241. pKa, part 3: ccCA in NWChem. Doing something wrong?

First of all, I'm having problems reproducing the output from 'task ccca' by following the methods described in J. Chem. Theory Comput 2008, 4, 328-334 (scaling 0.9854) or Mol. Phys. 2009,107(8-12),1107-1121. The discrepancies are the energies reported for the MP2/cc-pVTZ-DK and CCSD(T)/cc-PVTZ which leads to a difference in calculated relativistic and correlation corrections. More about that at some other time.

Here's using ccCA in NWChem on acetic acid/acetate and formic acid/formate.
More about how it works in another post.

Basically, the way I am using it the results are very, very poor with  ccCA. All I can think is that I must be doing something wrong.

---

INPUT files 

Acetic acid input:

Title "aceticacid"
Start  aceticacid

echo

charge 0

geometry autosym units angstrom
 C     -0.312051     -1.36877     0.00000
 H     -0.929226     -1.55822     -0.878253
 H     -0.929226     -1.55822     0.878253
 H     0.548700     -2.02934     0.00000
 C     0.150590     0.0606620     0.00000
 O     -0.897092     0.922315     0.00000
 H     -0.521850     1.81528     0.00000
 O     1.29371     0.435169     0.00000
end

basis
* library "cc-pvtz"
end

dft
  mult 1
  direct
  noio
  XC b3lyp
  grid fine
  mulliken
end

driver
  default
end

ccca
  optimize
end

task ccca

Acetate input:

Title "acetate_ccca"
Start  acetate_ccca
echo
charge -1

geometry autosym units angstrom
 C     -0.0311237     -1.36218     0.00000
 H     0.501926     -1.73727     0.878691
 H     0.501926     -1.73727     -0.878691
 H     -1.05131     -1.75101     0.00000
 C     -0.00500996     0.204086     0.00000
 O     1.14247     0.706045     0.00000
 O     -1.12049     0.771493     0.00000
end

basis
* library "cc-pvtz"
end

dft
  mult 1
  direct
  noio
  XC b3lyp
  grid fine
  mulliken
end

driver
  default
end

ccca
   optimize
end

task ccca

Formic acid input:

Title "formicacid"
Start  formicacid

echo

charge 0

geometry autosym units angstrom
 C     0.410955     -0.132154     0.00000
 H     1.50430     -0.0475164     0.00000
 O     -0.134104     1.09718     0.00000
 H     -1.09846     0.988665     0.00000
 O     -0.203188     -1.15938     0.00000
end

basic
* library "cc-pvtz"
end

dft
  mult 1
  direct
  noio
  XC b3lyp
  grid fine
  mulliken
end

driver
end

ccca
   optimize
end

task ccca

Formate input:

Title "formate"
Start  formate

echo

charge -1

geometry autosym units angstrom
 C     0.00000     0.00000     0.329396
 H     0.00000     0.00000     1.47310
 O     -1.13532     0.00000     -0.189103
 O     1.13532     0.00000     -0.189103
end

basis "ao basis" spherical print
* library "cc-pvtz"
END

dft
  mult 1
  direct
  noio
  XC b3lyp
  grid fine
  mulliken
end

driver
end

ccca
   optimize
end

task ccca

---

OUTPUT 

Acetic acid

 Temperature                      =   298.15K
 frequency scaling parameter      =   0.9889

 Zero-Point correction to Energy  =   38.155 kcal/mol  (  0.060805 au)
 Thermal correction to Energy     =   41.060 kcal/mol  (  0.065434 au)
 Thermal correction to Enthalpy   =   41.653 kcal/mol  (  0.066378 au)

 Total Entropy                    =   69.467 cal/mol-K
   - Translational                =   38.179 cal/mol-K (mol. weight =  60.0211)    - Rotational                   =   23.830 cal/mol-K (symmetry #  =        1)
   - Vibrational                  =    7.458 cal/mol-K

 Cv (constant volume heat capacity) =   14.439 cal/mol-K
   - Translational                  =    2.979 cal/mol-K
   - Rotational                     =    2.979 cal/mol-K
   - Vibrational                    =    8.480 cal/mol-K


 ccCA: calculations done, now printing results
 
 ccCA-P  reference energy =   -228.82035086993045     
 ccCA-S3 reference energy =   -228.82800135561300     
 ccCA-S4 reference energy =   -228.82030423449530     
 ccCA-PS3 reference energy=   -228.82417611277174     
 DK correction            =  -0.13322049012506909     
 CCSD(T) correction       =   -4.8762979862686961E-002
 CV correction            =  -0.20936881324035994     
 ---------------------------
 Total ccCA-P   energy    =   -229.21170315315857     
 Total ccCA-S3  energy    =   -229.21935363884111     
 Total ccCA-S4  energy    =   -229.21165651772341     
 Total ccCA-PS3 energy    =   -229.21552839599985     
 
 Thermochemistry available:
            ZPE   =   6.0851792771826778E-002
 ccCA-P   E+ZPE   =  -229.15085136038675     
 ccCA-S3  E+ZPE   =  -229.15850184606930     
 ccCA-S4  E+ZPE   =  -229.15080472495160     
 ccCA-PS3 E+ZPE   =  -229.15467660322804     
 Wrote ccCA-P    energy to the RTDB 
 Leaving ccCA module...

 Task  times  cpu:     5565.6s     wall:     5650.7s

Acetate

 Temperature                      =   298.15K
 frequency scaling parameter      =   0.9889

 Zero-Point correction to Energy  =   29.591 kcal/mol  (  0.047157 au)
 Thermal correction to Energy     =   31.853 kcal/mol  (  0.050762 au)
 Thermal correction to Enthalpy   =   32.446 kcal/mol  (  0.051706 au)

 Total Entropy                    =   64.067 cal/mol-K
   - Translational                =   38.129 cal/mol-K (mol. weight =  59.0133)
   - Rotational                   =   23.739 cal/mol-K (symmetry #  =        1)
   - Vibrational                  =    2.199 cal/mol-K

 Cv (constant volume heat capacity) =   11.235 cal/mol-K
   - Translational                  =    2.979 cal/mol-K
   - Rotational                     =    2.979 cal/mol-K
   - Vibrational                    =    5.276 cal/mol-K

 ccCA: calculations done, now printing results
 
 ccCA-P  reference energy =   -228.25857936176124     
 ccCA-S3 reference energy =   -228.26625083689740     
 ccCA-S4 reference energy =   -228.25849407721080     
 ccCA-PS3 reference energy=   -228.26241509932930     
 DK correction            =  -0.13318127658752132     
 CCSD(T) correction       =   -4.4728554700242285E-002
 CV correction            =  -0.20921905251765338     
 ---------------------------
 Total ccCA-P   energy    =   -228.64570824556665     
 Total ccCA-S3  energy    =   -228.65337972070282     
 Total ccCA-S4  energy    =   -228.64562296101622     
 Total ccCA-PS3 energy    =   -228.64954398313472     
 
 Thermochemistry available:
            ZPE   =   4.7193435242008613E-002
 ccCA-P   E+ZPE   =  -228.59851481032464     
 ccCA-S3  E+ZPE   =  -228.60618628546081     
 ccCA-S4  E+ZPE   =  -228.59842952577421     
 ccCA-PS3 E+ZPE   =  -228.60235054789271     
 Wrote ccCA-P    energy to the RTDB 
 Leaving ccCA module...

 Task  times  cpu:     3859.1s     wall:     3910.2s

Formic acid

 Temperature                      =   298.15K
 frequency scaling parameter      =   0.9889

 Zero-Point correction to Energy  =   20.909 kcal/mol  (  0.033320 au)
 Thermal correction to Energy     =   22.902 kcal/mol  (  0.036497 au)
 Thermal correction to Enthalpy   =   23.495 kcal/mol  (  0.037441 au)

 Total Entropy                    =   59.329 cal/mol-K
   - Translational                =   37.387 cal/mol-K (mol. weight =  46.0055)    - Rotational                   =   21.008 cal/mol-K (symmetry #  =        1)
   - Vibrational                  =    0.934 cal/mol-K

 Cv (constant volume heat capacity) =    8.703 cal/mol-K
   - Translational                  =    2.979 cal/mol-K
   - Rotational                     =    2.979 cal/mol-K
   - Vibrational                    =    2.744 cal/mol-K

 ccCA: calculations done, now printing results

 ccCA-P  reference energy =   -189.56748775122853
 ccCA-S3 reference energy =   -189.57364633780318
 ccCA-S4 reference energy =   -189.56733835209894
 ccCA-PS3 reference energy=   -189.57056704451585
 DK correction            =  -0.11856238070660652
 CCSD(T) correction       =   -3.0831132609506540E-002
 CV correction            =  -0.16057296161548607
 ---------------------------
 Total ccCA-P   energy    =   -189.87745422616013
 Total ccCA-S3  energy    =   -189.88361281273478
 Total ccCA-S4  energy    =   -189.87730482703054
 Total ccCA-PS3 energy    =   -189.88053351944745

 Thermochemistry available:
            ZPE   =   3.3346398704552728E-002
 ccCA-P   E+ZPE   =  -189.84410782745556
 ccCA-S3  E+ZPE   =  -189.85026641403022
 ccCA-S4  E+ZPE   =  -189.84395842832598
 ccCA-PS3 E+ZPE   =  -189.84718712074289
 Wrote ccCA-P    energy to the RTDB
 Leaving ccCA module...

