Too Short CN Bond Length, Experimentally Found in Cobalt Cyanide: An ab Initio Molecular Orbital Study Rei Okuda, Tsuneo Hirano and Umpei Nagashima Grid Technology Research Center, AIST, Japan WG01

FeNC Fe N C 2.01(5) Å 1.03(8) Å Å Å r e B 0 ( 6  9/2 ) = (13) cm -1 B 0 = (2) cm -1 B e = cm -1, B 0 = cm -1 Exp. (LIF) Lie & Dagdian (2001) Calc. Exp. (MW) Sheridan and Ziurys (2004) CoCN B 0 ( 3  4 ) = (23) MHz Å Å Co C N Calc Å Å r e B e = MHz NiCN Ni C N (28) Å (29) Å r 0 ( 2  5/2 ) B 0 ( 2  5/2 ) = (30) cm -1 B e = cm -1, B 0 ( 2  5/2 ) = cm -1 Exp. (LIF) Kingston, Merer, Varberg (2002) Å1.166 Å r e Calc. (MW) Sheridan, Ziurys (2003) B 0 ( 2  5/2 ) = (5) cm -1 LIF (1) Å r 0 ( 2  5/2 ) (1) ÅMW However, difference in B 0 is small: FeNC calc -1.2 % NiCN calc 1.1 % DeYonker, et al. (2004, JCP) (MR-SDCI+Q) r e (Fe-N) = Å r e (C-N) = Å → B e = cm -1

C-N Bond length / Å FeNC CoCN NiCN Obs. (r 0 ) 1.03(8) Calc. (r e ) Difference Ionicity (Metal-Ligand) can be estimated from the C-N bond length: M  +  -  (CN)  - The transferred electron goes into  *(CN) orbitals  weaken the CN bond. ( i.e. lengthen the CN 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 ) cf. Exp. r 0 (NC): MgNC Å AlNC Å CN Å cf. Calc. (Hirano, et al. JMS, 2002) r e (NC) MgNC Å Our Calc. level: FeNC, CoCN, and NiCN MR-SDCI+Q + E rel And, hence, floppiness in bending motion should be Fe-NC > Co-CN > Ni-CN, since the more ionic, the more floppy.

C-N Bond length / Å FeNC CoCN NiCN Obs. (r 0 ) 1.03(8) Calc. (r e ) Difference Now, we know Ionicity and, hence, floppiness: Fe-NC > Co-CN > Ni-CN cf. Exp. r 0 (NC): MgNC Å AlNC Å CN Å cf. Calc. (Hirano, et al. JMS, 2002) r e (NC) MgNC Å Our Calc. level: FeNC, CoCN, and NiCN MR-SDCI+Q + E rel To go further, we need the knowledge of the Three-dimensional Potential Energy Surfaces. How do we rationalize the reverse order in r 0 ? r 0 : Fe-NC < Co-CN < Ni-CN We have to switch the concept of bending motion. Mg N C Co N C G Model (a) Model (b) (24) (59) (26) Model (b) can explain the the reverse order in r 0 : Fe-NC < Co-CN < Ni-CN

Ab Initio MO calculations on First-row Transition Metal Radicals: Difficult. Open 3d shells  many quasi-degenerated states Must keep Correct Degeneracy in Symmetry when the radical is treated in C 2v symmetry, instead of C  v. Linear molecule under C 2v Difficulty to avoid mixing, especially, between 3  and 3  states. In many cases, a state should be described by Multi-Configuration. Relativistic effect correction should be necessary for Spectroscopic Accuracy Multireference-SDCI / [Roos ANO (Co), aug-pVQZ (C,N)] Active spaces: 3s,3p, 3d, 4s (Co) and 2s, 2p (C,N) Relativistic correction by Cowan-Griffin approach in perturbation method

Wavefunction –Construction of MCSCF guess by merging Co + ( 3 F) and CN - ( 1  ) MCSCF orbitals –Multi-Reference Single and Double Configuration Interaction (MR-SDCI) -- Davidson’s type corrections were added to the MR-SDCI calculation (denoted as +Q). –The relativistic corrections (E rel ) have been included using the Cowan-Griffin approach by computing expectation values of the mass-velocity and one-electron Darwin terms. Active space –3s, 3p, 3d and 4s shells of Co, and 2s and 2p shells of CN Program –MOLPORO2002 suite of quantum chemistry programs Details of MO Calculations

