Matter Modeling Asked on November 7, 2021

A simple calculation with Molpro 2012 on H2 molecule in cc-pvtz basis produces a molden file with 28 molecular orbitals. Each MO is defined with 30 AO/MO coefficient, but the number of symmetric AOs is 32, and the number of contractions is 28.

```
memory, 200, m
basis = cc-pvtz;
symmetry nosym;
geomtyp = xyz;
geometry = {
2
H 0.00000000 0.00000000 -0.46904000
H 0.00000000 0.00000000 0.46904000
}
{rhf;
WF, 2, 1, 0;
}
put, molden, h2.molden;
---
```

Part of Molpro output

```
NUMBER OF PRIMITIVE AOS: 34
NUMBER OF SYMMETRY AOS: 32
NUMBER OF CONTRACTIONS: 28 ( 28A )
```

**Why the number of AO/MO coefficients is not equal to the number of symmetric AOs or the number of contractions?**

Okay, so there are many layers to this question. cc-pVTZ for H is [5s2p1d/3s], which comes out to 3 + 2*3 + 5 = 3+6+5 = 14 basis functions per atom, which are composed of 16 primitives (the contracted s function).

Now, while there are 1 and 3 cartesians for the s and p shells, for the d shell you have 6 cartesian functions but only 5 spherical functions. This is important, since Gaussian-basis integrals are evaluated in the cartesian basis, and then contracted to get the spherical-basis integral. (There are closed-form relations for this translation.)

For H2, you then have

- 2*14 = 28 contracted basis functions; this is the "number of contractions".
- 2*15 = 30 contracted cartesian basis functions, which is thus probably the format which Molden is using.
- 2*16 = 32 primitive Gaussian basis functions with spherical D functions, this appears to be the "symmetry AOs".
- 2*18 = 34 primitive Gaussian cartesian basis functions; this is the "primitive AOs".

Hope this helps.

Answered by Susi Lehtola on November 7, 2021

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