Quantum number, azimuthal rotational

The wavefunctions corresponding to the motion of a particle on the surface of a sphere are known as spherical harmonics. The mathematical form that they take depends upon two quantum numbers the first is ntp and the second is the azimuthal quantum number /. The rotational kinetic energy of the particle is quantized according to the equation ... 

The functions, here occurring in standard order, are our standard basis functions for the real irreducible representations of the full three-dimensional rotation-reflection group, Rg x I, and for its subgroups, Aoft. and Coo . All functions are normalized to 4nj(2l- -1), where / is the azimuthal quantum number. 

In order to preserve the invariance of charge distributions under rotation of the local coordinate axes of each atom, the integrals K% eSPq and (pp qq) are assumed to be independent of the azimuthal quantum number of atomic orbitals, i.e. the same value is used for any 2 s and 2 p orbitals. Finally, it should be noted that in the case of a electrons the zero-differential-overlap approximation cannot be justified as completely as for n electrons by arguing about orthogonalized Lowdin orbitals, because the expression of the S la matrix cannot be limited to first-order terms 70,71,72). 

We have replaced the rotational quantum number J by /, since this is the usual notation in atomic systems. The quantum number / is called the azimuthal quantum number and characterizes the total angular momentum of the atom,... 

We have two atoms with m and m electrons respectively their azimuthal quantum numbers are / and their character on reflection w and to, and their partitions z and z. We put r and r for — z and m — z (the r s then mean something like the core momentum). Our task consists in that we want to know the terms of the molecule for fixed nuclei (electronic terms) which result from these atoms by adiabatically uniting the nuclei, i.e. their representation char2u teristics under permutation of the electronic centres of mass and reflection-rotation about the Z-axis. The spin-free eigenfunctions of the atoms are and wherein the index C distinguishes between the ( ) — (Jli) eigenfunctions that belong to the partition z. 

---