Hybridization in the Description of
John W. George University of Massachusetts Amherst
Homonuclear Diatomic Molecules
T h e elementary treatment of chemical bonding usually employs energy level diagrams for homonuclear diatomic molecules as descriptive introdnction to the molecular orbital theory of bonding. Such molecules as Hz, Np, and F2 may be considered, and physical properties such as bond lengths, bond strengths, ctc. rationalized using this approach. The success of the method in predicting the observed triplet ground state of the O2 molecule (Table 1) is commonly cited as evidence of the validity of the molecular orbital view of the chemical bond. I n these introductory considerations the single bond of the Lizmolecule and the non-existence of a Bez species are predicted by placing the appropriate number of elect,rons in the bonding and antibondiog molecular orbitals resulting from the interaction of the 2s atomic functions of the atoms concerned (Table 2). In these, and heavier molecules, the 1s atomic functions overlap insignificantly and the KK notation designates two nonbonding orbitals, each occupied by an electron pair. For the Bz molecule the two unpaired electron spins demand a degeneracy in the molecular orbital energy level immediately above the u.*2s level. In the case of C2 some uncertainty has existed concerning the ground state identity, but the most recent work (1) makes it clear that a singlet state lies a scant 0.076 electron volts below a triplet state. Both Bp and C2 molecules are then represented by adding to the doubly degenerate s,2p levels two and four electrons, respectively. The 14 electron N2 molecule may be described without reference to the order of r,2p and u,2p ,levels, but the paramagnetic Oz molecule, hke Blr requlres degeneracy of the energy levels to which the final two elect.rons of the molecule are assigned. This necessitates locating the s,*2p levels below the u,*2p level. The higher bond dissociation energies found for Oz+ and F2+molecular ions (2),as compared with Oz and Fx, support this order of molecular orbitals. Correlation diagrams (S), relating the energies of orbitals in the united and in the fully separated conditions of the nuclei, suggest that the a,2p level, which for Table 1. Ground State Terms, Internuclear Distances, and Dissociation Energies of Second Row Homonuclear Diatomic Molecules
Ground Moleade
atate term
Lip
152
-
Be*
1 5 :
B2
a&
C*
'&
Nz
'20
F,
'Zn
0%
/
Internuclear distance (A)
%
Dissociation Energy, ev
~
...
...
1.59
3.0
1 9d
5 0
1.44
1.OU
Journal o f Chemical Education
widely separat,ed atoms would lie above the u,2p level, falls below the u,2p level with decreasing internuclear distance. Because of this and other energy level crossings in correlation diagrams the order of molecular orbitals for a given n~oleculemust be determined by appeal to experiment. The adoption of the order u,2s < u.*2s < ~ , 2 p< u,2p < ~ , * 2 p< u,*2p appears to serve well the Lip through Fz sequence. To accompany the correlation diagram explanation a physical argument is used in which, as two identical atoms approach each other along the z axis, the p, orbitals interact more strongly than the degenerate p, and p, orbitals until, a t some smaller internuclear distance, the lateral overlap of p, and p, orbitals becomes more significant, and a corresponding decrease of the s.2p level below u,2p occurs. Throughout the discussion thus far the use of pure s and p functions in the formation of molecular orbitals has been stressed although there is no necessity to do so. Thus, it has been pointed out (4) that a satisfactory description of N2 is achieved if the molecular orbitals are constructed using hybridized atomic functions. Each nitrogen atom is assigned two hybrid orbitals formed by mixing the sand p, functions. As indicated in Figure 1 the hybrid 4, is composed of a large s contribution and lies above the s level of the isolated atom. Hybrid orbital @Z is principally p, in character and lies just below the atomic p level. Figure 1 further indicates that the interaction of 4, orbitals of the two atoms is much less significant than that of the 4%orbitals. Thus, the molecular orbital energy levels arising from 41 interact'ions are effectively degenerate (the inert pairs of the N2 molecule), but the energies of bonding and antibonding orbitals from @* interaction are widely separated. The short internuclear distance and the high bond strength of the N2molecule are thus rat,ionalized in the usual way as arising from one sigma and two pi bonds. The bonding characteristics of boron and carbon in their molecules and ions are invariably described, just as is done for nitrogen in its conlponnd substances, in terms of hybridized atomic orbitals. I t would thus appear reasonable and consistent to attempt the use of hybridization procedures for the B, and Cz molecules as
Table 2. Order and Occupancy of Molecular Orbitals for Second Row Homonuclear Diatomic Molecules
well. Because a variety of s-p hybrids has been employed in discussing boron and carbon in combination with other elements some flexibility is present in choosing the hybridiiation schemes to be applied to the Bz and Cz molecules.
