Questions about the Hartree Fock Method and Methane Molecules

[davidfur]

Hey all !

I've got a few questions regarding the Hartree Fock method which I'm not so sure about...
Will HF result in a good estimate of the interaction energy between two Methane molecules ?
and what about the structure and symmetry of Methane molecule ? (I know that as far as structure is concerend, it's better to work with VSEPR)

Will HF fail with dealing with N2 because of large relativistic effects ?
Can HF predict the structure of shells experimentally measured for the electronic density in atoms ?

I know HF is based on the Born Oppenheimer aprox. and it starts with slater type orbitals, but not so sure about when HF fails to predict correctly.
Any help will be greatly appreciated !

 

[SpectraCat]

Hey all !

I've got a few questions regarding the Hartree Fock method which I'm not so sure about...
Will HF result in a good estimate of the interaction energy between two Methane molecules ?

No .. the interaction between two methane molecules is very weak .. only van der Waals dispersion interactions contribute, and HF does a horrible job of accounting for those, because it doesn't include electron correlation.

and what about the structure and symmetry of Methane molecule ? (I know that as far as structure is concerend, it's better to work with VSEPR)

The HF structure for methane should be pretty good .. the lengths of the CH bonds will probably be a bit shorter than the experimental value, but it will have the correct tetrahedral geometry. VSEPR is not a calculation method .. it is only a set of guidelines for predicting bond angles in simple molecules.

Will HF fail with dealing with N2 because of large relativistic effects ?

Yes and no ... HF definitely will not include the relativistic effects, however, it is also missing other contributions (such as electron correlation, and the correct representation of electron exchange), which will like contribute much larger errors to the energy.

Can HF predict the structure of shells experimentally measured for the electronic density in atoms ?

I don't know what you are trying to ask ...

I know HF is based on the Born Oppenheimer aprox. and it starts with slater type orbitals, but not so sure about when HF fails to predict correctly.
Any help will be greatly appreciated !

HF is hardly used in practice any more ... it has been supplanted by density functional methods, which work on the same principles, but also include a better handling of electron exchange, and electron correlation, which HF doesn't treat at all. DFT is far from perfect however ... for the most accurate work, people turn to post-HF methods, such as Moeller-Plesset perturbation theory (MPn), configuration interaction (CI), and coupled cluster (CC) methods. Also, some problems, particularly those involving chemical reactions, cannot be accurately represented with a single Slater determinant (HF and DFT methods only work for wavefunctions that can be represented as single Slater determinants). For these cases, you need to turn to multi-reference methods, which include complete active space SCF (CASSCF) and multi-reference configuration interaction (MRCI), just to name a couple.

 

[cgk]

HF is hardly used in practice any more ...

I'd like to second everything you said before, but this statement should be clarified: HF is of course used as first step for the post-HF methods you mention. So it actually is used in practice, very often, but not on its own. It's main task is to give to give a reference wave function for more accurate methods[1].

[1] And, on a side note: In most molecular programs DFT and HF share a common implementation, so there learning HF in theory or practical application is not irrelevant.


For the OP:
(i) There are no special relativistic effects in N2. Like in most small molecules composed of first row atoms, you have to expect around 1 kJ/mol or less as relativistic effect on energy differences.
(ii) HF does describe the shell structure of atoms. However, that is not much of a feat considering that the shell structure is basically a theoretical construct /based/ on a HF interpretation of the atoms. Additionally, straight HF will give you non-spherical orbitals for non-spherical atoms. Many people don't like that and will recommend you to do a state-averaged HF instead.