SpringerLink
Log in

Quantum mechanics in Earth sciences: a one-century-old story

  • LINCEI PRIZEWINNERS
  • Published:
Rendiconti Lincei. Scienze Fisiche e Naturali Aims and scope Submit manuscript

Abstract

Nowadays, it is possible to calculate, at the ab initio level, large classes of properties of condensed matter, from the crystal structure and mechanical properties, to the thermodynamics, and therefore the stability in a given environment and in a range of temperature and pressure conditions. Predictions from calculations of this type can be used to estimate geophysical properties such as densities of mantle rocks as they change along geotherms, the geotherms themselves, phase transitions and their features, seismic velocity profiles to be compared with models derived from other paradigms and techniques. Moreover, known facts and observations concerning structure, behaviour, properties of materials and properties of whole complex systems of materials can be explained or at least rationalized within a common and very general frame that is at the basis of all the currently known physics and chemistry. However, the development of ideas, paradigms and related techniques did not come out all of a sudden, but steadily proceeded from the early days till now, without a real solution of continuity. During the time, quantum mechanics heavily contributed to create a language, a set of basic ideas and a frame of mind that is extensively used by chemists and crystallographers to interpret the relevant facts. What we know today, and how we currently apply quantum mechanics to systems of our interest, is largely dependent upon the path followed during the years to implement the theory in practical and efficient algorithms to make calculations for real systems. This paper will present a brief review of the paths followed, along with their motivations, since those early and heroic days of physics at the beginning of the last past century. The aim is to provide the reader with a general view of the subject that could possibly drive her/him toward the choice of more specific papers from the huge literature, concerning more restricted and specialized topics.

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

Access this article

Log in via an institution

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. However, it seems that Einstein was not aware of the Michelson and Morley findings when he wrote his paper in 1905 (Einstein 1905).

  2. Consider two electrons: each has always the same spin; however, their spin vectors may differ in the orientation; the latter one is specified by the three components of the vector along the axes of a Cartesian frame. Due to the commutation rules of the angular momentum operators, only one component of the spin vector can be precisely assigned and, by convention, this is the z component. The variable s given in the text is exactly such component, and it can assume only two possible values: 1/2 or \(-1/2\) in units of \(\hbar \). In the jargon, when it is said that two electrons have the same spin (spin parallel electrons), the z component of it is meant; the same is true for spin paired electrons: they have different (opposite) values of the z component.

  3. In systems having no spin unpaired electrons, in a non-relativistic approximation, an orbital (\(\zeta \)) gives rise to two spin orbitals (\(\eta _1\) and \(\eta _2\)) having the same orbital part (\(\zeta )\) and two different spin functions (\(\sigma _1\) and \(\sigma _2\)): \(\eta _i(x)=\zeta (r)\cdot \sigma _i(s)\).

  4. Although all pointwise correlation effects are short ranged if compared to mean field effects described at the Hartree–Fock level, they can be classified in two categories: short-range and long-range effects, where the adjectives short and long have here a relative meaning inside this further classification. Dispersion forces are ascribed to such long-range correlation effects, and are generally not properly accounted for by DFT functionals; DFT correlation functionals are instead effective in dealing with the short-range effects.

  5. This is at the core of the Born–Oppenheimer approximation that separates the nuclear motion from the electron motion, justified by the large difference of mass of the two types of particles.

References

  • Aliatis I, Lambruschi E, Mantovani L, Bersani D, Ando S, Gatta D, Gentile P, Salvioli-Mariani E, Prencipe M, Tribaudino M, Lottici PP (2015) A comparison between ab initio calculated and measured Raman spectrum of triclinic albite (\(\text{ NaAlSi }_3 \text{ O }_8\)). J Raman Spectrosc 46:501–508

    Article  CAS  Google Scholar 

  • Anderson OL (1995) Equation of state of solids for geophysics and ceramic science. Oxford monographs on geology and geophysics, vol 31. Oxford University Press, New York

    Google Scholar 

  • Anzolini C, Prencipe M, Alvaro M, Romano C, Vona A, Lorenzon S, Smith EM, Brenker FE, Nestola F (2018) Depth of formation of super-deep diamonds: Raman barometry of \(\text{ CaSiO }_3\)-walstromite inclusions. Am Mineral 103:69–74

    Article  Google Scholar 

  • Aquilano D, Bruno M, Rubbo M, Pastero L, Massaro FR (2015) Twin laws and energy in monoclinic hydroxyapatite, \(\text{ Ca }_5(\text{ PO }_4)_3(\text{ OH })\). Cryst Growth Des 15:411–418

    Article  CAS  Google Scholar 

  • Ashcroft NW, Mermin ND (1976) Solid state physics. Saunders College Publishing, Philadelphia

    Google Scholar 

  • Bader RFW (1994) Atoms in molecules. International series of monographs in chemistry, vol 22. Oxford University Press, Oxford

    Google Scholar 

  • Bader RFW (2009) Bond paths are not chemical bonds. J Chem Phys 113:10391–10396

    Article  CAS  Google Scholar 

  • Bader RFW, Austen MA (1997) Properties of atoms in molecules: atoms under pressure. J Chem Phys 107:4271–4285

