Bond population

The ring-opening mechanism was well supported by the snapshots and the overlap bond population obtained from TB-QCMD simulations, where the formation of new C-H and La-C bonds and the dissociation of La-H and proximal C-C bonds could be tracked. The obtained dynamic ring opening mechanism was similar to the static mechanism, however, a novel transition state was also proposed for insertion reaction of alkenes, with tetrahedral h4-coordination. This example perfectly illustrates the importance of mutual interplay between high-level first principle methodologies and simplified methodologies derived from ab initio quantum chemistry, massively applicable for real systems. 

R3 R2 and R2 Ri gauche interactions however, for the same set of substituents, an increase in the steric requirements of either Rj or R3 will influence only one set of vicinal steric interactions (Rj R2 or R3 R2). Some support for these conclusions has been cited (eqs. [6] and [7]). These qualitative arguments may also be relevant to the observed populations of hydrogen- and nonhydrogen-bonded populations of the aldol adducts as well (see Table 1, entries K, L). Unfortunately, little detailed information exists on the solution geometries of these metal chelates. Furthermore, in many studies it is impossible to ascertain whether the aldol condensations between metal enolates and aldehydes were carried out under kinetic or thermodynamic conditions. Consequently, the importance of metal structure and enolate geometry in the definition of product stereochemistry remains ill defined. This is particularly true in the numerous studies reported on the Reformatsky reaction (20) and related variants (21). 

The atomic and bond overlap population analysis of bulk ZnS is listed in Table 9.4. The overlap population may be used to assess the covalent or ionic nature of a bond. A high value of the bond population indicates a covalent bond, while a low... 

With increasing p-character, bond populations and the overlap between hybrid orbitals forming the bond orbital decrease. (We note that calculations based on non-... 

Though this correction does not seem to have been considered, we must note that its effect is far from negligible when compounds as different as NH3, N (CH3 )3 and NF3 are involved in these molecules, the nitrogen "a bond populations are 1.33, 1.22 and 1.53, respectively according to one determination, and 1.39,1.23 and 0.95 according to another 50 It can readily be appreciated that the correction for the charge effect may be as high as 2 MHz. 

A simplification can be effected, for unsymmetrically subsituted derivatives, by introducing a mean value of the a bonds population, namely (1/3) (2 + bi + b2), the results obtained for the V populations being quite similar to those of the symmetrically substituted derivatives... 

The A atom uses a valence p orbital for the formation of a a bond, population a. The two pn orbitals have identical populations, b. The cylindrically symmetrical field gradient lies along the A-B axis... 

If the interbond angle is 28 the fractional s character of the A-B hybrid a bond, population a, is (1 - cot20). If the third a orbital is occupied by... 

The asymmetry parameter in 1,2-disubstituted 5-nitroimidazoles decreases with increasing the substituent size. The n-electron density and N-l bond population is calculated according to the Townes-Dailey theory and described in detail by Dr. Lucken [1408] and Dr. Dolgushin [1409,1410] based on height with lengthening of the substituent on N-l [1411]. 

When a population analysis is performed for the various wavefunctions used above, for the hydrogen molecule, it is found that the overlap populations are always positive (indicating a flow of electron density into the overlap region between the nuclei) but that the predicted enhancement of the density in the bond region depends on which function is used for example, the MO and VB functions give bond populations... 

Ham, N.S. and Ruedenberg, K. (1958b). Energy Levels, Atom Populations, Bond Populations in the LCAO MO Model and in the FE MO Model. A Quantitative Analysis. J.Chem.Phys., 29, 1199-1214. 

As a simple example, bond indices, valencies, partitioned energies and atomic orbital bond populations for a formaldehydelH CO) molecule are listed... 

Table II shows bond parameters of various molecules, which are averaged if equivalent bonds exist. Well potentials are not adopted in DV-Xa calculatins here. The bond index(C-C) of CjH, or is 1, 2 or 3 respectively. The bond index (C-C) of is 1.4 and the bond index (B-F) of BFj is 1.2, both of which are sums of a (7 -bond and smaller n -bond contributions. The bond index(C-O) of CO near to 3 and its partitioned energy as large as that of C-C of C H suggest a triple bond formation. The bond indices (S-F) of SF, (B-B) of B H and (Fe-C) of FeCCjHj) (Fig.2) are smaller than 1. But the partitioned energies for those bonds are negative and explain their stabilities. On the other hand, the atomic orbital bond population for (Fe-C) of FelCjHj) is negative and can t explain its stability.

Molecule bond bond index partitioned Energy (eV) atomic orbital bond population... 

The reason why Mulliken s atomic orbital bond population between atoms sometimes becomes negative for bonds in stable molecules was suggested. 

Since the 2n orbitals of CO are antibonding with respect to the CO bond, population of the 2n orbitals weakens the CO bond. This can be observed using infrared spectroscopy, where one usually finds a lowering of the CO stretching frequency when CO becomes part of co-ordination complexes or adsorbs to surfaces. It implies significant backdonation. 

The meaning of the quantities evaluated in this way is quite clear. With each occupied one-electron wave-function is associated an energy s which for closed shell systems represents the ionisation potential from that level s) and this ionisation potential is, using the technique of photoelectron spectroscopy (93) measurable in principle and often, already in practice. The total energy can also be calculated, and represents the energy of formation of the system from infinitely separated nuclei (or nuclei with cores) and electrons. Net orbital populations, bond populations and gross populations are readily defined. 

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