Contributions to AEs

In the calculations presented so far, all electrons have been correlated. However, chemical reactions involve mainly the valence electrons, leaving the core electrons nearly unaffected. It is therefore tempting to correlate only the valence electrons and to let the core orbitals remain doubly occupied. In this way, we avoid the calculation of the nearly constant core-correlation energy, concentrating on the valence correlation energy. The freezing of the core electrons simplifies the calculations as there are fewer electrons to correlate and since it enables us to use the cc-pVXZ basis sets rather than the larger cc-pCVXZ sets. 

Nevertheless, core-correlation contributions to AEs are often sizeable, with contributions of about 10 kJ/mol for some of the molecules considered here (CH4, C2H2, and C2H4). For an accuracy of 10 kJ/mol or better, it is therefore necessary to make an estimate of core correlation [9, 56]. It is, however, not necessary to calculate the core correlation at the same level of theory as the valence correlation energy. We may, for example, estimate the core-correlation energy by extrapolating the difference between all-electron and valence-electron CCSD(T) calculations in the cc-pCVDZ and cc-pCVTZ basis sets. The core-correlation energies obtained in this way reproduce the CCSD(T)/cc-pCV(Q5)Z core-correlation contributions to the AEs well, with mean absolute and maximum deviations of only 0.4 kJ/mol and 1.4 kJ/mol, respectively. By contrast, the calculation of the valence contribution to the AEs by cc-pCV(DT)Z extrapolation leads to errors as large as 30 kJ/mol. 

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Before continuing, it has to be noted that the energy difference between the secondary and primary propene insertion, AEK 0, can be considered composed by two main contributions, electronic and steric. The steric contribution to AE po, due to steric interaction between the monomer, the growing chain and the ligand skeleton, was modeled successfully through simple molecular mechanics calculations [78-80], and was reviewed recently [11,24], For this reason in the following we will focus only on the electronic contribution to AEKgio. 

Table 1.10 Harmonic and anharmonic ZPVE contributions, and first-order relativistic contributions to AEs (kJ/mol).

However, the chromophoies used in SD experiments imdergo small changes in the solute intramolecular potential. Fmthermore, since they are large polyatomics with many intramolecular vibrational modes, vibrational energy relaxation is expected to be very rapid. Thus, AE = AE. In all theories and in most simulations of SD, with a few exceptions, the intramolecular contribution to AE is neglected. 

The effect of ion concentrations appears only through the ionic conductivity a, as the parameters p and p for the ionic and dipole depolarization contributions to Ae are either 2/3 or 1 for "slip" or "stick" boundary conditions at the ion surface, and the factor (e - edipole contribution (e - e ) to the sum e of dipole and induced dipole (e ) polarizations of solvent. 

A significant stripon-svivon contribution to Ae close to EF (at energies around e p e ) is obtained with svivons around their energy minimum at ko (see Fig. 3). As was discussed above, such a contribution should be found (in most cuprates) in BZ areas around the antinodal points, as has been widely observed (see e.g. Ref. [8]). 

AEA represents the change in volume due to changes in bond lengths and angles. It is this contribution to AE that is connected to the reaction mechanism in terms of the relative positions of the atoms in reactants and the activated complex. The absolute size of A has been concluded to be approximately +10 cm mol for bond cleavage and approximately —10 cm moE for bond formation in reactions of organic molecules [430]. 

Similar considerations apply to C=0, which is a highly nonpolar molecule. The proton of HF prefers to approach the C atom rather than the O, consistent with the direction of the dipole moment of the CO molecule. The red shift of the FDF stretch is severalfold larger for OC---HF than for CO--HF the stretch of this HF bond in the former complex, although small, is consistent with a H-bond, while there is no measurable stretch in CO--HF. The energetics indicate a H-bond may indeed exist in OC---HF, with an electronic contribution to AE of some —3.6 kcal/mol, as compared to only —1.1 kcal/mol in CO—HF. 

Following similar arguments, one would expect Case II, where the decrease in energy results from a decrease in the repulsive contributions to AE, to be characteristic of processes dominated by increases in internuclear separations of bonded atoms or, equivalently, for the reverse process, an energy increase resulting from an increase in repulsive interactions because of dominant decreases in internuclear separations. Considered from the point of view of AE > 0, Case I is exemplified by barriers to internal rotation and Case II by barriers to inversion. Payne and Allen (1977) have discussed various combinations of energy components in the classification of barriers as repulsive or attractive dominant. 

Semi-quantitative molecular orbital scheme for VOX3 under C3, symmetry energy scale in electron-volts (eV). The LUMOs, at around — lO.SeV, are represented by essentially empty V(3d) levels. Main HOMOs contributing to AE are in bold. Indications underneath the energy level bars are percentages of V(3d) contributions to these levels. The nonbonding n(X) do not contribute. Redrawn from ref. 2. 

Enthalpic and entropic contributions to AE° (see Equation 2). Differences of 50 mV are considered to be significant... 

A new empirical study of the c.d. (n — tt ) of ketones shows that any strained carbon-carbon bonds of the molecular framework which are either a,/S-related to the carbonyl group or coupled to it through an extended periplanar zig-zag of bonds appear to make contributions to Ae which are larger, in the consignate... 

Table 4 Orbital eigenvalues (in a.u.) and orbital contributions to AE (in Hz) for the chiral molecule CHBrClF reduced to an atom-centred expansion.

The results of Clayfield and Lumb relate entirely to the loss of configurational entropy of the polymer chains on close approach of the particles, due either to the presence of the impenetrable surface of the opposite particle or the polymer chains that are attached to that particle. In the early papers, the effect of the solvent on the conformation of the macromolecules was ignored but an attempt was made to include the role of solvency in some of the later publications. Notwithstanding this, essentially what Clayfield and Lumb calculated was the elastic contribution to Ae repulsive free energy of interaction between sterically stabilized particles. As such, their results are manifestly unable to explain the observed flocculation of sterically stabilized particles that is induced by decreasing the solvency of the dispersion medium. Even if only for this reason, the assertion by Osmond et al. (1975) that the Clayfield and Lumb theory was the best available at that time is clearly untenable. 

One can classify the contributions to AE according to the order in which they depend on the coefficients k> 1) of weakly occupied natural orbitals of the jR-th pair. Most contributions are of fourth (or higher) order in the dk and also of second (or higher) order in the overlap integrals Sff of weakly occupied natural orbitals of different pairs, and are therefore neg%ible. 

The chiroptical behaviour of cisoid conjugated dienes, already known to be controlled by a combination of diene helicity and axial chirality effects, is further influenced by methyl substituents on the unsaturated carbon atoms. The observed methyl group contributions are not susceptible to a simple interpretation, for in some cases [e.g. at C-2 or C-3 in a 2,4-diene (24), or at C-3 in a 19-nor-l,3-diene (25)] the signs of methyl group contributions to Ae and to the rotatory strength (R) are opposite. Computer resolution showed that the c.d. and u.v. absorption curves are of composite form, with up to five vibronic components. Moreover the wavelength shifts accompanying methyl substitution do not accurately follow the Fieser-Woodward rules. It is concluded that... 

Two factors contribute to AE band broadening. The first is due to the motion of M atoms in the plasma, a so-called Doppler effect and the second is broadening due to collisions. Doppler broadening, symbolized by AXj), depends on the wavelength chosen, the kinetic temperature and the molecular weight of the metal of interest and can be predicted as follows (109) ... 

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