Okay, let's tackle at least one problem here. Consider the rotation of 1,2-dichloroethane (BP86/cc-pVDZ):
![rotation of dichloroethane][1]
These conformational changes can be further rationalised:
- **C** and **C'** are the same conformation, since these are mirror images.
- The same applies to **B** and **B'**.
- **A** and **C** are local minima and can be referred to as *conformes* in the above given way
- **B** and **D** are transition states - they are not stable.
If you consider the rotation **A** to **C** as a reaction, this state would mark the maximum energy needed for the conversion. I believe with *reactions* it is meant, that an accurate description of the transition state by InChI is not possible.
----------
For the term non-local chirality I suggest you look at [BINAP][2] or [BINOL][3].
![structure of BINAP][4]
In this case I have used a slightly abridged version of BINAP for educational purposes, where $\ce{Ph -> Me}$.
![R-BINAP][5] ![S-BINAP][6]
Other wonderful examples of non-local chirality include [helicenes][7], which have helical chirality. Here is one example of a fancy [azonia derivative of hexahelicene][8] ([parent compound and links][9]). The structure is available at the [Cambridge Crystallographic Data Centre (CCDC) Database][10]. I removed the anion and converted it to xyz coordinates which I include in the appendix. Here are the structures, left *P*-chirality, right *M*-chirality:
![scheme of 8a-azonia[6]helicene][11]
![P-8a-azonia[6]helicene][12]![M-8a-azonia[6]helicene][13]
On another account of non/local chirality, there is the planar chirality, as can be seen in *trans*-[Cyclooctene][14] (the bottom two). For further reading I suggest [Neuenschwander *et.al.* "The Conformations of Cyclooctene: Consequences for Epoxidation Chemistry."][15]
![Structures of cyclooctene][16]
----------
[Markush Structures][17] are a kind of summary structure for certain compound classes. A very simple example would be a monosubstituted biphenyl system, where the upper structure is a representation of all three below. However, it is noteworthy, that each instance of a Markush structure can be well explained by InChI.
![biphenyl markush structure][18]
More complicated structures are often used in patents and in other scientific publications, usually specifically referring to a very general procedure or mechanism. I found one on wikipedia commons, that could well represent a million molecules:
![markush structure][19]
----------
And another way to break the InChI are [clusters][20]. Although the definition is not very specific, the $\ce{[KO{}^{\mathit{t}}Bu]_4}$ tetramer ([wikipedia][21], [chemspider][22]) certainly contains one. While the monomer can be described via InChI, the tetra- or Polymer should fail. It was published by [Chisholm *et.al.* in Polyhedron][23] and the `*.cif` file can be obtained from CCDB. I cleaned it up a little bit and included the `*.xyz` in the appendix. You can quite nicely see the $\ce{K4}$ tetrahedral cluster in the middle (hydrogens omitted for clarity).
![molecular structure of the potassium butoxide tetramer][24]
----------
Last but not least, I'd like to cover the matter of complicated organometallic molecules. As such I'd like to introduce the [Grubbs' catalysts][25]. [Grubbs][26] obtained the [Nobel Prize in Chemistry 2005][27] for his research in conjunction with Yves Chauvin and Richard R. Schrock. One of the key publications was ["Ring-opening metathesis polymerization (ROMP) of norbornene by a Group VIII carbene complex in protic media"][28]. The crystal structure can also be obtained at CCDC. Another example stems from "[Synthesis and Applications of $\ce{RuCl2(=CHR')(PR3)2}$: The Influence of the Alkylidene Moiety on Metathesis Activity][29]" and is also available via CCDC. This structure can also be found in the appendix. It is generally known as a 1st generation Grubbs catalyst (Hydrogens omitted for clarity).
![scheme of Grubbs I][30]![molecular structure of Grubbs I][31]
----------
#Appendix
The following section contains the nuclear coordinates in `*.xyz`(XMol) file format and angstroms as unit. (If not denoted otherwise, structures are obtained at BP86/cc-pVDZ.)
