Atomic Charges in the Quadrupole Solvation Energy Calculations

A procedure is described and tested for the use of atomic charges instead of bond dipole moments in the calculations, based on the reaction field theory, of quadrupole term of the solvation energy.     

MBOHO calculations of C?H stretching frequencies in hydrocarbons and heterosubstituted hydrocarbons

Based on the generalized relationship for calculating the nuclear spin–spin coupling constants and the correlation of the bond stretching frequencies with the coupling constants, a novel generalized reationship, which includes the contributions of not only the hybrid orbitals, but also the net atomic charges, is introduced for calculation of the bond stretching frequencies and employed to elucidate the C? H stretching frequencies in hydrocarbons and heterosubstituted hydrocarbons on the basis of the MBOHO calculation employing the CNDO /2 approximation. By use of the obtained concrete realtionships, one can get different ν _CH value for the C? H bonds existing in different chemical environments, which is coincident with chemical intuition. The calculated numerical results show that for hydrocarbons the contribution of the net atomic charges can be neglected, but it is necessary for heterosubstituted hydrocarbons to include the contribution of the net atomic charges to the C? H stretching frequencies. The calculated C? H stretching frequencies are in good ageement with the experimental data, which shows its reasonableness. © 1994 John Wiley & Sons, Inc.     

On the charge distribution in ethanes and disilanes and correlations with equilibrium bond lengths; an ab initio study

The equilibrium electronic wave-functions for a series of fluoro- and chloro-ethanes and disilanes of general formula M₂H_6−nX_n, (M=C, Si; X=F, Cl), were analysed by the most commonly used methods for electron distribution, using the Mulliken and Löwdin populations, natural atomic orbital (NAO) populations and atoms in molecules (AIM) electron densities. Although the numerical values for local atomic charges vary greatly, all the methods correlate, but in markedly differing ways. The Mulliken charges seem the most selective in relation to systematic change of substituents in the current type of molecular structure. A number of examples occur where the AIM charges at C, Si centres are effectively identical in different molecules, where some differences might have been anticipated. These are often distinguished by Mulliken populations. The fluoroethanes exemplify this, since a plot of the AIM charges (for example on either the F or H centres) against the Mulliken charges for all members of the series, shows three nearly parallel lines, corresponding to those centres with 0, 1 or 2 fluorine atoms on the centre under study. The bond critical points at which the AIM charges are determined seem to be counter to intuition in some cases. This is a density rather than atomic orbital size issue however. The Mulliken and NAO charges seem more reasonable than those from the AIM method. There is an unexpected correlation of the local bond dipoles from the Mulliken analyses, with the calculated equilibrium bond lengths. These correlations lead to bond length values for the non-polarised bonds MX, which agree with data based on covalent radii for some bonds.     

Geometry-dependent atomic charges: Methodology and application to alkanes,aldehydes, ketones,and amides

A general methodology for deriving geometry-dependent atomic charges is presented. The main ingredient of the method is a model that describes the molecular dipole moment in terms of geometry-dependent point charges. The parameters of the model are determined from ab initio calculations of molecular dipole moments and their Cartesian derivatives at various molecular geometries. Transferability of the parameters is built into the model by fitting ab initio calculations for various molecules simultaneously. The results show that charge flux along the bonds is a major contributing factor to the geometry dependence of the atomic charges, with additional contributions from fluxes along valence angles and adjacent bonds. Torsion flux is found to be smaller in magnitude than the bond and valence angle fluxes but is not always unimportant. A set of electrostatic parameters is presented for alkanes, aldehydes, ketones, and amides. Transferability of these parameters for a host of molecules is established to within 3 ?5% error in the predicted dipole moments. A possible extension of the method to include atomic dipoles is outlined. With the inclusion of such atomic dipoles and with the set of transferable point charges and charge flux parameters, it is demonstrated that molecular electrostatic potentials as well as electrostatic forces on nuclei can be reproduced much better than is possible with other models (such as potential derived charges). © 1995 by John Wiley & Sons, Inc.     

Theoretical study of ketenimine: Geometry,electronic properties,force constants and barriers to inversion and rotation

Non-empirical calculations of the structure and properties of ketenimine have been performed using nine Gaussian basis sets. Values for the bond lengths and angles, HOMO and LUMO energies, atomic charges, overlap populations, dipole moments, bond energies, force constants and barriers to nitrogen inversion and internal rotation are predicted.     

