What is the optimal basis set for a full CI calculation of low Z elements?

[squealer]

Hi,

I running a full CI calculation for low Z elements (up to Ne) in order to obtain the lowest lying electronic energy levels.

I can't seem to get correct results even though I'm using 1-electron states from first 4-6 electron shells. I am also using singly and doubly excited multi-electron states (wrt the ground state).

The errors I get in the ground state are around 5% of it's value ?

Is this error normal for a full CI like the one I described ?

If so how many 1-e states is it necessary to include to get the first excited energies correctly ?

Appreciate any help.

Thanks.

 

[cgk]

What kind of basis set do you use and what kind of program? What are your reference values? What do you mean with "using 1-electron states from first 4-6 electron shells"?

I mean, depending on which program you use, doing such an calculation should be a matter of writing:

geometry={Ne}
basis=cc-pVDZ
rhf
fci

(btw: this gives
!FCI STATE 1.1 Energy -128.679025053952
where the 1s core electron is frozen).

You need to be more specific on what you intend to accomplish and how.

 

[squealer]

Clarifications:
1) I need to calculate the energy splittings between the ground state and the first excited electronic states for Z < 10. I diagonalize the multi-electron hamiltonian in a truncated multi-electron space.

2) I use the spherical harmonics of the hydrogen atom exact solution for a given Z. For example the 2-shell basis is: 1s,2s,2p (m=-1,0,1) both spins => 10 basis functions.

3) My multi-electron space is built from determinants of the above one-electron states, but only those determinants that differ in 2 one-electron states from the configuration close to the ground state. Eg. for lithium the ground state is close to |1s1s2s>: |1s2p2p> is used, |2p2p2p> is not used.

4) I've written my own MATLAB code. For example for He I get with 2 shells:
Egnd = -78.1eV vs -79eV (NIST data)
E1st - Egnd = 19.1eV vs 19.8eV
E2nd - Egnd = 19.2eV vs 20.6eV

For Z > 2 I get non-sensical results. Should I be getting more accurate results ?
How accurate results can you get ?

 

[cgk]

I guess your main problem are the 1-particle states which you use. You should really use a standard quantum chemistry basis set instead, and also use a real quantum chemistry program. The hydrogen-like functions cannot even represent the Hartree-Fock part of the total energy!

In order to obtain accurate energies, you need to use large basis sets. MUCH larger than what you are using. Including a few hydrogen-like basis functions is not even remotely enough. In order to obtain (correlation-) energies accurate to 1 kcal/mol you would need to use an extrapolation based on at least VQZ/V5Z basis sets (the latter go up to h functions on Ne).

That being said, methods like multi-configuration CI or high order single reference CI/CC methods are really NOT something you can write up yourself in matlab. My recommendation woiuld be to get familiar with some established quantum chemistry program (my personal choice is MOLPRO), which can do such things, and do them well.

 

[squealer]

Thanks for the reply. What are the VQZ/V5Z sets ? Are these orthogonal sets of functions ?

 

[cgk]

These are non-orthogonal sets of contracted Gauss-Type Orbitals (GTO). The full name would be cc-pVQZ/cc-pV5Z (correlation consistent polarized valence n-tuple zeta). These are the most widely used standard basis sets for systematic high-accuracy calculations (also called Dunning-type basis sets).

You might want to read http://link.aip.org/link/?jcp/90/1007 .

Basically, such basis sets resemble 'atomic natural orbital' basis sets in a largely simplified fashion. Your main problem for the non-hydrogen elements, however, is most likely that the functional form you choose is not able to represent the Hartree-Fock part of the energy (i.e., the orbitals you would get if you had only a single determinant. This makes up for 99% of the total energy). Hydrogen-like functions are really not up to the task, that is why in quantum chemistry contracted Gauss-type orbitals are used (adjusted to each individual element).

 

[squealer]

Thanks. I think the problem might be the basis set. Because, my multi-electron wavefunction is a sum of determinants of 1-electron wavefunctions, so the hartree-fock part plus the correlation, i should be getting in theory.