Experimental and Theoretical Study of Sigma‐Bond Electronic Transitions in Alkanes
1.W. J. Potts, J. Chem. Phys. 20, 810 (1952).
2.L. B. Clark, doctoral thesis, University of Washington, 1963.
3.E. E. Barnes, doctoral thesis, University of Washington, 1960.
4.We wish to thank Professor A. Novick for his generosity in loaning us this instrument.
5.This is shown to be consistent with the theory developed later in Appendix III.
6.S. Katagiri and C. Sandorfy [Theoret. Chim. Acta 4, 203 (1966)] have carried out Pariser and Parr type calculations on methane, ethane, and propane. They predict that there will be a collection of singlet‐singlet transitions, susceptible of being described as involving excitations in C‐H and C‐C bonds, and all having excitation energies in the range 70–90 kK (as observed). Actually, the particular parameterization they employ results in C‐H absorptions predicted as coming somewhat to the red of C‐C absorptions. It is not believed that this theoretical finding should be interpreted as constituting a serious objection to our interpretation, nor is it believed that the possible validity of our interpretation constitutes a serious objection to the broad conclusions which can be drawn from Katagiri’s and Sandorfy’s theoretical treatment.
7.Here, as with ethane, the C‐H absorptions were shifted 1 kK to the blue before being subtracted from the total alkane spectra.
8.J. A. Pople and D. P. Santry [Mol. Phys. 7, 269 (1964)], find that delocalization of electrons between geminal bonds (those emanating from a common center) is a consequence of the difference in energy between the 2s and 2p orbitals of carbon, and that delocalization between vicinal bonds (having no center in common) is obtained by introducing π‐type resonance integrals between nonbonded (in the usual valence structure) p orbitals on neighboring carbons. However, direct bonding between next‐nearest neighbor atoms tend to oppose the former effect, and the dominant effect should be the π‐type delocalization.
9.E. G. McRae and M. Kasha, Physical Processes in Radiation Biology (Academic Press Inc., New York, 1964), pp. 23–42.
10.In the absence of electron exchange between bonds, the anti‐symmetrization of Φ with respect to interchanges of electrons between bonds has no dynamical consequences and need not be carried out.
11.We choose the phases of the wavefunctions representing excitation in a bond such that β comes out negative.
12.H. H. Jahn and E. Teller, Proc. Roy. Soc. London A161, 220 (1937).
13.G. Herzberg and E. Teller, Z. Physik. Chem. (Leipzig) B21, 410 (1933).
14.R. Pariser and R. G. Parr, J. Chem. Phys. 21, 466, 767 (1953).
15.The same final results, as are obtained with the bond‐orbital description used here, can be obtained starting from a set of completely delocalized symmetry‐adapted molecular orbitals, related to the bond orbitals through a unitary transformation. The bond‐orbital approach, being easier to interpret at sight, brings out the connection between the independent‐systems and the molecular‐orbital descriptions of molecular systems.
16.The authors are indebted to Dr. M. T. P. Holden, who carried out the computation of the integrals over atomic orbitals using the program entitled DIATOM.
17.Here, and in several higher alkanes, the absorption bands overlap severely, resulting in shoulders and ill‐defined bumps. A thorough comparison of experiment and calculation is difficult to make. However, in all of the spectra reported here, the results from several exposures on several plates are represented, and their consistency indicates that all the features shown, such as the bumps at 79.5 and 82.5 kK in the pentane spectrum, are real and characteristic of the compounds.
18.R. D. Brown and V. G. Krishna, J. Chem. Phys. 45, 1482 (1966).
19.One question which must be asked is whether the observed transitions might not be all of the molecular Rydberg type. Attempts to fit the observed transitions into Rydberg series, with due regard to band overlapping and molecular perturbations, have failed to produce a reasonable assignment scheme applicable over the whole set of spectra.
20.By integrated intensity, we mean the area under the curve of ε vs logλ, as is conventional.
21.L. S. Bartell and D. A. Kohl, J. Chem. Phys. 39, 3097 (1963).
22.The dominant interactions are those between adjacent excitations, and are the same for all conformers. See also Ref. 17.
23.G. Herzberg, Molecular Structure and Molecular Spectra (D. Van Nostrand Co., Inc., New York, 1945), Vol. 2, pp. 344–345.
24.D. M. Humphries, A. D. Walsh, and P. A. Warsop, Discussions Faraday Soc. 35, 137 (1963).
25.K. G. Denbigh, Trans. Faraday Soc. 36, 936 (1940).
26.Atomic units are used in most of the general equations. However, we prefer to express transition‐moment lengths in angstroms and energies in kilokaysers when referring to results concerning definite molecules. As it turns out, one can use Eq. (A1) to caculate energies in kilokaysers if he places the factor 116 before the equation and expresses the distances in angstroms.
27.This procedure adapts itself readily to the use of scale drawings and models.
28.The molecular parameters assumed were 1.10 Å for the C‐H bond length and for the H‐C‐H bond angles.
29.The excitation is in or, roughly,
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