Structure linear correlations

The indazole molecular structure (Figure 11) shows the tautomeric proton bonded to N-1 (1//-indazole. Section 4.04.1.5.1). A linear correlation between the bond lengths and the bond orders calculated by the CNDO/2 method was observed (74T2903). 

The most common manifestation of extrathermodynamic relationships is a linear correlation between the logarithms of rate or equilibrium constants for one reaction series and the logarithms of rate or equilibrium constants of a second reaction series, both sets being subjected to the same variation, usually of structure. For illustration, suppose the logarithm of the rate constants for a reaction series B is linearly correlated with the logarithm of the equilibrium constants for a reaction series A, with substituent changes being made in both series. The empirical correlation is... 

The Group IV elements also show a linear correlation of their octahedral shear moduli, C44(lll) with chemical hardness density (Eg/2Vm).This modulus is for for shear strains on the (111) planes. It is a measure of the shear stiffnesses of the covalent bonds. The (111) planes lie normal to the bonds that connect the atoms in the diamond (or zinc blende) structure. In terms of the three standard moduli for cubic symmetry (Cn, Q2, and C44), the octahedral shear modulus is given by C44(lll) = 3CV1 + [4C44/(Cn - Ci2)]. Since the (111) planes have three-fold symmetry, they have only one shear modulus. The bonds across the octahedral planes have high resistance to shear which probably results from electron correlation in the bonds (Gilman, 2002). 

The analysis of the magnetic and structural data reported by Ryabova revealed a linear correlation between the Fe-S bond distance and the effective magnetic moment [106]. 

Bartlett has derived a method181 for proving that a putative transition state analog exerts its inhibitory power from successfully mimicking the transition state. If a series of structurally-related inhibitors (all containing the identical core chemical structure meant to simulate the transition state) bind to the target enzyme with log (fQ) values that linearly correlate (slope = 1) with the log (KMlkcai) values of the same series of structurally-related substrates, then... 

This section considers recent attempts to extrapolate from observed structures to the experimentally unattainable transition state structures for bond making and breaking reactions. (Transition state structures for conformational changes are experimentally observable in the crystal in favourable cases, as described in Section 3, pages 135-136.) The approach builds on the regular correlations between structure and reactivity, particularly the linear correlations with bond length described in the previous section. 

Since the rate constants of bimolecular diffusion-limited reactions in isotropic solution are proportional to T/ these data testify to the fact that the kt values are linearly dependent on the diffusion coefficient D in water, irrespective of whether the fluorophores are present on the surface of the macromolecule (human serum albumin, cobra neurotoxins, proteins A and B of the neurotoxic complex of venom) or are localized within the protein matrix (ribonuclease C2, azurin, L-asparaginase).1 36 1 The linear dependence of the functions l/Q and l/xF on x/t] indicates that the mobility of protein structures is correlated with the motions of solvent molecules, and this correlation results in similar mechanisms of quenching for both surface and interior sites of the macromolecule. 

Linear anodic potential sweep, 30 256-257 Linear correlations, structure effects, 29 160-161... 

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