Large Amplitude Bending Motion: Computational Molecular Spectroscopy and Experiments of Transition-Metal Containing Isocyanide and Cyanides.

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WG13 63 rd Columbus 2008/Jun/18 Large Amplitude Bending Motion: Computational Molecular Spectroscopy and Experiments of Transition-Metal Containing Isocyanide and Cyanides. Tsuneo HIRANO, a,b Rei OKUDA, b Umpei NAGASHIMA, b Per JENSEN c a Ochanomizu University (Japan), b RICS-AIST (Japan), and c University of Wuppertal (Germany)

The effects of large amplitude bending motion gave rise to a longstanding debate: CsOH: D.M. Lide, R.L. Kuczkowski, J. Chem. Phys., 46, 4768 (1967). D.M. Lide, C. Matsumura, J. Chem. Phys., 50, 3080 (1969) RbOH: C. Matsumura, D.R. Lide, J. Chem. Phys., 50, 71 (1969) r_c : M. Nakata, K. Kuchitsu, et al., J. Mol. Spec., 83,118 (1980) OCCl2 J. Mol. Spec., 86,241 (1981) OCCl2 J. Mol. Struc., 320,179 (1994) OCS, etc. r m (2) : J.K.G. Watson, et al., J. Mol. Spec., 196,102 (1999) K.A. Walker, et al., J. Mol. Spec., 209, 178 (2001) Theory AlNC/AlCN, GaNC/GaCN, InNC/InCN However, mostly forgotten in recent experimental studies.

FeNC Exp. (LIF) Lie & Dagdian (2001) Calc. B 0 = 0.1452 (2) cm -1 B 0 ( 6 D 9/2 ) = 0.14447(13) cm -1 2.01(5) Å 1.03(8) Å Fe ----------- N ----- C 1.935 Å 1.182 Å r e B e = 0.14251 cm -1, B 0 = 0.14341 cm -1 CoCN Exp. (MW) Sheridan and Ziurys (2004) B 0 ( 3 F 4 ) = 4208.827(23) MHz 1.88270 Å 1.13133 Å Co ---------- C ----- N Calc. 1.854 Å 1.168 Å r e B e = 4209.9 MHz, B 0 ( 3 F 4 ) = 4229.1 MHz NiCN Exp. (LIF) Kingston, Merer, Varberg (2002) B 0 ( 2 D 5/2 ) = 0.1444334(30) cm -1 LIF MW Calc. (MW) Sheridan, Ziurys (2003) B 0 ( 2 D 5/2 ) = 0.14443515(5) cm -1 1.8292(28) Å 1.1591(29) Å r 0 ( 2 D 5/2 ) 1.8293(1) Å 1.1590(1) Å r 0 ( 2 D 5/2 ) Ni ---------- C ------ N 1.8141 Å 1.1665 Å r e B e = 0.14552 cm -1, B 0 ( 2 D 5/2 ) = 0.14559 cm -1 However, Difference in B 0 is small: FeNC calc -1.2 % CoCN calc 0.5 % NiCN calc 0.8 %

C-N Bond length / Å FeNC CoCN NiCN Obs. (r 0 ) 1.03(8) 1.131 1.159 Calc. (r e ) 1.182 1.168 1.167 Difference/Å -0.15 (13%) -0.037-0.008 Our Calc. level: FeNC, CoCN, and NiCN MR-SDCI+Q + E rel cf. Exp. r 0 (NC): MgNC 1.169 Å AlNC 1.171 Å CN 1.172 Å cf. Calc. (Hirano, et al. JMS, 2002) r e (NC) MgNC 1.1814 Å Ionicity (Metal-Ligand) can be estimated from the C-N bond length: M d+ - (CN) d- The transferred electron goes into s*(cn) orbital weakens the CN bond. ( i.e. lengthens this bond). Hence, the iconicity of the Metal-Ligand bond should be in this order, Fe-NC > Co-CN > Ni-CN (from ab initio r e ) And, hence, floppiness in bending motion should be Fe-NC > Co-CN > Ni-CN, since the more ionic, the more floppy.