 Task  times  cpu:     1369.3s     wall:     1407.5s

Formate

 Temperature                      =   298.15K
 frequency scaling parameter      =   0.9889

 Zero-Point correction to Energy  =   12.385 kcal/mol  (  0.019737 au)
 Thermal correction to Energy     =   14.252 kcal/mol  (  0.022713 au)
 Thermal correction to Enthalpy   =   14.845 kcal/mol  (  0.023656 au)

 Total Entropy                    =   56.927 cal/mol-K
   - Translational                =   37.321 cal/mol-K (mol. weight =  44.9976)
   - Rotational                   =   19.229 cal/mol-K (symmetry #  =        2)
   - Vibrational                  =    0.377 cal/mol-K

 Cv (constant volume heat capacity) =    7.310 cal/mol-K
   - Translational                  =    2.979 cal/mol-K
   - Rotational                     =    2.979 cal/mol-K
   - Vibrational                    =    1.351 cal/mol-K


 ccCA: calculations done, now printing results
 
 ccCA-P  reference energy =   -189.01189831122844     
 ccCA-S3 reference energy =   -189.01808726799254     
 ccCA-S4 reference energy =   -189.01171261173857     
 ccCA-PS3 reference energy=   -189.01499278961049     
 DK correction            =  -0.11851294005154500     
 CCSD(T) correction       =   -2.6430727035545942E-002
 CV correction            =  -0.16057463040127118     
 ---------------------------
 Total ccCA-P   energy    =   -189.31741660871680     
 Total ccCA-S3  energy    =   -189.32360556548090     
 Total ccCA-S4  energy    =   -189.31723090922694     
 Total ccCA-PS3 energy    =   -189.32051108709885     
 
 Thermochemistry available:
            ZPE   =   1.9751889903778755E-002
 ccCA-P   E+ZPE   =  -189.29766471881302     

 ccCA-S3  E+ZPE   =  -189.30385367557713     
 ccCA-S4  E+ZPE   =  -189.29747901932316     
 ccCA-PS3 E+ZPE   =  -189.30075919719508     
 Wrote ccCA-P    energy to the RTDB 
 Leaving ccCA module...

---

Solvation energy

Solvation energy may seem easy to calculate, but difficult to calculate accurately using implicit methods, in particular for ions. I used the optimized structures from above, and then did a single-point COSMO (rsolv 0. Not ideal)  at RDFT(b3lyp)/cc-pVTZ/

Acetic acid: -8.59 kcal/mol
Acetate: -72.33 kcal/mol
Formic acid: -8.90
Formate: -72.59 kcal/mol
H+: -624.61 kcal/mol (lit. value)

---

Free energies:  
G: ccCA-P+(Hcorr-T*Scorr)
 G(acetic acid): -229.21170315315857*627.503+(41.653-298.15*69.467/1000)-8.59
 G(acetate): -228.64570824556665*627.503+(32.446-298.15*64.067/1000)-72.33
 G(formic acid): -189.87745422616013*627.503+(23.495-298.15*59.329/1000)-8.90
 G(formate):  -189.31741660871680*627.503+(14.845-298.15*56.927/1000)-72.59
 G(H+): -6.28 kcal/mol (lit. value) -264.61 (lit. value)=-270.89 kcal/mol

---

Results: Direct approach:
Don't forget to account for the standard state. R=1.9858775(34)×10⁻³ kcal/(K.mol)
DG(acetic/acetate)=G(acetate)+G(H+)-G(acetic)+RT*ln(1/24.46)=
(-228.64570824556665*627.503+(32.446-298.15*64.067/1000)-72.33-270.89)-(-229.21170315315857*627.503+(41.653-298.15*69.467/1000)-8.59)+1.9858775*298.15*log(1/24.46)/1000=
11.0435795929699 kcal/mol=46.2063370169861 kJ/mol =>
pKa=DG*log10(e)/RT=
11.0435795929699*log10(e)/(1.9858775*10**(-3)*298.15)
=8.1 (which is very bad -- it should be close to 4.75)

DG(formic/formate)=G(formate)+G(H+)-G(formic)-RT*ln(1/24.46)=
(-189.31741660871680*627.503+(14.845-298.15*56.927/1000)-72.59-270.89)-(-189.87745422616013*627.503+(23.495-298.15*59.329/1000)-8.90)+1.9858775*298.15*log(1/24.46)/1000=
7.01850845285312 kcal/mol=29.3654393667375 kJ/mol
pKa=5.1 (which is quite bad -- it should be close to 3.75)

---

Results: Isodesmic approach
From an older post:
"Assuming that we know that formic acid has a pKa of 3.75, then DG_solution=pKa*RT/log(e)=3.75*8.314*298.15/log10(e)/1000=21.404 kJ/mol. The reverse reaction is -21.404 kJ/mol."
That's about 5.116 kcal/mol

DG(acetate)+DG(formic)-(DG(acetic)+DG(formate))+DG(ref)=
((-228.64570824556665*627.503+(32.446-298.15*64.067/1000)-72.33)+(-189.87745422616013*627.503+(23.495-298.15*59.329/1000)-8.90))-((-229.21170315315857*627.503+(41.653-298.15*69.467/1000)-8.59)+(-189.31741660871680*627.503+(14.845-298.15*56.927/1000)-72.59))+5.116=
4.02507114014588 kcal/mol+5.116 kcal/mol =9.14107114014588 kcal/mol <=> pKa= 6.7
Which is better, but still not as good as here.

Using the E+zpe energies doesn't help much:
((-228.59851481032464*627.503+(32.446-298.15*64.067/1000)-72.33)+(-189.84410782745556*627.503+(23.495-298.15*59.329/1000)-8.90))-((-229.15085136038675*627.503+(41.653-298.15*69.467/1000)-8.59)+(-189.29766471881302*627.503+(14.845-298.15*56.927/1000)-72.59))+5.116=
9.10100587110175 kcal/mol <=> pKa=6.68

I really have no idea why the results are so bad when I had reasonable results with DFT/b3lyp/6-31++G** which should be worse than the E(CBS)+E(CC)+E(CV)+E(DK) approach for calculating electronic energies.

Solvation energies are a bit different and could explain some of the difference. Using the solvation energies from here I got:
((-228.64570824556665*627.503+(32.446-298.15*64.067/1000)-73.23)+(-189.87745422616013*627.503+(23.495-298.15*59.329/1000)-9.99))-((-229.21170315315857*627.503+(41.653-298.15*69.467/1000)-9.32)+(-189.31741660871680*627.503+(14.845-298.15*56.927/1000)-72.47))+5.116=
7.76107114008302 kcal/mol <=> pKa=5.69. Not 4.75, but closer.

Using rsolv 1.3 I get

((-228.64570824556665*627.503+(32.446-298.15*64.067/1000)-71.09)+(-189.87745422616013*627.503+(23.495-298.15*59.329/1000)-6.37))-((-229.21170315315857*627.503+(41.653-298.15*69.467/1000)-6.53)+(-189.31741660871680*627.503+(14.845-298.15*56.927/1000)-71.90))+5.116=
10.1610711401063 kcal/mol which is bad.

---

More thinking.
  This paper says that the gas phase free energy for the deprotonation of acetic acid should be 341.1 kcal/mol
(-228.64570824556665*627.503+(32.446-298.15*64.067/1000)-6.82)-(-229.21170315315857*627.503+(41.653-298.15*69.467/1000))=340.75 kca/mol
We're within 1 kcal/mol 

The same paper states 338.5 kcal/mol for formic acid:
(-189.31741660871680*627.503+(14.845-298.15*56.927/1000)-6.82)-(-189.87745422616013*627.503+(23.495-298.15*59.329/1000))=336.67 kca/mol

For our direct solution phase pKa calculation formic acid was off by about 1.9 kcal/mol which is similar to the error here.

240. Harmonic frequency scaling in NWChem

...is difficult to find information about, but apparently it IS possible:
http://www.emsl.pnl.gov/docs/nwchem/nwchem-support/2012/08/0021._NWCHEM_FW:_BOUNCE_nwchem-users_emsl.pnl

Example input:

Title "acetate"

Start  acetate

echo

charge -1

geometry autosym units angstrom
 C     0.0191498     0.0215213     0.0191498
 H     -0.621688     -0.620669     0.658428
 H     0.658428     -0.620669     -0.621688
 H     -0.628475     0.649316     -0.628475
 C     0.881900     0.883055     0.881900
 O     1.74905     0.315740     1.74905
 O     0.799516     2.22959     0.799516
end

basis
* library "cc-pvtz"
end

dft
  mult 1
  direct
  noio
  XC b3lyp
  grid fine
  mulliken
end

driver
end

set vib:scalefreq  0.9854

task dft optimize
task dft freq

which gives:

 Temperature                      =   298.15K
 frequency scaling parameter      =   0.9854

 Zero-Point correction to Energy  =   29.486 kcal/mol  (  0.046990 au)
 Thermal correction to Energy     =   31.752 kcal/mol  (  0.050601 au)
 Thermal correction to Enthalpy   =   32.345 kcal/mol  (  0.051544 au)

 Total Entropy                    =   64.086 cal/mol-K
   - Translational                =   38.129 cal/mol-K (mol. weight =  59.0133)
   - Rotational                   =   23.739 cal/mol-K (symmetry #  =        1)
   - Vibrational                  =    2.218 cal/mol-K

 Cv (constant volume heat capacity) =   11.268 cal/mol-K
   - Translational                  =    2.979 cal/mol-K
   - Rotational                     =    2.979 cal/mol-K
   - Vibrational                    =    5.309 cal/mol-K

c.f.

 Temperature                      =   298.15K
 frequency scaling parameter      =   1.0000

 Zero-Point correction to Energy  =   29.923 kcal/mol  (  0.047686 au)
 Thermal correction to Energy     =   32.173 kcal/mol  (  0.051272 au)
 Thermal correction to Enthalpy   =   32.766 kcal/mol  (  0.052215 au)

 Total Entropy                    =   64.008 cal/mol-K
   - Translational                =   38.129 cal/mol-K (mol. weight =  59.0133)
   - Rotational                   =   23.739 cal/mol-K (symmetry #  =        1)
   - Vibrational                  =    2.141 cal/mol-K

 Cv (constant volume heat capacity) =   11.132 cal/mol-K
   - Translational                  =    2.979 cal/mol-K
   - Rotational                     =    2.979 cal/mol-K
   - Vibrational                    =    5.173 cal/mol-K

236. Calculating pKa, part 1:Example (attempt) of an isodesmic reactions in NWChem

Back to learning about computational approaches to chemistry. The usual warnings apply: why would you trust anything that I say about anything? I'm writing anonymously, and I may misunderstand things at times. So make sure that you compare what I write with that of other sources and make up your own mind.

Anyway, I found a fairly detailed presentation in which they were using Gaussian 98 here: https://www.uow.edu.au/~adamt/Trevitt_Research/Links_files/pKa%20workshop%20slides.pdf

---

While that should be ok to reproduce, it's not that straightforward to do even with Gaussian, since G09 and G03 don't report solvation parameters in the same way (or detail) as G98.

I'm also a lot keener on NWChem than Gaussian for various reasons, not least that it's 'free' (both libre and gratis) while Gaussian inc. has been accused of doing somewhat unfriendly things in the name of protecting their business interests.

