From free-energy profiles to activation free energies
<jats:p> Given a chemical reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) discriminating between R and P, we define the free-energy profile (FEP) as the logarithm of the marginal Boltzmann distribution of the CV. This FEP i...
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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AIP Publishing
2022
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| Online Access: | https://hdl.handle.net/1721.1/145517 |
| _version_ | 1826205416637333504 |
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| author | Dietschreit, Johannes CB Diestler, Dennis J Hulm, Andreas Ochsenfeld, Christian Gómez-Bombarelli, Rafael |
| author2 | Massachusetts Institute of Technology. Department of Materials Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Materials Science and Engineering Dietschreit, Johannes CB Diestler, Dennis J Hulm, Andreas Ochsenfeld, Christian Gómez-Bombarelli, Rafael |
| author_sort | Dietschreit, Johannes CB |
| collection | MIT |
| description | <jats:p> Given a chemical reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) discriminating between R and P, we define the free-energy profile (FEP) as the logarithm of the marginal Boltzmann distribution of the CV. This FEP is not a true free energy. Nevertheless, it is common to treat the FEP as the “free-energy” analog of the minimum potential energy path and to take the activation free energy, [Formula: see text], as the difference between the maximum at the transition state and the minimum at R. We show that this approximation can result in large errors. The FEP depends on the CV and is, therefore, not unique. For the same reaction, different discriminating CVs can yield different [Formula: see text]. We derive an exact expression for the activation free energy that avoids this ambiguity. We find [Formula: see text] to be a combination of the probability of the system being in the reactant state, the probability density on the dividing surface, and the thermal de Broglie wavelength associated with the transition. We apply our formalism to simple analytic models and realistic chemical systems and show that the FEP-based approximation applies only at low temperatures for CVs with a small effective mass. Most chemical reactions occur on complex, high-dimensional PES that cannot be treated analytically and pose the added challenge of choosing a good CV. We study the influence of that choice and find that, while the reaction free energy is largely unaffected, [Formula: see text] is quite sensitive. </jats:p> |
| first_indexed | 2024-09-23T13:12:48Z |
| format | Article |
| id | mit-1721.1/145517 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:12:48Z |
| publishDate | 2022 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1455172022-10-01T13:46:44Z From free-energy profiles to activation free energies Dietschreit, Johannes CB Diestler, Dennis J Hulm, Andreas Ochsenfeld, Christian Gómez-Bombarelli, Rafael Massachusetts Institute of Technology. Department of Materials Science and Engineering <jats:p> Given a chemical reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) discriminating between R and P, we define the free-energy profile (FEP) as the logarithm of the marginal Boltzmann distribution of the CV. This FEP is not a true free energy. Nevertheless, it is common to treat the FEP as the “free-energy” analog of the minimum potential energy path and to take the activation free energy, [Formula: see text], as the difference between the maximum at the transition state and the minimum at R. We show that this approximation can result in large errors. The FEP depends on the CV and is, therefore, not unique. For the same reaction, different discriminating CVs can yield different [Formula: see text]. We derive an exact expression for the activation free energy that avoids this ambiguity. We find [Formula: see text] to be a combination of the probability of the system being in the reactant state, the probability density on the dividing surface, and the thermal de Broglie wavelength associated with the transition. We apply our formalism to simple analytic models and realistic chemical systems and show that the FEP-based approximation applies only at low temperatures for CVs with a small effective mass. Most chemical reactions occur on complex, high-dimensional PES that cannot be treated analytically and pose the added challenge of choosing a good CV. We study the influence of that choice and find that, while the reaction free energy is largely unaffected, [Formula: see text] is quite sensitive. </jats:p> 2022-09-20T14:29:28Z 2022-09-20T14:29:28Z 2022-08-28 2022-09-20T14:23:22Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/145517 Dietschreit, Johannes CB, Diestler, Dennis J, Hulm, Andreas, Ochsenfeld, Christian and Gómez-Bombarelli, Rafael. 2022. "From free-energy profiles to activation free energies." The Journal of Chemical Physics, 157 (8). en 10.1063/5.0102075 The Journal of Chemical Physics Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf AIP Publishing American Institute of Physics (AIP) |
| spellingShingle | Dietschreit, Johannes CB Diestler, Dennis J Hulm, Andreas Ochsenfeld, Christian Gómez-Bombarelli, Rafael From free-energy profiles to activation free energies |
| title | From free-energy profiles to activation free energies |
| title_full | From free-energy profiles to activation free energies |
| title_fullStr | From free-energy profiles to activation free energies |
| title_full_unstemmed | From free-energy profiles to activation free energies |
| title_short | From free-energy profiles to activation free energies |
| title_sort | from free energy profiles to activation free energies |
| url | https://hdl.handle.net/1721.1/145517 |
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