Results of H2 molecule Hamiltonian expectation value calculation with symmetric space and ant-symmetric space wavefunctions.
This is covered in pages 341-345, section 8.4 Hydrogen Molecule, in Griffiths 3rd Edition.

Df[x_]:=1/x-(1+1/x) Exp[-2 x]

Xf[x_]:=(1+x) Exp[-x]

Iff[x_]:=(1+x+(1/3) x^2) Exp[-x]

D2[x_]:=1/x-(1/x +11/8 + (3/4) x +(1/6) x^2) Exp[-2 x]

Itwid[x_]:= (1-x+(1/3) x^2) Exp[x]

X2[x_]:= Exp[-2 x] (5/8-(23/20) x -(3/5) x^2 - (1/15) x^3) + (6/(5 x)) Iff[x]^2 (EulerGamma + Log[x] + (Itwid[x]/Iff[x])^2 ExpIntegralEi[-4 x] - 2 (Itwid[x]/Iff[x]) ExpIntegralEi[-2 x])

HPlusbyE1[x_]:= 2(1-1/x+((2 Df[x]-D2[x]+(2 Iff[x] Xf[x]-X2[x]))/(1+Iff[x]^2)))

HMinusbyE1[x_]:= 2(1-1/x+((2 Df[x]-D2[x]-(2 Iff[x] Xf[x]-X2[x]))/(1-Iff[x]^2)))

Plot[{-HPlusbyE1[x], -HMinusbyE1[x]}, {x,0.5,6}, AxesOrigin->{0,-2}, PlotStyle->{Green, Red}]

Plot[{-HPlusbyE1[x], -HMinusbyE1[x]}, {x,0.4,6}, AxesOrigin->{0,-2}, PlotRange->{-2.5,-0.1}, PlotStyle->{Green, Red}]