# Possible to Calculate Electronic Charge Distributions/Densities for Organic Molecules?

I was wondering if there are any programs that can calculate the electronic charge distributions around an organic molecule, possibly in the form of a volumetric charge volume density? I am reading up about using DFT programs that (correct me if I'm wrong) I believe may be able to tell us something about finding the charge density.

I'm working on a project that involves obtaining the electric field values surrounding an organic molecule. My current approach involves finding a function for the molecule's electronic volume charge density and doing a volume integral to get the electric field.

Is this a potentially valid method? If not, what else should I look into?

• Even I'm searching for it.
– Uday
Feb 12, 2018 at 0:41
• It's possible to calculate the electrostatic potential at points around a molecule. Is that what you're after? Feb 12, 2018 at 17:05
• The problems is that programs let alone do very little. Yes they do exist and for sure there are specialists or chemists knowing enouggh to help, here. . Feb 12, 2018 at 19:38
• Every DFT program computes the electronic density, i.e., the negative charge density due to electrons. The positive charge density is a sum of Dirac distributions over $\mathbb{R}^3$ given by the nuclear positions and their charges. Are you looking for the electrostatic potential? If you have Gaussian and molden, you can visualize the electronic density and ESP given the right input. Feb 12, 2018 at 20:55
• It is not clear what you want to analyze, so you may want to check out electrostatic potential maps: chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/…
– Greg
Feb 13, 2018 at 10:44

If I understand correctly, you want the total electric field at some point $\mathbf{r}$ due to a molecule. This will have at least three components. The first due to the electric field from the nuclei. This can be calculated classically from the field due to point charges. The second due to the dipole moment of a molecule. This can also be calculated completely classically (though you will have to use some electronic structure calculation to get the dipole and direction). Finally, you will need to find the total charge density of the electrons.

The charge density can be found using either DFT or any post-Hartree Fock method such as MP2 or CCSD(T), etc. When using something like MP2, you will get the charge density from the molecular orbitals. You can do this manually, but one code I know of that will give you the relevant information from the HF orbitals is NWChem. You will want to use the dplot command. This allows you to print out electron densities for each orbital using a grid. You will want to use a fine enough grid to capture the actual spatial changes in density. Notice that you also provide limits i x, y, and z. This is because, in principle, the charge density extends to infinity in all directions. Thus, you will want to choose a cutoff where the density is sufficiently small as to be negligible. Then, you can again calculate the field due to the electron density from classical equations which can be found online or in an E&M textbook. You can either calculate the field discretely from the points on the grid, or fit it to some functional form and then do a true integral over the density.

Another way to do this is to use a code which will give you approximate charges per atom from some type of population analysis such as Mulliken charges. You can do this with Gaussian using population keyword. This will aggregate the nuclear charge and the electronic charge into one field. Fair warning, however, Mulliken charges (and all population analyses) are approximate and not even necessarily physical.

There may be other ways to do this from DFT, but I surprisingly cannot find any software packages that do this directly.

• We've decided to follow your suggestion and try out the DPLOT functionality of NWChem, and I had a few followup questions about NWChem specifically: 1) Is there a way to be able to visualize the electron density from the output Gaussian file? We have tried avogadro, but it seems tojust show a ball-and-stick model of the molecule. 2) Is there an easier way to input the structure/geometry of the molecule for NWChem? Any way we can translate a typical 3d model of a molecule into the input for NWchem? Thank you so much for the pointers, it has been of great help to us! Feb 26, 2018 at 18:34
• @phill I have only ever used the molden option to visualize orbitals using Molden. Molden will then calculate electron densities from these orbitals. I do not know what you mean by your second question. There are various programs which output xyz coordinates from a ball and stick model and then these can be used in a geometry optimization. I would suggest asking another question about this on SE as I usually don't use these programs but I know there are people here who could answer that question. Feb 26, 2018 at 18:41