed to the number of roots. The resulting new set of vectors is already a much better approximation to the true eigenvectors entering the next macrocycle.

## .DVMAXIT¶

Number of macrocycles you want to allow. For large problems requiring a lot of memory, DVMAXSP can be reduced leading to more macrocycles. If convergence is still unsatisfactory one slowly increases DVMAXSP.

## .DVCONV¶

Requested convergence of the eigenvalues. Usually a convergence of 1.0E-06 is absolutely sufficient.

## .DVREORT¶

Force reorthogonalization of ADCEVEC.XX start vectors initially and in each macrocycle. This may be useful if eigenvectors of a previous incomplete run that are not perfectly orthogonal shall be reused. This is unnecessary in a regular run since the trial spece during a Davidson run is kept strictly orthogonal and serves as the construction space for the true eigenvectors of the Hamilton matrix.

## .SKIPCC¶

With this keyword you can restart the calculation at a very advanced stage after the sorting step of the two-electron integrals. Therefore you skip SCF, MOLTRA and integral sorting (OOOO, VOOO, …). This is if a POLPRP run only needs to be executed. Works in serial and parallel. The only files you should provide are the ftXX.YY files containing the sorted integral batches, MDPROP (needed for transition moments) and MRCONEE among the .inp and .mol file. In parallel run this works only if you have an underlying shared file system, so each node can access their own ftXX.nodenumber file.

The default values are

- ::
DVROOTS 5 DVMAXSP 200 DVMAXIT 5 DVCONV 1.0E-05 DVREORT = .false. SKIPCC = .false.