# RELADC, FANOADC and LANCZOS¶

This section lists the available keywords for RELADC, FanoADC and the closely connected iterative LANCZOS diagonalizer in the new input format maintained in DIRAC.

If you want to perform RELADC/LANCZOS calculations for the one- and two-particle propagator or a FanoADC calculation you invoke all of them by setting the .RELADC keyword in the **WAVE FUNCTION Section.

The RELADC/LANCZOS calculation is then individually controlled in the **RELADC and **LANCZOS input sections.

The FanoADC calculation is a special case of a one-particle propagator calculation. Therefore the keywords are part of the **RELADC section.

## *RELADC¶

### .DOSIPS¶

Do Single Ionization Potentials. If you intend to do single ionization spectra calculations then set this keyword. Closely related to SIP calculations is the keyword

### .ADCLEVEL¶

Here you determine the perturbational order for a SIP calculation.

```
ADCLEVEL = 1 strict second order
ADCLEVEL = 2 extended second order
ADCLEVEL = 3 third order + constant diagrams
```

*Default:*

`ADCLEVEL = 3 (including constant diagrams)`

*Input example:*

```
.ADCLEVEL
2
```

### .SIPREPS¶

Integer array of length 32. Specifies the symmetries of the one-hole final states (SIP) to be calculated. If you do not enter this array all symmetries are checked for possible final states and those are calculated in the respective perturbational order. You can also specify symmetries individually if you are interested only in a few by listing the number of requested symmetries followed by the individual irrep numbers.

*Default:*

`SIPREPS(1:32) = 0 (no symmetries preselected, all are calculated)`

*Input example:*

```
.SIPREPS
8
1,3,5,7,17,19,21,23
```

### .READQKL¶

Read back previously calculated constant diagrams in SIP runs. This is a restart option to avoid the most time consuming step in SIP runs. The constant diagrams for all symmetries are stored in the file QKLVAL.

### .NOCONS¶

Block calculation of constant diagrams in third-order SIP calculations. ADC is still executed up to third order but in the hole/hole block the (time consuming) constant diagrams are omitted. Skipping constant diagrams reduces accuracy but increases speed considerably. Not recommended for production runs.

### .VCONV¶

Determines convergence of the inverse iteration in the calculation of the constant diagrams. If these iterations take much time you can reduce tightness by setting VCONV to 1.0E-05, 1.0E-04 asf. Check accuracy of results when you activate this option.

*Default:*

```
VCONV=1.0E-06
```

*Input example:*

```
.VCONV
1.0E-04
```

### .DOFULL¶

Lanczos is automatically invoked in a single and double ionization calculation. If you want to invoke an additional full diagonalizer set this keyword. Attention: ADC matrices can become very large. A full diagonalization is therefore supported only for matrix dimensions up to 5000 x 5000 and is useful for test purposes only.

### .DOLANC¶

Additionally invoke a Lanczos diagonalizer in the excitation calculation (not recommended because Davidson is superior in this case). Lanczos is automatically invoked in SIP/DIP runs.

### .DODAVI¶

Activate the Davidson diagonalizer in the excitation run. At the moment Davidson is only effective in combination with DOEXCI. If not specified, Davidson will not start in the excitation run. In the next release the user has to activate the desired diagonalizer explicitly because the then available lifetime calculations do not require a complete diagonalization of the ADC matrix.

### .DODIPS¶

Do Double Ionization Potentials. If you intend to do double ionization spectra calculations then set this keyword. The keyword .ADCLEVEL does not apply to DIP runs because the perturbational order is set fixed to ‘extended second order’.

*Default:*

```
DODIPS = F
```

### .DIPREPS¶

Integer array of length 32. Specifies the symmetries of the two-hole final states (DIP) to be calculated. If you do not enter this array all symmetries are checked for possible final states and those are calculated in the respective perturbational order. You can also specify symmetries individually if you are interested only in a few. Input is analogous to SIPREPS.

*Default:*

`DIPREPS(1:32) = 0 (no symmetries preselected, all are calculated)`

### .ADCTHR¶

In DIP calculations only matrix elements whose amount is larger than ADCTHR will be written to disk. This is due to the large matrices occurring in DIP runs. Tests have shown that you can reduce matrix size by a factor of two setting ADCTHR to 1.0E-05 with an accuracy loss in the meV region. Perform accuracy tests for production runs since the behavior is system-dependent.

