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"1. Basis set (geometry optimised in 3-21g)
profile
end
(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 |
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.
