Correlation diagram Walsh

This approach is useful because it allows quantitative analysis via Walsh correlation diagrams to be made without extensive calculations. Figure 5.11 may clarify the approach. Initially the extra half-plane is at x = 0 and atom C is covalently bonded to atom A. When the half plane moves to the mid-glide position, x = b/2, the activation complex, ACB forms (Figure 5.10). Finally, when the half-plane moves to x = b, the pair CB forms a new covalent bond. Symbolically ... 

Fig. 3. Walsh correlation diagrams, a State energy levels for methylene (Jordan and Longuet-Higgins, 1962). 6 MO levels after Walsh (1963). c MO levels after Atkins and Symons (1967) and Hayes (1966) above the break, ci-type orbitals have been included their effect on the energy of some MO s is indicated by the small arrows.

Figure 2.3. The Walsh correlation diagram illustrating the changes in the n, n, and a orbital energies as thiophosgene is distorted from a planar to a pyramidal conformation.

The Walsh correlation diagram (6) predicts a ground state electronic configuration of A for a 21 valence electron molecule. In addition, the existence of two doublet excited states is highly probable. We omit these excited states since no spectroscopic information is available on these states for isoelectronic molecules which would allow us to estimate the relative term values. 

Conjugated chains, 14, 46 Correlation diagrams, 44, 50 Cyclobutadiene, 171 Cyclobutane, 47, 222 orbital ordering, 26 through-space interactions, 26 Walsh orbitals, 27 Cyclobutene, 200 Cyclohexane, 278 Cyclohexene (half-boat), 274 Cyclopen tadiene, 225 Cvclopen tadienone, 269 Cyclopentadienyl anion, 237 Cyclopentane, 254 Cyclopen ten e, 241 Cyclopropane, 41, 47, 153 construction of orbitals, 19, 22 Walsh orbitals, 22, 36, 37 Cyclopropanone, 48, 197 bond lengths, 38 Cyclopropen e, 49, 132 reactivity, 40... 

A good deal of information on small radicals can be obtained from Walsh diagrams (77). These correlation diagrams allow the estimation of molecular geometry from the mere knowledge of the number of valence electrons. The procedure and arguments are similar to those presented by Mulliken (78), who discussed the shapes of ABl molecules in ground and excited states and interpreted their electronic spectra. 

For qualitative discussions, Walsh diagrams (see Sec. I.C.2.) have proved to be very useful, for example, in determining the structures of AB2, AB3, and HAAH molecules in ground and excited states. These correlation diagrams show how MO levels change on passing from one extreme molecular geometry to another. 

Figure 1. Walsh type orbital correlation diagram (EH MO calculations [6]) for transforming linear H3P-Pt-PH3 (D3h) to a bent (C2V) geometry. Only the valence MOs and the relevant metal contributions to the MO wave functions are shown. 

The most widely used qualitative model for the explanation of the shapes of molecules is the Valence Shell Electron Pair Repulsion (VSEPR) model of Gillespie and Nyholm (25). The orbital correlation diagrams of Walsh (26) are also used for simple systems for which the qualitative form of the MOs may be deduced from symmetry considerations. Attempts have been made to prove that these two approaches are equivalent (27). But this is impossible since Walsh s Rules refer explicitly to (and only have meaning within) the MO model while the VSEPR method does not refer to (is not confined by) any explicitly-stated model of molecular electronic structure. Thus, any proof that the two approaches are equivalent can only prove, at best, that the two are equivalent at the MO level i.e. that Walsh s Rules are contained in the VSEPR model. Of course, the transformation to localised orbitals of an MO determinant provides a convenient picture of VSEPR rules but the VSEPR method itself depends not on the independent-particle model but on the possibility of separating the total electronic structure of a molecule into more or less autonomous electron pairs which interact as separate entities (28). The localised MO description is merely the simplest such separation the general case is our Eq. (6)... 

Burdett has also applied the AOM to the rationalisation of the geometries of main group molecules (38). Correlation diagrams (analogous to Walsh diagrams) can be constructed to show the angular dependence of MO energies, and the shapes of simple... 

Figure 9.4 shows Walsh s diagram expressing the orbital correlation and suggesting the variation in orbital energy with bond angle. 

Problem 9-15. Could the same predictions be made from a simple electron repulsion argument If n pairs of electrons must be accommodated in the valence-shell molecular orbitals, then assume simply that they will be as far apart as possible. Up to four electrons will push each other as far apart as possible, to create linear geometry more than four must be distributed more densely, so that the angle between the substituents will be less that 180°. Does this simple hypothesis explain everything that Walsh s rules do Is there any advantage to using Walsh s correlation diagram analysis ... 

The MOs and electronic states of carbene have been discussed in Chapter 7. The orbital and state correlation diagrams for addition of CH2 to ethylene is shown in Figure 14.9. The Walsh bonding picture for the MOs of cyclopropane requires that the and a MOs of the ethylene also be included in the diagram. The a2 and least-motion pathway preserves a vertical plane of symmetry (as well as the other elements of the C2v point group), and the... 

Cyclopropane bond angle, 16 bonding, 84-85 correlation diagrams, 207 electronic states, 207 hybridization, 16 point group of, 5 structure of, 16, 84 Walsh orbitals, 85 Cyclopropanes... 

To be specific, we show in Figure 9, following Walsh, the correlation diagram as we go from a linear HAH molecule to the case when the HAH angle is 90°. In the linear molecule, the classification of the lowest states is quite clear, into two a states, even and odd, and into a doubly degenerate nu non-bonding state,... 

The N3 group is linear. (A recent value for the NNN angle in Ba(N3)a crystal is 179-7 0-2° .) This is in agreement with the correlation diagram of Walsh which predicts that ABa or BAG molecules with 16 or less valence electrons should be linear in their ground states. (See section III.G.) The azide radical and Nj are symmetrical. The N-—N distance in the radical is only 0-015 A longer than in N. The two molecules differ in one non-bonding electron (sections I.G and I.D). and this is expected to have little effect on the bond properties. 

The correlation diagram of Walsh ( ) predicts a bent configuration for BClg" (18 valence electrons) with a bond angle... 

The correlation diagram of Walsh (4) for HAB molecules predicts a linear configuration for LiOH (seven valence electrons) with the unpaired electron in a pi orbital. Therefore, the electronic ground state of LiOH should be A first excited state... 

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