The electronic structure and properties of Ni(C ₆ H _4-n F _n )(CO) ₂ (C ₆ H ₄ =benzyne, n=1-4) complexes have been investigated using hybrid density functional B3LYP theory. Both aromatic natures and nucleus independent chemical shift (NICS) of the benzyne rings have been analyzed. Among mono-, di-, and tri-fluorinated complexes, 3-F, 3,6-F, and 4-H are the most stable isomers, respectively. NICS values calculated at the several points above the ring centers are consistent with those based on the relative energies of the complexes. The atoms in molecules (AIM) analysis indicates that Ni-C bond distance is well correlated with the electron density of a ring critical point (ρ _rcp ) in all species. Benzyne has been the subject of many theoretical and experimental investigations 1 - 6 because it is found as an intermediate of many important organic or biochemical reactions. 3 , 7 - 8 Since the first attempt for making metal complexes using benzyne by by Wittig and Bickelhaupt in 1958, 9 many benzyne complexes have been successfully prepared, 10 - 13 for example, M. A. Bennett et al . 14 synthesized organometallic compounds, NiL ₂ (C ₆ H ₄ )(L = PCy ₃ , P ⁱ Pr ₃ ; Cy = cyclohexyl, ⁱ Pr = isopropyl). K. R. Deaton and M. S. Gin studied the reactions of nickel(0)-benzyne complexes with symmetrically substituted 1,3-diynes in the presence of triethylphosphine, which lead to the regioselective formation of 2,3-dialkynyl naphthalenes 15 . In the present study, the quantum chemical methods were used in order to gain a deeper insight into the structure and bonding of Ni(C ₆ H _4-n F _n )(CO) ₂ (C ₆ H ₄ = benzyne, n = 1 - 4) complexes and phenomena of the substituent effect in a benzyne ring. All calculations were carried out with the Gaussian 03 suite of program. 16 Light atoms (C, H, O and F) were described by the standard 6-31+G(d) basis set. 17 Ni was described by the effective core potential (ECP) of Wadt and Hay pseudo-potential 21 with a double-ξ valance using the LANL2DZ basis set. 18 - 20 Geometry optimization was performed using Becke’s hybrid three-parameter exchange functional and the nonlocal correlation functional of Lee, Yang, and Parr (B3LYP). 22 A vibrational analysis was performed at each stationary point which corresponds to an energy minimum. The nucleus-independent chemical shift (NICS) 23 , 24 has been defined as the absolute magnetic shielding computed at the center of a ring in a molecule. NICS(0.0), NICS(0.5), NICS(1.0), NICS(1.5) and NICS(2.0) were calculated at 0 (center), 0.5, 1.0, 1.5, and 2.0 Å above the ring, respectively. The AIM2000 program 25 was used for the topological analysis of electron density, and the characteristics of ring critical points (RCPs) were taken into account: density at RCP (ρ(r _c )), and its Laplacian (∇ ² ρ(r _c )). The calculated energy values of the compounds in this work are listed along with the selective bond angles in 1. When the compounds are classified with geometric isomers, 3-F, 3,6-F, and 4-H are the most stable isomer in each group. The structures of the Ni(C ₆ H _4-n F _n )(CO) ₂ complexes were optimized by DFT calculations ( . 1 ). The C-C bond lengths in the benyne-Ni complexes seem to be related with the changes in aromaticity. The C1-C6 bond distance of benzyne (1.386 Å) becomes elongated to 1.393 Å when benzyne forms a complex with Ni(CO) ₂ in H₄ . In contrast, this bond tends to decrease as the number of F atoms increase in the complex if the most stable isomers of the fluorinated complexes are considered: 1.382 Å ( 3-F ), 1.380 Å ( 3,6-F ), 1.377 Å ( 4-H ), and 1.378 Å ( F₄ ). The bond distances of Ni-C(benzyne) decrease, and the Ni-C(O) bonds increase, revealing that the fluorination of benzyne reduces the back-donation of electron densities of Ni to the carbonyls. This observation is supported by the increase of Ni charges in the fluorinated complexes ( 2 ): 0.420 ( H₄ ) to 0.421 ( 3-F ), 0.432 ( 3,6-F ), 0.432 ( 4-H ), and 0.438 ( F₄ ). The bond angles around Ni atom also show a systematic trend that the C1-Ni-C2 bond angles increase while the C7-Ni-C8 ones decrease in the fluorinated complexes. The HOMO and LUMO energies of the compounds in 3 show that all the Ni-complexes have higher HOMO and lower LUMO energies than those of benzyne, respectively. The HOMO—LUMO gap energies tend to decrease as the number of F atoms increases. The symmetric and asymmetric stretching modes of CO are displayed in 2 and the calculated frequencies of CO ligands, ν(CO), have been presented in 3 . These values increase in fluorinated complexes when the most stable isomers are considered. The IR spectroscopy experimental results show that in NiL ₂ (C ₆ H ₄ ) (L=PCy ₃ , Cy = cyclohexyl), the CI-C2 bond length of 1.332 Å is greater than the value of 1.29 Å typical of most ML ₂ (alkyne) complexes, but the lengthening on coordination relative to the free ligand (Δr = 0.08-0.09 Å) is about the same. 11 Correspondingly, the ν(C≡C) value of ca. 1580 cm ^-1 in ML ₂ (C ₆ H ₄ ) (M = Ni, Pt) complexes is less than the value of ca. 1700 cm ^-1 found in ML ₂ (alkyne) complexes, but the decrease relative to the free ligand is of the same order (ν(C≡C)= 400-500 cm ^-1 ) in both series. In the Ni(C ₆ H _4-n F _n )(CO) ₂ systems, the r(C1-C2) in complexes is greater than free benzyne (Δr _max = 0.083 Å in F4 molceule). On the other hand, the