Linear bond length alternation

V-UV Application First Excited State of Linear Polyenes. The first electronic absorption band of perfect linear aromatic polyenes (CH)X, or perfect polyacetylene shifts to the red (to lower energies) as the molecule becomes longer, and the bond length alternation (BLA) would be zero. This was discussed as the free-electron molecular orbital theory (FEMO) in Section 3.3. If this particle-in-a-box analysis were correct, then as x > oo, the energy-level difference between ground and first excited state would go to zero. This does not happen, however first, because BLA V 0, next, because these linear polyenes do not remain linear, but are distorted from planarity and linearity for x > 6. 

The non linear dependence of Arp on HOMA results from the definitions of these parameters the first one is a quadratic function of the differences of bond lengths, whereas the other is a linear one. It is worth mentioning here that the main contribution to the variability of HOMA index for chelate chain comes out from the GEO term, i.e., it is due to changes in bond length alternation, whereas the contribution due to the bond elongation is chaotic and insignificant. Figure 7 presents the dependence of EN and GEO on Arp. 

In order to assess the accuracy of the dynamic SDMRG technique, we have performed a series of model calculations we computed the dynamic linear polarizabilities (0(0 )) and third-order polarizabilities (7(0 , 01,0 )) corresponding to the third harmonic generation (THG), for the Hubbard and J7—V polyene-like chains of up to 20 sites with and without dimerizations (note that the dimerization parameter S reflects the degree of carbon-carbon bond-length alternation along the polyene chain nonzero S leads to alternating t and V values while zero 5 means uniform t and V). 

Figure 4. (A) Structures of the neutral N(n) and polar P(n) (substituted by the strongest acceptor) carotenoids. Molecular geometries were optimized using AM 1 modeP in Gaussian 98 package. Calculations were done for chain lengths of n = 5. 10. 20. and 40 double bonds (B) Variation of the bond-length alternation (top) and total charge Qa (bottom) along the chain in polar P(40) molecule (C) Linear absorption spectra calculated with line width r = 0.2 eV of the N(20) (dashed lines) and P(20) (solid lines) molecules contour plots of electronic modes which domi nate the absorption spectra of N(20) and P(20). Reprinted with permission from ref 81. Copyright 1997 American Chemical Society.

Gorman, C. B., and Marder, S. R., An investigation of the interrelationships between linear and nonlinear polarizabilities and bond-length alternation in conjugated organic molecules. Pro. Natl. Acad. Sci, USA, 90, 11297-11301 (1993). 

In order to compare the energies of linear and cyclic polyenes in which the bond lengths alternate, we must study the union of methyl with an odd AH radical in which the bond lengths alternate. Consider, for example, allyl ... 

Peierls distortion [1] in one dimension (ID) is an inherent trait of linear conjugated polymers, leading to a bond length alternation (BLA). The usual chemical nomenclature for it is conjugation. Examples include polyacetylene and polyyne, two materials which have been studied by the physics and chemistry community for a very long time (see, e.g. the book [2] and the papers cited therein). For... 

Rusznyak A, Zolyomi V, Kiiiti J, Yang S, Kertesz M (2005) Bond-length alternation and charge transfer in a linear carbon cheiin encapsulated within a single-walled carbon nanotube. Phys Rev B 72(15) 155420(6)... 

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