*Default:*

`ADCTHR = 0.0 (all nonzero matrix elements are written to disk)`

*Input example:*

```
.ADCTHR
1.0E-05
```

### .FANO¶

This keyword activates the FanoADC module. It requires the specification of the initial and final states to be investigated. By running the default calculation settings, specified ionization spectra are calculated as well. This can be turned off by using the keyword .FANOONLY.

*Default:*

```
False
```

For a Fano calculation it is crucial to use a proper (and normally large) basis set. It has been shown, that it is beneficial to add KBJ exponents to the atoms themselves or to ghost atoms surrounding the system in order to span a basis for the interaction region of the final state and the outgoing electron. By this the user should take care not to loose symmetry by specifying the positions of ghost atoms.

More information about the proper selection of basis sets can be found in the PhD thesis of Elke Fasshauer (link).

### .FANOIN¶

Here the initially ionized state is specified by symmetry and relative spinor number. The following example chooses the first spinor in the first symmetry to be the initial state:

```
.FANOIN
1 # symmetry
1 # relative spinor number
```

You can find a table of spinors, their symmetries and relative and absolute
spinor numbers at the beginning of every ADC calculation with the *same* active
space.
For the case of the Auger process of a neon atom, this looks like:

```
Spinor Abelian Rep. Energy Recalc. Energy
O 1 1 1g -32.8174679811 -32.8174680470
O 2 2 1g -1.9358495110 -1.9358495652
O 1 3 -1g -32.8174679811 -32.8174680470
O 2 4 -1g -1.9358495110 -1.9358495652
O 1 5 1u -0.8528295909 -0.8528295926
O 2 6 1u -0.8482685119 -0.8482685445
O 1 7 -1u -0.8528295909 -0.8528295926
O 2 8 -1u -0.8482685119 -0.8482685445
O 1 9 3u -0.8482685155 -0.8482685461
O 1 10 -3u -0.8482685155 -0.8482685461
.
.
virtual orbitals
```

which means, that the first spinor of the first symmetry (1g) which represents the Ne1s orbital is chosen as the initially ionized state.

### .FANOCHNL¶

Autoionization processes decay via several channels into different final states. These are specified in this section. In the first line the number of channels , let us call it N, needs to be given. In the second line the number of two-hole configurations for each channel is specified. If you chose 2 channels, you need to put two numbers here!

The following lines give details about the channels. For every channel a maximum 4 letter shortcut has to be specified followed by the two-hole configurations of describing the final state. They have to be pairs of absolute spinor numbers.

*Take care: The number of 2-hole-configurations of a channel has to be the same as you specified in the upper part. The 4 letter shortcut has to start at the beginning of the line. Do not include a space.*

This part is at the moment no black box method and the user is required to think carefully about the selection of these final states and not to forget a possible channel. On the other hand, this gives a lot of control to the user to specify exactly what he/she wants to calculate.

Again the Neon atom as example:

```
.FANOCHNL
3 # number of channels N
1,12,15 # number of hole configurations of the different channels
s2 # descriptor of 2s-2 final state
2 4 # two-hole configuration of 2s-2 final state
sp
2 5
2 6
2 7
2 8
2 9
2 10
4 5
4 6
4 7
4 8
4 9
4 10
p2
5 6
5 7
5 8
5 9
5 10
6 7
6 8
6 9
6 10
7 8
7 9
7 10
8 9
8 10
9 10
```

If you change the Hamiltonian you will have to change the channel specification as well!

### .FANOONLY¶

This keyword enforces to run only a FanoADC run and overwrite every other calculation of the one-particle propagator.

*Default:*

```
False
```

### .DOEXCI¶

Activate calculation of excited energies and states using the four-component polarization propagator. An excited state has even number of electrons and is therefore classified according to the bosonic irreducible representations of the corresponding molecular point group. If only one or a few final states should be calculated use the following keyword:

### .EXCREPS¶

Integer array of length 32. Specifies the symmetries of the excited final states to be calculated. If you do not enter this array all symmetries are checked for the occurrence of possible final states and those are calculated in the respective perturbational order.

*Default:*

`EXCREPS(1:32) = 0 (no symmetries preselected, all are calculated)`

*Input example:*

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

### .DOXEXT¶

Logical variable. If set true extended ADC(2) calculations will be performed (default = .false.).

