# How to obtain electron charge density per unit volume about a water molecule using SlowQuant?

@Nike Dattani's answer to How to “get my feet wet” in Density Functional Theory by simulating a water molecule using Python recommends SlowQuant. I've used the install instructions for Linux on my MacOS and it seems to work.

Initially the tests failed because factorial2 has been moved from scipy.misc to scipy.special. I edited MIpython.py and BasisSet.py adding import scipy.special as spe and changing scp.factorial2 to spe.factorial2 in three places in each file and all tests now pass, and I get the following output:

$python SlowQuant.py H2O.csv settingExample.csv 0.1089320182800293 INTEGRALS Iter Eel 1 -66.7536308450 -58.7512637840 6.71128773e+01 6.57412977e+00 2 -85.6091201524 -77.6067530914 -1.88554893e+01 6.02202187e+00 7.40515875e-01 3 -86.6677593084 -78.6653922474 -1.05863916e+00 1.07013952e-01 7.40515875e-01 0.006840229034423828 HF 4.0531158447265625e-06 PROPERTIES 2.1457672119140625e-06 Perturbation 2.1457672119140625e-06 QFIT 9.5367431640625e-07 CI 2.1457672119140625e-06 CC 0.1327359676361084 Execution time  So while I've been splashed my feet are not fully wet yet. Question: What are the next steps to obtaining a 3D distribution of electronic charge in the molecule? This is all new to me. I have seen Mulliken charges and Löwdin charges mentioned in the properties page of the documentation, perhaps something like this is what I'm after? But when I added a line at the bottom of the script, I just got an error. 10;;; 1;1.63803684;1.136548823;0.0 8;0.0;-0.143225817;0.0 1;-1.63803684;1.136548823;0.0 Charge;Mulliken;;  I get Traceback (most recent call last): File "SlowQuant.py", line 95, in <module> results = run(mol, set) File "SlowQuant.py", line 58, in run basis = BS.bassiset(input, set['basisset']) File "/your-name-here/SlowQuant/slowquant/basissets/BasisSet.py", line 195, in bassiset if basisload[j+1,0] == 'FOR' and writecheck == 1: IndexError: index 176 is out of bounds for axis 0 with size 176  Ultimately I hope to draw some imaginary electric field lines myself and that's a challenge and topic of its own, but for right now I just need a way to get charge density per unit volume. ## 1 Answer Firstly regarding the SlowQuant problems: In the version of SlowQuant you are using, the program takes two files as input. 1. The molecules file with the coordinates, number of electrons, and atom IDs. 2. The settings file, see; https://slowquant.readthedocs.io/en/latest/Examples.html. It is in the settings file you would want to add "Charge;Mulliken" If you have any problems with the code I can be reached by PM on https://www.reddit.com/user/ErikRK Also if you want to add any features or have any bug fixed feel free to make a pull request on https://github.com/erikkjellgren/SlowQuant Secondly you the charge density The Mulikken charges and Lowdin charges is not quite what you are looking for. If you want the charge density of the electrons in a point in space, this is what we also know as the electron density, and it is defined as follows: $$\rho\left(\boldsymbol{r}\right)=\sum_{pq}\Omega_{pq}\left(\boldsymbol{r}\right)D_{pq}$$ Here $$D$$ is the density matrix and $$\Omega$$ is the overlap distribution of two atomic orbitals and given as: $$\Omega_{pq}(\boldsymbol{r}) = \phi_p(\boldsymbol{r})\phi_q(\boldsymbol{r})$$ You will therefore have to evaluate the value of the basis functions in a point in space, and then weight them by the molecular orbital coefficients. • Yes$\rho(r)\$ is just what I'm looking for, thanks! I'm quite excited about using SlowQuant to learn how to do DFT calculations and then to begin to understand how they work from the outside-in, and having such an incredibly easy to install and to use package is going to make this easier and more accessible. Thank you for your speedy response and for making SlowQuant available to everyone! :-) – uhoh Mar 14 at 23:34
• This could have been featured as a "Hot Network Question" but Erik's answer came on March 14 and the Q was asked on March 11, and questions older than 72 hours no longer qualify for HNQ. I did ping Erik on March 11 though! – Nike Dattani Mar 25 at 15:15