<?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="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2016-7-3-427-432</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-1215</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="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>Development of an orbital-free approach for simulation of multi-atomic nanosystems with covalent bonds</article-title><trans-title-group xml:lang="ru"><trans-title>Development of an orbital-free approach for simulation of multi-atomic nanosystems with covalent bonds</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Zavodinsky</surname><given-names>V. G.</given-names></name><name name-style="western" xml:lang="en"><surname>Zavodinsky</surname><given-names>V. G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>153 Tikhookeanskaya str., 680042 Khabarovsk</p></bio><bio xml:lang="en"><p>153 Tikhookeanskaya str., 680042 Khabarovsk</p></bio><email xlink:type="simple">vzavod@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Gorkusha</surname><given-names>O. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Gorkusha</surname><given-names>O. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>54 Dzerzhinskogo str., 680000 Khabarovsk</p></bio><bio xml:lang="en"><p>54 Dzerzhinskogo str., 680000 Khabarovsk</p></bio><email xlink:type="simple">ogarok@rambler.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Institute for Material Science<country>Россия</country></aff><aff xml:lang="en">Institute for Material Science<country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru">Institute of Applied Mathematics<country>Россия</country></aff><aff xml:lang="en">Institute of Applied Mathematics<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2016</year></pub-date><pub-date pub-type="epub"><day>20</day><month>08</month><year>2025</year></pub-date><volume>7</volume><issue>3</issue><fpage>427</fpage><lpage>432</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Zavodinsky V.G., Gorkusha O.A., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Zavodinsky V.G., Gorkusha O.А.</copyright-holder><copyright-holder xml:lang="en">Zavodinsky V.G., Gorkusha O.A.</copyright-holder><license 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://nanojournal.ifmo.ru/jour/article/view/1215">https://nanojournal.ifmo.ru/jour/article/view/1215</self-uri><abstract><p>On the example of the three-atomic clusters Al3, Si3, and C3, it is shown that an orbital-free version of the density functional theory may be used for finding equilibrium configurations of multi-atomic systems with both metallic and covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies are found to be in good agreement with known data.</p></abstract><trans-abstract xml:lang="ru"><p>On the example of the three-atomic clusters Al3, Si3, and C3, it is shown that an orbital-free version of the density functional theory may be used for finding equilibrium configurations of multi-atomic systems with both metallic and covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies are found to be in good agreement with known data.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Orbital-free</kwd><kwd>density functional</kwd><kwd>covalent bonding</kwd><kwd>angle dependence</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Orbital-free</kwd><kwd>density functional</kwd><kwd>covalent bonding</kwd><kwd>angle dependence</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Wang Y.A., Carter E.A. Orbital-free kinetic-energy density functional theory. In: Progress in Theoretical Chemistry and Physics, Kluwer, Dordrecht, 2000, 117 p.</mixed-citation><mixed-citation xml:lang="en">Wang Y.A., Carter E.A. Orbital-free kinetic-energy density functional theory. In: Progress in Theoretical Chemistry and Physics, Kluwer, Dordrecht, 2000, 117 p.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Huajie Chen, Aihui Zhou. Orbital-Free Density Functional Theory for Molecular Structure Calculations. Numerical Mathematics: Theory, Methods and Applications, 2008, 1, P. 1–28.</mixed-citation><mixed-citation xml:lang="en">Huajie Chen, Aihui Zhou. Orbital-Free Density Functional Theory for Molecular Structure Calculations. Numerical Mathematics: Theory, Methods and Applications, 2008, 1, P. 1–28.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Baojing Zhou, Ligneres V.L., Carter E.A. Improving the orbital-free density functional theory description of covalent materials. Journal Chemical Physics, 2005, 122, P. 044103–13.