Accuracy

 

Accuracy of PM6

A frequently asked question is, "Which method in MOPAC is the most accurate?"  Although apparently a simple question, there is no simple answer.  Several years of work went into developing the PM6 method, and that work made extensive use of the experience gained during the development of the earlier methods.  So my answer would be, "PM6."  But if you were to accept that answer, you would also need to trust that what I said was also accurate.  When there is the opportunity to see an unbroken chain of logic from raw experimental data to a summary of a statistical analysis of the errors in various properties for various methods, that is almost infinitely preferable to hearing someone say, "trust me."

Raw data with references on the basic set of ~7600 species used in the analysis.
A statistical package can be downloaded that will allow a wide range of comparisons of AM1, PM3, and PM6.
A comparison of various hydrogen bonded structures predicted by PM6 with reference X-Ray structures
The ability of PM6 to reproduce bond-alternation
Users might be interested in a very quick summary of advantages and disadvantages of the various methods.

                Average Unsigned Errors in PM6 Predictions

  Quantity PM6 PM5 PM3 AM1   Units
  DHf 8.01 22.19 18.20

22.86

  Kcal/mol
  Bond Lengths 0.091 0.123 0.104 0.130   Angstroms 
  Angles 7.86 9.55 8.50 8.77   Degrees
  Dipoles 0.85 1.12 0.72 0.67   Debye
  I.P.s 0.50 0.50 0.68 0.63   eV
 

Other Tables of Results

  Quantity Average Unsigned Error
   DHf  (PM6 and other semiempirical)* (Depends on set used)
   Bond-lengths (PM6 and other semiempirical) (Depends on set used)
  DHf  (PM6 and ab-initio)* 4.44 kcal/mol
  Relative conformer energies 2.35 kcal/mol
  Nitrogen pyramidalization 5.0 degrees
  Hydrogen bond energies 1.70 kcal/mol
  Intermolecular interactions using PM6-DH2 0.37 kcal/mol
  Intermolecular interactions using PM6-DH+  
  Water Dimerization energies 1.04 kcal/mol (one value)
  Polarizability volume (3) 2.1%
  Vibrational freqencies (cm-1) 14%
  Entropy 3.16 cal/(degree.mole)
  pKa 0.31
  Cp (heat capacity) 1.48 cal/(degree.mole)

* DHf is the heat required to form one mole of the gaseous compound
from its elements in their standard state, at 298K. 
             

Known severe errors in PM6

 Type of error

 Example
Two sodium ions bind together because the core-core repulsion is too small  
Relative energies of neutral and Zwitterionic species -NH2 + -OH <=> -NH3+ + -O-
Geometry of Fe(CO)5 is predicted to be C4v, should be D3h  Ref. Fe(CO)5 and  PM6 Fe(CO)5
Ferrocene is predicted to be C2v not D5d or D5h.  
Fe(III)X6, 6A1g, is distorted from the octahedral symmetry  FeF6
Oxalic acid is twisted, should be planar Oxalic acid
Heat of reaction: Oxalic acid = CO2 +C(OH)2 is in error by ~30 kcal/mol Oxalic acid heat of reaction
R-(R-O-C=O)-NH2-R is stable, should decompose to R-COO-R + R-NH2 amine-carboxylic acid
Biphenyl torsion is predicted to be 57 degrees, should be 45 degrees  
N-(Benzylidene)aniline is predicted to be cis, should be trans  
Iodine - non-bonded oxygen too close, 2Angstroms, should be ~3Angstroms  
H(+) is in error by -54 kcal/mol These species are unlikely to be found in biochemical systems.  The faults cannot easily be corrected by re-parameterization.
Methylene triplet is predicted to be linear, should be bent
Ag7 decomposes into Ag +3 Ag2  
SiO2 is predicted to be bent, it should be linear. The O-Si-O angle in silica is predicted to be too large All forms of crystal SiO2, except hexagonal beta tridymite
Non-bonding Br - N interactions are bonding. HCN - BrCH3
Non-bonding S - N interactions are bonding. Me2C=S - N(Me)3
Non-bonding S - O interactions are bonding. Me2O - S=CH2

Non-bonding S - Cl(-) interactions are bonding.

H2C=S - Cl(-)
Non-bonding S - S interactions are bonding.  
Non-bonding Se - Se interactions are bonding.  
Non-bonding Se - I interactions are bonding.  
Non-bonding Te - Cl interactions are bonding.  
Non-bonding Br - O interactions are bonding.  
Non-bonding Br - Br interactions are bonding.  
Non-bonding I - O interactions are bonding.  
Non-bonding I - I interactions are bonding.  
Non-bonding N - I interactions are bonding.  
Non-bonding Cl(-) -H interactions are bonding.  
Pyramidal enolate to planar (CH3-CO(-)=CH2) energy difference is too large (14, should be 6 kcal/mol)  
BrF3 is predicted to be D3h should be C2v  
PrF5 is predicted to be D3h should be C4v  
TiH4 collapses  
[Re2Cl8]= has two bridging Cl atoms  
(Please report errors as soon as they are found)  

Known errors in MOPAC2009

By default, UHF CH4 + F generates an electronic excited state

 

Accuracy of operations within MOPAC2009

Geometry optimization
Precision levels
Keyword "PRECISE"
Reasons for low precision
Setting the Gradient Norm (GNORM)
SCF criteria:
   Test for self-consistency (SELCON and SCFCRT)
   Setting the absolute SCF criterion (SCFCRT)
   Setting the relative SCF Criterion (RELSCF)
   Monitoring SCF convergence using PL