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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.
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The pathway products are computed by using Kurnikov's HARLEM program, which is available from http://www. kurnikov.org/.
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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
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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.
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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.
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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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-
91
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-
0001437693
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Anisimov, V. I.; Zaanen, J.; Andersen, O. K. Phys. Rev. B 1991, 44, 943-954.
-
(1991)
Phys. Rev. B
, vol.44
, pp. 943-954
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-
Anisimov, V.I.1
Zaanen, J.2
Andersen, O.K.3
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92
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-
0001075886
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Anisimov, V. I.; Solovyev, I. V.; Korotin, M. A.; Czyz.yk, M. T.; Sawatzky, G. A. Phys. Rev. B 1993, 48, 16929-16934.
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Anisimov, V. I.; Solovyev, I. V.; Korotin, M. A.; Czyz.yk, M. T.; Sawatzky, G. A. Phys. Rev. B 1993, 48, 16929-16934.
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-
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-
93
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-
84868936437
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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.
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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.
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