WG 01 Too Short CN Bond Length Experimentally

WG 01 Too Short CN Bond Length, Experimentally Found in Cobalt Cyanide: An ab Initio Molecular Orbital Study Grid Technology Research Center, AIST, Japan Rei Okuda, Tsuneo Hirano and Umpei Nagashima

Fe. NC Co. CN Exp. (LIF) Lie & Dagdian (2001) Exp. (MW) Sheridan and Ziurys (2004) B 0(3 F 4) = 4208. 827(23) MHz 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. 182 Å re 1. 935 Å Calc. 1. 88270 Å 1. 13133 Å Co ----- C ----- N Calc. 1. 854 Å 1. 168 Å re Be= 0. 14251 cm-1, B 0 = 0. 14341 cm-1 Be= 4209. 9 MHz Ni. CN Exp. (LIF) Kingston, Merer, Varberg (2002) B 0 (2 D -1 5/2) = 0. 1444334(30) cm (MW) Sheridan, Ziurys (2003) B 0 (2 D 5/2) = 0. 14443515(5) cm-1 LIF MW 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 Calc. 1. 811 Å 1. 166 Å re Be = 0. 14590 cm-1, B 0(2 D 5/2) = 0. 14595 cm-1 However, difference in B 0 is small: Fe. NCcalc -1. 2 % Ni. CNcalc 1. 1 % De. Yonker, et al. (2004, JCP) (MR-SDCI+Q) re(Fe-N) = 1. 940 Å re(C-N) = 1. 182 Å → Be = 0. 1420 cm-1

C-N Bond length / Å Fe. NC Co. CN Ni. CN Obs. (r 0) 1. 03(8) 1. 131 1. 159 Calc. (re) 1. 182 1. 168 1. 166 Difference -0. 15 -0. 037 -0. 007 Our Calc. level: Fe. NC, Co. CN, and Ni. CN MR-SDCI+Q + Erel cf. Exp. r 0(NC): Mg. NC 1. 169 Å Al. NC 1. 171 Å CN 1. 172 Å cf. Calc. (Hirano, et al. JMS, 2002) re(NC) Mg. NC 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 initio re ) • 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 Fe. NC Co. CN Ni. CN Obs. (r 0) 1. 03(8) 1. 131 1. 159 Calc. (re) 1. 182 1. 168 1. 166 Difference -0. 15 -0. 037 -0. 007 Now, we know Ionicity and, hence, floppiness: Our Calc. level: Fe. NC, Co. CN, and Ni. CN MR-SDCI+Q + Erel cf. Exp. r 0(NC): Mg. NC 1. 169 Å Al. NC 1. 171 Å CN 1. 172 Å cf. Calc. (Hirano, et al. JMS, 2002) re(NC) Mg. NC 1. 1814 Å Fe-NC > Co-CN > Ni-CN 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. Model (a) Mg (24) Model (b) can explain the reverse order in r 0 : Fe-NC < Co-CN < Ni-CN To go further, we need the knowledge of the Three-dimensional Potential Energy Surfaces. N C (26) Model (b) Co (59) C G (26) N

Ab Initio MO calculations on First-row Transition Metal Radicals: Difficult. • Open 3 d 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 C 2 v symmetry, instead of C v. • Linear molecule under C 2 v 3 3 Difficulty to avoid mixing, especially, between F and P states. • Relativistic effect correction should be necessary for Spectroscopic Accuracy Multireference-SDCI / [Roos ANO (Co), aug-p. VQZ (C, N)] Active spaces: 3 s, 3 p, 3 d, 4 s (Co) and 2 s, 2 p (C, N) Relativistic correction by Cowan-Griffin approach in perturbation method

Details of MO Calculations • Wavefunction – Construction of MCSCF guess by merging Co+ (3 F) and CN- (1 S) 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 – 3 s, 3 p, 3 d and 4 s shells of Co, and 2 s and 2 p shells of CN • Program – MOLPORO 2002 suite of quantum chemistry programs

Potential Energy Curves of Co. CN: MR-SDCI+Q+Erel • • Triplet State Quintet State – R(C-N) = 1. 17、∠Co. CN = 180. 0 – r(C-N) = 1. 17、∠Co. CN = 180. 0 5Σ Energy(Hartree) 3Π 5Π 3Σ 3Δ 5Δ Only 0. 0036 hartree= 802 cm-1 3Φ r(Co-C) The ground state is predicted to be 3 F state 5Φ r(Co-C)

