[Schrödinger]

So I'm trying to find the single point energies of certain molecules.

What I want to know is, what happens if I optimize geometry using a certain basis set, say 3-21G, I can get the energy directly from the output file. Now if I do an SPE calculation using 6-31G on this optimized geometry,  get another value. Can we say generally that one method is better than the other? If so, which one?

The variational principle may not be at work, so I can't blindy say one is better just because the energy is lower, right?

[curiouscat]

So I'm trying to find the single point energies of certain molecules.

What I want to know is, what happens if I optimize geometry using a certain basis set, say 3-21G, I can get the energy directly from the output file. Now if I do an SPE calculation using 6-31G on this optimized geometry,  get another value. Can we say generally that one method is better than the other? If so, which one?

How were you planning to? On which criterion? Lower energy?

The variational principle may not be at work, so I can't blindy say one is better just because the energy is lower, right?

I don't think you can. Can you state what you mean  by the variational principle? Been a while since I took those classes.

[Schrödinger]

The variational theorem states that any ground state energy calculated using a trial wavefunction is always greater than or equal to the true ground state energy of the molecule.

So, if the wavefunctions used are all trial waefunctions which have the same boundary conditions as th true wavefuntions would have, then I'd most certainly be using the variational principle. This would mean that in case I obtain an energy via 6-31G that is lower than 3-21G, then I can safely assume that the 6-31G value is closer to the true ground state energy, although it is not equal to the true energy.

[curiouscat]

The variational theorem states that any ground state energy calculated using a trial wavefunction is always greater than or equal to the true ground state energy of the molecule.

So, if the wavefunctions used are all trial waefunctions which have the same boundary conditions as th true wavefuntions would have, then I'd most certainly be using the variational principle. This would mean that in case I obtain an energy via 6-31G that is lower than 3-21G, then I can safely assume that the 6-31G value is closer to the true ground state energy, although it is not equal to the true energy.

I think that's only valid when comparing different trial-wavefunctions but with the same basis-set.  e.g. you couldn't use two different pseudopotentials or cutoffs and expect to compare the energies.

I'm not very sure though..

[juanrga]

So I'm trying to find the single point energies of certain molecules.

What I want to know is, what happens if I optimize geometry using a certain basis set, say 3-21G, I can get the energy directly from the output file. Now if I do an SPE calculation using 6-31G on this optimized geometry,  get another value. Can we say generally that one method is better than the other? If so, which one?

The variational principle may not be at work, so I can't blindy say one is better just because the energy is lower, right?

The comparison has to be made to experiment or the result of a full CI (with a large basis set). In your case you are using an extended basis, therefore you would expect a better energy value.

[Schrödinger]

Thanks for the input guys! Appreciate it