Skip to main content
SpringerLink
Log in

Bonding Changes Along Solid-Solid Phase Transitions Using the Electron Localization Function Approach

  • Chapter
  • First Online:
Modern Charge-Density Analysis

Abstract

Recent computational developments on the application of the Electron Localization Function in the solid state allow to perform a rich characterization of chemical changes along phase transitions induced by thermodynamic variables in crystals. Chemical entities, in the sense of the Lewis theory, can be idengified and classified according to the role they play in these processes. Covalent (SiO2), ionic (BeO), molecular (CO2, O2), and metallic (Na, K) systems have been selected to illustrate the ability of ELF to gain insight into the global understanding of the transformations. Detailed topological analysis of the bonding reconstruction process clearly distinguishes transitions where the bonding nature of the solid is not altered, and just a reorganization takes place, to those where the chemical pattern suffers a dramatic change. We have highlighted the close relationship between energy, structure and bonding across several transition pathways and how ELF can be of help to anticipate pressure induced emerging structures and to discard among competitive transition mechanism

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371:683–686

    Article  CAS  Google Scholar 

  2. Gatti C (2005) Chemical bonding in crystals: new directions. Z Kristallogr 220:399–457

    Article  CAS  Google Scholar 

  3. Savin A, Jepsen O, Flad J, Andersen L, von Schnering HG, Preuss H (1992) Electron localization in solid-state structures of the elements: the diamond structure. Angew Chem Int Ed Engl 31:187–188

    Article  Google Scholar 

  4. Fässler TF (2003) The role of non-bonding electron pairs in intermetallic compounds. Chem Soc Rev 32:80–86

    Article  CAS  Google Scholar 

  5. Savin A, Nesper R, Wengert S, Fässler T (1997) ELF: the electron localization function. Angew Chem Int Ed Engl 36:1809–1832

    Article  Google Scholar 

  6. Silvi B, Gatti C (2000) Direct space representation of the metallic bond. J Phys Chem A 104:947–953

    Article  CAS  Google Scholar 

  7. Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular systems. J Chem Phys 92:5397–5403

    Article  CAS  Google Scholar 

  8. von Weizsäcker CF (1935) Zur Theorie der Kernmassen. Z Phys 96:431–458

    Article  Google Scholar 

  9. Savin A, Becke AD, Flad J, Nesper R, Preuss H, von Schnering HG (1991) A new look at electron localization. Angew Chem Int Ed Engl 30:409–412

    Article  Google Scholar 

  10. Burdett JK, McCormick TA (1998) Electron localization in molecules and solids: the meaning of ELF. J Phys Chem A 102:6366–6372

    Article  CAS  Google Scholar 

  11. Nalewajski RF (2005) Electron localization function as information measure. J Phys Chem A 44:10038–10043

    Article  CAS  Google Scholar 

  12. Dobson JF (1991) Interpretation of the Fermi hole curvature. J Chem Phys 94:4328–4332

    Article  CAS  Google Scholar 

  13. Kohout M, Pernal K, Wagner FR, Grin Y (2004) Electron localizability indicator for correlated wavefunctions. I. Parallel-spin pairs. Theor Chem Acc 112:453–459

    Article  CAS  Google Scholar 

  14. Silvi B (2003) The spin-pair compositions as local indicators of the nature of the bonding. J Phys Chem A 107:3081–3085

    Article  CAS  Google Scholar 

  15. Matito E, Silvi B, Duran M, Solà MJ (2006) Chem Phys 125:024301

    Google Scholar 

  16. Silvi B (2004) How topological partitions of the electron distributions reveal delocalization. Phys Chem Chem Phys 6:256–260

    Article  CAS  Google Scholar 

  17. Abraham RH, Marsden JE (1994) Foundations of mechanics. Addison Wesley, Reading

    Google Scholar 

  18. Haussermann U, Wengert S, Hoffmann P, Savin A, Jepsen O, Nesper R (1994) Localization of electrons in intermetallic phases containing aluminum. Angew Chem Int Ed Engl 33:2069–2073

    Article  Google Scholar 

  19. Martín Pendás A, Francisco E, Blanco MA (2008) Electron-electron interactions between ELF basins. Chem Phys Lett 454:396–403

    Article  CAS  Google Scholar 

  20. Lewis GN (1916) The atom and the molecule. J Am Chem Soc 38:762–785

    Article  CAS  Google Scholar 

  21. Silvi B (2002) The synaptic order: a key concept to understand multicenter bonding. J Molec Struct 614:3–10

    Article  CAS  Google Scholar 

  22. Mezey PG (1994) Quantum-chemical shape - new density domain relations for the topology of molecular bodies, functional-groups, and chemical bonding. Can J Chem 72:928–935