See here and here for an example, and then here for a rebuttal from Gaussian inc. I know that EMSL/Pacific Northwest National Lab that develop NWChem and ECCE are prohibited from using Gaussian since they are considered as being competitors.

---

Back to science.

Our test example will be acetate, and we'll use formic acid to correct our results.
The fact that this post is very long is due to the amount of detail supplied -- I prefer to show some of the more obvious things so that people can learn from what I post -- and I learn by writing the post.

But first let's just do everything using direct methods.

We work with a thermochemical cycle:

IF we can't calculate the DG_solution directly (i.e. too expensive) we can optimise our structures in the gas phase, and then calculate the solvation energy for those structures.

Then DG_sol=DG_gas+DG_solvation(B)-DGsolvation(A).
(more generally sum of DG_solv(prod) - sum of DG_solv(reactants)).


1. pKa of Acetic acid using direct methods

We can either do
H3CCOOH -> H3COO- + H+
or
H3CCOOH + H2O -> H3COO- + H3O+

Steps:
Optimise acetic acid and acetate in the gas phase and do frequency calculations to get the enthalpy and entropy. Then use the gas phase structures and do single point calculations using COSMO to get the electrostatic solvation energies. Finally, use standard state corrections.

A. Optimise acetic acid in the gas phase and do frequency calculation

Title "aceticacid_gas"
Start  aceticacid_gas
echo
charge 0

geometry autosym units angstrom
 C     0.0402340     0.0308110     0.0402340
 H     -0.600803     -0.611482     0.679201
 H     0.679201     -0.611482     -0.600803
 H     -0.607055     0.659335     -0.607055
 C     0.903928     0.890481     0.903928
 O     0.814831     2.23989     0.814831
 O     1.78275     0.299052     1.78275
 H     2.25438     1.03276     2.25438
end

basis "ao basis" spherical print
  H library "6-31++G**"
  O library "6-31++G**"
  C library "6-31++G**"
END

dft
  mult 1
  direct
  noio
  XC b3lyp
  grid fine
  mulliken
end

driver
  default
end

task dft optimize
task dft freq

which gives

         Total DFT energy =     -229.102415550663
      One electron energy =     -550.833155571059
           Coulomb energy =      230.555870626149
    Exchange-Corr. energy =      -29.497734561879
 Nuclear repulsion energy =      120.672603956126

 Numeric. integr. density =       31.999999816803

     Total iterative time =      3.6s

and

 Temperature                      =   298.15K
 frequency scaling parameter      =   1.0000

 Zero-Point correction to Energy  =   38.683 kcal/mol  (  0.061646 au)
 Thermal correction to Energy     =   41.568 kcal/mol  (  0.066243 au)
 Thermal correction to Enthalpy   =   42.160 kcal/mol  (  0.067186 au)

 Total Entropy                    =   69.198 cal/mol-K
   - Translational                =   38.179 cal/mol-K (mol. weight =  60.0211)
   - Rotational                   =   23.855 cal/mol-K (symmetry #  =        1)
   - Vibrational                  =    7.164 cal/mol-K

 Cv (constant volume heat capacity) =   14.327 cal/mol-K
   - Translational                  =    2.979 cal/mol-K
   - Rotational                     =    2.979 cal/mol-K
   - Vibrational                    =    8.368 cal/mol-K

So that G=-229.102415550663*(627.503 kcal/Hartree)+(42.160 kcal/mol-298.15*(69.198 cal/molK)/1000)=-1.4372e+05 kcal/mol

B. Optimise acetate in the gas phase and do frequency calculation

Title "acetate_gas"

Start  acetate_gas

echo

charge -1

geometry autosym units angstrom
 C     0.0405721     0.0285481     0.0405721
 H     -0.601438     -0.613690     0.678620
 H     0.678620     -0.613690     -0.601438
 H     -0.605857     0.658809     -0.605857
 C     0.904975     0.886806     0.904975
 O     0.825186     2.23364     0.825186
 O     1.77103     0.316179     1.77103
end

basis "ao basis" spherical print
  H library "6-31++G**"
  O library "6-31++G**"
  C library "6-31++G**"
END

dft
  mult 1
  direct
  noio
  XC b3lyp
  grid fine
  mulliken 
end

driver
  default
end

task dft optimize
task dft freq                     

which gives

         Total DFT energy =     -228.540046314754
      One electron energy =     -539.474204198295
           Coulomb energy =      229.063209931484
    Exchange-Corr. energy =      -29.339040486703
 Nuclear repulsion energy =      111.209988438759

 Numeric. integr. density =       32.000000595562

     Total iterative time =      2.9s

and

 Temperature                      =   298.15K
 frequency scaling parameter      =   1.0000

 Zero-Point correction to Energy  =   30.023 kcal/mol  (  0.047845 au)
 Thermal correction to Energy     =   32.271 kcal/mol  (  0.051427 au)
 Thermal correction to Enthalpy   =   32.863 kcal/mol  (  0.052371 au)

 Total Entropy                    =   64.022 cal/mol-K
   - Translational                =   38.129 cal/mol-K (mol. weight =  59.0133)
   - Rotational                   =   23.766 cal/mol-K (symmetry #  =        1)
   - Vibrational                  =    2.127 cal/mol-K

 Cv (constant volume heat capacity) =   11.112 cal/mol-K
   - Translational                  =    2.979 cal/mol-K
   - Rotational                     =    2.979 cal/mol-K
   - Vibrational                    =    5.153 cal/mol-K

so that G=-228.540046314754*(627.503 kcal/Hartree)+(32.271 kcal/mol-298.15*(64.022 cal/molK)/1000)=-1.4338e+05 kcal/mol

Putting A and B together: (-228.540046314754*(627.503)+(32.271-298.15*(64.022/1000)))-(-229.102415550663*(627.503)+(42.160-298.15*(69.198/1000)))=344.54 kcal/mol

We haven't accounted for solvation or the proton yet.

C. Solvation of acetic acid

Title "aceticacid_solvation"
Start  aceticacid_solvation

echo

charge 0

geometry autosym units angstrom
 C     -0.313400     -1.37257     0.00000
 H     -0.932151     -1.56367     -0.882188
 H     -0.932151     -1.56367     0.882188
 H     0.551887     -2.03461     0.00000
 C     0.149260     0.0607660     0.00000
 O     1.30165     0.439500     0.00000
 O     -0.897630     0.927778     0.00000
 H     -0.523912     1.82535     0.00000
end

basis "ao basis" spherical print
  H library "6-31++G**"
  O library "6-31++G**"
  C library "6-31++G**"
END

dft
  mult 1
  direct
  noio
  XC b3lyp
  grid fine
  mulliken
end

cosmo
end

task dft energy

which gives

                  COSMO solvation results
                  -----------------------

                 gas phase energy =      -229.1024156124
                 sol phase energy =      -229.1172649438
 (electrostatic) solvation energy =         0.0148493315 (    9.32 kcal/mol)

D. Solvation of acetate

Title "acetate_solvation"
Start  acetate_solvation

echo

charge -1

geometry autosym units angstrom
 C     -0.0308736     -1.36399     0.00000
 H     0.503418     -1.74042     0.882388
 H     0.503418     -1.74042     -0.882388
 H     -1.05531     -1.75261     0.00000
 C     -0.00485953     0.199667     0.00000
 O     -1.12642     0.778065     0.00000
 O     1.14855     0.713544     0.00000
end

basis "ao basis" spherical print
  H library "6-31++G**"
  O library "6-31++G**"
  C library "6-31++G**"
END

dft
  mult 1
  direct
  noio
  XC b3lyp
  grid fine
  mulliken
end

cosmo
end

task dft energy

which gives

                  COSMO solvation results
                  -----------------------
  
                 gas phase energy =      -228.5400463128
                 sol phase energy =      -228.6567490452
 (electrostatic) solvation energy =         0.1167027324 (   73.23 kcal/mol)

Putting A, B and solvation energies together: 
[(-228.540046314754*(627.503)+(32.271-298.15*(64.022/1000)))-(-229.102415550663*(627.503)+(42.160-298.15*(69.198/1000)))]-[73.23-9.32]=344.54-63.910=280.63 kcal/mol

E. The Proton
If you try to do any calculations on an isolated proton you get and SCFE of zero, and you won't do much better in terms of thermochemical data. Yet, monoatomic gases obviously still posses entropy and enthalpy. Instead, the document I cite above uses the ideal gas partition function for ideal monoatomic gases which gives a value of 6.28 kcal/mol for the free energy of a proton.  The last reference states that the free energy for a proton in the gas phase is experimentally determined to be -6.28 kcal/mol and that the free energy of hydration is -264.61 kcal/mol (experimental).

[(-228.540046314754*(627.503)+(32.271-298.15*(64.022/1000)))-6.28-(-229.102415550663*(627.503)+(42.160-298.15*(69.198/1000)))]-[73.23+264.61-9.32]=338.26-328.52=9.74 kcal/mol =40.752 kJ/mol
We're not done yet though -- make sure to continue to 'F. Standard States'

F. Standard States

We know that

DG=DG^0+RT ln (Q).

We have a bit of a problem. We're doing calculations in the gas phase (pressure) but looking at predicting solution values (concentration). Also, I don't fully get it yet, so my explanation is probably a bit fuzzy.

 So if A+B-> C+D we get Q=(C*D)/(A*B) but for A -> C+D we get Q=(C*D)/(A) or (1 bar x1 bar/1 bar)= 1 bar = 101350 Pa => nRT/P=1*8.314*298.15/101350=0.024458 m3= 24.46 L. The concentration of each species is 1 mol/bar which in volume terms means 1/24.46 L.

And the A -> C + D situation is what we have if we look at
HA -> H+ + A-

So,
Q=((1/24.46)*(1/24.46)/(1/24.46))=1/2.4.46 which gives
DG=DG^0-RTln(24.46)=DG^0-7924.9 J/mol

Thus, we need to correct for the standard state: 40.752 -7924.9/1000=32.827 kJ/mol

G. Calculating pKa

Since (in solution so that concentrations are 1 M)
DG=DG^0+RTln(K), where K=([H3COO][H+])/([H3COOH])
DG=DG^0+(RT ln([HCOO]/[H3COOH])+RTln (10^(-pH)), where RT ln([HCOO]/[H3COOH])=RTln(1/1)=0 so
DG=DG^0+RTln (10^(-pH))=DG^0+RT log (10^(-pH)/log(e)=DG^0-(RT/log(e)) * pH
Which for equilbrium, where pH=pKa and DG=0, turns into
pKa=DG^0*log(e)/RT

pKa= DG*log(e)/(RT)=(32.827*1000)*log(e)/(8.314*298.15)=5.75

Not that great as predictions go (exp: pKa=4.75). Looking at some of the literature one error lies in the size of the solvation energies. Possibly one should tune the parameters used in the COSMO.

