Two-electron correlation: Diabatic states

The Schr\"odinger equation for two-electron systems is examined using hyperspherical coordinates. It is shown that the eigenvalues for the angular operator can be obtained through a variational principle. The definition of diabatic states is discussed and the transformation between adiabatic and diabatic states is found. The effect of the transformation on the off-diagonal elements of the interaction matrices U, P, and Q is examined. It is shown that the behavior of reduced density can be used to characterize the adiabatic states for $L=1$ along with the symmetry around α=π4. Also the effect of increasing the charge of the nucleus is examined.