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Rei Okuda , Tsuneo Hirano and Umpei Nagashima

WG01. 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. FeNC. CoCN. Exp. (MW) Sheridan and Ziurys (2004). Exp. (LIF) Lie & Dagdian (2001).

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Rei Okuda , Tsuneo Hirano and Umpei Nagashima

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  1. WG01 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

  2. FeNC CoCN Exp. (MW) Sheridan and Ziurys (2004) Exp. (LIF) Lie & Dagdian (2001) B0(3F4) = 4208.827(23) MHz B0 = 0.1452 (2) cm-1 B0 (6D9/2) = 0.14447(13) cm-1 1.03(8) Å 2.01(5) Å 1.88270 Å 1.13133Å Fe ----------- N ----- C Co ---------- C ----- N 1.182 Å re Calc. 1.168 Å re Calc. 1.935 Å 1.854 Å Be= 0.14251 cm-1, B0 = 0.14341 cm-1 Be= 4209.9 MHz NiCN Exp. (LIF) Kingston, Merer, Varberg (2002) B0 (2D5/2) = 0.1444334(30) cm-1 However, difference in B0 is small: (MW) Sheridan, Ziurys (2003) B0 (2D5/2) = 0.14443515(5) cm-1 FeNCcalc -1.2 % NiCNcalc 1.1 % LIF 1.8292(28) Å 1.1591(29) Å r0(2D5/2) MW 1.8293(1) Å 1.1590(1) Å r0(2D5/2) Ni ---------- C ------ N Calc. 1.811 Å 1.166 Å re Be = 0.14590 cm-1, B0(2D5/2) = 0.14595 cm-1 DeYonker, et al. (2004, JCP) (MR-SDCI+Q) re(Fe-N) = 1.940 Å re(C-N) = 1.182 Å →Be = 0.1420 cm-1

  3. Our Calc. level: FeNC, CoCN, and NiCN MR-SDCI+Q + Erel C-N Bond length / Å FeNC CoCN NiCN Obs. (r0) 1.03(8) 1.131 1.159 Calc. (re) 1.182 1.168 1.166 Difference -0.15 -0.037 -0.007 cf. Exp. r0(NC): MgNC 1.169 Å AlNC 1.171 Å CN 1.172 Å cf. Calc. (Hirano, et al. JMS, 2002) re(NC) MgNC 1.1814 Å • Ionicity (Metal-Ligand) can be estimated from the C-N bond length: Md+-(CN)d- The transferred electron goes into p*(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 initiore ) • And, hence, floppiness in bending motion should be Fe-NC > Co-CN > Ni-CN , since the more ionic, the more floppy.

  4. Model (a) We have to switch the concept of bending motion. (24) Mg (26) N C Model (b) can explain the the reverse order in r0 : Fe-NC < Co-CN < Ni-CN Model (b) C (59) Co (26) N G Our Calc. level: FeNC, CoCN, and NiCN MR-SDCI+Q + Erel C-N Bond length / Å FeNC CoCN NiCN Obs. (r0) 1.03(8) 1.131 1.159 Calc. (re) 1.182 1.168 1.166 Difference -0.15 -0.037 -0.007 cf. Exp. r0(NC): MgNC 1.169 Å AlNC 1.171 Å CN 1.172 Å cf. Calc. (Hirano, et al. JMS, 2002) re(NC) MgNC 1.1814 Å Now,we know Ionicity and, hence, floppiness: Fe-NC > Co-CN > Ni-CN How do we rationalize the reverse order in r0 ? r0: Fe-NC < Co-CN < Ni-CN To go further, we need the knowledge of the Three-dimensional Potential Energy Surfaces.

  5. Multireference-SDCI / [Roos ANO (Co), aug-pVQZ (C,N)] Active spaces: 3s,3p, 3d, 4s (Co) and 2s, 2p (C,N) Ab Initio MO calculations on First-row Transition Metal Radicals: Difficult. •Open 3d shells many quasi-degenerated states • In many cases, a state should be described by Multi-Configuration. • Must keep Correct Degeneracy in Symmetry when the radical is treated in C2v symmetry, instead of Cv. • Linear molecule under C2v Difficulty to avoid mixing, especially, between 3F and 3P states. • Relativistic effect correction should be necessary for Spectroscopic Accuracy Relativistic correction by Cowan-Griffin approach in perturbation method

  6. Details of MO Calculations • Wavefunction • Construction of MCSCF guess by merging Co+ (3F) and CN- (1S) 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 (Erel) 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