2. Isodemic reaction/correction

Using formic acid
This approach is based on 1) the similarity between two compounds and 2) us knowing the DG_solution parameter for one of them.

Assuming that we know that formic acid has a pKa of 3.75, then DG_solution=pKa*RT/log(e)=3.75*8.314*298.15/log10(e)/1000=21.404 kJ/mol. The reverse reaction is -21.404 kJ/mol.

We skip a few steps.
Here are the calculated parameters for formic acid (using the same method as above):

Formic acid


SCFE: -189.772804709496 Hartree
Enthalpy correction: 23.773 kcal/mol
Entropy correction: 59.339 cal/mol
Solvation energy: 9.99 kcal/mol

Formate
SCFE:  -189.217943605798 Hartree
Enthalpy correction: 15.016 kcal/mol
Entropy correction: 56.992 cal/mol
Solvation energy: 72.47 kcal/mol

[Just for kicks we quickly look at what the prediction is:
accounting for everything (solvation, proton etc.)
((-189.217943605798*627.503+(15.016-298.15*56.992/1000)-72.47) +(-6.28-264.61))-(-189.772804709496*627.503+(23.773-298.15*59.339/1000)-9.99)=6.7498 kcal/mol
6.7498*4.184-7924.9/1000=20.316 kJ/mol <=> pKa=1000*20.316*log10(e)/(8.314*298.15)=3.56]

The isodesmic approach:

Here we look at
H3CCOOH + -OOCH -> H3CCOO- +HOOCH

This combined reaction has a
DG_solution=DG_solution(acetic acid/acetate)+DG_solution(formate/formic acid)
<=>
DG_solution(acetic acid/acetate)= DG_solution-DG_solution(formic acid/formate)
=DG_solution-(-21.404 kJ/mol)
=DG_gas+[DG_sol(acetate)+DG_sol(formic acid)-DG_sol(acetic acid)-DG_sol(formate)]+21.404 kJ/mol
=
(-228.540046314754*(627.503)+(32.271-298.15*(64.022/1000)))+(-189.772804709496*627.503+(23.773-298.15*(59.339/1000)))-(-229.102415550663*(627.503)+(42.160-298.15*(69.198/1000)))-(-189.217943605798*627.503+(15.016-298.15*(56.992/1000)))+(-73.23-9.99+9.32+72.47)+5.116 kcal/mol= 8.11 kcal/mol= 33.93 kJ/mol

Here we don't need to fiddle with standard states or experimental values for solvation of the proton.

pKa= DG*log(e)/(RT)=(33.93*1000)*log(e)/(8.314*298.15)=5.94
which is even worse than before...
We want ca 27 kJ/mol = 6.48 kcal/mol. Paradoxically this may be due to the ab initio approach to the pKa of formic acid actually giving a very reasonable value.

Using Propanoic acid
So let's try the isodesmic approach using propanoic acid as our reference instead.


Propanoic acid


SCFE:  -268.419515785389 Hartree
Enthalpy correction:  60.894 kcal/mol
Entropy correction:  75.184 cal/mol
Solvation energy:  8.15 kcal/mol

Propanoate
SCFE:   -267.857478200414 Hartree
Enthalpy correction: 52.096 kcal/mol
Entropy correction:  75.392 cal/mol
Solvation energy:  72.14 kcal/mol

pKa=4.86 <=> 27.739 kJ/mol= 6.63 kcal/mol

(-228.540046314754*(627.503)+(32.271-298.15*(64.022/1000)))+(-268.419515785389*627.503+(60.894-298.15*(75.184/1000)))-(-229.102415550663*(627.503)+(42.160-298.15*(69.198/1000)))-(-267.857478200414*627.503+(52.096-298.15*(75.392/1000)))+(-73.23-8.15+9.32+72.14)+6.63 kcal/mol=7.4324 kcal/mol=31.097

pKa= DG*log(e)/(RT)=(31.097*1000)*log(e)/(8.314*298.15)=5.45

It's a bit better, but still a bit off.

3. Conclusion:
The isodesmic approach is not magic and it relies on the similarity of two compounds, one for which there are experimental data, causing similar computational issues. Under the right conditions it's a useful approach, whereas under other conditions -- where a body of experimental data exists -- it might just be easier to determine the correlation between experimental and calculated data via fitting.

The approach worked better for the acetate/propanoate pair than the formate/acetate pair -- and one would consider acetic acid and propanoic acid to be more similar than formic acid and the higher acids. We're still far off from obtaining a perfect result though.

An additional problem is obviously the sensitivity of pKa to the DG -- one pH unit is about 1.36 kcal/mol, which is very small given the usual errors in DFT level calculations. I've seen indications online (google!) that the accuracy of b3lyp is about 3 kcal/mol, and one can always debate the accuracy of a highly empirical method like COSMO.

229. Compile ATLAS (+ gromacs, nwchem) on AMD FX 8150 on Debian Testing (Wheezy)

Xianyi's openblas doesn't seem to be ready for AMD FX 8150 yet. I've played with ATLAS in the past, but  for some reason didn't see the same performance with NWChem and ATLAS as I saw with NWChem and Openblas, so I never ended up using it.

I'm also having issues using openblas with CPMD and quantum espresso, and ATLAS is a well-established, respectable project, so it's time to give it another shot. As in most cases in these situations, it's probably a matter of PEBKAC.

Building ATLAS
Anyway. On we go...

mkdir /opt/ATLAS
chown ${USER} /opt/ATLAS
mkdir ~/tmp
cd ~/tmp
wget http://www.netlib.org/lapack/lapack-3.4.1.tgz
 wget http://downloads.sourceforge.net/project/math-atlas/Developer%20%28unstable%29/3.9.72/atlas3.9.72.tar.bz2
tar xvf atlas3.9.72.tar.bz2
cd ATLAS/

Edit ATLAS/Make.top
change the V on line 6 to lowercase i.e. from
- $(ICC) -V 2>&1 >> bin/INSTALL_LOG/ERROR.LOGto
- $(ICC) -v 2>&1 >> bin/INSTALL_LOG/ERROR.LOG
mkdir build/
cd build/

sudo apt-get install cpufreq-utils

cat /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor

ondemand

sudo cpufreq-set -g performance

Unfortunately that only takes care of cpu0:

cat /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor

performance

but

cat /sys/devices/system/cpu/cpu1/cpufreq/scaling_governor

ondemand

So...since we have 8 cores (cpu0-cpu7):

sudo cp /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor /sys/devices/system/cpu/cpu1/cpufreq/scaling_governor
sudo cp /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor /sys/devices/system/cpu/cpu2/cpufreq/scaling_governor
sudo cp /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor /sys/devices/system/cpu/cpu3/cpufreq/scaling_governor
sudo cp /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor /sys/devices/system/cpu/cpu4/cpufreq/scaling_governor
sudo cp /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor /sys/devices/system/cpu/cpu5/cpufreq/scaling_governor
sudo cp /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor /sys/devices/system/cpu/cpu6/cpufreq/scaling_governor
sudo cp /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor /sys/devices/system/cpu/cpu7/cpufreq/scaling_governor

OK, we're ready to compile:
.././configure --prefix=/opt/ATLAS -Fa alg '-fPIC' --with-netlib-lapack-tarfile=$HOME/tmp/lapack-3.4.1.tgz --shared

Some of the info that's important is:

OS configured as Linux (1)
Assembly configured as GAS_x8664 (2)
Vector ISA Extension configured as  AVXFMA4 (4,496)
Architecture configured as  AMDDOZER (34)
Clock rate configured as 3600Mhz

If that checks out you don't need to manually set your architecture. To get a list over options, do
 make xprint_enums ; ./xprint_enums

If all is well,

make
make install

You should now be done.

Linking Gromacs against ATLAS

export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/lib/openmpi/lib:/opt/ATLAS/lib
#single precision
export LDFLAGS="-L/opt/fftw/fftw-3.3.2/single/lib -L/opt/ATLAS/lib -lsatlas -ltatlas -lgfortran"
export CPPFLAGS="-I/opt/fftw/fftw-3.3.2/single/include -I/opt/ATLAS/include"
./configure --disable-mpi --enable-float --with-fft=fftw3 --with-external-blas --with-external-lapack --program-suffix=_spatlas --prefix=/opt/gromacs/gromacs-4.5.5
make -j6 2>make.err 1>make.log
make install

#double precision
make distclean
export LDFLAGS="-L/opt/fftw/fftw-3.3.2/double/lib -L/opt/ATLAS/lib -lsatlas -ltatlas -lgfortran" 
export CPPFLAGS="-I/opt/fftw/fftw-3.3.2/double/include -I/opt/ATLAS/include"
./configure --disable-mpi --disable-float --with-fft=fftw3 --with-external-blas --with-external-lapack --program-suffix=_dpatlas --prefix=/opt/gromacs/gromacs-4.5.5
make -j6 2>make2.err 1>make2.log
make install

#single + mpi
make distclean
export LDFLAGS="-L/opt/fftw/fftw-3.3.2/single/lib -L/opt/ATLAS/lib -lsatlas -ltatlas -lgfortran"
export CPPFLAGS="-I/opt/fftw/fftw-3.3.2/single/include -I/opt/ATLAS/include"
./configure --enable-mpi --enable-float --with-fft=fftw3 --with-external-blas --with-external-lapack --program-suffix=_spmpiatlas --prefix=/opt/gromacs/gromacs-4.5.5
make -j6 2>make3.err 1>make3.log
make install

#double + mpi
make distclean
export LDFLAGS="-L/opt/fftw/fftw-3.3.2/double/lib -L/opt/ATLAS/lib -lsatlas  -ltatlas  -lgfortran" 
export CPPFLAGS="-I/opt/fftw/fftw-3.3.2/double/include -I/opt/ATLAS/include"
./configure --enable-mpi --disable-float --with-fft=fftw3 --with-external-blas --with-external-lapack --program-suffix=_dpmpiatlas --prefix=/opt/gromacs/gromacs-4.5.5
make -j6 2>make4.err 1>make4.log
make install

Linking NWChem against ATLAS

export LARGE_FILES=TRUE
export TCGRSH=/usr/bin/ssh
export NWCHEM_TOP=`pwd`
export NWCHEM_TARGET=LINUX64
export NWCHEM_MODULES="all"
export BLASOPT="-L/opt/ATLAS/lib -lsatlas -ltatlas"
export USE_MPI=y
export USE_MPIF=y
export USE_MPIF4=y
export MPI_LOC=/usr/lib/openmpi/lib
export MPI_INCLUDE=/usr/lib/openmpi/include
export LIBRARY_PATH="$LIBRARY_PATH:/usr/lib/openmpi/lib:/opt/ATLAS/lib"
export LIBMPI="-lmpi -lopen-rte -lopen-pal -ldl -lmpi_f77 -lpthread"
export LDFLAGS="-I/opt/ATLAS/include"
cd $NWCHEM_TOP/src
make clean
make nwchem_config
make FC=gfortran 2> make.err 1>make.log
export FC=gfortran
cd $NWCHEM_TOP/contrib
./getmem.nwchem

227. New compute node using AMD FX-8150. Gromacs, nwchem performance/benchmarks

Update: reconfiguring your nwchem binary using getmem.nwchem can speed things up considerably. Most of the runtimes are obtained without using getmem.nwchem and are thus all using the same amount of memory, regardless of what is available. Binaries which have been reconfigured are shown as such.

