Huckel calculations bonding

The simplest molecular orbital method to use, and the one involving the most drastic approximations and assumptions, is the Huckel method. One str ength of the Huckel method is that it provides a semiquantitative theoretical treatment of ground-state energies, bond orders, electron densities, and free valences that appeals to the pictorial sense of molecular structure and reactive affinity that most chemists use in their everyday work. Although one rarely sees Huckel calculations in the resear ch literature anymore, they introduce the reader to many of the concepts and much of the nomenclature used in more rigorous molecular orbital calculations. 

The Huckel method and is one of the earliest and simplest semiempirical methods. A Huckel calculation models only the 7t valence electrons in a planar conjugated hydrocarbon. A parameter is used to describe the interaction between bonded atoms. There are no second atom affects. Huckel calculations do reflect orbital symmetry and qualitatively predict orbital coefficients. Huckel calculations can give crude quantitative information or qualitative insight into conjugated compounds, but are seldom used today. The primary use of Huckel calculations now is as a class exercise because it is a calculation that can be done by hand. 

CNDO/2 and extended Huckel calculations 74> of 13 (X = S) revealed a small difference in energy between the planar and nonplanar structure, both with bond alternation. These results can be translated into the valence bond structure corresponding to a cyclic thioether. 

The interactions between the [W(calix)] metal fragment and the ethylene moiety has been analyzed using the extended Huckel calculations (see Chart 4).22b As supported by the structural parameters of 31, the dxz is no longer available for -it donation from the calixarene oxygens in the xz plane, thus explaining the strong C2v distortion of the [ [ Bu -cal ix 14]-(0)4 W] unit observed in the X-ray structure of 31, with the two WO bonds in the metal-ethylene plane ca. 0.2 A longer than... 

Using a similar approach, Evans and co-workers obtained values of hsi = -1.50, kcsi = 0.55, 8 = 0.15 for a series of trimethylsilyl-substituted naphthalene radical anions based on a Q value of -26.1 49). For phenyltrimethylsilylacetylene radical anion, the values of the heteroatom parameters that gave the best fit of the Huckel calculated spin densities with experimental values, using a Q value of 28, were hs, = -1.3, and kCSi = 0.65 when a 8 value of 0.1 was assumed. A resulting C—Si 7r-bond order of about 0.3 is obtained 43). 

Figure 3. ixxxx/ lo calculated from a Huckel-like bond alternated chain as a function of the number of sites (N). The ratio of the coupling between p-orbitals in single vs. multiple bonds determines the saturation of the 7/CV70 plot (here the ratio is 0.79 to model a polyene). 70 is the hyperpolarizability of an isolated double bond. 

Octahedral olefin-alkyne d4 complexes are characterized by a one-to-one match of each of the three metal dir orbitals with a ligand tt function as mentioned above. Three constructive two-center-two-electron metal-ligand tt bonds result. Extended Huckel calculations on W(H2C=CH2)-(HC=CH)(S2CNH2)2 produce the dv level ordering shown in Fig. 16... 

Steric factors probably prohibit simultaneous rotation of the olefin and alkyne C2 units which would crowd all four metal-bound carbons into the same plane. Separate rotation of each unsaturated ligand was explored theoretically using the EHMO method. Rotation of the olefin destroys the one-to-one correspondence of metal-ligand tt interactions. Overlap of the filled dxz orbital with olefin n is turned off as the alkene rotates 90°, creating a large calculated barrier for olefin rotation (75 kcal/mol). Alkyne rotation quickly reveals an important point the absence of three-center bonds involving dir orbitals allows the alkyne to effectively define the linear combinations of dxy and dyz which serve as dn donor and dir acceptor orbitals for 7T and ttx, respectively. Thus there should be a small electronic barrier to alkyne rotation (the Huckel calculation with fixed metal... 

The extended Huckel calculations (45) start from an unbridged geometry where the OC—Mo—CO and Mo—Mo—C bond angles are both 90° while the Mo—Mo—Cp bond angle is set to 125.3°. This leads to a bond description including characteristic five below two frontier orbitals shown in Fig. 3. The five highest occupied molecular orbitals are 7r, 8, ir, 8, and a and allow a correlation with the triple bond assigned on the basis of the 18-electron rule. 

The third mechanism, suggested by R. Hoffmann as a result of extended Huckel calculations, also involves trimethylene but gives it special properties that would lead to correlated conrotation of the terminal methylenes. Specifically, the calculations suggested that the C-H a bonds of the central methylene could be used as a kind of pseudo-p -orbital... 

After establishing that the central bond is composed almost solely of p orbitals on each of the two carbons, it remains to establish the orientation of these orbitals with respect to each other. The two possible extremes are a overlap in which the two orbitals are oriented towards each other or n bonding for which they are parallel. Extended Huckel calculations performed by Yonezawa and coworkers assign a large n character to this bond. On the other hand, a 5 1 ratio of p-cr to p-7r bonding was reported on the basis of ab initio calculations. Other ab initio calculations (STO-3G) suggest that the bond is bent outward but differ as to the extent (45° and 30.8° Thus one may conclude that the central bond of bicyclobutane, although formally a o bond, contains appreciable n character. 

We have also carried out Huckel calculations on the various backbone geometries considered in this paper, rfuckel theory only considers nearest neighbor overlap integrals, p, for the backbone carbon atoms and has no sensitivity to bond angles. The... 

N.m.r., X-ray photoelectron studies, and extended Huckel calculations on HgCl2Py2 indicate a moderate amount of electron transfer to the metal from pyridine relative to ZnQ2py2 the filled mercury d-orbitals do not participate in bonding. Dipole moment studies on Cdl2py2 have been made, while stability constant studies for the formation of complexes between Cd and pyridine in water, water-MeOH, and water-DMF mixtures show the formation of the species [CdlpylJ (x = 1—3). A structural determination of Hg(N03)2(py)2(H20)2 reveals mercury in a distorted octahedral environment consisting of two water and two pyridine ligands (Hg—N =... 

Once more, we use butadiene as the example Fig. 4-10 shows the total bond-orders of all bonds in butadiene, including the C—H bonds which normally do not feature in the considerations of a Huckel calculation (since they are pure, single, tr-bonds, their total bond-order will be, on these assumptions, precisely unity). By examination of a diagram of this sort it would be a trivial matter to add up the total order of all the bonds which terminate on some particular atom, r let us call this sum the total bond-number for this atom and denote it Nr. For example, it is clear that... 

Fig. 8.10. Migration of the ML2 fragment as mapped by four structures. The structure on the left closely resembles the ground state, the one on the right the transition state, as determined by extended HUckel calculations on H3CjNi(PH3)2. Note that the ML2 moiety rotates w.r.t. the cyclic ene, as M migrates from one C-C bond to the next...

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