Accuracy

• Many students have reported numbers as they are given by the program, this is not sensible. Remember that the accuracy to which you report a number tells the reader the relative error level. For the methods you are using,
• the energy will have an error of ≈ 5 kJ/mol, and we normally work to units of 1 kJ/mol, so how much is this in atomic units (which are hartree)?
  • 1 hartree or au = 2625.4999 kJ/mol
  • therefor 1 kJ/mol is 0.00038 au
  • thus energies in au need to be recorded up to 6dp to allow us to round properly to the nearest kJ/mol, although 5dp is ok
  • see below for other important points regarding energies
• dipole moment is accurate to about 2 decimal places, ie 0.01 Debye.
• frequencies in wavenumbers are by convention reported with no decimal places and for the methods you are using in this course you need to know that there is a known systematic error of around 10%, this is because we use a harmonic approximation for vibrations that are actually anharmonic. Note that 10% is around 10cm^-1 for vibrations in the order of several 100cm^-1 but for very high energy vibrations like C-H stretches this can be as much as 300 cm^-1 . (the situtation is actually more complex, but this is a good first point of call)
• intensities are rounded to the nearest whole integer and in fact the accuracy is much less that this, but this is the convention
• bond distances are accurate to ≈ 0.001 Å
• bond angles are accurate to ≈ 1°
• population analysis charges are accurate to ≈ 0.01e
• MO energies are given in Hartree or au, 1 hartree is equal to 27.2114 eV, orbital energies are usually reported in eV up to 0.01eV

important Have you reported values consistently and to the correct accuracy?

Energies

• Many students have reported energies incorrectly, because the energy is HIGHLY dependent on the method, basis set and details of a calculation. The total energy of molecules cannot be compared, this is a very important point!
  • the total energy for a system is reported only for the purpose of ensuring others can repeat your calculations, and hence reference to this energy.
  • you should report your total energies in atomic units (AU), but make no attempt to interpret or compare them
  • relative energies are sensible things to calculate and compare. For example the energy difference between two isomers
  • report relative energies in kJ/mol
  • relative energies can only be computed for systems with exactly the same number and type of atoms
  • all components MUST be computed with exactly the same method/basis set/computational details (eg things like scf=tight)
  • relative energies for reactions can be reported but they MUST be balanced
  • for example to determine the energy of association of the acid base pair
    NH₃ + BH₃ -> H₃B:NH₃
    compute E(adduct)-[E(NH₃)+E(BH₃)]