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1. rotational invariance

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Psi4 inputs for different grid generation schemes

• When using Psi4’s in-built cubic grid

set cubeprop_tasks ['esp'] 
set cubic_grid_spacing [1.1785, 1.1785, 1.1785] 
set cubic_grid_overage [8.0, 8.0, 8.0] # size of the cubic grid (default = 4 Bohr)

e, wfn = energy('HF', return_wfn=True)
cubeprop(wfn)

• When using a user-specified grid points specified in grid.dat(should be located in the same directory with Psi4 input)

E,wfn = prop('HF' , properties = ['GRID_ESP'], return_wfn=True)

* Generation of FCC grid used for charge fitting

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(1) Generate a box containing the molecule and fill it with FCC grid pts;

(2) Select grid points which are inside the outer boundary and outside the inner boundary (a shell of points);

(3) Store selected points to grid.dat

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1. rotational invariance

Procedure:

(1) Rotated a test molecule(MeOH) by multiples of 0.5 degree about an axis (100 frames)

(2) Generated both cubic grid(using Psi4 in-built feature) and FCC grid, ran ESP generation on each grid, for cubic grid, selected points using the same outer and inner boundary with FCC grids and used for charge fitting.

(3) RESP two stage fit charges were calculated from each frame and calculated standard deviation of charges.

2. translational transitional invariance