Orbitals in formaldehyde

Fig. 2.1. Energy levels of molecular orbitals in formaldehyde (HOMO Highest Occupied Molecular Orbitals LUMO Lowest Unoccupied Molecular Orbitals) and possible electronic transitions.

Absorption of visible or ultraviolet radiation promotes electrons to higher-energy orbitals in formaldehyde. Infrared and microwave radiation are not energetic enough to induce electronic transitions, but they can change the vibrational or rotational motion of the molecule. 

Complex molecules may not possess any symmetry elements, or if they do, the localizations of the electrons can so distort the electron cloud that its symmetry bears little relation to the molecular symmetry. In such cases it may be best to revert to a description of states in terms of the individual orbitals. As an example, we will consider formaldehyde, although a molecule as simple as this is probably best described by the group-theoretical term symbol of the last paragraph. The last filled orbitals in H2CO can easily be shown to be. ..(jtco)2 (no)2, where no represents the nonbonding orbital on the O atom and the two electrons in it are the lone pair. The first unfilled orbitals in formaldehyde are the tt 0 and rr o antibonding orbitals. Promotion of one... 

The polarisation of the carbonyl group is away from carbon towards oxygen in the bonding orbital, and the opposite in the antibonding orbital, as usual. The wire-mesh pictures in Fig. 1.53 show more realistically an outer contour of these two orbitals in formaldehyde itself. Note that in Figs 1.52 and 1.53, it appears from the shape of the outer contour that the electron population in the bonding orbital is very similar on oxygen to that on carbon. 

Figure 6.2 A schematic representation of bonding and anti-bonding orbitals in formaldehyde.

The other geometric parameters in the S, state also show variations in the two molecules. The elongation of the double bond on excitation is substantially larger in CHjO, consistent with the greater n orbital stability, the less localized nature of the n orbital and the less stable n orbital in formaldehyde. Although the CH bond contracts by 0.19 A in both molecules, the HCH angle opens by 4.4° in thioformaldehyde and only 2.2° in formaldehyde. 

Figure 2 Carbon atomic orbitals in formaldehyde (RHF/6-31IG basis), plotted along the C-H bond axis, showing (a) the 2s NAO (solid) vs. non-orthogonal PNAO (dashed) (b) the three outermost s-type basis AOs of the 6-3110 " basis set. Note the small nodal feature at the adjacent H that distinguishes the 2s NAO and PNAO, whereas Gaussian basis AOs lack nodal structure even in the core region of the C Is electrons...

For example, in formaldehyde, H2CO, one forms sp hybrids on the C atom on the O atom, either sp hybrids (with one p orbital "reserved" for use in forming the n and 7i orbitals and another p orbital to be used as a non-bonding orbital lying in the plane of the molecule) or sp hybrids (with the remaining p orbital reserved for the n and 7i orbitals) can be used. The H atoms use their 1 s orbitals since hybridization is not feasible for them. The C atom clearly uses its sp2 hybrids to form two CH and one CO a bondingantibonding orbital pairs. 

This difference is due to the two lone pairs on the oxygen. Of the six valence electrons on the oxygen atom, two are involved in the double bond with the carbon, and the other four exist as two lone pairs. In Chapter 4, we ll examine the IR spectra for these two molecules. The orbitals suggest that we ll find very different frequencies for the two systems. In Chapter 9, we ll look at the transition to the first excited state in formaldehyde. ... 

In absorption and fluorescence spectroscopy, two important types of orbitals are considered the Highest Occupied Molecular Orbitals (HOMO) and the Lowest Unoccupied Molecular Orbitals (LUMO). Both of these refer to the ground state of the molecule. For instance, in formaldehyde, the HOMO is the n orbital and the LUMO is the n orbital (see Figure 2.1). 

Ellis, Squire, and Jaffe have carried out a detailed study of the spin-orbit coupling in formaldehyde and azulene. The wave functions were calculated using the CNDO/S method, which is more general than the PPP method discussed earlier and also allows ff-orbitals to be included. Let us review their findings on formaldehyde ... 

Table 4. Spin-orbit matrix elements in formaldehyde...

