Computational Molecular Spectroscopy: Fe-containing Molecules of Astrochemical Interest
Tsuneo Hirano,1,2 Umpei Nagashima,2 and Per Jensen3
1)
Ochanomizu University, Japan
2)
National Institute of Advanced Industrial Science and Technology, Japan3)

Physikalische und Theoretische Chemie, Bergische Universität, Germany

Although Fe is known to have a large cosmic abundance comparable to those of Mg and Si, theonly iron-containing molecules so far detected in the cosmic environment are FeH in sunspots [1]and FeO toward Sgr B2 [2,3]. In 1994, we made a preliminary ab initio calculation on FeCO asa candidate for observation in interstellar space [4], but attempts by Kasai et al to detect it inspace failed [5,6]. Then we started ab initio calculations on several Fe-containing molecules ofastrochemical interest, including FeC [7], FeN [8], FeS, FeCO, FeNC [9], FeCN [10], FeOH
[11,12].
We discuss here the molecular properties of 𝑋𝑋� 6∆ FeNC, 𝑋𝑋� 6∆ FeCN, and 𝑋𝑋� 6A’(6∆) FeOH.
The last two of these have not yet been observed spectroscopically, and hence the predicted
spectra are shown in Fig. 1 and Fig. 2, respectively. The ab initio calculations are done at thelevel of MR-SDCI+Q+ Erel/[Roos ANO (Fe), aug-cc-pVQZ (C, N, O, H)].
The equilibrium structuresof FeNC and FeCN arelinear. The equilibrium
structure of FeOH is bentwith a barrier of 273 cm-1
at linearity, which is justabove
thebending
zero-point energy of 194
cm-1, so that 𝑋𝑋� 6A’ FeOH
is a quasi-linear molecule.
The geometrical constantsof these molecules are
given in Table 1.
The Fe atoms in thesethree molecules are boundto their ligands through anionic bond, so that thebending potentials areshallow and give large
amplitude bending motion.
We
havecalculatedro-vibrationally averaged
bond lengths for variousFig. 1 Predicted spectra for the 𝑋𝑋� 6∆ FeCN: (a) rotation spectrum, (b) ν1(at 2153 cm-1), (c) ν2 (at 170 cm-1), and (d) ν3 (at 423 cm-1), simulated at
12 K [10].

Table 1 Ab initio calculated molecular constants at the MR-SDCI+Q+Erel level.
108 DJ/cm-1

Molecule

B0/cm-1𝑋𝑋� 6∆ FeNC b)Exp. [13]𝑋𝑋� 6∆ FeCN c)
𝑋𝑋� 6A’ FeOH d)

0.14274
4.84
0.14447(13)0.12380
4.12

re(M-ligand) re(C-N) or/Åre(O-H) / Å
1.93542.01(5), r0
2.04841.80591.18231.03(8), r0
1.1681
0.9520Bond angle/degrees
180.0
180.0
180.0
134.2

<ρ� >0 (δρ� ) a)
/degreesa) The bond angle deviation from linearity with quantum dynamical uncertainty in parentheses.
b) Ref. [9]. c) Ref. [10]. d) Refs. [11,12].

13(7)

10(5)
39(14)

vibrational states as expectation values in terms of variational MORBID
wavefunctions. The r0 structure andthe bond angle supplement <ρ� >0 (i.e.
the angle deviation from linearity)
thus determined are included in Table
1.
It should be noted that even for alinear molecule, whose equilibrium
structure is linear, the ro-vibrationallyaveragedstructuredeviates
substantially from linearity due to thelarge amplitude bending motion. Itshould also be noted that, for thequasi-linear molecule 𝑋𝑋� 6A’ FeOH,
the <ρ� >0 value is quite close to theequilibrium bond angle. Whetherthe molecule is linear or quasi-linear
or bent can be distinguished by theYamada-Winnewisser quasilinearity
parameter γ0 [14],Fig. 2 Predicted spectra of the 6A’ (6∆) FeOH Renner-degeneratestates (at 10 K) [11].

E(𝑣𝑣 = |𝑙𝑙 | = 1) − E(𝑣𝑣 = |𝑙𝑙 | = 0)γ0 = 1 − 4 × E(𝑣𝑣 2= 2,2|𝑙𝑙 | = 0) −E(𝑣𝑣2 = 2|𝑙𝑙 |= 0) .
2222

It was found that for the linear molecules FeNC and FeNC, γ0 ≈ −1.0, and for the quasi-linear
molecule FeOH, γ0 = 0.1. Thus, at the early stage of the analysis of the experimentallyobtained infrared spectrum, one can identify the relevant molecule being linear, or quasi-linear,or bent.
Another molecule we consider here is FeCO. Many spectroscopic studies have been reportedfor 𝑋𝑋� 3Σ− FeCO (see ref. [15], for example), but none for a 5Σ− FeCO. Our recent prediction at
the MR-SDCI+Q+Erel/[Roos ANO (Fe, C, O)] level for the a 5Σ− FeCO is as follows. This is alinear molecule, with equilibrium structures re(Fe−C) = 1.843 Å, re(C−O) = 1.153 Å, ∠e(Fe-C-O)= 180°. The MORBID analysis gives ro-vibrationally averaged structures as r0(Fe−C) = 1.845 Å,r0(C−O) = 1.157 Å, and <ρ� >0 =9°(4°) with B0 = 0.13422 cm-1 (4023.7 MHz). γ0 = −1.0 as is
expected for a linear molecule. We think that it would be worthwhile to characterize thismolecule further spectroscopically and to search for it in interstellar space.
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