ν(C≡C) values increase in complexes rather than free benzyne ( 3 ). Along with the vibration analysis, we could compute ¹ H-NMR chemical shifts for the set of compounds by GIAO method. The calculated chemical shifts of protons are listed in 4. The H3 - H6 signals of H₄ are expected to appear at down-field compared with those in benzyne, indicating that the complexation makes the benzyne ring more electron-deficient. When the F atom is introduced to H4, some of protons shift to up-field although a systematic trend is not clearly detected. This is probably due to the induction effect of the electronegative F atom which attracts electrons again from Ni to the benzyne moiety. The benzyne ¹³ C chemical shifts provide some support for aromaticity. The experimental d values for C1 and C2 in NiL ₂ (C ₆ H ₄ ) (L=PCy ₃ , Cy=cyclohexyl) are 145.2 ppm. 11 Also, the computed ¹³ C NMR chemical shifts of the Ni(C ₆ H _4-n F _n )(CO) ₂ are compatible with aromticity ( 1 ). As an effort to discuss the use of NICS as a measure of aromaticity, we have calculated NICS values from the center of the ring to 2.0 Å above the plane along the z-axis of the benzyne ring. The shape of NICS profile with respect to the distance from the ring center falls into two categories. In addition, for all species, we have localized both the NICS maxima and minima, and determined the distances to the center of the ring at which they occur ( 5 ). For each benzyne, tri-, and tetra-fluorinated species and H₄ , the highest absolute value of NICS closes to the center of the ring. Both mono- and di-fluorinated species have a maximum about 0.5 Å to the ring center. It is possible that induced magnetic fields generated by the σ aromaticity are particularly large in the center of the ring. However, the molecular systems having π aromaticity have a minimum NICS at the certain distances from the center of the ring. There is a linear correlation between NICS(0.0) and NICS(0.5) values in all complexes: R ² = 0.968, not shown. As it is difficult to separate the σ and π contributions to the electron density at the bond critical point, the ρ(r) values can be used to evaluate bond strength for different types of bonds ( 6 ). The different values of ρ(r) and ∇ ² ρ(r) for the Ni-C bonds evidently indicate the relative Ni-C bond strengths. This result is in agreement with the geometrical analysis, showing that the Ni-C bond of Ni(C ₆ H ₄ )(CO) ₂ is longer than other species. On the other hand, the Ni-C bonds in all structures have positive values of ∇ ² ρ(r) which is indicative of the close shell interaction. The value of electron density and its Laplacian estimated at bond critical point of NiC(benzyne) correlate very well with the strength of the bond, as well as with its length, since, as it is well known, both the strength and length of a bond are mutually dependent. A good relationship is present between Σρ(NiC _benzyne ) values and Σr(NiC _benzyne ) (R ² =0.994). Similarity, Σ∇ ² ρ(NiC _benzyne ) values obeys a linear relationship (R ² =0.941), too. The comparison of electron density in the bond critical points of Ni-C(benzyne) and Ni-C(O) shows that ρ(Ni-C _benzyne ) is smaller than ρ(Ni-C(O)). This trend is wellmatched with the results of the geometrical analysis. The bond ellipticity is defined as ε=(λ ₁ /λ ₂ )-1, where |λ ₁ |≥|λ ₂ |. It provides a quantitative measurement of the π character of the bond. The plane of the π distribution is uniquely specifies by the direction of the axis associated with the curvature of smallest magnitude, λ ₂ . The ε(NI-C) values show that the Ni-C bond in fluorinated rings has a smaller π-character in comparison with Ni(C ₆ H ₄ )(CO) ₂ ( 6 ). Further useful information on the chemical bond properties is obtainable from the total electron energy density (H(ρ)) and its components, a kinetic electron energy density (G(ρ), positive by definition) and a potential electron energy density (V(ρ), negative by definition). The following relation is known for H(ρ) and its components: In the region of the bond critical point for the weak closed-shell inter-atomic interactions (Ni-C), the kinetic energy density dominates with the G(ρ) magnitude being slightly greater than the potential energy density |V(ρ)|, which implies that the total energy density H(ρ) is positive and closes to zero. For the strong covalent interactions (Ni-C), V(ρ) dominates over the kinetic energy density and H(λ) < 0. This usually accompany with ∇ ² ρ > 0 for H(λ) > 0, and ∇ ² ρ < 0 for H(ρ) < 0. At the ring critical point of benzyne, both the electron density ρ(3,+1) and Laplacian of electron density ∇ ² ρ(3,+1) have been calculated for all complexes ( 7 ). It is observed that these values become smaller in the fluorinated complexes when they are compared with those of benzyne and H₄ . We investigated the structures and frontier orbitals of the Ni(C ₆ H _4-n F _n )(CO) ₂ (C ₆ H ₄ =benzyne, n=1-4) complexes. The results suggest that 3-F, 3,6-F, 4-H isomers are most stable among the mono-, di-, tri-fluorinated complexes, respectively. Using the stable ones, both vibration and ¹ H-NMR shifts were calculated and analyzed. The NICS calculations confirmed the aromaticity in the benzyne rings of the compounds. Using the analyses of both electron densities and energy densities, we could explain the characters of the Ni-C bonds in complexes.