Hydrogen molecule true wave function

For hydrogen, the Ramsey theory is relatively easy to apply, but, as we see in Section 4.5, external perturbations from neighboring functional groups and solvent molecules are of comparable magnitude to the basic electronic terms, so that the theory is quantitatively of little practical value. For other nuclei, this theory could predict chemical shielding rather accurately if we had true wave functions and knowledge of the energies of all excited states. In practice, approximations must be made, but acceptable results can be obtained provided some fundamental aspects are kept in mind. 

This leads to a very bad description of the H2 molecule at long internuclear distances with the Hartree-Fock method. The true wave function should contain, among other things, both the covalent structure (i.e. the Heitler-London function) and the ionic structures. However, for long internuclear distances the Heitler-London function should dominate, because it corresponds to the (exact) dissociation limit (two ground-state hydrogen atoms). The trouble is that, with fixed coefficients, the Hartree-Fock function overestimates the role of the ionic stmcture for long interatomic distances. Fig. 10.4 shows that the Heitler-London function describes the electron correlation (Coulomb hole), whereas the Hartree-Fock function does not. 

The true meaning of both quantum and relativity theories, which has been demonstrated [1] to emerge only in four-dimensional formalism, has serious implications for the three-dimensional theories of atomic and molecular structure. Nonclassical attributes of atomic matter, such as electron spin, are associated with four-dimensional hypercomplex functions, known as quaternions, and cannot be accounted for by classical three-dimensional models, which include wave mechanics as traditionally formulated. The notorious failure of quantum chemistry to model the structure of non-hydrogen atoms and molecules is a manifestation of the same problem. The awareness that atomic and molecular structures are classical three-dimensional concepts dictates the use of classical rather than four-dimensional quantum models for their characterization. 

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