2.Approximate Treatment of the H2" Trial function: Consider a limiting behavior of the H2*ground-state electronic wave function as R approaches p=CalSa +CplSp (7.16) -e-n When R goes zero,we get the He'ion,which has the ground-state wave function(Z=2) 2 1\π (7.17) Note that at the R=0the trial function(7.16)goes to (G+c2) e V Comparing with (7.17),we see that (7.16)has the wrong limiting behavior at R =0.We can fix things by multiplying ra and ro in the exponentials by a variational parameter k=k(R).For correct limiting behavior at zero and infinite internuclear distance,we have K(0)=2,k(oc)=1 We thus take as the trial function 0=Ca功sa+C691sb (7.18) where k 4π -e-kn (7.19)2. Approximate Treatment of the H2 + Trial function: Consider a limiting behavior of the H2 + ground-state electronic wave function as R approaches ∝. a a b b ϕ = c 1s + c 1s (7.16) a br b r a s e s e − − = = π π 1 , 1 1 1 When R goes zero, we get the He+ ion, which has the ground-state wave function (Z=2) r e 2 3 2 − π (7.17) Note that at the R = 0 the trial function (7.16) goes to r c c e− + π 1 ( ) 1 2 . Comparing with (7.17), we see that (7.16) has the wrong limiting behavior at R = 0. We can fix things by multiplying ra and rb in the exponentials by a variational parameter k = k(R). For correct limiting behavior at zero and infinite internuclear distance, we have K(0) = 2, k(∝) =1 We thus take as the trial function a sa b sb c c ϕ = φ1 + φ 1 (7.18) where a b kr sb kr sa e k e k − − = = π φ π φ 3 1 3 1 , (7.19)