<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">dan</journal-id><journal-title-group><journal-title xml:lang="ru">Доклады Национальной академии наук Беларуси</journal-title><trans-title-group xml:lang="en"><trans-title>Doklady of the National Academy of Sciences of Belarus</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1561-8323</issn><issn pub-type="epub">2524-2431</issn><publisher><publisher-name>The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.29235/1561-8323-2024-68-1-36-45</article-id><article-id custom-type="elpub" pub-id-type="custom">dan-1173</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ХИМИЯ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>CHEMISTRY</subject></subj-group></article-categories><title-group><article-title>Квантовохимические расчеты термодинамических характеристик некоторых гетерогенных каталитических процессов c использованием многослойных кластерных моделей</article-title><trans-title-group xml:lang="en"><trans-title>Quantum-chemical calculations of thermodynamic characteristics of some heterogeneous catalytic processes with the use of multilayer cluster models</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8344-8438</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Рагойжа</surname><given-names>Е. Г.</given-names></name><name name-style="western" xml:lang="en"><surname>Ragoyja</surname><given-names>E. G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Рагойжа Екатерина Георгиевна – старший преподаватель.</p><p>Ул. Ленинградская, 14, 220006, Минск</p></bio><bio xml:lang="en"><p>Ragoyja Ekaterina G. – Senior Lecturer.</p><p>14, Leningradskaya Str., 220006, Minsk</p></bio><email xlink:type="simple">kateragoyja@yandex.by</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9714-9087</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Матулис</surname><given-names>В. Э.</given-names></name><name name-style="western" xml:lang="en"><surname>Matulis</surname><given-names>V. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Матулис Виталий Эдвардович – канд. хим. наук, доцент.</p><p>Ул. Ленинградская, 14, 220006, Минск</p></bio><bio xml:lang="en"><p>Matulis Vitaly E. – Ph. D. (Chemistry), Associate Professor.</p><p>14, Leningradskaya Str., 220006, Minsk</p></bio><email xlink:type="simple">vitaly_matulis@lyceum.by</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5006-2715</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ивашкевич</surname><given-names>О. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Ivashkevich</surname><given-names>O. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ивашкевич Олег Анатольевич – академик, д-р хим. наук, гл. науч. сотрудник.</p><p>Ул. Ленинградская, 14, 220006, Минск</p></bio><bio xml:lang="en"><p>Ivashkevich Oleg A. – Academician, D. Sc. (Chemistry), Chief Researcher.</p><p>14, Leningradskaya Str., 220006, Minsk</p></bio><email xlink:type="simple">ivashkevicho@bsu.by</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8034-9568</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ляхов</surname><given-names>Д. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Lyakhov</surname><given-names>D. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ляхов Дмитрий Александрович – науч. сотрудник.</p><p>23955, Тувал</p></bio><bio xml:lang="en"><p>Lyakhov Dmitry A. – Researcher.</p><p>23955, Thuwal</p></bio><email xlink:type="simple">dmitry.lyakhov@kaust.edu.sa</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Михельс</surname><given-names>Д.</given-names></name><name name-style="western" xml:lang="en"><surname>Michels</surname><given-names>D.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Михельс Доминик – научный сотрудник.</p><p>23955, Тувал</p></bio><bio xml:lang="en"><p>Michels Dominik – Researcher.