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Volumn 5, Issue 2, 2009, Pages 307-323

Evaluation of electronic coupling in transition-metal systems using DFT: Application to the hexa-aquo ferric-ferrous redox couple

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EID: 65249089673     PISSN: 15499618     EISSN: None     Source Type: Journal    
DOI: 10.1021/ct800340v     Document Type: Article
Times cited : (43)

References (93)
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    • Landau, L. D. Phys. Z. Sowjetunion 1932, 1, 88-98. ibid. 1932, 2, 46-51.
    • Landau, L. D. Phys. Z. Sowjetunion 1932, 1, 88-98. ibid. 1932, 2, 46-51.
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    • Zener, C. Proc. R. Soc. London A 1932, 137, 696-702. ibid. 1933, 140, 660-668.
    • Zener, C. Proc. R. Soc. London A 1932, 137, 696-702. ibid. 1933, 140, 660-668.
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    • Indeed, the poor convergence is a common feature for selfconsistent field calculations on open-shell transition-metal systems both within the unrestricted or open-shell restricted Hartree-Fock (HF) and the unrestricted DFT approaches, see: Neese, F. Chem. Phys. Lett. 2000, 325, 93-98.
    • Indeed, the poor convergence is a common feature for selfconsistent field calculations on open-shell transition-metal systems both within the unrestricted or open-shell restricted Hartree-Fock (HF) and the unrestricted DFT approaches, see: Neese, F. Chem. Phys. Lett. 2000, 325, 93-98.
  • 39
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    • For bRevity, the spin dependence is not explicitly shown; however, the index i can be defined in such a way to distinguish the spin state.
    • For bRevity, the spin dependence is not explicitly shown; however, the index i can be defined in such a way to distinguish the spin state.
  • 47
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    • the above article the HOMO-LUMO gap is derived from the nominal (fractionally occupied) HOMO and LUMO, DOI: 10.1039/b705105k. In
    • Barcaro, G.; Fortunelli, A. Faraday Discuss. 2008, DOI: 10.1039/b705105k. In the above article the HOMO-LUMO gap is derived from the nominal (fractionally occupied) HOMO and LUMO.
    • (2008) Faraday Discuss
    • Barcaro, G.1    Fortunelli, A.2
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    • The validity of this consideration when s approaches zero is clearly not affected by the fact that the HOMO can result from a wrong linear combination of d-like orbitals.
    • The validity of this consideration when s approaches zero is clearly not affected by the fact that the HOMO can result from a wrong linear combination of d-like orbitals.
  • 53
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    • According to the second-order energy correction in the stationary perturbation theory the mixing between two levels is determined not only by the difference between their unperturbed energies, but also by the matrix element of the perturbation Hamiltonian term between the corresponding orbital states. The latter depends also on the orbital localization. On the other hand, the KS level structure and the shapes of the orbitals reflect the approximate degeneracy of the two metal sites. Therefore, each level in the multiplet can mix in a similar way with couples of very close levels ek corresponding to symmetrically arranged orbitals
    • According to the second-order energy correction in the stationary perturbation theory the mixing between two levels is determined not only by the difference between their unperturbed energies, but also by the matrix element of the perturbation Hamiltonian term between the corresponding orbital states. The latter depends also on the orbital localization. On the other hand, the KS level structure and the shapes of the orbitals reflect the approximate degeneracy of the two metal sites. Therefore, each level in the multiplet can mix in a similar way with couples of very close levels ek corresponding to symmetrically arranged orbitals.
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    • Ferretti, A.; Ruini, A.; Bussi, G.; Molinari, E.; Caldas, M. J. Phys. Rev. B 2004, 69, 205205. (b) Ferretti, A. DTI program, 2005; available from http://www.s3.infm.it/dti on request. Contact information: ferretti.andrea@unimore.it.
    • (a) Ferretti, A.; Ruini, A.; Bussi, G.; Molinari, E.; Caldas, M. J. Phys. Rev. B 2004, 69, 205205. (b) Ferretti, A. DTI program, 2005; available from http://www.s3.infm.it/dti on request. Contact information: ferretti.andrea@unimore.it.
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    • The pathway products are computed by using Kurnikov's HARLEM program, which is available from http://www. kurnikov.org/.
    • The pathway products are computed by using Kurnikov's HARLEM program, which is available from http://www. kurnikov.org/.
  • 75
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    • The correlation between ab initio transfer integrals and pathway products can be measured by the correlation coefficients, which are rT,V, 0.51 and rT,VU, 0.69. The probabilities of finding at least equal values of those coefficients, if the corresponding data sets are uncorrelated, are P9(r≥rT,V 16% and P 9(r≥rT,V, 4, respectively. These values can be compared with the commonly accepted threshold of 5% for delimiting significant correlations. The two probabilities get closer to each other by excluding the two nuclear configurations not including the hydrogen bond in the best ET pathway. In fact, in this event we obtain rT,V, 0.73 and rT,VU, 0.76, from whichP7(r ≥rT,V, 6% and P7(r≥r T,VU), 5, respectively
    • T,VU) ) 5%, respectively.
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    • The two estimates differ by about 1.4 standard deviations. The one-tail probability of obtaining a discrepancy which is at least 1.4 standard deviations is 8%. In other words, by assuming that our average value complies with a normal distribution centered on the expected (i.e., experimental) transfer integral, the probability that our single valuation of the rms electronic coupling gives a result at least as large as 11.0 × 10-3 eV is 8%. Therefore, according to the usual 5% criterion the discrepancy between the two values is not significant.
    • The two estimates differ by about 1.4 standard deviations. The one-tail probability of obtaining a discrepancy which is at least 1.4 standard deviations is 8%. In other words, by assuming that our average value complies with a normal distribution centered on the expected (i.e., experimental) transfer integral, the probability that our single valuation of the rms electronic coupling gives a result at least as large as 11.0 × 10-3 eV is 8%. Therefore, according to the usual 5% criterion the discrepancy between the two values is not significant.
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    • In ref 3 the Condon approximation is tested on the apex-toapex conformation by translating the reactants along the metal-metal direction
    • In ref 3 the Condon approximation is tested on the apex-toapex conformation by translating the reactants along the metal-metal direction.
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    • The argument can be suitably extended to the generic orbital. However, the analysis provided in the main text is appropriate for evaluation of the transfer integral
    • The argument can be suitably extended to the generic orbital. However, the analysis provided in the main text is appropriate for evaluation of the transfer integral.
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    • The symbol s is here adopted, in place of the commonly used σ, to avoid confusion with the notation for the Gaussian broadening parameter.
    • The symbol s is here adopted, in place of the commonly used σ, to avoid confusion with the notation for the Gaussian broadening parameter.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.