The short summary: I first wasn't that happy with my choice of the the AMD FX-8150, but after sorting out the ACML libs and getting things benchmarked I'm much more satisfied. The only situation in which I'm not seeing this processor outclass the other systems seems to be that using the Commercial Ab Initio Package, which arrived as a precompiled binary (Portland Fortran).

In general it seems that the FX 8150 is about 10% faster than the i5-2400 for the computations I've tested here -- but beware that the AMD processor is using the machine vendor math libs, while the intel unit is using openblas.

Note that the AMD Phenom II X6 1055T is SLOWER with the ACML libs than with Openblas.

The Lengthy Preamble
I seem to remember promising myself not to get another AMD since, while they may or may not be 'the good guys' (e.g. the Intel/Dell thingy), empirically I keep on seeing my Quadcore Intel i5-2400 3.1 GHz sweeping the floor with my Phenom II X6 1055T 2.8 GHz. Sure, part of the issue is the clock frequency, but  the difference seems to be a lot bigger than that.

At any rate, I ended up building a new node for my little cluster. Remember that these are Australian prices. Oh, how I miss you, Newegg -- not just because of the price, but because of the choice.

Luckily it seems like my choice of the FX-8150 has paid off. Also, at the moment of writing the intel i5-2400 and the AMD fx-8150 sell for the same price locally.

---

The Setup

It's basically an eight-core 3.6 GHz box with 16 GB RAM (expandable to 32 Gb, 4 slots) and a 7200 rpm HDD. I've heard the eight-core FX 8150 uncharitably described as a quad-core with advanced hyper-threading, but I wouldn't be qualified to comment. Interestingly, sinfo registers it as a quad core, while htop and all other programs considers it an 8-core. Finally, looking at this image it looks like the whole 8 core thing is a bit of a cheat -- the whole 4 floating point vs 8 integer processing units.

Gigabyte GA-990FXA-D3 AM3 990FX DDR3 Motherboard AU$ 128 Link
AMD AM3+ x8 FX-8150 3.6Ghz Boxed CPU AU$209 Link
PV316G186C0K 16G Kit(8Gx2) DDR3 1866 AU$ 129 Link
Hitachi 3.5" Desktar 1TB SATA3 HDD 7200rpm AU$83 Link
Corsair GS800 V2 ATX Power Supply Unit AU$ 138 Link
TP-LINK TG-3269 PCI Gigabit PCI Network Card AU$ 8Link
ASUS Vento TA-U11 without PSU AU$99 Link
ASUS 1GB GF210 PCI-E VGA Card Link

NOTE that the mobo does NOT have onboard video. I didn't pick up on that before buying the parts, but luckily had an old ATI card floating around.

The fan on the PSU is a bit annoying. It stays off for the most part (some posts say it should never be completely off, one post said it should be) but starts up in a weird way -- basically the electricity is given in small jolts. Or it's just broken. Other than that it works fine.

---

Preparation
It's for reasons like these I write this blog. After having installed debian testing I set up NFS, added the box as a node under Sun Grid Engine (Link), set up Gaussian (Link), and compiled Gromacs.

I encountered separate issues trying to compile Openblas (Bulldozer cores aren't supported) and Nwchem with internal libs (odd stuff). I've given up on Openblas and managed to compile nwchem against the AMD ACML. Same went for gromacs -- I eventually recompiled gromacs against ACML. Maybe it's unfair to compare ACML vs Openblas on the i5-2400, but ACML is free, MKL isn't.

---

Performance -- setup
Note that while I do use NFS it's not in the 'traditional way'. Each node exports a local folder to the front node so that SGE can see it. However, when you run your calcs everything is stored in a local folder, and using a locally compiled version of the number crunching software. In other words, network performance should not affect the benchmarks.

Neon is NOT using openblas, while Boron and Tantalum are. Xianyi's version of openblas won't compile on Bulldozer at the moment (it seems). I will rebuild gromacs with the ACML libs and do the benchmark again.

Also, please note that these 'benchmarks' aren't absolute -- I'm not an expert on optimising performance. You can probably use them to get an idea of the relative computational grunt of the different hardware combinations though.

FX 8150 is a lot more fun with ACML. The Phenom II 1055T is no fun with ACML.

I recompiled nwchem and gromacs on Boron (see below) to see what ACML vs Openblas would be like. I've yet to run those jobs, but will post the results when I have.

Unlike the FX-8150, the Phenom II X6 1055T does not support AVX, FMA3 or FMA4.

---

Configuration:
Boron (B): Phenom II X6 2.8 GHz, 8Gb RAM (2.8*6=16.8 GFLOPS predicted)
Neon (Ne): FX-8150 X8 3.6 GHz, 16 Gb RAM (3.6*8=28.8 GFLOPS predicted (int), 3.6*4=14.4 GFLOPS (fpu))
Tantalum (Ta): Quadcore i5-2400 3.1 GHz, 8 Gb RAM (3.1*4=12.4 GFLOPS predicted)
Vanadium (V):  Dual socket 2x Quadcore Xeon X3480 3.06 GHz, 8Gb. CentOS (ROCKS 5.4.3)/openblas.

---

Results

Gromacs --double (1 ns 6x6x6 nm tip4p water box; dynamic load balancing, double precision, 500k steps)
B  :  10.662 ns/day (11.8  GFLOPS, runtime 8104 seconds)***
B  :    9.921 ns/day ( 10.9 GFLOPS, runtime 8709 seconds)**
Ne:  10.606 ns/day (11.7  GFLOPS, runtime 8146 seconds) *
Ne:  12.375 ns/day (13.7  GFLOPS, runtime 6982 seconds)**
Ne:  12.385 ns/day (13.7  GFLOPS, runtime 6976 seconds)****
Ta:  10.825 ns/day (11.9  GFLOPS, runtime 7981 seconds)***
V :   10.560 ns/dat (11.7  GFLOPS, runtime 8182 seconds)***
*no external blas/lapack.
**using ACML libs
*** using openblas
**** using ATLAS

Gromacs --single (1 ns 6x6x6 nm tip4p water box; dynamic load balancing, single precision, 500 k steps)
B  :   17.251 ns/day (19.0 GFLOPS, runtime 5008 seconds)***
Ne:   21.874 ns/day (24.2 GFLOPS, runtime  3950 seconds)**
Ne:   21.804 ns/day (24.1 GFLOPS, runtime 3963  seconds)****
Ta:   17.345 ns/day (19.2 GFLOPS, runtime  4982 seconds)***
V :   17.297 ns/day (19.1 GFLOPS, runtime 4995 seconds)***
*no external blas/lapack.
**using ACML libs
*** using openblas
**** using ATLAS

NWChem (opt biphenyl cation, cp-md/pspw):
B  :   5951 seconds**
B  :   4084 seconds ***
B  :   1988 seconds***x
Ne:   3689 seconds**
Ta :   4102 seconds***
V :    5396 seconds***

*no external blas/lapack.
**using ACML libs
*** using openblas
x Reconfigured using getmem.nwchem

NWChem (opt biphenyl cation, geovib, 6-31G**/ub3lyp):
B  :  2841 seconds **
B  :  2410 seconds***
B  :  2101 seconds ***x
Ne: 1665 seconds **
Ta : 1785 seconds***
Ta : 1789 seconds***x

V  : 2600 seconds***

*no external blas/lapack.
**using ACML libs
*** using openblas
x Reconfigured using getmem.nwchem

A Certain Commercial Ab Initio Package (Freq calc of pre-optimised H₁₄C₁₉O₃ at 6-31+G*/rb3lyp):
B  :    2h 00 min (CPU time 10h 37 min)
Ne:   1h 37 min (CPU time: 11h 13 min)
Ta:   1h 26 min (CPU time: 5h 27 min)
V  :   2h 15 min (CPU time 15h 50 min)
Using precompiled binaries.

---

More:
Since I couldn't use Xianyi's openblas with FX 8150 I downloaded the AMD ACML. I've had issues with that before, which is why I haven't been using that as a rule. This time I was motivated enough to hammer it out though. Anyway, here's the cpuid output from the acml 5.2.0:

./cpuid.exe 
Chip manufacturer: AuthenticAMD
AuthenticAMD family 15 extended family 6 model 1
Model Name: AMD FX(tm)-8150 Eight-Core Processor        
Chip supports SSE
Chip supports SSE2
Chip supports SSE3
Chip supports AVX
Chip does not support FMA3
Chip supports FMA4

See the other post from today about build nwchem with acml (hint: use the fma4_int64 libs but avoid mp).

Here's 1055T:

Chip manufacturer: AuthenticAMD
AuthenticAMD family 15 extended family 1 model 10
Model Name: AMD Phenom(tm) II X6 1055T Processor
Chip supports SSE
Chip supports SSE2
Chip supports SSE3
Chip does not support AVX
Chip does not support FMA3
Chip does not support FMA4

---

Issues

Openblas:
You will get SGEMM related errors trying to build openblas according to the instructions I've posted on this site before. Apparently it has to do with the way the architecture is autoselected during build. Or something. I couldn't make it work.