Now, we know Ionicity and, hence, floppiness: Fe-NC > Co-CN > Ni-CN r 0 (Obs.): (1.03) (1.131) ( 1.159) Model (a) Mg (24) N (26) C Model (b) Fe (56) G (26) The more floppy, the shorter the CN bond length projected to the molecular axis becomes. To go further, we need the knowledge of the Three-dimensional Potential Energy Surfaces.

Our Strategy in Computational Molecular Spectroscopy 1) Three-dimensional potential energy surface by the ab initio MO method: MR-SDCI + Q + E rel 2) Fit the potential to an analytical potential function 3) The 2nd-order perturbation treatment 4) Variational calculations with MORBID or RENNER

FeNC 6 D i MR-SDCI+Q+E rel /[Roos ANO(Fe), aug-cc-pvqz(c,n)] Perturbational Method Calc. Exp. 6 D i a) Calc. Exp. 6 D i a) r e (Fe-N) /Å 1.9354 2.01(5) (r 0 ) w e (11) /cm -1-11.8 r e (N-C) /Å 1.1823 1.03(8) (r 0 ) w e (22) /cm -1-4.0 a e (Fe-N-C)/deg 180.0 180.0 w e (33) /cm -1-3.7 B e /cm -1 0.1425 w e (12) /cm -1-4.9 B 0,W=9/2 /cm -1 0.14278 b 0.14447(13) w e (13) /cm -1-3.7 D J * 10 8 / cm -1 4.83 w e (23) /cm -1 8.6 E e /Eh -1364.1941735 g 22 /cm -1 2.66 a 1 / cm -1 0.00055 n 1 (N-C) /cm -1 2060 a 2 / cm -1-0.00147 n 2 (Fe-N-C) /cm -1 102 a 3 / cm -1 0.00061 n 3 (Fe-N) /cm -1 475 464.1(42) w 1 (N-C) /cm -1 2090 Zero-Point E. /cm -1 1385 w 2 (Fe-N-C) /cm -1 109 z 12 /cm -1-0.97 w 3 (Fe-N) /cm -1 476 z 23 /cm -1-0.24 A so /cm -1-83 L-doubling/cm -1 0.00038 [cf. FeF ( 6 D i ) -78.15] c m e /D -4.59 (Expec. Value -4.74) a (LiF) Lie, et al. (2001). b Difference 1.2 % c Allen and Ziurys (1997)

Expectation values from MORBID analysis: FeNC (v 1, v 2 l2, v 3 ) <r(fe-n)>/å <r(n-c)>/å <r(fe-n) cos(h)>/å <r(n-c) cos(t)>/å <r>/degree (0,0 0,0) 1.967 1.187 1.964 1.164 13(7) (0,1 1e,f,0) 1.971 1.187 1.965 1.141 20(7) (0,2 0,0) 1.970 1.188 1.960 1.113 25(12) (1,0 0,0) 1.969 1.195 1.965 1.169 13(7) (0,0 0,1) 1.976 1.187 1.972 1.159 13(7) cf. Equil. Struct. 1.935 1.182 0.0 Exp. r 0 2.01(5) 1.03(8) 0.0 (Lie et al., 2001) The <r(n-c)>, ~1.187 Å, a little longer than r e (N-C), does not change unless the C-N bond is excited. Physically meaningful, proper quantity. Exp. r 0 is not the averaged projection onto a-axis. No physical meaning! Exp. model is inadequate!! Explicit treatment of large amplitude bending motion is necessary. -

