M. K. Orloff and N. B. C O L ~ U P American Cyanamid Company Chemical Reseorch Division Stamford, Connecticut 06904
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Illustrated Molecular Orbitals of Formaldehyde
In a recent article in this Journal, R. J. Olcott presented a visualization of the molecular orbitals of formaldehyde.1 In our presentation we have used a different approach which complements Olcott's discussion and which contributes to the overall understanding of the electronic structure of formaldehyde. Our calculated molecular orbitals of formaldehyde2 numbered in order of increasing energy are illustrated in the figure. These are for valence electrons only and do not include the 1s orhitals on carbon and oxygen. The molecular orbitals are arranged by symmetry species for the Czu point group. Five molecular orbitals are in the totally symmetric A1 species, three in the Bz species (antisymmetrical with respect to the xz plane), and two in the BI species (antisymmetrical with respect to the yz plane). Lines of constant values are drawn for the y z plane (containing all the nuclei) for the A1 and Bz species, and for the xz plane for the BI species (the a orbitals). These lines enclose antinodal regions where the electrons spend most of their time and there is a nodal surface between antinodal regions which have different signs. I t can be seen that, within one symmetry species, the numher of nodes in the molecular orbital increases as the energy of the molecular orbital increases. The orhitals below the dotted line, MO 1-6, are all doubly occupied with paired electrons in the ground state. The electron densities and overlap populations3 for the
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individual MO's in formaldehyde have been calculated from the CND0/2 wavefunctions and are given in Table 1. In the figure to the left of each MO is the electron density for the particular MO occupied by two electrons, in descending order for the oxygen, carbon, and one hydrogen atom. This numher times 100, divided by 2, gives the percent of its time an electron spends in the vicinity of that atom. To the right of each MO is the overlap population for that particular MO occupied by two electrons in descending order for the CO bond and one CH bond. It can be seen that every time this overlap population is negative there is a wavefunction node between the two atoms involved. Oleott, R. J., J. CHEM. EDUC., 49,614 (1972). Wavefunctions calculated by the semiempirical CND0/2 method of Pople and eo-workers;Pople, J. A,, Santry, D. P., and Segal, G . A., J Chem. Phys. 43, S 129 (1965); Pople, J. A,, and Segal, G. A., J. Chem. Phys. 43, S 136 (1965); 44,3289 (1966). Mulliken, R. S., J Chem. Phys. 23,1833 (1955).
Table 1. Electron Densities and Overlap Populations For Individual MO's in Formaldehyde
The molecular orbitals of formaldehyde
400 /Journal ot Chemical Education
Table 2. Total Electron Densities and Overlap Populations for Formaldehyde
A molecular orbital can he characterized as bonding, antibonding, or non-hooding between two given atoms if the overlap population for the single MO is a large positive numher, a large negative numher, or a number close to zero, respectively. It is clear from an examination of Tahle 1 that the electrons in all the MO's are delocalized over the whole molecule hut it is also clear that usually some particular overlap population or electron density distribution will stand out which characterizes the predominant nature of that MO. An examination of Tahle 1 indicates that the ground electronic state for formaldehyde can he roughly designated in order of increasing energy as [(lso)z(lsc)2](aco)z-
(UCM)~(U'CH)~(~O)~(~CO~~(~'~)~(~*CO~~~U*CH~~~
(Zco)O where primed and unprimed ucH and no orhitds are antisymmetric and symmetric, respectively, and starred orbitals are antihonding and unfilled in the ground state. T h e simplified nature of these descriptive MO designations should not be forgotten however. The totaI electron densities and overlap populations are listed in Table 2. The electron densities show that the oxygen has slightly more than 6 valence electrons and carbon slightly less than 4 valence electrons reflecting their relative electronegativities. It can also be seen that the CO and CH atom p a i n are bonded because they have large positive overlap populations whereas the HH and OH atom pairs are nearly non-bonding because their overlap populations are close to zero. In the case of the H H atom pair for example, it can he seen in Table 1 that in the A1 species the HH atom pairs are all bonding hut this is compensated by the fact that in the Bz species the HH atom pairs are all antihonding. (They are non-bonding in the BI species.) In conclusion, we see how an analysis of the individual molecular orbitals in formaldehyde permits a better understanding of the composite electronic structure of the ground state of the molecule.
Volume 50, Number 6 , June 1973 / 401
