Simple electronic structure

The other approach, which is somewhat more general, is to perform a simple electronic structure calculation to determine the degree of delocalization within the tt-system. This approach is used in the MM2 and MM3 force fields, often denoted MMP2 and MMP3. The electronic structure calculation is of the Pariser-Pople-Parr (PPP)... 

Clear and simple electronic structure which can be well described by the... 

Finally, Yb111 possesses a single emission line in the range 0.98-1.03 pm, owing to its extremely simple electronic structure with one unpaired electron. Typical spectra of these three NIR-emitting ions are presented in fig. 4. 

Metal atoms with a simple electronic structure show very different effects when we compare vapor-phase dimers and crystals. The differences are large and of opposite sign in the case of alkali metals and alkaline earth metals. The dimers of alkaline metal atoms in the gas phase, Li2, Naj etc., are characterized by a weak covalent... 

To give more breadth to our discussion of the connections between molecules and solids we now consider examples of systems in which one can see transition-metal complexes. They are of pedagogical interest because their simple electronic structures can be used to good effect in elementary treatments of the electronic structure of coordination compounds. 

In the sections below we will describe in detail the known photochemistry of di-, tri-, and tetranuclear metal clusters. Results will be discussed in simple electronic structural terms. 

Problem 1.1 Which of the following would you expect to be ionic, and which non-ionic Give a simple electronic structure for each, showing only valence shell electrons. 

Problem 1.2 Give a likely simple electronic structure for each of the following, assuming them to be completely covalent. Assume that every atom (except hydrogen, of course) has a complete octet, and that two atoms may share more than one pair of electrons. 

For transformation to framework structures, information about the type and character of the ordering is important, since it affects the energy barriers associated with the transition. Solid nitrogen is an important system for such studies because of the stability and simple electronic structure of the isolated molecule. Moreover, solid nitrogen has been well extensively studied theoretically, and accurate experimental data provide an important test of condensed matter theory [4-8]. 

For complexes with relatively simple electronic structures (e.g. d1 and d9 species), DFT Xa methods have demonstrated useful accuracy for both d-d and CT features, especially when Slater s transition state formalism [15] is used. The d-d and CT transition energies of chlorocuprates (II) have been well studied [113-115] and the observed transition energies can be reproduced to about 1000 cm "1 or better. MSXa calculations [114] also predict relative intensities in reasonable agreement with experiment. 

It is relevant to the issue of understanding the simple electronic structures of DESs to note that the variationally optimized orbital wavefunction of Ref. [36] gave the position of the 2s2p P° state at 61.3 eV above the ground state, in satisfactory agreement with the accurate value of 61.1 eV that was to come in the 1960s from calculations that accounted for electron correlation [3]. 

Since hardness measures the HOMO-LUMO gap in Huckel or in Hartrec-Fock theories [37] it is natural to look for ways to incorporate the hardness in simple electronic structure theories. Thus, the new ideas of bond electronegativity and bond hardness have been introduced and a semiempirical density functional theory of molecular electronic structure and chemical binding outlined [39], To illustrate the energy expressions in PPP theories including electron repulsion terms are given by [40]... 

Often, the scalings needed to finitize the P — oo and P —> 1 limits have been considered independently of one another. For example, for simple electronic structure problems, the above aims can be (and usually have been) met by means of the scalings... 

The simple electronic structure of sodium also renders the application of other types of models relatively easy and extendable to relatively large sizes. See e.g. Hiickel calculations and MC structural search (R. Poteau and F. Spiegelmann, Phys. Rev. B 45, 1878 (1992) and J. Chem. Phys. 98, 6540 (1993) Erratum 99, 10089 (1993)) or the so-called spherically averaged pseudopotential (SAPS) model (M. D. Glossman, J. A. Alonso and M. P. Iniguez, Phys. Rev. B 47, 4747 (1993)). This is a simplified atomistic scheme, in which the external potential (written as the sum of the atomic pseudopotentials) acting on the electrons is developed in spherical harmonics around the cluster center of mass, and only the spherical component is retained in the solution of the KS equations. 

Owing to their relatively simple electronic structure, the alkali trimers can be regarded as such model systems, to study, for example the principles of intramolecular vibrational redistribution (IVR) in photoexcited molecules or clusters. Among the alkali trimers Naa, especially when excited to its electronic B state, seems to be the best known. It acts in this section as a prototype for exploration of details of photoinduced IVR processes in real-time. Figure 3.35 sketches the principle of the experimental approach for triatomic s systems such as the Jahn-Teller distorted Naa B system. Compared to the investigations on the dimer systems, the only difference is that the energy surfaces involved get a dittle more complicated. 

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