1,2-dichloroethane **A**
C 0.000000000 0.000000000 0.000000000
C 0.000000000 0.000000000 1.521307000
Cl 1.723641000 0.000000000 -0.593797000
H -0.486731000 -0.904743000 -0.410753000
H -0.486731000 0.904743000 -0.410753000
Cl -1.723641000 0.000000000 2.115104000
H 0.486731000 -0.904743000 1.932060000
H 0.486731000 0.904743000 1.932060000
1,2-dichloroethane **B**
C 0.030242000 0.085780000 -0.007620000
C -0.030242000 0.085780000 1.528927000
Cl 1.518312000 -0.758527000 -0.631286000
H -0.837191000 -0.442465000 -0.444148000
H 0.070555000 1.115212000 -0.412109000
Cl -1.518312000 -0.758527000 2.152593000
H 0.837191000 -0.442465000 1.965455000
H -0.070555000 1.115212000 1.933416000
1,2-dichloroethane **C**
C 0.066377000 0.127741000 0.004558000
C -0.066377000 0.127741000 1.516749000
Cl 1.083384000 -1.241726000 -0.615213000
H -0.919786000 0.050600000 -0.492443000
H 0.568277000 1.063384000 -0.317636000
Cl -1.083384000 -1.241726000 2.136520000
H 0.919786000 0.050600000 2.013750000
H -0.568277000 1.063384000 1.838943000
1,2-dichloroethane **D**
C 0.164887000 0.141535000 -0.000240000
C -0.164887000 0.141535000 1.521547000
Cl 0.337146000 -1.473219000 -0.795160000
H -0.633932000 0.666019000 -0.558099000
H 1.123149000 0.665665000 -0.177529000
Cl -0.337146000 -1.473219000 2.316468000
H 0.633932000 0.666019000 2.079406000
H -1.123149000 0.665665000 1.698836000
***R*-BINAP**
C -0.086423000 -0.055821000 -0.031546000
C -0.090885000 -0.047699000 1.480085000
C 1.148913000 -0.158515000 2.237313000
C 1.064686000 -0.139089000 3.676951000
C -0.131097000 -0.014450000 4.357670000
C -1.357362000 0.116010000 3.652970000
C -1.345263000 0.107319000 2.211098000
P 2.768926000 -0.321256000 1.451350000
H 1.988600000 -0.233144000 4.265654000
H -0.135982000 -0.008251000 5.459401000
C -2.590782000 0.269421000 4.370415000
C -2.623021000 0.305506000 1.559779000
C 0.437392000 1.073619000 -0.788457000
C 0.410661000 0.991852000 -2.228054000
C -0.079670000 -0.105834000 -2.908992000
C -0.579162000 -1.233570000 -2.204534000
C -0.579999000 -1.219208000 -0.762676000
P 1.107602000 2.557133000 -0.001640000
H 0.790955000 1.839345000 -2.816335000
H -0.077540000 -0.112552000 -4.010726000
C -1.063317000 -2.378355000 -2.921905000
C -1.047368000 -2.424579000 -0.111239000
C -3.792005000 0.431032000 3.705083000
H -2.558632000 0.263827000 5.471798000
H -4.735477000 0.552772000 4.258523000
C -3.797353000 0.457087000 2.279022000
H -2.662047000 0.340912000 0.466043000
H -4.750761000 0.602046000 1.748556000
C -1.503463000 -3.517255000 -0.830391000
H -1.036094000 -2.475958000 0.982488000
H -1.854657000 -4.415344000 -0.299810000
C -1.523650000 -3.499569000 -2.256520000
H -1.052652000 -2.347534000 -4.023279000
H -1.890198000 -4.377463000 -2.809877000
C 4.061075000 -0.509159000 2.730645000
C 2.844045000 -1.846744000 0.446017000
C 1.585856000 3.772639000 -1.280334000
C -0.173490000 3.383258000 1.008127000
H 0.254332000 4.289560000 1.485098000
H -1.067700000 3.703930000 0.418133000
H -0.532498000 2.717241000 1.815764000
