Full quantum determination of the quasiequilibrium constant involved in the formation of ozone

Forty years ago, measurements of enrichments in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mmultiscripts><a:mi mathvariant="normal">O</a:mi><a:mprescripts/><a:none/><a:mn>18</a:mn></a:mmultiscripts></a:math> in stratospheric ozone <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mtext>O</c:mtext><c:mn>3</c:mn></c:msub></c:math> revealed a value significantly greater than statistically expected and roughly equal in heavy isotopes <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mmultiscripts><d:mi mathvariant="normal">O</d:mi><d:mprescripts/><d:none/><d:mn>17</d:mn></d:mmultiscripts></d:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mmultiscripts><f:mi mathvariant="normal">O</f:mi><f:mprescripts/><f:none/><f:mn>18</f:mn></f:mmultiscripts></f:math>. Despite numerous experimental and theoretical studies, this mass-independent fractionation (MIF) still remains unexplained. However, it is now accepted that its origin comes from isotopic effects found in the recombination reaction <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi mathvariant="normal">O</h:mi><h:mo>+</h:mo><h:msub><h:mtext>O</h:mtext><h:mn>2</h:mn></h:msub><h:mo>+</h:mo><h:mi>M</h:mi><h:mo>→</h:mo><h:msub><h:mtext>O</h:mtext><h:mn>3</h:mn></h:msub></h:mrow><h:mo> </h:mo><h:mo>+</h:mo><h:mo> </h:mo><h:mi>M</h:mi></h:math> where <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mi>M</j:mi></j:math> is a stabilizer, even if the theoretical origin of the isotope effects found in this reaction is still not known. Here we study the first of the two steps involved in this reaction, namely, the rapid quasiequilibrium <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi mathvariant="normal">O</k:mi><k:mo>+</k:mo><k:msub><k:mi mathvariant="normal">O</k:mi><k:mn>2</k:mn></k:msub></k:mrow><k:mo> </k:mo><k:mo>⇌</k:mo><k:mo> </k:mo><k:msubsup><k:mi mathvariant="normal">O</k:mi><k:mn>3</k:mn><k:mo>*</k:mo></k:msubsup></k:math> process where <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:msubsup><o:mi mathvariant="normal">O</o:mi><o:mn>3</o:mn><o:mo>*</o:mo></o:msubsup></o:math> is metastable ozone. The quasiequilibrium constant for this process is obtained from a full quantum dynamical approach. These high-level calculations yield the most accurate value of this quantity to date for <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:mmultiscripts><q:mi mathvariant="normal">O</q:mi><q:mn>3</q:mn><q:none/><q:mprescripts/><q:none/><q:mn>48</q:mn></q:mmultiscripts></q:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"><s:mmultiscripts><s:mi mathvariant="normal">O</s:mi><s:mn>3</s:mn><s:none/><s:mprescripts/><s:none/><s:mn>50</s:mn></s:mmultiscripts></s:math>. These reference results constitute a crucial stage for a better understanding of the ozone formation reaction, and could therefore help to unravel the mystery of MIF. Published by the American Physical Society 2024