Electro-static potential fitting

For small molecular systems, the electro-static potential (ESP) fitting method [70,71,72] is useful to determine an effective charge of each atom, while the ESP fitting method cannot be applied for large molecules and bulk systems, since there are not enough sampling points for atoms far from surface areas in the ESP fitting method. In the ESP fitting method an effective point net charge on each atom is determined by a least square method with constraints so that the sum of the electro-static potential by effective point charges can reproduce electro-static potential calculated by the DFT calculation as much as possible. The ESP fitting charge is calculated by the following two steps:

(1) SCF calculation
After finishing a usual SCF calculation, you have two output files:

    System.Name.out
    System.Name.vhart.cube

There is no additional keyword to generate the two files which are default output files by the SCF calculation, while the keyword 'level.of.fileout' should be 1 or 2.

(2) ESP fitting charge
Let us compile a program code for calculating the ESP fitting charge. Move the directory 'source' and then compile as follows:

    % make esp
  

When the compilation is completed normally, then you can find an executable file 'esp' in the directory 'work'. The ESP fitting charge can be calculated from two files 'System.Name.out' and 'System.Name.vhart.cube' using the program 'esp'. For example, you can calculate them for a methane molecule shown in the Section 'Input file' as follows:

    % ./esp met -c 0 -s 1.4 2.0
  

Then, it is enough to specify the file name without the file extension, however, two files 'met.out' and 'met.vhart.cube' must exist in the directory 'work'. The options '-c' and '-s' are key parameters to specify a constraint and scale factors. You can find the following statement in the header part of a source code 'esp.c':

   -c      constraint parameter 
           '-c 0' means charge conservation 
           '-c 1' means charge and dipole moment conservation  
   -s      scale factors for vdw radius
           '-s 1.4 2.0' means that 1.4 and 2.0 are 1st and 2nd scale factors

In the ESP fitting method, we support two constraints, charge conservation and, charge and dipole moment conservation. Although the latter can reproduce charge and dipole moment calculated by the DFT calculation, it seems that the introduction of the dipole moment conservation gives often physically unacceptable point charges especially for a relatively large molecule. Thus, we would like to recommend the former constraint. The sampling points are given by the grids in real space between two shells of the first and second scale factors times van der Waals radii [73]. In the above example, 1.4 and 2.0 correspond to the first and second scale factors. The calculated result appears in the standard output (your display) as follows:

 % ./esp met -c 0 -s 1.4 2.0

******************************************************************
******************************************************************
 esp: effective charges by a ESP fitting method
 Copyright (C), 2004, Taisuke Ozaki 
 This is free software, and you are welcome to         
 redistribute it under the constitution of the GNU-GPL.
******************************************************************
******************************************************************

Constraint: charge 
Scale factors for vdw radius    1.40000    2.00000
Number of grids in a van der Waals shell = 28464
Volume per grid =    0.0235870615 (Bohr^3)
Success

  Atom=   1  Fitting Effective Charge= -0.93558216739
  Atom=   2  Fitting Effective Charge=  0.23389552572
  Atom=   3  Fitting Effective Charge=  0.23389569182
  Atom=   4  Fitting Effective Charge=  0.23389535126
  Atom=   5  Fitting Effective Charge=  0.23389559858

  Magnitude of dipole moment    0.0000015089 (Debye)
  Component x y z     0.0000003114   -0.0000002455   -0.0000014558
RMS between the given ESP and fitting charges (Hartree/Bohr^3)= 0.096515449505