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Transferability of Urey‐Bradley Force Constants. I. Calculation of Force Constants on a Digital Computer
1.The current literature has been summarized by Bellamy [The Infrared Spectra of Complex Molecules (Methuen and Company, Ltd., London, 1958)]. However, many more spectra and correlations exist in the working files of practicing spectroscopists; for example, our file at The Dow Chemical Company contains more than 12 000 spectra of pure compounds.
2.H. C. Urey and C. A. Bradley, Phys. Rev. 38, 1969 (1931).
3.D. F. Heath and J. W. Linnett, Trans. Faraday Soc. 44, 873 (1948).
4.T. Shimanouchi, J. Chem. Phys. 17, 245, 848 (1949).
5.T. Shimanouchi, J. Chem. Soc. Japan 74, 266 (1953).
6.H. C. Urey, Nature 181, 1458 (1958).
7.W. T. King, dissertation, University of Minnesota (1956).
8.J. C. Decius, J. Chem. Phys. 17, 1315 (1949).
9.Actually, because of the symmetrical nature of F it is necessary to take only indices.
10.In machine computation the advantage of molecular symmetry is not so much in the reduction of the order of the problem but rather in the fact that, once the observed frequencies have been separated into different species by inferrences from band shapes, depolarization ratios, etc., this separation may be retained throughout the calculation.
11.E. B. Wilson, Jr., J. Chem. Phys. 7, 1047 (1939).
12.Previous workers have used a Jacobian method to determine Urey‐Bradley force constants, but have used different approaches to obtain the J matrix. Miyazawa [J. Chem. Soc. Japan, Pure Chem. Sec. 76, 1132 (1955)] considers a variation ( in one of the UB force constants and through a matrix obtains (i.e., ) which is equivalent to a single element of (JZ) Mann, Shimanouchi, Meal, and Fano,13 obtained the Jacobian by a method similar to Miyazawa’s, but contrary to our practice, they did not redetermine the Jacobian for each refinement but merely at the beginning and before the final refinement. Curtis [dissertation, University of Minnesota (1959)] has independently developed a method of handling J exactly like ours with the exception that he prefers to express Z in symmetry coordinates, thereby sacrificing the convenience of assembling Z from standard submatrices with a computer.
13.D. E. Mann, T. Shimanouchi, J. H. Meal, and L. Fano, J. Chem. Phys. 27, 43 (1957).
14.J. H. Wilkinson, Proc. Cambridge Phil. Soc. 50, 536 (1954).
15.See, for example, the Decius tables of G‐matrix elements. E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw‐Hill Book Company, Inc., New York, 1955), p. 55 ff.
16.In a symmetrical molecule this complication arises when we wish to include complete sets of equivalent coordinates to carry the molecular symmetry through into the secular equation. However, even with molecules of lower symmetry we have found that inclusion of redundant coordinates improves the Urey‐Bradley force field: for example, in a study of the planar vibrations of the carbonyl halides we found it impossible to transfer force constants calculated from a force field which included only two of the angles around the carbon atom.
17.S. Califano (private communication).
18.B. L. Crawford and W. H. Fletcher, J. Chem. Phys. 19, 141 (1951);
18.Bryce L. Crawford, Jr., J. Chem. Phys. 20, 977 (1952)., J. Chem. Phys.
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