  7. Potential Energy Curves of CoCN: MR-SDCI+Q+Erel • Quintet State • R(C-N) = 1.17、∠CoCN = 180.0 • Triplet State • r(C-N) = 1.17、∠CoCN = 180.0 5Σ 3Π 5Π 3Σ Energy(Hartree) 3Δ 5Δ Only 0.0036 hartree= 802 cm-1 5Φ 3Φ r(Co-C) r(Co-C) The ground state is predicted to be 3F state

  8. Molecular constant of CoCN X3F MR-SDCI+Q+Erel Calc. Exp. 3F4a) Calc. Exp. 3F4a) re(Co-C) /Å 1.85411.8827(7) (r0)wexe(11) /cm-1 -10.9 re(C-N) /Å1.1677 1.1313(10)(r0)wexe (22) /cm-1 -7.7 ae(Co-C-N)/deg 180.0 180.0 wexe (33) /cm-1 -2.2 Be /MHz 4209.9wexe(12) /cm-1 -3.4 B0 /MHz 4234.8b4208.827(23)wexe (13) /cm-1 -4.4 DJ /MHz 0.001080.001451(10)wexe (23) /cm-1 35.6 Ee /Eh -1484.7591917 g22 /cm-1 8.0 a1 /MHz 10.5 n1(C-N) /cm-1 2163 a2 /MHz -24.7 n2 (Co-C-N) /cm-1 239 a3 /MHz -12.1 n3(Co-C) /cm-1 571 ~478 (?) w1(C-N)/cm-1 2191 Zero-Point E./cm-11608 w2(Co-C-N) /cm-1 238z12/cm-1 -0.98 w3(Co-C) /cm-1 542 z 23/cm-1 -0.22 Aso /cm-1-242 -133.3 (assumed)L-doubling/cm-10.00018 [cf. CoH (3F) -242.7]c me /D -6.993 (Expec. Value -7.464) a (MW) Sheridan, et al. (2004). b Difference 0.6 %c Varberg, et al. (1989)

  9. -1484.66 1Φ -1484.67 -1484.68 -1484.69 19050 cm-1 -1484.70 -1484.71 -1484.72 -1484.73 5Φ -1484.74 3Δ -1484.75 3Φ -1484.76 -1484.77 1.80 1.85 1.90 1.95 2.00 2.05 2.10 The perturber 1F could bethe 3D state ( ~ 802 cm-1 above). 3F3↔ 3D3 Spin-orbit Interaction Scheme, Sheridan, Flory, and Ziurys (2004) ? MR-SDCI+Q+Erel ASO = -242 cm-1 (cf. CoH -242.7 cm-1) DE(1F – 3F) = ~ 31 cm-1 ASO(3F) = -133.3 cm-1 (assumed)

  10. C-N Bond length / Å FeNC CoCN NiCN Obs. (r0) 1.03(8) 1.131 1.159 Calc. (re) 1.182 1.168 1.166 Difference -0.15 -0.037 -0.007 (%) -12.9 -3.2 -0.6 Model (a) (24) Mg (26) N C Model (b) C (59) Co (26) N G Summary Our Model (b) and ab inito calculations can rationalize the discrepancies. Then, WHAT does the experimentally obtained r0 values for CoCN mean ? The difference between experimental and predicted values indicates the existence of large-amplitude bending motion. However, experimentally derived r0 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 methodto derive physically-sound, and meaningful r0 from experiments for this type of floppy molecule !!!

  11. Acknowledgment: We thank Prof. Ziurys and Sheridan, University of Arizona, for providing us the detailed information on B0 and r0’s of CoCN prior to their publication.

  12. Calc. Exp.a Calc. Exp.a re(Fe-N) /Å 1.93542.01 ± 0.05 (r0)wexe(11) /cm-1 -12.9 re(N-C) /Å1.1823 1.03± 0.05 (r0)wexe (22) /cm-1 -3.5 ae(Fe-N-C)/deg 180.0 180.0wexe (33) /cm-1 -2.5 Be /cm-10.14251wexe(12) /cm-1 -4.5 B0 /cm-10.14337b0.1452(2) wexe (23) /cm-1 9.4 DJ x 108/cm-1 4.83g22 /cm-1 2.50 Ee /Eh -1364.1941735 n1(N-C) /cm-1 2058 a1 /cm-1 0.00057 n2 (Fe-N-C) /cm-1 103 a2 /cm-1-0.00147n3(Fe-N) /cm-1 478 464.1± 4.2 a3 /cm-10.00066Zero-Point E./cm-1 138 w1(N-C)/cm-12090z12/cm-1-0.97 w2(Fe-N-C) /cm-1 109 z23/cm-1-0.24 w3(Fe-N) /cm-1 476 L-doubling/cm-1 0.00382 Aso /cm-1-85.4 [cf. FeF (6D) -76]cme /D -4.59 (Expec. Value -4.74) a(LIF) Lie & Dagdian (2001). b difference -1.3 %c Allen and Ziurys (1997) FeNC X6D MR-SDCI+Q+Erel/[Roos ANO(Fe), aug-cc-pVQZ(N,C)]