Comparison of atomic charges derived via different procedures

Atomic charges were obtained from ab initio molecular orbital calculations using a variety of procedures to compare them and assess their utility. Two procedures based on the molecular orbitals were examined, the Mulliken population analysis and the Weinhold–Reed Natural Population Analysis. Two procedures using the charge density distribution were included; the Hirshfeld procedure and Bader's Atoms in Molecules method. Charges also were derived by fitting the electrostatic potential (CHELPG) and making use of the atomic polar tensors (GAPT). The procedures were first examined for basis set independence, and then applied to a group of hydrocarbons. The dipole moments for these molecules were computed from the various atomic charges and compared to the total SCF dipole moments. This was followed by an examination of a series of substituted methanes, simple hydrides, and a group of typical organic compounds such as carbonyl derivatives, nitriles, and nitro compounds. In some cases, the ability of the charges to reproduce electrostatic potentials was examined. © John Wiley & Sons, Inc.     

Electrostatic interactions in molecular mechanics (MM2) calculations via PEOE partial charges I. Haloalkanes

The PEOE (partial equalization of orbital electronegativity) procedure has been modified slightly and reparametrized for haloalkanes to calculate partial atomic charges suitable for evaluation of dipole moments and electrostatic energies in conjunction with molecular mechanics (MM2) calculations. Dipole moments of 66 haloalkanes are calculated with an average absolute deviation of 0.14 D from experimental values. The conformational energies of 40 compounds have been calculated and the agreement with experimental data is generally good and compares well with calculations by the IDME (induced dipole moment and energy) method. In addition, carbon and proton charges correlate well with C-1s core binding energies and ¹H-NMR (nuclear magnetic resonance) shifts for halomethanes. The most striking benefit of treating electrostatics through a set of partial charges compared to the standard MM2 bond dipole approach is demonstrated by calculations on 1,4-disubstituted cyclohexanes, for which standard MM2 fails to predict the most stable conformation.     

New approach to the semiempirical calculation of atomic charges for polypeptides and large molecular systems

Starting from the bond polarization theory (BPT), a new semiempirical method for the calculation of net atomic charges is developed. The bond polarization theory establishes a linear dependence of atomic charges from the bond polarization energy. This energy is calculated from the hybrid orbitals forming a bond and the point charges within the neighborhood. Empirical parameters are introduced for the polarity of an unpolarized bond and for the change of the atomic charge with σ- and π-bond polarization. Because these parameters are linear, they can be calibrated directly using net atomic charges from ab initio calculations. This procedure was performed using the charges from STO3G calculations on a set of 18 amino acids. Using the two parameters for CH, OH, σ-CO, and NH bonds and the three parameters for CC, CO, and CN bonds, the 350 ab initio charges can be reproduced with high accuracy by solving sets of linear equations for the charges. The calculation of charges for large molecular systems including all inter- and intramolecular mutual polarizations requires only a few seconds (up to 100 atoms) or minutes (700 atoms) on a PC. This procedure is well suited for the application in molecular mechanics or molecular dynamics programs to overcome the limitations of most force fields used up to now. One of the weakest points in these programs is the use of fixed or topological charges to define the electrostatic potential. As an application of the new method, we calculated the interaction energy of an ion with valinomycin. This ring molecule forms octahedral oxygen cages around ions like potassium and acts thereby as selective ion carrier. To accomplish this function, valinomycin has to strip off the hydratization spheres of the ions, and therefore its preference for certain types of ions could be deduced from the interaction energies. © 1994 by John Wiley & Sons, Inc.     

Charge distributions and multipole moments in molecules

The consideration of multipole moments is suggested as a new criterion for the validity of assignments of atomic charges in molecules. The total quadrupole and octupole moments generated by our definition of atomic charges are compared with the exact moments of the underlying wavefunction for various basis sets in selected diatomics. The analysis includes also total overlap and total dipole moment partitioning as well as 1σ MO overlap partitioning. All considerations together allow us to assess the validity of our charge definition as compared to Mulliken's and Löwdin's and the quality of the basis set.     

极性分子键角与键偶极矩的关系

研究了基态极性分子的键角和键偶极矩之间的关系。我们采用原子偶极矩校正的Hirshfeld （ADCH）电荷来计算键偶极矩,利用电子的局域函数和键临界点处的局域函数值来分析键的电子结构。通过对IVA族（IVA = C,Si,Ge）、VA族（VA = N,P,As ）、VIA族（VIA = O,S,Se）和VIIA族（VIIA = F,Cl,Br）元素形成的系列共价型基态分子,以及环状基态分子的键角和键偶极矩数据进行分析,发现在键的电子结构类似的情况下,由于键偶极矩的排斥作用,这些分子的键角随键偶极矩的增加而增大。这一发现有助于加深我们对分子几何结构的认识。     

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.     

Experimental atomic charges from infrared intensities. Comparison with “ab initio” values

Atomic charges can be derived from observed infrared intensities and molecular dipole moments. The atomic charges so drived for a series of simple organic molecules are compared with atomic electron population data computed by quantum-mechanical calculations at various levels. It is shown that experimental charges agree very well with those computed by 6-31G^**.     

