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I did a TDDFT calculation using B3LYP functional and ground state optimized structure in NWCHEM. The TDDFT portion of the output is the following:

----------------------------------------------------------------------------
  Root   1 singlet a              0.124505160 a.u.                3.3880 eV 
  ----------------------------------------------------------------------------
     Transition Moments    X -0.67477   Y -0.16090   Z -0.00926
     Transition Moments   XX -3.72551  XY  0.33692  XZ  0.29211
     Transition Moments   YY  1.03517  YZ -0.47531  ZZ  0.23052
     Dipole Oscillator Strength                    0.0399490230
     Electric Quadrupole                           0.0000000711
     Magnetic Dipole                               0.0000000066
     Total Oscillator Strength                     0.0399491007
 
     Occ.  118  a   ---  Virt.  119  a   -0.98715 X
     Occ.  118  a   ---  Virt.  120  a    0.09973 X
     Occ.  118  a   ---  Virt.  121  a    0.09163 X
  ----------------------------------------------------------------------------
  Root   2 singlet a              0.137354088 a.u.                3.7376 eV 
  ----------------------------------------------------------------------------
     Transition Moments    X -0.76724   Y -0.18948   Z -0.00938
     Transition Moments   XX -0.14340  XY  0.42578  XZ  0.40121
     Transition Moments   YY -3.78588  YZ -0.70760  ZZ  0.22932
     Dipole Oscillator Strength                    0.0571987020
     Electric Quadrupole                           0.0000000795
     Magnetic Dipole                               0.0000001012
     Total Oscillator Strength                     0.0571988827
 
     Occ.  117  a   ---  Virt.  119  a    0.06721 X
     Occ.  118  a   ---  Virt.  119  a   -0.08427 X
     Occ.  118  a   ---  Virt.  120  a   -0.97488 X
     Occ.  118  a   ---  Virt.  121  a    0.16187 X
  ----------------------------------------------------------------------------
  Root   3 singlet a              0.146507598 a.u.                3.9867 eV 
  ----------------------------------------------------------------------------
     Transition Moments    X -1.29377   Y -0.16851   Z -0.08944
     Transition Moments   XX -3.80151  XY -0.41951  XZ  0.03490
     Transition Moments   YY -2.01247  YZ -0.69574  ZZ  0.28749
     Dipole Oscillator Strength                    0.1670425890
     Electric Quadrupole                           0.0000000814
     Magnetic Dipole                               0.0000000321
     Total Oscillator Strength                     0.1670427025
 
     Occ.  117  a   ---  Virt.  119  a    0.46050 X
     Occ.  118  a   ---  Virt.  119  a   -0.10314 X
     Occ.  118  a   ---  Virt.  120  a   -0.09062 X
     Occ.  118  a   ---  Virt.  121  a   -0.85863 X
     Occ.  118  a   ---  Virt.  122  a   -0.06947 X
     Occ.  118  a   ---  Virt.  124  a   -0.08528 X
     Occ.  118  a   ---  Virt.  126  a   -0.06728 X
  ----------------------------------------------------------------------------
  Root   4 singlet a              0.148144715 a.u.                4.0312 eV 
  ----------------------------------------------------------------------------
     Transition Moments    X  0.71163   Y  0.25036   Z -0.00906
     Transition Moments   XX -0.55692  XY -1.07219  XZ -0.77683
     Transition Moments   YY  3.20588  YZ  0.77510  ZZ -0.25256
     Dipole Oscillator Strength                    0.0562132776
     Electric Quadrupole                           0.0000001164
     Magnetic Dipole                               0.0000002325
     Total Oscillator Strength                     0.0562136265
 
     Occ.  117  a   ---  Virt.  119  a    0.87602 X
     Occ.  118  a   ---  Virt.  120  a    0.12925 X
     Occ.  118  a   ---  Virt.  121  a    0.44044 X
     Occ.  118  a   ---  Virt.  122  a    0.08258 X
     Occ.  118  a   ---  Virt.  124  a    0.07882 X
  ----------------------------------------------------------------------------
  Root   5 singlet a              0.154029225 a.u.                4.1914 eV 
  ----------------------------------------------------------------------------
     Transition Moments    X  1.06235   Y -1.10313   Z -0.02692
     Transition Moments   XX 12.18774  XY  1.28925  XZ  0.69277
     Transition Moments   YY-12.48775  YZ  0.01961  ZZ -0.04038
     Dipole Oscillator Strength                    0.2409235301
     Electric Quadrupole                           0.0000030040
     Magnetic Dipole                               0.0000000646
     Total Oscillator Strength                     0.2409265987
 
