Revisiting the Spectrum of Co(CN)63-: The Role of Correlation, Solvation, and Vibronic and Spin-Orbit Couplings.

In the present work, we revisit the spectrum of the hexacyanocobaltate(III) ion, [Co(CN)6]3-, which has been considered a prototype complex in the coordination chemistry, with modern quantum chemistry methods. The main features have been describing by revealing the role of different effects, such as vibronic coupling, solvation and spin-orbit coupling. The UV-vis spectrum is composed by two bands (1A1g → 1T1g and 1A1g → 1T2g), characterized by singlet-singlet metal-centered transitions, and a more intense third one, characterized by charge transfer transition. There is also a small band shoulder. The first two are symmetry-forbidden transitions in the Oh group. Their intensity can only be explained by a vibronic coupling mechanism. For the band shoulder, additional to vibronic coupling, spin-orbit coupling is also necessary, since the transition is characterized as singlet to triplet, 1A1g → 3T1g.

Comparison among several vibronic coupling methods.

A comparison of four approaches to account the vibronic coupling in photoabsorption is performed. The methods considered are nuclear ensemble (NE), direct vibronic coupling (DVC), adiabatic Hessian (AH), and vertical gradient (VG). The case study is the symmetry-forbidden [Formula: see text] [Formula: see text]A[Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text]A[Formula: see text] (n [Formula: see text] [Formula: see text]) transition in formaldehyde. Being forbidden in the equilibrium geometry, this transition is entirely induced by vibronic coupling and constitutes an appropriate case to study the performance of different methods. From DVC, it is found that mode 1 (C=O out-of-plane bending) is the most inducing, followed by mode 6 (in-plane C-H asymmetric stretching) and finally by mode 2 (in-plane C-H asymmetric bending). We were able to correlate 17 out of 20 structures obtained from NE with these modes, showing that these two methods, although different in principle, give comparable results. The simulated spectra were obtained for all methods and compared, and each one has its own advantage. In what concerns the transition studied, NE gives the best description of the spectrum, DVC is the only one that easily gives an absolute value for OOS, and AH and VG are the computationally less expensive methods. From the latter two, VG is the less demanding on computational grounds, since it does not require the excited state Hessian.