for an electronic wave function is first solved to obtain for different values of . Es then plays role of a potential well in analysis of nuclear wave functions . Rotational energy levels The first term in the above nuclear wave function equation corresponds to kinetic energy of nuclei due to their radial motion. Term represents rotational kinetic energy of the two nuclei, about their center of mass, in a given electronic state Φs. Possible values of the same are different rotational energy levels for the molecule. Orbital angular momentum for the rotational motion of nuclei can be written as where is the total orbital angular momentum of the whole molecule and is the orbital angular momentum of the electrons. If internuclear vector R is taken along z-axis, component of along z-axis - Nz - becomes zero as Hence Since molecular wave function Ψs is a simultaneous eigenfunction of and , where J is called rotational quantum number and J can be a positive integer or zero. where . Also since electronic wave function Φsis an eigenfunction of , Hence molecular wave function is also an eigenfunction of with eigenvalue . Since and are equal, Ψs is an eigenfunction of Jz with same eigenvalue ±Λħ. As |J| ≥ Jz, we have . So possible values of rotational quantum number are Thus molecular wave function Ψs is simultaneous eigenfunction of , and . Since molecule is in eigenstate of Lz, expectation value of components perpendicular to the direction of z-axis (internuclear line) is zero. Hence and Thus Putting all these results together, The Schrödinger equation for the nuclear wave function can now be rewritten as where E′s now serves as effective potential in radial nuclear wave function equation. Sigma states Molecular states in which the total orbital momentum of electrons is zero are called sigma states. In sigma states . Thus . As nuclear motion for a stable molecule is generally confined to a small interval around where corresponds to internuclear distance for minimum value of potential , rotational energies are given by, with is moment of inertia of the molecule corresponding to equilibrium distance and is called rotational constant for a given electronic state . Since reduced mass μ is much greater than electronic mass, last two terms in the expression of are small compared to . Hence even for states other than sigma states, rotational energy is approximately given