On the use of AM1 and MNDO wave functions to compute accurate electrostatic charges

A new strategy to evaluate accurate electrostatic charges from semiempirical wave functions is reported. The rigorous quantum mechanical molecular electrostatic potentials computed from both MNDO and AM1 wave functions are fitted to the point-charge molecular electrostatic potential to obtain the electrostatic charges. The reliability of this strategy is tested by comparing the semiempirical electrostatic charges for 21 molecules with the semiempirical Mulliken charges and with the ab initio STO-3G and 6-31G* electrostatic charges. The ability of the dipoles derived from the semiempirical electrostatic and Mulliken charges as well as from the SCF charge distributions to reproduce the ab initio 6-31G* electrostatic dipoles and the gas phase experimental values is determined. The statistical analysis clearly point out the goodness of the semiempirical electrostatic charges, specially when the MNDO method is used. The excellent relationships found between the MNDO and 6-31G* electrostatic charges permit to define a scaling factor which allows to accurately reproduce the 6-31G* electrostatic charge distribution as well as the experimental dipoles from the semiempirical electrostatic charges.     

Atomic charges derived from a fast and accurate method for electrostatic potentials based on modified AM1 calculations

Atomic charges derived from a recently described approach to the very rapid computation of AM1 electrostatic potentials (ESP) accurately parallel, but are ca. 20% smaller than, the corresponding HF/6-31G* values. The dipole moments computed from the AM1 charges are virtually identical to those derived directly from the wave function and in rather better agreement with the experimental values than those computed using the HF/6-31G* charges. Unlike other approaches to the semiempirical calculation of ESP-derived charges, the present method also yields near HF/6-31G* quality potentials close to the molecular periphery. For medium-sized organic molecules (40-100 basis functions), the method is approximately two orders of magnitude faster than those involving prior deorthogonalization of AM1 wave function and explicit computation of the full ESP integral matrix. © 1994 by John Wiley & Sons, Inc.     

Semiempirical treatment of electrostatic potentials and partial charges in combined quantum mechanical and molecular mechanical approaches

A semiempirical treatment of electrostatic potentials and partial charges is presented. These are the basic components needed for the evaluation of electrostatic interaction energies in combined quantum mechanical and molecular mechanical approaches. The procedure to compute electrostatic potentials uses AM1 and MNDO wave functions and is based on one previously suggested by Ford and Wang. It retains the NDDO approximation and is thus both easy to implement and computationally efficient. Partial atomic charges are derived from a semiempirical charge equilibration model, which is based on the principle of electronegativity equalization. Large sets of ab initio restricted Hartee-Fock (RHF/6-31G*) reference data have been used to calibrate the semiempirical models. Applying the final parameters (C, H, N, O), the ab initio electrostatic potentials are reproduced with an average accuracy of 20% (AM1) and 25% (MNDO), respectively, and the ab initio potential derived charges normally to within 0.1 e. In most cases our parameterized models are more accurate than the much more expensive quasi ab initio techniques, which employ deorthogonalized semiempirical wave functions and have generally been preferred in previous applications. © 1996 John Wiley & Sons, Inc.     

Conformational dependence of the electrostatic potential-derived charges of dopamine: Ramifications in molecular mechanics force field calculations in the gas phase and in aqueous solution

The electrostatic potential-derived charges for the catecholamine neurotransmitter dopamine were calculated at the STO-3G and 6-31G* basis sets for six different molecular conformations. The degree of variance of the charges with changing conformations was examined. The 6-31G* basis set produced charges that were more sensitive to changes in conformation than those derived from the STO-3G electrostatic potentials. The implication of the charge variations in molecular mechanics calculations was also investigated. The molecular mechanics results in the gas phase exhibited a variance depending upon the charge set used. The force field calculations varied much less when aqueous solvation was included in the calculations through a continuum model. © 1993 John Wiley & Sons, Inc.     

