Librations of hybridization tetrahedra

The terms of this type must be summed over all bonds between the heavy atoms. The formulae eqs. (3.100), (3.101) represent the potential energy of the molecular system as a quadratic function on small variations of the variables wf. This may be used either in a frame of a linear response analysis of reaction of the system of hybridization tetrahedra to various perturbations or (if the hybridization tetrahedra are supplied by fictitious inertia momenta) as potential energy of the system of the tetrahedra in a frame of a Car-Parinello-like [46] procedure. 

The interaction of the neighbor hybridization tetrahedra is particularly simple if the tetrahedra involved correspond to the sp3 hybridized atom with equivalent bonds. In this case the HOs in the equilibrium are collinear with the bond vectors so that the 3x3 matrix in eq. (3.101) becomes  

The above formulae are modified in the NDDO parametrization where the librations of the hybridization tetrahedra of nonbonded atoms also couple through the electrostatic forces acting between corresponding multipoles. 

---