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Volumn 126, Issue 12, 2004, Pages 3845-3855

Covalent versus Electrostatic Nature of the Strong Hydrogen Bond: Discrimination among Single, Double, and Asymmetric Single-Well Hydrogen Bonds by Variable-Temperature X-ray Crystallographic Methods in β-Diketone Enol RAHB Systems

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL STRUCTURE; DIFFRACTION; RESONANCE; X RAY CRYSTALLOGRAPHY;

EID: 1642416324     PISSN: 00027863     EISSN: None     Source Type: Journal    
DOI: 10.1021/ja030213z     Document Type: Article
Times cited : (253)

References (89)
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    • Bayes's theorem, on which Bayesian statistics is based (Molina, E. C. Two Papers by Bayes with Commentaries; Hafner Publishing Company: New York, 1963) has received increasing attention in the past decade as a tool for data treatment and interpretation which can take advantage of all a priori information available for a better understanding of experimental results (Sivia, D. S. Data Analysis. A Bayesian Tutorial; Oxford University Press: Oxford, 2003; Gilmore, C. J. Acta Crystallogr. 1996, A52, 561). In the present case, it can be written as p(PT-pathway|Data) ∝ p(Data|PT-pathway)· p(PT-pathway) where p = probability of; p(PT-pathway) = prior = what we already know about the distribution function of the possible PT-pathways (described after the Introduction); p(Data|PT-pathway) = likelihood = what we predict to be the experimental results for any given pathway; p(PT-pathway|Data) = posterior = our new knowledge of the distribution function of the possible PT-pathways updated with respect to the prior by means of the new experimental results collected. The posterior is assumed to become an updated prior for future studies. Table of likelihoods, that is the results of the different tests expected for the PT-pathways of the prior, is given in Table S5 of Supporting Information.
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    • Molina, E.C.1
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    • Bayes's theorem, on which Bayesian statistics is based (Molina, E. C. Two Papers by Bayes with Commentaries; Hafner Publishing Company: New York, 1963) has received increasing attention in the past decade as a tool for data treatment and interpretation which can take advantage of all a priori information available for a better understanding of experimental results (Sivia, D. S. Data Analysis. A Bayesian Tutorial; Oxford University Press: Oxford, 2003; Gilmore, C. J. Acta Crystallogr. 1996, A52, 561). In the present case, it can be written as p(PT-pathway|Data) ∝ p(Data|PT-pathway)· p(PT-pathway) where p = probability of; p(PT-pathway) = prior = what we already know about the distribution function of the possible PT-pathways (described after the Introduction); p(Data|PT-pathway) = likelihood = what we predict to be the experimental results for any given pathway; p(PT-pathway|Data) = posterior = our new knowledge of the distribution function of the possible PT-pathways updated with respect to the prior by means of the new experimental results collected. The posterior is assumed to become an updated prior for future studies. Table of likelihoods, that is the results of the different tests expected for the PT-pathways of the prior, is given in Table S5 of Supporting Information.
    • (2003) Data Analysis. A Bayesian Tutorial
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    • Bayes's theorem, on which Bayesian statistics is based (Molina, E. C. Two Papers by Bayes with Commentaries; Hafner Publishing Company: New York, 1963) has received increasing attention in the past decade as a tool for data treatment and interpretation which can take advantage of all a priori information available for a better understanding of experimental results (Sivia, D. S. Data Analysis. A Bayesian Tutorial; Oxford University Press: Oxford, 2003; Gilmore, C. J. Acta Crystallogr. 1996, A52, 561). In the present case, it can be written as p(PT-pathway|Data) ∝ p(Data|PT-pathway)· p(PT-pathway) where p = probability of; p(PT-pathway) = prior = what we already know about the distribution function of the possible PT-pathways (described after the Introduction); p(Data|PT-pathway) = likelihood = what we predict to be the experimental results for any given pathway; p(PT-pathway|Data) = posterior = our new knowledge of the distribution function of the possible PT-pathways updated with respect to the prior by means of the new experimental results collected. The posterior is assumed to become an updated prior for future studies. Table of likelihoods, that is the results of the different tests expected for the PT-pathways of the prior, is given in Table S5 of Supporting Information.
    • (1996) Acta Crystallogr. , vol.A52 , pp. 561
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    • note
    • Q plot of Figure 5a is described in note 21 of ref 2d.
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    • note
    • Q,calc| not greater than 0.06.
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    • note
    • (e) Compound of ref 22a has been classified as SW-NB by the authors and DW-LB by ourselves.
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    • note
    • (a) Reference 9d and references therein.


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