## *LANCZOS¶

Once the ADC matrices are stored in packed form on disk they are diagonalized by the iterative Lanczos algorithm. The spectral information is written to the files SSPEC.#irrep (SIPs), DSPEC.#irrep (DIPs) and XSPEC.#irrep (EXC). Hereby the ionization potential, the pole strength and the error estimate are written in a line terminated by the ‘@’ for grep purposes. Immediately after this line follows the (indented) configuration information belonging to this final state. This is imaginable as a one-hole, two-hole or hole-particle Slater-determinant forming this state in zeroth order. Strictly speaking, the configuration coefficients refer to the intermediate state basis. Note: For excitation calculations Lanczos is not the first choice. Better to activate Davidson via the kayword .DODAVI

### .SIPITER, .DIPITER, .EXCITER¶

Determines the number of Lanczos iterations in a SIP, DIP or EXC calculation for all symmetries. There is no need to specify the number of iterations per symmetry because the convergence behaviour is similar within a specific ionization class. However, DIP calculations can require substantially more iterations for a comparable accuracy. Due to the iterative nature of the Lanczos diagonalizer the edge values converge very fast and some may be reproduced if SIPITER or DIPITER are set to high values. These reproduced eigenvalues are spurious and will be projected out from the final result. If one observes very many spurious solutions (mainly in the SIP case) it is recommended to reduce SIPITER accordingly. Note that Lanczos is not activated automatically in EXC runs.

*Default:*

```
SIPITER = 500, DIPITER = 500, EXCITER = 500.
```

*Input example:*

```
.SIPITER
1000
.DIPITER
2500
.EXCITER
1500
```

### .SIPPRNT, .DIPPRNT, .EXCPRNT¶

Real values. These two variables only control screen output of the calculated eigenvalues and have no influence on the results in the (SDX)SPEC files. You can enter the threshold in eV up to which computed IPs (SIPs, DIPs or EXCs) will be printed on screen. Sometimes one is only interested in a few lowest IPs and the screen output suffices.

*Default:*

`SIPPRNT = 50.0, DIPPRNT = 50.0, EXCPRNT = 20.0.`

*Input example:*

```
.SIPPRNT
20.0
.DIPPRNT
100.0
.EXCPRNT
50.0
```

### .SIPEIGV, .DIPEIGV, .EXCEIGV¶

For each chosen symmetry selected by the XXXREPS array a lower and upper energy boundary value for the corresponding method are specified. Only within this energy range the long eigenvectors are calculated. This is more user-friendly since one can not anticipate the number of eigenvectors to be expected in a certain energy range.

*Default:*

`0.0 0.0 (no eigenvectors calculated)`

*Input example:*

```
.SIPEIGV #(same for .DIPEIGV and EXCEIGV)
4 # number of lines of ranges to follow
10.0 20.0
20.0 30.0
0.0 0.0
10.0 15.0
```

### .DOINCORE¶

This keyword activates an incore Lanczos diagonalization. If you run jobs on machines with large core memory you can speed up the diagonalization considerably by transferring large parts of the ADC matrix to memory. This is especially noticeable in DIP jobs because the matrices are much larger than in the single ionization case. Attention: Be aware that the operating system allows you to allocate as much memory as you want. If there is not enough physical memory the OS starts to swap portions of the memory to disk. You have to avoid this situation since your job will not terminate in time. Check carefully that the memory you request is physically available!

### .DVXXXXX¶

The following keywords all start with DV and control the iterative Davidson diagonalizer effective in the excitation module.

### .DVROOTS¶

This is the main keyword that tells the diagonalizer how many of the lowest roots you wish to calculate. Be aware that for higher roots convergence is harder to achieve and therefore requires more Davidson iterations.

### .DVMAXSP¶

Here you define the maximum size of the Krylov space that is generated. In general, this number is ten to twenty times the number of requested roots in order to achieve convergence of approximately 1.0E-06 which is perfectly sufficient. The algortihm performs so-called microiterations up to the size of DVMAXSP. Then one macroiteration has terminated. The resulting vectors then serve as start vectors for the next set of microiterations leading to considerably improved excited eigenstates. (Default = 50). The number of macroiterations is fixed by the keyword

### .DVMAXIT¶

This number normally ranges between 5 and 20 for harder cases. Default value is 5.

### .DVCONV¶

Here you determine the convergence of the eigenvalues (default = 1.0E-05). Sometimes a bit tighter values are desired. You can choose that but be aware that very tight thresholds lead to many iterations and sometimes to instabilities of the algorithm.