Conformational preferences for hydroxyl groups in substituted tetrahydropyrans

Quantum mechanical (ab initio and semiempirical) and force field calculations are reported for representative torsion potentials in several tetrahydropyran derivatives. The overall agreement between the various methods is quite good except that the AMBER torsion profiles are sensitive to the choice of atomic point charges. Using electrostatic potential (ESP) derived atomic point charges determined with the STO-3G basis set we find that AMBER is able to match the best quantum mechanical results quite well. However, when the point charges are derived using the 6-31G* basis set we find that scaling the intramolecular electrostatic nonbond interactions is necessary. AM1 does not work very well for these compounds when compared to the ab initio methods and, therefore, should only be used in cases when ab initio calculations would be prohibitive. Based upon our results we feel that any force field that makes use of 6-31G* ESP derived atomic point charges will need to scale intramolecular interactions. Implications of scaling intramolecular interactions to the development of force fields based on 6-31G* ESP derived atomic point charges are discussed. © 1992 by John Wiley & Sons, Inc.     

Multicenter point charge model for high-quality molecular electrostatic potentials from AM1 calculations

The natural atomic orbital/point charge (NAO-PC) model based upon the AM1 wave function has been developed to calculate molecular electrostatic potentials (MEPs). Up to nine point charges (including the core charge) are used to represent heavy atoms. The positions and magnitudes of the eight charges that represent the atomic electron cloud are calculated from the natural atomic orbitals (NAOs) and their occupations. Each hybrid NAO is represented by two point charges situated at the centroid of each lobe. The positions of the centroids and the magnitudes of the charges were obtained by numerical integration of the Slater-type hybrids and the results used to set up polynomials and look-up tables that replace the integration step in the actual MEP calculation. The MEPs calculated using this method are found to be in better agreement with those obtained using RHF/6-31G* than those obtained from the AM1 wave function using Coulson charges or with MOPAC-ESP. The MEP calculations are extremely fast and have, for instance, been incorporated into an interactive graphics package. © 1993 John Wiley & Sons, Inc.     

Suitability of the PM3-derived molecular electrostatic potentials

A systematic study of the suitability of PM3-derived molecular electrostatic potentials (MEPs) is presented. Forty-six MEP minima, 81 electrostatic charges, and 17 electrostatic dipoles were determined at the PM3 level and compared with those obtained from the ab initio 6-31G* wave function, as well as from the semiempirical MNDO and AM1 wave functions. The statistical results of the comparison analysis between semiempirical and ab initio 6-31G* MEPs show that PM3 is in general reliable for the study of the MEP minima but a mediocre method as a source of electrostatic charges. © 1993 John Wiley & Sons, Inc.     

Atomic charges derived from electrostatic potentials: A detailed study

A new algorithm for fitting atomic charges to molecular electrostatic potentials is presented. This method is non-iterative and rapid compared to previous work. Results from a variety of gaussian basis sets, including STO-3G, 3-21G and 6-31G*, are presented. Charges for a representative collection of molecules, comprising both first and second row atoms and anions are tabulated. The effects of using experimental and optimized geometries are explored. Charges derived from these fits are found to adequately reproduce SCF dipole moments. A small split valence representation, 3-21G, appears to yield consistently good results in a reasonable amount of time.     

Potential-derived point-charge model study of electrostatic interactions in DNA base components

Ab initio electrostatic potentials obtained using STO-3G wavefunctions for guanine, cytosine, adenine, and thymine are used to calculate potential-derived (PD) point charges for these base components. Calculated PD point charges are used to estimate the electrostatic contributions to hydrogen-bonding and stacking interaction energies of ten sequence isomers of B-DNA. These estimates are in excellent agreement with the results of the more elaborate segmental multipole moment expansion technique.     

Molecular electrostatic potentials and partial atomic charges from correlated wave functions: Applications to the electronic ground and excited states of 3-methylindole

Procedures have been developed to generate molecular electrostatic potentials based on correlated wave function from ab initio or semiempirical electronic structure programs. A new algorithm for point-wise sampling of the potential is described and used to obtain partial atomic charges via a linear, least squares fit between classical and quantum mechanical electrostatic potentials. The proposed sampling algorithm is efficient and promises to introduce less rotational variance in the potential derived partial charges than algorithms applied previously. Electrostatic potentials and fitted atomic charges from ab initio (HF/6–31G* and MP2/6-31G*) and semiempirical (INDO/S; HF, SECI, and SDCI) wave functions are presented for the electronic ground (S₀) and excited (¹L_b, ¹L_a) states of 3-methylindole. © 1992 by John Wiley & Sons, Inc.     