H 1.997887000 4.670081000 -0.777298000
H 2.377005000 3.362349000 -1.938832000
H 0.749130000 4.118465000 -1.941170000
H 5.044249000 -0.601334000 2.227532000
H 4.100503000 0.383637000 3.385840000
H 3.944572000 -1.404262000 3.395364000
H 3.842692000 -1.931312000 -0.030903000
H 2.674387000 -2.779210000 1.039384000
H 2.087489000 -1.826871000 -0.361580000
***S*-BINAP**
C -1.383946000 -3.448543000 -2.256996000
C -1.065989000 -2.266144000 -2.910129000
C -0.652376000 -1.110469000 -2.179491000
C -0.563545000 -1.177237000 -0.738280000
C -0.899026000 -2.413534000 -0.098700000
C -1.299620000 -3.519323000 -0.838209000
C -0.154302000 -0.008671000 0.004167000
C 0.166467000 1.182512000 -0.673969000
C 0.072046000 1.221328000 -2.098779000
C -0.323252000 0.113168000 -2.831301000
C -0.061735000 -0.093981000 1.507135000
C -1.110430000 0.372113000 2.322674000
C -0.989013000 0.267385000 3.742090000
C 0.132224000 -0.289631000 4.336601000
C 1.210137000 -0.777916000 3.542877000
C 1.113248000 -0.682564000 2.103804000
C 2.206553000 -1.174312000 1.320794000
C 3.329975000 -1.726929000 1.922868000
C 3.419059000 -1.820539000 3.340084000
C 2.377998000 -1.353835000 4.130094000
P -2.590653000 1.186493000 1.502738000
C -3.750658000 -0.293139000 1.402088000
P 0.636241000 2.692004000 0.339668000
C 2.511918000 2.555623000 0.253510000
C -3.385046000 2.079953000 2.947654000
C 0.388676000 4.078351000 -0.898992000
H -1.802841000 0.635802000 4.383638000
H 0.202504000 -0.360978000 5.434128000
H 0.319305000 2.150696000 -2.632672000
H -0.386992000 0.166196000 -3.930250000
H 2.436377000 -1.419019000 5.228476000
H 4.313241000 -2.262708000 3.805535000
H 2.146133000 -1.110484000 0.224695000
H 4.157224000 -2.097887000 1.298347000
H -0.834575000 -2.478936000 0.997042000
H -1.552289000 -4.458551000 -0.322477000
H -1.128190000 -2.199481000 -4.008215000
H -1.700498000 -4.331984000 -2.832408000
H 2.950535000 3.473538000 0.698290000
H 2.842563000 1.687658000 0.858736000
H 2.884117000 2.439555000 -0.786611000
H 0.678948000 5.023670000 -0.395042000
H 0.990357000 3.982867000 -1.828352000
H -0.686746000 4.150262000 -1.160750000
H -4.302108000 2.573768000 2.564446000
H -3.673500000 1.421270000 3.794842000
H -2.700063000 2.872570000 3.312044000
H -4.742112000 0.063129000 1.051704000
H -3.359638000 -1.014277000 0.656570000
H -3.871382000 -0.807607000 2.379049000
***M*-8a-azonia\[6\]helicene** (from crystal structure)
N 3.565811000 0.259443000 13.724558000
C 7.445232000 -1.196589000 12.564039000
C 8.629416000 -1.762757000 12.151335000
C 8.885324000 -1.978555000 10.783139000
C 7.914184000 -1.694865000 9.864763000
C 6.665024000 -1.171130000 10.265448000
C 5.584378000 -1.088690000 9.330104000
C 4.339207000 -0.800151000 9.738213000
C 4.088732000 -0.406137000 11.083608000
C 2.763235000 -0.187914000 11.543327000
C 2.522579000 0.029096000 12.830042000
C 3.246403000 0.443720000 15.064121000
C 4.198045000 0.692252000 15.970654000
C 5.531025000 0.961394000 15.546639000
C 6.527506000 1.327523000 16.488699000
C 7.769629000 1.675468000 16.086777000