</p><p>23955, Thuwal</p></bio><email xlink:type="simple">dominik.michels@kaust.edu.sa</email><xref ref-type="aff" rid="aff-3"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Белорусский государственный университет</institution></aff><aff xml:lang="en"><institution>Belarusian State University</institution></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Научно-исследовательский институт физико-химических проблем Белорусского государственного университета</institution></aff><aff xml:lang="en"><institution>Research Institute for Physical Chemical Problems of the Belarusian State University</institution></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Научно-технологический университет имени короля Абдаллы</institution></aff><aff xml:lang="en"><institution>King Abdullah University of Science and Technology</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>04</day><month>03</month><year>2024</year></pub-date><volume>68</volume><issue>1</issue><fpage>36</fpage><lpage>45</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Рагойжа Е.Г., Матулис В.Э., Ивашкевич О.А., Ляхов Д.А., Михельс Д., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Рагойжа Е.Г., Матулис В.Э., Ивашкевич О.А., Ляхов Д.А., Михельс Д.</copyright-holder><copyright-holder xml:lang="en">Ragoyja E.G., Matulis V.E., Ivashkevich O.A., Lyakhov D.A., Michels D.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://doklady.belnauka.by/jour/article/view/1173">https://doklady.belnauka.by/jour/article/view/1173</self-uri><abstract><p>Исследованы подходы к оценке изменения энтальпии, энтропии и энергии Гиббса в ходе процессов адсорбции и гетерогенных каталитических реакций на основании данных квантовохимических расчетов. На основании сравнения с экспериментальными данными по адсорбции CO на поверхности анатаза (TiO2) показана применимость разработанной многослойной кластерной модели для расчета энергии (энтальпии) адсорбции. Проанализированы данные по способам расчета изменения энтропии при гетерогенных процессах, показана применимость теорий идеального двумерного газа и идеального двумерного решетчатого газа для оценки конфигурационного вклада в энтропию гетерогенного процесса. Рассчитаны плотность центров адсорбции на поверхности (101) анатаза, а также заселенность, соответствующая стандартному состоянию идеального двумерного газа. Показана согласованность изученных моделей при небольших заселенностях, а также установлены границы их применимости.</p></abstract><trans-abstract xml:lang="en"><p>The approaches to estimating the changes in enthalpy, entropy, and Gibbs energy of adsorption processes and heterogeneous catalytic reactions on the basis of the quantum chemical calculation data were studied. By comparing with the experimental data on CO adsorption on the anatase (TiO2) surface, the applicability of the developed multilayer cluster model for calculation of the adsorption energy (enthalpy) was shown. The data on the calculation methods of the entropy change in heterogeneous processes were analyzed. The use of the theories of an ideal two-dimensional gas and an ideal two-dimensional lattice gas for estimating a configuration contribution to the entropy of a heterogeneous process was studied. The density of adsorption centers on the (101) anatase surface and the population corresponding to the standard state of an ideal two-dimensional gas were calculated. The consistency of the studied models at low populations was shown, and the limits of their applicability were established.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>гетерогенные каталитические процессы</kwd><kwd>DFT</kwd><kwd>кластерные модели</kwd><kwd>расчет термодинамических функций</kwd><kwd>адсорбция</kwd><kwd>конфигурационная энтропия</kwd></kwd-group><kwd-group xml:lang="en"><kwd>heterogeneous catalytic processes</kwd><kwd>DFT</kwd><kwd>cluster models</kwd><kwd>thermodynamic functions calculations</kwd><kwd>adsorption</kwd><kwd>configuration entropy</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена при финансовой поддержке БРФФИ в рамках совместного белорусскокитайского проекта (грант № Х22КИ-026)</funding-statement><funding-statement xml:lang="en">The work was carried out with financial support from the BRFFR within the framework of a joint Belarusian-Chinese project (grant no. X22КИ-026)</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">DFT Study of NO Reduction Process on Ag/γ-Al2O3 Catalyst: Some Aspects of Mechanism and Catalyst Structure / V. E. Matulis [et al.] // J. Phys. Chem. C. – 2021. – Vol. 125, N 1. – P. 419–426. https://doi.org/10.1021/acs.jpcc.0c08417</mixed-citation><mixed-citation