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Сyclo[18]Carbon: Insight Onto Electronic Structure

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Сyclo[18]Carbon: Insight Onto Electronic Structure Electronic Supporting Information for Сyclo[18]Carbon: Insight into Electronic Structure, Aromaticity and Surface Coupling Glib V. Baryshnikov,a,b,* Rashid R. Valiev,c,d Artem V. Kuklin,a,e Dage Sundholm,d and Hans Ågren f,a,* a Division of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, 10691, Stockholm, Sweden b Department of Chemistry and Nanomaterials Science, Bohdan Khmelnytsky National University, 18031, Cherkasy, Ukraine c Research School of Chemistry & Applied Biomedical Sciences, National Research Tomsk Polytechnic University, Lenin Avenue 30, Tomsk 634050, Russia d Department of Chemistry, Faculty of Science, University of Helsinki, FIN-00014, Helsinki, Finland e Division of Theoretical Physics and Wave Phenomena, Siberian Federal University, 79 Svobodniy av., Krasnoyarsk 660041, Russia f College of Chemistry and Chemical Engineering, Henan University, Kaifeng, Henan 475004, P.R. China Computational details The molecular structure of cyclo[18]carbon in the ground closed-shell singlet electronic state of polyyne has been optimized at the DFT level of theory in the gas phase using the BMK,1 BHandLYP,2 M06-2X,3 wB97XD4 functionals and 6-311++G(d,p)5–7 basis set. The molecular structure of the cumulene-type cyclo[18]carbon, which corresponds to the transition state for the bond-length inversion between two polyyne forms, has been optimized by using the QST3 procedure.8,9 The same functionals (BMK, BHandLYP, M06-2X, wB97XD) and basis set (6-311++G(d,p)) have been used in the TS calculations. We also employed the 6-31G(d),10 cc-pvTZ and def-TZV11 basis sets at the M06-2X level in the optimization of the ground-state polyyne and transition-state cumulene structures in order to check the basis-set dependence of the obtained results. The obtained structures agree with the ones obtained at the M06-2X/6-311++G(d,p) level. In order to prove that the calculated transition state cumulene-type geometry of cyclo[18]carbon corresponds to the genuine transition state between two polyyne-type ground state geometries with inverted position of single and triple bonds an internal reaction coordinate (IRC) scan by the HPC algorithm12 has been carried out. For both reaction path directions we have found the correct evolution of TS cumulene-type geometry into the corresponding polyyne forms. The results are presented in figure S1. The Gaussian 16 software13 was used in these DFT calculations. Figure S1. IRC profile for the triple bond shift in polyyne-type cyclo[18]carbon thought the cumulene-type transition state (corresponds to the energy maximum on the IRC curve). Magnetically induced current densities (current strengths) were calculated using the gauge-including magnetically induced currents (GIMIC) method.14,15 The NMR shielding calculations required for GIMIC computations were performed at the M06-2X/def2-TZVP16 level of theory using the Turbomole program package.17 Ring-current strengths (I, nA T-1) were obtained by integrating the current density that flows through the planes (contours) intersecting the chemical bonds. We used three different contours to cover: 1) the in and out orbitals; 2) only in-plane in orbitals; 3) only the out-of-plane (perpendicular molecular plane) out orbitals. Geometry optimization of the ground state polyyne and transition state cumulene structures of cyclo[18]carbon was also carried out using the ab initio complete active self-consistent space field (CASSCF) method with 8 electrons in 8 orbitals. The CASSCF calculations show that the largest contribution from a closed-shell singlet determinant is 0.95 for both structures, suggesting that the ground state is a closed-shell singlet state. The 6-311++G(d,p) basis set was used for all CASSCF calculation. The CASSCF calculations were performed using the Firefly software.18,19 The density functional theory (DFT) calculations on cyclo[18]carbon on the NaCl surface were carried out using the Perdew–Burke–Ernzerhof (PBE) exchange- correlation functional20 in periodic boundary conditions (PBC) and the projector- augmented wave (PAW) method21 as implemented in the Vienna Ab-initio Simulation Package (VASP).22,23 The van der