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I am trying to do a simple TDDFT calculation in both Gaussian and ORCA from the exact same reference Geometry. I am using the same functional (making sure to use b3lyp/g in ORCA to ensure this) and basis set. And yet my results are showing significant difference. I am attaching the input of Gaussian and ORCA respectively below

%nprocshared=20
%mem=4GB
#p td=(singlets,nstates=8) b3lyp/cc-pvdz

tddft-b3lyp-ccbvdz

0 1
 C                  4.45143600    2.73106800    0.00000000
 C                  3.61628300    1.62294900    0.00000000
 C                  2.21893400    1.80672100    0.00000000
 C                  1.66757200    3.11685300    0.00000000
 C                  2.54605100    4.22247600    0.00000000
 C                  3.92022500    4.03659100    0.00000000
 H                  1.71737100   -0.24322100    0.00000000
 H                  5.53378000    2.58612200    0.00000000
 H                  4.02613700    0.61062500    0.00000000
 C                  0.23548300    3.23807000    0.00000000
 H                  2.12225200    5.22957100    0.00000000
 H                  4.59105500    4.89745300    0.00000000
 C                 -0.57411500    2.14004900    0.00000000
 C                  0.00000000    0.82082500    0.00000000
 H                 -0.20202400    4.23984100    0.00000000
 H                 -1.66145000    2.20341300    0.00000000
 C                 -1.24551500   -2.68544300    0.00000000
 C                 -2.46715000   -1.99407400    0.00000000
 C                 -3.67831300   -2.67573200    0.00000000
 C                 -3.64334700   -4.07886900    0.00000000
 C                 -2.42235100   -4.76927200    0.00000000
 C                 -1.20258200   -4.07556800    0.00000000
 C                 -0.12926800   -1.68697900    0.00000000
 C                 -0.74306200   -0.36908600    0.00000000
 C                 -2.20356400   -0.50939000    0.00000000
 H                 -4.62064100   -2.12451100    0.00000000
 H                 -4.57840100   -4.64401100    0.00000000
 H                 -2.42399500   -5.86177600    0.00000000
 H                 -0.24540600   -4.60044300    0.00000000
 N                  1.36356400    0.73013200    0.00000000
 O                 -3.06944900    0.36115800    0.00000000
 O                  1.08395700   -1.95504700    0.00000000

and for ORCA

%pal
        nprocs 16
end

%tddft
        nroots 8
        triplets true
        tda = false
end

*xyz 0 1
C                  4.45140000    2.73110000    0.00000000
C                  3.61630000    1.62290000    0.00000000
C                  2.21890000    1.80670000    0.00000000
C                  1.66760000    3.11690000    0.00000000
C                  2.54610000    4.22250000    0.00000000
C                  3.92020000    4.03660000    0.00000000
H                  1.71740000   -0.24320000    0.00000000
H                  5.53380000    2.58610000    0.00000000
H                  4.02610000    0.61060000    0.00000000
C                  0.23550000    3.23810000    0.00000000
H                  2.12230000    5.22960000    0.00000000
H                  4.59110000    4.89750000    0.00000000
C                 -0.57410000    2.14000000    0.00000000
C                  0.00000000    0.82080000    0.00000000
H                 -0.20200000    4.23980000    0.00000000
H                 -1.66150000    2.20340000    0.00000000
C                 -1.24550000   -2.68540000    0.00000000
C                 -2.46720000   -1.99410000    0.00000000
C                 -3.67830000   -2.67570000    0.00000000
C                 -3.64330000   -4.07890000    0.00000000
C                 -2.42240000   -4.76930000    0.00000000
C                 -1.20260000   -4.07560000    0.00000000
C                 -0.12930000   -1.68700000    0.00000000
C                 -0.74310000   -0.36910000    0.00000000
C                 -2.20360000   -0.50940000    0.00000000
H                 -4.62060000   -2.12450000    0.00000000
H                 -4.57840000   -4.64400000    0.00000000
H                 -2.42400000   -5.86180000    0.00000000
H                 -0.24540000   -4.60040000    0.00000000
N                  1.36360000    0.73010000    0.00000000
O                 -3.06940000    0.36120000    0.00000000
O                  1.08400000   -1.95500000    0.00000000
*

But the outputs I am getting are quite different ! As illustrated below

For Gaussian

 Excited State   1:      Triplet-A'     2.2054 eV  562.19 nm  f=0.0000  <S**2>=2.000
      71 -> 72         0.69787
 This state for optimization and/or second-order correction.
 Total Energy, E(TD-HF/TD-DFT) =  -897.759895906
 Copying the excited state density for this state as the 1-particle RhoCI density.

