Abstract
The semiclassical determination of N(E;J) and ρ(E;J), the specific number and density of quantum states at energy E, and fixed total angular momentum J, by Monte Carlo integration of phase space is compared to recent exact quantum calculations on H+3 and HD+2, which yielded lists of up to 900 quantum states for single values of J. This allows for the first time tests of such a procedure to be made without assuming anything about separability or harmonicity of the potentials. The excellent agreement between semiclassical and quantum state counts shows that the semiclassical numerical computation is a viable and simple method for the determination of state numbers and densities in small molecules with a precision of the order of 1%. For J=0, the procedure has been extended to state numbers for the different symmetry species occuring in H+3 and HD+2.
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