Quantum mechanical oscillator strength sumsSlpar;krpar;are used to find rigorous upper and lower bounds to van der Waals coefficients for twohyphen; and threehyphen;body interactions and to the sums themselves. It is shown that any two sums of any multipole order give a bound to any other sum and either a bound or an estimate for the like force constant for that multipole. An average energy function is defined in terms of the sums; a particular limiting case of this function gives an excellent approximation for force constants (rms deviation for 19 cases: 0.25percnt;) and depends solely on the value and slope ofSlpar;krpar;atkthinsp;equals;thinsp;minus;thinsp;2. The results are tested on data for 18 dipole cases: H, He, Ne, Ar, Kr, Xe, Li, Na, K, Rb, Cs, Hg, H2, N2, CH4, He(21S), He(23S), Heplus;; and 1 quadrupole case: H.
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