Localized electron populations

Figure 8.18 The localized electron populations of the t2g and Eg states for two Ni d ions in NiO. The average configuration is d but transport of electrons through the material would produce d and d centers.

In the LDM, the sum of the matrix elements in any row or corresponding column equals the atomic population N(fli) (by the first equality of Eq. 3.5) and hence the sum of the column sums or row sums equals the total molecular electron population. The trace of the LDM is the localized electron population (Moc) of the molecule (Eq. 3.8), and the delocalized electron population can be obtained by difference (Eq. 3.9). 

Natural population analysis is carried out in terms of localized electron-pair bonding units. Here are the charges computed by natural population analysis (the essential output is extracted) ... 

As in the case of iron chemistry, most valuable information concerning bond properties (anisotropic electron population of molecular orbitals) and local structure may be extracted from quadrupole-split Ru spectra. This has been... 

Fig. 7.2 indicates the electron distribution of HO of carbon monoxide which largely localizes at the carbon atom 79>. This orbital resembles a lone-pair AO on the carbon atom and leads to the expectation that the carbon atom would behave as the electron-donating centre. As a matter of fact, the CO molecule coordinates with a metal cation by M—C—O type linkage (M represents a metal cation) in various metal carbonyl compounds. It is of interest to remark that the total electron population of the CO molecule has been shown by recent reliable calculation 80> to be rich on the oxygen atom in place of the carbon atom. 

As an example. Fig. 18 shows the diabatic electronic population probability for Model I. The quantum-mechanical results (thick line) are reproduced well by the QCL calculations, which have assumed a localization time of to = 20 fs. The results obtained for the standard QCL (thin full line) and the energy-conserving QCL (dotted line) are of similar quality, thus indicating that the phase-space distribution p]](x, p) at to = 20 fs is similar for the two schemes. Also shown in Fig. 18 are the results obtained for a standard surface-hopping calculation (dashed line), which largely fail to match the beating of the quantum reference. 

Figure 2b depicts a strong acceptor bond for a Na atom. It is formed from the weak bond depicted in Fig. 2a, for example, as a result of the capture and localization of a free electron, that is, as a result of the transformation of a Na+ ion of the lattice serving as an adsorption center, into a neutral Na atom. We obtain a bond of the same type as in the molecules H2 or Na2. This is a typically homopolar two-electron bond formed by a valence electron of the adsorbed Na atom and an electron of the crystal lattice borrowed from the free electron population. The quantum-mechanical treatment of the problem 2, 8) shows that these two electrons are bound by exchange forces which in the given case are the forces keeping the adsorbed Na atom at the surface and at the same time holding the free electron of the lattice near the adsorbed atom. 

Hence the approach privileged here, based on Eq. (4.47), that uses the variations of effective nuclear-electronic potential energies Ay g dictated by local atomic electron populations. Regarding the latter, they are deduced along classical lines, rooted in molecular wavefunctions that determine the electron density at any given point in space. 

There is one particular n that merits special attention. It reflects simple customary ideas The electron-attracting power of otherwise similar atoms decreases as their electron populations increase, thus opposing charge separation. This concept views local charge variations as events occurring most reluctantly, suggesting that the carbon atoms found in alkanes should be very similar to one another, conceivably differing as little as possible from one another. 

The regioselectivity associated with the nitration of the 7-bromo-l,5-benzodiazepinone 9, which occurred at C-8 and C-9, was examined by considering the relative atomic charge densities, total pz electron population, and the electron population density of the highest occupied molecular orbital (HOMO) at each site. The it-localization energy of the two C-8 and C-9 nitration transition state cr-complexes was better able to predict the observed ratio of products, which favors nitration at C-9 by 3 1 <2003M1629, 2004HAC263>. 

Since electron population is a pure number and global softness has the units of reciprocal energy, local softness logically has these units too, but the practice is to simply state that all these terms are in atomic units . 

These local mapping transformations, relating AIM electron populations (charges) to bond lengths, can be easily generalized into relations involving collective electron-population- and/or nuclear-position-displacements, e.g., PNM and nuclear normal modes. For example, the bond-stretching normal vibrations, 2b, defined by the fb principal directions, O = d lb/8Rb,... 

In the multipole refinement of TPPFe(THF)2, a D4h local symmetry was imposed on the iron atom which explains that only four dt population parameters were derived inspection of Table 4 leads to the same conclusion derived qualitatively from the examination of the deformation maps i.e., the 5 2g state is the main contributor to the ground state of the complex. This interesting calculation of d electron population calculations was also performed on other coordination compounds like metal carbonyls [38] and metal carbynes [39]. 

Since about 10 years ago (thermal) helium beams have been used for the diagnostics of fusion boundary plasmas as they can penetrate relatively far because of the high ionization potential of the atoms (nearly 25eV) [61,62]. From the line ratios of the triplet and singlet lines one can derive local electron temperatures and densities (Fig. 6.18) provided the population rates and their equipartition times are known and allow the application of a steady state model [63], The corresponding rates have been improved during the last few years, and although it is now a well-established technique, there are still open questions and scope for future developments. 

Y3+ or La3+ cations. Consequently, the additional electron populates an antibonding Trg orbital thereby reducing the bond order and increasing the C-C distance. Reality is a little more complicated since there are low-lying d orbitals on these metals. Consequently a metallic d band overlaps with the C2 TTg band as shown below. For this reason, the electron is partly localized in the metal d band and partly localized in the C2 band. Nevertheless the C-C distance in these materials is chiefly governed by the electron count of the metal. 

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