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By August Chelkowski

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G. [7]) Finally it should be noted that on the formal variable change (23) it follows that: (40) where IQI is either plus or minus one according to whether Q corresponds to a proper rotation or to an improper rotation. 26 It is convenient first to derive a body-fixed expression for the space-fixed angular momentum operator as given by the second term on the right in (21). LW = -iIQICD {)1! A (41) There is at this stage an element of choice for the definition of the body-fixed angular momentum. In this work it will be chosen as (42) and with the aid of (31) it is possible to show that the components of the operators with this choice obey the standard commutation conditions.

The l-electron term in N L H may evidently be written as N = i=l L[L Err(i)]ii(i)[L Eu(i)] i=l r (50) N = L L l4>r(ri) < 4>rliil4>. (ri)1 i=l r,3 = L < 4>rl iil4>. > Er. r •• in which N Er. (i) (51) i=! is the usual symmetric sum of l-electron operators (now the generators of orbital rotations) while 16 hitself appears only within the numerical coefficient < 4>rlhl4>, >. The situation is analogous to that obtaining in Fock space and (51) is closely parallel to (23). s,t,u. This Hamiltonian contains only the unitary group generators (and their products) along with numerical parameters (1- and 2-electron integrals) which relate to the molecule studied and the choice of basis set: it provides a well-defined model of a chemical system and its exact eigenfunctions are attainable - corresponding to the full-CI or basis set limit.

Calar tripie products are also invariant. but they change sign under improper operations. Thi. and related matter. ed in [6J. 25 where the elements of (;t can be shown to be dependent on internal variables only using the fact that the qk can be written as functions of the scalar products of the 1i' Thus it is possible to write: (34) where 818':!!. and 8189. are column matrices of 3 and 3N - 6 partial derivatives respectively. ) to the 1. rom (23). Thus because the ~ cannot be functions of the 1!.

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