 Excited State   2:      Triplet-A'     2.7123 eV  457.12 nm  f=0.0000  <S**2>=2.000
      71 -> 73         0.68579

 Excited State   3:      Triplet-A"     2.9511 eV  420.12 nm  f=0.0000  <S**2>=2.000
      67 -> 72         0.13139
      70 -> 72         0.18527
      70 -> 73         0.63488
      70 -> 74         0.12092
      70 -> 77        -0.10365

 Excited State   4:      Triplet-A'     2.9974 eV  413.64 nm  f=0.0000  <S**2>=2.000
      65 -> 74         0.11727
      68 -> 72        -0.28302
      69 -> 72         0.43278
      69 -> 75        -0.11938
      71 -> 74        -0.37857

 Excited State   5:      Triplet-A"     3.1360 eV  395.35 nm  f=0.0000  <S**2>=2.000
      67 -> 72        -0.19672
      67 -> 73         0.26224
      70 -> 72         0.58230
      70 -> 73        -0.17749

 Excited State   6:      Triplet-A'     3.3072 eV  374.89 nm  f=0.0000  <S**2>=2.000
      66 -> 72        -0.15152
      66 -> 73         0.52175
      68 -> 72        -0.17519

and the same thing for ORCA

STATE  1:  E=   0.079273 au      2.157 eV    17398.4 cm**-1 <S**2> =   2.000000
    70a ->  71a  :     0.961371
    70a ->  75a  :     0.010646
     Symmetry: A'

STATE  2:  E=   0.097752 au      2.660 eV    21454.2 cm**-1 <S**2> =   2.000000
    64a ->  72a  :     0.012920
    65a ->  72a  :     0.022427
    65a ->  76a  :     0.010776
    70a ->  72a  :     0.917057
     Symmetry: A'

STATE  3:  E=   0.106496 au      2.898 eV    23373.1 cm**-1 <S**2> =   2.000000
    64a ->  73a  :     0.022177
    67a ->  71a  :     0.159342
    67a ->  73a  :     0.015615
    68a ->  71a  :     0.373134
    68a ->  73a  :     0.025981
    68a ->  74a  :     0.023621
    70a ->  73a  :     0.266489
    70a ->  74a  :     0.016846
     Symmetry: A'

STATE  4:  E=   0.108359 au      2.949 eV    23782.0 cm**-1 <S**2> =   2.000000
    66a ->  71a  :     0.034693
    66a ->  72a  :     0.014649
    66a ->  73a  :     0.010149
    69a ->  71a  :     0.067229
    69a ->  72a  :     0.806209
    69a ->  73a  :     0.029132
    69a ->  76a  :     0.021241
     Symmetry: A"

As you can see, we have a difference of about 0.05 eV which shouldn't be the case as everything is supposed to be the same. I posted the same problem on ORCA forum but was not able to sort out a solution, here are the things I tried:

  • When I used the TDA approximation in both, they both gave exact results till the fifth decimal place in electron volt.
  • I tried to run a HF energy calculation for both, I saw the energy results (In Hartrees) began to differ from the sixth decimal place ORCA = -892.3214627659 Gaussian = -892.3214698.

Given these details, I would really love it if someone could point out what I am doing wrong in this regard. I assume there is some hidden parameter that is defaulted to different values for both. I tried the tightscf but to no significant improvement. Please let me know what I might be doing wrong.

Thanks in advance !

