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/631G(d,p) opt. Parameters: ~ Ethane. Rotations around CC bonds; left is “normal”, allanti conformer.
Comments:
1) The Kimball model results for these three conformers have been computed with the optimized coordinates of HF/631G(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 allanti geometry has the highest stability. For the showcase butane the conformational energy changes are nearly local. If the rotation of two CH2groups 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 xyplane of a straight C12H26 molecule with one gauche CH2pair. The red insert shows the chain after a rotation of 120° between the 6th and 7th CH2 groups around the pivot CC bond depicted in green. The red half protrudes into the zdirection, of course, as the Newman projection in the zy plane, right, shows. 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/631G(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
ELECTRONELECTRON POTENTIAL ENERGY = 824.7226234605
NUCLEUSELECTRON POTENTIAL ENERGY = 2436.1402405026
NUCLEUSNUCLEUS 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
ELECTRONELECTRON POTENTIAL ENERGY = 869.6918869887
NUCLEUSELECTRON POTENTIAL ENERGY = 2526.0345885471
NUCLEUSNUCLEUS 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
ELECTRONELECTRON POTENTIAL ENERGY = 891.2365886585
NUCLEUSELECTRON POTENTIAL ENERGY = 2569.0813383356
NUCLEUSNUCLEUS POTENTIAL ENERGY = 738.8595684708

TOTAL POTENTIAL ENERGY = 938.9851812063
TOTAL KINETIC ENERGY = 469.3901678066
VIRIAL RATIO (V/T) = 2.0004364079
