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A while ago I wrote a simple program that takes in an FCIDUMP file (generated by MOLRPO) and can determine matrix elements (or construct the whole FCI matrix), with the help of this forum in this thread.

However, I didn't use any of the values at the top of the file, except for NORB and NELEC (which in the string representation were just half the length of the string and the number of ones). Presumably these serve to reduce the size of the matrix somehow (maybe something with group theory), or have something to do with the irrep of the determinants. What do these parameters mean?

Perhaps it would also be helpful to work with an example, like the minimal STO-3G basis H2 (separation 1.4 bohr), if I use my program (which is hopefully correct...) I get an FCI matrix:

[[-1.83100004  0.          0.          0.          0.          0.18125791]
 [ 0.         -1.24609329  0.          0.          0.          0.        ]
 [ 0.          0.         -1.06483537  0.18125791  0.          0.        ]
 [ 0.          0.          0.18125791 -1.06483537  0.          0.        ]
 [ 0.          0.          0.          0.         -1.24609329  0.        ]
 [ 0.18125791  0.          0.          0.          0.         -0.25370925]]

However, I know from Szabo and Ostlund (e.g. using pg 162) that this is reduced to

[[-1.8310000369984170       0.18125779940066075]
 [0.18125779940066075      -0.25371106084836703]]

How do I get here given the following?

NORB=  2,NELEC=  2,MS2= 0,
ORBSYM=1,5,
ISYM=1,
OCC=  1,  0,  0,  0,  0,  0,  0,  0,
CLOSED=  1,  0,  0,  0,  0,  0,  0,  0,

And do the parameters give any extra information besides what is in the matrix?

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    $\begingroup$ +1 but "minimal basis set" could mean STO-3G or STO-2G or STO-6G, MINAO, etc. so perhaps you can be more specific (or give the page number for the Szabo and Ostlund book) if you want someone to be able to reproduce those numbers. $\endgroup$ Apr 8 at 1:41
  • $\begingroup$ Good point, I updated the post. I used STO-3G, I'm not sure about the page number but I think pg 162 should help, and I used MOLPRO to generate the FCIDUMP file (the PySCF function in the previous question I found just by searching the web). $\endgroup$
    – tmph
    Apr 8 at 15:12
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MS2 is related to the spin. Specifically, it is the number of unpaired electrons. Your molecule is a singlet, which is why it says 0.

ORBSYM is the list of symmetries for each orbital. In this case $\ce{H2}$ is in $D_{\infty h}$ but almost all electronic structure codes do not support non-Abelian groups, so instead we would almost always use $D_{2h}$. The FCIDUMP format was invented by Peter Knowles, and the writing and reading of FCIDUMP files would have been implemented in MOLPRO long before other software, so assuming this FCIDUMP was written by MOLPRO, you can figure out what the 1 and 5 mean from the $D_{2h}$ table here (Table 2). This tells us that the first molecular orbital is of type $A_g$ and the second is of type $B_{1u}$. That makes sense because in your minimal basis set with only 2 spatial orbitals, you have $\sigma$ and $\sigma^*$ bonding and anti-bonding orbitals. You mentioned PySCF in the other question, and unfortunately they have a different convention for labeling the irreps of $D_{2h}$, in which $A_g=0$ and $B_{1u}=5$, which is not what you have in your FCIDUMP, perhaps because you didn't use PySCF to print the FCIDUMP, or because the PySCF documentation has an error. My open source "Quantum Chemistry Cheat Sheet" will help you translate between the languages of many of the most popular electronic structure programs, and here I'll just copy and paste from there the relevant information for $D_{2h}$ since you're dealing with $\ce{H2}$:

$D_{2h}$ irrep MOLPRO MRCC CFOUR PySCF
$s$ $A_g$ 1 1 1 0
$p_z$ $B_{1u}$ 5 6 5 5
$p_y$ $B_{2u}$ 2 7 2 6
$p_x$ $B_{3u}$ 3 8 3 7
$d_{xy}$ $B_{1g}$ 4 2 4 1
$d_{xz}$ $B_{2g}$ 6 3 7 2
$d_{yz}$ $B_{3g}$ 7 4 6 3
$d_z^2$ $A_g$ 1 1 1 0
$d_{x^2-y^2}$ $A_g$ 1 1 1 0
$f_{xyz}$ $A_u$ 8 5 8 4

By the way if you don't like how the $d_{x^2 - y^2}$ orbital turns out in the table, you might consider supporting my feature request to fix that bug 😊.

ISYM is the overall symmetry of the molecule. $A_g \times B_{1u} = A_g$, which was labeled as 1 in the program that you used to print that FCIDUMP.

OCC are the occupied orbitals for each irrep of the point group, which in this case is $D_{2h}$ so there's 8 entries there. Only an $A_g$ orbital is occupied, so the entries for all other irreps is 0, and the $A_g$ irrep has only one occupied orbital, which is the $\sigma$ bonding orbital, so we have a 1 there. This means the anti-bonding $\sigma^*$ orbital does not have any electrons in it.

CLOSED are the closed orbitals, with the same convention as OCC. Since there's 2 electrons in the one occupied orbital, we have a "closed" orbital. It would be open if it didn't have 2 electrons in it.

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  • $\begingroup$ Sorry for getting back so late. Does the bold text in your answer by OCC imply the reduced size somehow or do you reduce the CI matrix some other way? I guess I am confused how to use this information meaningfully. $\endgroup$
    – tmph
    Apr 13 at 19:41
  • $\begingroup$ @tmph The bold text says that the bonding orbital has 2 electrons and the anti-bonding orbital has 0 electrons, which makes sense for a system with 2 electrons and 2 orbitals, that's in the ground electronic state. You can use the spin (MS2) and spatial symmetry (ISYM) to reduce the number of determinants, and hence the number of CI coefficients, but that would have to be left for a different question, or more likely, two separate questions because I foresee more people being able to answer the question about spin and far fewer people being able to (or willing to) answer about spatial sym. $\endgroup$ Apr 14 at 1:56

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