NwChem:
I tried building nwchem with the internal libs, but had no luck. See other posts on this blog for general instructions. Building with the AMD ACML worked fine though.

---

Files:

NWChem (opt biphenyl cation, cp-md/pspw):

Title "Test 1"
Start  biphenyl_cation_twisted-1
echo
charge 1
geometry autosym units angstrom
 C     0.00000     -3.54034     0.00000
 C     -1.20296     -2.84049     -0.216000
 C     -1.20944     -1.46171     -0.206253
 C     0.00000     -0.721866     0.00000
 C     1.20944     -1.46171     0.206253
 C     1.20296     -2.84049     0.216000
 C     0.00000     0.721866     0.00000
 C     1.20944     1.46171     -0.206253
 C     1.20296     2.84049     -0.216000
 C     -1.20944     1.46171     0.206253
 C     0.00000     3.54034     0.00000
 C     -1.20296     2.84049     0.216000
 H     0.00000     -4.62590     0.00000
 H     -2.12200     -3.38761     -0.395378
 H     -2.13673     -0.938003     -0.401924
 H     2.12200     -3.38761     0.395378
 H     2.12200     3.38761     -0.395378
 H     -2.13673     0.938003     0.401924
 H     0.00000     4.62590     0.00000
 H     -2.12200     3.38761     0.395378
 H     2.13673     0.938003     -0.401924
 H     2.13673     -0.938003     0.401924
end
nwpw
  simulation_cell
     lattice_vectors
      2.000000e+01 0.000000e+00 0.000000e+00
      0.000000e+00 2.000000e+01 0.000000e+00
      0.000000e+00 0.000000e+00 2.000000e+01
  end
  mult 2
  np_dimensions -1  -1
  tolerances 1e-7  1e-7
end
driver
  default
end
task pspw optimize

NWChem (opt biphenyl cation, geovib, 6-31G**/ub3lyp):

Title "Test 2"
Start  biphenyl_cation_twisted
echo
charge 1
geometry autosym units angstrom
 C     0.00000     -3.56301     0.00000
 C     -1.13927     -2.85928     -0.393841
 C     -1.13879     -1.46545     -0.394153
 C     0.00000     -0.742814     0.00000
 C     1.13879     -1.46545     0.394153
 C     1.13927     -2.85928     0.393841
 C     0.00000     0.742814     0.00000
 C     1.13879     1.46545     -0.394153
 C     1.13927     2.85928     -0.393841
 C     -1.13879     1.46545     0.394153
 C     0.00000     3.56301     0.00000
 C     -1.13927     2.85928     0.393841
 H     0.00000     -4.64896     0.00000
 H     -2.02827     -3.39662     -0.711607
 H     -2.02148     -0.928265     -0.727933
 H     2.02827     -3.39662     0.711607
 H     2.02827     3.39662     -0.711607
 H     -2.02148     0.928265     0.727933
 H     0.00000     4.64896     0.00000
 H     -2.02827     3.39662     0.711607
 H     2.02148     0.928265     -0.727933
 H     2.02148     -0.928265     0.727933
end
basis "ao basis" cartesian print
  H library "6-31G**"
  C library "6-31G**"
END
dft
  mult 2
  XC b3lyp
  mulliken
end
driver
end
task dft optimize
task dft freq numerical

226. ACML libs and nwchem -- what libs to choose to avoid 'Singularity in Pulay matrix' hang.

The problem:
If I compile nwchem against the acml libs (gfortran64_fma4 in acml-5-2-0-gfortran-64bit.tgz) everything appears to go fine, but once I try to run stuff I get

           Memory utilization after 1st SCF pass:
           Heap Space remaining (MW):       12.94            12937848
          Stack Space remaining (MW):       13.11            13107006
   convergence    iter        energy       DeltaE   RMS-Dens  Diis-err    time
 ---------------- ----- ----------------- --------- --------- ---------  ------
 d= 0,ls=0.0,diis     1    -74.9488845804 -7.49D+01  1.85D-02  1.70D-01     0.4
  Singularity in Pulay matrix. Error and Fock matrices removed.

and then the node hangs with 100% CPU.

The (obvious) solution:

To some this will be obvious, but to someone not skilled in the art, like myself, it isn't.

Of course, I could've just RTFM...but what academic does that?

"ACML and MKL can support 64-bit integers if the appropriate library is chosen. For MKL, one can choose the ILP64 Version of Intel® MKL, while for ACML the int64 libraries should be chosen, e.g. in the case of ACML 4.4.0 using a PGI compiler /opt/acml/4.4.0/pgi64_int64/lib/libacml.a"

So, when you go to download your libraries from the AMD website make to download at a minimum the 64 integer file (e.g.acml-5-2-0-gfortran-64bit-int64.tgz).

How I built nwchem:

export LARGE_FILES=TRUE
export TCGRSH=/usr/bin/ssh
export NWCHEM_TOP=`pwd`
export NWCHEM_TARGET=LINUX64
export NWCHEM_MODULES="all"
#export PYTHONVERSION=2.7
export PYTHONHOME=/usr
export BLASOPT="-L/opt/acml/acml5.2.0/gfortran64_fma4_int64/lib -lacml"
export USE_MPI=y
export USE_MPIF=y
export USE_MPIF4=y
export MPI_LOC=/usr/lib/openmpi/lib
export MPI_INCLUDE=/usr/lib/openmpi/include
export LIBRARY_PATH="$LIBRARY_PATH:/usr/lib/openmpi/lib:/opt/acml/acml5.2.0/gfortran64_fma4_int64/lib"
export LIBMPI="-lmpi -lopen-rte -lopen-pal -ldl -lmpi_f77 -lpthread"
cd $NWCHEM_TOP/src
make clean
make nwchem_config
make FC=gfortran 2> make.err 1>make.log
export FC=gfortran
cd ../contrib ./getmem.nwchem

Don't forget to add the acml libs to the LD_LIBRARY_PATH in your ~/.bashrc, e.g.

export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/lib/openmpi/lib:/opt/acml/acml5.2.0/gfortran64_fma4_int64/lib

200. How long will your nwchem frequency calc take?

Update 19/12/12: Having done a lot more frequency calculations since I posted this I sincerely doubt that this approach works.

Original post
Because I'm stuck waiting for the results of frequency calcs on some large transition metal clusters, I've become interested in understanding the output of frequency calculations in progress. After all, why wait 15 days for a results if there are early signs that the calculation has gone haywire?

Also, it might just be me, but frequency calculations are not that easy to restart, so you want to make sure that you give them enough wall time to finish if you use a queue manager.

I'm sure most of this could be appreciated by RTFM, but who has time for that?

So this is what the calc does:
After the usual boredom of reading in the geometry and doing an energy calculation, followed by an MO analysis, the computational fun starts.

Each cycle contains the following reports:

1. Total Density - Mulliken Population Analysis
2. Spin Density - Mulliken Population Analysis
3. Total Density - Lowdin Population Analysis
4. Spin Density - Lowdin Population Analysis
5. Expectation value of S2:  
6. NWChem DFT Module
7.   Caching 1-el integrals 
8.       Total Density - Mulliken Population Analysis
9.       Spin Density - Mulliken Population Analysis

with the exception of the first cycle, which also look at the alpha-beta orbital overlaps, the centre of mass, moments of inertia and does a multipole analysis of density and save an initial hessian.

Each cycle ends with a report of the energy for that vibration:

         Total DFT energy =    -3297.032399945703

      One electron energy =   -26618.764098759657

           Coulomb energy =    12938.745973154924

    Exchange-Corr. energy =     -382.742230868704

 Nuclear repulsion energy =    10765.727956527733

 Numeric. integr. density =      441.999974968347

     Total iterative time =   7947.4s

If you do cat nwch.nwout|egrep "Total iterative time|Total DFT energy" you can see the progress:

        Total DFT energy =    -3297.032416366805
     Total iterative time =  12146.0s
         Total DFT energy =    -3297.032399945703
     Total iterative time =   7947.4s
         Total DFT energy =    -3297.032399544749
     Total iterative time =   7946.0s
         Total DFT energy =    -3297.032406934719
     Total iterative time =   7945.8s
         Total DFT energy =    -3297.032405026814

You now have an idea of how long each step takes. But how many steps in total? I think it's 3N steps, where N is the number of atoms.

For my 50 atoms POM using the values above it'd be roughly 8000 s * 150 = 13 days 22 hours.

Which seems about right...

cat nwch.nwout|grep 'Total DFT'|gawk 'END {print NR}'

66

so I've got another 8 days before I can get my hand on some juicy thermochemical data...

Time to start preparing lectures...

198. Nwchem -- freeze core and tddft on benzene

UPDATE: it's taken a while, but I've tested this on a large polyoxometalate cluster (>10 group 5/6 atoms and >30 oxygens) -- with a total of ca 700 alpha and beta orbitals, respectively, I froze 200 core orbs and used 3-21G/3-21G* w/ ub3lyp. The frozen core calculation took 44% of the time the full calculation took. The spectra look identical to within 3 nm (18 roots -- only 2 intermediate transitions have been shifted. All other transitions are identical). The full calc took 7 days and 4 hours, while the frozen calc took 3 days and 4 hours. 

Original post:
Benzene has 21 occupied α and 21 occupied β orbitals.

How many core orbitals can we freeze when looking at electronic transitions, how does freezing core orbitals affect the energies, and what are the performance gains, if any?

I used the following relevant statements

tddft
    cis
    freeze core X
    nroots 24
end
task tddft energy

Also, xc b3lyp and 6-31++g**.

Freeze core 10 means freeze 10 α and freeze 10 β orbitals.

Results:

Frozen Runtime    Transitions with f>0
0          1111 s     6.7835, 6.8038, 6.8042, 7.3479, 7.3496
5          1107 s     6.7835, 6.8038, 6.8042, 7.3480, 7.3498
10        1063 s     6.7838, 6.8040, 6.8045, 7.3761, 7.3862
15        1063 s     6.5878, 6.7840, 6.8042, 6.8046
20          719 s     6.8038, 6.8355, 7.1692, 7.5334, 8.1866

Evaluation:
We're not really looking at what's right or wrong -- the main goal is to understand how the results are affected (we might accidentally get 'right' answer doing something stupid). Freezing more than 10 α/β orbitals leads to significant differences in predicted transitions.

