The Electronegativity Equalization Method I: Parametrization and Validation for Atomic Charge Calculations

Abstract

The applicability of the electronegativity equalization method (EEM) is investigated for the fast calculation of atomic charges in organic chemistry, with an emphasis on medicinal chemistry. A large training set of molecules was composed, comprising H, C, N, O, and F, covering a wide range of medicinal chemistry. Geometries and atomic charges are calculated at the B3LYP/6-31G* level, and from the calculated charges, effective electronegativity and hardness values are calibrated in a weighted least-squares fashion. The optimized parameter set is compared to other theoretical as well as experimental values and origins of the differences discussed. An approach toward extension of EEM to include new atoms is introduced. The quality of the EEM charges is assessed by comparison with B3LYP/6-31G* charges calculated for a set of medicinal molecules, not contained in the training set. The EEM approach is found to be a very powerful way to obtain ab initio quality charges without the computational cost of the ab initio approach.

Critical analysis and extension of the Hirshfeld atoms in molecules

“…As a test set, 168 molecules have been chosen containing C, H, N, O, F, and Cl atoms. The test set is available as supplementary material 41 and comprises the entire set previously used in electronegativity equalization studies by Bultinck et al 42,43 This set contains sufficiently diverse molecules with typical functional groups to allow the study of the performance of the new method. In total 2122 atoms are present in the test set, with 1082 H, 712 C, 125 N, 110 O, 65 F, and 28 Cl atoms.…”

ACKS2: Atom-condensed Kohn-Sham DFT approximated to second order

“…A minimization of this energy (with a constraint on the total charge) leads to a set of linear electronegativity equations, whose solution yields ab initio quality atomic charges at minimal computational cost. After the introduction of EEM in the seminal paper of Mortier, 4 the model was extensively validated and applied to diverse chemical systems, including inorganic solids, 5-12 organic molecules, [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] biomolecular systems [30][31][32][33] and metal-organic frameworks. 34 These successes are the basis for the wide-spread adoption of EEM as a polarizable force field (PFF) used in high-throughput in-silico screening 35 and in molecular mechanics force fields.…”

Negative Fukui functions: New insights based on electronegativity equalization

“…Taking as an example the CO molecule, and using the calibrated values for the effective hardness for C and O, 17,18 it is easily predicted that a discontinuity should arise near 0.60 Å. Doing the EEM calculations using the algebraic expressions given previously, this discontinuity is indeed found.…”

“…They are atoms-in-molecules properties, and were obtained previously from calibration against a large set of molecules representing a wide range of medicinal chemistry. 17,18 Once these parameters are available, Fukui functions can be calculated directly from Eq. ͑6͒ at the very high speed of several millions of molecules/hour on an average PC.…”

“…In both cases the EEM matrix equations are worked out explicitly, and those situations where discontinuities are found are examined. In the numerical examples effective hardness parameters are taken from Bultinck et al 17,18 These are based on calibrations from MPA. It should, however, be stressed that other population analysis methods, such as NPA 29 or Hirshfeld charges, 27 produce the same conclusions.…”