Calculated relative energies

Calculated relative energy of explosive released on detonation and subsequent expansion of detonation gases relative to HMX. 

In order to calculate total energies with a chemical accuracy of 1 kcal/mol, it is necessary to use sophisticated methods for including electron correlation and large basis sets, which is only computationally feasible for small systems. Instead the focus is usually on calculating relative energies, trying to make the errors as constant as possible. 

All structures Number of imaginary frequencies = 1. For ab initio calculations Relative energies are ZPE-corrected (scaUiig factor, 0.89). 

The calculated relative energies of all the possible intermediates involved in the photochemical isomerization are collected in Fig. 4 (OOOJOC2494). In this case the irradiation can involve the excited singlet state, and then the formation of Dewar isomer is possible. As in 2-methylfuran, the fission of a O—Cq, bond in the triplet state of the molecule is not so favored as in furan. The corresponding biradicals... 

Calculated Relative Energies oe Isomeric Dihydro-1,2,4-triazines Compared TO 2,5-Dihydro-1,2,4-triazine 98... 

The calculated relative energies of the most important MO s are given in Fig. 9, together with the excitation energies, derived from the optical absorption spectrum. 

Fig. 9. Calculated relative energies (in kK) of the most important MO s (a) and spectral excitation energies derived from the electronic absorption spectrum (b) of ClFe(Et2

Calculated Relative Energies (kcal moP1) for R2MOfl... 

B3PW91 /TZV Calculated Relative Energies (kcalmol 1 with zpe Correction) for 1Fe(CO)3(C2H4)+CO and 1Fe(CO)3(C2H4)+C2H4 Reactions... 

TABLE 7. Calculated relative energies at the Cl level (in kcalmol )21S (ATM = absolute true minima, TM = true minima, SP = saddle point, CP2 = critical point of index 2)... 

Figure 10. Calculated relative energies (in kcal/mol) of cydoheptatrienylidene spin states (4a), relative to cycloheptatetraene (3a).55-57...

Recent ab initio calculations have shown, in agreement with the conclusions reached by OEMO theory, that the most stable conformation of methyl vinyl ether is the Cs conformer176). The calculated relative energies of the four conformations of methyl vinyl ether at the STO-3G and 4-31G levels are shown above along with the appropriate indices of nonbonded attraction. As can be seen, the greater stability of the Cs conformation can be attributed to an attractive 1,5 pi nonbonded interaction. 

Table 44. Calculated relative energies of conformers of HO2F and F2O2...

Scheme 6.102 Calculated relative energies of 1,2,4,6-cycloheptatetraene (5), the closed-shell 2,4,6-cycloheptatrienylidene (5-Z,) and the open-shell 5-D.

Scheme 9.10 Calculated relative energies for minimized structures of allenyl- and propargylmagnesium hydride and the related hydroxy analogues.

Table 7.5 Calculated relative energies Erei and and BDEs De (Do) (kcal/mol) with respect to singlet Fe(CO)4 and L (L = CS, N2, NO+, CN, NC, t 2-C2H4,7/2-C2H2, CCH2) CH CF2, PH3) PF3j NH3) NF3) and j 2-H2). ...

Tab. 16.1 Calculated relative energies of transition states and products for the cyclization of 10.

Ab /wt/o-Calculated Relative Energies (in kcal/mol) of (CHNH)2 Isomers... 

Calculated relative energies for a small selection of structural isomers are compared with experimental values and with the results of G3 calculations in Table 6-11. These have been drawn from a much more extensive set of comparisons found in Appendix A6 (Tables A6-24 to A6-31). Mean absolute errors from the full set of comparisons are collected in Table 6-12, and a series of graphical comparisons involving Hartree-Fock, EDF1, B3LYP and MP2 models... 

Fig. 1.3.6 Structure of the allyl aminosulfoxonium ylide 30 according to ab-initio calculations. Rel. energy 0.0 kcal mob Ca—S 163 pm, a ZCa 356 °.

Schleyer and coworkers40 studied in detail the energetic relationships between silabenzene 8 and four of its isomers, 13-16. However, as this study is quite old, the calculated relative energies of 8 and 13-16, which have been calculated only at HF/3-21G( )//HF/STO-3G, are probably only approximate and higher level calculations are required for a more reliable estimate of these relative energies. 

Houck and coworkers postulate that the origin of the regioselectivity is at the biradicalforming step and directly affected by the polarity of the alkene. The /J-carbon, considered as nucleophilic, adds rapidly to the less substituted side of the electron-deficient alkene, whereas a position considered as an a-acyl radical (more electrophilic than an alkyl radical) adds rapidly to the less substituted side of electron-rich alkenes. The calculated relative energies for the addition of jtjt triplet acrolein to different substituted alkenes at the first bond-forming step (Table 3) are found to be in good agreement with experimental values determined in the photoaddition of cyclohexenone to the related alkene. 

Actually, nonbonding interactions are already included in the torsional term (as gauche-butane interactions) we might have used an ethane-type torsional function and accounted for CH3/CH3 interactions entirely with nonbonded terms. However, in comparing calculated relative energies the torsional term will cancel out. 

As has been pointed out, the ZPE-corrected ab initio energy is preferred over the uncorrected for calculating relative energies. At the end of a calculation lolal (HF or correlated) is given if we wish to include ZPE and get a frequency calculation is necessary. The format in which these quantities appear at the end of a calculation depends on the program. 

Figure 2 Calculated relative energies in kcal mol 1 of HCS2N3 isomers by the MPW1 PW91/cc-pVTZ method.

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