C 8.044342000 1.864594000 14.697195000
C 9.259232000 2.459858000 14.281133000
C 9.466841000 2.806590000 12.982045000
C 8.445715000 2.608977000 12.035743000
C 7.265466000 1.985829000 12.396483000
C 7.061105000 1.553020000 13.720492000
C 5.833567000 0.912900000 14.172787000
C 4.884651000 0.303088000 13.284635000
C 5.151668000 -0.288539000 12.002691000
C 6.444932000 -0.841371000 11.632053000
H 7.296301000 -1.066868000 13.466331000
H 9.304643000 -2.036748000 12.840647000
H 9.760406000 -2.388329000 10.496986000
H 8.038683000 -1.964007000 8.943383000
H 5.780686000 -1.333585000 8.395468000
H 3.604979000 -0.909262000 9.084780000
H 2.029733000 -0.315211000 10.922946000
H 1.672696000 0.060618000 13.273677000
H 2.290439000 0.327335000 15.253240000
H 3.954366000 0.824398000 16.914659000
H 6.255785000 1.333585000 17.427224000
H 8.447606000 1.891266000 16.702563000
H 9.925491000 2.630800000 14.988120000
H 10.286033000 3.200604000 12.619714000
H 8.559741000 2.909640000 11.135042000
H 6.570317000 1.891266000 11.711236000
***M*-8a-azonia\[6\]helicene** (from BP86/STO-3G)
N 0.241946000 3.510759000 13.746203000
C -1.207087000 7.492952000 12.512135000
C -1.801472000 8.692275000 12.089683000
C -2.102492000 8.912745000 10.707738000
C -1.853647000 7.899258000 9.772330000
C -1.278056000 6.643678000 10.182732000
C -1.146616000 5.553783000 9.229249000
C -0.770948000 4.283969000 9.646130000
C -0.392477000 4.045979000 11.023979000
C -0.161103000 2.688046000 11.484550000
C 0.042219000 2.428893000 12.821687000
C 0.400500000 3.183323000 15.136378000
C 0.639392000 4.176721000 16.059802000
C 0.949043000 5.527644000 15.625469000
C 1.361398000 6.519481000 16.597330000
C 1.808770000 7.766658000 16.182869000
C 1.981223000 8.066019000 14.770425000
C 2.627560000 9.287588000 14.362758000
C 2.913363000 9.530579000 13.012425000
C 2.578886000 8.546652000 12.028110000
C 1.916409000 7.363991000 12.392255000
C 1.565834000 7.097902000 13.763105000
C 0.907348000 5.851096000 14.211296000
C 0.281492000 4.885356000 13.292158000
C -0.309154000 5.144896000 11.968134000
C -0.894790000 6.445456000 11.575101000
H -1.007504000 7.339193000 13.585554000
H -2.048406000 9.472285000 12.834293000
H -2.558542000 9.868716000 10.388465000
H -2.123797000 8.035037000 8.708340000
H -1.422274000 5.738729000 8.172836000
H -0.763274000 3.430969000 8.943112000
H -0.251900000 1.843110000 10.776492000
H 0.087281000 1.420761000 13.274365000
H 0.295196000 2.107892000 15.372408000
H 0.697253000 3.916258000 17.133249000
H 1.320711000 6.254708000 17.669775000
H 2.110372000 8.530075000 16.926174000
H 2.921715000 10.016221000 15.141242000
H 3.423497000 10.463796000 12.708003000
H 2.853573000 8.716110000 10.969950000
H 1.691114000 6.611596000 11.618453000
**$\ce{KO{}^{\mathit{t}}Bu}$ tetramer** (from crystal structure)
K -1.309381000 -1.309381000 -1.309381000
O -1.313567000 1.313567000 -1.313567000
C -2.107232000 2.107232000 -2.107232000
C -3.502008000 2.298114000 -1.478495000
H -3.842748000 1.465100000 -1.465100000
H -4.060420000 2.821364000 -2.059512000
