Building molecular charge distributions from fragments: Application to HIV-1 protease inhibitors

Interaction energies are a function of the molecular charge distribution. In previous work, we found that the set of atomic partial charges giving the best agreement with experimental vacuum dipole moments were from density functional theory calculations using an extended basis set. Extension of such computations to larger molecules requires an atomic partial charge calculation beyond present computational resources. A solution to this problem is the calculation of atomic partial charges for segments of the molecule and reassociation of such fragments to yield partial charges for the entire molecule. Various partitions and reassociation methods for five molecules relevant to HIV-1 protease inhibitors are examined. A useful method of reassociation is introduced in which atomic partial charges for a large molecule are computed by fitting to the combined electrostatic potential calculated from the fragment partial charges. As expected, the best sites for partitions are shown to be carbon—carbon rather than carbon—nitrogen bonds. © 1997 by John Wiley & Sons, Inc.     

Topological analysis of the molecular charge density and impact sensitivy models of energetic molecules

Important explosives of practical use are composed of nitroaromatic molecules. In this work, we optimized geometries and calculated the electron density of 17 nitroaromatic molecules using the Density Functional Theory (DFT) method. From the DFT one-electron density matrix, we computed the molecular charge densities, thus the electron densities, which were then decomposed into electric multipoles located at the atomic sites of the molecules using the distributed multipole analysis (DMA). The multipoles, which have a direct chemical interpretation, were then used to analyze in details the ground state charge structure of the molecules and to seek for correlations between charge properties and sensitivity of the corresponding energetic material. The DMA multipole moments do not present large variations when the size of the Gaussian basis set is changed; the largest variations occurred in the range 10-15% for the dipole and quadrupole moments of oxygen atoms. The charges on the carbon atoms of the aromatic ring of each molecule become more positive when the number of nitro groups increases and saturate when there are five and six nitro groups. The magnitude and the direction of the dipole moments of the carbon atoms, indicators of site polarization, also depend on the nature of adjacent groups, with the largest dipole value being for C-H bonds. The total magnitude of the quadrupole moment of the aromatic ring carbon atoms indicates a decrease in the delocalized electron density due to an electron-withdrawing effect. Three models for sensitivity of the materials based on the DMA multipoles were proposed. Explosives with large delocalized electron densities in the aromatic ring of the component molecule, expressed by large quadrupole values on the ring carbon atoms, correspond to more insensitive materials. Furthermore, the charges on the nitro groups also influence the impact sensitivity.     

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.     

The ab initio charge deformation density of bicyclobutane from an extended gaussian basis

The charge deformation density of bicyclobutane has been derived from SCF wavefunctions computed with two contracted gaussian bases, of double-zeta and double-zeta-plus-polarization quality. Carbon—carbon bond peaks are displaced to the outside of the three-carbon rings, the peak in the bridge bond being flatter and further from the CC line than those in the non-fused bonds. Inclusion of polarization functions broadens these peaks so that they merge in a flat plateau inside each cyclopropane triangle. The side bonds are also bent slightly out of the ring plane, evidently by non-bonded repulsion between the methylene carbon atoms. Partitioning into atomic fragments produces almost neutral atoms but the CH dipoles add up to give a molecular moment of 0.685 D, in excellent agreement with experiment. They also contribute to a net charge contraction towards the center of mass, whose calculated anisotropy agrees satisfactorily with the measured quadrupole moments. Multipole moments of the atomic deformation densities and inner moments of the total molecular charge about the atomic centers provide a detailed quantitative characterization of the charge distribution.     

Local and nonlocal density functional calculations of the molecular structure of isomeric thiadiazoles

The chemistry of thiadiazoles and their derivatives is of considerable interest in chemistry owing to their pharmacological and potential industrial applications. In this context, a detailed study of isomeric thiadiazole molecules has been done using local (SVWN; Slater, and Vosko, Wilk and Nusair) and nonlocal (BLYP; Becke, and Lee, Yang and Parr) density functionals and optimizing the molecular geometries by means of the gradient technique. A charge sensitivity analysis of the studied molecule has been performed by resorting to density functional theory, obtaining several sensitivity coefficients such as the molecular energy, net atomic charges, global and local hardness, global and local softness and Fukui functions. With these results and the analysis of the dipole moments, the molecular electrostatic potentials and the total electron density maps, several conclusions have been inferred about the preferred sites of chemical reaction of the studied compounds. The condensed Fukui functions are shown to be one of the best criteria for predicting chemical reactivity.     