    Article  CAS  Google Scholar 

  23. Kohout M, Wagner F, Grin Y (2002) Electron localization function for transition-metal compounds. Theor Chem Acc 108:150–156

    Article  CAS  Google Scholar 

  24. Calatayud M, Andrés J, Silvi B (2001) The hierarchy of localization basins: a tool for the understanding of chemical bonding exemplified by the analysis of the VOx and VOx + (x = 1 − 4) systems. Theoret Chem Acc 105:299–308

    Article  CAS  Google Scholar 

  25. Savin A, Silvi B, Colonna F (1996) Topological analysis of the electron localization function applied to delocalized bonds. Can J Chem 74:1088–1096

    Article  CAS  Google Scholar 

  26. Contreras-García J, Martín Pendás A, Silvi B, Recio JM (2009) Computation of local and global properties of the electron localization function topology in crystals. J Chem Theor Comp 5:164–173

    Article  CAS  Google Scholar 

  27. Contreras-García J, Martín Pendás A, Silvi B, Recio JM (2008) Useful applications of the electron localization function in high-pressure crystal chemistry. J Phys Chem Solids 69:2204–2207

    Article  CAS  Google Scholar 

  28. Kohout M, Savin A (1996) Atomic shell structure and electron numbers. Int J Quantum Chem 60:875–882

    Article  CAS  Google Scholar 

  29. Contreras-García J, Martín Pendás A, Silvi B, Recio JM (2009) Bases for understanding polymerization under pressure: the practical case of CO2. J Phys Chem B 113:1068–1073

    Article  CAS  Google Scholar 

  30. Goddard WA, Wilson CW Jr (1972) The role of kinetic energy in chemical binding. Theor Chim Acta (berl) 26:211–230

    Article  CAS  Google Scholar 

  31. Bickelhaupt FM, Baerends EJ (2000) Kohn-sham density functional theory: predicting and understanding chemistry. Rev Comput Chem 15:1–86

    Article  CAS  Google Scholar 

  32. Cooper DL, Ponec R (2008) A one-electron approximation to domain-averaged Fermi hole analysis. Phys Chem Chem Phys 10:1319–1329

    Article  CAS  Google Scholar 

  33. Ruedenberg K (1962) The physical nature of the chemical bond. Rev Modern Phys 34: 326–376

    Article  CAS  Google Scholar 

  34. Wiberg KB (1968) Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane. Tetrahedron 24:1083–1096

    Article  CAS  Google Scholar 

  35. Buerger J (1951) Phase transformation in solids. Wiley, New York

    Google Scholar 

  36. Gracia L, Contreras-García J, Beltrán A, Recio JM (2009) Bonding changes across the α-cristobalite → stishovite transition path in silica. High Press Res 29:93–96

    Article  CAS  Google Scholar 

  37. Bytheway I, Gillespie RJ, Tang TH, Bader RFW (1995) Core distortions and geometries of the difluorides and dihydrides of Ca, Sr, and Ba. Inorg Chem 34:2407–2414

    Article  CAS  Google Scholar 

  38. Vajeeston P, Ravindran P, Vidya R, Fjellvag H, Kjekshus A (2003) Huge-pressure-induced volume collapse in LiAlH4 and its implications to hydrogen storage. Phys Rev B 68:212101

    Article  CAS  Google Scholar 

  39. Huang LP, Durandurdu M, Kieffer J (2006) Transformation pathways of silica under high pressure. Nat Mater 5:977–981

    Article  CAS  Google Scholar 

  40. Klug DD, Rousseeau R, Uehara K, Bernasconi M, Page YL, Tse JS (2001) Ab initio molecular dynamics study of the pressure-induced phase transformations in cristobalite. Phys Rev B 63:104106

    Article  CAS  Google Scholar 

  41. Liu J, Topor L, Zhang J, Navrotsky A, Liebermann RC (1996) Calorimetric study of the coesite-stishovite transformation and calculation of the phase boundary. Phys Chem Miner 23:11–16

    Article  CAS  Google Scholar 

  42. Silvi B, Jolly LH, Darco PJ (1992) Pseudopotential periodic Hartree-Fock study of the cristobalite to stishovite phase transition. Mol Struct 92:1–9