xml:lang="en">Matulis V. E., Ragoyja E. G., Ivashkevich O. A., Lyakhov D. A., Michels D. DFT Study of NO Reduction Process on Ag/ γ-Al2O3 Catalyst: Some Aspects of Mechanism and Catalyst Structure. Journal of Physical Chemistry C, 2021, vol. 125, no. 1, pp. 419–426. https://doi.org/10.1021/acs.jpcc.0c08417</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Рагойжа, Е. Г. Разработка подхода к квантовохимическим исследованиям катализаторов восстановления оксидов азота на основе диоксида титана и гетерополикислот / Е. Г. Рагойжа, В. Э. Матулис, О. А. Ивашкевич // Свиридовские чтения: сб. ст. / редкол.: О. А. Ивашкевич (пред.) [и др.]. – Минск, 2022. – Вып. 18. – С. 54–66.</mixed-citation><mixed-citation xml:lang="en">Ragoyja E. G., Matulis V. E., Ivashkevich O. A. Development of the approach to quantum chemical study of nitrogen oxides reduction catalysts based on titanium dioxide and heteropolyacids. Sviridov Readings. Minsk, 2022, vol. 18, pp. 54−66 (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Correlating DFT-Calculated Energy Barriers to Experiments in Nonheme Octahedral FeIVO Species / K. B. Cho [et al.] // Chem. Eur. J. – 2012. – Vol. 18, N 33. – P. 10444–10453. https://doi.org/10.1002/chem.201200096</mixed-citation><mixed-citation xml:lang="en">Cho K. B., Kim E. J., Seo M. S., Shaik S., Nam W. Correlating DFT-Calculated Energy Barriers to Experiments in Nonheme Octahedral FeIVO Species. Chemistry – A European Journal, 2012, vol. 18, no. 33, pp. 10444–10453. https://doi.org/10.1002/chem.201200096</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Synergistic Effects of Keggin-Type Phosphotungstic Acid-Supported Single-Atom Catalysts in a Fast NH3-SCR Reaction / C. H. Lin [et al.] // Inorg. Chem. – 2022. – Vol. 61, N 48. – P. 19156–19171. https://doi.org/10.1021/acs.inorgchem.2c02759</mixed-citation><mixed-citation xml:lang="en">Lin C. H., Qin R. C., Cao N., Wang D., Liu C.-G. Synergistic Effects of Keggin-Type Phosphotungstic Acid-Supported Single-Atom Catalysts in a Fast NH3–SCR Reaction. Inorganic Chemistry, 2022, vol. 61, no. 48, pp. 19156–19171. https://doi.org/10.1021/acs.inorgchem.2c02759</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Piccini, G. Ab Initio Calculation of Rate Constants for Molecule-Surface Reactions with Chemical Accuracy / G. Piccini, M. Alessio, J. Sauer // Angew. Chem. Int. Ed. – 2016. – Vol. 55, N 17. – P. 5235–5237. https://doi.org/10.1002/anie.201601534</mixed-citation><mixed-citation xml:lang="en">Piccini G., Alessio M., Sauer J. Ab initio Calculation of Rate Constants for Molecule-Surface Reactions with Chemical Accuracy. Angewandte Chemie International Edition, 2016, vol. 55, no. 17, pp. 5235–5237. https://doi.org/10.1002/anie.201601534</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Anharmonic Correction to Adsorption Free Energy from DFT-Based MD Using Thermodynamic Integration / J. Amsler [et al.] // J. Chem. Theory Comput. – 2021. – Vol. 17, N 2. – P. 1155–1169. https://doi.org/10.1021/acs.jctc.0c01022</mixed-citation><mixed-citation xml:lang="en">Amsler J., Plessow P. N., Studt F., Bučko T. Anharmonic Correction to Adsorption Free Energy from DFT-Based MD Using Thermodynamic Integration. Journal of Chemical Theory and Computation, 2021, vol. 17, no. 2, pp. 1155–1169. https://doi.org/10.1021/acs.jctc.0c01022</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">De Wispelaere, K. Toward Computing Accurate Free Energies in Heterogeneous Catalysis: a Case Study for Adsorbed Isobutene in H-ZSM-5 / K. De Wispelaere, P. N. Plessow, F. Studt // ACS Phys. Chem. Au. – 2022. – Vol. 2, N 5. – P. 399–406. https://doi.org/10.1021/acsphyschemau.2c00020</mixed-citation><mixed-citation xml:lang="en">De Wispelaere K., Plessow P. N., Studt F. Toward Computing Accurate Free Energies in Heterogeneous Catalysis: a Case Study for Adsorbed Isobutene in H-ZSM-5. ACS Physical Chemistry Au, 2022, vol. 2, no. 5, pp. 399–406. https://doi.org/10.1021/acsphyschemau.2c00020</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Gaussian 16, Revision E.01 / M. J. Frisch [et al.]. – Gaussian, Inc., Wallingford CT, 2016.</mixed-citation><mixed-citation xml:lang="en">Frisch M. J., Trucks G. W., Schlegel H. B. [et al.]