Atomic charges,dipole moments,and Fukui functions using the Hirshfeld partitioning of the electron density

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.     

Restrained point-charge models for disaccharides

Various methods for deriving atomic partial charges from the quantum chemical electrostatic potential and moments have been tested for the sucrose molecule. We show that if no further information is used, the charges on some carbon atoms become large and charge patterns involving these atoms are badly determined and poorly transferable. Adding lone-pairs on the ether oxygen atoms or dividing the molecule into smaller fragments did not cure the instabilities. We develop a method, CHELP-BOW0, that restrains charges toward zero with different weights for different atoms. These harmonic restraints preserve the linear form of the least-squares equations, which are solved in a single step using singular-value decomposition. CHELP-BOW0 improves the chemical transferability of the charges compared to unrestrained methods, and slightly improves their conformational transferability. It introduces a modest degradation of the fit compared to unrestrained CHELP-BOW (mean average deviation of the potential 0.00016 vs. 0.00010 a.u.). A second new method, CHELP-BOWC, avoids the need for restraints by including several conformations in the fit, weighting each according to its estimated energy in solution. CHELP-BOWC charges are more transferable than CHELP-BOW or CHELP-BOW0 charges to conformations not included in the training set. Restraints to zero charge do not further improve transferability of the CHELP-BOWC charges. We, therefore, recommend CHELP-BOW charges for rigid molecules and CHELP-BOWC charges for flexible molecules.     

Quantum theory of atoms in molecules charge-charge flux-dipole flux models for the infrared intensities of X(2)CY (X = H, F, Cl; Y = O, S) molecules

The molecular dipole moments, their derivatives, and the fundamental IR intensities of the X2CY (X = H, F, Cl; Y = O, S) molecules are determined from QTAIM atomic charges and dipoles and their fluxes at the MP2/6-311++G(3d,3p) level. Root-mean-square errors of +/-0.03 D and +/-1.4 km mol(-1) are found for the molecular dipole moments and fundamental IR intensities calculated using quantum theory of atoms in molecules (QTAIM) parameters when compared with those obtained directly from the MP2/6-311++G(3d,3p) calculations and +/-0.05 D and 51.2 km mol(-1) when compared with the experimental values. Charge (C), charge flux (CF), and dipole flux (DF) contributions are reported for all the normal vibrations of these molecules. A large negative correlation coefficient of -0.83 is calculated between the charge flux and dipole flux contributions and indicates that electronic charge transfer from one side of the molecule to the other during vibrations is accompanied by a relaxation effect with electron density polarization in the opposite direction. The characteristic substituent effect that has been observed for experimental infrared intensity parameters and core electron ionization energies has been applied to the CCFDF/QTAIM parameters of F2CO, Cl2CO, F2CS, and Cl2CS. The individual atomic charge, atomic charge flux, and atomic dipole flux contributions are seen to obey the characteristic substituent effect equation just as accurately as the total dipole moment derivative. The CH, CF, and CCl stretching normal modes of these molecules are shown to have characteristic sets of charge, charge flux, and dipole flux contributions.     

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.     

A study of the radiation chemistry of phosphorous compounds

The partial charges of atoms of a number of organophosphorous compounds were calculated by the method of iterative partial equalization of orbital electron negativity (PEOE) presented by Gasteiger and Marsili, and from the calculated partial charges of carbon atoms of the ester alkyl groups in three stereoisomers each for tributylphosphate and dibutylphenylphosphonate, it was found that in all cases the carbon at the α-position to oxygen possesses the largest density of positive charge, such that the C_α—C_β bonds were more readily broken than other C—C bonds. The experimental results supported this conclusion by examining the G-values of gaseous alkane (alkene) radiation products. From the low temperature measured esr spectra of several phosphates and phosphonates γ-irradiated at 77°K and it was seen that these spectra were composed of several radicals formed by different reaction processes. Like TMP, the esr spectrum of dimethyl methylphosphate irradiated in low temperature contained also four kinds of radicals. The net atomic charges as well as the values of mulliken population matrix condensed to atoms were calculated by CNDO/2 MO and by ab initio MO methods for comparison. In all cases the net atomic charges of the carbon in C—P bonds were positive. Since the phosphoryl radical was found in esr spectrum of DMMP, it implied that the C—P bonds were also broken during irradiation. In our work, the products of C—P fission were truly found and their G-values were determined by gas chromatography. For studying of energy transfer, two binary systems (TBP-DPPP and TBP-benzene) were irradiated and the G-values of polymer, di-and monobasic acids were measured and compared. In these systems the intermolecular energy transfer were predominate. DPPP had higher scavenging effect than benzene.     

