Severity: Warning
Message: file_get_contents(https://...@pubfacts.com&api_key=b8daa3ad693db53b1410957c26c9a51b4908&a=1): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests
Filename: helpers/my_audit_helper.php
Line Number: 176
Backtrace:
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 176
Function: file_get_contents
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 250
Function: simplexml_load_file_from_url
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 1034
Function: getPubMedXML
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3152
Function: GetPubMedArticleOutput_2016
File: /var/www/html/application/controllers/Detail.php
Line: 575
Function: pubMedSearch_Global
File: /var/www/html/application/controllers/Detail.php
Line: 489
Function: pubMedGetRelatedKeyword
File: /var/www/html/index.php
Line: 316
Function: require_once
Instanton theory relates the rate constant for tunneling through a barrier to the periodic classical trajectory on the upturned potential energy surface, whose period is τ = ℏ/(kBT). Unfortunately, the standard theory is only applicable below the "crossover temperature," where the periodic orbit first appears. This paper presents a rigorous semiclassical (ℏ → 0) theory for the rate that is valid at any temperature. The theory is derived by combining Bleistein's method for generating uniform asymptotic expansions with a real-time modification of Richardson's flux-correlation function derivation of instanton theory. The resulting theory smoothly connects the instanton result at low temperature to the parabolic correction to Eyring transition state theory at high-temperature. Although the derivation involves real time, the final theory only involves imaginary-time (thermal) properties, consistent with the standard version of instanton theory. Therefore, it is no more difficult to compute than the standard theory. The theory is illustrated with application to model systems, where it is shown to give excellent numerical results. Finally, the first-principles approach taken here results in a number of advantages over previous attempts to extend the imaginary free-energy formulation of instanton theory. In addition to producing a theory that is a smooth (continuously differentiable) function of temperature, the derivation also naturally incorporates hyperasymptotic (i.e., multi-orbit) terms and provides a framework for further extensions of the theory.
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Source |
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http://dx.doi.org/10.1063/5.0237368 | DOI Listing |
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