</mixed-citation><mixed-citation xml:lang="en">Baojing Zhou, Ligneres V.L., Carter E.A. Improving the orbital-free density functional theory description of covalent materials. Journal Chemical Physics, 2005, 122, P. 044103–13.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Karasiev V.V., Trickey S.B. Issues and challenges in orbital-free density functional calculations. Computational Physics Communications, 2012, 183, P. 2519–2527.</mixed-citation><mixed-citation xml:lang="en">Karasiev V.V., Trickey S.B. Issues and challenges in orbital-free density functional calculations. Computational Physics Communications, 2012, 183, P. 2519–2527.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Karasiev V.V., Chakraborty D., Shukruto O.A., Trickey S.B. Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations. Physical Review B, 2013, 88, P. 161108–13(R).</mixed-citation><mixed-citation xml:lang="en">Karasiev V.V., Chakraborty D., Shukruto O.A., Trickey S.B. Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations. Physical Review B, 2013, 88, P. 161108–13(R).</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Wesolowski T.A. Approximating the kinetic energy functional Ts[ρ]: lessons from four-electron systems. Molecular Physics, 2005, 103, P. 1165–67.</mixed-citation><mixed-citation xml:lang="en">Wesolowski T.A. Approximating the kinetic energy functional Ts[ρ]: lessons from four-electron systems. Molecular Physics, 2005, 103, P. 1165–67.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Hung L., Carter E.A. Accurate Simulations of Metals at the Mesoscale: Explicit Treatment of 1 Million Atoms with Quantum Mechanics. Chemical Physics Letters, 2009, 475, P. 163–170.</mixed-citation><mixed-citation xml:lang="en">Hung L., Carter E.A. Accurate Simulations of Metals at the Mesoscale: Explicit Treatment of 1 Million Atoms with Quantum Mechanics. Chemical Physics Letters, 2009, 475, P. 163–170.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Zavodinsky V.G., Gorkusha O.A. Quantum-Mechanical Modeling without Wave Functions. Physics of the Solid States, 2014, 56 (11), P. 2329–35.</mixed-citation><mixed-citation xml:lang="en">Zavodinsky V.G., Gorkusha O.A. Quantum-Mechanical Modeling without Wave Functions. Physics of the Solid States, 2014, 56 (11), P. 2329–35.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Kohn W., Sham J.L. Self-Consistent Equations including Exchange and Correlation Effects. Phys. Rev. A, 1965, 140, P. 1133–38.</mixed-citation><mixed-citation xml:lang="en">Kohn W., Sham J.L. Self-Consistent Equations including Exchange and Correlation Effects. Phys. Rev. A, 1965, 140, P. 1133–38.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Hohenbeg H., Kohn W. Inhomogeneous Electron Gas. Physical Review B, 1964, 136, P. 864–871.</mixed-citation><mixed-citation xml:lang="en">Hohenbeg H., Kohn W. Inhomogeneous Electron Gas. Physical Review B, 1964, 136, P. 864–871.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Sivasathya S., Thiruvadigal D.J. The effects of defects on electron transport in metallic single wall carbon nanotubes. Nanosystems: physics, chemistry, mathematics, 2013, 4 (3), P. 405–408.</mixed-citation><mixed-citation xml:lang="en">Sivasathya S., Thiruvadigal D.J. The effects of defects on electron transport in metallic single wall carbon nanotubes. Nanosystems: physics, chemistry, mathematics, 2013, 4 (3), P. 405–408.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Hariharan R.M., Thiruvadigal D.J. Effect of anchoring atoms on transport properties of a carbon-dimer based molecular junctions: a first principles study. Nanosystems: physics, chemistry, mathematics, 2013, 4 (2), P. 294–298.</mixed-citation><mixed-citation xml:lang="en">Hariharan R.M., Thiruvadigal D.J. Effect of anchoring atoms on transport properties of a carbon-dimer based molecular junctions: a first principles study. Nanosystems: physics, chemistry, mathematics, 2013, 4 (2), P. 294–298.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Polyakov E.A., Vorontsov-Velyaminov P.N. Exact classical stochastic representations of the many-body quantum dynamics. Nanosystems: physics, chemistry, mathematics, 2015, 6 (4), P. 501–512.</mixed-citation><mixed-citation xml:lang="en">Polyakov E.A., Vorontsov-Velyaminov P.N. Exact classical stochastic representations of the many-body quantum dynamics. Nanosystems: physics, chemistry, mathematics, 2015, 6 (4), P. 501–512.