Electronic structure INDEX

The symbols X and denote the quantum mechanical coordinates of the nuclei and electrons, respectively. The index p runs over electronic structures and y over geometries. 

The conformational mobility of a chromophoric main-chain polymer is often connected to its electronic structure. Therefore, changes in the UV-visible absorption spectra and/or chiroptical properties are spectroscopically observable as thermo-, solvato-, piezo-, or electrochromisms. It is widely reported that o-conjugating polysilanes exhibit these phenomena remarkably clearly.34 However, their structural origins were controversial until recently, since limited information was available on the correlation between the conformational properties of the main chain, electronic state, and (chir)optical characteristics. In 1996, we reported that in various polysilanes in tetrahydrofuran (THF) at 30°C, the main-chain peak intensity per silicon repeat unit, e (Si repeat unit)-1 dm3 cm-1, increases exponentially as the viscosity index, a, increases.41 Although conventional viscometric measurements often requires a wide range of low-dispersity molecular-weight polymer samples, a size exclusion chromatography (SEC) machine equipped with a viscometric detector can afford... 

Z. Zhao, B. J. Braams, H. Fukuda, M. L. Overton, and J. K. Percus, The reduced density matrix method for electronic structure calculations and the role of three-index representabihty conditions. J. Chem. Phys. 120, 2095 (2004). 

As shown, for example, by calculations of the structural index A, the aromaticity of alumobenzene (112) is still lower than that in borabenzene. Calculations (MNDO) have shown the ground state of this molecule to be, in contrast to benzene, triplet (3B,). Even so, the 67r-electron structure of (112) is more stable than the 47r-electronic one. However, the difference between their energies (36.6 kcal/mol) is nearly twice as small as that for the corresponding structures of borabenzene. 

Here, the index 0 indicates that X are taken at u = 0. Although c(s) changes sign under the inversion of S, physical quantities like Tc depend only on the absolute value of C S). These are given in Table 2 for KDP and DKDP. The interaction Htl reflects the difference in the electronic structure between the donor and acceptor oxygen ions [38,39,44, 45]. 

The three curves shown in Fig. 3 are the ones calculated by using this Hamiltonian. Here, f J1 is the electronic transfer T between the fiu orbital a of the mth C60 molecule and the fiu orbital b of the nth C o molecule, where a and b denote x, y, and z f is chosen so as to reproduce the result of the electronic structure calculations. We also use spin electron in the flu orbital a of the mth C60 molecule. Furthermore, is the band energy of the flu electron of the band index a (a = 1,2, and 3) and the wavenumber k the band energies are obtained by diagonalizing the Hamiltonian H0 and we use ak(J(akli) to denote the corresponding creation (annihilation) operators. 

More recently the idea of quantitative comparison of electron structure of the molecules was revived by Carbo [28] who proposed for this purpose the similarity index rAB, expressing the desired similarity of two molecules A and B in terms of density matrices (Eq. 2)... 

The compound 3-phenyl-anhydro-5-thiolo-l,2,3,4-oxatriazolium oxide 5 (R =Ph) has been incorporated into polymer fdms where its electronic structure and density contribute equally to the measured changes in photoinduced refractive index. Its analogue, 3-phenyl-anhydro-5-hydroxy-l,2,3,4-oxatriazolium oxide 4 (R1=Ph), has been employed as a filter C1999MI6772, 2002MI2290>. 

M. Dolg and H. Stoll, Electronic structure calculations for molecules containing lanthanide atoms 60 7 Author index 731... 

It was shown that the solvent effect is generally significant and that it therefore needs to be taken into account properly. For nonpolar structures such as the bare tt backbone of TSB such an effect has been found to follow closely the refraction index of the medium though deviations may occur as a result of the nature of the excited states involved. Such deviations are more prominent when polar groups are attached to the tt backbone and become quite large for the dipolar structure of NATSB. It was shown by Frediani et al. [117] that to enhance the solvent effect it is more important to have a solvent with a high refractive index and that the static polarity of the solvent plays a minor role for the nondipolar structures which are known as the most promising ones. Another source of solvent dependence can also be found in how the electronic structure of the... 

Photochromism is a reversible phototransformation of a chemical species between two forms having different absorption spectra [17-20], Photochromic compounds reversibly change not only the absorption spectra but also their geometric and electronic structures. The geometric and electronic structural changes induce some changes in physical properties, such as fluorescence, refractive index, polarizability and electric conductivity. When the photochromic compounds are used as spin couplers , the magnetic interaction can be controlled by photoirradiation. 

The density functional theory of Hohenberg, Kohn and Sham [173,205] has become the standard formalism for first-principles calculations of the electronic structure of extended systems. Kohn and Sham postulate a model state described by a singledeterminant wave function whose electronic density function is identical to the ground-state density of an interacting /V-clcctron system. DFT theory is based on Hohenberg-Kohn theorems, which show that the external potential function v(r) of an //-electron system is determined by its ground-state electron density. The theory can be extended to nonzero temperatures by considering a statistical electron density defined by Fermi-Dirac occupation numbers [241], The theory is also easily extended to the spin-indexed density characteristic of UHF theory and of the two-fluid model of spin-polarized metals [414],... 

Cyclic systems with 4m + 2 carbon atoms are characterized by the aromatic index m. At the lowest level (m = 0) ethylene formally corresponds to a 2-membered ring. The electronic structure shown in Figure 6.1 is consistent with aromatic electron distribution. Benzene (m = 1) is the prototype of properly cyclic aromatics. The molecular o-a-m conserves the sum of atomic angular momenta. The odd couples with the screening function are delocalized around the ring, with zero o-a-m. 

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