Molecular constant of Co. CN X 3 F MR-SDCI+Q+Erel Calc. Exp. 3 F 4 a) Calc. Exp. 3 F 4 a) re(Co-C) /Å 1. 8541 1. 8827(7) (r 0) wexe(11) /cm-1 -10. 9 wexe (22) /cm-1 ae(Co-C-N)/deg 180. 0 wexe (33) /cm-1 Be /MHz 4209. 9 wexe(12) /cm-1 B 0 /MHz 4234. 8 b 4208. 827(23) wexe (13) /cm-1 DJ /MHz 0. 00108 0. 001451(10) wexe (23) /cm-1 -7. 7 Ee /Eh -1484. 7591917 8. 0 re(C-N) /Å 1. 1677 a 1 /MHz 10. 5 a 2 /MHz -24. 7 a 3 /MHz -12. 1 w 1(C-N) /cm-1 2191 w 2(Co-C-N) /cm-1 238 w 3(Co-C) /cm-1 542 1. 1313(10)(r 0) g 22 /cm-1 -2. 2 -3. 4 -4. 4 35. 6 n 1(C-N) /cm-1 2163 n 2 (Co-C-N) /cm-1 239 n 3(Co-C) /cm-1 571 ~478 (? ) Zero-Point E. /cm-1 1608 z 12/cm-1 -0. 98 z 23/cm-1 -0. 22 Aso /cm-1 -242 -133. 3 (assumed) L-doubling/cm-1 0. 00018 [cf. Co. H (3 F) -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)

Spin-orbit Interaction Scheme, Sheridan, Flory, and Ziurys (2004) ? MR-SDCI+Q+Erel -1484. 66 1Φ -1484. 67 -1484. 68 -1484. 69 19050 cm-1 -1484. 70 -1484. 71 -1484. 72 -1484. 73 -1484. 74 -1484. 75 5Φ 3Δ 3Φ -1484. 76 -1484. 77 1. 80 1. 85 1. 90 1. 95 2. 00 2. 05 2. 10 ASO = -242 cm-1 (cf. Co. H -242. 7 cm-1) DE(1 F – 3 F) = ~ 31 cm-1 ASO(3 F) = -133. 3 cm-1 (assumed) The perturber 1 F could be the 3 D state ( ~ 802 cm-1 above). 3 F 3 ↔ 3 D 3

Summary Model (a) C-N Bond length / Å Fe. NC Co. CN Ni. CN Mg (24) N C (26) Obs. (r 0) 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 (b) Co C (59) Our Model (b) and ab inito calculations can rationalize the discrepancies. Then, WHAT does the experimentally obtained r 0 values for Co. CN 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 !!! G (26) N

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

Fe. NC X 6 D MR-SDCI+Q+Erel/[Roos ANO(Fe), aug-cc-p. VQZ(N, C)] Calc. Exp. a re(Fe-N) /Å 1. 9354 2. 01 ± 0. 05 (r 0) wexe(11) /cm-1 -12. 9 re(N-C) /Å 1. 1823 wexe (22) /cm-1 -3. 5 wexe (33) /cm-1 -2. 5 1. 03 ± 0. 05 (r 0) ae(Fe-N-C)/deg 180. 0 Be /cm-1 0. 14251 wexe(12) /cm-1 -4. 5 B 0 /cm-1 0. 14337 b 0. 1452(2) wexe (23) /cm-1 9. 4 DJ x 108/cm-1 4. 83 g 22 /cm-1 2. 50 Ee /Eh -1364. 1941735 n 1(N-C) /cm-1 2058 a 1 /cm-1 0. 00057 n 2 (Fe-N-C) /cm-1 103 a 2 /cm-1 -0. 00147 n 3(Fe-N) /cm-1 478 464. 1± 4. 2 a 3 /cm-1 0. 00066 Zero-Point E. /cm-1 138 w 1(N-C) /cm-1 2090 z 12/cm-1 -0. 97 w 2(Fe-N-C) /cm-1 109 z 23/cm-1 -0. 24 w 3(Fe-N) /cm-1 476 L-doubling/cm-1 0. 00382 Aso /cm-1 -85. 4 [cf. Fe. F (6 D) -76]c me /D -4. 59 ( Expec. Value -4. 74) a (LIF) Lie & Dagdian (2001). b difference -1. 3 % c Allen and Ziurys (1997)

