sign of transition dipole moment different passing from escf to egrad

[acapobia]

Dear all,

I had a very strange result from a few escf/egrad calculations (TURBOMOLE V5.10, TD-B3LYP/def2-TZVP), namely the signs of the elements of the transition dipole moment (both length and veloc. representations) from egrad are opposite to those from escf. The same (to me) puzzling behaviour affects transition quadrupole moment too. (see the log attached)

My molecule has C1 symmetry (so no re-orientation should occur); moreover I ran egrad keeping the same 'sing_a' file of the previous escf computation; more in detail, suppose I have 20 states; I first run escf, then i run egrad (a run once, obviously) for all the states having oscillator strength, say, greater than 0.1, starting from the highest state and ending to the lowest, always working in the same directory and never deleting any file.

Finally i add that the strange change of dipole signs is not observed on all states, just a few, in passing from escf to egrad.

Can anyone help me to understand what happens, what I'm missing, or what may be my mistake in doing computation? Of course I can post my coord as well as my mos and control files, or the whole directories, if needed.

Any help will be appreciated.
Thank you all very much.

Amedeo
from escf.out

                         2 singlet a excitation


 Total energy:                           -1913.887844774790   
[...]
Electric transition dipole moment (velocity rep.):

    x       -0.345409        Norm:                  4.584641
    y       -0.126716
    z        4.569855        Norm / debye:         11.653084

   
Electric transition dipole moment (length rep.):

    x       -0.352200        Norm:                  4.593280
    y       -0.125474
    z        4.578038        Norm / debye:         11.675042


 Magnetic transition dipole moment / i:

    x        0.000469        Norm:                  0.003957
    y        0.003923
    z        0.000219        Norm / Bohr mag.:      1.084601


 Electric quadrupole transition moment:

   xx        1.922410
   yy       -0.495180        1/3*trace:            -8.601323
   zz      -27.231199
   xy        0.218312
   xz        1.195466        Anisotropy:           28.210885
   yz        1.429154
   
   
  from egrad_state_2.out
   
                         2 singlet a excitation


 Total energy:                           -1913.887844725747   
[...]

 Electric transition dipole moment (velocity rep.):

    x        0.345410        Norm:                  4.584647
    y        0.126716
    z       -4.569860        Norm / debye:         11.653099


 Electric transition dipole moment (length rep.):

    x        0.352201        Norm:                  4.593286
    y        0.125474
    z       -4.578044        Norm / debye:         11.675057


 Magnetic transition dipole moment / i:

    x       -0.000469        Norm:                  0.003957
    y       -0.003923
    z       -0.000219        Norm / Bohr mag.:      1.084605


Electric quadrupole transition moment:

   xx       -1.922416
   yy        0.495180        1/3*trace:             8.601317
   zz       27.231186
   xy       -0.218311
   xz       -1.195505        Anisotropy:           28.210881
   yz       -1.429154

[acapobia]

ADDENDUM

I have carried out two more tests just now on H₂O without symmetry (no desy called in define)

and I have the same strange results as before with the def2-TZVP and def2-TZVPP basis sets; everything seems ok with SVP basis set; however (if possible, even more strange) dipole transition moments are different also in two egrad calculations, i.e. the first excited state has mu_trans=[0.0  0.42  0.0] in the output escf.out and egrad_state1.out, but mu_trans=[0.0  -0.42  0.0] in the output escf_state3.out /def2-TZVPP basis set.

Thanks again
Amedeo

[acapobia]

ADDENDUM 2

Ok, since a wavefunction is defined within a factor of phase (which makes its sign undetermined), it may be that TM evaluates the transition dipole moment sometimes as

< g | mu | e > (or < -g | mu | -e >, other times as

< g | mu | -e > (or < -g | mu | e >)

| g > being ground state, | e > being some excited state; this could explain the change of sign.

So, even if the observable from spectroscopy is | < g | mu | e >|² which does not depend on the sign of | e >, or | g >, is it possible to use a uniform (although arbitrary) criterion to assign a defined sign to a state | j > staring from the data of TM?
This could be important in evaluating terms of SOS-like expressions, like

< n | a | j >< j | b | k>< k | c | n >

(a,b,c, being x,y,z components of mu)
where one must be sure that the electronic states  come with the same sign in all the integrals,
e.g. | n > in 1^st and 3^rd integral.

Hope this will clarify my question.
Amedeo


 

[christof.haettig]

within each program and run the signs of molecular orbitals and/or excitation vectors are handled consistently, but they can cange between subsequent runs and or between the different programs. Anyway, as you pointed out, all observable properties computed by TM will be independent of these signs. Fixing them, might work well in most cases, but in cases of near degeneracies or near symmetries it can become difficult and there is no unique criterion for fixing the phase.
So, the advice is: compute all the data you need in a single program run.

Christof

[acapobia]

Thanks for your kind replay; I guessed my way yours was the most reasonable solution.

Now I'm quite sure ;-)

Amedeo

[ylniu]

Yes, I got the same result.

  When I calculated the derivative of transition dipole moment (\mu_{fi}) respect to the normal coordinate (Q_k), I set the normal displacement 0.1, 0.2, ...... , 1.0. Then x component of the transition dipole moment is like: -4.182, -4.181, 4.180, -4.180, 4.179, ...

  Because the sign of transition dipole moment <e| \mu_x |g> is undetermined, I set the result their absolute value: 4.182, 4.181, 4.180, 4.180, 4.179, ... Then I got a smooth curve of \mu_x(Q_k) respect to Q_k.

  In such a calculation, I can not find an unique criterion to fix the phase!

  Does anyone has some suggestions?