Accurate partial atomic charges for high-energy molecules using class IV charge models with the MIDI! basis set

We have recently developed a new class IV charge model for calculating partial atomic charges in molecules. The new model, called charge model 3 (CM3), was parameterized for calculations on molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br by Hartree–Fock theory and by hybrid density functional theory (HDFT) based on the modified Perdew–Wang density functional with several basis sets. In the present article, we extend CM3 for calculating partial atomic charges by Hartree–Fock theory with the economical but well balanced MIDI! basis set. Then, using a test set of accurate dipole moments for molecules containing nitramine functional groups (which include many high-energy materials), we demonstrate the utility of several parameters designed to improve the charges in molecules containing both N and O atoms. We also show that one of our most recently developed CM3 models that is designed for use with wave functions calculated at the mPWXPW91/MIDI! level of theory (where X denotes a variable percentage of Hartree–Fock exchange) gives accurate charge distributions in nitramines without additional parameters for N and O. To demonstrate the reliability of partial atomic charges calculated with CM3, we use these atomic charges to calculate polarization free energies for several nitramines, including the commonly used explosives 1,3,5-trinitro-s-triazine (RDX) and 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane (HNIW), in nitromethane. These polarization energies are large and negative, indicating that electrostatic interactions between the charge distribution of the molecule and the solvent make a large contribution to the free energy of solvation of nitramines. By extension, the same conclusion should apply to solid-state condensation. Also, in contrast to some other charge models, CM3 yields atomic charges that are relatively insensitive to the presence of buried atoms and small conformational changes in the molecule, as well as to the level of treatment of electron correlation. This type of charge model should be useful in the future development of solvation models and force fields designed to estimate intramolecular interactions of nitramines in the condensed phase.     

Class IV charge models: A new semiempirical approach in quantum chemistry

Summary We propose a new criterion for defining partial charges on atoms in molecules, namely that physical observables calculated from those partial charges should be as accurate as possible. We also propose a method to obtain such charges based on a mapping from approximate electronic wave functions. The method is illustrated by parameterizing two new charge models called AM1-CM1A and PM3-CM1P, based on experimental dipole moments and, respectively, on AM1 and PM3 semiempirical electronic wave functions. These charge models yield rms errors of 0.30 and 0.26 D, respectively, in the dipole moments of a set of 195 neutral molecules consisting of 103 molecules containing H, C, N and O, covering variations of multiple common organic functional groups, 68 fluorides, chlorides, bromides and iodides, 15 compounds containing H, C, Si or S, and 9 compounds containing C-S-O or C-N-O linkages. In addition, partial charges computed with this method agree extremely well with high-level ab initio calculations for both neutral compounds and ions. The CM1 charge models provide a more accurate point charge representation of the dipole moment than provided by most previously available partial charges, and they are far less expensive to compute.     

On the negative dipole moment derivatives of HRgX (Rg=He, Ar, Kr; X=F, Cl) molecules

The large dipole moment and the negative dipole moment derivatives with respect to H–Rg displacement of the neutral HRgX (Rg=He, Ar, Kr; X=F, Cl) molecules have been rationalised by a charge/charge flux/dipole flux decomposition of the charge density using the ChelpG method. This approach was also applied to the hydrogen halides HF and HCl for the sake of comparison. It was found that the dipole moment of HRgX is dominated by the large positive charge contribution while the negative dipole moment derivative of HRgX is due to the dominance of the negative charge flux contribution.     

Automated site-directed drug design: An assessment of the transferability of atomic residual charges (CNDO) for molecular fragments

Summary In this paper a database of atomic residual charges has been constructed for all the molecular fragments defined previously in a combinatorial search of the Cambridge Structural Database. The charges generated for the atoms in each fragment are compared with charges calculated for whole molecules containing those fragments. The fragment atomic charges lie within 1 S.D. of the mean for 68%, and within 2 S.D. for 91%, of the atoms whose charges were computed for whole molecules. The actual charges on any atom are strongly influenced by the adjacent connected atoms. There is a large spread of atomic residual charge within the fragments database.     

Kirchhoff atomic charges fitted to multipole moments: implementation for a virtual screening system

The Kirchhoff charge model is a viable method of generating inexpensive and electrostatically reasonable atomic charges for molecular mechanical force fields. The charging method uses a computationally fast algorithm based on the principle of electronegativity relaxation. Parameters of the method, orbital electronegativities and hardnesses, are fitted to reproduce reference, ab initio calculated dipole and quadrupole moments of a representative training set of neutral and charged organic molecules covering most medicinal chemistry relevant bonding situations. Transferability and accuracy of the derived parameters are confirmed on an external test set. Comparisons to other charge models are made. Implementation of the new Kirchhoff charges into a virtual screening engine is elucidated.     

