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In general the <Pi's mayor may not be the united-atom potentials. Their choice is dictated by the rapidity of convergence and the ease of the ensuing calculation. The most convenient choices are Coulomb and Hooke's law potentials; the corresponding WOO's are then, respectively, hydrogenic and Hermite functions. In the expansion in terms of WOO's, there exist in the secular determinant only three types of integrals: kinetic energy, nuclear attraction, and one-center electron repulsion integrals. Their evaluation (at least for hydrogenic or Hermite functions) is relatively uncomplicated. Problems of polycentric integrals naturally do not arise. The alternate expansion, in terms of \{fo, is superior in several respects. For well-chosen Coulomb potentials the EO's are just atomic (or ionic) term values where the electron repulsions are already minimized. Excellent tables' are available, enabling detailed calculations in restricted cases, including that in which the <p;'s are the true united-atom potentials. This semiempirical method is expected to converge faster than the corresponding ab initio calculation with the same <p;'S. 6 The true ¥'s are, of course, unknown, but adequate approximations can be had in terms of, for example, Hartree-Fock, Morse-Young-Haurwitz6 and even nodeless Slater orbitals. Only one type of integral, the nuclear attraction integrals, needs to be evaluated here. An added feature is that, since the electron repulsion terms are already incorporated in HO, it is unnecessary to write antisymmetric determinantal wave functions, i.e., products of orbitals obeying naively the exclusion principle will do. The choice of <p;, however, is limited in the semiempirical method because of existent data. For instance, the best choice for H2 is not the united-atom (He) potential, but that of the Hion; yet of the latter we have little knowledge beyond the ground state. The semiempirical method is most fruitful for problems of electronic spectra, where the absolute location of the ground state is unimportant. Otherwise, a more extensive table of ionization potentials would be required than is available. Nuclear attraction integrals up to (a 13do3do) are being evaluated with Slater orbitals of nonidentical exponents for 31 nuclear separations to 8 digit accuracy. The results will soon be published with applications.' The writer wishes to thank Professor Hertha Sponer for her interest and encouragement. * Supported by Duke University Research Council. 1 P. M. Morse and E. C. G. Stueckelberg, Phys. Rev. 33, 932 (1929). 2 F. A. Matsen, J. Chern. Phys. 21, 928 (1953). 3 R. D. Brown and F. A. Matsen, J. Chern. Phys. 21, 1298 (1953) . • Atomic Energy Levels compiled by Mrs. C. Moore (National Bureau of Standards, Washington, D. C.), two volumes in print. , This is analogous to the method of "atoms in molecules" of W. Moffitt [Proc. Roy. Soc. (London) A2l0, 245 (1951) ] but used in a different context. 6 Morse, Young, and Haurwitz, Phys. Rev. 48, 948 (1935). 7 After the completion of the first draft of the present note, the writer learned that Dr. R. K. Neshet has programmed the MIT Whirlwind computer to evaluate all free atom one-center integrals involving Slater orbitals, and Dr. L. C. Allen and Dr. R. K. N esbet together have independently developed an ab initio one-center method which is, however, different in emphasis from ours. See Quarterly Progress Report, Solid-State and Molecular Theory Group, MIT. July 15, 1955, pp. 27-29. The writer is indebted to Dr. Robert K. Nesbet for advance information.

Concentration Dependence of Solvent Shift in the C–H (and C–D) Stretching Frequencies of Chloroform and Pentachloroethane