Hydrogen atom overlap integral

In order to obtain nonzero spin densities even on hydrogen atoms in tt radicals, one has to take the one-center exchange repulsion integrals into account in the eigenvalue problem. In other words, a less rough approximation than the complete neglect of differential overlap (CNDO) is required. This implies that in the CNDO/2 approach also, o and n radicals have to be treated separately (98). 

In a Mulliken population analysis, the electron density of the overlap terms is equally divided between the two atoms. Since the overlap integrals S(2s F)(lsH) and S(2phydrogen atom is positively charged. 

It is conventional to label the internuclear axis in a diatomic molecule as z. Thus the three 2p(F) orbitals can be labelled 2p, 2py and 2p2 2px and 2py have their lobes directed perpendicular to the internuclear axis, and have nodal surfaces containing that axis, while 2pr clearly overlaps in o fashion with ls(H). (The reader may wonder whether this orientation of 2p, 2py and 2pz is obligatory, or whether it is chosen for convenience. For a spherically-symmetric atom, there are no constraints in choosing a set of three Cartesian axes. Any set of orthogonal p orbitals can be transformed into another equally acceptable set, by a simple rotation which does not change the electron density distribution of the atom. The overlap integral between a hydrogen Is orbital and the set of three 2p(F) orbitals is the... 

A small proton polaron is different in some aspects from the electron polaron that is, the hydrogen atom is able to participate in the lattice vibrations in principle (in any case it is allowable for excited states see Section II.F), but the electron cannot. This means that one more mechanism of phonon influence on the proton polaron is quite feasible. That is, phonon fluctuations would directly influence wave functions of the protons and thereby contribute to the overlapping of their wave functions. In other words, phonons can directly increase the overlap integral in concept. Such an approach allows one to describe the proton transfer without using the concept of transfer from site to site through an intermediate state. 

---