Representation of molecules by atomic charges: A new population analysis

For the calculation of atomic charges in molecules, a new fast procedure based on extended Mulliken population analysis is presented. The reliability of the new population analysis is tested within the AM1 approximation and the results are compared in detail with those obtained by different methods reported in the literature.     

A test of the Hirshfeld definition of atomic charges and moments

Summary The Hirshfeld population analysis scheme which carves the molecular density into atomic density contributions is tested. This method does not require a reference to basis sets or their respective locations, but is based on a different physical and mathematical footing. The advantage of this method is that, when the molecular deformation density converges to the true solution, the computed net charges will necessarily converge. This method also allows a straightforward definition for local moments. About 36 molecules have been used to compute the conventional Mulliken and Löwdin population analyses with STO3G, 6311G** and Dunning-Hay split valence basis sets. These results have been compared to the estimates provided by the Hirshfeld model. The charges found in the Hirshfeld method are smaller than those from the other methods.     

Atomic charges for molecular dynamics calculations

Atomic charges obtained with the fit of the ab initio electrostatic potential suffers of several defects, for instance, chemical meaning is not insured. We have employed a method recently put forward for deriving atomic charges which addresses the issue of chemical meaning and conformational transferability to N,N-dibutylacetamide and ethylenediaminetetraacetate. The charges have been used in molecular dynamics calculations where the interaction with a metallic cation is considered. We found structural parameters for the complexes in good agreement with the available experimental results.     

VESPA: A new,fast approach to electrostatic potential-derived atomic charges from semiempirical methods

An improved semiempirical method for computing electrostatic potential-derived atomic charges is described. It includes a very fast algorithm for the generation of the grid points around the molecule and the calculation of the electrostatic potential at these points. The dependency of the atomic point charges obtained on the number of grid points used in the fitting procedure is examined. For “buried” atoms a high density grid is necessary. It is possible to obtain 6–31G*-quality atom-centered point charges, even for phosphorus compounds, using AM1 or PM3. This approach can therefore be recommended for general use in QSAR or molecular mechanics for any organic and bioorganic system up to about 200 atoms. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 744–756, 1997     

Atomic charges based on spherical harmonics expansion at the atomic centers

Molecular orbitals are expanded in spherical harmonics functions around atomic centers. The expansion coefficient is a function of the distance from the nucleus and the quotient between this function and a corresponding atomic orbital is almost constant in the core region. The square of the quotient is used as a definition of an atomic charge component. The erratic dependence on the type of basis functions in the Mulliken method is thereby avoided. The relationship between the new charge and the Mulliken population is investigated and a new invariant Mulliken population is suggested.     

Effective atomic charges in alanine dipeptide

A new set of effective atomic charges of different conformers of alanine dipeptide is presented. These charges are obtained by fitting the electrostatic potential resulting from the ab initio SCF wave function of the system obtained in a 6-31G basis set. A specific fit procedure is used providing charges weakly dependent on the fit points as well as on the geometry of the molecule. It is shown that these charges retain a reasonable chemical meaning. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 473–482, 1999     

A method for calculating atomic charges in large molecules

A simple electronegativity method is used to calculate atomic charges for molecules of interest to biochemistry. These include purines, pyrimidines, and amino acids. Results are compared to those obtained from other theoretical methods (ab initio and semiempirical) as well as to nuclear magnetic resonance (NMR) data. Correlation is fair with CNDO results but very good for ab initio, DelRe, and other electronegativity methods. Good correlation was also achieved with NMR data. It is shown that a correction factor may be required in some cases and that important resonance effects need to be taken into account. Because of the small amount of calculational effort involved, these results suggest that this method could be quite useful in this field.     

Charge calculations in molecular mechanics. IX. A general parameterisation of the scheme for saturated halogen,oxygen and nitrogen compounds

Summary The CHARGE2 program for the calculation of partial atomic charges has been amended to include bond parameters for a number of organic functional groups, including halogens, nitrogen and oxygen. These minor amendments to the original scheme produce dipole moments for the fluoro and chloro compounds which are in complete agreement with the observed values.The less complete data sets for the bromo and iodo compounds are also well reproduced, and the dipole moments of a variety of mixed halo compounds are now in better agreement with experiment than previously.The calculated dipole moments of the saturated nitrogen and oxygen compounds are now in much better agreement than in the original scheme, thus the revised parameterisation may be employed with confidence to predict the electrostatic energies of these compounds.Furthermore, the revised scheme now gives a precise proportionality between the charge on the proton in a CH group and the ¹H chemical shift of the corresponding proton, allowing the general prediction, in principle, of ¹H chemical shifts. In addition, attempts to include variable electronegativity in the effect are described for fluoro compounds.For part VIII see Ref. 1.     