Waals interactions were treated by the Grimme D3 method.24 The plane-wave cutoff energy was set to 500 eV. To avoid interactions between neighbor images, the vacuum distance in the z direction was set to larger than 15 Å. The reciprocal space of the simulated supercell was sampled by 4 × 4 × 1 k-point grid using the Monkhorst-Pack scheme.25 The convergence criteria for forces acting on the atoms and electronic iterations were 10-3 eV/Å and 10-5 eV, respectively. The hybrid Heyd-Scuseria-Ernzerhof (HSE06) functional26,27 was employed to estimate the percentage of the exact Hartree-Fock exchange needed to obtain single-triple bond alternation. The results are presented in Figure S2. The mobility of cyclo[18]carbon on the NaCl surface was studied by using the nudge elastic band (NEB) method including the climbing image algorithm. To investigate the barrier between the two connected optimized geometries, seven additional images were generated. Figure S2. Bond-length dependence on the percentage of Hartree-Fock exchange contribution. The short and long bonds are represented in blue and red, respectively. References (1) Boese, A. D.; Martin, J. M. L. Development of Density Functionals for Thermochemical Kinetics. J. Chem. Phys. 2004, 121 (8), 3405–3416. (2) Becke, A. D. A New Mixing of Hartree–Fock and Local Density-Functional Theories. J. Chem. Phys. 1993, 98 (2), 1372–1377. (3) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120 (1–3), 215–241. (4) Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom–Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10 (44), 6615. (5) Frisch, M. J.; Pople, J. A.; Binkley, J. S. Self-Consistent Molecular Orbital Methods 25. Supplementary Functions for Gaussian Basis Sets. J. Chem. Phys. 1984, 80 (7), 3265–3269. (6) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. Self-Consistent Molecular Orbital Methods. XX. A Basis Set for Correlated Wave Functions. J. Chem. Phys. 1980, 72 (1), 650–654. (7) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. V. R. Efficient Diffuse Function-Augmented Basis Sets for Anion Calculations. III. The 3- 21+G Basis Set for First-Row Elements, Li-F. J. Comput. Chem. 1983, 4 (3), 294–301. (8) Li, X.; Frisch, M. J. Energy-Represented Direct Inversion in the Iterative Subspace within a Hybrid Geometry Optimization Method. J. Chem. Theory Comput. 2006, 2 (3), 835–839. (9) Peng, C.; Ayala, P. Y.; Schlegel, H. B.; Frisch, M. J. Using Redundant Internal Coordinates to Optimize Equilibrium Geometries and Transition States. J. Comput. Chem. 1996, 17 (1), 49–56. (10) Hehre, W. J.; Ditchfield, R.; Pople, J. A. Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules. J. Chem. Phys. 1972, 56 (5), 2257–2261. (11) Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90 (2), 1007–1023. (12) Hratchian H. P.; Schlegel, H. B. Accurate reaction paths using a Hessian based predictor–corrector integrator. J. Chem. Phys. 2004, 120 (21) 9918– 9924. (13) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H. et al. Gaussian 16, Revision C.01; Gaussian, Inc.: Wallingford CT, 2016. (14) Fliegl, H.; Taubert, S.; Lehtonen, O.; Sundholm, D. The Gauge Including Magnetically Induced Current Method. Phys. Chem. Chem. Phys. 2011, 13 (46), 20500. (15) Jusélius, J.; Sundholm, D.; Gauss, J. Calculation of Current Densities Using Gauge-Including Atomic Orbitals. J. Chem. Phys. 2004, 121 (9), 3952–3963. (16) Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7 (18), 3297. (17) Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H.; Kölmel, C. Electronic Structure Calculations on Workstation Computers: The Program System Turbomole. Chem. Phys. Lett. 1989, 162 (3), 165–169. (18) Granovsky, A. A. Firefly version 8 http://classic.chem.msu.su/gran/firefly/index.html. (19) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; et al. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14 (11), 1347–1363. (20) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865–3868. (21) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59 (3), 1758–1775. (22) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6 (1), 15–50. (23) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47 (1), 558–561. (24) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132 (15), 154104. (25) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev.
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