Faculty for Chemistry and Pharmacy - Group of Prof. Zipse

# Determining Atomic Charges using the CHELPG Scheme

In the CHELPG (= CHarges from ELectrostatic Potentials using a Grid based method) scheme by Breneman and Wiberg (J. Comp. Chem. 1990, 11, 361), atomic charges are fitted to reproduce the molecular electrostatic potential (MEP) at a number of points around the molecule. As a first step of the fitting procedure, the MEP is calculated at a number of gridpoints spaced 3.0 pm apart and distributed regularly in a cube. The dimensions of the cube are chosen such that the molecule is located at the center of the cube, adding 28.0 pm headspace between the molecule and the end of the box in all three dimensions. All points falling inside the van-der-Waals radius of the molecule are discarded from the fitting procedure. The following figure describes the situation for water as a simple example:

After evaluating the MEP at all valid grid points, atomic charges are derived that reproduce the MEP in the most optimum way. The only additional constraint in the fitting procedure is that the sum of all atomic charges equals that of the overall charge of the system. An input file for calculating the CHELPG charges for water is:

```#P HF/STO-3G pop=chelpg scf=(direct,tight)

HF/STO-3G//HF/STO-3G CHELPG charges for water (C2v structure)

0  1
O,0,-0.103524396,0.,-0.073843234
H,0,-0.0261242414,0.,0.9125411732
H,0,0.8543194092,0.,-0.3217953011
```

The results of the fitting procedure appear in the regular Gaussian output file as:

``` (Enter /scr1/g03/l602.exe)
Breneman (CHELPG) radii used.
Generate Potential Derived Charges using the Breneman model, NDens= 1.
Grid spacing= 0.300 Box extension= 2.800
NStep X,Y,Z=   20     25     22   Total possible points=       11000
Number of Points to Fit=    4014

**********************************************************************

Electrostatic Properties Using The SCF Density

**********************************************************************

Atomic Center    1 is at   0.000000  0.000000  0.127162
Atomic Center    2 is at   0.000000  0.758084 -0.508647
Atomic Center    3 is at   0.000000 -0.758084 -0.508647
4014 points will be used for fitting atomic charges
Fitting point charges to eletrostatic potential
Charges from ESP fit, RMS=   0.00088 RRMS=   0.05084:
Charge=   0.00000 Dipole=     0.0000     0.0000    -1.7225 Tot=     1.7225
1
1  O   -0.564045
2  H    0.282023
3  H    0.282023

```

Charges derived in this way don't necessarily reproduce the dipole moment of the molecule. If this latter characteristic is desired, the fitting process can be performed under the additional constraint of reproducing the overall molecular dipole moment:

```#P HF/STO-3G pop=(chelpg,dipole) scf=(direct,tight)

HF/STO-3G//HF/STO-3G CHELPG charges for water (C2v structure)
fitting also the molecular dipole moment

0  1
O,0,-0.103524396,0.,-0.073843234
H,0,-0.0261242414,0.,0.9125411732
H,0,0.8543194092,0.,-0.3217953011

```

CHELPG charges are frequently considered supperior to Mulliken charges as they depend much less on the underlying theoretical method used to compute the wavefunction (and thus the MEP). In order to illustrate this point, the atomic charge for the oxygen atom in water (experimental gas phase structure with r(O-H) = 95.72 pm and a(H-O-H) = 104.52o) has been calculated at several differrent levels of theory using the Mulliken as well as the CHELPG scheme:

level of theory CHELPG Mulliken
HF/STO-3G -0.617 -0.366
HF/3-21G -0.873 -0.728
HF/6-31G(d) -0.807 -0.866
HF/6-311+G(2d,1p) -0.750 -0.471
HF/cc-pVDZ -0.747 -0.305
HF/cc-pVTZ -0.738 -0.483
HF/cc-pVQZ -0.731 -0.526
Becke3LYP/cc-pVDZ -0.694 -0.255
Becke3LYP/cc-pVTZ -0.700 -0.432
Becke3LYP/cc-pVQZ -0.693 -0.487

While the Mulliken charges differ widely (between -0.255 and -0.866) with theoretical method and basis set choice, the CHELPG charges are much less variable (between -0.617 and -0.873). Moreover, the CHELPG charges are practically constant at either the Hartree-Fock or Becke3LYP level of theory provided that one of the correlation consistent basis sets is being used. Poor results are obtained even with the CHELPG scheme with small basis sets such as STO-3G or 3-21G.

One of the weak points of CHELPG (and other approaches based on fitting the MEP) is the treatment of larger systems, in which some of the innermost atoms are located far away from the points at which the MEP is evaluated. In such a situation, variations of the innermost atomic charges will not lead to significant changes of the MEP potential outside of the molecule and fitting of these atomic charges will therefore not result in meaningful results. It should also be remembered that atomic charges can depend strongly on the conformation of the molecule. Representative atomic charges for flexible molecules should therefore be derived as average values over several conformers. Using ethanol as an example, the charge parameters derived for the Cs symmetric conformer A and the C1 symmetric conformer B vary, in part, by almost 30%. The variation is, however, rather different for different parts of the system.

A detailed overview of the effects of the basis set and the Hamiltonian on the charge distribution in water can be found in: F. Martin, H. Zipse, J. Comp. Chem. 2005, 26, 97 - 105. A copy of the pdf file is available here.