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8.50 wfa

The WFA program of the MOLCAS program system provides various visual and quantitative wavefunction analysis methods. It is based on the libwfa [176] wavefunction analysis library. The interface to MOLCAS is described in Ref. [177].

The program computes natural transition orbitals (NTO) [178,179], which provide a compact description of one-electron excited states. Natural difference orbitals (NDO) [179] can be computed to visualize many-body effects and orbital relaxation effects [180]. A module for the statistical analysis of exciton wavefunctions is included [181,182], which provides various quantitative descriptors to describe the excited states. Output is printed for the 1-electron transition density matrix (1TDM) and for the 1-electron difference density matrix (1DDM). A decomposition into local and charge transfer contributions on different chromophores is possible through the charge transfer number analysis [183], which is available in connection with the external TheoDORE [184] program.

8.50.1 Installation

The WFA module is currently not installed by default. Its installation occurs via CMake. It requires a working HDF5 installation and access to the include files of the Armadillo C++ linear algebra library. In the current settings, external BLAS/LAPACK libraries have to be used. Use, e.g., the following commands for installation:



FC=ifort  cmake  -D  LINALG=MKL  -D  WFA=ON  -D  ARMADILLO_INC=../armadillo-7.300.0/include  ../openmolcas/


8.50.2 Dependencies

The WFA program requires HDF5 files, which are written by either SCF, RASSCF, or RASSI. In the case of RASSI, the TRD1 keyword has to be activated.


8.50.3 Files

8.50.3.1 Input files

FileContents
WFAH5All information that the WFA program needs is contained in this HDF5 file. The name can be adjusted with the H5FIle option.

8.50.3.2 Output files

FileContents
WFAH5The orbital coefficients of NOs, NTOs, and NDOs are written to the same HDF5 file that is also used for input.
*atomic.omThese are input files for the external TheoDORE program.

Extraction of the NOs, NTOs, and NDOs from the HDF5 file occurs with the external Molpy program. Call, e.g.:



penny  molcas.rassi.h5  --wfaorbs  molden


8.50.4 Input

The input for the WFA module is preceded by:

  &WFA

8.50.4.1 Keywords

Basic Keywords:

KeywordMeaning
H5FIleSpecifies the name of the HDF5 file used for reading and writing (e.g. $Project.scf.h5, $Project.rasscf.h5, $Project.rassi.h5). You either have to use this option or rename the file of interest to WFAH5.

REFStateIndex of the reference state for 1TDM and 1DDM analysis.

WFALevelSelect how much output is produced (0-4, default: 3).

Advanced keywords for fine grain output options and debug information:

KeywordMeaning
MULLikenActivate Mulliken population analysis.

LOWDinActivate Löwdin population analysis.

NXOActivate NO, NTO, and NDO analysis.

EXCItonActivate exciton and multipole analysis.

CTNUmbersActivate charge transfer number analysis and creation of *.om files.

H5ORbitalsPrint the NOs, NTOs, and/or NDOs to the HDF file.

DEBUgPrint debug information.

ADDInfoAdd info for molcas verify.

8.50.4.2 Input example



  *  Analysis  of  SCF  job
  &SCF  \\

  &WFA
  H5file  =  $Project.scf.h5  \\

  *  Analysis  of  RASSCF  job
  *  Reduced  output:  only  charge  transfer  numbers
  &RASSCF  \\

  &WFA
  H5file  =  $Project.rasscf.h5
  wfalevel  =  0
  ctnumbers  \\

  *  Analysis  of  RASSI  job,  use  the  TRD1  keyword
  *  Second  state  as  reference
  &RASSI
  TRD1  \\

  &WFA
  H5file  =  $Project.rassi.h5
  Refstate  =  2


8.50.5 Output

8.50.5.1 State/difference density matrix analysis (SCF/RASSCF/RASSI)

RASSCF analysis for state 2 (3) A or

RASSI analysis for state R_2

Descriptor Explanation
n_u Number of unpaired electrons $n_u=\sum_i\min(n_i, 2-n_i)$ [185,179]
n_u,nl Number of unpaired electrons $n_{u,nl}=\sum_i n_i^2(2-n_i)^2$
PR_NO NO participation ratio PRNO
p_D and p_A Promotion number pD and pA
PR_D and PR_A D/A participation ratio PRD and PRA
<r_h> [Ang] Mean position of detachment density $\vec{d}_D$ [182]
<r_e> [Ang] Mean position of attachment density $\vec{d}_A$
|<r_e - r_h>| [Ang] Linear D/A distance $\vec{d}_{D\rightarrow A} = \vec{d}_A - \vec{d}_D$
Hole size [Ang] RMS size of detachment density $\sigma_D$
Electron size [Ang] RMS size of attachment density $\sigma_A$

8.50.5.2 Transition density matrix analysis (RASSI)

RASSI analysis for transiton from state 1 to 2 (Tr_1-2)

Output listing Explanation
Leading SVs Largest NTO occupation numbers
Sum of SVs (Omega) $\Omega$, Sum of NTO occupation numbers
PR_NTO NTO participation ratio PRNTO [183]
Entanglement entropy (S_HE) $S_{H\vert E}=-\sum_i\lambda_i\log_2\lambda_i$ [186]
Nr of entangled states (Z_HE) ZHE=2SH|E
Renormalized S_HE/Z_HE Replace $\lambda_i\rightarrow \lambda_i/\Omega$
omega Norm of the 1TDM $\Omega$, single-exc. character
<r_h> [Ang] Mean position of hole $\langle\vec{x}_h\rangle_\mathrm{exc}$ [182]
<r_e> [Ang] Mean position of electron $\langle\vec{x}_e\rangle_\mathrm{exc}$
|<r_e - r_h>| [Ang] Linear e/h distance $\vec{d}_{h\rightarrow e} = \langle\vec{x}_e - \vec{x}_h\rangle_\mathrm{exc}$
Hole size [Ang] RMS hole size: $\sigma_h = (\langle\vec{x}_h^2\rangle_\mathrm{exc} - \langle\vec{x}_h\rangle_\mathrm{exc}^2)^{1/2}$
Electron size [Ang] RMS elec. size: $\sigma_e = (\langle\vec{x}_e^2\rangle_\mathrm{exc} - \langle\vec{x}_e\rangle_\mathrm{exc}^2)^{1/2}$
RMS electron-hole separation [Ang] $d_\mathrm{exc} = (\langle \left\vert\vec{x}_e - \vec{x}_h\right\vert^2\rangle_\mathrm{exc})^{1/2}$ [181]
Covariance(r_h, r_e) [Ang^2] $\mathrm{COV}\left(\vec{x}_h,\vec{x}_e\right) = \langle\vec{x}_h\cdot\vec{x}_e\r...
... \langle\vec{x}_h\rangle_\mathrm{exc}\cdot\langle\vec{x}_e\rangle_\mathrm{exc} $
Correlation coefficient $R_{eh} = \mathrm{COV}\left(\vec{x}_h,\vec{x}_e\right)/\sigma_h\cdot\sigma_e$


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Next: 8.51 The Basis Set Libraries Up: 8. Programs Previous: 8.49 vibrot