Mg. NC & Mg. CN Guélin, et al. (Astrophys. J, 1986) U-lines toward IRC + 10216 Carbon star B 0 = 5966. 82 MHz, Linear molecule (2 S) 1992 Summer at Nobeyama Mg. CN ? • Ishii, Hirano: ab Initio Calculations Should be Mg. NC ! (Ap. J, 1993) • Kagi, Kawaguchi, Hirano, Takano, and Saito: HSi. CC, HCCSi, HSCC, CCCl, etc. ? Mg. NC (X 2 S+) ACPF/TZ 2 p+f Microwave exp. a) (core-valence) (Kagi, et al. 　 　　　　　　 B 0 /MHz 5969. 3 5966. 8969 D 0 /MHz 0. 0029 0. 0042338 -1 w 2 /cm 90. 4 86 B a 2 /MHz -78. 5 -70. 2 　　 a Kawaguchi, Kagi, Hirano, et al. 1993 　　　 Mg. CN (X 2 S+) 　　 B 0 /MHz D 0 /MHz b ACPF/TZ 2 p+f Microwave exp. (core-valence) (Anderson, et al. b) 5089. 3 0. 0025 Anderson, et al. 1994 5094. 80351 0. 00277421

Rotational Constants (B 0) Exp. 2 Fe. N 1 D 5/2 Our Calc. Unit in cm-1 Previous Calcs. 0. 602793(17) 0. 60280246(25) 0. 60284 (0. 0%) DFT 0. 5693 (-5. 6 %) 0. 6099 (1. 2 %) Fe. S 15 Di 0. 20368 0. 20246 (0. 6%) MR-ACPF 0. 1911 (-6. 2 %) DFT 0. 2011 (-1. 3 %) Fe. C 13 Di 0. 67291212(6) 0. 66966 (-0. 5%) MR-SDCI 0. 6754 (0. 4 %) MR-SDCI 0. 6623 (-1. 6 %) 23 D 3 0. 55321(15) 0. 5521(10) 0. 54955 (-0. 5%) MR-SDCI 0. 5298 (4. 0 %) MR-SDCI 0. 5388 (-2. 4 %) 43 D 2 0. 56442(15) 0. 56153 (-0. 5%) MR-SDCI 0. 5417 (-4. 0 %) →　The error of predicted B 0 : 0. 5 – 0. 6 %

Predicted Spectroscopic Constants of Co. CN with Roos ANO (Co), aug-p. VQZ (C, N) MR-SDCI+Q+Erel Experiments Energy -1474. 35893 -1474. 418015 -1484. 759193 re(Co-C) /Å 1. 8854 1. 8832 1. 8541 1. 8827 re(C-N) /Å 1. 1628 1. 1677 1. 1313 ae(Co-C-N)/deg 180. 0 Be / cm-1 4123. 9 4119. 9 4209. 9 w 1(C-N) /cm-1 2236 2192 2191 w 2(Co-C-N) /cm-1 227 224 238 w 3(Co-C /cm-1 519 518 542

Co. H (X 3 F): Experimental values re/Å r 0/Å we/cm-1 n/cm-1 a/cm-1 E(5 F - 3 F) /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 B 0 value.

Co. H : 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 3Φ 4　 electronic ground state • Uncorrected spin-orbit correction – – – Bv, ω＝ B 0+(2 B 02/Aso*L)*Σ Aso (spin-orbit interaction constant) L（orbital angular momentum）＝ 3(Φstate） separation between Ω=3 and Ω=4 =-728 cm-1（＝Aso*L) Ω=|L+Σ| middle level of　3Φ, 3Φ 3 Ω=3 、Σ = 0 B 0 and B 1 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) – B 0 = 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 B 0 for ground state ensemble was determined by using Analysis of both observed 3Φ 4 and 3Φ 3 sublevels, （3Φ 2 was not observed）.

Co. H : Spin Orbit Splitting with Breit-Pauli Spin Orbit splitting between the ω= 4 and 3 　 cm-1 3Φ 3Π 5Φ 5Π Exp. -728± 3 g) Sekiya -693. 32 -224. 30 -404. 05 -134. 76 Wachters -655. 35 -212. 23 -384. 74 -128. 61 g) T. D. Varberg et al. J. Mol. Spectrosc. 138, 638(1989)