Multipole electrostatic model for MNDO-like techniques with minimal valence spd-basis sets

We report an implementation of an atomic multipole model (up to quadrupole) for calculating the electrostatic properties of molecules based on electron densities derived from MNDO-like NDDO-based semiempirical MO calculations with minimal s,p,d valence basis sets. The results were validated by a comparison of the calculated values of the molecular electrostatic potential with those obtained from fine grain numerical integrations (both with AM1*), B3LYP/6–31G(d) and MP2/6–31G(d). The DFT and ab initio potentials can be reproduced remarkably well (mean unsigned error <2 kcal mol⁻¹ e⁻¹) using simple linear regression equations to correct the AM1* (multipole) results. Dedicated to Prof. Karl Jug on the occasion of his 65th birthday     

Comparative study between ab initio and semiempirical electrostatic potentials on molecular surfaces

The electrostatic potentials of 21 molecules containing different functional groups has been computed at the ab initio RHF/6-31G* level on a series of solvent accessible surfaces and compared with MNDO, AM1, and PM3-derived pontentials. We analyzed in detail the distribution of electrostatic potentials on the surfaces around their maximum and minimum values and found out that consistently MNDO gives results similar to ab initio potentials. The actual values of the MNDO electrostatic potentials show a systematic deviation from the “correct” results, but the pattern of the MEP distribution on the surface is similar to that of the ab initio results. In contrast, PM3 fails in some cases to give even the correct number or distribution of “hot spots” of potential (low MEP) on the surface. AM1 behaves somewhere between these two semiempirical methods. As a conclusion, MNDO would be suggested as the best approach to analyses requiring a fast and efficient mapping of electrostatic potentials on simplified models of molecular surfaces. © 1993 John Wiley & Sons, Inc.     

Analysis of a large data base of electrostatic potential derived atomic charges

A large data base of 6-31G*, MNDO, AM1, and PM3 electrostatic potential (ESP) derived point charges of amino acids and monosaccharides is analyzed. We find that MNDO correlates well with 6-31G* ESP derived point charges, while AM1 and PM3 do so quite poorly. Furthermore, scaling MNDO ESP derived point charges enhances the ability of MNDO to reproduce 6-31G* results. We used our data base to attempt to derive a 6-31G* transferable charge model at an atom-by-atom level. We find that it is simple to derive a transferable model for monosaccharides, but for the amino acids statistical difficulties make this a less attractive approach. The transferable charge model for the monosaccharides is slightly better than MNDO, but scaled MNDO charges perform significantly better than the transferable model. We also carried out a QMD simulation on the alanine dipeptide to assess the fluctuations that would be expected in atomic point charges during the course of an MD simulation. Relatively large charge fluctuations are observed and their impact on molecular simulation is addressed. © 1992 by John Wiley & Sons, Inc.     

Accurate molecular electrostatic potentials based on modified PRDDO/M wave functions. I. Electrostatic potential derived atomic charges

A new approach for the calculation of electrostatic potential derived atomic charges is presented. Based on molecular orbital calculations in the PRDDO/M approximation, the new parametrized electrostatic potential (PESP) method is parametrized against ab initio MP2/6-31G** calculations. For a data set of 820 atoms in 145 molecules containing H, C, N. O, F, P, S, Cl, and Br (including hypervalent species), the PESP method achieves a mean absolute error of 0.037 e⁻ with a correlation coefficient of 0.990. Unlike other approximate approaches, no scaling factor is required to improve the agreement between PESP charges and the underlying ab initio results. PESP calculations are an order of magnitude faster than the simplest ab initio calculation (STO-3G) on large molecules while achieving a level of accuracy that rivals much more elaborate ab initio methods. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 955–969, 1997     

Fast,efficient generation of high‐quality atomic charges. AM1‐BCC model: I. Method

The AM1‐BCC method quickly and efficiently generates high‐quality atomic charges for use in condensed‐phase simulations. The underlying features of the electron distribution including formal charge and delocalization are first captured by AM1 atomic charges for the individual molecule. Bond charge corrections (BCCs), which have been parameterized against the HF/6‐31G* electrostatic potential (ESP) of a training set of compounds containing relevant functional groups, are then added using a formalism identical to the consensus BCI (bond charge increment) approach. As a proof of the concept, we fit BCCs simultaneously to 45 compounds including O‐, N‐, and S‐containing functionalities, aromatics, and heteroaromatics, using only 41 BCC parameters. AM1‐BCC yields charge sets of comparable quality to HF/6‐31G* ESP‐derived charges in a fraction of the time while reducing instabilities in the atomic charges compared to direct ESP‐fit methods. We then apply the BCC parameters to a small “test set” consisting of aspirin, d ‐glucose, and eryodictyol; the AM1‐BCC model again provides atomic charges of quality comparable with HF/6‐31G* RESP charges, as judged by an increase of only 0.01 to 0.02 atomic units in the root‐mean‐square (RMS) error in ESP. Based on these encouraging results, we intend to parameterize the AM1‐BCC model to provide a consistent charge model for any organic or biological molecule. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 132–146, 2000     

