Marcin Kirsz, Ciprian G. Pruteanu, Peter I. C. Cooke, Graeme J. Ackland
{"title":"Understanding solid nitrogen through molecular dynamics simulations with a machine-learning potential","authors":"Marcin Kirsz, Ciprian G. Pruteanu, Peter I. C. Cooke, Graeme J. Ackland","doi":"10.1103/physrevb.110.184107","DOIUrl":null,"url":null,"abstract":"We construct a fast, transferable, general purpose, machine-learning interatomic potential suitable for large-scale simulations of <mjx-container ctxtmenu_counter=\"60\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(2 0 1)\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"latinletter\" data-semantic-speech=\"normal upper N 2\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>N</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math></mjx-container>. The potential is trained only on high quality quantum chemical molecule-molecule interactions; no condensed phase information is used. Although there are no explicit or implicit many-molecule interaction terms, the potential reproduces the experimental phase diagram including the melt curve and the molecular solid phases of nitrogen up to <mjx-container ctxtmenu_counter=\"61\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(4 0 3 2)\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,2\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"0 3 2\" data-semantic-role=\"implicit\" data-semantic-speech=\"10 upper G upper P a\" data-semantic-type=\"infixop\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">1</mjx-c><mjx-c style=\"padding-top: 0.642em;\">0</mjx-c></mjx-mn><mjx-mspace data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"4\" data-semantic-role=\"space\" data-semantic-type=\"operator\" style=\"width: 0.4em;\"></mjx-mspace><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">G</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">P</mjx-c><mjx-c style=\"padding-top: 0.669em;\">a</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>. This demonstrates that many-molecule interactions are unnecessary to explain the condensed phases of <mjx-container ctxtmenu_counter=\"62\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(2 0 1)\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"latinletter\" data-semantic-speech=\"normal upper N 2\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>N</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math></mjx-container>. With increased pressure, transitions are observed from cubic <mjx-container ctxtmenu_counter=\"63\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"1\" data-semantic-content=\"0,2\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"leftright\" data-semantic-speech=\"left parenthesis alpha right parenthesis\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"3\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝛼</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"3\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-math></mjx-container>, which optimizes quadrupole-quadrupole interactions, through tetragonal <mjx-container ctxtmenu_counter=\"64\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"1\" data-semantic-content=\"0,2\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"leftright\" data-semantic-speech=\"left parenthesis gamma right parenthesis\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"3\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝛾</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"3\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-math></mjx-container>, which allows more efficient packing, to monoclinic <mjx-container ctxtmenu_counter=\"65\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"1\" data-semantic-content=\"0,2\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"leftright\" data-semantic-speech=\"left parenthesis lamda right parenthesis\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"3\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜆</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"3\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-math></mjx-container>, which packs still more efficiently. On heating, we obtain the hcp three-dimensional (3D) rotor phase <mjx-container ctxtmenu_counter=\"66\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"1\" data-semantic-content=\"0,2\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"leftright\" data-semantic-speech=\"left parenthesis beta right parenthesis\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"3\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝛽</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"3\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-math></mjx-container> and, at pressure, the cubic <mjx-container ctxtmenu_counter=\"67\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"delta\" data-semantic-type=\"identifier\"><mjx-c>𝛿</mjx-c></mjx-mi></mjx-math></mjx-container> phase which contains both 3D and 2D rotors, tetragonal <mjx-container ctxtmenu_counter=\"68\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(2 0 1)\"><mjx-msup data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"greekletter\" data-semantic-speech=\"delta Superscript asterisk\" data-semantic-type=\"superscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝛿</mjx-c></mjx-mi><mjx-script style=\"vertical-align: 0.363em;\"><mjx-mo data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" size=\"s\"><mjx-c>*</mjx-c></mjx-mo></mjx-script></mjx-msup></mjx-math></mjx-container> phase with 2D rotors, and the rhombohedral <mjx-container ctxtmenu_counter=\"69\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"epsilon\" data-semantic-type=\"identifier\"><mjx-c>𝜀</mjx-c></mjx-mi></mjx-math></mjx-container>. Molecular dynamics demonstrates where these phases are indeed rotors, rather than frustrated order. The model supports the metastability of the complex <mjx-container ctxtmenu_counter=\"70\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"iota\" data-semantic-type=\"identifier\"><mjx-c>𝜄</mjx-c></mjx-mi></mjx-math></mjx-container> phase, but not the reported existence of the wide range of bond lengths. The thermodynamic transitions involve both shifts of molecular centers and rotations of molecules: the onset of rotation is rapid, whereas motion of molecular centers is inhibited and we suggest that this is the cause of the experimentally observed sluggishness of transitions. Routine density functional theory calculations give a similar picture to the potential.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"44 1","pages":""},"PeriodicalIF":3.7000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.184107","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
We construct a fast, transferable, general purpose, machine-learning interatomic potential suitable for large-scale simulations of N2. The potential is trained only on high quality quantum chemical molecule-molecule interactions; no condensed phase information is used. Although there are no explicit or implicit many-molecule interaction terms, the potential reproduces the experimental phase diagram including the melt curve and the molecular solid phases of nitrogen up to 10GPa. This demonstrates that many-molecule interactions are unnecessary to explain the condensed phases of N2. With increased pressure, transitions are observed from cubic (𝛼), which optimizes quadrupole-quadrupole interactions, through tetragonal (𝛾), which allows more efficient packing, to monoclinic (𝜆), which packs still more efficiently. On heating, we obtain the hcp three-dimensional (3D) rotor phase (𝛽) and, at pressure, the cubic 𝛿 phase which contains both 3D and 2D rotors, tetragonal 𝛿* phase with 2D rotors, and the rhombohedral 𝜀. Molecular dynamics demonstrates where these phases are indeed rotors, rather than frustrated order. The model supports the metastability of the complex 𝜄 phase, but not the reported existence of the wide range of bond lengths. The thermodynamic transitions involve both shifts of molecular centers and rotations of molecules: the onset of rotation is rapid, whereas motion of molecular centers is inhibited and we suggest that this is the cause of the experimentally observed sluggishness of transitions. Routine density functional theory calculations give a similar picture to the potential.
期刊介绍:
Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide.
PRB covers the full range of condensed matter, materials physics, and related subfields, including:
-Structure and phase transitions
-Ferroelectrics and multiferroics
-Disordered systems and alloys
-Magnetism
-Superconductivity
-Electronic structure, photonics, and metamaterials
-Semiconductors and mesoscopic systems
-Surfaces, nanoscience, and two-dimensional materials
-Topological states of matter