CoCN X 3 F MR-SDCI+Q+E rel, Perturbation method Calc. Exp. 3 F 4 a) Calc. Exp. 3 F 4 a) r e (Co-C) /Å 1.8541 1.8827(7) (r 0 ) w e (11) /cm -1-10.9 r e (C-N) /Å 1.1677 1.1313(10)(r 0 ) w e (22) /cm -1-7.7 a e (Co-C-N)/deg 180.0 180.0 w e (33) /cm -1-2.2 B e /MHz 4209.9 w e (12) /cm -1-3.4 B 0 /MHz 4234.8 b 4208.827(23) w e (13) /cm -1-4.4 D J /MHz 0.00108 0.001451(10) w e (23) /cm -1 35.6 E e /Eh -1484.7591917 g 22 /cm -1 8.0 a 1 /MHz 10.5 n 1 (C-N) /cm -1 2163 a 2 /MHz -24.7 n 2 (Co-C-N) /cm -1 239 a 3 /MHz -12.1 n 3 (Co-C) /cm -1 571 ~478 (?) w 1 (C-N) /cm -1 2191 Zero-Point E. /cm -1 1608 w 2 (Co-C-N) /cm -1 238 z 12 /cm -1-0.98 w 3 (Co-C) /cm -1 542 z 23 /cm -1-0.22 A so /cm -1-242 -133.3 (assumed) L-doubling/cm -1 0.00018 [cf. CoH ( 3 F) -242.7] c m e /D -6.993 (Expec. Value -7.464) a (MW) Sheridan, et al. (2004). b Difference 0.6 % c Varberg, et al. (1989)

Expectation values from MORBID analysis: CoCN (v 1, v 2 l2, v 3 ) <r(co-c)>/ Å <r(c-n)>/ Å <r(c-n) cos(t)>/å < > / deg. (0,0 0,0) 1.873 1.172 1.161 8(5) (0,1 1e,f,0) 1.877 1.173 1.152 13(5) (0,2 0,0) 1.873 1.173 1.141 15(8) (1,0 0,0) 1.874 1.180 1.164 8(5) (0,0 0,1) 1.882 1.172 1.161 8(5) cf. Equil. Struct. 1.854 1.168 0.0 Exp. R 0,W=4 1.8827(7) 1.1313(10) 0.0 (Sheridan, et al., 2004) The <r(c-n)>, ~1.172 Å, a little longer than r e (C-N), does not change unless the C-N bond is excited. Physically meaningful, proper quantity. Exp. r 0 is not the averaged projection onto a-axis. No physical meaning! Exp. model is inadequate!! Explicit treatment of large amplitude bending motion is necessary. ρ

58 NiCN X 2 D i MR-SDCI+Q+E rel, Perturbation method Calc. Exp. Calc. Exp. r e (Ni-C) /Å 1.8141 1.8292(28) (r 0 ) a) w e (11) /cm -1-17.8 1.8293(1) (r 0 ) b) w e (22) /cm -1-96.3 r e (C-N) /Å 1.1665 1.1591(29) (r 0 ) a) w e (33) /cm -1 0.1 1.1590(2) (r 0 ) b) w e (12) /cm -1-4.2 a e (Co-C-N)/deg 180.0 180.0 w e (13) /cm -1 3.6 B e /cm -1 0.14552 0.143681446(40) b) w e (23) /cm -1 383.7 B 0 /cm -1 0.14567 0.144638234(56) b) g 22 /cm -1 96.4 B 0,W=5/2 /cm -1 0.14559 c) 0.144443511(53) b) n 1 (C-N) /cm -1 2161 F.C. inactive a) D J /cm -1 4.49 x10-8 4.99 x10-8 a) n 2 (Ni-C-N) /cm -1 251 246.1(16) a) E e /Eh -1612.0269135 n 3 (Ni-C) /cm -1 897 501.8(29) a) a 1 /cm -1 0.00052 Zero-Point E. /cm -1 1699 a 2 /cm -1-0.00072-0.000712 a) z 12 /cm -1-0.97-0.00074636(4) b) z 23 /cm -1-0.23 a 3 /cm -1 0.00060 L-doubling/cm -1 0.00018 w 1 (C-N) /cm -1 2199 A so /cm -1-613 -415.0(ass.) b) w 2 (Ni-C-N) /cm -1 254 m e /D -7.23 w 3 (Ni-C) /cm -1 511 (Expect. value: -7.56) e (Renner const.) 0.050 a (LIF) Kingston, et al. (2002). b (MW) Sheridan, et al. (2003). c Difference 0.8 %