    CAS  Google Scholar 

  43. Tsuchida Y, Yagi T (1990) New pressure-induced transformations of silica at room temperature. Nature 347:267–269

    Article  CAS  Google Scholar 

  44. O’Keeffe M, Hyde BG (1976) Cristobalites and topologically-related structures. Acta Crystallogr B 32:2923–2936

    Article  Google Scholar 

  45. Gibbs GV, Cox DF, Boisen MB, Downs RT, Ross NL (2003) The electron localization function: a tool for locating favourable proton docking sites in the silica polymorphs. Phys Chem Miner 30:305–316

    CAS  Google Scholar 

  46. Burt JB, Gibbs GV, Cox DF, Ross NL (2006) ELF isosurface maps for the Al2SiO5 polymorphs. Phys Chem Miner 33:138–144

    Article  CAS  Google Scholar 

  47. Cai YX, Wu S, Xu R, Yu J (2006) Pressure-induced phase transition and its atomistic mechanism in BeO: a theoretical calculation. Phys Rev B 73:184104

    Article  CAS  Google Scholar 

  48. Contreras-García J, Martín Pendás A, Recio JM (2008) How the electron localization function quangifies and pictures chemical changes in a solid: the B3 → B1 pressure induced phase transition in BeO. J Phys Chem B 112:9787–9794

    Article  CAS  Google Scholar 

  49. Park CJ, Lee SJ, Ko YJ, Chang KJ (1999) Theoretical study of the structural phase transformation of BeO under pressure. Phys Rev B 59:13501–13504

    Article  CAS  Google Scholar 

  50. Miao MS, Lambrecht WRL (2005) Universal Transition state for high-pressure zinc blende to rocksalt phase transitions. Phys Rev Lett 94:225501

    Article  CAS  Google Scholar 

  51. Dmitriev VP, Rochal SB, Gufan YM, Toledano P (1988) Definition of a transcendental order parameter for reconstructive phase transitions. Phys Rev Lett 60:1958–1961

    Article  CAS  Google Scholar 

  52. Krokidis X, Noury S, Silvi B (1997) Characterization of elementary chemical processes by catastrophe theory. J Phys Chem A 101:7277–7282

    Article  CAS  Google Scholar 

  53. Polo V, Andres J, Castillo R, Berski S, Silvi B (2004) Understanding the molecular mechanism of the 1,3-dipolar cycloaddition between fulminic acid and acetylene in terms of the electron localization function and catastrophe theory. Chem Eur J 10:5165–5172

    Article  CAS  Google Scholar 

  54. Mori P, Recio JM, Silvi B, Sousa C, Martín Pendás A, Luaña V, Illas F (2002) Rigorous characterization of oxygen vacancies in ionic oxides. Phys Rev B 66:075103

    Article  CAS  Google Scholar 

  55. Eremets MI, Hemley RJ, Mao H, Greforyanz E (2001) Semiconducting non-molecular nitrogen up to 240 GPa and its low-pressure stability. Nature 411:170–174

    Article  CAS  Google Scholar 

  56. Hemley RJ (2000) Effects of high pressure on molecules. Annu Rev Phys Chem 51:763–800

    Article  CAS  Google Scholar 

  57. Yoo C, Kohlmann H, Cynn H, Nicol MF, Iota V, Bihan TL (2002) Crystal structure of pseudo-six-fold carbon dioxide phase II at high pressures and temperatures. Phys Rev B 65:104103

    Article  CAS  Google Scholar 

  58. Contreras-García J, Recio JM (2009) From molecular to polymeric CO2: bonding transformations under pressure. High Press Res 29:113–117

    Article  CAS  Google Scholar 

  59. Morokuma K (1971) Molecular orbital studies of hydrogen bonds. III. C═O…H–O hydrogen bond in H2CO…H2O and H2CO…2H2O. J Chem Phys 55:1236–1244

    Article  CAS  Google Scholar 

  60. Iota V, Yoo C, Klepeis J, Jenei Z, Evans W, Cynn H (2007) Six-fold coordinated carbon dioxide VI. Nat Mater 6:34–38

    Article  CAS  Google Scholar 

  61. Leoni S, Carrillo-Cabrera W, Schnelle W, Grin Y (2003) BaAl2Ge2: synthesis, crystal structure, magnetic and electronic properties, chemical bonding, and atomistic model of the α → β phase transition. Solid State Sci 5:139–148

