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  <doc>
    <id>7065</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>425201</pageFirst>
    <pageLast>425201</pageLast>
    <pageNumber/>
    <edition/>
    <issue>42</issue>
    <volume>30</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Estimation of the infinitesimal generator by square-root approximation</title>
    <abstract language="eng">In recent years, for the analysis of molecular processes, the estimation of time-scales and transition rates has become fundamental. Estimating the transition rates between molecular conformations is—from a mathematical point of view—an invariant subspace projection problem. We present a method to project the infinitesimal generator acting on function space to a low-dimensional rate matrix. This projection can be performed in two steps. First, we discretize the conformational space in a Voronoi tessellation, then the transition rates between adjacent cells is approximated by the geometric average of the Boltzmann weights of the Voronoi cells. This method demonstrates that there is a direct relation between the potential energy surface of molecular structures and the transition rates of conformational changes. We will show also that this approximation is correct and converges to the generator of the Smoluchowski equation in the limit of infinitely small Voronoi cells. We present results for a two dimensional diffusion process and alanine dipeptide as a high-dimensional system.</abstract>
    <parentTitle language="eng">J. Phys.: Condens. Matter</parentTitle>
    <identifier type="doi">10.1088/1361-648X/aadfc8</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2018-09-07</enrichment>
    <author>Luca Donati</author>
    <submitter>Marcus Weber</submitter>
    <author>Martin Heida</author>
    <author>Bettina G. Keller</author>
    <author>Marcus Weber</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="persons" number="donati">Donati, Luca</collection>
  </doc>
  <doc>
    <id>9317</id>
    <completedYear>2024</completedYear>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>e27529</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>46</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-12-10</completedDate>
    <publishedDate>2024-12-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Accuracy of reaction coordinate based rate theories for modelling chemical reactions: insights from the thermal isomerization in retinal</title>
    <abstract language="eng">Modern potential energy surfaces have shifted attention to molecular simulations of chemical reactions. While various methods can estimate rate constants for conformational transitions in molecular dynamics simulations, their applicability to studying chemical reactions remains uncertain due to the high and sharp energy barriers and complex reaction coordinates involved. This study focuses on the thermal cis-trans isomerization in retinal, employing molecular simulations and comparing rate constant estimates based on one-dimensional rate theories with those based on sampling transitions and grid-based models for low-dimensional collective variable spaces. Even though each individual method to estimate the rate passes its quality tests, the rate constant estimates exhibit disparities of up to four orders of magnitude. Rate constant estimates based on one-dimensional reaction coordinates prove challenging to converge, even if the reaction coordinate is optimized. However, consistent estimates of the rate constant are achieved by sampling transitions and by multi-dimensional grid-based models.</abstract>
    <parentTitle language="eng">Journal of Computational Chemistry</parentTitle>
    <identifier type="arxiv">2312.12948</identifier>
    <identifier type="doi">10.1002/jcc.27529</identifier>
    <enrichment key="SubmissionStatus">epub ahead of print</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Simon Ghysbrecht</author>
    <author>Luca Donati</author>
    <author>Bettina G. Keller</author>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-15">MathPlusAA1-15</collection>
    <collection role="persons" number="donati">Donati, Luca</collection>
  </doc>
</export-example>
