Abstract:Using the LCAO-MO wavefunctions estimated by an extended Wolfsberg-Helmholz method, the first order static Jahn-Teller effect in CuF6 -4 has been calculated. The bond length difference between the long and the short bonds is found to be some 0.2 3,, in reasonable agreement with experiment.
“…It was estimated that The derivative is thus equal to 5.4 (kcal/mol) Å -1 , which is suggested to be the vibronic perturbation which promotes the spin transition in the system. This vibronic matrix element is higher than the corresponding vibronic matrix elements that are responsible for the Jahn−Teller (and pseudo-Jahn−Teller) effects in a number of Cu-containing complexes (including tunneling, vibronic reduction of spin−orbit coupling splitting, g -tensor in ESR spectra, and IR and electronic spectra). , Similar vibronic matrix elements have also been obtained for CuF 6 4- , Cu(H 2 O) 6 2+ , and CuCl 4 complexes. − The estimated rate constant for the spin−flip step itself is therefore quite large, k 2 = 8 × 10 10 s -1 (see the Appendix). 11 Crossing point between the quartet and doublet potential surfaces.…”
Section: Resultsmentioning
confidence: 53%
“…53,54 Similar vibronic matrix elements have also been obtained for CuF 6 4-, Cu(H 2 O) 6 2+ , and CuCl 4 complexes. [55][56][57][58] The estimated rate constant for the spin-flip step itself is therefore quite large, k 2 ) 8 × 10 10 s -1 (see the Appendix). |∂〈Ψ 1d |V S |Ψ 2d 〉/∂Q p | 2 ) 29.16 (kcal/mol) 2 Å -2…”
Section: Resultsmentioning
confidence: 99%
“…53,54 Similar vibronic matrix elements have also been obtained for CuF 6 4-, Cu(H 2 O) 6 2+ , and CuCl 4 complexes. [55][56][57][58] The estimated rate constant for the spin-flip step itself is therefore quite large, k 2 ) 8 × 10 10 s -1 (see the Appendix). The dipole transition integral in the harmonic approximation is equal to where m p is the reduced mass of the Q p vibration.…”
Dioxygen reduction in the oxidative half-reaction of copper amine oxidases (CAOs) has been studied quantum chemically using the hybrid density functional theory (B3LYP). The reductive activation of dioxygen is a spin-forbidden process for which substantial kinetic O-18 (but no deuterium) isotope effects have been found experimentally. The proposed mechanism was divided into three steps, and the last step was studied for two different potential energy surfaces: the quartet and the doublet surfaces. It is suggested that dioxygen reduction occurs through a spin transition that is induced by the exchange interaction between the unpaired spins of the Cu(II) ion and the O 2 -anion. The step involving this spin transition is suggested to be rate-limiting, which gives a rationalization for the puzzling experimental results when copper is substituted for other metals. The spin transition is triggered by the calculated vibronic perturbation of 5.4 (kcal/mol) Å -1 , which leads to a very fast rate of 8 × 10 10 s -1 for the spin transition. However, since the spin transition occurs at a calculated energy that is 18-20 kcal/mol higher than that of the reactant, this step could still be rate-limiting. The difference in the O-O bond distance between the resting state (free dioxygen) and the point of the spin transition provides an explanation for the oxygen isotope effect.