    Article  CAS  Google Scholar 

  62. Bridgman PW (1935) Theoretically interesting aspects of high pressure phenomena. Rev Mod Phys 7:1–33

    Article  CAS  Google Scholar 

  63. Savin A (2004) Phase transition in iodine: a chemical picture. J Phys Chem Solids 65:2025–2029

    Article  CAS  Google Scholar 

  64. Falconi S, Ackland GJ (2006) Ab initio simulations in liquid caesium at high pressure and temperature. J Phys Rev B 73:184204

    Article  CAS  Google Scholar 

  65. Militzer B, Hemley R (2006) Crystallography: solid oxygen takes shape. Nature 443:150–151

    Article  CAS  Google Scholar 

  66. Weck G, Loubeyre P, LeToullec R (2002) Observation of structural transformations in metal oxygen. Phys Rev Lett 88:035504

    Article  CAS  Google Scholar 

  67. Ma Y, Oganov AR, Glass CW (2007) Structure of the metallic ε-phase of oxygen and isosymmetric nature of the ε-ζ phase transition: Ab initio simulations. Phys Rev B 76:064101

    Article  CAS  Google Scholar 

  68. Tse JS, Yao Y, Klug DD, Desgreniers S (2008) Bonding in the e-phase of high pressure oxygen. J Phys Conf Ser 121:012006

    Article  CAS  Google Scholar 

  69. Espinosa E, Alkorta I, Elguero J, Molins E (2002) From weak to strong interactions: a comprehensive analysis of the topological and energetic properties of the electron density distribution involving XH…FY systems. J Chem Phys 117:5529–5542

    Article  CAS  Google Scholar 

  70. Shimizu K, Suhara K, Ikumo M, Eremets MI, Amaya K (1998) Superconductivity in oxygen. Nature 393:767–769

    Article  CAS  Google Scholar 

  71. Marqués M, Ackland GJ, Lundegaard LF, Contreras-García J, McMahon MI (2009) Potassium under pressure: a pseudobinary ionic compound. Phys Rev Lett 103:115501

    Article  CAS  Google Scholar 

  72. Hyde BG, Anderson S (1989) Inorganic crystal structures. Wiley, New York

    Google Scholar 

  73. Marqués M, Flórez M, Recio JM, Santamaría-Pérez D, Vegas A, García Baonza V (2006) Structure, Metastability, and electron density of Al lattices in light of the model of anions in metallic matrices. J Phys Chem B 110:18609–18618

    Article  CAS  Google Scholar 

  74. Vegas A, Santamaría-Pérez D, Marqués M, Flórez M, García Baonza V, Recio JM (2006) Anions in metallic matrices model: application to the aluminium crystal chemistry. Acta Crystallogr B 62:220–227

    Article  CAS  Google Scholar 

  75. Ma Y, Eremets M, Oganov AR, Xie Y, Trojan I, Medvedev S, Lyakhov AO, Valle M, Prakapenka V (2009) Transparent dense sodium. Nature 458:182–185

    Article  CAS  Google Scholar 

  76. Marqués M, Santoro M, Guillaume C, Gorelli F, Contreras-García J, Goncharov AF, Gregoryanz E (2011) Optical and electronic properties of dense sodium, Phys Rev B 83, 184106-1:184106-7

    Google Scholar 

  77. Seshadri R, Baldinozzi G, Felsera C, Tremel W (1999) Visualizing electronic structure changes across an angiferroelectric phase transition: Pb2MgWO6. J Mater Chem 9:2463–2466

    Article  CAS  Google Scholar 

  78. Seshadri R (2001) Visualizing lone pairs in compounds containing heavier congeners of the carbon and nitrogen group elements. Proc Indian Acad Sci (Chem Sci) 113:487–496

    Article  CAS  Google Scholar 

  79. McMahon MI, Nelmes RJ (2004) Incommensurate crystal structures in the elements at high pressure. Z Kristallogr 219:742–748

    Article  CAS  Google Scholar 

  80. McMahon MI, Nelmes RJ (2006) High-pressure structures and phase transformations in elemental metals. Chem Soc Rev 35:943–963

    Article  CAS  Google Scholar 

  81. Akahama Y, Kobayashi M, Kawamura H (1999) Simple-cubic → simple-hexagonal transition in phosphorus under pressure. Phys Rev B 59:8520–8525

    Article  CAS  Google Scholar 

  82. McMahon MI, Hejny C (2003) Pressure-Induced magnetization in FeO: evidence from elasticity and mosbauer spectroscopy. Phys Rev Lett 93:215502