     Occ.  116  a   ---  Virt.  119  a    0.08704 X
     Occ.  116  a   ---  Virt.  121  a    0.05730 X
     Occ.  116  a   ---  Virt.  126  a   -0.06016 X
     Occ.  117  a   ---  Virt.  119  a    0.05311 X
     Occ.  117  a   ---  Virt.  121  a   -0.11048 X
     Occ.  118  a   ---  Virt.  121  a    0.09638 X
     Occ.  118  a   ---  Virt.  122  a   -0.96960 X
     Occ.  118  a   ---  Virt.  126  a    0.05824 X
  ----------------------------------------------------------------------------
  Root   6 singlet a              0.160861901 a.u.                4.3773 eV 
  ----------------------------------------------------------------------------
     Transition Moments    X  0.03641   Y -0.03873   Z  0.00124
     Transition Moments   XX  4.34168  XY  0.32728  XZ  0.54758
     Transition Moments   YY -3.07040  YZ -0.31294  ZZ  0.02520
     Dipole Oscillator Strength                    0.0003032394
     Electric Quadrupole                           0.0000003184
     Magnetic Dipole                               0.0000001208
     Total Oscillator Strength                     0.0003036786
 
     Occ.  117  a   ---  Virt.  120  a   -0.96655 X
     Occ.  117  a   ---  Virt.  122  a    0.07250 X
     Occ.  118  a   ---  Virt.  120  a    0.05042 X
     Occ.  118  a   ---  Virt.  123  a    0.17409 X
     Occ.  118  a   ---  Virt.  124  a   -0.10164 X
     Occ.  118  a   ---  Virt.  126  a    0.05475 X

For my molecule experimental absorbance is at 321 nm or 3.8624 eV.

My question is that from my output which root should I compare with the experimental value?

Do I need to consider oscillator strength or I should take the root 1 value?

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  • 1
    $\begingroup$ +1 and welcome to our new community! Thank you for contributing your question here, and we hope to see much more of you in the future!! Please take a close look though at what I did here: mattermodeling.stackexchange.com/posts/4303/revisions and try to take it into account in your next question! $\endgroup$
    – Nike Dattani
    Feb 7, 2021 at 5:33
  • 2
    $\begingroup$ I think the oscillator strength indicates the intensity of the absorption. The first root may not always be the strongest peak in the spectrum. $\endgroup$
    – S R Maiti
    Feb 7, 2021 at 12:22
  • 2
    $\begingroup$ You should consider the states (roots) with non-zero oscillator strength. It means that the transition from the ground to excited state is allowed by the transition dipole moment rule. So, in your case root number 3 is the first excited state with oscillator strength of 0.16, whilst root number 5 is the second excited state with oscillator strength of 0.24. I am not an NWChem user but have been working on excited states. Hope this helps. $\endgroup$
    – Meilani Wibowo
    Feb 7, 2021 at 13:23
  • 1
    $\begingroup$ So in your case, if you want to compare with the experimental value (3.8624 eV), it will be root number 3. $\endgroup$
    – Meilani Wibowo
    Feb 7, 2021 at 15:16
  • 1
    $\begingroup$ @MeilaniWibowo It looks like your comments also helped the OP, so it may be better to combine these into the answer you posted. $\endgroup$
    – Tyberius ♦
    Feb 8, 2021 at 21:58

1 Answer 1

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You should consider the states (roots) with non-zero oscillator strength. It means that the transition from the ground to excited state is allowed by the transition dipole moment rule. So, in your case root number 3 is the first excited state with oscillator strength of 0.16, whilst root number 5 is the second excited state with oscillator strength of 0.24. So in your case, if you want to compare with the experimental value (3.8624 eV), it will be root number 3. For computing the emission spectra of a molecule you do need to optimise the excited state geometry first. Once you optimise the excited state geometry, then you can do the same procedure. For computing the fluorescence do optimise the lowest singlet excited state, whilst for computing the phosphorescence do optimise the lowest triplet excited state. Remember the Kasha's rule.

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