Gaussian basis functions used in NWChem
Clicked A Few Times
8:49:46 AM PDT - Mon, Aug 26th 2013
Hi,

Does gaussian basis functions correspond to the real atomic functions?
I tried to run hydrogen atom in dft theory and then checked the eigen-functions.

The basis I used is:
Summary of "ao basis" -> "" (spherical)

------------------------------------------------------------------------------

      Tag                 Description            Shells   Functions and Types

---------------- ------------------------------  ------  ---------------------

H                        aug-cc-pVDZ                5        9   3s2p


The final molecular orbital analysis is:
Vector    1  Occ=1.000000D+00  E=-4.993343D-01

             MO Center=  8.9D-18,  2.5D-18,  1.3D-18, r^2= 8.5D-01

  Bfn.  Coefficient  Atom+Function         Bfn.  Coefficient  Atom+Function  

 ----- ------------  ---------------      ----- ------------  ---------------

    1      0.589189  1 H  s                  2      0.489663  1 H  s


The hydrogen atom has just one electron populating the 1s atomic orbitals,
But why does the 2s gaussian basis function has contributions in the lowest level?

Forum Regular
10:01:07 AM PDT - Mon, Aug 26th 2013
Hi Alexx,
The design of Gaussian basis is a rather complex science/art. The overall aim is to construct a, preferentially, number of functions that span the space of shapes of orbitals accurately for a target set of properties. Aside from what the target properties are of a particular basis set and how the required accuracy is selected, there is also some freedom in how a basis set is represented. In principle one could choose basis functions such that there is a one-to-one correspondence between a basis function and a particular atomic orbital (see e.g. ANO basis sets), but one does not have to do that. Basis sets that use atomic orbitals have as a disadvantage that each basis function contains many exponents (often they are generally contracted basis sets) which leads to high integral evaluation costs unless the integral code has been designed to specifically support these kinds of basis sets. In segmented contracted basis sets one exponent contributes to only one basis function. This makes the integral evaluation cheaper but eliminates the one-to-one correspondence between basis functions and orbitals. For the physics these differences in representation do not matter as long as both representations span the same space of functions.
NWChem currently uses integral codes that have been designed for segmented contracted basis sets. Therefore it is beneficial to use basis sets where the basis functions are not atomic orbitals. The basis set you are using is a segmented contracted basis set and hence you got the result you showed. If you were to use the ANO-RCC basis set for Hydrogen you should get one coefficient that is much closer to one.
Best wishes, Huub


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