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Junchao Xia, Chen Huang, Ilgyou Shin, Carter E.A. Can orbital-free density functional theory simulate molecules? The Journal of Chemical Physics, 2012, 136, 084102(13).</mixed-citation><mixed-citation xml:lang="en">Junchao Xia, Chen Huang, Ilgyou Shin, Carter E.A. Can orbital-free density functional theory simulate molecules? The Journal of Chemical Physics, 2012, 136, 084102(13).</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Zavodinsky V.G., Gorkusha O.A. New Orbital-Free Approach for Density Functional Modeling of Large Molecules and Nanoparticles. Modeling and Numerical Simulation of Material Science, 2015, 5, P. 39–46.</mixed-citation><mixed-citation xml:lang="en">Zavodinsky V.G., Gorkusha O.A. New Orbital-Free Approach for Density Functional Modeling of Large Molecules and Nanoparticles. Modeling and Numerical Simulation of Material Science, 2015, 5, P. 39–46.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Carling K.M., Carter E.A. Orbital-free density functional theory calculations of the properties of Al, Mg and Al–Mg crystalline phases. Modelling and simulation in materials science and engineering, 2003, 11, P. 339–348.</mixed-citation><mixed-citation xml:lang="en">Carling K.M., Carter E.A. Orbital-free density functional theory calculations of the properties of Al, Mg and Al–Mg crystalline phases. Modelling and simulation in materials science and engineering, 2003, 11, P. 339–348.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Raghavachari K., Logovinsky V. Structure and bonding in small silicon clusters. Phys. Rev. Lett., 1985, 55, P. 2853–2856.</mixed-citation><mixed-citation xml:lang="en">Raghavachari K., Logovinsky V. Structure and bonding in small silicon clusters. Phys. Rev. Lett., 1985, 55, P. 2853–2856.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Van Orden A., Saykally R.J. Small carbon clusters: spectroscopy, structure, and energetics. Chemical Review, 1998, 98, P. 2313–57.</mixed-citation><mixed-citation xml:lang="en">Van Orden A., Saykally R.J. Small carbon clusters: spectroscopy, structure, and energetics. Chemical Review, 1998, 98, P. 2313–57.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Feng-Chuan Chuang, Wang C.Z., Ho K.H. Structure of neutral aluminum clusters Aln(2 ≤ n ≤ 23): Genetic algorithm tight-binding calculations. Phys. Rev. B, 2006, 73, 125431(7).</mixed-citation><mixed-citation xml:lang="en">Feng-Chuan Chuang, Wang C.Z., Ho K.H. Structure of neutral aluminum clusters Aln(2 ≤ n ≤ 23): Genetic algorithm tight-binding calculations. Phys. Rev. B, 2006, 73, 125431(7).</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Sarry A.M., Sarry M.F. To the density functional theory. Physics of Solid State, 2012, 54 (6), P. 1315–22.</mixed-citation><mixed-citation xml:lang="en">Sarry A.M., Sarry M.F. To the density functional theory. Physics of Solid State, 2012, 54 (6), P. 1315–22.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Fuchs M., Scheffler M. Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory. Computational Physics Communications, 1999, 119, P. 67–98.</mixed-citation><mixed-citation xml:lang="en">Fuchs M., Scheffler M. Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory. Computational Physics Communications, 1999, 119, P. 67–98.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Perdew J.P., Zunger A. Self-interaction correction to density functional approximation for many-electron systems. Physical Review B, 1981, 23, P. 5048–79.</mixed-citation><mixed-citation xml:lang="en">Perdew J.P., Zunger A. Self-interaction correction to density functional approximation for many-electron systems. Physical Review B, 1981, 23, P. 5048–79.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Ceperley D.M., Alder B.J. Ground state of the electron gas by a stochastic method. Physical Review Letters, 1980, 45, P. 566–569.</mixed-citation><mixed-citation xml:lang="en">Ceperley D.M., Alder B.J. Ground state of the electron gas by a stochastic method. Physical Review Letters, 1980, 45, P. 566–569.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Tomanek D., Schluter M.A. Structure and bonding of small semiconductor clusters. Phys. Rev. B, 1987, 36, P. 1208–17.</mixed-citation><mixed-citation xml:lang="en">Tomanek D., Schluter M.A. Structure and bonding of small semiconductor clusters. Phys. Rev. B, 1987, 36, P. 1208–17.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Mukhtarov A.P., Normurodov A.B., Sulaymonov N.T., Umarova F.T. Charge States of Bare Silicon Clusters up to Si8 by Non-Conventional Tight-Binding Method. Journal of nanoand electronic physics, 2015, 7, 01012(7).