Experimental and theoretical electronic charge densities in molecular crystals

Electronic charge density distribution in molecular systems has been described in terms of the topological properties. After briefly reviewing methods of obtaining charge densities from X-ray diffraction and theory, typical case studies are discussed. These studies include rings and cage systems, hydrogen bonded solids, polymorphic solids and molecular NLO materials. It is shown how combined experimental and theoretical investigations of charge densities in molecular crystals can provide useful insights into electronic structure and reactivity.     

Ab initio calculations of electrostatic potentials and deformation densities for a series of choline ester model systems

Ab initio LCAO-MO-SCF calculations using a double zeta basis set have been performed for the methyl esters of acetic acid, carbamic acid, methylcarbonic acid, and trifluoracetic acid, in order to model the corresponding choline esters. The systems have been compared by means of population analyses, electron density differences, electrostatic potentials and potential differences. The significance of the electrostatic potential in connection with crystal structure and packing has been studied. The differences in the proton affinity of the compounds have been correlated to differences in the potentials.     

Two-body densities and effective potentials

For an A-particle quantum system in a state Ψ, the movement of any pair of particles is studied. Using the corresponding two-body densities, the effective potential that determines the relative and center of mass movements of the pair of particles is built. Some aspects of the proposed general procedure are applied to different, functions used to describe the ground state of the helium atom. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 75–81, 2000     

Influence of polarization functions on molecular electrostatic potentials

We study the effects of d-polarization functions, centered on the heavy atoms, on the SCF molecular electrostatic potentials calculated for some molecules. The positions and energies of the minima found are very sensitive to the inclusion of polarization functions in the basis set used. The variations depend on the heavy atom involved and on the possible anisotropy of its charge distribution. These variations are particularly important for second-row atoms.     

Electron densities from the Brueckner Doubles method

Summary The concept of the Brueckner orbital is examined, following a resurgence of interest in wavefunctions constructed from them. The distinction between Self Consistent Field, Natural and Brueckner orbitals are discussed. Total electron densities are calculated for several examples, and correlation densities are studied. It is found that the Brueckner orbitals are more localised than SCF orbitals. The total electron density constructed from the Brueckner reference determinant with Brueckner orbitals gives qualitatively similar pictures as other correlated methods. Brueckner orbitals are found to show dissociation well.     

On the similarity between molecular electron densities, electrostatic potentials and bare nuclear potentials

The similarities among the molecular contours of three scalar fields, viz. electron density (ED), electrostatic potential (ESP) and bare nuclear potential (BNP) have been investigated. The topological resemblance between ESP and ED contour diagrams (as prompted by the Thomas-Fermi model) is more pronounced than that for BNP and ED contour diagrams (as predicted by the local density functional model of Parr, Gadre and Bartolotti) with three-membered ring systems as test cases. An analysis of critical points of these distributions has also been included. Thus it may be conjectured that ED maps may prove useful in predicting reactive sites in molecules.     

Theoretical studies on the molecular electron densities and electrostatic potentials in azacubanes

Energetics and the charge distributions in azacubanes (C₈NH_8–) have been obtained using the ab initio Hartree–Fock, second-order Mø øller–Plesset perturbation theory and hybrid density functional methods. For diazacubane to hexaazacubane the lowest-energy conformers have nitrogen atoms occupying the face opposite corners of a cube. The topography of the molecular electrostatic potential and the electron density of azacubane conformers have been investigated. The electrostatic potential studies have shown that successive substitution of nitrogen instead of CH groups of cubane engenders smaller and more localized electron-rich regions around the nitrogens of a cube. Further the bond ellipticity and the electron density at the bond critical point of the X–N bonds (X=C or N) in a cubanoid increase from azacubane to octaazacubane. The heats of formation of azacubanes calculated by the isodesmic reaction approach using different levels of theory correlate well with the electron density at the bond critical point of X–N (X=C or N) bonds in a cubanoid.     

Topography of approximate molecular electrostatic potentials

A new method is described for the approximation of the molecular electrostatic potential (MESP). This method is used for the study of the topography of small molecules. The critical points of the approximate and the exact MESP are compared. It is found that most of the critical points of the exact MESP are retained, but in regions where the exact MESP changes slowly near critical points the number of critical points of the approximate MESP can be reduced.     

