# A THEORETICAL STUDY OF FeNC IN THE $^6\Delta$ ELECTRONIC GROUND STATE

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 Title: A THEORETICAL STUDY OF FeNC IN THE $^6\Delta$ ELECTRONIC GROUND STATE Creators: Hirano, Tsuneo; Okuda, Rei; Nagashima, Umpei; Spirko, V.; Jensen, Per Issue Date: 2006 Publisher: Ohio State University Abstract: We report an {\it ab initio} calculation, at the MR-SDCI+Q+$E_{\rm rel}$/[Roos ANO (Fe), aug-cc-pVQZ (C, N)] level of theory, of the potential energy surface for $^6\Delta_i$ FeNC. From the {\it ab initio} results, we have computed values for the standard spectroscopic parameters of FeN$^{12}$C and FeN$^{13}$C. Analytical representations of the potential energy surfaces have been fitted through the {\it ab initio} points, and the resulting functions have been used for directly solving the rotation-vibration Schrodinger equation by means of the MORBID program and by means of an adiabatic-separation method. For $^6\Delta_i$ FeNC, our {\it ab initio} calculations show that the equilibrium structure is linear with $r_{\rm e}$(Fe-N) = 1.9354 \AA\ and $r_{\rm e}$(N-C) = 1.1823 \AA. We find that the bending potential is very shallow, and the MORBID calculations show that the zero-point averaged structure is bent with the expectation values $\langle r\mbox{(Fe-N)}\rangle$ = 1.9672 \AA, $\langle r\mbox{(N-C)}\rangle$ = 1.1866 \AA, and $\langle \bar\rho \rangle$ $=$ 180$^irc$ $-$ $\langle \angle\mbox{(Fe-N-C)} \rangle$ $=$ 13$^irc$. The experimentally derived bond length $r_0$(N-C) = 1.03(8) \AA\ reported for $^6\Delta_i$ FeNC by J. Lie and P. J. Dagdigian [{\it J. Chem. Phys.} {\bf 114}, 2137-2143 (2001)] is much shorter than the corresponding {\it ab initio} $r_{\rm e}$-value and the averaged value from MORBID. Our calculations suggest that this discrepancy is caused by the inadequate treatment of the large-amplitude bending motion of $^6\Delta_i$ FeNC. It would appear that for floppy triatomic molecules such as FeNC, $r_0$-values have little physical meaning, at least when they are determined with the effects of the large-amplitude motion being ignored, i.e., under the assumption that the $r_0$ structure is linear. URI: http://hdl.handle.net/1811/30916 Other Identifiers: 2006-MJ-01