Introduction :
We know all the systems want to be in a stable state, and the stable state is one in which it has the minimum possible energy. Same is true for the stereochemistry or the geometry of a molecule. The VSEPR theory considered that the most stable configuration of a molecule is one in which repulsive forces between the valence electron-pairs is minimum. In contrast, the molecular orbital theory (MOT) considers that the stable geometry of a molecule can be determined on the basis of the energy of molecular orbitals formed as a result of linear combination of atomic orbitals (LCAO). In 1953 A.D.Walsh proposed a simple pictoral approach to determine the geometry of a molecule considering and calculating the energies of molecular orbitals of the molecule.
The basic approach is to calculate the energies of molecular orbitals for two limiting structures, say linear or bent to 90° for an AB2 molecule, and draw a diagram showing how the orbitals of one configuration correlate with those of the other. Then depending on which orbitals are occupied, one or the other structure can be seen to be preferred. By means of approximate MO Theory implemented by digital computers, this approach has been extended and generalized in recent years.
Walsh's approach to the discussion of the shape of an AB₂ triatomic molecule (such as BeH, and H₂O) is illustrated in Fig. 1.8. The illustration shows an example of a Walsh diagram, a graph of the dependence of orbital energy on molecular geometry. A Walsh diagram for an BA or AB molecule is constructed by considering how the composition and energy of each molecular orbital changes as the bond angle changes from 90° to 180°. The diagram is in fact just a elaborate version of the correlation diagram.
Application to Triatomic Molecules :
The coordinate system for the AB,2 molecule is shown in Figure 1.8. The AB₂ molecule has C2, symmetry when it is bent and, when linear Dah symmetry. To simplify notations, however, the linear configuration is considered to be simply an extremum of the C2, symmetry. Therefore the labels given to the orbitals through the range 90°<< 180° are retained even when 0 = 180°. The symbols used to label the orbitals are derived from the orbital symmetry properties in a systematic way, but a detailed explanation is not given here. For present purposes, these designations may be treated simply as labels. (Fig. 1.7).
The A atom of AB₂ molecule will be assumed to have only s, px, py and pz orbitals in its valence shell, whereas each of the B atoms is allowed only a single orbital oriented to form a o bond to A. In the linear configuration P^x and P^z are equivalent non-bonding orbitals labelled 2a, and b, respectively. The orbitals SA and Pay interact with 61 and 62". o orbitals on the B atoms, to form one very strongly bonding orbital, la, one less strongly bonding orbital, 1b2, one less strongly bonding 3a, and 3b2. The ordering of these orbitals and in more detail, the approximate values of their energies can be estimated by an MO calculation. Similarly, for the bent molecule the MO energies may be estimated. Here only pz is non bonding, spacing and even the order of the other orbitals is function of the angle of bending 0. The complete pattern of orbital energies, over a range of 0, is obtained with typical input parameters. This is shown in the figure 1.8. Calculations in the Huckel approximation are simple to perform and give the correct general features of the diagram but for certain cases (e.g. ABE) very exact computations are needed for an unambiguous prediction of structure.
Form the approximate diagram (Fig. 1.8) it is seen that an AB₂ molecule (one with no lone pairs) is more stable when linear then when bent. The Ib, orbital drops steadily in energy form = 90° to 180°; while the energy of the la, orbitals is fairly insensitive to angle.
For an AB E molecule the results are ambiguous, because the trend in the energy of the 2a, orbital approximately offsets that of the 1b2 orbiral.
For AB2E2 molecules, the result should be the same as for AB E. Since the energy of b, orbirtal is independent of the angle. Thus it is not clear in this approach that AB E molecules should necessarily be bent, but all known ones are.
The H₂O Molecule :
Because of its unique importance, this molecule has been subjected to more detailed study than any other AB2E2 molecule. A correlation diagram calculated specially for H2O is shown in the figure. Although it differs in detail for the general AB2E2 shown in the figure it is encouraging to see that the important qualitative features are the same. The general purpose diagram pertains to a situation in which there is only a small energy difference between the ns and np orbitals of the central atom. As stated in discussing that general purpose diagram, it is not clear whether an ABE, molecule ought necessarily to be bent.
In the diagram calculated expressly for H2O the lowest level's is practically pure 2s and its energy is essentially constant for all angles. It can be determined from this diagram that the energy is minimized at an angle of 106", essentially in accord with the experimental value of 104.5°. (Fig. 1.9).
BeH2 Molecule :
The simplest AB₂ molecule in Period 2 is the transient gas-phase BeH2 molecule (BeH, normally exists as a polymeric solid), in which there are four valence electrons. These four electrons occupy the lowest two molecular orbitals. If the lowest energy is achieved with the molecule angular, then that will be its shape. We can decide whether the molecule is likely to be angular by accommodating the electrons in the lowest two orbitals corresponding to an arbitrary bond angle in Fig. 1.7. We then note that the HOMO decreases in energy on going to the right of the diagram and that the lowest total energy is obtained when the molecules is linear. Hence, BeH, is predicted to be linear and to have configuration lo 20. In CH₂, which has two more electrons than BEH₂, three of the molecular orbital must be occupied. In this case, the lowest energy is achieved if the molecule is angular and has configuration 1 la 2a11b.
The principal feature that determines whether or not the molecule is angular is whether the 2a, orbital is occupied. This is the orbital that has considerable A-2s character in the angular molecule but not in the linear molecule.
Application to Penta Atomic Molecules :
For peta-atomic molecules examples of CH, and SF, may be taken for consideration. For these molecules, two geometries are possible: one a symmetrical tetrahedral and the other, a distorted tetrahedral geometry (or a tetragonal geometry of relatively lower symmetry).
CH4 Molecule :
Methane, CH4, has eight valence electrons. During bonding, for orbitals [a,g (2s) and tju (2p)] of carbon, and one [ag (1s)] orbital of eachfour hydrogen atoms take part. Overlapping of these eight orbitals, eight molecular orbitals are formed, the four bonding (2og or 2a, and 2to or 2t,) and the four antibonding (2og* and 2t*o). The eight valency electrons of CH, molecule are distributed in the four bonding molecular orbitals (Electronic Configuration, 22). In the tetrahedral geometry due to overlapping with the orbitals of hydrogen atom the energy of 2a,g and 2t, orbitals is considerably reduced. In contrast, in the distorted geometry, comparatively less overlapping of tu orbitals with the hydrogen orbitals (as compared to that in the tetrahedral geometry) the energy of 2t, molecular orbitals increases. Thus the geometry of CHA molecule is symmetrical tetrahedral, rather than a distorted tetrahedral.
SF4 - Molecule :
In the valence shall of sulphur atom, in SF, molecule, in addition to 3s (ag) and 3p (tu) orbitals, 3d (t2g and eg) orbitals are also present. During the bonding, 2p, orbital of each of the four fluoring atoms take part. As a result for bonding (2a, and 2t₁) and four antibonding (2a, 21) molecular orbitals formed; while the d-orbitals [a (dz²), b,(dx² - y²) and t (dy, dz. dy,)] are present as non-bonding molecular orbitals. Ten valency electrons of SF4 molecule remain distributed in the four bonding and one non-bonding molecular orbitals, resulting in 2a.2. 3a configuration. As in the distorted geometry, overlapping of 2t, orbitals is comparatively greater (thus reducing their energy) and the filling in 3a, orbital considerably reduce the energy of the system as compared to that in the regular tetrahedral structure. Hence SF, molecule has a distorted tetrahedral geometry, rather than a regular tetrahedral structure.
Thus we can say 'Walsh Diagrams' are complementary to the VSEPR concept.
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