Manual:RELADC
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Relativistic Green's function (propagator) module RELADC written by Markus Pernpointner.
Propagators (Green's functions) are a very useful tool for the calculation of ionization energies, electron affinities, excitation energies, double ionization energies and so forth. The mathematical form of the propagator reveals the type of physical property which is described but does not necessarily point to an efficient solution strategy. One way to achieve this is the method of (A)lgebraic (D)iagrammatic (C)onstruction originally formulated by Schirmer [1]. Hereby the diagonal representation of the propagator is transformed to a nondiagonal form by formally inserting a completeness relation in an arbitrary basis which does not have to be specified further because this is just a formal step. But now the nondiagonal form is expanded into orders of perturbation theory and compared to the known diagrammatic expansion of the propagator order by order. By this procedure the matrix entries of the nondiagonal expansion can be determined and calculated resulting in the ADC matrix. The final diagonalization of the ADC matrix then yields the desired eigenvalues (poles) and eigenvectors (spectral intensities).
In the current version of DIRAC a four-component realization of ADC providing single [2] and double [3] ionization potentials (SIPs and DIPs) is available starting from a *closed shell* reference determinant. Open-shell ADC based on a single reference (e.g. high-spin states) can be done in principle but the theoretical basis is not very sound for this. The four-component ADC is based on the Dirac-Coulomb operator and officially termed as DC-ADC. Be aware that for the moment RELADC has to be compiled with the -i8 compiler flag that means 64bit Integers are required. This will soon be abandoned.
The following perturbational orders are implemented in DC-ADC:
SIPs: strict second order (ADC-2), extended second order (ADC-2e) and third order (ADC-3); DIPs: extended second order (ADC-2e).
Only little input is needed for program control and is given via a &RELADC &END Namelist directive. It should be mentioned that as in any method treating electron correlation the active orbital space also in this case determines the quality of the results. Since after construction of the ADC matrix a final diagonalization is required for obtaining the total spectrum (in the space of active occupied orbitals, of course) a Lanczos diagonalizer is invoked as well. Controlling the diagonalizer also occurs via Namelist starting with &LANINP &END.
RELADC similar to many post-DHF programs sets out from the transformed totally antisymmetric two-electron integrals 
. Therefore the **MOLTRA step is required and automatically invoked if the .4INDEX keyword is not given.
Contents |
&RELADC &END -- Control propagator calculation
DOSIPS,DODIPS
Logical variables. These invoke the main tasks of calculating Single Ionization Potentials via DOSIPS=T and/or Double ionization potentials via DODIPS=T. Either of them can be specified individually or simultaneously.
Default:
DOSIPS = F, DODIPS = F
ADCLEVEL
Integer variable. Specifies the perturbational order for the SIP calculation only. Remember: the order for DIPs is always extended second order.
ADCLEVEL = 1 strict second order ADCLEVEL = 2 extended second order ADCLEVEL = 3 third order + constant diagrams
Default:
ADCLEVEL = 3
XREPS
Integer array of length 32. Specifies the symmetries of the one-hole final states (SIP) to be calculated. Individual specification is useful if one is interested in a few symmetries only. However, for the double ionizations (DIPs) the determination of final state symmetries is more complicated and done automatically by the program. Therefore the XREPS directive has no influence on DIP calculations and all DIP final states are calculated in whatever symmetry they may occur.
Default:
XREPS(*) = 0 no symmetries preselected.
READQKL
Logical variable. If the constant diagrams were calculated in a previous ADC(3) run (time consuming step) they can be read back in via the file QKLVAL. If this file does not exist an automatic recalculation is performed.
Default:
READQKL = F
DOCONST
Logical variable. Turns off the calculation of constant diagrams in an ADC(3) run (if DOCONST = F). All other perturbational orders of the matrix blocks are retained. This option is be useful for the precise analysis of individual contributions.
Default:
DOCONST = T
VCONV
Double precision variable. Determines convergence of the inverse iteration in the calculation of the constant diagrams. The threshold is set to 1.0E-06 being sufficent regarding the overall methodological accuracy.
Default:
VCONV=1.0E-06
&LANINP &END -- Control Lanczos diagonalizer
This is a second Namelist controlling the Lanczos diagonalizer. The spectral information is written to the files SSPEC.#irrep (SIPs) and DSPEC.#irrep (DIPs). 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 the one-hole or two-hole Slater-determinant forming this state in zeroth order. The suffix #irrep corresponds to the final state symmetry. For each symmetry calculated one therefore gets one (DS)SPEC file.
SIPITER,DIPITER
Integer variables. Determines the number of Lanczos iterations in a SIP or DIP calculation. 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.
Default:
SIPITER = 500, DIPITER = 500.
SIPPRNT,DIPPRNT
Real variables. These two variables only control Screen output of the calculated eigenvalues and have no influence on the results in the (DS)SPEC files! You can enter the threshold in eV up to which computed IPs (SIPs or DIPs) 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.
SIPEIGV
Integer array of length 32 with the same structure as XREPS. For each chosen symmetry in XREPS you specify here the number of requested long eigenvectors corresponding to the ADC matrix.
The following files are created by activating long eigenvector calculation: a) LONGEVC.#irrep: it contains the number of requested eigenvectors in binary format (real or complex) for a specific irrep and is used in subsequent lifetime calculations. b) the file EVCANAL.#irrep: it is generated in human readable form and contains the same information as LONGEVC.#irrep but with all the contributing configurations (main and satellite contributions to a specific final state). The creation of long eigenvectors invokes a second set of Lanczos iterations. The usual hole analysis and spectrum generation is not affected and long eigenvectors are only needed if one wants to analyze the satellite structure of a specific singly ionized final state or for lifetime calculations of the ionized state (coming soon).
Default:
SIPEIGV(*)=0
Examples
References
- ↑ J. Schirmer and L. S. Cederbaum and O. Walter, New approach to the one-particle Green's function for finite Fermi systems, Phys. Rev. A 28, 1237 (1983) .
- ↑ M. Pernpointner, The one-particle Green's function method in the Dirac–Hartree–Fock framework. II. Third-order valence ionization energies of the noble gases, CO and ICN, J. Chem. Phys. 121, 8782 (2004) .
- ↑ M. Pernpointner, The four-component two-particle propagator for the calculation of double ionization spectra of heavy-element compounds I. Method., J. Phys. B 43, 205102 (2010) .
