I'm a computational noob -- I'm stronger in the computer department than the computational one. The following will most likely only be useful to other newcomers like myself. Anyway...
The authors used ub3lyp/g-31g** and g03. While it may have taken a substantial amount of time in 2000, today the entire paper can be reproduced in a few hours on a simple beowulf cluster. So I set out to do just that -- partly to make sure that I understood the approach, partly to make sure that g09 and g03 gave the same results, and also importantly to make sure i can use nwchem for these calculations if I so desire. I'm getting to the point where nwchem is almost as fast as gaussian for some calculations (cosmo excepted...) and I much prefer the nwchem syntax and python support.
For biphenyl, g09 gave (in Hartree)
Neutral, ground state: -463.3219416650 (geometry opt)
Cation, neutral geometry:-463.0352702000 (single point calc)
Cation, cation geometry: -463.0422747850 (geometry opt)
Neutral, cation geometry: -463.3157130000 (single point calc)
That works out to a total energy of ca 0.36 eV -- same as in the paper
while nwchem gave
Neutral, ground state: -463.3219454524 (geometry opt)
Cation, neutral geometry: -459.0525026266 (single point calc)
Cation, cation geometry: -463.0422952505 (geometry opt)
Neutral, cation geometry: -459.0556262940 (single point calc)
The order of the stabilities don't even match!
Recalculating the energies by adding
dft
grid fine
.....
end
gave the 'correct' results:
Cation, neutral geometry: -463.0353366421
Neutral, cation geometry: -463.3157251871
which gives about 0.36 eV
Here's what puzzles me a bit: you definitely need to add 'fine' in nwchem, and that's what g09 defaults to. But the energies reported for the optimised structures (cation, cation geometry and neutral, ground state) must have been calculated using a fine grid too or one would presume that they'd be off too. Repeating this with the other structures in the paper gives the same result.
Anyway, if you get weird and wacky energies from you single point calcs maybe you should make sure you've specified the dft grid size consistently.
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