**UPDATE:**there was an error in the earlier version where I gave the wrong energy for the b3pw91 functional in nwchem. In the old version the energy I provided was very close to that of acm in nwchem rather than b3pw91 in g09.

Note that for a large molecule with a medium sized basis set (101 atoms, ca 1100 functions, ca 2200 primitives) the energy difference between b3pw91 in g09 and b3pw91 in nwchem as defined below is 0.0124 Hartree, which is pretty big (7.8 kcal/mol), although in absolute terms it's quite small (nwchem: -6187.741840960054 Hartree. g09: -6187.75427966 Hartree).

The difference is a lot smaller for the small molecule in the example below.

**Original post:**

According to http://www.nwchem-sw.org/index.php/Special:AWCforum/st/id721/Are_these_definitions_correct_fo....html

**b3pw91**(as defined in Gaussian 09) and

**acm**(as defined in nwchem) are identical.

Looking at the energies I've been getting, that's not true when it comes to G09 and NWCHEM.

That acm and b3pw91 are the same

*should*be reasonable --

**b3**indicates that it's Becke's 3-parameter hybrid exchange correlation functional model, which is also known as the Adiabatic Connection Method (ACM).

For historical reasons, g98 implemented the ACM as B3LYP, by using

**LYP instead of PW91,**and using VWN_1_RPA and a few other tricks -- see section 2 in http://verahill.blogspot.com.au/2013/06/446-b3lyp-and-wah-confusion.html

Then it would stand to reason that B3PW91 would be the 'canonical' version of Becke's 3-parameter functional.

Looking at http://www.nwchem-sw.org/index.php/Release62:Density_Functional_Theory_for_Molecules

*acm*is defined as

xc HFexch 0.2 slater 0.8 becke88 nonlocal 0.72 vwn_5 1 Perdew91 0.81

(there are several versions of VWN -- I know it's vwn_5 from the output)

Either way, using acm in a single energy calculation (no optimisation) in nwchem on a water molecule with 6-31+G* (acm/6-31+G*) gives

-76.358375905073 Hartree

G09 using B3PW91/6-31+G* (manually defined basis set so we're using the same form in both nwchem and g09) gives

-76.3557851653 Hartree

nwchem using

xc HFexch 0.2 slater 0.8 becke88 nonlocal 0.72 vwn_5 1 Perdew91 0.81gives

-76.358375905072 Hartree

and nwchem using

obtained from http://myweb.liu.edu/~nmatsuna/gamess/refs/howto.dft.html,givesXC HFexch 0.20 slater 0.80 becke88 nonlocal 0.72 perdew91 0.81 pw91lda 1.00

-76.355784373093Hartree

This last definition is thus equivalent to b3pw91 in g09.

The gaussian manual is less than helpful. In fact it is quite misleading:

"These functionals have the form devised by Becke in 1993 [Becke93a]:

A*E_{X}^{Slater}+(1-A)*E_{X}^{HF}+B*ΔE_{X}^{Becke}+E_{C}^{VWN}+C*ΔE_{C}^{non-local}

[..]B3LYPuses the non-local correlation provided by the LYP expression, and VWN functional III for local correlation (not functional V). [..]B3P86specifies the same functional with the non-local correlation provided by Perdew 86, andB3PW91specifies this functional with the non-local correlation provided by Perdew/Wang 91.

**Addendum:**

While I think B3PW91

*should*be the same as ACM in nwchem (note that nwchem does not have b3pw91 as a keyword), I decided to have a look at how different packages define b3pw91.

**nwchem**-- doesn't exist. Manual.

**g09**(this post) -- xc HFexch 0.20 slater 0.80 becke88 nonlocal 0.72 perdew91 0.81 pw91lda 1.00

**gamess US**(here) -- xc HFexch 0.20 slater 0.80 becke88 nonlocal 0.72 perdew91 0.81 pw91lda 1.00

**PQS**(page 52, manual) Paraphrased:

"B3PW91 -- hybrid 3-parameter HF-DFT functional comprising combination of Slater local exchange, Becke nonlocal exchange, VWN 5 local correlation and PW91 nonlocal correlation together with a portion (20%) of the exact Hartree-Fock exchange (original 3-parameter hybrid recommended by Becke)". That to me sounds like ACM.

**Turbomol**-- not available. Manual.

**Orca**-- "B3PW The three-parameter hybrid version of PW91". Not informative.

**molpro**-- doesn't exist. manual

**Dalton**-- (page 285, manual).

"B3PW91 3-parameter Becke-PW91 functional, with PW91 correlation functional. Note that PW91c includes PW92c local correlation, thus only excess PW92c local correlation is required (coe cient of 0.19).So the local correlation is 1*PW92c= 0.81 PW91c + 0.19 PW92c. This is, I presume, is quite different from VWN.

Combine HF=0.2 Slater=0.8 Becke=0.72 PW91c=0.81 PW92c=0.19"

**Q-Chem**-- "B3PW91 (B3 Exchange + PW91 correlation)". Not explicit enough for me.

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