I am trying to compute the lowest singlet excited state vibrations at the CC2/def2-TZVPP level of theory for cis-planar conformer of bithiophene molecule.

The standard procedure I follow begins with geometry optimization for the excited state, then switching from C2v to C1 symmetry, having copied firs the gradient file

obtained during the geometry optimization into the submit directory.

The NumForce module (with level=cc2, central and ecnomic options) is then used and the calculations go smoothly till the hessian, aoforce output files are produced.

There is, however, one imaginary frequency that corresponds to the torsional motion of the rings along the central C-C bond. This normally indicates a saddle point, which is in fact present in the ground state (in which gosh-conformers are the optimum structures). In the S1 state, however, increase coupling between the pi electrons of different rings makes the inter-ring bond acquire a partly double character and rigidifies it, so the structure is expected to be actually planar. This has been reported in literature several times and my own experience also supports such a picture.

In order to check whether the imaginary frequency is some artifact of the numerical procedure or a genuine find, I have conducted DFT calculations (with B3LYP and cam-B3LYP functionals), which both returned all-real frequencies for the S1 excited states. Moreover, I have made a relaxed potential energy scan with respect to the inter-ring rotation and it also shows that the planar conformation corresponds to the minimum on the PES. Finally, I used screwer to distort geometry in the direction of the imaginary frequency normal mode and then reoptimized the structure without any symmetry constraints (C1). The outcome was - again - a planar structure and the same imaginary frequency obtained for it in the NumForce calculations.

It, I think, confirms that the imaginary frequency is some numerical artifact. I tried to remove it by 1. increasing the convergence criteria for the orbitals, 2. changing the size of the geometry distortions in NumForce, 3. switching from ecnomic to cartesian displacements. None of those changed anything.

Please, advise me what can be the reason for such behaviour and how can I possibly get rid of the imaginary frequency. I need to interpret a helium temperature spectra and so I need vg quality of normal modes, including the low-frequency ones.

Yours sincerely

Marcin Andrzejak