Delocalization energies calculation

C2 mixed in than the p orbitals of Cl and C3 —in fact, just the right amount to have C2 neutral and Cl and C3 each with V2 when this MO is filled with two paired electrons. The delocalization energy calculated for the cation is (2a + l.Zlji) — (la + 2/3) = 0.82/3 or about 16 kcal if /3 is taken to be 19 kcal. Thus in every respect the simple VB and MO methods give the same representation of the 2-propenyl carbocation. 

For discussion of the pitfalls of using 7r-electron density and/or delocalization energy calculations for predictive purposes in pyridines and indoles, see J. Ridd, Phys. Methods Heterocyclic Chem. 1, 109 (1963) see also Abramovitch and Saha (ref. 52) p. 230. 

Delocalization energy calculated by the omega method (M. Hida, unpublished data). 

A modification of the method for calculation of the energy of the hypothetical localized molecules results in a better correlation between the delocalization energy calculated by HMO theory and experimentally observed stability. A series of... 

Empirical resonance Vertical resonance Delocalization energies ] Calculated resonance energies ... 

Calculate the delocalization energies of the positive ion, free radical, and negative ion of the allvl model. 

Spectroscopically determined values of P vai y, but they aie usually around —2.4 eV. In the section on resonance stabilization, we saw that thermodynamic measurements of the total resonance stabilization of butadiene yield 11 and 29 kJ mol according to the reference standard chosen. Calculate the delocalization energy of buta-1,3-diene in units of p. Determine two values for the size of the energy unit p from the thermochemical estimates given. Do these agree well or poorly with the spectroscopic values ... 

Interatomic distances calculated from the detailed analysis of rotational fine structure of the UV spectrum of pyrazine are in close agreement with those observed in (7) and (8), with the calculated bond lengths for C—C of 1.395, C—N 1.341 and C—H 1.085 A (60DIS(20)4291). Thermochemical data have provided a figure of 75 kJ moP for the delocalization energy of the pyrazine ring (B-67MI21400). 

Repeat your analysis fox phenoxy radical. Instead of charge, focus on the spin density. Calculate the delocalization energy using phenoxy radical at phenol geometry. Is it of the same order of magnitude as that for phenoxy anion Explain. 

Two independent molecular orbital calculations (HMO method) of delocalization energies for isoindole and isoindolenine tautomers agree that the isoindole form should possess the more resonance stabilization. The actual difference calculated for isoindole-isoindolenine is about 8 kcal/mole, but increases in favor of the isoindole with phenyl substitution at position 1 (Table VI).Since isoindole and isoindolenine tautomers have roughly comparable thermodynamic stabilities, the tautomeric proce.ss is readily obser-... 

The di-n-propyl cyclopropenyl cation failed to photolyze either in aqueous acid or organic solvents, with or without sensitizers. A possible explanation in the discrepancy between the triphenyl system and this one lies in the calculated energy differences between the cations and their corresponding radicals. In the triphenyl system this energy difference is 0-5 3 or 16 kcal/mol, while in the di-n-propyl case it is 1 00)3 or 32 kcal/ mol, based on calculated delocalization energies for the two species. 

The rates of radical-forming thermal decomposition of four families of free radical initiators can be predicted from a sum of transition state and reactant state effects. The four families of initiators are trarw-symmetric bisalkyl diazenes,trans-phenyl, alkyl diazenes, peresters and hydrocarbons (carbon-carbon bond homolysis). Transition state effects are calculated by the HMD pi- delocalization energies of the alkyl radicals formed in the reactions. Reactant state effects are estimated from standard steric parameters. For each family of initiators, linear energy relationships have been created for calculating the rates at which members of the family decompose at given temperatures. These numerical relationships should be useful for predicting rates of decomposition for potential new initiators for the free radical polymerization of vinyl monomers under extraordinary conditions. 

The most important results of the linear free energy equations in this study (Table IV) are the applications to which they can be used. For a new free radical initiator, belonging to any of the four radical forming reactions of this study, equation 6 should be useful to predict the rate of decomposition with reasonable accuracy. All that is needed is an HMD calculation to obtain the pi-delocalization energy for the radical formed in the reaction (R ) and an estimate of the steric A values for groups bonded to the central carbon of R. ... 

Ring strain energies30) and aromatic delocalization energies must also be parameterized and calculated. This is handled automatically in EROS and makes use of the ring perception routine mentioned earlier15). 

This conclusion, nevertheless, should not be considered categorical but it points to the necessity of careful consideration of the correlation between the AEdis value and the part of it that relates to cyclic electron delocalization. It has been shown by use of TRE calculations of aromatic benzene and antiaromatic cyclobutadiene molecules that in the case of benzene the distortion into a Kekule-type structure is characterized by a change of the aromatic cyclic Tr-electron delocalization energy in an opposite direction... 

The lability of thieno[3,4-6]thiophene (3) and other iso-annelated systems, such as benzo[c]thiophene and benzole] furan, may be due to the strain effect (Mills-Nixon effect see also Zwanenburg et alP and references therein) in the condensed five-membered ring. The stability of the iso-annelated dithienothiophenes 7—9 is noteworthy. Simple LCAO MO method calculations on benzo[c]thiophene indicate that its instability is due to low specific delocalization energy and high free valence index at position 1. 

Triazine has not yet been prepared, and until fairly recently there were no well-documented examples of monocyclic 1,2,3-triazine derivatives. Early estimates of the potential degree of stability of 1,2,3-triazine were made on the basis of the theoretical resonance energy the results obtained indicated a delocalization energy of about 25 kcal/mole, which implies that the ring system should be reasonably stable and certainly amenable to synthesis. Many other related molecular orbital (MO) calculations have been carried out on similar systems more recently. 

Localized MP2 (LMP2) models have already been shown to provide results which are nearly indistinguishable from MP2 models for both thermochemical calculations (see Chapter 12) and for calculation of conformational energy differences (see Chapter 14). Activation energy calculations provide an even more stringent test. Transition states necessarily involve delocalized bonding, which may in turn be problematic for localization procedures. 

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