Ethene computed

Three (small) variations:
  • Ethene with two C(pz) "orbitals", overlapping for π-bond. The pz are localized above each C core, perpendicular to the xy-plane containing the nuclei. The structure is near the experimental values except for the HCH angle, that is a bit over 120° instead of 117°. No adjustments brings this down.
  • Same as above, but pz orbitals are forced slightly towards the center of the C-C σ-bond. This creates an HCH angle of 116°. However, this model does not give exactly 2.000... for the virial ratio, indicating that it is not at an exact energy minimum. If the x distance away from the C-cores is input as additional variable, the minimization undoes it to zero.
  • Ethene with fused C(pz), centered on C-C σ-bond. This model spontaneously assumes an HCH angle of 117.25° without adjustments. It is a relaxed energy minimum structure with zero Hellmann-Feynman forces, and actually the same as Perego's ethene with slightly different parameters.

    • That's the final, relaxed, version you were asked to produce. Hope, your result is the same! This Class is now over. If you have constructed bananas, too bad! - don't wait to eat them.

    I forget to attach the solution for B2H6. Can you furnish it ?
    As of June 08, 2013, nobody has done this homework. I come to the conclusion, that either nobody has read this site to this rather hidden corner, or that (s)he has not been interested, or not motivated to do a little exploration beyond styrofoam Kimball or even Bent TS models of pure fantasy without scientific justification nor value.
    So here is my solution or its CDF and two projections of the computed model. The protonated "double bonds" must overlap! Shame to HAB! Otherwise no reasonable molecule is possible.


    This is in accord with an MP2/6-31G(d) optimization. The NBO-7 = HOMO-1 clearly shows the accumulation of charge in the B-B axis:


    or the same (Kohn-Sham) orbital from a CPMD 3.15.3 computation:



    It is very interesting that the new approach of Su and GoddardIII (2009) with FSGO's and using their program eFF (J.Su & W.A.Goddard III, JCP 131,244501(2009), Fig. 13), left model, leads to a similar molecular construct as the Kimball result, right: