Electron density relationship

I. Alkorta et al., Bond length-electron density relationships From covalent bonds to hydrogen bond interactions. Struct. Chem. 9, 243-247 (1998)... 

Figure Bl.9.12. The schematic diagram of the relationships between the one-dimensional electron density profile, p(r), correlation fiinction y (r) and interface distribution fiinction gj(r).

The Fermi contact density is defined as the electron density at the nucleus of an atom. This is important due to its relationship to analysis methods dependent... 

Molecular volumes are usually computed by a nonquantum mechanical method, which integrates the area inside a van der Waals or Connolly surface of some sort. Alternatively, molecular volume can be determined by choosing an isosurface of the electron density and determining the volume inside of that surface. Thus, one could find the isosurface that contains a certain percentage of the electron density. These properties are important due to their relationship to certain applications, such as determining whether a molecule will fit in the active site of an enzyme, predicting liquid densities, and determining the cavity size for solvation calculations. 

Electrophilic substitution reactions of unsubstituted quinoxaline or phenazine are unusual however, in view of the increased resonance possibilities in the transition states leading to the products one would predict that electrophilic substitution should be more facile than with pyrazine itself (c/. the relationship between pyridine and quinoline). In the case of quinoxaline, electron localization calculations (57JCS2521) indicate the highest electron density at positions 5 and 8 and substitution would be expected to occur at these positions. Nitration is only effected under forcing conditions, e.g. with concentrated nitric acid and oleum at 90 °C for 24 hours a 1.5% yield of 5-nitroquinoxaline (19) is obtained. The major product is 5,6-dinitroquinoxaline (20), formed in 24% yield. 

As this example illustrates, plots such as these can be useful for providing a qualitative understanding of the electron density and its relationship to reactivity, but you would be wise to use and interpret them with care. It is all too easy to unintentionally manipulate such illustrations to create the effect that one expects to observe. For example, any one slice or isosurface of the electron density can be used to argue for a given viewpoint. It is important to examine and visualize the entire volumetric data set before reaching conclusions based on it. ... 

The ab initio methods used by most investigators include Hartree-Fock (FFF) and Density Functional Theory (DFT) [6, 7]. An ab initio method typically uses one of many basis sets for the solution of a particular problem. These basis sets are discussed in considerable detail in references [1] and [8]. DFT is based on the proof that the ground state electronic energy is determined completely by the electron density [9]. Thus, there is a direct relationship between electron density and the energy of a system. DFT calculations are extremely popular, as they provide reliable molecular structures and are considerably faster than FFF methods where correlation corrections (MP2) are included. Although intermolecular interactions in ion-pairs are dominated by dispersion interactions, DFT (B3LYP) theory lacks this term [10-14]. FFowever, DFT theory is quite successful in representing molecular structure, which is usually a primary concern. 

Figure 2 displays a qualitative correlation between the increase or decrease in CO desorption temperature and relative shifts in surface core-level binding energies (Pd(3d5/2), Ni(2p3/2), or Cu(2p3/2) all measured before adsorbing CO) [66]. In general, a reduction in BE of a core level is accompanied by an enhancement in the strength of the bond between CO and the supported metal monolayer. Likewise, an opposite relationship is observed for an increase in core-level BE. The correlation observed in Figure 2 can be explained in terms of a model based on initial-state effects . The chemisorption bond on metal is dominated by the electron density of the occupied metal orbital to the lowest unoccupied 27t -orbital of CO. A shift towards lower BE decreases the separation of E2 t-Evb thus the back donation increases and vice versa. 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

Chapters 8 and 9 are devoted to a discussion of applications of the VSEPR and LCP models, the analysis of electron density distributions to the understanding of the bonding and geometry of molecules of the main group elements, and on the relationship of these models and theories to orbital models. Chapter 8 deals with molecules of the elements of period 2 and Chapter 9 with the molecules of the main group elements of period 3 and beyond. 

Wiener, J. J. M., J. S. Murray, M. E. Grice, and P. Politzer. 1997. Relationships Between Bond Dissociation Energies, Electronic Density Minima and Electrostatic Potential Minima. Mol. Phys. In press. 

The similarity between the bonding models for transition metal carbene and carbyne complexes was noted in Section II. That the reactivity of the metal-carbon double and triple bonds in isoelectronic carbene and carbyne complexes should be comparable, then, is not surprising. In this section, the familiar relationship between metal-carbon bond reactivity and metal electron density is examined for Ru and Os carbyne complexes. 

Mezey, P.G., Z. Zimpel, P. Warburton, P.D. Walker, D.G. Irvine, X.D. Huang, D.G. Dixon, and B.M. Greenberg. 1998. Use of quantitative shape-activity relationships to model the photoinduced toxicity of polycyclic aromatic hydrocarbons electron density shape features accurately predict toxicity. Environ. Toxicol. Chem. 17 1207-1215. 

A comparison of the rate constants for the [Cun(FLA)(IDPA)]+-cata-lyzed autoxidation of 4/-substituted derivatives of flavonol revealed a linear free energy relationship (Hammett) between the rate constants and the electronic effects of the para-substituents of the substrate (128). The logarithm of the rate constants linearly decreased with increasing Hammett o values, i.e. a higher electron density on the copper center yields a faster oxidation rate. 

For a spherically symmetric charge distribution, an exact relationship between the electrostatic potential and the electron density is the Poisson equation ... 

This equation shows the relationship between the one-electron function, yx(r r,), and the main part of the energy functional—the rest of the functional, which is the electron-electron repulsion, depends on y2(ri, r2). The last term is also a functional of the one-electron density. In the new reformulation of DFT, the methodology is... 

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