Taking oscillation strength into account and plotting it, we see that we really don't want to overdo it with the number of frozen cores -- 15 and 20 frozen cores yield results that are about as predictable as a coin toss. We also don't see any overwhelming performance gains, but that may well be due to the size and computational cost (or lack thereof) of the system.

Octave code:

spec1=load('bz631gppdd_cosmo.dat');

spec2=load('bz631gppdd_cosmo_f5.dat');
spec3=load('bz631gppdd_cosmo_f10.dat');
spec4=load('bz631gppdd_cosmo_f15.dat');
spec5=load('bz631gppdd_cosmo_f20.dat');

gau= @(x,c,w,i) i*(1/(w*sqrt(2*pi))).*exp(-0.5.*((x-c)./w).^2);
x=linspace(160,200,200);
y1=cumsum(gau(x,1241.25./spec1(:,2),4,spec1(:,3)));
y2=cumsum(gau(x,1241.25./spec2(:,2),4,spec2(:,3)));
y3=cumsum(gau(x,1241.25./spec3(:,2),4,spec3(:,3)));
y4=cumsum(gau(x,1241.25./spec4(:,2),4,spec4(:,3)));
y5=cumsum(gau(x,1241.25./spec5(:,2),4,spec5(:,3)));


subplot(3,2,1)
 plot(x,y1(rows(y1),:))
 axis([160 200 0 0.2]);
 title('0 frozen');
 subplot(3,2,3)
 plot(x,y2(rows(y2),:))
 axis([160 200 0 0.2]);
 title('5 frozen');
 subplot(3,2,5)
 plot(x,y3(rows(y3),:))
 axis([160 200 0 0.2]);
 title('10 frozen');
 subplot(3,2,2)
 plot(x,y4(rows(y4),:))
 axis([160 200 0 0.2]);
 title('15 frozen');
 subplot(3,2,4)
 plot(x,y5(rows(y5),:))
 axis([160 200 0 0.2]);
 title('20 frozen');
 subplot(3,2,6)
  plot(x,y1(rows(y1),:),x,y2(rows(y2),:), x, y3(rows(y3),:), x,y4(rows(y4),:),x,y5(rows(y5),:))
  axis([160 200 0 0.2]);
 title('');

195. Frequency calcs in NWChem

It's no secret that I'm a computational 'noob'. As such as I'm learning both by reading and by doing.

The doing part consists of checking 1) what the time penalty for different methods is and 2) what the accuracy/differences between different methods are.

Again, these are short calculations for simple molecules. Longer calculations with more exciting features (unpaired electrons, closely spaced MOs, highly negative charges etc.) may well behave completely different.

Today's focus is vibrational calcs.

Test Molecule: CHClF(OH) (chloro-fluoro-methanol)

  1 Title "Freq_test"
  2 
  3 Start  Freq_test
  4 
  5 echo
  6 
  7 charge 0
  8 
  9 geometry noautosym units angstrom
 10  C     0.0416942     -0.501783     0.399137
 11  H     0.0442651     -0.499048     1.48122
 12  O     1.21393     -1.00985     -0.0746688
 13  H     1.25125     -0.957351     -1.06923
 14  F     -1.08480     -1.08768     -0.134571
 15  Cl     -0.120345     1.41214     -0.0717951
 16 end
 17 
 18 ecce_print ecce.out
 19 
 20 basis "ao basis" cartesian print
 21   H library "3-21G"
 22   F library "3-21G"
 23   Cl library "3-21G"
 24   O library "3-21G"
 25   C library "3-21G"
 26 END
 27 
 28 dft
 29   mult 1
 30   odft
 31   mulliken
 32 end
 33 
 34 task dft energy
 35 task dft freq

All geometries were optimised in the gas phase using 3-21G.

0. Some useful statements:

hessian      print "hess_follow"
                 profile
end

1. Basis set (geometry optimised in 3-21g)
(time/enthalpy/entropy/scfe)
3-21G:              81s    24.984 kcal/mol    69.235 cal/mol-K   -671.17956992206 Hartree
6-31G:            105s    21.885 kcal/mol    68.793 cal/mol-K   -674.478768966106
6-31++G**:    399s   21.734 kcal/mol     68.818 cal/mol-K   -674.573524091623
cc-pVDZ:        325s    21.682 kcal/mol    68.819 cal/mol-K   -674.594059146606
aug-cc-pVDZ:  901s   21.605 kcal/mol    68.840 cal/mol-K   -674.623145113155

LANL2DZ(C)/6-+G* 262s  24.923 kcal/mol 68.981 cal/mol-K  -674.539040349134
UHF/aug-cc-pVDZ   373 s 26.196  kcal/mol 68.228 cal/mol-K -672.85402652170

Cation:
3-21G:               ---     21.164 kcal/mol     74.407 cal/mol-K    -670.763278724519 Hartree
6-31G:              142s   21.153 kcal/mol     74.645 cal/mol-K    -674.089132280731
6-31++G**:      637s   21.192 kcal/mol    73.768 cal/mol-K    -674.178146586266
cc-pVDZ:          399s   21.153 kcal/mol    73.736 cal/mol-K    -674.210312017948
aug-cc-pVDZ:   1776s 21.089 kcal/mol     73.774 cal/mol-K   -674.228204222891

LANL2DZ(C)/6-+G* 454s 24.795 kcal/mol  74.293 cal/mol-K -674.140922359750
UHF/aug-cc-pVDZ  741s 26.002 kcal/mol  72.462 cal/mol-K  -672.518095855130

2. Thermochemistry (ΔG of oxidation; gas phase)
3-21G:            -5.3620 kcal/mol +  261.22 kcal/mol =  6.814 V*
6-31G:            -2.4768 kcal/mol +  244.50 kcal/mol =  6.214 
6-31++G**:    -2.0178 kcal/mol+  248.10 kcal/mol =  6.390 
cc-pVDZ:        -1.9950 kcal/mol + 240.80 kcal/mol =  6.075 
aug-cc-pVDZ: -1.9871 kcal/mol + 247.83 kcal/mol =  6.380

LANL2DZ(C)/6-+G* -1.7118 kcal/mol + 249.82 kcal/mol = 6.478
UHF/aug-cc-pVDZ -1.4564 kcal/mol +210.80 kcal/mol = 4.797

* vs SHE=4.281 eV

3. Solvation (cosmo/water/scfe)
neutral
3-21g:                66s    22.097 kcal/mol    68.875 cal/mol-K   -671.1936338426 Hartree
6-31g:                82s    22.277 kcal/mol    68.609 cal/mol-K   -674.4934780299
6-31++g**:       277s   21.493 kcal/mol    69.353 cal/mol-K  -674.586704959695
cc-pVDZ:          266s   21.869 kcal/mol    68.808 cal/mol-K  -674.605608009070
aug-cc-pVDZ:    712s  22.116 kcal/mol    69.596 cal/mol-K   -674.635237990779

LANL2DZ(C)/6-31+G* 180s  25.022 kcal/mol   69.073 cal/mol-K -674.552417717602
UHF/aug-cc-pVDZ 412s  24.083 kcal/mol 70.519 cal/mol-K  -672.868085966222

cation (solvation energy)**

3-21G:               --- /26s        21.164 kcal/mol     74.407 cal/mol-K     -670.881469242560 Hartree
6-31G:              142s/51s      21.153 kcal/mol     74.645 cal/mol-K     -674.175491218588
6-31++G**:      637s/111s   21.192 kcal/mol    73.768 cal/mol-K      -674.267298880087
cc-pVDZ:          399s/129s   21.153 kcal/mol    73.736 cal/mol-K      -674.294609415029
aug-cc-pVDZ:   1776s/311s 21.089 kcal/mol     73.774 cal/mol-K     -674.316552324118

LANL2DZ(C)/6-31+G* 454s 24.795 kcal/mol  74.293 cal/mol-K -674.232656980139
UHF/aug-cc-pVDZ   741s 26.002 kcal/mol  72.462 cal/mol-K -672.451040948823
** UHF can't be used with COSMO according to nwchem. Instead we use the cation thermo calcs in the gas phase and use the scfe from a cosmo calc.

Thermochemistry*** (using gas phase freq for both cation and neutral species with scfe w/ cosmo given in parentheses):

3-21G:            -2.5824+195.88=  4.101 V (3.981 V)
6-31G:            -2.9236+199.54=  4.245 V (4.265 V)
6-31++G**:   -1.6173+200.43=  4.341 V (4.324 V)
cc-pVDZ:       -2.1853+195.15=  4.087 V (4.095 V)
aug-cc-pVDZ: -2.2727+199.98= 4.293 V (4.305 V)

LANL2DZ(C)/6-31+G*  -0.41322+200.65= 4.402
UHF/aug-cc-pVDZ 1.3397+261.7 (!)= 7.126
* vs SHE=4.281 eV

*** using freq calc of neutral species with cosmo, vs freq calc of cation in gas phase and energy w/ cosmo

4. Spectra
We'll use octave for this. First, using cat and gawk, I put the x/y coordinates in a file.

gauss= @(x,f,i,sigma)  i.*1./(sigma.*sqrt(2*pi)).*exp(-0.5.*((x-f)./sigma).**2)
subplot(3,2,1); axis([0 4000 0 2])
spc=load('321g.spc');sf=spc(:,1); si=spc(:,2);x=linspace(0,4000,800);spec=cumsum(gauss(x,sf,si,75)); 
title("321g"); plot(x,spec(18,:))
subplot(3,2,2)
spc=load('ccpvdz.spc');sf=spc(:,1); si=spc(:,2);x=linspace(0,4000,800);spec=cumsum(gauss(x,sf,si,75));
title("ccPVDZ");plot(x,spec(18,:))
subplot(3,2,3)
spc=load('631g.spc');sf=spc(:,1); si=spc(:,2);x=linspace(0,4000,800);spec=cumsum(gauss(x,sf,si,75));
title("631g"); plot(x,spec(18,:))
subplot(3,2,4)
spc=load('augccpvdz.spc');sf=spc(:,1); si=spc(:,2);x=linspace(0,4000,800);spec=cumsum(gauss(x,sf,si,75));
title("aug-ccPVDZ");plot(x,spec(18,:))
subplot(3,2,5)
spc=load('631gppdd.spc');sf=spc(:,1); si=spc(:,2);x=linspace(0,4000,800);spec=cumsum(gauss(x,sf,si,75));
title("631++g**"); plot(x,spec(18,:))

From top to bottom: Left: 3-21G, 6-31G, 6-31++G**. Right: cc-pVDZ, aug-cc-pVDZ

5. Conclusions
It may seem weird that as a test case I picked a species I don't have any reference potential for. However, the goal here was to understand how the basis set affects the results, without being distracted by such things as Real Life.