Atomic and molecular energies as functionals of the electrostatic potential

Starting from the Hohenberg–Kohn theorem, atomic and molecular energies have been expressed rigorously as functionals of the electronic electrostatic potential, V_elec(r). Explicit formulations have been derived for the functionals representing the kinetic energy and electronic interaction contributions to the total energies.Acknowledgements. The assistance of Dr. Jane S. Murray is greatly appreciated.Contribution to the Jacopo Tomasi Honorary Issue     

The electrostatical molecular potential — A tool for the prediction of electrostatic molecular interaction properties

Starting from the molecular potential we get, by using elementary electrostatics, information about energetically favoured regions for interaction with ions and dipoles around H₂O and H₂CO. The molecule-dipole interaction is represented by the electric field patterns.     

Molecular surface electrostatic potentials in the analysis of non-hydrogen-bonding noncovalent interactions

Electrostatic potentials computed on molecular surfaces are used to analyse some noncovalent interactions that are not in the category of hydrogen bonding, e.g. “halogen bonding”. The systems examined include halogenated methanes, substituted benzenes,s-tetrazine and l,3-bisphenylurea. The data were obtained byab initio SCF calculations.     

Chemical insight into electron density and wave functions: software developments and applications to crystals, molecular complexes and materials science

This paper overviews the work made by our group during the past 10–15 years on crystalline systems, semiconductor surfaces, molecular complexes and on materials of interest for technological applications, such as the defective silicon or the novel generation thermoelectric materials. Our main aim of extracting chemical insight into the analysis of electron densities and computed wave functions is illustrated through a number of examples. The recently proposed Source Function analysis is reviewed and a few of its more interesting applications are summarized. Software package developments, motivated by the need of a direct comparison with experiment or by the help these packages can provide for interpreting complex experimental outcomes, are described and future directions outlined. A particular emphasis is given to the TOPOND and TOPXD programs, which enable one to analyze theoretical and experimental crystalline densities using the rigorous framework of the Quantum Theory of Atoms in Molecules, due to Bader.     

MEPSIM: A computational package for analysis and comparison of molecular electrostatic potentials

Summary MEPSIM is a computational system which allows an integrated computation, analysis, and comparison of molecular electrostatic potential (MEP) distributions. It includes several modules. Module MEPPLA supplies MEP values for the points of a grid defined on a plane which is specified by a set of three points. The results of this program can easily be converted into MEP maps using third-parties graphical software. Module MEPMIN allows to find automatically the MEP minima of a molecular system. It supplies the cartesian coordinates of these minima, their values, and all the geometrical relationships between them (distances, angles, and dihedral angles). Module MEPCOMP computes a similarity coefficient between the MEP distributions of two molecules and finds their relative position that maximizes the similarity. Module MEPCONF performs the same process as MEPCOMP, considering not only the relative position of both molecules but also a conformational degree of freedom of one of them. The most recently developed module, MEPPAR, is another modification of MEPCOMP in order to compute the MEP similarity between two molecules, but only taking into account a particular plane. The latter module is particularly useful to compare MEP distributions generated by systems of aromatic rings. MEPSIM can use several wavefunction computation approaches to obtain MEP distributions. MEPSIM has a menu type interface to simplify the following tasks: creation of input files from output files of external programs (GAUSSIAN and AMPAC/MOPAC), setting the parameters for the current computation, and submitting jobs to the batch queues of the computer. MEPSIM has been coded in FORTRAN and its current version runs on VMS/VAX computers.     

On the molecular electrostatic potentials obtained with CNDO and INDO wave functions

Molecular electrostatic potentials computed with CNDO/2 and INDO wave functions are shown to present systematic differences with respect to ab initio potentials in the case of out-of-plane potentials and in-plane vicinal hetero atoms in planar hetero molecules.     

