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But if one were to provide the correct extended transition state Fock matrix to Multiwfn (read from a file) then it should give the exact result?
Ah, yes I see now, that explains it.
Should have read the manual.
Hi, 
Very nice to see the availability of ETS-NOCV in Multiwfn. This will be extremely useful.
I'm struggling a bit though to reproduce the orbital-interaction term by combining ORCA and Multiwfn.
I'm trying to reproduce the numbers of of ammonia borane from this article:
https://pubs.acs.org/doi/pdf/10.1021/jp209712s
This is the original author of the ETS-NOCV method and it uses the ADF implementation and the  theory level is BP86/TZ2P.
The geometry (of the monomer) is given in the SI.
For the monomer (M) in the Table of the paper we have (BP86/TZ2P level of theory):
dominant orbital interaction: -65.5 kcal/mol
total orbital interaction: -75.8 kcal/mol
total interaction: -44.7 kcal/mol
-----------------------------------------
If I read in Molden files (generated by ORCA using BP86/def2-QZVP) for the dimer and the two monomers (making sure to have reordered the coordinates appropriately) I get with Multiwfn:
dominant orbital interaction: -58.08 kcal/mol
total orbital interaction: -70.170 kcal/mol
total interaction: -45.257 kcal/mol
So the total interaction energy is fairly well reproduced ~0.5 kcal/mol error (pretty good, considering different Slater vs. GTO basis sets) but the total or individual orbital interaction are off by >5 kcal/mol.
For the ETS step in Multiwfn I tried to read in both the Fock matrix directly (from ORCA outputfile, using -1 option) and also to recalculate the Fock matrix based on the orbital-energies information present in the Molden file (-2 option).
If I use the ETS-NOCV implementation in ORCA instead I am able to reproduce the ADF-values really well:
dominant orbital interaction: -65.827 kcal/mol
total orbital interaction: -76.112 kcal/mol
total interaction: -45.257 kcal/mol (identical to that before)
Total orb interaction is off by only 0.31 kcal/mol and the dominant interaction is off by only 0.33 kcal/mol.
So I suspect a bug in Multiwfn but maybe only for the ETS part, not the NOCV:
The largest eigenvalue for the dominant pair is: -0.557 when using the ORCA implementation
The largest eigenvalue for the dominant pair is: -0.55726 when using the Multiwfn implementation, so identical.
Anyone got any ideas?
Geometry that I used:
B        0.000035390     -0.000019910     -0.125149000
H        1.174850000     -0.000074730     -0.440064000
H       -0.587435000     -1.017410000     -0.440035000
H       -0.587331000      1.017440000     -0.440002000
N       -0.000044690     -0.000077070      1.533410000
H       -0.953218000     -0.000162730      1.904150000
H        0.476727000     -0.825587000      1.903830000
H        0.476593000      0.825494000      1.903860000
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