Triplet State –r(C-N) = 1.17 、∠ CoCN = Quintet State –R(C-N) = 1.17 、∠ CoCN = Π3Π 3Φ3Φ 3Δ3Δ 3Σ3Σ 5Π5Π 5Φ5Φ 5Σ5Σ 5Δ5Δ r(Co-C) Energy(Hartree) r(Co-C) Only hartree= 802 cm -1 The ground state is predicted to be 3  state Potential Energy Curves of CoCN: MR-SDCI+Q+Erel

Molecular constant of CoCN X 3   MR-SDCI+Q+E rel Calc. Exp. 3  4 a) Calc. Exp. 3  4 a) r e (Co-C) /Å (7) (r 0 )  e x e (11) /cm r e (C-N) /Å (10)(r 0 )   e x e (22) /cm a e (Co-C-N)/deg  e x e (33) /cm B e /MHz  e x e (12) /cm B 0 /MHz b (23)  e x e (13) /cm D J /MHz (10)  e x e (23) /cm E e /Eh g 22 /cm  1 /MHz (C-N) /cm  2 /MHz (Co-C-N) /cm  3 /MHz (Co-C) /cm ~478 (?)  1 (C-N) /cm Zero-Point E. /cm  2 (Co-C-N) /cm  12 /cm  3 (Co-C) /cm  23 /cm A so /cm (assumed)  -doubling/cm [cf. CoH ( 3  ) ] c  e /D ( Expec. Value ) a (MW) Sheridan, et al. (2004). b Difference 0.6 % c Varberg, et al. (1989)

Spin-orbit Interaction Scheme, Sheridan, Flory, and Ziurys (2004) A SO ( 3  ) = cm -1 (assumed) A SO = -242 cm -1 (cf. CoH cm -1 )  E( 1  – 3  ) = ~ 31 cm -1 ? The perturber 1  could be  the 3  state ( ~ 802 cm -1 above)  3  3  ↔ 3  Φ3Φ 5Φ5Φ 1Φ1Φ 3Δ3Δ cm -1 MR-SDCI+Q+E rel

Mg N C Co N C G Model (a) Model (b) (24) (59) (26) Then, WHAT does the experimentally obtained r 0 values for CoCN mean ? The difference between experimental and predicted values indicates the existence of large-amplitude bending motion. However, experimentally derived r 0 value, in this case, has No-physical meaning for the understanding of the chemical bond except showing how floppy the molecule is in bending motion. We need to explore a new method to derive physically-sound, and meaningful r 0 from experiments for this type of floppy molecule !!! C-N Bond length / Å FeNC CoCN NiCN Obs. (r 0 ) 1.03(8) Calc. (r e ) Difference (%) Our Model (b) and ab inito calculations can rationalize the discrepancies. Summary

Acknowledgment: We thank Prof. Ziurys and Sheridan, University of Arizona, for providing us the detailed information on B 0 and r 0 ’s of CoCN prior to their publication.

FeNC X 6   MR-SDCI+Q+E rel /[Roos ANO(Fe), aug-cc-pVQZ(N,C)] Calc. Exp. a Calc. Exp. a r e (Fe-N) /Å ± 0.05 (r 0 )  e x e (11) /cm r e (N-C) /Å ± 0.05 (r 0 )   e x e (22) /cm a e (Fe-N-C)/deg  e x e (33) /cm B e /cm  e x e (12) /cm B 0 /cm b (2)  e x e (23) /cm D J x 10 8 /cm g 22 /cm E e /Eh (N-C) /cm  1 /cm (Fe-N-C) /cm  2 /cm (Fe-N) /cm ± 4.2  3 /cm Zero-Point E. /cm  1 (N-C) /cm  12 /cm  2 (Fe-N-C) /cm  23 /cm  3 (Fe-N) /cm  -doubling/cm A so /cm [cf. FeF ( 6  ) -76] c  e /D ( Expec. Value -4.74) a (LIF) Lie & Dagdian (2001). b difference -1.3 % c Allen and Ziurys (1997)