  13. MgNC (X2S+) ACPF/TZ2p+f Microwave exp. (core-valence) (Kagi, et al.a) B /MHz 5969.3 5966.8969 0 D /MHz 0.0029 0.0042338 0 w -1 /cm 90.4 86 2 a B /MHz -78.5 -70.2 2 Kawaguchi, Kagi, Hirano, et al. 1993 a MgCN (X2S+) ACPF/TZ2p+f Microwave exp. (core-valence) (Anderson,et al.b) B /MHz 5089.3 5094.80351 0 D /MHz 0.0025 0.00277421 0 Anderson, et al. 1994 b 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 & MgCN Guélin, et al. (Astrophys. J, 1986) U-lines toward IRC + 10216 Carbon star B0 = 5966.82 MHz, Linear molecule (2S) HSiCC, HCCSi, HSCC, CCCl, etc.?

  14. Rotational Constants (B0) Unit in cm-1 Exp. Previous Calcs. Our Calc. 12D5/2 0.60284 (0.0%) FeN 0.602793(17) 0.60280246(25) DFT 0.5693 (-5.6 %) DFT 0.6099 (1.2 %) FeS 15Di 0.20246 (0.6%) 0.20368 MR-ACPF 0.1911 (-6.2 %) DFT 0.2011 (-1.3 %) 13Di FeC 0.66966 (-0.5%) 0.67291212(6) MR-SDCI 0.6754 (0.4 %) MR-SDCI 0.6623 (-1.6 %) 0.54955 (-0.5%) 23D3 0.55321(15) 0.5521(10) MR-SDCI 0.5298 (4.0 %) MR-SDCI 0.5388 (-2.4 %) 43D2 0.56153 (-0.5%) MR-SDCI 0.5417 (-4.0 %) 0.56442(15) →The error of predicted B0 : 0.5 – 0.6 %

  15. Predicted Spectroscopic Constants of CoCN with Roos ANO (Co), aug-pVQZ (C,N)

  16. CoH (X 3F): Experimental values re/År0/Å        we/cm-1n/cm-1a/cm-1E(5F - 3F) /cm-1 • Stevens, et al. (1987) 6625 ± 110 • Lipus, et al. (1989) 1926.7 1857.5 0.21974 • S. Beaton, K.M. Evenson, J. Brown. (1994) FIR-LMR 1.5138435(80)  1.5252* • R.S. Ram, P.F. Bernath, and S.P. Davis (1996) IR-emission FT (W=4) 1.531291(8) 1.54262(W = 4)*     1858.7932(32) 0.212444(93) [1.5160 * 1.5271* ]       (W=3) 1.5170** 1.5280**  *Corrected by us for Spin-Orbit interaction ** Calcd. by us from their B0 value.

  17. CoH : Correction of Spin-Orbit Interaction and Rovibrational Interaction • Ram, Bernath, Davis, J. Mol. Spectrosc. 175, 1-6 (1996) • re = 1.531291(8) A • equilibrium internuclear distance of the lowest spin component in the 3Φ4electronic ground state • Uncorrected spin-orbit correction • Bv,ω＝ B0+(2B02/Aso*L)*Σ • Aso (spin-orbit interaction constant) • L（orbital angular momentum）＝3(Φstate） • separation between Ω=3 and Ω=4 =-728cm-1（＝Aso*L) • Ω=|L+Σ| middle level of3Φ, 3Φ3 Ω=3 、Σ = 0 • B0 and B1 can give extrapolation vale to re • Spin-orbit correction gives re = 1.5170 • They corrected rovibration interaction • a was measured by the difference of Bv,ω between v = 0 and v=1 of a Ωstate • Bｖ,j = Be+α*(ｖ + 1/2)*(J+1) • B0 = Be + 0.5*α (v = 0、rotational quantum number = 0) • Beaton, Evenson, Brown, J. Mol. Spectrosc. 164, 395-415 (1994) • re = 1.5138435(80) A • equilibrium internuclear distance of 3Φ electronic ground state ensemble • Rotation constant B0 for ground state ensemble was determined by using Analysis of both observed 3Φ4 and 3Φ3 sublevels, （3Φ2 was not observed）.

  18. CoH : Spin Orbit Splitting with Breit-Pauli g) T. D. Varberg et al. J. Mol. Spectrosc. 138, 638(1989)

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