The observed spectra can be divided into two group: 3-21G/6-31G vs 6-31++G**/cc-pVDZ/aug-cc-pVDZ. Polarization (and diffuse functions) seem to play a large role.

In terms of thermochemistry, not surprisingly aug-cc-pVDZ and 6-31++G** give very similar results since they both implement pol/diff functions. The computational cost is, however, significantly higher for aug-cc-pVDZ than 6-31++G**, at least in nwchem.

There is also little difference between doing freq calculations in gas phase vs using cosmo when it comes to the calculated redox potential for the more extensive basis sets.

3-21G gives very varying results, with it giving the highest potential in the gas phase but the second lowest potential with cosmo. cc-pVDZ consistently gives the lowest potential.

UHF/ROHF/HF are fast, but wildly inaccurate. LANL2DZ/6-31+G* looks ok, results-wise, but the thermodynamic corrections are actually much smaller in conjunction with COSMO than the other methods, which is suspicious.

If given the time I may post a more detailed analysis of polarisation vs diffuse functions later.

191. Thinking about Molecular volume -- and is cosmo/nwchem yielding the right ones?

Disclaimer:
I'm an neither a theoretical nor computational chemist. I'm an analytical/inorganic chemist who likes computers. Don't trust my conclusions. This is more like thinking aloud.

The problem:
The underlying impetus is that of molecular volume: if we have a set of scatter points in space which define the surface of a molecule, how can we extract the volume? In particular as we're actually given the surface points by in the form of a cosmo.xyz file by COSMO (and yes, nwchem also outputs a volume - more about that later) there's no reason why we won't do the calculations ourselves. Also, there's at least one example of comparing results from a few major software packages, where nwchem was the odd one out.

Because it's good to know how to use Octave and bash, I'll show the commands as well.

The COSMO parameters used were
cosmo
    rsolv 0
end

[come to think of it: why bother with
and nwchem returned

 atomic radii =
 --------------
    1  6.000  2.000
    2  6.000  2.000
    3  6.000  2.000
    4  6.000  2.000
    5  6.000  2.000
    6  6.000  2.000
    7  1.000  1.300
    8  1.000  1.300
    9  1.000  1.300
   10  1.000  1.300
   11  1.000  1.300
   12  1.000  1.300

and a volume of ca 74.5 ų

Processing:

me@Be:~$ head cosmo.xyz 

                  325
 cosmo charges
 Bq   2.1848085582473193      -0.38055253987610238        1.5251498369435705       -9.3089382062078174E-004
 Bq   1.6134835908159706      -0.59877925881345084        1.8782480854375714       -3.3706153046646758E-003
 Bq  0.43449121346899733      -0.59877925881345084        1.8782480854375714       -3.9739778624157118E-003
 Bq   1.0239874021424840      -0.23823332776127137        1.8683447179254316       -1.6433149723942275E-003

OK, we need to remove the first two lines, and the first column.

me@Be:~$ tail -n +3 cosmo.xyz|gawk '{print $2,$3,$4,$5}'> cos2.xyz

Start octave.

octave:1> bz=load('cos2.xyz');
octave:2> x=bz(:,1);y=bz(:,2);z=bz(:,3);c=bz(:,4);
octave:3> plot3(x,y,z)

Paradoxically, this would be fairly easy to do with a 'normal-size' physical object (e.g. water displacement, or area on a 2D project: draw it, cut it out, weigh it and use the density of the paper)

 Computationally, we need to think about it though. The most logical approach seems to be to take all x,y data points with a small range of values of z=z_i±dz, project them on a 2D surface, calculate the area within, and multiply it by dz. Do this for all values of z.

octave:4> plot(y,z,'*')

But how to calculate the area inside an arbitrary two-dimensional figure then? If we can pick a point in the 'centre' of the figure, we can draw repeated triangles with this point as one of the corners. It's easy to calculate the area of a triangle, so we just need to sum the areas of the triangles. All we need to know is how to find such a central point to use as a corner. Also, there are problems when dz is too large and the 'border' becomes fuzzy.

octave:5> plot(y(1:25),z(1:25),'*')

In fact, at this stage there may well be pre-canned algorithms to help us.

octave:6>H=convhull(y(1:25),z(1:25));
octave:7>plot(y(H),z(H))
octave:8>hold
octave:9>plot(y(1:25),z(1:25),'*')

That way we can reduce the number of points to the ones defining the encircling figure.

octave:10>area(y(H),z(H))

That still doesn't give us the area (I think matlab does though). Since it's centred around the x axis we could probably use cumsum(abs(z(H))), but that's not general enough. In fact, there'd be so much  quality analysis required in order to make sure that we include enough, but not too many, points in our slices that it quickly becomes a chore.

So we'll take a step back. Turns out it's even easier:

octave:11>[H V]=convhulln([x y z]);

This probably isn't how you're supposed to plot it, but it works:

octave:13>trisurf(H,x,y,z)

trisurf plot

octave:12>V

gives V=104.07  Å³ (c.f. Nwchem/cosmo ca 74.5 ų for rsolv=0.)

Now that doesn't look good, but it has been noted nwchem/cosmo gives volumes which are about half of what every other program gives. See here and here:

">Cosmo produced volumes, which were twice as small
> as those obtained by PCM, while surfaces where by about 15% bigger in
> Cosmo."

I think nwchem actually isn't returning values of the wrong magnitude -- I think the value returned by nwchem is the molecular volume, while the other programmes return the solvent accessible surface-based volume. But what is in cosmo.xyz?

It appears to be a little bit more complex than that though.

---

We can open the cosmo.xyz file in jmol, but calculating the volume from these would be meaningless due to the way jmol works.

Instead we'll have to use the VdW radii of the xyz coordinates of the (unoptimised) molecule:

$ isosurface sasurface 0.5 volume
isosurface1 created with cutoff=0.0; isosurface count: 1
isosurfaceVolume = 141.06999
$ isosurface sasurface 0.225 volume
isosurface1 created with cutoff=0.0; isosurface count: 1
isosurfaceVolume =104.452415
$ isosurface solvent 0 volume
isosurface1 created with cutoff=0.0; isosurface count: 1
isosurfaceVolume = 79.09731
$ isosurface solvent volume
isosurface1 created with cutoff=0.0; isosurface count: 1
isosurfaceVolume = [80.26721490808025]
$ isosurface molecular volume
isosurface2 created with cutoff=0.0; isosurface count: 2
isosurfaceVolume = [80.58888982478977]
$ isosurface sasurface 0.2 area
isosurface1 created with cutoff=0.0; isosurface count: 1
isosurfaceArea = 118.730934

Making sense?

sasurface generates a solvent accessible surface. We can generate a value similar to what we saw from the cosmo.xyz points by forcing the sasurface probe radius..

The vdw radii of H and C are 1.2 and 1.7 Å, but COSMO uses 1.3 and 2.0.

Look at this plot again:

The height goes from -2 to 2, which agrees with the large 2.0 Å VDW radius for C that COSMO uses. The volume outputted by Nwchem is the molecular volume (as actually is stated). 

 number of -cosmo- surface points =      176
 molecular surface =    125.008 angstrom**2
 molecular volume  =     74.512 angstrom**3
(electrostatic) solvation energy =         0.0052128678 (    3.27 kcal/mol)

The molecular volume for rsolv=0 is 74.5 Å³ which is fairly close to isosurface sasurface 0 volume. Area is trickier, and requires isosurface sasurface 0.23 volume to yield anything close.

I don't think it's a coincidence that isosurface sasurface 0.225 volume gives a reasonable agreement with the cosmo.xyz, since 1.7+0.225=1.925 which is ca 2 (we only add 0.1 for H).

I'm sure all this is in the manual somewhere. But there's nothing like learning through doing.

The conclusions:
* NWchem returns a volume based on the vdw radii, not the solvent cavity
* cosmo.xyz contains points defining the surface according to the vdw radii that cosmo uses
* These are two different sets of vdw radii
* You can't compare the output of different software packages if they aren't outputting the same data
* The reported NWChem volume does depend on rsolv, the cosmo vol doesn't
* The cosmo.xyz volume is insensitive to rsolv, but sensitive to radius as expected. As far as I understand, the cosmo volumes are based solely on the vdw radii (as supplied to cosmo)
* I haven't quite figured out how, but looking at the dependency of rsolve vs defining vdw radii for cosmo, the radii used to calculate the nwchem volume is is certainly affected.

Increase rsolv=0.0, increase vdw +0.0: 74.51/104.07/3.27
Increase rsolv=0.5, increase vdw +0.0: 58.0/103.96/3.01
Increase rsolv=1.0, increase vdw +0.0: 54 /103.87/2.95
Increase rsolv=0.0, increase vdw +0.1: 84.79/115.10/2.72
Increase rsolv=0.1, increase vdw +0.1: 82.68/115.10/2.63
Increase rsolv=0.27, increase vdw +0.1: 71.84/114.97/2.56
Increase rsolv=0.0, increase vdw +0.2: 96.59/126.83/2.22
Increase rsolv=0.1, increase vdw +0.2: 85.70/126.68/2.09
increase rsolv=0.70, increase vdw +0.2: 74.68/126.56/2.01

My only real conclusion at this point is that you have to be extremely careful about what you do. This is not easy.

---

A Certain Commercial Programme (ACCP):

Using pcm:

scrf=(pcm,solvent=water) -- this uses vdw radii.

GePol: Cavity volume                                =      134.665 Ang**3
GePol: Cavity surface area                          =    143.132 Ang**2

Let's see if we can do this in jmol:

$ isosurface sasurface 0.5 area
isosurface1 created with cutoff=0.0; isosurface count: 1
isosurfaceArea = 144.25595
$ isosurface sasurface 0.46 volume
isosurface1 created with cutoff=0.0; isosurface count: 1
isosurfaceVolume = 135.33589

PCM is less of a mystery now.

ACCP has a few more options though.
Using IPCM with 50 points. This uses the isodensity volume.

Volume of Solute Cavity = 8.026500E+02
Total "Solvent Accessible Surface Area" of Solute = 4.485628E+02

I've been told that the units are in Bohr³ and Bohr². That translates to 118.94 ų and 125.61ų, respectively, which sounds about right.