MgNC & MgCN Guélin, et al. (Astrophys. J, 1986) U-lines toward IRC Carbon star B 0 = MHz, Linear molecule ( 2  ) HSiCC, HCCSi, HSCC, CCCl, etc. ? 1992 Summer at Nobeyama MgCN ? Ishii, Hirano: ab Initio Calculations Should be MgNC ! (ApJ, 1993) Kagi, Kawaguchi, Hirano, Takano, and Saito: Microwave experiments Obsd. Sep., 1992 (ApJ, 1993) MgNC (X 2  + ) ACPF/TZ2p+f Microwave exp. B 0 /MHz D 0 /MHz  2 /cm  2 B /MHz a Kawaguchi, Kagi, Hirano, et al MgCN (X 2  + ) ACPF/TZ2p+f Microwave exp. B 0 /MHz D 0 /MHz b Anderson, et al (core-valence) (Kagi, et al. a ) (core-valence) (Anderson,et al. b )

Rotational Constants (B 0 ) 2323 (-0.5%) MR-SDCI (4.0 %) MR-SDCI (-2.4 %) 4343 (-0.5%) MR-SDCI (-4.0 %) 13i13i (-0.5%) MR-SDCI (0.4 %) MR-SDCI (-1.6 %) Unit in cm -1 FeC (15) (10) (15) (6) FeS FeN 1 2  5/ (0.0%) DFT (-5.6 %) DFT (1.2 %) (17) (25) 15i15i (0.6%) MR-ACPF (-6.2 %) DFT (-1.3 %) Exp. Our Calc. → The error of predicted B 0 : 0.5 – 0.6 % Previous Calcs.

MR-SDCIMR-SDCI+QMR-SDCI+Q+E rel Experiments Energy r e (Co-C) /Å r e (C-N) /Å a e (Co-C-N)/deg180.0 B e / cm  1 (C-N) /cm  2 (Co-C-N) /cm  3 (Co-C /cm Predicted Spectroscopic Constants of CoCN with Roos ANO (Co), aug-pVQZ (C,N)

CoH (X 3  ): Experimental values r e /Å r 0 /Å  e /cm -1 /cm -1  /cm -1 E( 5  - 3  ) /cm -1 Stevens, et al. (1987) 6625 ± 110 Lipus, et al. (1989) S. Beaton, K.M. Evenson, J. Brown. (1994) FIR-LMR (80) * R.S. Ram, P.F. Bernath, and S.P. Davis (1996) IR-emission FT (  =4) (8) (  = 4)* (32) (93) [ * * ] (  =3) ** ** *Corrected by us for Spin-Orbit interaction ** Calcd. by us from their B 0 value.

CoH : Correction of Spin-Orbit Interaction and Rovibrational Interaction Ram, Bernath, Davis, J. Mol. Spectrosc. 175, 1-6 (1996) –r e = (8) A –equilibrium internuclear distance of the lowest spin component in the 3 Φ 4 electronic ground state Uncorrected spin-orbit correction –B v,ω ＝ B 0 +(2B 0 2 /A so *  )*Σ –A so (spin-orbit interaction constant) –  （ orbital angular momentum ）＝ 3(Φstate ） –separation between Ω=3 and Ω=4 =-728cm -1 （＝ A so *  ) –Ω=|  +Σ| middle level of 3 Φ, 3 Φ 3 Ω=3 、 Σ = 0 –B 0 and B 1 can give extrapolation vale to r e Spin-orbit correction gives r e = They corrected rovibration interaction –  was measured by the difference of B v,ω between v = 0 and v=1 of a Ωstate –B ｖ,j = B e +α*( ｖ + 1/2)*(J+1) –B 0 = B e + 0.5*α (v = 0 、 rotational quantum number = 0) Beaton, Evenson, Brown, J. Mol. Spectrosc. 164, (1994) –re = (80) A –equilibrium internuclear distance of 3 Φ electronic ground state ensemble Rotation constant B 0 for ground state ensemble was determined by using Analysis of both observed 3 Φ 4 and 3 Φ 3 sublevels, （ 3 Φ 2 was not observed ）.

CoH : Spin Orbit Splitting with Breit-Pauli g) T. D. Varberg et al. J. Mol. Spectrosc. 138, 638(1989) Spin Orbit splitting between the ω= 4 and 3 cm -13Φ3Φ 3Π3Π 5Φ5Φ 5Π5Π Exp.-728±3 g) Sekiya Wachters