Two-electron correlation: Diabatic states

The Schrödinger 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 $\mathit{U}$, $\mathit{P}$, and $\mathit{Q}$ is examined. It is shown that the behavior of reduced density can be used to characterize the adiabatic states for $L=1\mathrm{}$ along with the symmetry around $\alpha =\frac{\pi }{4}$. Also the effect of increasing the charge of the nucleus is examined.