“…It was estimated that The derivative is thus equal to 5.4 (kcal/mol) Å -1 , which is suggested to be the vibronic perturbation which promotes the spin transition in the system. This vibronic matrix element is higher than the corresponding vibronic matrix elements that are responsible for the Jahn−Teller (and pseudo-Jahn−Teller) effects in a number of Cu-containing complexes (including tunneling, vibronic reduction of spin−orbit coupling splitting, g -tensor in ESR spectra, and IR and electronic spectra). , Similar vibronic matrix elements have also been obtained for CuF 6 4- , Cu(H 2 O) 6 2+ , and CuCl 4 complexes. − The estimated rate constant for the spin−flip step itself is therefore quite large, k 2 = 8 × 10 10 s -1 (see the Appendix). 11 Crossing point between the quartet and doublet potential surfaces.…”
Section: Resultsmentioning
confidence: 53%
“…53,54 Similar vibronic matrix elements have also been obtained for CuF 6 4-, Cu(H 2 O) 6 2+ , and CuCl 4 complexes. [55][56][57][58] The estimated rate constant for the spin-flip step itself is therefore quite large, k 2 ) 8 × 10 10 s -1 (see the Appendix). |∂〈Ψ 1d |V S |Ψ 2d 〉/∂Q p | 2 ) 29.16 (kcal/mol) 2 Å -2…”
Section: Resultsmentioning
confidence: 99%
“…53,54 Similar vibronic matrix elements have also been obtained for CuF 6 4-, Cu(H 2 O) 6 2+ , and CuCl 4 complexes. [55][56][57][58] The estimated rate constant for the spin-flip step itself is therefore quite large, k 2 ) 8 × 10 10 s -1 (see the Appendix). The dipole transition integral in the harmonic approximation is equal to where m p is the reduced mass of the Q p vibration.…”
Dioxygen reduction in the oxidative half-reaction of copper amine oxidases (CAOs) has been studied quantum chemically using the hybrid density functional theory (B3LYP). The reductive activation of dioxygen is a spin-forbidden process for which substantial kinetic O-18 (but no deuterium) isotope effects have been found experimentally. The proposed mechanism was divided into three steps, and the last step was studied for two different potential energy surfaces: the quartet and the doublet surfaces. It is suggested that dioxygen reduction occurs through a spin transition that is induced by the exchange interaction between the unpaired spins of the Cu(II) ion and the O 2 -anion. The step involving this spin transition is suggested to be rate-limiting, which gives a rationalization for the puzzling experimental results when copper is substituted for other metals. The spin transition is triggered by the calculated vibronic perturbation of 5.4 (kcal/mol) Å -1 , which leads to a very fast rate of 8 × 10 10 s -1 for the spin transition. However, since the spin transition occurs at a calculated energy that is 18-20 kcal/mol higher than that of the reactant, this step could still be rate-limiting. The difference in the O-O bond distance between the resting state (free dioxygen) and the point of the spin transition provides an explanation for the oxygen isotope effect.
“…Further calculations by Ballhausen and Johansen using linear combination of atomic orbitals methods were also deemed not accurate enough to calculate the second-order vibronic coupling. 24 A later paper by Pryce et al discusses both higher-order elastic and vibronic terms. 25 First, they point out that the third-order elastic term would support a positive Q 3 distortion in any reasonable potential model, due to the fact that the two M -O bonds are contracted twice as much as the other four.…”
Section: A the Isolated Jahn-teller Centermentioning
Fundamental aspects of the cooperative Jahn-Teller effect are investigated using density functional theory in the generalized gradient approximation. LiNiO 2 , LiMnO 2 , and LiCuO 2 are chosen as candidate materials as they possess small, intermediate, and large cooperative Jahn-Teller distortions, respectively. The cooperative distortion is decomposed into the symmetrized-strain modes and kϭ0 optical phonons, revealing that only the E g and A 1g strain modes and E g and A 1g kϭ0 optical-phonon modes participate in the cooperative distortion. The first-principles results are then used to find values for the cooperative Jahn-Teller stabilization energy and the electron-strain and electron-phonon coupling. It is found that the dominant source of anisotropy arises from the third-order elastic contributions, rather than second-order vibronic contributions. Additionally, the importance of higher-order elastic coupling between the E g and A 1g modes is identified, which effectively causes expansion of A 1g-type modes and allows for a larger E g distortion. Finally, the strain anisotropy induced by the antiferromagnetically ordered states is shown to cause a significant difference in the cooperative Jahn-Teller stabilization energy for the different orientations of the cooperative distortion.
“…Theoretical arguments alone, however, afford no further information about the nature of the distortions; for example, they do not explain why the tetragonally distorted elongated octahedron is so much more common than the compressed tetragonal or rhombically distorted arrangements (Lohr & Lipscomb, 1963;Ballhausen & Johansen, 1965;Clack & Farrimond, 1971; and references therein). Presumably, the exact nature and direction of distortion is dictated by the identity and environment of the ligands to which the Cu ion is coordinated.…”
from diffractometer intensity measurements. The overall packing arrangements in the three structures are broadly similar, but whilst the Cu n ions in the arylsulphonates are in elongated, near tetragonally distorted, octahedral environments, that in the o-camphor-10-sulphonate is better described as a rhombically distorted octahedron. Details of these, and related structures, may be rationalized in terms of Jahn-Teller distortions and hydrogen bonding.
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