Atomic dipole moments calculated using analytical molecular second-moment gradients

We have implemented analytical second-moment gradients for Hartree-Fock and multiconfigurational self-consistent-field wave functions. The code is used to calculate atomic dipole moments based on the generalized atomic polar tensor (GAPT) formalism [Phys. Rev. Lett. 62, 1469 (1989)], and the proposal of Dinur and Hagler (DH) for the calculation of atomic multipoles [J. Chem. Phys. 91, 2949 (1989)]. Both approaches display smooth basis-set convergence toward a well-defined basis-set limit and give reasonable electron correlation effects on the calculated atomic properties. However, the atomic charges and atomic dipole moments obtained from the GAPT partitioning scheme are unable to provide even qualitatively meaningful molecular quadrupole moments for some molecules, and thus the atomic multipole moments calculated in this scheme cannot be considered well suited for analyzing the electron density in molecules and for calculating intermolecular interaction energies. In contrast, the DH approach gives atomic charges and dipole moments that by definition exactly reproduce the molecular quadrupole moments. The approach of DH is, however, restricted to planar molecules and thus suffers from not being applicable to molecules of arbitrary shape. Both the GAPT and DH approaches give rather poor results for octupole and hexadecapole moments, indicating that at least atomic quadrupole moments are required for an accurate representation of the molecular charge distribution in terms of atomic electric moments.     

Local and nonlocal density functional calculations of the molecular structure of isomeric thiadiazole monoxides

Conjugated organic heterocycles are systems of growing interest in materials science in view of the potential applications in fields such as electronics, photonics, sensors, or corrosion protection. The study of their molecular properties serves as a model for the prediction of the behavior of potentially conductive oligomers and polymers. A detailed analysis of isomeric thiadiazole monoxide molecules has been done using Hartree–Fock and local (SVWN) and nonlocal (BLYP, B3LYP) density functionals and optimizing the molecular geometries by means of the gradient technique. A charge sensitivity analysis of the studied molecules has been performed by resorting to density functional theory, obtaining several sensitivity coefficients such as the molecular energy, net atomic charges, global and local hardness, global and local softness, and Fukui functions. With these results and the analysis of the dipole moments, the molecular electrostatic potentials and the total electron density maps, several conclusions have been inferred about the preferred sites of chemical reaction of the studied compounds. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 105–115, 2001     

The currant bun model of simple molecules

The model of a molecule previously introduced by the authors, in which most of the electronic charge is represented by point charges on the nuclei, in the lone pairs and bonds, and the remainder is in a diffuse function which represents the outer electrons, is here extended. Molecules with several heavy atoms require several diffuse functions, one for each heavy atom, in addition to one at the centre of nuclear charge. In an electric field the centre of each diffuse function moves against a harmonic restoring force and this gives rise to the polarizability of the molecule. When two molecules interact the movement of this function produces the dispersion force. The model thus embodies all the long range forces between molecules in a more accurate and simpler way than was possible earlier.     

The kinetic energy of molecular charge distributions and molecular stability

This paper examines the relationship between the topographical features of a molecular charge distribution and the kinetic energy of the system. Specifically, the spatial contributions to the kinetic energy are related to the Laplacian of the total charge density and to the gradients of the natural-orbital densities. It is concluded that a necessary requirement for molecular stability is the existence of a net negative curvature for the molecular charge distribution in the internuclear region. It is shown that the charge density accumulated in the internuclear region of a stable molecule is distributed in such a way as to keep the accompanying increase in the kinetic energy to a minimum. A comparison of the contributions to the kinetic energy from the atomic and molecular charge distributions indicates that in the formation of a stable molecule the contribution from the molecular charge density in the binding region is decreased relative to that of the atoms.