Atomic multiplets are treated by wave mechanics, without using group theory. In part 1 Hund's scheme for multiplet classification is derived directly from theory. Part 2 is devoted to the computation of the energy distances between multiplets, and comparison of these distances with experiment in some typical examples. There is no treatment of the separations between the various terms of a multiplet, since that has been done elsewhere, but only between one multiplet and another. It is found that Hund's rule, that terms of large L and S values lie lowest, has no general significance; the present theory leads to the same results as the rule when it is obeyed experimentally, but many cases which were exceptions to that rule are in agreement with the theory. The method of calculation of multiplet distances is described in sufficient detail, with the necessary tables of coefficients, etc., so that further checks with experiment could easily be made.