RESP charges#
The restrained electrostatic potential (RESP) charge model [BCCK93, CCBK95] represents an improvement to the Merz–Kollman (MK) scheme as the ESP figure-of-merit is rather insensitive to variations in charges of atoms buried inside the molecule.
Fig. 9 Dependence of figure-of-merit, \(\chi^2_\mathrm{esp}\), with respect to variations in atomic charges. Four separate atoms are here considered.#
To avoid unphysically high magnitudes of the charges of interior atoms, a hyperbolic penalty function is added
so that the diagonal matrix elements of the \(A\)-matrix in MK scheme become equal to
with a dependency on the partial charge. Consequently, RESP charges are obtained by solving the matrix equation iteratively until the charges and Lagrange multipliers become self-consistent. In addition to that, the RESP charge model allows for the introduction of constraints on charges of equivalent atoms due to symmetry operations or bond rotations.
Let us determine the RESP charges for methanol at the Hartree–Fock/6-31G(d) level of theory. We will require the partial charges of the hydrogen atoms in the methyl group to be identical.
Show code cell source
methanol_xyz = """6
H 1.2001 0.0363 0.8431
C 0.7031 0.0083 -0.1305
H 0.9877 0.8943 -0.7114
H 1.0155 -0.8918 -0.6742
O -0.6582 -0.0067 0.1730
H -1.1326 -0.0311 -0.6482
"""
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import veloxchem as vlx
First, we determine the reference state of the system.
molecule = vlx.Molecule.read_xyz_string(methanol_xyz)
basis = vlx.MolecularBasis.read(molecule, "6-31G*", ostream=None)
scf_drv = vlx.ScfRestrictedDriver()
scf_drv.ostream.mute()
scf_results = scf_drv.compute(molecule, basis)
Second, we calculate the RESP charges with the compute method of the RespChargesDriver class.
resp_drv = vlx.RespChargesDriver()
resp_drv.update_settings({"equal_charges": "1 = 3, 1 = 4"})
resp_charges = resp_drv.compute(molecule, basis, scf_results, "resp")
Show code cell output
RESP Charges Driver Setup
===========================
Number of Conformers : 1
Number of Layers : 4
Points per Square Angstrom : 1.0
Total Number of Grid Points : 420
First Stage Fit
-----------------
Restraint Strength : 0.0005
Restrained Hydrogens : No
Max. Number of Iterations : 50
Convergence Threshold (a.u.) : 1e-06
*** Charge fitting converged in 9 iterations.
No. | Atom | Constraints | Charges (a.u.)
--------------------------------------------
1 H 0.075643
2 C 0.117258
3 H 0.013902
4 H 0.013047
5 O -0.639004
6 H 0.419154
--------------------------------------------
Total Charge : 0.000000
Fit Quality
-------------
Relative Root-Mean-Square Error : 0.139861
Second Stage Fit
------------------
Restraint Strength : 0.001
Restrained Hydrogens : No
Max. Number of Iterations : 50
Convergence Threshold (a.u.) : 1e-06
*** Charge fitting converged in 4 iterations.
No. | Atom | Frozen | Constraints | Charges (a.u.)
----------------------------------------------------
1 H No 0.033747
2 C No 0.118610
3 H No 1 0.033747
4 H No 1 0.033747
5 O Yes -0.639004
6 H Yes 0.419154
----------------------------------------------------
Total Charge : 0.000000
Fit Quality
-------------
Relative Root-Mean-Square Error : 0.203249
Reference:
J. Phys. Chem. 1993, 97, 10269-10280.
Third, we print out the results.
print("Atom RESP charge")
print(20 * "-")
for label, resp_charge in zip(molecule.get_labels(), resp_charges):
print(f"{label :s} {resp_charge : 18.6f}")
print(20 * "-")
print(f"Total: {resp_charges.sum() : 13.6f}")
Atom RESP charge
--------------------
H 0.033747
C 0.118610
H 0.033747
H 0.033747
O -0.639004
H 0.419154
--------------------
Total: 0.000000
Compared to the ESP results, it is noted that the partial charge of the buried carbon atom is here lower (0.12 a.u.) as to be expected from the design of the RESP scheme.
Note
The RESP charge model is based on the quantum mechanical electrostatic potential calculated at the Hartree–Fock/6-31G(d) level of theory because it overestimates the gas-phase dipole moments in a way that it imitates approximately polarization effects in aqueous protein environments.