Approximate sizes of monoatomic negative ions with fractional nuclear charge using electrostatic potentials

Summary Using the criterion that for negative monoatomic ions withN electrons, the location of minimum in the electrostatic potentialV(r) gives an approximate estimate of ionic radii,r _m. Calculations of the latter are reported for quark atoms with fractional nuclear chargesZ=N– andN– , respectively. Quark atoms withN=1–10, 18 and 36 have also been considered.     

Prediction of densities for solid energetic molecules with molecular surface electrostatic potentials

The densities of high energetic molecules in the solid state were calculated with a simplified scheme based on molecular surface electrostatic potentials (MSEP). The MSEP scheme for density estimation, originally developed by Politzer et al., was further modified to calculate electrostatic potential on a simpler van der Waals surface. Forty-one energetic molecules containing at least one nitro group were selected from among a variety of molecular types and density values, and were used to test the suitability of the MSEP scheme for predicting the densities of solid energetic molecules. For comparison purposes, we utilized the group additivity method (GAM) incorporating the parameter sets developed by Stine (Stine-81) and by Ammon (Ammon-98 and -00). The absolute average error in densities from our MSEP scheme was 0.039 g/cc. The results based on our MSEP scheme were slightly better than the GAM results. In addition, the errors in densities generated by the MSEP scheme were almost the same for various molecule types, while those predicted by GAM were somewhat dependent upon the molecule types.     

Wave functions derived from experiment. V. Investigation of electron densities,electrostatic potentials,and electron localization functions for noncentrosymmetric crystals

The constrained Hartree-Fock method using experimental X-ray diffraction data is extended and applied to the case of noncentrosymmetric molecular crystals. A new way to estimate the errors in derived properties as a derivative with respect to added Gaussian noise is also described. Three molecular crystals are examined: ammonia [NH(3)], urea [CO(NH(2))(2)], and alloxan [(CO)(4)(NH)(2)]. The energetic and electrical properties of these molecules in the crystalline state are presented. In all cases, an enhancement of the dipole moment is observed upon application of the experimental constraint. It is found that the phases of the structure factors are robustly determined by the constrained Hartree-Fock model, even in the presence of simulated noise. Plots of the electron density, electrostatic potential, and the electron localization function for the molecules in the crystal are displayed. In general, relative to the Hartree-Fock model, there is a depletion of charge around hydrogen atoms and lone pair regions, and a build-up of charge within the molecular framework near nuclei, directed along the bonds. The electron localization function plots reveal an increase in the pair density between vicinal hydrogen atoms.     

A non-Marcus model for electrostatic fluctuations in long range electron transfer

We propose a new model for the elementary act of electron transfer between two species in solution. The central idea is that the solution in the immediate vicinity of each species may be represented by an equivalent circuit consisting of a Debye circuit shunted by a resistor. Based on this insight, we derive a new formula for the one-dimensional potential energy profile of a coupled donor–acceptor pair at finite (but large) separation d, along a charge-fluctuation reaction co-ordinate, at fixed radii of the transition states. The corresponding reorganisation energy of the reaction is also derived, and it is found to differ from that in the Marcus theory. In particular, the new model predicts that the reorganisation energy is independent of the static dielectric constant of the solution, whereas the old model predicts a strong dependence. The difference is traced to the fact that the Marcus theory omits consideration of the work required to form the charge fluctuations and focuses instead on the work required to localise the charge fluctuations. In general, the equivalent circuit approach permits many of the difficult-to-derive equations of non-equilibrium polarisation theory to be written down by inspection.     

Quantum chemical study on the interaction of some bisphosphonates and Ca2+: The role of molecular electrostatic potentials in the prediction of binding geometry

Summary Molecular electrostatic potentials have been used to model the calcium binding properties of some bisphosphonate drugs, which are used to treat various bone diseases. The mechanism of action involves the binding of bisphosphonates to the bone surface, where calcium plays an important role. Electrostatic potential maps derived from ab initio partial charges have been compared with both the crystal structure and the fully optimized ab initio structure of (dichloro)methylenebisphosphonate-calcium ion complex. Molecular electrostatic potentials can correctly predict the calcium binding geometry of bisphosphonate-type compounds and this type of information can be used in the practical drug design work.