Post-HF-Methoden

Higher ab initio methods

• There are three kinds of error in using the Hartree Fock method with practicable-sized basis sets
• We would get a lower absolute energy, and better relative energies, if we used a bigger basis set
• As basis set size goes up, the energy converges to a theoretical limit
• This unreachable limit is the 'Hartree Fock Limit'
• When we look at single electrons in an average field of the rest, we take no account of time dependence
• The positions of individual electrons at particular instants are correlated
• This error in the HF method is called 'Correlation Energy'
• We have taken no account of relativity
• Electrons move faster near to heavy nuclei, so their masses change
• Important for heavier transition metals or heavy main group atoms, e.g. Sn or I
• There should be a relativistic correction
• Altogether

E_True  =  E_{HF practical}  -  E_{basis set error}  -  E_correlation  -  E_relativistic
• A basis set error always has to be tolerated:  the question is whether to spend calculation time on a bigger basis set, or whether to spend it on reducing the other errors by using a higher method.  This kind of question is discussed in Hehre's 'Practical Strategies for Electronic Structure Calculations'
• Some of the relativistic error can be removed by using Effective Core Potential (ECP) basis sets for heavy atoms
• Core basis functions are left out of the basis set and the effect of the core electrons is represented by parameterised electrostatic potential functions instead
• The potentials can include a relativistic correction
• Leaving out basis functions saves SCF calculation time, but calculating forces for a geometry optimisation takes longer.  These efficiencies balance out for medium weight elements
• ECP basis sets are quicker only for the bromine period and below
• ECP cannot be used where core electron properties are required, e.g. for NMR shieldings
• What to do about correlation energy is the crunch problem
• It is particularly important for loosely bound molecules, like transition states
• The traditional next method above HF is MP2
• MP2 calculates a correlation correction after a HF calculation, but takes much longer
• Because it is slow, the MP2 method is only practicable for small molecules
• MP2 is often used for single point calculations to get more accurate energies, after geometries have been found at the HF level
• Since 1996, Density Functional (DF) methods are being used instead of MP2
• DF methods calculate correlation, working directly with electron density instead of with MOs
• A DF method replaces HF, rather than being an additional step, as is MP2
• DF methods often contain a certain number of preoptimised parameters:  these are not changed by the ordinary user
• The most popular DF method for organic molecules at present is B3LYP
• Since 2000, we are finding that MPW1PW91 is better for inorganic molecules
• These (and other) DF methods are built into Gaussian and some PC packages, and are called up by name
• DF methods are quicker than MP2, but may be less accurate
• For moderate sized molecules, they are always slower than HF, but for large molecules they should be faster, if used with the same sized basis set
• DF does not always produce better results than HF, though it usually takes longer:  properties such as NMR shieldings may be predicted more poorly, especially for lighter elements
• DF methods are usually better than HF for calculating small energy differences
• Some journal referees think HF methods are old-fashioned, and require authors to at least try DF methods

Die transparenteste Post-Hartree-Fock-Methode ist CI bzw. MCSCF.