    Google Scholar 

  83. Marqués M, Ackland GJ, Lundegaard LF, Falconi S, Hejny C, McMahon MI, Contreras-García J, Hanfland M (2008) Origin of incommensurate modulations in the high-pressure phosphorus IV phase. Phys Rev B 78:054120

    Article  CAS  Google Scholar 

  84. Fujihisa H, Akahama Y, Kawamura H, Ohishi Y, Gotoh Y, Yamawaki H, Sakashita M, Takeya S, Honda K (2007) Incommensurate structure of phosphorus phase IV. Phys Rev Lett 98:175501

    Article  CAS  Google Scholar 

  85. Ormeci A, Rosner H (2004) Electronic structure and bonding in antimony and its high pressure phases. Z Kristallogr 219:370–375

    Article  CAS  Google Scholar 

  86. Glass CW, Oganov AR, Hansen N (2006) USPEX: evolutionary crystal structure prediction. Comput Phys Commun 175:713–720

    Article  CAS  Google Scholar 

  87. Martonak R, Laio A, Bernasconi M, Ceriani C, Raiteri P, Parrinello M (2005) Z Kristallogr 220:489–498

    Article  CAS  Google Scholar 

  88. Winkler B, Pickard CJ, Milman V, Thimm G (2001) Systematic prediction of crystal structures. Chem Phys Lett 337:36–42

    Article  CAS  Google Scholar 

  89. Flórez M, Marqués M, Contreras-García J, Recio JM (2009) Quantum-mechanical calculations of zircon to scheelite transition pathways in ZrSiO4. Phys Rev B 79:104101

    Article  CAS  Google Scholar 

  90. Marqués M, Contreras-García J, Flórez M, Recio JM (2008) On the mechanism of the zirconreidite pressure induced transformation. J Phys Chem Solids 69:2277–2280

    Article  CAS  Google Scholar 

  91. Lang M, Zhang F, Lian J, Trautmann C, Neumann R, Ewing RC (2008) Irradiation-induced stabilization of zircon (ZrSiO4) at high pressure. Earth Planet Sci Lett 269:291–295

    Article  CAS  Google Scholar 

  92. Liu LG (1979) High-pressure phase transformations in baddeleyite and zircon, with geophysical implications. Earth Planet Sci Lett 44:390–396

    Article  CAS  Google Scholar 

  93. Ono S, Tange Y, Katayama I, Kikegawa T (2004) Equations of state of ZrSiO4 phases in the upper mantle. Am Mineral 89:185–188

    CAS  Google Scholar 

  94. Reid AF, Ringwood AE (1969) Newly observed high pressure transformations in Mn3O4, CaAl2O4, and ZrSiO4. Earth Planet Sci Lett 6:205–208

    Article  CAS  Google Scholar 

  95. Knittle E, Williams Q (1993) High-pressure Raman spectroscopy of ZrSiO4: observation of the zircon to scheelite transition at 300 K. Am Mineral 78:245–252

    CAS  Google Scholar 

  96. van Westrenen W, Frank MR, Hanchar JM, Fei Y, Finch RJ, Zha CS (2004) In situ determination of the compressibility of synthetic pure zircon (ZrSiO4) and the onset of the zircon-reidite phase transition. Am Mineral 89:197–203

    Google Scholar 

  97. Kusaba K, Syono Y, Kikuchi M, Fukuoka K (1985) Shock behavior of zircon: phase transition to scheelite structure and decomposition. Earth Planet Sci Lett 72:433–439

    Article  CAS  Google Scholar 

  98. Kusaba K, Yagi T, Kikuchi M, Syono Y (1986) Structural considerations on the mechanism of the shock-induced zircon-scheelite transition in ZrSiO4. J Phys Chem Solids 47:675–679

    Article  CAS  Google Scholar 

  99. Kresse G, Furthmuller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169–11186

    Article  CAS  Google Scholar 

  100. Perdew JP, Wang Y (1992) Accurate and simple analytic representation of the electron-gas correlation energy. Phys Rev B 45:13244–13249

    Article  Google Scholar 

  101. Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59:1758–1775

    Article  CAS  Google Scholar 

  102. Monkhorst HJ, Pack JD (1976) Special points for Brillouin-zone integrations. Phys Rev B 13:5188–5192

    Article  Google Scholar 

  103. Blanco MA, Francisco E, Luaña V (2004) GIBBS: isothermal-isobaric thermodynamics of solids from energy curves using a quasi-harmonic Debye model. Comput Phys Commun 158:57–72

