Ammonia dimer & frustrated hydrogen bonds

[godotalgorithm]

This fault was reported over email by Prof. Rafael Soares at UFRGS, and (with his permission) I am moving the report and any subsequent discussions here.

The ammonia dimer is a simple system with a pair of frustrated hydrogen bonds in its equilibrium structure, which leads to a very flat potential energy surface. However, PM6-D3H4 and PM7 both predict a lower-energy structure with a single hydrogen bond:

 PM7
 AMMONIA-1-AMMONIA-20-270deg

  N     0.34614165 +1    0.0908430 +1    1.0403318 +1     0     0     0
  H     0.99773933 +1   31.3992414 +1 -191.0515577 +1     1     0     0
  H     0.99832974 +1  109.7150396 +1 -112.6425894 +1     1     2     0
  H     0.99740113 +1  109.6154729 +1  120.3005020 +1     1     2     3
  N     3.25170869 +1  117.7850598 +1 -112.8090938 +1     1     2     3
  H     0.99582962 +1  106.0993432 +1   16.3398407 +1     5     1     2
  H     1.00386850 +1    5.6804647 +1  136.2706360 +1     5     1     2
  H     0.99566270 +1  106.3377317 +1  -99.9780239 +1     5     1     2

Focusing on PM7, the frustrated dimer is a metastable state with a binding energy of 4.4 kcal/mol while the single-bond dimer produces a binding energy of 5.8 kcal/mol. A high-level reference calculation (QZ/CCSD(T) energies on TZ/MP2 structures) gives a 3.1 kcal/mol binding for the frustrated dimer and 2.7 kcal/mol binding for the single-bond dimer. This can be interpreted as a limitation of the simple hydrogen-bond corrections used by PM7, which is not a good description of frustrated hydrogen bonds. However, this crossing of energies is also close to the highest level of accuracy (1 kcal/mol) that we can seriously hope for any routine quantum chemistry calculation, which is a problem that can occur in relatively flat potential energy surfaces - small errors in energy can cause large geometric changes to the lowest-energy structure.

MOPAC's historical strategy for dealing with erroneous equilibrium geometries has been to add them as "erratic" structures to the reference data and providing some higher-level theoretical energies since they don't have accompanying experimental data. This hasn't yet been done for weakly-bonded structures, and this example would be a good candidate for an "erratic" structure.