Warning

Only the calculation of the density is tested for open shell configurations (and relies on a correct .OCCUPATION). All other properties are only tested for closed shell systems and should not be trusted for open shell systems without a thorough testing.

# **VISUAL¶

## Sampling¶

### .LIST¶

Calculate various densities in few points. Scalar and vector densities are written to the standard output file. Example (3 points; coordinates in bohr):

```
.LIST
3
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
```

### .LINE¶

Calculate various densities along a line. Example (line connecting two points; 200 steps; coordinates in bohr):

```
.LINE
0.0 0.0 0.0
0.0 0.0 5.0
200
```

Scalar and vector densities are written to files `plot.line.scalar`

and `plot.line.vector`

, respectively,
and should be saved after calculation, e.g.

```
pam --get=plot.line.scalar ...
```

The first three columns of the output files gives the coordinates (x, y, z) of the point. It is then followed by one/three columns giving the value of the scalar/vector density in that point.

### .RADIAL¶

Compute radial distributions

by performing Lebedev angular integration over a specified number of even-spaced radial shells out to some specified distance from a specified initial point. Example (coordinates and distance in bohr):

```
.RADIAL
0.0 0.0 0.0
10.0
200
```

The first line after the keyword specifies the initial point, here chosen to be the origin.
The second and third line is the distance and step size, respectively.
Scalar and vector densities are written to files `plot.radial.scalar`

and `plot.radial.vector`

, respectively,
and should be saved after calculation, e.g.

```
pam --get=plot.radial.scalar ...
```

### .2D¶

Calculate various densities in a plane. The plane is specified using 3 points that have to form a right angle. Example (coordinates in bohr):

```
.2D
0.0 0.0 0.0 !origin
0.0 0.0 10.0 !"right"
200 !nr of points origin-"right"
0.0 10.0 0.0 !"top"
200 !nr of points origin-"top"
```

Scalar and vector densities are written to files `plot.2d.scalar`

and `plot.2d.vector`

, respectively, and should be saved after calculation, e.g.

```
pam --get=plot.2d.scalar ...
```

### .2D_INT¶

Integrate various densities in a plane using Gauss-Lobatto quadrature. The plane is specified using 3 points that have to form a right angle. Example (coordinates in bohr):

```
.2D_INT
0.0 0.0 0.0 !origin
0.0 0.0 10.0 !"right"
10 !nr of tiles to the "right"
0.0 10.0 0.0 !"top"
10 !nr of tiles to the "right"
5 !order of the Legendre polynomial for each tile
```

### .3D¶

Calculate various densities in 3D and write to cube file format. Example (coordinates in bohr):

```
.3D
40 40 40 ! 40 x 40 x 40 points
```

Scalar and vector densities are written to files `plot.3d.scalar`

and `plot.3d.vector`

, respectively, and should be saved after calculation, e.g.

```
pam --get=plot.3d.scalar ...
```

Scalar densities are also written to a Gaussian cube file `plot.3d.cube`

.

### .3D_IMP¶

Calculate various densities in 3D on an imported grid and write to text file format (imported grid does not have to be regular). Example:

```
.3D_IMP
numerical_grid ! a grid file on which various densities will be calculated; the file should have 3 columns with x, y, z coordinates of grid points
grid_units ! grid units (choose from: 'angstrom' or 'au')
```

Another usage is calculating various densities in 3D on an imported grid (does not have to be regular) Example:

```
.3D_IMP
grid_file ! a file with x,y,z-coordinates of grid points
```

### .3DFAST¶

Fast evaluation of the molecular electrostatic potential. Example (coordinates in bohr):

```
.3DFAST
40 40 40 ! 40 x 40 x 40 points
```

### .3D_ADD¶

Add space around the cube file. Default (coordinates in bohr):

```
.3D_ADD
4.0
```

### .3D_INT¶

Integrate densities in 3D.

## Modification of densities¶

### .CARPOW¶

Scale densities by Cartesian product \(x^iy^jz^k\). The keyword is followed by three integers specifying the exponents \((i,j,k)\). Example:

```
.DENSITY
.CARPOW
1 0 0
```

is equivalent to the specification:

```
.EDIPX
```

### .RADPOW¶

Scale densities by a radial power \(r^{n}\). The keyword is followed by three integers specifying the exponent \(n\). Example:

```
.DENSITY
.RADPOW
1
```

allows to the calculation of radial expectation values \(<r>\) with respect to the origin.