</mixed-citation><mixed-citation xml:lang="en">Mukhtarov A.P., Normurodov A.B., Sulaymonov N.T., Umarova F.T. Charge States of Bare Silicon Clusters up to Si8 by Non-Conventional Tight-Binding Method. Journal of nanoand electronic physics, 2015, 7, 01012(7).</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Nayak S.K., Khanna S.N., Jena P.J. Evolution of bonding in AlnN clusters: A transition from nonmetallic to metallic character. Physical Review B, 1998, 57, P. 3787–90.</mixed-citation><mixed-citation xml:lang="en">Nayak S.K., Khanna S.N., Jena P.J. Evolution of bonding in AlnN clusters: A transition from nonmetallic to metallic character. Physical Review B, 1998, 57, P. 3787–90.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Matrnez A., Vela A. Stability of charged aluminum clusters. Physical Review B, 1994, 49, 17464(4).</mixed-citation><mixed-citation xml:lang="en">Matrnez A., Vela A. Stability of charged aluminum clusters. Physical Review B, 1994, 49, 17464(4).</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Karton A., Tarnopolsky A., Martin J.M.L. Atomization energies of the carbon clusters Cn (n = 2 − 10) revisited by means of W4 theory as well as density functional, Gn, and CBS methods. International Journal of Interface between Chemistry and Physics, 2009, 107, P. 977–1003.</mixed-citation><mixed-citation xml:lang="en">Karton A., Tarnopolsky A., Martin J.M.L. Atomization energies of the carbon clusters Cn (n = 2 − 10) revisited by means of W4 theory as well as density functional, Gn, and CBS methods. International Journal of Interface between Chemistry and Physics, 2009, 107, P. 977–1003.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Afshar M., Babaei M., Kordbacheh A.H. First principles study on structural and magnetic properties of small and pure carbon clusters (Cn, n = 2 − 12). Journal of Theoretical and Applied Physics, 2014, 8, P. 103–108.</mixed-citation><mixed-citation xml:lang="en">Afshar M., Babaei M., Kordbacheh A.H. First principles study on structural and magnetic properties of small and pure carbon clusters (Cn, n = 2 − 12). Journal of Theoretical and Applied Physics, 2014, 8, P. 103–108.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">McCarthy M.C., Thaddeus P. Rotational spectrum and structure of Si3. Physical Review Letters, 2003, 90, 213003(4).</mixed-citation><mixed-citation xml:lang="en">McCarthy M.C., Thaddeus P. Rotational spectrum and structure of Si3. Physical Review Letters, 2003, 90, 213003(4).</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Liu B., Lu Z.Y., et al. Ionization of medium-sized silicon clusters and the geometries of the cations. Journal of Chemical Physics, 1998, 109, P. 9401–09.</mixed-citation><mixed-citation xml:lang="en">Liu B., Lu Z.Y., et al. Ionization of medium-sized silicon clusters and the geometries of the cations. Journal of Chemical Physics, 1998, 109, P. 9401–09.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Raghavachari K., Rohlfing C.M. Bonding and stabilities of small silicon clusters: A theoretical study of Si7–Si10. Journal of Chemical Physics, 1988, 89, P. 2219–34.</mixed-citation><mixed-citation xml:lang="en">Raghavachari K., Rohlfing C.M. Bonding and stabilities of small silicon clusters: A theoretical study of Si7–Si10. Journal of Chemical Physics, 1988, 89, P. 2219–34.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Tse J.S. Electronic structure of the dimer and trimer of aluminium. Theoretical Chemistry (Journal of Molecular Structures), 1988, 165, P. 21–24.</mixed-citation><mixed-citation xml:lang="en">Tse J.S. Electronic structure of the dimer and trimer of aluminium. Theoretical Chemistry (Journal of Molecular Structures), 1988, 165, P. 21–24.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Beckstedte M., Kley A., Neugebauer J., Scheffler M. Density functional theory calculation for poly-atomic systems: electronic structure, static and elastic properties and ab initio molecular dynamics. Computational Physics Communications, 1997, 107, P. 187–205.</mixed-citation><mixed-citation xml:lang="en">Beckstedte M., Kley A., Neugebauer J., Scheffler M. Density functional theory calculation for poly-atomic systems: electronic structure, static and elastic properties and ab initio molecular dynamics. Computational Physics Communications, 1997, 107, P. 187–205.</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>