. Gaussian 16, Revision E.01. Gaussian, Inc., Wallingford CT, 2016.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Simon, S. How does basis set superposition error change the potential surfaces for hydrogen bonded dimers? / S. Simon, M. Duran, J. J. Dannenberg // J. Chem. Phys. – 1996. – Vol. 105, N 24. – P. 11024–11031. https://doi.org/10.1063/1.472902</mixed-citation><mixed-citation xml:lang="en">Simon S., Duran M., Dannenberg, J. J. How does basis set superposition error change the potential surfaces for hydrogen bonded dimers? Journal of Chemical Physics, 1996, vol. 105, no. 24, pp. 11024–11031. https://doi.org/10.1063/1.472902</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">A Multitechnique Study of CO Adsorption on the TiO2 Anatase (101) Surface / M. Setvin [et al.] // J. Phys. Chem. C. – 2015. – Vol. 119, N 36. – P. 21044–21052. https://doi.org/10.1021/acs.jpcc.5b07999</mixed-citation><mixed-citation xml:lang="en">Setvin M., Buchholz M., Hou W., Zhang C., Stöger B., Hulva J., Simschitz T., Shi X., Pavelec J., Parkinson G. S., Xu M., Wang Y., Schmid M., Wöll C., Selloni A., Diebold U. A Multitechnique Study of CO Adsorption on the TiO2 Anatase (101) Surface. Journal of Physical Chemistry C, 2015, vol. 119, no. 36, pp. 21044–21052. https://doi.org/10.1021/acs.jpcc.5b07999</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Thermodynamics of Carbon Monoxide Adsorption on Polycrystalline Titania Studied by Static Adsorption Microcalorimetry / X. Xia [et al.] // Langmuir. – 2007. – Vol. 23, N 22. – P. 11063–11066. https://doi.org/10.1021/la7014594</mixed-citation><mixed-citation xml:lang="en">Xia X., Busser W., Strunk J., Muhler M. Thermodynamics of Carbon Monoxide Adsorption on Polycrystalline Titania Studied by Static Adsorption Microcalorimetry. Langmuir, 2007, vol. 23, no. 22, pp. 11063–11066. https://doi.org/10.1021/la7014594</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Xia, X. Entropy of adsorption of carbon monoxide on energetically heterogeneous surfaces / X. Xia, R. Naumann d’Alnoncourt, M. Muhler // J. Therm. Anal. Calorim. – 2007. – Vol. 91. – P. 167–172. https://doi.org/10.1007/s10973-007-8440-x</mixed-citation><mixed-citation xml:lang="en">Xia X., Naumann d’Alnoncourt R., Muhler M. Entropy of adsorption of carbon monoxide on energetically heterogeneous surfaces. Journal of Thermal Analysis and Calorimetry, 2007, vol. 91, pp. 167–172. https://doi.org/10.1007/s10973-007-8440-x</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Cox, J. D. CODATA Key Values for Thermodynamics / J. D. Cox, D. D. Wagman, V. A. Medvedev. – New York, 1984. – 271 p.</mixed-citation><mixed-citation xml:lang="en">Cox J. D., Wagman D. D., Medvedev V. A. CODATA Key Values for Thermodynamics. New York, 1984. 271 p.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Campbell, C. T. Equilibrium Constants and Rate Constants for Adsorbates: Two-Dimensional (2D) Ideal Gas, 2D Ideal Lattice Gas, and Ideal Hindered Translator Models / C. T. Campbell, L. H. Sprowl, L. Árnadóttir // J. Phys. Chem. C. – 2016. – Vol. 120, N 19. – P. 10283–10297. https://doi.org/10.1021/acs.jpcc.6b00975</mixed-citation><mixed-citation xml:lang="en">Campbell C. T., Sprowl L. H., Árnadóttir L. Equilibrium Constants and Rate Constants for Adsorbates: Two-Dimensional (2D) Ideal Gas, 2D Ideal Lattice Gas, and Ideal Hindered Translator Models. Journal of Physical Chemistry C, 2016, vol. 120, no. 19, pp. 10283–10297. https://doi.org/10.1021/acs.jpcc.6b00975</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Rezaee, M. The role of brookite in mechanical activation of anatase-to-rutile transformation of nanocrystalline TiO2: An XRD and Raman spectroscopy investigation / M. Rezaee, S. M. Mousavi Khoie, K. H. Liu // CrystEngComm. – 2011. – Vol. 13, N 16. – P. 5055–5061. https://doi.org/10.1039/c1ce05185g</mixed-citation><mixed-citation xml:lang="en">Rezaee M., Mousavi Khoie S. M., Liu K. H. The role of brookite in mechanical activation of anatase-to-rutile transformation of nanocrystalline TiO2: An XRD and Raman spectroscopy investigation. CrystEngComm, 2011, vol. 13, no. 16, pp. 5055–5061. https://doi.org/10.1039/c1ce05185g</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