### .SCALE¶

Scale densities by a factor. Default:

```
.SCALE
1.0
```

### .DSCALE¶

Scale densities *down* by a factor.
Default:

```
.DSCALE
1.0
```

## Densities¶

### .DENSITY¶

Compute number density \(n(\mathbf{r})\) . Example (unperturbed density):

```
.DENSITY
DFCOEF
```

Another example (perturbed density, first response vector):

```
.DENSITY
PAMXVC 1
```

### .DENGRA¶

Compute number density gradient \(\grad n(\mathbf{r})\) in addition to the number density \(n(\mathbf{r})\). Example (unperturbed density gradient):

```
.DENGRA
DFCOEF
```

### .DENHES¶

Compute number density Hessian \(H(n(\mathbf{r}))\) in addition to the number density \(n(\mathbf{r})\) and to the number density gradient \(\grad n(\mathbf{r})\). Example (unperturbed density Hessian):

```
.DENHES
DFCOEF
```

### .RDG¶

Compute the reduced density gradient \(\frac{1}{2(3\pi^2)^{1/3}}\frac{|\grad n(\mathbf{r})|}{n(\mathbf{r})^{4/3}}\). Example:

```
.RDG
DFCOEF
```

### .SIGNL2¶

Compute the signed electron density \(sign(\lambda_2) * n(\mathbf{r})\), where \(\lambda_2\) is the second eigenvalue of the number density Hessian \(H(n(\mathbf{r}))\). Example:

```
.SIGNL2
DFCOEF
```

### .ELF¶

Compute the electron localization function. Example:

```
.ELF
DFCOEF
```

### .GAMMA5¶

Compute the electron chirality density. Example:

```
.GAMMA5
DFCOEF
```

### .J¶

Compute the current density \(\mathbf{j}(\mathbf{r})=-e\psi_{i}^{\ast}c\boldsymbol{\alpha}\psi_{i}\). Example (use first response vector):

```
.J
PAMXVC 1
```

### .JDIA¶

Compute the nonrelativistic diamagnetic current density. Example:

```
.JDIA
DFCOEF
```

### .JX¶

Compute the x-component \(j_{x}(\mathbf{r})=-e\psi_{i}^{\ast}c\alpha_{x}\psi_{i}\) of the current density. Example (use first response vector):

```
.JX
PAMXVC 1
```

### .JY¶

Compute the y-component \(j_{y}(\mathbf{r})=-e\psi_{i}^{\ast}c\alpha_{y}\psi_{i}\) of the current density. Example (use first response vector):

```
.JY
PAMXVC 1
```

### .JZ¶

Compute the z-component \(j_{z}(\mathbf{r})=-e\psi_{i}^{\ast}c\alpha_{z}\psi_{i}\) of the current density. Example (use first response vector):

```
.JZ
PAMXVC 1
```

### .DIVJ¶

Compute the divergence of the current density. Example (use first response vector):

```
.DIVJ
PAMXVC 1
```

### .ROTJ¶

Compute the curl of the current density. Example (use first response vector):

```
.ROTJ
PAMXVC 1
```

### .BDIPX¶

Compute the x-component \(m^{[1]}_{x}(\mathbf{r})=-\frac{1}{2}(\mathbf{r}\times\mathbf{j})_{x}\) of the magnetic dipole operator. Example (use first response vector):

```
.BDIPX
PAMXVC 1
```

### .BDIPY¶

Compute the y-component \(m^{[1]}_{y}(\mathbf{r})=-\frac{1}{2}(\mathbf{r}\times\mathbf{j})_{y}\) of the magnetic dipole operator. Example (use first response vector):

```
.BDIPY
PAMXVC 1
```

### .BDIPZ¶

Compute the z-component \(m^{[1]}_{z}(\mathbf{r})=-\frac{1}{2}(\mathbf{r}\times\mathbf{j})_{z}\) of the magnetic dipole operator. Example (use first response vector):

```
.BDIPZ
PAMXVC 1
```

### .BEDCOS¶

Compute the Hermitian part of the full effective light-matter interaction

where appears the wave vector \(\mathbf{k}\) and the polarization vector
\(\boldsymbol{\epsilon}\). In accordance with the quaternion symmetry scheme of DIRAC an imaginary \(i\) will be inserted in the Hermitian part to make it time-symmetric. It should be noted that this is an *ungerade* operator.