The natural atomic orbital point charge model for PM3: Multipole moments and molecular electrostatic potentials

The natural atomic orbital/point (NAO-PC) model originally developed to calculate molecular electrostatic potentials (MEPs) and multiple moments based on the AM1 wave function has been extended to PM3. As for AM1, NAO-PC/PM3 reproduces dipole moments calculated by the standard PM3 method very well. There is also a surprisingly good correlation between experimental and calculated quadrupole moments. The MEPs calculated using PM3/NAO-PC are found to be in better agreement with those given by RHF/6-31G* than those obtained from the PM3 wave function using Coulson charges. On the other hand, the NAO-PC model is often slightly worse then the method implemented in MOPAC-ESP. The MEPs calculated using our model based on the PM3 wave function are often in better agreement with those given by RHF/6-31G* than those obtain with AM1. © 1994 by John Wiley & Sons, Inc.     

Comparative molecular field analysis of artemisinin derivatives: Ab initio versus semiempirical optimized structures

Based on the belief that structural optimization methods, producing structures more closely to the experimental ones, should give better, i.e. more relevant, steric fields and hence more predictive CoMFA models, comparative molecular field analyses of artemisinin derivatives were performed based on semiempirical AM1 and HF/3-21G optimized geometries. Using these optimized geometries, the CoMFA results derived from the HF/3-21G method are found to be usually but not drastically better than those from AM1. Additional calculations were performed to investigate the electrostatic field difference using the Gasteiger and Marsili charges, the electrostatic potential fit charges at the AM1 level, and the natural population analysis charges at the HF/3-21G level of theory. For the HF/3-21G optimized structures no difference in predictability was observed, whereas for AM1 optimized structures such differences were found. Interestingly, if ionic compounds are omitted, differences between the various HF/3-21G optimized structure models using these electrostatic fields were found.     

Fast,efficient generation of high-quality atomic charges. AM1-BCC model: II. Parameterization and validation

We present the first global parameterization and validation of a novel charge model, called AM1-BCC, which quickly and efficiently generates high-quality atomic charges for computer simulations of organic molecules in polar media. The goal of the charge model is to produce atomic charges that emulate the HF/6-31G* electrostatic potential (ESP) of a molecule. Underlying electronic structure features, including formal charge and electron delocalization, are first captured by AM1 population charges; simple additive bond charge corrections (BCCs) are then applied to these AM1 atomic charges to produce the AM1-BCC charges. The parameterization of BCCs was carried out by fitting to the HF/6-31G* ESP of a training set of >2700 molecules. Most organic functional groups and their combinations were sampled, as well as an extensive variety of cyclic and fused bicyclic heteroaryl systems. The resulting BCC parameters allow the AM1-BCC charging scheme to handle virtually all types of organic compounds listed in The Merck Index and the NCI Database. Validation of the model was done through comparisons of hydrogen-bonded dimer energies and relative free energies of solvation using AM1-BCC charges in conjunction with the 1994 Cornell et al. forcefield for AMBER.(13) Homo- and hetero-dimer hydrogen-bond energies of a diverse set of organic molecules were reproduced to within 0.95 kcal/mol RMS deviation from the ab initio values, and for DNA dimers the energies were within 0.9 kcal/mol RMS deviation from ab initio values. The calculated relative free energies of solvation for a diverse set of monofunctional isosteres were reproduced to within 0.69 kcal/mol of experiment. In all these validation tests, AMBER with the AM1-BCC charge model maintained a correlation coefficient above 0.96. Thus, the parameters presented here for use with the AM1-BCC method present a fast, accurate, and robust alternative to HF/6-31G* ESP-fit charges for general use with the AMBER force field in computer simulations involving organic small molecules.