# Why is the active space for the dinitrogen cation defined this large in my example?

I have a Molpro script which computes $$\ce{N2^+}$$ potential energies.

The significant part is the input for the wave function:

 {multi;
occ,3,2,2,0,3,2,2,0;
closed,1,0,0,0,1,0,0,0;
wf,13,5,1;
state,3;
}


Why is the active space specified by OCC flag so large? It specifies 14 molecular orbitals, which means that both nitrogen should habe 7 atomic orbitals. Which atomic orbitals are additionally included?

The ground states of $$\ce{N2^+}$$ molecule has this electron configuration:

Thich can be specified as occ,3,1,1,0,2,0,0,0;.

What advantage does occ,3,2,2,0,3,2,2,0; have in the script and how can I understand and visualize those additional orbitals?

### Explanation of OCC card

The OCC card in Molpro specifies symmetries of the orbitals in active space. In this case, they're specified in $$D_\mathrm{}$$ point group, according the following table:

$$D_\mathrm{2h}\\ \begin{array}{ccc} \hline \text{No.} & \text{Name} & \text{Function}\\ 1& \mathrm{A_g} & s \\ 2& \mathrm{B_{3u}} & x \\ 3& \mathrm{B_{2u}} & y \\ 4& \mathrm{B_{1g}} & xy \\ 5& \mathrm{B_{1u}} & z \\ 6& \mathrm{B_{2g}} & xz \\ 7& \mathrm{B_{3g}} & yz \\ 8& \mathrm{A_u} & xyz \\ \hline \end{array}$$

The active space is a truncation of the full CI space. Hence, including more virtual orbitals will lower the energy and eventually approach the FCI limit. The larger the active space, the more accurate the results.

The smaller active space will give you a good qualitative description. But if your results turn out to be quantitatively wrong, increasing the active space is one way to improve them.

To get an idea about the higher orbitals, take a close look to the Molpro output. You might want to check the Print options, to get all desired energies and orbital coefficients. Furthermore, you can use for example put to create molden files and create 3D isosurface plots of all MOs.

### Possible active spaces

The smallest meaningful would be to include the singly occupied $$3\sigma_g$$ orbital, together with its anti-bonding pendant $$3\sigma_u$$. Furthermore all the $$1\pi$$ orbitals should be included. This makes a CAS(5,6):

occ,   3,1,1,0,3,1,1,0
closed,2,0,0,0,2,0,0,0


Your occ,3,1,1,0,2,0,0,0 card actually excludes the anti-bonding $$3\sigma_u$$ and $$1\pi_g$$ orbitals, which corresponds to a ROHF calculation.

The next larger space would be the full valence active space, covering the whole $$2s2p$$ AO shell:

occ,   3,1,1,0,3,1,1,0
closed,1,0,0,0,1,0,0,0


Addtionally one could also include the $$1s$$ core orbitals with closed,0

The next thing to include would be the next higher lying virtual orbitals coming from the $$3s3p$$ AO shell: occ,5,2,2,0,5,2,2,0. After that one could go on with the $$3d$$ and $$4s4p$$ shells.

The occ,3,2,2,0,3,2,2,0 card would include the bonding $$2\pi_u (3p_{x/y})$$ and anti-bonding $$2\pi_g (3p_{x/y})$$ orbitals, but not the $$4\sigma_{g/u} (3s)$$ and $$5\sigma_{g/u} (3p_z)$$ which are similar in energy.