Dispersion descriptor

The universal quantitative dispersion descriptor [1] can be calculated either approximately based on tabulated vdW radii, or more accurately based on computed electron density isosurfaces. Dispersion is modelled with the D3 [2] or D4 [3] methods (the latter requires an external program).

Preparing input

There are two options for using surfaces based on the electron density.

Cube

Electron density in Gaussian cube format. Cube files can be generated by various quantum-chemical programs, including Gaussian.

Multiwfn

Exported surface from the Multiwfn program generated with the surface analysis module (option 12 in the main menu). After generating the surface, it should be exported to a file using the hidden option 66. This generates a file, “vtx.pdb” that can be read by ᴍᴏʀғᴇᴜs. For more information, see Section 3.15.4 of the Multiwfn manual.

Module

The Dispersion class is provided to calculate and store the dispersion descriptors.

Example

>>> elements, coordinates = read_geometry("corannulene.xyz")
>>> disp = Dispersion(elements, coordinates)
>>> disp.print_report()
Surface area (Ų): 284.6
Surface volume (ų): 290.0
P_int (kcal¹ᐟ² mol⁻¹ᐟ²): 20.8
>>> disp.atom_p_int[1]
30.19400992973631

By default, the molecular surface is constructed from vdW spheres and an internal D3 code is used. The choice of vdW radii can be changed from the default of rahm with radii_type=<str>. Custom radii can be supplied with radii=<list>. Density of points on the vdW surface is controlled with density=<float>. Dispersion coefficients can be read from the output of Grimme’s D3 and D4 programs with the load_coefficients method. To suppress the internal D3 code, set calculate_coefficients=False appropriately. To use another surface, suppress the vdW surface creation with point_surface=False and use the surface_from_cube or surface_from_multiwfn methods.

Example with external cube and coefficients files

>>> elements, coordinates = read_xyz("corannulene.xyz")
>>> disp = Dispersion(elements, coordinates, point_surface=False)
>>> disp.load_coefficients("d4_corannulene", "d4")
>>> disp.surface_from_cube("corannulene.cub")
>>> disp.compute_p_int()
>>> disp.print_report()
Surface area (Ų): 248.0
Surface volume (ų): 247.8
P_int (kcal¹ᐟ² mol⁻¹ᐟ²): 27.2
>>> disp.atom_p_int[1]
40.907980526799534

To exclude atoms from the calculation, the atom indices (starting at 1) should be provided with excluded_atoms=<list>. This can for example be used to calculate substitutent P_int values.

Grimme’s dftd4 program can be used to calculate the dispersion coefficients with the D4 method. The accompanying dftd4 python package must also be installed in the same Python environment as Morfeus. An example is given below:

Example with Grimme’s dftd4 code

>>> elements, coordinates = read_xyz("pme3.xyz")
>>> disp = Dispersion(elements, coordinates, compute_coefficients=False)
>>> disp.compute_coefficients(model="gd4")
>>> disp.compute_p_int()
>>> disp.print_report()
Surface area (Ų): 178.4
Surface volume (ų): 157.8
P_int (kcal¹ᐟ² mol⁻¹ᐟ²): 20.1

The D4 model is available with ‘gd4’ and the internal D3 code with ‘id3’. The maximum order of the dispersion coefficients can be set with the keyword argument ‘order’, but should be left by the non-expert user at the default setting of 8 (i.e. C₆ and C₈)

For more detailed information, use help(Dispersion) or see the API: Dispersion

Note

Use the command line flag --molc6 to get the dftd4 program to print the dispersion coefficients.

Command line script

The command line script provides access to the basic functionality through the terminal.

Example

$ morfeus dispersion tBu.xyz - - print_report
Surface area (Ų): 142.6
Surface volume (ų): 121.2
P_int (kcal¹ᐟ² mol⁻¹ᐟ²): 13.2

Background

The 🍺P_int dispersion descriptor was introduced by Pollice and Chen as a quantitative descriptor for dispersion interactions [1]. ᴍᴏʀғᴇᴜs can calculate P_int based on an electron density isosurface, as in the original article. In addition, we have found that a very fast method based on surfaces constructed from vdW radii correlate well with P_int from electron densities, at a fraction of the cost.

References

[1] (1,2)

Robert Pollice and Peter Chen. A universal quantitative descriptor of the dispersion interaction potential. Angewandte Chemie, International Edition, 58(29):9758–9769, 2019. doi:10.1002/anie.201905439.

[2]

Stefan Grimme, Jens Antony, Stephan Ehrlich, and Helge Krieg. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. The Journal of Chemical Physics, 132(15):154104, 2010. doi:10.1063/1.3382344.

[3]

Eike Caldeweyher, Christoph Bannwarth, and Stefan Grimme. Extension of the D3 dispersion coefficient model. The Journal of Chemical Physics, 147(3):34112, 2017. doi:10.1063/1.4993215.