H -3.516240000 2.821364000 -0.619528000
O -1.313567000 -1.313567000 1.313567000
O 1.313567000 -1.313567000 -1.313567000
K -1.309381000 1.309381000 1.309381000
K 1.309381000 1.309381000 -1.309381000
C -1.478495000 3.502008000 -2.298114000
C -2.298114000 1.478495000 -3.502008000
K 1.309381000 -1.309381000 1.309381000
C -2.107232000 -2.107232000 2.107232000
C 2.107232000 -2.107232000 -2.107232000
O 1.313567000 1.313567000 1.313567000
H -1.465100000 3.842748000 -1.465100000
H -2.059512000 4.060420000 -2.821364000
H -0.619528000 3.516240000 -2.821364000
H -1.465100000 1.465100000 -3.842748000
H -2.821364000 2.059512000 -4.060420000
H -2.821364000 0.619528000 -3.516240000
C -1.478495000 -3.502008000 2.298114000
C -3.502008000 -2.298114000 1.478495000
C -2.298114000 -1.478495000 3.502008000
C 3.502008000 -1.478495000 -2.298114000
C 1.478495000 -2.298114000 -3.502008000
C 2.298114000 -3.502008000 -1.478495000
C 2.107232000 2.107232000 2.107232000
H -1.465100000 -3.842748000 1.465100000
H -2.059512000 -4.060420000 2.821364000
H -0.619528000 -3.516240000 2.821364000
H -3.842748000 -1.465100000 1.465100000
H -4.060420000 -2.821364000 2.059512000
H -3.516240000 -2.821364000 0.619528000
H -1.465100000 -1.465100000 3.842748000
H -2.821364000 -2.059512000 4.060420000
H -2.821364000 -0.619528000 3.516240000
H 1.465100000 -1.465100000 -3.842748000
H 3.842748000 -1.465100000 -1.465100000
H 4.060420000 -2.059512000 -2.821364000
H 3.516240000 -0.619528000 -2.821364000
H 2.059512000 -2.821364000 -4.060420000
H 0.619528000 -2.821364000 -3.516240000
H 1.465100000 -3.842748000 -1.465100000
H 2.821364000 -4.060420000 -2.059512000
H 2.821364000 -3.516240000 -0.619528000
C 1.478495000 2.298114000 3.502008000
C 3.502008000 1.478495000 2.298114000
C 2.298114000 3.502008000 1.478495000
H 1.465100000 1.465100000 3.842748000
H 2.059512000 2.821364000 4.060420000
H 0.619528000 2.821364000 3.516240000
H 3.842748000 1.465100000 1.465100000
H 4.060420000 2.059512000 2.821364000
H 3.516240000 0.619528000 2.821364000
H 1.465100000 3.842748000 1.465100000
H 2.821364000 4.060420000 2.059512000
H 2.821364000 3.516240000 0.619528000
**Grubbs I catalyst**
Ru 1.923022 1.782458 4.279841
Cl 3.508375 2.054525 6.061616
P 0.620071 3.495015 5.336792
C 2.967497 2.881791 3.239789
Cl 0.101984 1.197998 2.838894
P 2.855052 -0.401312 3.741075
C 2.954465 3.343954 1.839333
Cl 3.310061 4.678711 -2.473972
C 1.880873 3.257547 0.960743
C 1.973325 3.667349 -0.352875
C 3.185197 4.168660 -0.812833
C 4.252303 4.292067 0.012884
C 4.145603 3.890748 1.341393
C -0.637087 4.207002 4.175769
C -1.979932 4.694567 4.692950
C -2.932151 4.983356 3.538285
C -2.339331 5.946324 2.517809
C -0.957803 5.505405 2.056512
C -0.041546 5.252113 3.235271
C 1.483967 4.856669 6.241316
C 0.518279 5.817396 6.934517
C 1.256971 6.738015 7.899778
C 2.346867 7.495106 7.161401
C 3.302557 6.547168 6.465690
C 2.565538 5.630984 5.497585
C -0.333586 2.698072 6.719178
C -1.014762 1.418485 6.241149
C -1.859827 0.796208 7.358000
C -1.043744 0.536540 8.601177
