Large occupied - unoccupied orbital energy gaps

[LCLTurboUser]

Hello Turbomole forum.

I'm having an issue involving the calculated HOMO-LUMO gaps in small cationic aromatic systems.
Essentially what I'd like to do is use the HOMO-LUMO energy gaps to establish structure-property relationships.

Using protonated pyridine as an example, I calculated the verticals (CC2/aug-cc-pVDZ) which produced the correct vertical excitation energies.

 +================================================================================+
 | sym | multi | state |          CC2 excitation energies       |  %t1   |  %t2   |
 |     |       |       +----------------------------------------+--------+--------+
 |     |       |       |   Hartree    |    eV      |    cm-1    |    %   |    %   |
 +================================================================================+
 | a   |   1   |   1   |    0.1947486 |    5.29938 |  42742.388 |  90.68 |   9.32 |
 | a   |   1   |   2   |    0.2341869 |    6.37255 |  51398.073 |  90.61 |   9.39 |
 | a   |   1   |   3   |    0.2783338 |    7.57385 |  61087.214 |  92.31 |   7.69 |
 | a   |   1   |   4   |    0.2787401 |    7.58490 |  61176.379 |  90.34 |   9.66 |
 | a   |   1   |   5   |    0.2944330 |    8.01193 |  64620.573 |  92.68 |   7.32 |
 +================================================================================+

However, upon inspecting the orbital energies using the -eiger command I noticed the HOMO-LUMO gap was +11.63eV... which is over twice as large as the first excited state (HOMO-LUMO dominated transition) vertical transition energy. 

Total energy =   -247.0946506573 H =     -6723.7913769 eV

 HOMO-LUMO Separation
   HOMO:    21.    21 a     -0.55373713 H =    -15.06796 eV
   LUMO:    22.    22 a     -0.12630268 H =     -3.43687 eV
   Gap :                    +0.42743445 H =    +11.63109 eV

Number of MOs=    192, Electrons=     42.00, Symmetry: c1

   Nr.   Orbital    Occupation       Energy
   38.    38 a                     +0.035359 H =        +0.962 eV
   37.    37 a                     +0.033222 H =        +0.904 eV
   36.    36 a                     +0.029379 H =        +0.799 eV
   35.    35 a                     +0.011010 H =        +0.300 eV
   34.    34 a                     +0.004734 H =        +0.129 eV
   33.    33 a                     +0.003932 H =        +0.107 eV
   32.    32 a                     +0.002314 H =        +0.063 eV
   31.    31 a                     -0.015121 H =        -0.411 eV
   30.    30 a                     -0.025702 H =        -0.699 eV
   29.    29 a                     -0.037591 H =        -1.023 eV
   28.    28 a                     -0.045515 H =        -1.239 eV
   27.    27 a                     -0.047398 H =        -1.290 eV
   26.    26 a                     -0.067403 H =        -1.834 eV
   25.    25 a                     -0.069002 H =        -1.878 eV
   24.    24 a                     -0.083024 H =        -2.259 eV
   23.    23 a                     -0.093839 H =        -2.554 eV
   22.    22 a                     -0.126303 H =        -3.437 eV
   21.    21 a        2.000        -0.553737 H =       -15.068 eV
   20.    20 a        2.000        -0.600803 H =       -16.349 eV
   19.    19 a        2.000        -0.727333 H =       -19.792 eV
   18.    18 a        2.000        -0.728034 H =       -19.811 eV
   17.    17 a        2.000        -0.786614 H =       -21.405 eV
   16.    16 a        2.000        -0.816320 H =       -22.213 eV
   15.    15 a        2.000        -0.834458 H =       -22.707 eV
   14.    14 a        2.000        -0.879664 H =       -23.937 eV
   13.    13 a        2.000        -0.884839 H =       -24.078 eV
   12.    12 a        2.000        -0.977433 H =       -26.597 eV
   11.    11 a        2.000        -1.080018 H =       -29.389 eV
   10.    10 a        2.000        -1.089840 H =       -29.656 eV
    9.     9 a        2.000        -1.257654 H =       -34.223 eV
    8.     8 a        2.000        -1.302341 H =       -35.439 eV
    7.     7 a        2.000        -1.524904 H =       -41.495 eV
    6.     6 a        2.000       -11.451863 H =      -311.621 eV

Apologies if my questions are basic but:

Am I calculating the orbital energies incorrectly?
if so, how can I calculate the true energies for the HOMO-LUMO orbitals?

I have attached the control and ricc2 files.

Many thanks in advance,
LCLTurboUser

[antti_karttunen]

Hi,

eiger reports the HOMO-LUMO gap for the Hartree-Fock ground state. Vertical excitation energies obtained with the CC2 method can be very different from the HOMO-LUMO gap of the HF ground state.

Best,
Antti

[LCLTurboUser]

Hyvää päivää Antti,

Thanks for your explanation, that makes sense.
Just to follow that point up:

Is there a method to calculate/extract the orbital energies using CC2?
The energies will be used to construct a Kohn-Sham energy diagram.

Kind regards,
LCLTurboUser

[antti_karttunen]

Hi,

First, one clarification: ab initio MO theory (HF, CC2, ...) will not give you information for constructing a Kohn-Sham energy diagram (Kohn-Sham orbitals are a DFT concept).

CC2 will not give you a new set of molecular orbitals. If you want to work with canonical MOs to draw some energy diagrams, you could set the energy of HOMO to zero and then schematically draw excitations to LUMO etc. based on CC2 vertical excitation values. And plot the relecant canonical MOs next to these energy levels.

But, rather than using the canonical orbitals, which always becomes a mess at some point, I suggest that you use either natural transition orbitals or excited state density differences to analyze your excitations. More information in manual sections 19.1.6 and 10.3.3.

Best,
Antti