Question

(14 points) Write Slater determinants for all possible spin states of the first excited state of He (one electron in the 1s orbital, the other in the 2s orbital). Indicate the S (sum of all e spins) and Ms (vector sum of e spins) values of the corresponding wavefunctions. Evaluate the Slater determinants to obtain the total wavefunctions we wrote in class. Hint: The wavefunctions with σ (1,2) and σ (1,2) require two Slater determinants to correctly represent them.

Answer 1

First excited state of H e dividedby 2 H e rightarrow 1 s^2 L = l_1 + l_2 = 0 s_1 = s_2 = 1/2 s = 1 (spins, parallel) s = 0 spins, paired Excited state (a) when spin are paired (s = 0), (T = 0) Term symbol �s_0 (singlet) (b) when spin are parallel (s = 1), (J = 1) Term symbol: 3_s_1 (Triplet) For H e value of s o M_s rightarrow rightarrow 0 s o M_s = plusminus 1/2 =_(+ 1/2) (- 1/2) = 0 slater determinant dividedby Wave function (Psi) Wave function Psi = Vertical-bar 1s (1) alpha (1) 1s (1) beta (1) 1s (2)alpha (2) 1s (2) beta (2) 1s (3) alpha (3) 1s (3) beta (3) 1s (4) alpha (4) 1s (4) beta (4) Vertical-bar The diagonal of the determinant is H e = 1s alpha (1) 1s beta (1)