A practical procedure for the determination of electrostatic charges of large molecules

Summary A practical procedure for the precise determination of electrostatic charges, which are evaluated by fitting the rigorous quantum mechanical molecular electrostatic potential to a monopole-monopole expression, is presented. The proposal of this procedure arises from the study of the minimum requirements necessary to obtain reliable electrostatic charges. Such a study is focused on: (i) the dependence of the electrostatic charges on the set of points where the quantum mechanical and the monopole-monopole molecular electrostatic potentials are fitted; thus, both the influence of the number of points and their distribution in layers located out of the van der Waals radii of the atoms are examined, and (ii) the reliability of the use of fractional models for the evaluation of electrostatic charges of large molecules. Results point out that the optimum number of points is defined by a density of points ranging from 0.45 to 0.60 points/Ų when four layers (separated by 0.2 Å) are considered. Nevertheless, the use of only two layers (separated by 0.4 Å) for large molecules is recommended, thus enabling one to obtain reliable charges at a reduced computational cost. Moreover, results justify the use of fractional models for the determination of electrostatic charges of extremely large molecules, even when aromatic structures exist.     

Solvated ensemble averaging in the calculation of partial atomic charges

In the calculation of partial atomic charges, for use in molecular mechanics or dynamics simulations, it is common practice to select only a single conformation for the molecule of interest. For molecules that contain rotatable bonds, it is preferable to compute the charges from several relevant conformations. We present here results from a charge derivation protocol that determines the partial charges by averaging charges computed for conformations selected from explicitly solvated MD simulations, performed under periodic boundary conditions. This approach leads to partial charges that are weighted by a realistic population of conformations and that are suitable for condensed phase simulations. This protocol can, in principle, be applied to any class of molecule and to nonaqueous solvation. Carbohydrates contain numerous hydroxyl groups that exist in an ensemble of orientations in solution, and in this report we apply ensemble averaging to a series of methyl glycosides. We report the extent to which ensemble averaging leads to charge convergence among the various monosaccharides and among the constituent atoms within a given monosaccharide. Due to the large number of conformations (200) in our ensembles, we are able to compute statistically relevant standard deviations for the partial charges. An analysis of the standard deviations allows us to assess the extent to which equivalent atom types may, nevertheless, require unique partial charges. The configurations of the hydroxyl groups exert considerable influence on internal energies, and the limits of ensemble averaged charges are discussed in terms of these properties.     

Atomic charges in the multiple scattering molecular orbital method

The concept of atomic charges in molecular orbital theory is discussed. A definition which pays special attention to the behaviour of the orbitals close to the atomic nuclei, is suggested. This new definition is particularly simple to apply in the multiple scattering method. Some transition metal complexes are considered as examples. The existence of the back donation effect is demonstrated for a series of octahedral cyanides.Supported by NFR, the Swedish Natural Science Research Council.     

A simple method for calculating reliable atomic charges in large molecules

Modifications are made to a previously developed scheme for calculating atomic charge which uses orbital electronegativity and which requires minimal calculational effort. The introduced changes are a result of deficiencies noted in the earlier method which were due to an inadequate accounting of effects from neighboring atom charges. Results obtained using the modified scheme for both model compounds as well as larger molecules of interest to biochemistry are compared to previous results and also to several levels of ab initio calculations. It is shown that a definite improvement is obtained and that the present method gives very good correlations with each calculational level. Comparisons are also made with other methods that use electronegativity theory. It is shown that the present scheme represents a definite improvement over alternate orbital electronegativity methods and is roughly comparable to a higher level scheme that utilizes atomic electronegativity values. A discussion comparing the latter method with the present one is included. Because of the small amount of calculational effort involved, the results indicate that the present method could be quite useful in providing reliable atomic charges for large molecular systems.     

A combined electronegativity equalization and electrostatic potential fit method for the determination of atomic point charges

We report an approach for the determination of atomic monopoles of macromolecular systems using connectivity and geometry parameters alone. The method is appropriate also for the calculation of charge distributions based on the quantum mechanically determined wave function and does not suffer from the mathematical instability of other electrostatic potential fit methods.