Water symmetry orbitals

The NMRD profiles of V0(H20)5 at different temperatures are shown in Fig. 35 (58). As already seen in Section I.C.6, the first dispersion is ascribed to the contact relaxation, and is in accordance with an electron relaxation time of about 5 x 10 ° s, and the second to the dipolar relaxation, in accordance with a reorientational correlation time of about 5 x 10 s. A significant contribution for contact relaxation is actually expected because the unpaired electron occupies a orbital, which has the correct symmetry for directly overlapping the fully occupied water molecular orbitals of a type (87). The analysis was performed considering that the four water molecules in the equatorial plane are strongly coordinated, whereas the fifth axial water is weakly coordinated and exchanges much faster than the former. The fit indicates a distance of 2.6 A from the paramagnetic center for the protons in the equatorial plane, and of 2.9 A for those of the axial water, and a constant of contact interaction for the equatorial water molecules equal to 2.1 MHz. With increasing temperature, the measurements indicate that the electron relaxation time increases, whereas the reorientational time decreases. 

If we choose the oxygen 2s orbital for bonding and leave the 2orbital nonbonding (from the symmetry point of view the opposite choice or a mixed orbital would do just as well actually if the two arbitals are close in energy, they mix), the MOs of the water molecule can be constructed as shown in Figure 6-18. These MOs are compared with the calculated contour diagrams of the water molecular orbitals in Figure 6-19. 

The s and orbitals of nitrogen both have Aj symmetry, and the pair p, Py has E symmetry, exactly the same as the representations of the hydrogen I5 orbitals. Therefore, all orbitals of nitrogen are capable of combining with the hydrogen orbitals. As in water, the orbitals are grouped by symmetry and then combined. 

The functions put into the determinant do not need to be individual GTO functions, called Gaussian primitives. They can be a weighted sum of basis functions on the same atom or different atoms. Sums of functions on the same atom are often used to make the calculation run faster, as discussed in Chapter 10. Sums of basis functions on different atoms are used to give the orbital a particular symmetry. For example, a water molecule with symmetry will have orbitals that transform as A, A2, B, B2, which are the irreducible representations of the C2t point group. The resulting orbitals that use functions from multiple atoms are called molecular orbitals. This is done to make the calculation run much faster. Any overlap integral over orbitals of different symmetry does not need to be computed because it is zero by symmetry. 

There is always a transformation between symmetry-adapted and localized orbitals that can be quite complex. A simple example would be for the bonding orbitals of the water molecule. As shown in Figure 14.1, localized orbitals can... 

The possible wave functions for the molecular orbitals for molecules are those constructed from the irreducible representations of the groups giving the symmetry of the molecule. These are readily found in the character table for the appropriate point group. For water, which has the point group C2 , the character table (see Table 5.4) shows that only A1 A2, B1 and B2 representations occur for a molecule having C2 symmetry. 

Figure 1. An Fe(H20)62+-Fe(HgO)6s+ complex at the traditional inner-sphere contact distance with the inner-sphere complexes (Th symmetry) oriented to give overall S6 symmetry. This geometry is favorable for transfer of an electron between t g-5d atomic orbitals (AO s, which have

The significant values calculated for the occupied SMOs in the water dimer are given in Table II. and Table III. (only for orbitals which have relevant contributions due to the symmetry). 

The electrons which are important for the bonding in the water molecule are those in the valence shell of the oxygen atom 2s22p4. It is essential to explore the character of the 2s and 2p orbitals, and this is done by deciding how each orbital transforms with respect to the operations associated with each of the symmetry elements possessed by the water molecule. 

Symmetry Properties of the Hydrogen 1 s Orbitals in the Water Molecule Group Orbitals... 

One very important difference between VSEPR theory and MO theory should be noted. The MOs of the water molecule which participate in the bonding are three-centre orbitals. They are associated with all three atoms of the molecule. There are no localized electron pair bonds between pairs of atoms as used in the application of VSEPR theory. The existence of three-centre orbitals (and multi-centre orbitals in more complicated molecules) is not only more consistent with symmetry theory, it... 

The discussion of the distortion of the water molecule from a linear to a bent shape allows a tentative general conclusion to be reached. This is that if a distortion of a molecule from a particular symmetry allows two MOs to mix, so that the lower occupied orbital is stabilized at the expense of the higher vacant orbital, such a distortion will occur and will confer stability on the distorted molecule. A gain of stability will only occur if the two orbitals concerned in the stabilization process are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO).. If both orbitals are doubly occupied, interaction between them does not lead to any change in stability. The generality of this conclusion is explored further in the next sections of this chapter and in Chapter 6. 

A second type of force between water molecules and the metal consists of the dispersion forces. Dispersion forces (or London forces) can be seen classically as follows A time-averaged picture of any atom shows spherical symmetry because the charge due to the electrons orbiting around the nucleus is smoothed out in time. An instantaneous picture of, say, a hydrogen atom, would, however, show a proton here and an electron there—two charges separated by a distance. Hence, every atom has an instantaneous dipole moment of course, the time average of all these dipole moments is zero. This instantaneous dipole will induce an instantaneous dipole in a contiguous atom, and an instantaneous dipole-dipole force will arise. When these... 

The orbital degeneracies noted in point 3 above and seen in Figure 2.4 reflect the symmetry of the molecule s nuclear framework. Notice that the conventional picture of two equal lone pairs in water, sometimes displayed as rabbit ears, is not supported by the energies of the two highest occupied MOs of water. In fact, the lone pairs resemble the proper group MOs shown in Figure 1.8. 

Let us examine the behaviour of py orbital m water under the symmetry operation of the point group C2 (Figure 2.13a). Rotation around the z-axis changes sign of the wave function, hence under Ca, Py orbital is... 

Like water, it has the symmetry of point group C2e. When the MOs of formaldehyde molecule as given in the figure are subjected to the symmetry operations of this group, n-orbital is observed to transform as bx and n orbital as ba as shown below ... 

Table 1. Convergence in a CASSCF calculation on water, with a DTP basis. The approximate super-CI method was used with and without quasi-Newton update. The active space comprised 8 orbitals (4a12b1, 2b2 in C2v symmetry), yielding 492 CSF s. The Is orbital was inactive.

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