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Unfortunately, the standard theory is only applicable below the \u201ccrossover temperature,\u201d where the periodic orbit first appears. This paper presents a rigorous semiclassical (\u210f \u2192 0) theory for the rate that is valid at any temperature. The theory is derived by combining Bleistein\u2019s method for generating uniform asymptotic expansions with a real-time modification of Richardson\u2019s 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.<\/jats:p>","DOI":"10.1063\/5.0237368","type":"journal-article","created":{"date-parts":[[2024,11,13]],"date-time":"2024-11-13T06:28:54Z","timestamp":1731479334000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":15,"title":["Semiclassical instanton theory for reaction rates at any temperature: How a rigorous real-time derivation solves the crossover temperature problem"],"prefix":"10.1063","volume":"161","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6546-2925","authenticated-orcid":false,"given":"Joseph E.","family":"Lawrence","sequence":"first","affiliation":[{"name":"Simons Center for Computational Physical Chemistry, New York University , New York, New York 10003, and , New York, New York 10003,","place":["USA USA"]},{"name":"Department of Chemistry, New York University , New York, New York 10003, and , New York, New York 10003,","place":["USA USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2024,11,13]]},"reference":[{"key":"2024111310574980400_c1","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1063\/1.1749604","article-title":"The activated complex in chemical reactions","volume":"3","year":"1935","journal-title":"J.\u00a0Chem. 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