Expectation values from MORBID analysis: 58 NiCN (v 1, v l 2 2, v 3 ) <r(ni-c)> <r(c-n)> <r(ni-c) cos(h)> <r(c-n) cos(t)> < > / Å / Å / Å / Å / degrees (0,0 0,0) 1.842 1.171 1.839 1.160 9(5) (0,1 0,0) 1.849 1.171 1.845 1.153 13(5) (0,2 0,0) 1.846 1.171 1.841 1.145 15(8) (0,0 0,1) 1.849 1.171 1.846 1.158 (1,0 0,0) 1.844 1.178 1.841 1.168 cf. Equil. Struct. 1.814 1.167 0.0 Exp. r 0,W=5/2 1.8293(1) 1.1590(2) 0.0 (Sheridan, et al., 2003) The <r(c-n)>, ~1.171 Å, a little longer than r e (C-N), does not change unless the C-N bond is excited. Physically meaningful, proper quantity. Again, experimental r 0 (C-N) is much smaller than <r(c-n)> 0! Exp. model is inadequate!! Explicit treatment of large amplitude bending motion is necessary. ρ

Now we can make quantitative arguments. i) Floppiness in bending motion Qualitatively from the C-N bond length: FeNC >> CoCN NiCN (r e / Å) 1.182 1.168 1.167 Bending force constant (aj -1 ) from the 3-D PES FeNC >> CoCN > NiCN cf. FeCO 0.036 0.151 0.180 0.364 Bending potential: FeNC >> CoCN > NiCN FeNC CoCN 58 NiCN

ii) CN bond lengths: MORBID Expectation value Ro-vibrationally averaged MORBID structure FeNC CoCN NiCN r e (C-N) /Å 1.182 1.168 1.166 r 0 (C-N) /Å 1.187 1.172 1.171 < r - > / deg. 13(7) 8(5) 9(5) Both r e (C-N) and r e (C-N) fall inside of the normal C-N bond length 1.16-1.19 Å. MORBID expectation value of the bond length r 0 : a little longer than the equilibrium bond length r e. keeps almost constant unless the associated bond is vibrationally excited. physically sound bond length to characterize a chemical bond even for molecules showing large amplitude bending motion. Although the equilibrium structure is linear, the ro-vibrationally averaged structure is bent. This is our answer to the longstanding debate : How to treat a large amplitude bending motion.

Summary: Too-short CN bond lengths C-N Bond length / Å FeNC CoCN NiCN Obs. (r 0 ) 1.03(8) 1.131 1.159 Calc. (r e ) 1.182 1.168 1.166 (r 0 ) 1.187 1.172 1.171 Difference -0.157-0.041-0.012 in r 0 (%) -13.2-3.5-1.0 Then, WHAT does the experimentally derived r 0 values mean? No physical meaning!!! The difference between experimental and predicted values indicates the existence of large-amplitude bending motion. Conventional method to derive r 0 value is inadequate for these molecules showing large-amplitude bending motion,

Why the Conventional method to derive r 0 value is inadequate? Observe B 0 s for isotopologues. derive r 0 s, assuming linear structure in the moment of inertia calcs. interpret the thus derived r 0 s as the projection average onto the a-axis in the bending motion, because B 0 s are employed. However, NO average over bending motion is taken into account in this procedure! Now, the turn is in the experimental side. Explicit treatment of large amplitude bending motion is necessary.

Acknowledgment: We thank Dr. Yoshio Tanaka for proving us their CPU resources at Grid Research Center, AIST, Japan. Part of this research was supported by the program Core Research for Evolutional Science and Technology (CREST), Japan Science and Technology Agency, and by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie. References; FeNC: T. Hirano, R. Okuda, U. Ngashima, V. Špirko, P. Jensen, J. Mol. Spectrosc., 236 (2006) 234-247 CoCN: T. Hirano, R. Okuda, U. Nagashima, P. Jensen, Mol. Phys. 105 (2007) 599-611. NiCN: T. Hirano, R. Okuda, U. Nagashima, P. Jensen, Chem. Phys., 346 (2008) 13-12.

Every linear poly-atomic (more than diatomic) molecule is bent, even when the equilibrium structure is linear. Suppose the rovibronic wavefucntion be described by a two-dimensional harmonic-oscillator in bending and rotational normal coordinates, q a and q b. When decoupled from rotation about the molecular axis, the averaged angle for bending motion becomes as r q 2 2 a qb > 0, r is the bond angle supplement.

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