3.7 Custom operation, promolecular and deformation properties (options 0, -1, -2)¶
3.7.1 Custom operation for multiple wavefunctions (0)¶
In main functions 3, 4 and 5, there is a subfunction that allows you to set custom operation for multiple wavefunctions. Supported operators include + (add), − (minus), * (multiply), / (divide), there is no upper limit of the number of wavefunctions involved in custom operation. For example, if the first loaded wavefunction after booting up Multiwfn is a.wfn, then in the setting step of custom operation you inputted 2 (viz. there are two wavefunctions will be put into “custom operation list” and thus will be operated with a.wfn in turn), then you inputted -,b.wfn and *,c.wfn, the property finally you get will be [(property of a.wfn) - (property of b.wfn)] * (property of c.wfn). If you are confused, you can consult the example in Sections 4.5.4 and 4.5.5.
Sometimes the molecular structure in the first loaded file and that in the subsequently loaded files are not identical, the grid points you set will be for the first loaded file, all of the other files will share the same grid setting.
Avoid using custom operation in conjunction with main functions -4, -3 and 6, otherwise you may get absurd result.
3.7.2 Promolecular and deformation properties (-1, -2)¶
If you selected subfunction -1 in main functions 3, 4 or 5 before choosing a property (viz. a real space function), what you finally get will be promolecular property. Promolecular property is the superposition property of atoms in their free-states
If the property you chose is electron density, then the promolecular property is generally referred to as promolecular density
This is an artificial density that corresponds to the state when the molecule has formed but the density has not relaxed.
Deformation property is the difference between actual property and promolecular property of a molecule under the same geometry
If the property is chosen as electron density, then the deformation property is generally called deformation density or known as electronic bonding charge distributions (BCD), which is very useful for analyzing charge transfer and bonding nature. Application example of deformation density can be found from my paper Acta Phys. -Chim. Sin., 34, 503 (2018) and Angew. Chem. Int. Ed., 137, e202504895 (2025) DOI: 10.1002/anie.202504895.
3.7.3 Generation of atomic wavefunctions¶
Evaluation of promolecular and deformation properties and some functions in Multiwfn request atomic wavefunction files, such as calculating Hirshfeld, VDD and ADCH charges, fuzzy atomic space analysis and orbital composition analysis based on Hirshfeld partition, etc. The process of generating atomic .wfn files are exactly the same.
After you select subfunctions -1 or -2 to study promolecular and deformation properties, Multiwfn checks whether .wfn files of all elements involved in present system have been presented in “atomwfn” subdirectory of current directory, if not, Multiwfn automatically invokes Gaussian to generate the missing element .wfn files and sphericalizes their densities. If the path of Gaussian executable file (“gaupath” parameter in settings.ini) is incorrect or has not been defined, Multiwfn will ask you to input the path of Gaussian executable file. The basis set for generating the element wavefunctions can be arbitrarily set by user, however it is suggested to use the same basis set as the molecular wavefunction.
The newly generated element wavefunction files or those taken from “atomwfn” directory are stored in “wfntmp” subdirectory in current directory. They will be translated to actual position of the atoms in present system, meanwhile atomic indices will be added to the .wfn filename (e.g. "Cr 30.wfn"). These are the files that will directly be used to calculate promolecular and deformation properties.
Details and skills¶
If you want to avoid the step of generating element wavefunctions every time, you can move the .wfn files that without number suffix (such as C .wfn) from “wfntmp” directory to “atomwfn” directory (if “atomwfn” directory is non-existing, build it yourself), next time if Multiwfn detected that all needed element .wfn files have already been presented in “atomwfn” folder, then Multiwfn will directly use them. Multiwfn only invokes Gaussian to calculate the missing element .wfn files.
“atomwfn” subdirectory in “examples” directory contains element wavefunction files of all first four rows, they were generated under 6-31G*, and they have been sphericalized. If you want to use them, simply copy the "atomwfn" directory to current folder.
Note
There is a quick way to generate all first four-rows element wavefunction files: the file “examples\genatmwfn.pdb” contains all first four-rows atoms, load it into Multiwfn and generate promolecular property, after the calculation of element wavefunctions is finished, copy the .wfn files that without suffix in “wfntmp” directory to “atomwfn” directory.
If your system involves elements heavier than Kr, Multiwfn is unable to generate atom wavefunction files by invoking Gaussian and sphericalize their density automatically; in that cases you have to calculate and sphericalize atom wavefunctions manually, and then put them into “atomwfn” directory, Multiwfn will directly use them.
The default theoretical method for generating wavefunction for main group elements in first four-rows (index from 1 to 20 and 31 to 36) is ROHF, for the transition metals in the fourth row, UB3LYP is used. In general, the promolecular and deformation properties are insensitive to theoretical method. If you want to specify theoretical method yourself, you can input theoretical method and basis set at the same time with slash as separator, for example BLYP/6-311G*. Do not add “RO” or “U” prefix since they will be added automatically. If error occurs during generation of atom wavefunctions, please check Gaussian input and output files in “wfntmp” directory carefully.
Notice that the maximum character length of the path of .wfn file permitted by Gaussian is only 60! The path will be truncated and cause error if the length exceeded this threshold. So do not put Multiwfn in the directory with too long path!
3.7.4 Sphericalization of atom wavefunction¶
The main purpose of Multiwfn supporting promolecular and deformation property is for generating promolecular and deformation density, however, electron density of most elements in free and ground state is not in spherical symmetry, hence will lead to orientation dependence problem. To tackle it, atomic electron density must be sphericalized. However, there is no unique way to do this. In Multiwfn, atom electron density is sphericalized by modifying atom wavefunction artificially, here I describe the detail. If you want to skip the sphericalization step, simply set the “ispheratm” in settings.ini to 0.
For elements in IV A group, Multiwfn uses \(sp^{3}\) configuration to replace \(s^{2}\)\(p^{2}\) ground state by default. This treatment is reasonable, since in most molecules these atoms are in \(sp^{3}\) hybridization. For VI A, VII A and Fe, Co, Ni, Multiwfn equalizes the occupation number of orbitals within the same shell; for example, oxygen has two singly occupied 2p orbitals and one doubly occupied 2p orbitals in ground state, the number of electrons in this shell is 4, so Multiwfn sets the occupation number of all the three orbitals to 4/3. This method works because the shapes of occupied orbitals are always nearly identical, regardless of the original occupation number is one or two. However, the difference between virtual orbital and occupied orbital is remarkable, thus Multiwfn uses another method to sphericalize electron density of elements in III A group, as well as Sc, Ti and V. In this method, the singly occupied orbitals are duplicated and rotated. Taking boron as example, assume that the singly occupied 2p orbital is directing along Z-axis, Multiwfn replicates this orbital twice and turn them toward X-axis and Y-axis respectively, finally the occupation numbers of the three orbitals are set to 1/3. (Users needn’t to check the orientation of singly occupied orbital by themselves). If you hope that Multiwfn sphericalizes atoms in IV A group in such manner instead of using \(sp^{3}\) configuration, set “SpherIVgroup” in settings.ini to 1.
Notice that the sphericalization methods used in Multiwfn are closely related to wavefunction type, the methods fail if unrestricted wavefunction is used for main group elements or restricted open-shell wavefunction is used for transition metals. These methods also fail if Hartree-Fock method is used for transition metals, because orbital order produced by HF is different from most DFT cases (the HF’s order is wrong, 4s is higher than 3d).