### .BEDSIN¶

Compute the anti-Hermitian part of the full effective light-matter interaction

where appears the wave vector \(\mathbf{k}\) and the polarization vector
\(\boldsymbol{\epsilon}\). It should be noted that this is a *gerade* operator.

### .BEDFIX¶

Specify the wave vector \(\mathbf{k}\) and the polarization vector \(\boldsymbol{\epsilon}\) when using the full light-matter interaction. The orientation of the wave and polarization vector is given by specification of the angles \(\theta\), \(\phi\) and \(\chi\), see the .BED keyword for more details. In addition the user has to specify the angular frequency $omega$ which fixes the length of the wave vector \(\mathbf{k}\) since we have

For instance, to specify that the wave vector is along the \(z\) -axis, the polarization vector along the \(x\) - axis for an excitation energy at \(\omega=49.138\) a.u. we set

```
.BEDFIX
0.0 0.0 0.0 49.138
```

### .EDIPX¶

Compute the x-component \(Q^{[1]}_{x}(\mathbf{r})=xn(\mathbf{r})\) of the electric dipole.

### .EDIPY¶

Compute the y-component \(Q^{[1]}_{y}(\mathbf{r})=yn(\mathbf{r})\) of the electric dipole.

### .EDIPZ¶

Compute the z-component \(Q^{[1]}_{z}(\mathbf{r})=zn(\mathbf{r})\) of the electric dipole.

### .ESP¶

Compute the electrostatic potential. Example:

```
.ESP
DFCOEF
```

### .ESPE¶

Compute the electronic part of the electrostatic potential.

### .ESPN¶

Compute the nuclear part of the electrostatic potential.

### .ESPRHO¶

Compute the electrostatic potential times density.

### .ESPERHO¶

Compute the electronic part of the electrostatic potential times density.

### .ESPNRHO¶

Compute the nuclear part of the electrostatic potential times density.

### .NDIPX¶

Compute the NMR shielding density, with the “X”-component of the nuclear magnetic dipole moment and the selected component of the magnetically-induced current density (by the chosen record on PAMXVC file) as perturbing operators.

### .NDIPY¶

Compute the NMR shielding density, with the “Y”-component of the nuclear magnetic dipole moment and the selected component of the magnetically-induced current density (by the chosen record on PAMXVC file) as perturbing operators.

### .NDIPZ¶

Compute the NMR shielding density, with the “Z”-component of the nuclear magnetic dipole moment and the selected component of the magnetically-induced current density (by the chosen record on PAMXVC file) as perturbing operators.

### .NICS¶

Compute the NMR shielding density in a selected point in space. Is used to calculate NICS. Example:

```
.NICS
1.2 -1.0 2.0
```

will calculate the NMR shielding in point (1.2, -1.0, 2.0). This keyword can be used only with one of: NDIPX, NDIPY, NDIPZ keywords.

### .READJB¶

Use the grid and the magnetically-induced current density (jB) from a file to calculate the jB-dependent densities, e.g. the NMR shielding density or the magnetizability density. Example:

```
.READJB
file_name ! a file with x,y,z-coordinates of grid points and jB vector field
```

### .SMALLAO¶

Force evaluation of small component basis functions.

### .OCCUPATION¶

Specify occupation of orbitals. Example (neon atom):

```
.OCCUPATION
2
1 1-2 1.0
2 1-3 1.0
```

The first line after the keyword gives the number of subsequent lines to read. In each line, the first number is the fermion ircop. In molecules with inversion symmetry there are two fermion ircops: gerade (1) and ungerade (2). Otherwise there is a single fermion ircop (1). The specification of the fermion ircop is followed by the range of selected orbitals and their occupation. If a single orbital is specified a single number is given instead of the range.

Another example (water):

```
.OCCUPATION
1
1 1-5 1.0
```

Another example (nitrogen atom):

```
.OCCUPATION
2
1 1-2 1.0
2 1-3 0.5
```

### .LONDON¶

Activate LAO contribution. This keyword is followed by a letter “X”, “Y” or “Z” indicating the component of an external perturbing magnetic field. For example:

```
.LONDON
X
```

### .NONE¶

Select “none” connection when when plotting LAO perturbed densities.

### .NODIRECT¶

Skip direct LAO contribution when plotting perturbed densities.

### .NOREORTHO¶

Skip LAO reorthonormalization contribution when plotting perturbed densities.

### .NOKAPPA¶

Skip orbital relaxation contribution when plotting perturbed densities.