# Calculating the electrostatic potential of a molecule: what is a good 3D Poisson equation solver? [closed]

I was wondering if anybody can recommend an easy-to-use library/program to solve the 3D Poisson equation $$\nabla^2 V(r,\theta,\phi) = \rho(r,\theta,\phi)$$ with vanishing solutions at infinity:

$$V(r,\theta,\phi) = \int d^3\mathbf{r}'\frac{\rho(\mathbf{r}')}{|\mathbf{r}-\mathbf{r}'|},$$

where $$\mathbf{r} \rightarrow (r,\theta,\phi)$$. Here $$\rho$$ is a discrete + continuous charge density. The intended application is to calculate the electrostatic potential of a model polyatomic molecule composed of static, point-like nuclear charges and an arbitrary continuous electron density.

This question is a follow up to: 3D Poisson equation solver for arbitrary charge distribution? , which remains unanswered.

I am looking for a library, which is straightforward to use and which does not invoke the multipole expansion. There are plenty of solvers available on the market. I am familiar with three:

1. The Fenics project (finite element methods)
2. The 'multipoles' python library (solutions in the form of the multipole expansion)
3. COMSOL Multiphysics (not a freeware, finite elements),

but if anybody has a good experience with some other library (ideally in python or Fortran), sharing this experience here would be appreciated. The widely used J. Burkardt's libraries do not seem to contain such a solver routine.

Ideally, I wish to define the charge distribution $$\rho$$ (on a grid or analytically) and receive the value of the potential $$V$$ at any point $$(r,\theta,\phi)$$, without too much hustle.

• I'm sorry this question hasn't seemed to get a lot of attention. While its certainly on-topic for this site, you may have better luck on the Computational Science SE.
– Tyberius
Nov 10, 2021 at 19:35
• In what functional form is the continuous part of $\rho$ given? There are dedicated solvers for the special cases where $\rho$ is given as (apart from a finite number of point charges) a linear combination of Gaussian functions or Slater functions. If you are interested in an algorithm that is applicable to $\rho$ given by an arbitrary formula, then these solvers would have to be ruled out Feb 7, 2022 at 12:49
• I haven't looked thoroughly, but there's always APBS: poissonboltzmann.org Feb 8, 2022 at 20:45
• Emil, how are you doing with this now? Were the comments by Geoff and wzkchem5 helpful? Feb 24, 2022 at 3:36
• This question has been closed as it seems to be abandoned. It can be reopened if someone wants to add an answer or the OP addresses questions/suggestions in the comments.
– Tyberius
Feb 24, 2022 at 14:27