Total energy difference

Table 13-6. Computed total energy differences [kcal/mol] and distances [A] for the proton transfer in malonaldehyde enol (6-311++G(d,p) basis). 

Gunnarsson, O., Jones, R. O., 1985, Total Energy Differences Sources of Error in Local-Density Approximations , Phys. Rev. B, 31, 7588. 

Table III summarizes the reported relative energies appropriate to the BC, Si—AB, and B—AB sites for the H—B pair in silicon. In many calculations, the B—AB site has been predicted from calculations to be not only higher in energy than the BC site but also to be a saddle point for reorientation between equivalent BC sites. Some calculations predict that the Si—AB site may be metastable, consistent with evidence from channeling and PAC studies. The computed total-energy differences, however, between the stable (BC) and metastable (Si—AB) configurations might be too large to explain the simultaneous observation of both species at the reported temperatures.

The second theoretical approach uses an ab initio or tight-binding approach to the description of electronic structure. Determination of the interlayer magnetic coupling can be achieved by calculating the total energy difference, A = — ap,... 

Figure 4- Left Density of states (DOS) of cage-like and amorphous structures of Au clusters with 18 and 20 atoms, calculated at the LDA and GGA levels of theory. Right Total energy difference between cage-like and compact equilibrium structures of cationic, neutral, and anionic clusters with 18 (starts), 20 (crosses), and 32 (circles) atoms.

Figure 6. Second total energy difference (upper panel) and HOMO-LUMO gap (lower panel) for the lowest energy equilibrium structures of AunTM+ clusters...

The differences in aromaticity follow the results of theoretical analyses on the acidity of the NH proton of the pyrrole fragment of furo[ ]pyrroles <2000PJC207> and are nicely reflected in the observed stability of both systems. The total energy difference between methyl 4f/-furo[3,2- ]pyrrole-5-carboxylate 8a and methyl 6f/-furo[2,3- ]pyr-role-5-carboxylate 31a is rather small (—7.2 kj mol ) indicating the higher stability of the former system. However, if the increase of energy of the appropriate anions is compared (relative to the parent molecules), then it indicates that formation of 67/-furo[2,3-7]pyrrole-5-carboxylate anion is much easier (by —22.5 kJ mol ) than formation of 4//-furo[3,2- ]pyrrole-5-carboxylate anion. 

The corresponding procedure is carried out in the case of hole transfer, now with use of the ionization energies of the symmetric and antisymmeric linear combination of HOMO S. From eq.(29) follows that the total energy difference at the avoided crossing, equal to the electronic factor, can be obtained as an orbital energy difference between two MO s which are sum and difference of the electron exchanging donor and acceptor MO s < >d and < >a, respectively. 

Such tautomeric equilibria, which may be crucial for the understanding and appropriate description of phase equilibria, can technically be treated in the same way as conformational equilibria in COSMO-RS. Unfortunately, we must be aware that the total energy differences between the tautomers may be in error by 8 kJ/mol or even more, if we calculate them on our default DFT/COSMO level. To gain an accurate description of such phenomena, it is therefore necessary to correct the COSMO energy differences either by comparison with higher level QM calculations, or by treating them as adjustable parameters. 

Table 5 Stokes shift, i.e. difference between absorption and emission energy gaps calculated as total energy differences within the A-SCF approach. All values are in eV...

This quantum chemical calculation was made at the respectable DZP level, where the authors made the generally reasonable assumption that zero-point energy and 0-298 kJ corrections largely cancel in the ca 22 kJ mol -1 total energy difference of vinylamine and its more stable, but likewise unisolated, acetalimine isomer. 

The EHT total energy differs from the Hartree-Fock total energy EHF by the neglect of the nuclear-nuclear repulsion energy ENN and by the overcounting of electron-electron repulsion and exchange. The energy difference is... 

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