Nuclear permutational symmetry

Abstract When considering the work of Carl Ballhausen on vibrational spectra, it is suggested that his use of the Born-Oppenheimer approximation is capable of some refinement and extension in the light of later developments. A consideration of the potential energy surface in the context of a full Coulomb Schrodinger Hamiltonian in which translational and rotational motions are explicitly considered would seem to require a reformulation of the Born-Oppenheimer approach. The resulting potential surface for vibrational motion should be treated, allowing for the rotational motion and the nuclear permutational symmetry of the molecule. 

For homonuclear molecules, the initial and final rotational states must belong to the same ortho/para nuclear permutation symmetry. For example, in the H2(X1E+) —> (X2E ) +e photoionization transition, the even No and N+... 

However, even if this approach is regarded as giving a satisfactory account of chemical structure, it still remains to j ustify by full quantum mechanical means the treatment of the nuclei that it involves. But at present such a justification still eludes us. It may be in the future that the multiple well approach to nuclear permutational symmetry will be shown to be properly founded and thus the eigenvalues of the molecular Hamiltonian to be just those anticipated from the previous approach even so one will stUl be left with eigenfunctions which exhibit full permutation and rotation-inversion symmetry and it seems impossible to anticipate anything at aU like classical chemical structure from these using the standard quantum mechanical machinery. 

PERMUTATIONAL SYMMETRY AND THE ROLE OF NUCLEAR SPIN IN THE VIBRATIONAL SPECTRA OF MOLECULES IN DOUBLY DEGENERATE ELECTRONIC STATES ... 

IT. Total Molecular Wave Functdon TIT. Group Theoretical Considerations TV. Permutational Symmetry of Total Wave Function V. Permutational Symmetry of Nuclear Spin Function VT. Permutational Symmetry of Electronic Wave Function VIT. Permutational Symmetry of Rovibronic and Vibronic Wave Functions VIIT. Permutational Symmetry of Rotational Wave Function IX. Permutational Symmetry of Vibrational Wave Function X. Case Studies Lis and Other Systems... 

As pointed out in the previous paragraph, the total wave function of a molecule consists of an electronic and a nuclear parts. The electrons have a different intrinsic nature from nuclei, and hence can be treated separately when one considers the issue of permutational symmetry. First, let us consider the case of electrons. These are fermions with spin and hence the subsystem of electrons obeys the Fermi-Dirac statistics the total electronic wave function... 

The permutational symmetry of the rotational wave function is determined by the rotational angular momentum J, which is the resultant of the electronic spin S, elecbonic orbital L, and nuclear orbital N angular momenta. We will now examine the permutational symmetry of the rotational wave functions. Two important remarks should first be made. The first refers to the 7 = 0 rotational... 

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