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

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

8.50.2 Dependencies

8.50.3 Files

8.50.3.1 Input files

8.50.3.2 Output files

File	Contents
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.:

8.50.4 Input

8.50.4.1 Keywords

Keyword	Meaning
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).

Keyword	Meaning
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*.

8.50.4.2 Input example

8.50.5 Output

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

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 p_D and p_A
`PR_D` and `PR_A`	D/A participation ratio PR_D and PR_A
`<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)

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)`	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 $\langle\vec{x}_h\rangle_\mathrm{exc}$ [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`	$R_{eh} = \mathrm{COV}\left(\vec{x}_h,\vec{x}_e\right)/\sigma_h\cdot\sigma_e$