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  • 1
    $\begingroup$ Could it be that in one of the packages, excitations out of the core orbitals are included, and in the other they are not? That would fit with the TDA being consistent. $\endgroup$ Jan 17 at 12:06
  • $\begingroup$ You mention HF giving the same single point energies between the two programs, did B3LYP? If it differs significantly for the initial energy/orbitals, then the TDDFT will almost surely be different. $\endgroup$
    – Tyberius
    Jan 17 at 16:38
  • $\begingroup$ It seems that your input files are not consistent with your outputs. In your Gaussian input file you requested for singlet states, but the output shows triplet states. And your ORCA input does not include functional and basis set information. Could you post the exact input files that led to your output, just in case the reason of the difference lies in the part of the input that you didn't post? $\endgroup$
    – wzkchem5
    Jan 18 at 19:06

2 Answers 2

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These may not be the causes of the issue, but some things to consider:

  1. By default, Orca uses the RI approximation for DFT calculations. According to @SRMaiti, Gaussian might have RI implemented under the name 'density fitting'; however, I do not think it is on by default. You need to make sure to include NoRI in your Orca input to avoid it.
  2. The grids/integrals in Gaussian and Orca are different (Gaussian has much larger/finer integrals, which should, theoretically, produce more precise results). In Orca, you should probably use at least DefGrid3.
  3. Default convergence tolerances will be different between Gaussian and Orca. Probably best to use verytightscf in Orca.
  4. My understanding is that, even though you can use a cc-pvdz basis set in both Gaussian and Orca, they are still slightly different in how they are implemented. It's something to do with the way the coordinate system works. I could be wrong about this, though, but I have a vague memory of reading that somewhere.

It is possible that there are some other differences between the two programs which are specific to their TDDFT implementations, but I don't use TDDFT so I cannot help with that. But it's worth keeping in mind that, in general, as far as I am aware, when comparing the default settings in Gaussian and Orca, Gaussian will prioritises accurate results, whereas Orca seems to prioritise fast results.

Just to make it clear, I am not saying that one program is less accurate than the other—you can run very accurate calculations in both—just letting you know what to look out for.

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3
  • $\begingroup$ One minor point on Gaussian16, I believe you can actually run some calculations with RI. It is called "density fitting" there, which as I understand is the same thing. But it probably is not as tightly integrated with every module as in Orca. $\endgroup$
    – S R Maiti
    Jan 19 at 10:58
  • $\begingroup$ @SRMaiti good to know—I'll edit my answer. Thank you! $\endgroup$ Jan 20 at 10:55
  • $\begingroup$ gaussian.com/densityfit this is the Gaussian webpage for density fitting. It seems Gaussian16 can only do this for pure DFT functionals (i.e. no hybrid functional), and only works on the Coulomb part. (And this is off by default if the keyword or aux basis is not specified) $\endgroup$
    – S R Maiti
    Jan 20 at 15:11
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To my knowledge (and depending on the version you use) ORCA uses RI-J and semi-numerical exchange (COSX) by default which might have a larger influence on the RPA TDDFT values in contrast to the TDA TDDFT ones? To answer that I ran a quick check with Turbomole to have a third option and also to compare RI-J/COSX to the non-RI/COSX results.

Results without any technical tricks or approximations (no RI, no COSX, just plain DFT):

No. Exc. energy (Eh) energy (eV) energy (cm-1) energy (nm) Osc.(vel) Osc.(len)
1 a' 0.081022 2.20472 0.17782269D+05 562.358 0.88132878 0.92585267
2 a' 0.099666 2.71204 0.21874084D+05 457.162 0.11816715 0.13580095
1 a" 0.108444 2.95092 0.23800783D+05 420.154 0.00045973 0.00031559
3 a' 0.110137 2.99698 0.24172289D+05 13.697 0.02083900 0.02021690
2 a" 0.115230 3.13556 0.25289985D+05 395.413 0.00007985 0.00012440
4 a' 0.121520 3.30673 0.26670553D+05 374.945 0.40035164 0.44081543
3 a" 0.138418 3.76654 0.30379186D+05 329.173 0.00000937 0.00003855
4 a" 0.151245 4.11560 0.33194527D+05 301.254 0.00093093 0.00049491

so Gaussian and Turbomole give the same results up to about 1meV (most likely due to different DFT grids used).

To check the influence of RI-J and COSX, I also ran those calculations using Turbomole to get the deviations:

raw DFT with RI-J with RI-J+COSX
2.20472 2.20472 2.20508
2.71204 2.71239 2.71078
2.95092 2.95105 2.94974
2.99698 2.99717 2.99650
3.13556 3.13544 3.13856
3.30673 3.30707 3.30659
3.76654 3.76660 3.76723
4.11560 4.11558 4.11933

This indicates that the deviations between Gaussian and ORCA results probably do not stem from the ‚numerical tricks‘ RI and COSX.

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