4.2.54. WFA

Warning

This program requires a submodule

The WFA program of the Molcas program system provides various visual and quantitative wavefunction analysis methods. It is based on the libwfa [198] wavefunction analysis library. The interface to Molcas is described in Ref. [199].

The program computes natural transition orbitals (NTO) [200][201], which provide a compact description of one-electron excited states. Natural difference orbitals (NDO) [201] can be computed to visualize many-body effects and orbital relaxation effects [202]. A module for the statistical analysis of exciton wavefunctions is included [203][204], 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 [205], which is available in connection with the external TheoDORE [206] program.

4.2.54.1. 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/

4.2.54.2. 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.

4.2.54.3. Files

4.2.54.3.1. Input files

WFAH5
All information that the WFA program needs is contained in this HDF5 file. The name can be adjusted with the H5FIle option.

4.2.54.3.2. Output files

WFAH5
The orbital coefficients of NOs, NTOs, and NDOs are written to the same HDF5 file that is also used for input.
*atomic.om
These 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

4.2.54.4. Input

The input for the WFA module is preceded by:

&WFA

4.2.54.4.1. Keywords

Basic Keywords:

H5FIle
Specifies 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.
REFState
Index of the reference state for 1TDM and 1DDM analysis.
WFALevel
Select how much output is produced (0-4, default: 3).

Advanced keywords for fine grain output options and debug information:

MULLiken
Activate Mulliken population analysis.
LOWDin
Activate Löwdin population analysis.
NXO
Activate NO, NTO, and NDO analysis.
EXCIton
Activate exciton and multipole analysis.
CTNUmbers
Activate charge transfer number analysis and creation of *.om files.
H5ORbitals
Print the NOs, NTOs, and/or NDOs to the HDF file.
DEBUg
Print debug information.
ADDInfo
Add info for molcas verify.

4.2.54.4.2. 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

4.2.54.5. Output

4.2.54.5.1. 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 \(n_u=\sum_i\min(n_i, 2-n_i)\) [207][201]
n_u,nl Number of unpaired electrons \(n_{u,nl}=\sum_i n_i^2(2-n_i)^2\)
PR_NO NO participation ratio \(\text{PR}_{\text{NO}}\)
p_D and p_A Promotion number \(p_D\) and \(p_A\)
PR_D and PR_A D/A participation ratio \(\text{PR}_D\) and \(\text{PR}_A\)
<r_h> [Ang] Mean position of detachment density \(\vec{d}_D\) [204]
<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 \(\sigma_A\)

4.2.54.5.2. 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 \(\text{PR}_{\text{NTO}}\) [205]
Entanglement entropy (S_HE) \(S_{H|E}=-\sum_i\lambda_i\log_2\lambda_i\) [208]
Nr of entangled states (Z_HE) \(Z_{HE}=2^{S_{H|E}}\)
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 \(\langle\vec{x}_h\rangle_{\text{exc}}\) [204]
<r_e> [Ang] Mean position of electron \(\langle\vec{x}_e\rangle_{\text{exc}}\)
|<r_e - r_h>| [Ang] Linear e/h distance \(\vec{d}_{h\rightarrow e} = \langle\vec{x}_e - \vec{x}_h\rangle_{\text{exc}}\)
Hole size [Ang] RMS hole size: \(\sigma_h = (\langle\vec{x}_h^2\rangle_{\text{exc}} - \langle\vec{x}_h\rangle_{\text{exc}}^2)^{1/2}\)
Electron size [Ang] RMS electron size: \(\sigma_e = (\langle\vec{x}_e^2\rangle_{\text{exc}} - \langle\vec{x}_e\rangle_{\text{exc}}^2)^{1/2}\)
RMS electron-hole separation [Ang] \(d_{\text{exc}} = (\langle \left|\vec{x}_e - \vec{x}_h\right|^2\rangle_{\text{exc}})^{1/2}\) [203]
Covariance(r_h, r_e) [Ang^2] \(\text{COV}\left(\vec{x}_h,\vec{x}_e\right) = \langle\vec{x}_h\cdot\vec{x}_e\rangle_{\text{exc}} - \langle\vec{x}_h\rangle_{\text{exc}}\cdot\langle\vec{x}_e\rangle_{\text{exc}}\)
Correlation coefficient \(R_{eh} = \text{COV}\left(\vec{x}_h,\vec{x}_e\right)/\sigma_h\cdot\sigma_e\)