Figure 2.16 Molecular orbitals, their approximate energy levels and types of transitions in formaldehyde molecule.

The highest occupied molecular orbital (HOMO) in formaldehyde and heteroaldehydes, H2C=E, is the lone pair at E (nE), and the second highest MO (SOMO) is the C=E 77-bonding orbital. The LUMO is the 77 CE orbital composed of the antibonding combination of pz(C) and pz(E). The ionization energy of the HOMO in formaldehyde is 10.88 eV and of the SOMO 14.5 eV, as determined by photoelectron spectroscopy.33 The ionization energy of the HOMO and the SOMO both decrease considerably when the oxygen atom in formaldehyde is replaced by sulfur or selenium (see Fig. 1, data are compiled from Refs. 33-37). 

In a structural formula the bonds are of course localized between pairs of atoms, so that the corresponding bonding and antibonding orbitals are by implication localized in the same way. This picture of localized orbitals is adequate in general for the a orbitals of single bonds, and also for the tt orbitals of isolated double bonds such as the one in formaldehyde. The important difference between diatomic and polyatomic molecules, which was alluded to above, arises when the molecule contains alternating single and... 

The formaldehyde molecule is planar in its ground state (Figure 7-6). We first construct three strong a bonds involving thje carbon, the two hydrogen, and the oxygen atoms. Since the angles in the plane all are approximately 120°, we construct three equivalent orbitals in the xy plane which are directed from carbon toward Hx, H2, and O. For this purpose we hybridize the three carbon atomic orbitals 2s, 2px, and 2py. From three orbitals we can construct three linearly independent hybrid orbitals. 

The carbon-oxygen double bond in aldehydes and ketones is similar and can be described in either of these two ways. If we adopt the iocalised-orbital description, formaldehyde will have two directed lone pairs in place of two of the C-H bonds in ethylene. In this case the axes of these hybrid orbitals will be in the molecular plane (unlike the oxygen lone pairs in water). Either the components of the double bond or the lone pairs can be transformed back into symmetry forms. The alternative description of the lone pairs would he one er-type along the 0-0 direction and one jr-type with axis perpendicular to the 0-0 bond hut in the molecular plane. It is the latter orbital which has the highest energy, so that an electron is removed from it in. ionisation or excitation to the lowest excited state. 

Note pz in formaldehyde symbolizes a nonbonding orbital on the oxygen atom. b See ref. 17. 

PROBLEM 7.21 Describe the hybridization of the carbon atom in formaldehyde, H2C=0, and make a rough sketch of the molecule showing the orbitals involved in bonding. 

Lin (145) has carried out an extensive theoretical investigation of the radiative and nonradiative mechanisms involving vibronic, spin-orbit, and vibronic-spin-orbit coupling in formaldehyde. Earlier, Yeung (254) calculated the SVL values of Tg, and Yeung and Moore (255) calculated the SVL values of x g. Lin used the left-hand Cartesian coordinate system in which planar formaldehyde lies in the x-z plane rather than in the y-z planes for the right-hand coordinate, which is accepted as the standard spectroscopic convention. Here, we adhere to the latter... 

Considerations of orbital symmetry are frequently grossly simplified in that, for example, the pi orbitals of a carbonyl group would be treated as having the same symmetry as those of ethene, and the fact that the carbonyl group in, for example, camphor (unlike that in formaldehyde) has no mirror planes would be ignored. These simplified considerations nevertheless afford the basis of one approach to the understanding of the rules that indicate whether pericyclic... 

In this simple valence bond model, the bonding in formaldehyde is described by three localized tr-orbitals, one localized x-orbital, and two equivalent oxygen lone-pairs. A major... 

FIGURE 17.1 Similarities between the orbital hybridization models of bonding in (a) ethylene and ( >) formaldehyde. Both molecules have the same number of electrons, and carbon Is sp -hybrldlzed in both. In formaldehyde, one of the carbons Is replaced by an sp -hybrldlzed oxygen (shown in red). Oxygen has two unshared electron pairs each pair occupies an sp -hybrldlzed orbital. Like the carbon-carbon double bond of ethylene, the carbon-oxygen double bond of formaldehyde Is composed of a two-electron cr component and a two-electron tr component. 

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