    Article  CAS  Google Scholar 

  104. Otero-de-la-Roza A, Martín Pendás A, Blanco MA, Luaña V (2009) Critic: a new program for the topological analysis of solid-state electron densities. Comput Phys Commun 180:157–166

    Article  CAS  Google Scholar 

  105. Kohout M, Savin A (1997) Influence of core-valence separation of electron localization function. J Comput Chem 18:1431–1439

    Article  CAS  Google Scholar 

  106. Saunders VR, Dovesi R, Roetti R, Causá M, Harrison NM, Orlando R, Zicovich-Wilson CM (1998) CRYSTAL98 user’s manual. University of Torino, Torino

    Google Scholar 

  107. Contreras-García J, Recio JM (2010) Electron delocalization and bond formation under the ELF framework. heoretica Chimica Acta 128:411–418

    Google Scholar 

Download references

Acknowledgments

The authors want to thank L. Contreras-García for proof reading the manuscript. Financial support from Spanish MEC and FEDER programs (MAT2006-13548-C02-02) and MALTA-Consolider Ingenio 2010 Program (Project CSD2007-00045) is gratefully acknowledged. JCG thanks the Fulbright program for a Ruth Lee Kennedy travel grant.

Author information

Authors and Affiliations

  1. MALTA-Consolider Team and Departamento de Química Física, Universidad de Oviedo, E-33006, Oviedo, Spain

    Julia Contreras-García & José M. Recio

  2. SUPA, School of Physics and Centre for Science at Extreme Conditions, The University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ, UK

    Miriam Marqués

  3. Laboratoire de Chimie Théorique (UMR-CNRS 7616), Université Pierre et Marie Curie, 3 rue Galilée, 94200, Ivry sur Seine, France

    Bernard Silvi

Authors
  1. Julia Contreras-García
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miriam Marqués
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bernard Silvi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. José M. Recio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Julia Contreras-García .

Editor information

Editors and Affiliations

  1. Istit. di Scienze e Tecn. Molec. del CNR, c/o Dipt di Chim. Fis. ed Elettrochim., CNR-ISTM, Via Golgi 19, Milano, 20133, Italy

    Carlo Gatti

  2. , Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, Bern, 3012, Switzerland

    Piero Macchi

Appendix: Computational Methods

Appendix: Computational Methods

First-principles total-energy calculations were carried out within the density-functional theory (DFT) formalism with a plane-wave pseudopotential approach, as implemented in the Vienna ab initio simulation package [99]. We have used both, LDA and GGA levels of calculation using standard exchange-correlation functionals as Perdew-Wang ones [100], and the projector augmented wave (PAW) all-electron description of the electron-ion-core interaction [101]. Brillouin zone integrals were approximated using the method of Monkhorst and Pack [102], and the energies converged to 1 meV with respect to k-point density and 0.2 meV with respect to planewave cutoff. Upon compression, we calculated the total energy (E) at a number of selected values of the volume (V) for each lattice, relaxing the atomic coordinates and lattice parameters subjected to the constraints of symmetry and volume conservation. All structural relaxations were performed via a conjugate-gradient minimization of the total energy using the Methfessel-Paxton method. For the final calculation of the optimized crystal structures the tetrahedron method with Blöchl correction was used. The variation with hydrostatic pressure of the lattice parameters and atomic coordinates has been obtained by means of numerical and standard equations of state fittings to the sets of computed (E, V) points [103]. This procedure also provides G(p) curves in the static approximation (zero temperature and neglecting zero point vibrational contributions).

Analysis of ELF topologies along the transition pathways has been possible thanks to an automated and efficient code developed by the authors [26, 27]. The algorithm is able to completely characterize the topology induced by ELF in solids, including idengification and characterization of all critical points and basin integration. It is based on the fact that this topology presents two well-differentiated regions. On the one hand, the valence, which can be determined following previous crystalline topological methods [104]. On the other hand, the core, whose sphericity holds the key for designing new automated algorithms. In order to ensure a reliable and quantitative analysis of the ELF topology, all-electron wavefunctions are required [105]. To this end, the VASP optimized structures were recalculated with the CRYSTAL98 code [106] using the same exchange and correlation functionals as in the pseudopotential calculations.

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Contreras-García, J., Marqués, M., Silvi, B., Recio, J.M. (2011). Bonding Changes Along Solid-Solid Phase Transitions Using the Electron Localization Function Approach. In: Gatti, C., Macchi, P. (eds) Modern Charge-Density Analysis. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3836-4_18

Download citation

Publish with us

Policies and ethics

Search

Navigation