Quantitative electronic Lewis structure derived from nuclear coordinates of molecules:
Three Conformers of C12H26: Summary


Original computations: C12H26.nb, C12H26_1.nb, C12H26_2.nb
(ES  28 March/15/16 February 2019).
Structures from HF/6-31G(d,p) opt. Parameters: ~ Ethane. Rotations around C-C bonds; left is “normal”, all-anti conformer.

C12H26_all_1.gif
          

Comments:

1) The Kimball model results for these three conformers have been computed with the optimized coordinates of HF/6-31G(d,p) runs with Gamess™. These results are within very small error limits identical to the first principles computations, given below 5).
We have used parameters optimized for ethane. The parameters are the same for the three cases.

2) Among the energy (derived) values, the four categories Vtot, Ttot, Etot, and Vir show very small differences of a size and direction expected for such conformers. Compare to the values perpetrated in any text of Organic Chemistry for butane, staggered, gauche, eclipsed, a few kcal/mol. It turns out that the normal, staggered, “straight” hydrocarbon model with all-anti geometry has the highest stability. For the showcase butane the conformational energy changes are nearly local. If the rotation of two CH2-groups from anti to gauche happens in the middle of a larger hydrocarbon, dramatic changes happen. The molecular chain after the rotation bends slightly back on the part before the rotation and changes the potential energy to a large extent “through space”. As example, the picture, below left, is a projection on the xy-plane of a straight C12H26 molecule with one gauche CH2-pair. The red insert shows the chain after a rotation of 120° between the 6th and 7th CH2 groups around the pivot C-C bond depicted in green. The red half protrudes into the z-direction, of course, as the Newman projection in the zy plane, right, shows.
C12H26_all_2.gif     C12H26_all_new_3.gif
3) These changes manifest themselves differently in the components Vee, Vnn, and Vne. While the first two increase, the latter decreases such that the total change adds up to nearly zero. But the not compensated rest is comparable to the total conformational energy change. Hence, this is not only a local effect as the showcase butane suggests. I do not know of any chemistry text which mentions these effects. They are a clear indication that the chemist’s local interpretation of chemical bonding falls short: From the straight C12H26 hydrocarbon on top of the first page, left, to the most perturbed conformer, right, the nuclear repulsion energy Vnn increases by 10%, ~ +42’000 kcal/mol, Vee by 7.9%, ~ +41’000 kcal/mol, while Vne decreases nearly by the sum of these values, ~ -83’000 kcal/mol!

4) The total, minute, energy changes make such conformation conversions thermally possible, even near standard temperature. But, there is a huge reshuffling of energy components connected to it. In order to show that this is not an artifact of Kimball’s model, the next paragraph summarizes first principles quantum chemical computations of the same three molecules, which  exhibit the same changes in the potential energy components. Chemical consequences, if there are, will be described elsewhere.

5) HF/6-31G(d,p) optimized results for comparison with Kimball:

               1:           ONE ELECTRON ENERGY =   -1966.7241588161
                            TWO ELECTRON ENERGY =     824.7226234605
                       NUCLEAR REPULSION ENERGY =     672.3858266897
                                                  ------------------
                                   TOTAL ENERGY =    -469.6157086659
             
             ELECTRON-ELECTRON POTENTIAL ENERGY =     824.7226234605
              NUCLEUS-ELECTRON POTENTIAL ENERGY =   -2436.1402405026
               NUCLEUS-NUCLEUS POTENTIAL ENERGY =     672.3858266897
                                                  ------------------
                         TOTAL POTENTIAL ENERGY =    -939.0317903524
                           TOTAL KINETIC ENERGY =     469.4160816865
                             VIRIAL RATIO (V/T) =       2.0004252666
-            -------------------------------------------------------
               2:           ONE ELECTRON ENERGY =   -2056.6313621553
                            TWO ELECTRON ENERGY =     869.6918869887
                       NUCLEAR REPULSION ENERGY =     717.3331909000
                                                  ------------------
                                   TOTAL ENERGY =    -469.6062842665
             
             ELECTRON-ELECTRON POTENTIAL ENERGY =     869.6918869887
              NUCLEUS-ELECTRON POTENTIAL ENERGY =   -2526.0345885471
               NUCLEUS-NUCLEUS POTENTIAL ENERGY =     717.3331909000
                                                  ------------------
                         TOTAL POTENTIAL ENERGY =    -939.0095106583
                           TOTAL KINETIC ENERGY =     469.4032263918
                             VIRIAL RATIO (V/T) =       2.0004325873
-            -------------------------------------------------------
               3:           ONE ELECTRON ENERGY =   -2099.6911705290
                            TWO ELECTRON ENERGY =     891.2365886585
                       NUCLEAR REPULSION ENERGY =     738.8595684708
                                                  ------------------
                                   TOTAL ENERGY =    -469.5950133997
             
             ELECTRON-ELECTRON POTENTIAL ENERGY =     891.2365886585
              NUCLEUS-ELECTRON POTENTIAL ENERGY =   -2569.0813383356
               NUCLEUS-NUCLEUS POTENTIAL ENERGY =     738.8595684708
                                                  ------------------
                         TOTAL POTENTIAL ENERGY =    -938.9851812063
                           TOTAL KINETIC ENERGY =     469.3901678066
                             VIRIAL RATIO (V/T) =       2.0004364079
 

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