.rswf — Real-Space Probability Density

Generated when the -r --rswf [holeIndex=0] flag is provided, for the first $n$ excitons chosen with -n --states [n=8].

The .rswf file contains the real-space probability density $P(\mathbf{r})$ of the first few exciton wavefunctions, computed by fixing the hole position and evaluating the squared amplitude of the wavefunction as a function of the electron position in real space.

Format

The file is organized in blocks, one for each exciton. Each block contains:

x   y   z   P
...
#
x   y   z   P
...
#

Where:

x, y, z: Coordinates of each unit cell vector (in $Å$)
P: Squared amplitude $| \psi_X(\mathbf{r}) |^2$

Each block is separated by a # delimiter.

Units

Coordinates are in $[x]=Å$

Calculation

The probability density is computed as:

\[P(\bm{r}) = \left| \psi_X(\bm{r}, \bm{r}_h) \right|^2 = \sum_{n} \left| \psi^{X}_{n}(\bm{r}, \bm{r}_h) \right|^2\]

where:

$\mathbf{r}_{h}$ is the fixed hole position (specified by –rswf [holeIndex])
$\psi^{X}_{n}$ denotes the exciton component over orbital $n$
The sum is over orbitals centered at $\mathbf{r}$

By default, Xatu evaluates this for the first 8 exciton states, or as defined by the user with --states [n].

Post-processing

The .rswf output is used by the provided script rkwf.py to visualize or analyze the real-space distribution of excitons.