Diatomic molecules charge distribution

As mentioned above and discussed in Chapter 2, atomic charges were often obtained in the past from dipole moments of diatomic molecules, assuming that the measured dipole moment equal to the bond length times the atomic charge. This method assumes that the molecular electron density is composed of spherically symmetric electron density distributions, each centered on its own nucleus. That is, the dipole moment is assumed to be due only to the charge transfer moment Mct. and the atomic dipoles Malom are ignored. 

For hetercnuclear diatomic molecules, the atomic energy-level mismatch does not vanish, so that <5 0. Hence, the electronic charge distribution... 

Fig. 5.41 The distribution of the electron density (charge density) p for a homonuclear diatomic molecule X2. One nucleus lies at the origin, the other along the positive z-axis (the z-axis is commonly used as the molecular axis). The xz plane represents a slice through the molecule along the z-axis. The —p = f(x, z) surface is analogous to a potential energy surface E = /(nuclear coordinates), and has minima at the nuclei (maximum value of p) and a saddle point, corresponding to a bond critical point, along the z axis (midway between the two nuclei since the molecule is homonuclear)...

The MOs in the diatomic molecules discussed above have only two coefficients, so their chemical interpretation poses few problems. The situation becomes slightly more complicated when the molecule is polyatomic or when each atom uses more than one AO. Overlap population and net atomic charges can then be used to give a rough idea of the electronic distribution in the molecule. 

Coincidence techniques have been used to study both of the singly charged positive ions resulting from dissociation in the ion source of a doubly charged ion formed by El [125], The translational energy distributions of both product ions were determined with a number of diatomic molecules. ... 

In Chapter 1 we saw that in moving from homonuclear to heteronuclear diatomics a new factor enters - the atom characters are distributed differently over the filled and unfilled MOs. As only the filled orbitals contribute to the atomic charges, the Mulliken charge distribution reflects the polarity of the molecule. Similar information for the HOMO and FUMO permitted us to discuss properties such as Lewis acidity and basicity in terms of frontier-orbital characteristics. As we were able to unravel the DOS of the metal chain in terms of AO type, we can also interrogate the DOS of a heteroatomic system for information on the distribution of atomic character over the total DOS. That is, we can reveal the contributions or character of a chosen atom to the DOS. We can begin to appreciate the power of this tool by... 

Hoffmann-Ostenhof and Morgan (1981) were able to prove that the ground-state charge distribution of a one-electron homonuclear diatomic molecule can exhibit maxima in p only at the positions of the nuclei. In this proof an important inequality is used (Hoffmann-Ostenhof and Hoffman-Ostenhof 1977),... 

Fig. 6.3. Contour maps of the ground-state electronic charge distributions for the second- and thrid-row diatomic hydrides showing the positions of the interatomic surfaces. The first set of diagrams (a) also includes a plot for the ground state of the Hj molecule. The outer density contour in these plots is 0.001 au. The remaining contours increase in valne according to the scale given in the Appendix (Table A2). (a) The left-hand side 2, LiH 2, BeH 2, BH 2 right-hand side CH n, NH 2", OH n, HF 2+. (b)The left-hand side NaH 2-, MgH 2+, AIH 2+, SiH right-hand side PH 2-, SH "H. HCI 2. ...

Properties of the charge density at the (3, — 1) critical point for a number of diatomic molecules are given in Table 7.4 and, for some polyatomic molecules, in Table 7.5. Contour and relief maps of the Laplacian distributions for some of these molecules are shown in Figs 7.15-7.17. 

Fio. E7.2. Contour maps of the charge distribution showing the position of the interatomic surfaces for ionic diatomic molecules. The outer contour is 0.002 au with succeeding values as given in the Appendix (Table A). 

The contents of Part 1 is based on such premises. Using mostly 2x2 Hiickel secular equations, Chapter 2 introduces a model of bonding in homonuclear and heteronuclear diatomics, multiple and delocalized bonds in hydrocarbons, and the stereochemistry of chemical bonds in polyatomic molecules in a word, a model of the strong first-order interactions originating in the chemical bond. Hybridization effects and their importance in determining shape and charge distribution in first-row hydrides (CH4, HF, H20 and NH3) are examined in some detail in Section 2.7. 

Studies on molecular charge distributions and chemical binding due to Bader and co-workers include the first-row homonuclear diatomics (Bader et al., 1967a), the first-row diatomic hydrides (Bader et al., 1976b), the first-row 12- and 14-electron diatomic series (Bader and Bandrauk, 1968a), the second-row diatomic hydrides (Cade et al., 1969), and the excited, ionized, and electron-attached states of several diatomic molecules (Cade et al., 1971). Bader (1970, 1975,1981), Deb (1973), and Mulli-ken and Ermler (1977) review their works in some detail. 

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