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 = {

H       0.00000000     0.00000000    -0.46904000
H       0.00000000     0.00000000     0.46904000

 WF, 2, 1, 0;

put, molden, h2.molden;

Part of Molpro output

 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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.