bonds for which sp2 hybridization is associated with each carbon atom. The use of a splitting pattern, qualitatively similar to that employed for Bz, gives, on addition of the requisite number of electrons, a singlet ground state for the C? molecule. I t is important to note, in the description of these diatomic molecules, the nonequivalent character of the hybrid orbitals employed. As a result of the inequality of s and p contributions to the hybrids of any one of the three molecules, the characteristics of +I differ from those of +z;for the B2 (or Cp) molecule the two +2 orbitals are, of course, fully equivalent to each other.
;a Figure 1. Energy levels for Nn molecule using hybnd atomic orbitals. Columns 1 and 5 represent atomic orbitals d two N otomr, colvmnr 2 and 4 the atomic orbitals ofter hybridization, ond solvmn 3 the resulting molecular orbitoh.
Iu the case of the B2molecule the experimentally determined B-B bond length of 1.59 A (6) is significantly shorter than the B-B single bond distances of 1.67 and 1.75 A found in BzFa and BzClr, respectively (6). This shortening may be attributed to a high degree of s character in the atomic orbitals used in bond formation (7). Thus, in Figure 2, which represents an energy level diagram making use of trigonal hybridiiation, the +I function has an s character much greater than the 33% associated with the usual sp2 hybrid orbital, and a correspondingly smaller p character. The two degenerate hybrids will be oriented in such a way that their interactions with the corresponding & orbitals on the second boron atom will be weak. In other words, the smaller lobes of the corresponding +? orbitals of the two atoms will overlap each other a t a wide angle to the hond axis and the splitting of the resulting molecular orbitals, as shown in Figure 2, will be small. Using the aufbau principle it is seen that the addition of the correct number of electrons to the molecular orbitals results in two unpaired electrons for the -ground state configuration of the Bp molecule. For the C2 molecule the C-C distance of 1.24 is nerhans most commonlv associated with a double or triple carbon-carbon linkage. It is suggested that a high s orbital contribution to the +I orbitals, plus honding contributions from the molecular orbitals arising from +Z orbital overlap, result in substantial shortening of the 1.46 A length characteristic of carbon-carbon
Figure 2. tals.
Energy levels for 8%and Cs molecules wing hybrid atomic orbi-
That other hybridization schemes could be employed in discussing Bzand C?,andthat the O2and Fzmolecules may also be described using a hybridization approach (8),serve to emphasize the availability of alternative descriptions in qualitative molecular orbital treatments of these and other molecules. The usual procedure of invoking hybridized atomic orbitals for carbon, boron, and nitrogen in their compounds argues for continuing the practice in the case of these homonuclear diatomic molecules. By so doing, a bonding molecular orbital of sigma symmetry is consistently found to lie next above the antibonding n.*ls level for each of the second row homonuclear diatomic molecules. Literature Cited (1) BALLIK, E. A,, AND RAMSAY, D. A., Ast7ophysi~alJ . , 137,61 (1963). (2) ICYKOWSKI, R. P., A N D MARGRATE, J. L., J. Chem. Phys., 30, 403 (1957). (3) COULSON, C. A., "Valence," 1st ed., Oxford University Press, London, 1952, p. 92. (4) J A F F ~H. , H., AND ORCHIN, M., Telrahedron, 10, 212 (1960). A. E., AND HERZBERG, G., Can. J. Res., 18A, 165 (5) DOUGLAS, (1940). (6) TREFONAS, L., AND LIPSCOMB, W., J. Chem. Phus., 28, 54 (1958). (7) BENT,H., Chem. Reus., 61, 275 (1961), J. CHEM.EDUC.,37, 616 (1960). (8) JAFF*,H. H., AND ORCHIN, M., "Theory and Application of
Ultraviolet Spectroscopy," John Wiley and Sons, Ine., New York, 1962, p. 54.
Volume 42, Number 3, March 1965
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