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The series expansion for the zero-point energy of a system of harmonic oscillators derived by BIGELEISEN and GOLDSTEIN has been examined in detail. The convergence properties have been tested as a function of the reduced frequency, and the error produced in truncating the series has been found. Calculations of zero-point energy sums by solving the secular equations for isotopically substituted series of hydrogen, methane, ethylene, ethane, and benzene molecules have been made and the results are discussed in terms of the first- and second-order isotope sum rules.

Note on the Calculation of Zero-Point Energies and Isotopic Zero-Point Energy Differences by a Taylor's Series Expansion