A molecular mechanics (MM3) study of fluorinated hydrocarbons

A molecular mechanics study of small saturated hydrocarbons (up to C-6), substituted by up to six fluorines was carried out with the MM3 force field. Perfluorobutane and Teflon were also studied. A parameter set was developed for use in the calculation of bond lengths, bond angles, torsion angles, conformational energies, barriers to rotation, dipole moments, moments of inertia and vibrational frequencies for these compounds. The results are in good agreement with experiment when only one or two fluorines are present, but some rather large discrepancies were noted when the F/H ratio becomes high. These can be taken into account only by using a force field more complicated than MM3. Some of the requirements of such a force field are delineated. Some pertinent ab initio results are also reported in this article.     

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.     

Real-time propagation of the reduced one-electron density matrix in atom-centered orbitals: application to multielectron dynamics of carbon clusters C(n) in the strong laser pulses

We present a time-dependent density functional theory (TDDFT) study on the electron dynamics of small carbon clusters C(n) (n = 9, 10) exposed to a linearly polarized (LP) or circularly polarized (CP) oscillating electric field of ultrafast laser with moderate laser intensity. The multielectron dynamics is described by propagating the reduced one-electron density matrix in real-time domain. The high harmonic generation (HHG) spectra of emission as well as the time evolution of atomic charges, dipole moments and dipole accelerations during harmonic generation are calculated. The microscopic structure-property correlation of carbon chains is characterized. It is found that the electron responses of C(n) to the laser field oscillation become nonadiabatic as the field intensity is larger than 1.4 x 10(13) W/cm(2). The nonadiabatic multielectron effect is displayed by an explicit fluctuation on the induced atomic charges and the instantaneous dipole acceleration and by observing the additional peaks other than those predicted from the spectral selection rule in HHG spectra of C(n) as well. The origin of these additional peaks is elucidated. The atomic charges of C(n) in LP and CP laser pulses experience different type of oscillations as expected. In the linear structure C9, the atomic charges at the two ends experience larger amplitude oscillations than those near the chain center whereas the induced charges on each atom of C10 experience the equal amplitude oscillations in the CP laser pulse.     

Point atomic multipole moments for simulation of electrostatic potential and field in all-siliceous zeolites

Calibration method of atomic multipole moments (AMMs) is presented with respect to geometries of all-siliceous zeolite models obtained with X-ray diffraction (XRD) methods. Mulliken atomic charges and AMMs are calculated for all-siliceous types possessing small size elementary unit cells at the hybrid density functional theory (DFT) (B3LYP) and general gradient approximation (GGA) Perdew-Burke-Ernzerhof (PBE) levels and then used to fit the dependences versus geometry variables for the Mulliken charges and versus special coordinate for the AMMs. Fitted and exact charges and AMMs are used to compute electrostatic potential (EP) and electric field (EF) for all-siliceous zeolites with CRYSTAL. A possibility of application of the point AMMs to quantum mechanical/molecular mechanics computations or classic simulation of physical adsorption is evaluated. The considered models expand over wide range of structural parameters and could be applied even to amorphous all-siliceous systems.     

Atomic multipoles: Electrostatic potential fit,local reference axis systems,and conformational dependence

Currently, all standard force fields for biomolecular simulations use point charges to model intermolecular electrostatic interactions. This is a fast and simple approach but has deficiencies when the electrostatic potential (ESP) is compared to that from ab initio methods. Here, we show how atomic multipoles can be rigorously implemented into common biomolecular force fields. For this, a comprehensive set of local reference axis systems is introduced, which represents a universal solution for treating atom‐centered multipoles for all small organic molecules and proteins. Furthermore, we introduce a new method for fitting atomic multipole moments to the quantum mechanically derived ESP. This methods yields a 50–90% error reduction compared to both point charges fit to the ESP and multipoles directly calculated from the ab initio electron density. It is shown that it is necessary to directly fit the multipole moments of conformational ensembles to the ESP. Ignoring the conformational dependence or averaging over parameters from different conformations dramatically deteriorates the results obtained with atomic multipole moments, rendering multipoles worse than partial charges. © 2012 Wiley Periodicals, Inc.     

Comparative characteristics of a tryptophan molecule in the gas phase and water

The L and D isomers of the tryptophan (Trp) molecule and the (Trp)⁺ cation in the gas phase and water are calculated at the DFT level to reveal the effect of water considered in the dielectric continuum approximation on the electronic characteristics of the molecule. The distribution of effective atomic charges and bond lengths enables the prediction of the most probable parts of the chemical bond cleavage during the fragmentation of the molecule under the ionizing particle flux. These data are supplemented with a calculation of fragmentation energies. Zwitterionic structures characterized by the appearance of considerable dipole moments and a change in their orientation with respect to the ground state are distinguished among the possible isomeric forms in water.