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I have found that 6-31G* is similar to def2-SVP e.g..

What would be the criteria for comparing similar basis set?

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1 Answer 1

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"What would be the criteria for comparing similar basis set?"

Gaussian basis sets are usually characterized by the numerical values of the exponents and the contraction coefficients. If these numbers are precisely the same, then the basis sets are precisely the same. On a more coarse level, basis sets can be compared based on the number of exponents/contraction-coefficients (e.g. if you find two different cc-pVDZ basis sets, we can expect that they will have the same numbers of exponents and contraction coefficients of each type, but there might be slight differences in the numerical values of the exponents depending on how converged the calculations were when building the basis set).

Also, you can compare the SCF or post-SCF energies (or any properties) that are obtained using the basis sets, and often we will conclude that a basis set is "better" if it gives lower energies when using a variational method such as the Hartree-Fock method or CISD, however this is not always the case, because a lot of basis sets are optimized to provide good values for properties or for energy differences or for smooth extrapolation to the complete basis set limit, rather than to get the lowest possible variational energy for a single-point total energy.

As for 6-31G* and def2-SVP, let's look at these basis sets for the element H, from basissetexchange.org using the NWChem Format. 6-31G* has the following exponents and contraction coefficients for S-type functions:

H    S
      0.1873113696E+02       0.3349460434E-01
      0.2825394365E+01       0.2347269535E+00
      0.6401216923E+00       0.8137573261E+00
H    S
      0.1612777588E+00       1.0000000

Contrarily, def2-SVP has the following exponents and contraction coefficients:

H    S
     13.0107010              0.19682158E-01
      1.9622572              0.13796524
      0.44453796             0.47831935
H    S
      0.12194962             1.0000000
H    P
      0.8000000              1.0000000

Notice that not a single number is the same, and the def2-SVP basis set in fact has an additional line for P-type functions (of which there will actually be three extra functions: Pz, Px, Py). However these basis sets can be considered "similar" due to having the same number of S-type exponents and contraction coefficients (although the numerical values of them are very different).

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