C -0.361483 1.805588 9.075860
C 0.493782 2.427234 7.979254
C 2.628515 -0.975242 1.991593
C 3.236690 -0.059043 0.937820
C 2.687448 -0.416553 -0.435697
C 2.971677 -1.856587 -0.778868
C 2.466883 -2.799363 0.290130
C 2.999176 -2.423218 1.675026
C 4.622054 -0.540862 4.248552
C 5.523290 0.453308 3.517538
C 6.887074 0.518241 4.175936
C 7.549339 -0.842629 4.233326
C 6.649166 -1.859830 4.903939
C 5.271941 -1.927013 4.232992
C 1.995357 -1.737789 4.704830
C 2.010202 -1.452357 6.212537
C 1.292567 -2.535071 7.008639
C -0.120796 -2.764155 6.507353
C -0.110733 -3.109699 5.031603
C 0.567738 -2.010334 4.218268
H 3.716836 3.154747 3.670969
H 1.120535 2.917815 1.276640
H 1.189061 3.632874 -0.962082
H 5.017596 4.645026 -0.262690
H 4.792512 4.003484 1.897392
H -0.815388 3.399122 3.615754
H -1.902150 5.510235 5.223685
H -2.378700 3.974732 5.228704
H -3.726326 5.342882 3.821555
H -3.181986 4.184074 3.125510
H -2.984577 6.066660 1.748479
H -2.250423 6.781889 2.909669
H -1.054116 4.674447 1.537657
H -0.576082 6.145292 1.467384
H 0.723372 4.965838 2.939787
H 0.125317 6.138803 3.761321
H 1.921040 4.375890 6.908583
H 1.676706 6.235725 8.636983
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[1]: https://i.sstatic.net/TCW7d.png
[2]: http://de.wikipedia.org/wiki/BINAP
[3]: http://de.wikipedia.org/wiki/BINOL
[4]: https://upload.wikimedia.org/wikipedia/commons/thumb/d/d6/BINAP_Enantiomers_Structural_Formulae_V.1.svg/350px-BINAP_Enantiomers_Structural_Formulae_V.1.svg.png
[5]: https://i.sstatic.net/UyAMJ.jpg
[6]: https://i.sstatic.net/waqGx.jpg
[7]: http://en.wikipedia.org/wiki/Helicene
[8]: http://dx.doi.org/10.1107/S0108270102023739
[9]: http://www.chemspider.com/Chemical-Structure.89294.html
[10]: http://www.ccdc.cam.ac.uk/pages/Home.aspx
[11]: https://i.sstatic.net/lfhuZ.gif
[12]: https://i.sstatic.net/aH98d.jpg
[13]: https://i.sstatic.net/IAvn9.jpg
[14]: http://en.wikipedia.org/wiki/Cyclooctene
[15]: http://dx.doi.org/10.1021/jo202176j
[16]: https://upload.wikimedia.org/wikipedia/commons/thumb/7/77/Cycooctene_Isomers_Structural_Formulae.png/298px-Cycooctene_Isomers_Structural_Formulae.png
[17]: http://en.wikipedia.org/wiki/Markush_structure
[18]: https://i.sstatic.net/YE0gp.png
[19]: https://upload.wikimedia.org/wikipedia/commons/9/9e/Markush_structure.png
[20]: http://goldbook.iupac.org/CT06769.html
[21]: http://en.wikipedia.org/wiki/Potassium_tert-butoxide
[22]: http://www.chemspider.com/Chemical-Structure.63266.html
[23]: http://dx.doi.org/10.1016%2FS0277-5387%2800%2980154-0
[24]: https://i.sstatic.net/YoBsv.jpg
[25]: http://en.wikipedia.org/wiki/Grubbs%27_catalyst
[26]: http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2005/grubbs-facts.html
[27]: http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2005/
[28]: http://dx.doi.org/10.1021/ja00036a053
[29]: http://dx.doi.org/10.1021/ja952676d
[30]: https://upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Grubbs_Catalyst_1st_Generation.svg/200px-Grubbs_Catalyst_1st_Generation.svg.png
[31]: https://i.sstatic.net/KCcIa.jpg