Electron molecules

Truhlar D G (ed) 1984 Resonances in Electron-Molecule Scattering, van der Waals Complexes, and Reactive Chemical Dynamics (ACS Symp. Ser. 263) (Washington, DC American Chemical Society)... 

Flail R I and Read F FI 1984 Electron-Molecule Collisions ed I Shimamura and K Takayanagi (New York Plenum)... 

The close-coupling equations are also applicable to electron-molecule collision but severe computational difficulties arise due to the large number of rotational and vibrational channels that must be retained in the expansion for the system wavefiinction. In the fixed nuclei approximation, the Bom-Oppenlieimer separation of electronic and nuclear motion pennits electronic motion and scattering amplitudes f, (R) to be detemiined at fixed intemuclear separations R. Then in the adiabatic nuclear approximation the scattering amplitude for ... 

Let us consider a model of the vertical (i.e. at fixed molecular geometry) detachment or attaclunent of an electron to an A-electron molecule. 

Christophorou L G (ed) 9Q4 Electron-Molecule Interactions and Their Applications (Or ando, FL Academic)... 

The symmetry argument actually goes beyond the above deterniination of the symmetries of Jahn-Teller active modes, the coefficients of the matrix element expansions in different coordinates are also symmetry determined. Consider, for simplicity, an electronic state of symmetiy in an even-electron molecule with a single threefold axis of symmetry, and choose a representation in which two complex electronic components, e ) = 1/v ( ca) i cb)), and two degenerate complex nuclear coordinate combinations Q = re " each have character T under the C3 operation, where x — The bras e have character x. Since the Hamiltonian operator is totally symmetric, the diagonal matrix elements e H e ) are totally symmetric, while the characters of the off-diagonal elements ezf H e ) are x. Since x = 1, it follows that an expansion of the complex Hamiltonian matrix to quadratic terms in Q. takes the form... 

The concept of biradicals and biradicaloids was often used in attempts to account for the mechanism of photochemical reactions [2,20,129-131]. A biradical (or diradical) may be defined as [132] an even-electron molecule that has one bond less than the number permitted by the standard rules of valence. 

Unlike nitrogen monoxide, nitrogen dioxide has properties more typical of an odd electron molecule. It is a coloured (brown), reactive gas which dimerises to the diamagnetic colourless gas dinitrogen tetroxide, N2O4. in which the odd electron is paired. The structure of dinitrogen tetroxide can be represented as a resonance hybrid of ... 

By extension of Exercise 6-1, the Hamiltonian for a many-electron molecule has a sum of kinetic energy operators — V, one for each electron. Also, each electron moves in the potential field of the nuclei and all other electrons, each contiibuting a potential energy V,... 

Thus two electrons exit the reaction zone, leaving a positively charged species (M ) called an ion (in this case, a molecular ion). Strictly, M" is a radical-cation. This electron/molecule interaction (or collision) was once called electron impact (also El), although no impact actually occurs. 

Weak interactions may occur between molecules (intermolecular association) as well as within a molecule (intramolecular) for chalcogen-nitrogen ring systems. This behaviour is especially significant for odd electron species, e.g., [EsNa]" (4.14, E = S, Se) and [PhCNaEa] (4.15, E = S, Se), both of which are seven r-electron molecules. As mentioned in the previous section, it also occurs for the eight r-electron dithiatriazines 4.10... 

Nitric oxide is the simplest thermally stable odd-electron molecule known and, accordingly, its electronic structure and reaction chemistry have been very extensively studied. The compound is an intermediate in the production of nitric acid and is prepared industrially by the catalytic oxidation of ammonia (p. 466). On the laboratory scale it can be synthesized from aqueous solution by the mild reduction of acidified nitrites with iodide or ferrocyanide or by the disproportionation of nitrous acid in the presence of dilute sulfuric acid ... 

Molecular geometry depends not only on the constituent atoms, but also on the total number of electrons. Molecules with identical formulas but with varying numbers of electrons may prefer different geometries. 

The total electronic wavefunction is the product of a spatial part and a spin part it is it(r) times a(s) or /3(s) for this one-electron molecule. There are thus two different quantum states having the same spatial part i/r(r). In the absence of a magnetic field, these are degenerate. 

Hiickel s model was not originally presented in terms of the HF model, but I want you to think in HF-LCAO terms for the remainder of the chapter. So, imagine a simple rr-electron molecule such as ethene (Figure 7.1). 

Consider now the behaviour of the HF wave function 0 (eq. (4.18)) as the distance between the two nuclei is increased toward infinity. Since the HF wave function is an equal mixture of ionic and covalent terms, the dissociation limit is 50% H+H " and 50% H H. In the gas phase all bonds dissociate homolytically, and the ionic contribution should be 0%. The HF dissociation energy is therefore much too high. This is a general problem of RHF type wave functions, the constraint of doubly occupied MOs is inconsistent with breaking bonds to produce radicals. In order for an RHF wave function to dissociate correctly, an even-electron molecule must break into two even-electron fragments, each being in the lowest electronic state. Furthermore, the orbital symmetries must match. There are only a few covalently bonded systems which obey these requirements (the simplest example is HHe+). The wrong dissociation limit for RHF wave functions has several consequences. 

Figure 7.5 (page 177) shows the geometries predicted by the VSEPR model for molecules of the types AX2 to AX. The geometries for two and three electron pairs are those associated with species in which the central atom has less than an octet of electrons. Molecules of this type include BeF2 (in the gas state) and BF3, which have the Lewis structures shown below ... 

Hamiltonian operator, 2,4 for many-electron systems, 27 for many valence electron molecules, 8 semi-empirical parametrization of, 18-22 for Sn2 reactions, 61-62 for solution reactions, 57, 83-86 for transition states, 92 Hammond, and linear free energy relationships, 95... 

Example shows that no energy barrier exists for the combination of two NO2 molecules to form N2 O4. The activation energy for this reaction is zero because NO2 is an odd-electron molecule with a lone electron readily... 

Table 12.1. Electron-molecule reactions and parameters of their rate constants...

The case of interaction between an even-electron molecule A and an odd-electron molecule B can be discussed in a similar manner. Eq. (3.20) is modified to be... 

As has been mentioned in Chap. 5, the singly occupied MO in odd-electron molecules and radicals plays the role of HO or LU or both MO s according to the orbital energy relationship and the orbital overlapping situation. The importance of SO distribution is easily understood... 

Experiments designed to probe these ideas have been carried out for NO colliding in high vibrational states on Au(lll). Before considering the results of these experiment, let us first look at how vibration might lead to unusual interactions with metal electrons. Molecules in vibrational states as high as NO(r = 15) undergo nuclear excursions that influence their... 

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