    Article  CAS  Google Scholar 

  • Bader RFW, Essen H (1984) The characterization of atomic interactions. J Chem Phys 80:1943–1960

    Article  CAS  Google Scholar 

  • Bader RFW, Gillespie RJ, MacDougall PJ (1988) A physical basis for the VSEPR model of molecular geometry. J Am Chem Soc 110:7329–7336

    Article  CAS  Google Scholar 

  • Balan E, Saitta AM, Allard T, Fuchs Y, Mauri F (2002) First-principles modeling of the infrared spectrum of lizardite. Am Mineral 87:1286–1290

    Article  CAS  Google Scholar 

  • Bass JD, Sinogeikin SV, Li B (2008) Elastic properties of minerals: a key for understanding the composition and temperature of Earths interior. Elements 4:165–170

    Article  CAS  Google Scholar 

  • Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38:30983100

    Article  Google Scholar 

  • Becke AD (1993) Density-functional thermochemistry. 3. The role of exact exchange. J Chem Phys 98:5648–5652

    Article  CAS  Google Scholar 

  • Belmonte D (2017) First principles thermodynamics of minerals at HP-HT conditions: MgO as a prototypical material. Minerals 7:183

    Article  CAS  Google Scholar 

  • Belmonte D, Ottonello G, Zuccolini MV (2013) Melting of alpha-\(\text{ Al }_2 \text{ O }_3\) and vitrification of the undercooled alumina liquid: ab initio vibrational calculations and their thermodynamic implications. J Chem Phys 138:064507

    Article  CAS  Google Scholar 

  • Belmonte D, Ottonello G, Zuccolini MV, Attene M (2017a) The system \(\text{ MgO-Al }_2 \text{ O }_3- \text{ SiO }_2\) under pressure: a computational study of melting relations and phase diagrams. Chem Geol 461:54–64

    Article  CAS  Google Scholar 

  • Belmonte D, Ottonello G, Zuccolini MV (2017b) Ab initio-assisted assessment of the CaO–SiO\(_2\) system under pressure. Calphad 59:12–30

    Article  CAS  Google Scholar 

  • Berlin T (1951) Binding regions in diatomic molecules. J Chem Phys 19:208–213

    Article  CAS  Google Scholar 

  • Born M, Huang K (1954) Dynamical theory of crystal lattices. Clarendon Press, Oxford

    Google Scholar 

  • Bruno M, Rubbo M, Pastero L, Massaro FR, Nestola F, Aquilano D (2015) Computational approach to the study of epitaxy: natural occurrence in diamond/olivine and aragonite/zabuyelite. Cryst Growth Des 15:2979–2987

    Article  CAS  Google Scholar 

  • Bruno M, Rubbo M, Aquilano D, Massaro FR, Nestola F (2016) Diamond and its olivine inclusions: a strange relation revealed by ab initio simulations. Earth Planet Sci Lett 435:31–35

    Article  CAS  Google Scholar 

  • Causà M, Dovesi R, Roetti C, Kotomin E, Saunders VR (1987) A periodic ab initio Hartree–Fock calculation on corundum. Chem Phys Lett 140:120–123

    Article  Google Scholar 

  • Chai JD, Gordon MH (2008) Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections. Phys Chem Chem Phys 10:6615–6620

    Article  CAS  Google Scholar 

  • Connolly JAD (2005) Computation of phase equilibria by linear programming: a tool for geodynamic modeling and its application to subduction zone decarbonation. Earth Planet Sci Lett 236:524–541

    Article  CAS  Google Scholar 

  • Corno M, Busco C, Civalleri B, Ugliengo P (2006) Periodic ab initio study of structural and vibrational features of hexagonal hydroxyapatite \(\text{ Ca }_{10}(\text{ PO }_4)_6(\text{ OH })_2\). Phys Chem Chem Phys 8:2464–2472

    Article  CAS  Google Scholar 

  • Coulson CA (1955) The contributions of wave mechanics to chemistry. J Chem Soc 2069–2084

  • Crawford TD, Schaefer HF (2007) An introduction to coupled cluster theory for computational chemists. In: Lipkowitz KB, Boyd DB (eds) Reviews in computational chemistry, vol 14. VCH Publishers, New York, pp 33–136

    Chapter  Google Scholar 

  • Cremer D (2001) Density functional theory: coverage of dynamic and non-dynamic electron correlation effects. Mol Phys 99:1899–1940

    Article  CAS  Google Scholar 

  • D’Arco Ph, Mustapha S, Ferrabone M, Nöel Y, De La Pierre M, Dovesi R (2013) Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids. J Phys Condens Matter 25:355401

    Article  CAS  Google Scholar 

  • Davisson C, Germer LH (1927) The scattering of electrons by a single crystal of nickel. Nature 119:558–560

    Article  CAS  Google Scholar 

  • De La Pierre M, Belmonte D (2016) Ab initio investigation of majorite and pyrope garnets: lattice dynamics and vibrational spectra. Am Mineral 101:162–174

    Article  Google Scholar 

  • De La Pierre M, Orlando R, Maschio L, Doll K, Ugliengo P, Dovesi R (2011) Performance of six functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in the simulation of vibrational and dielectric properties of crystalline compounds. The case of forsterite \(\text{ Mg }_2 \text{ SiO }_4\). J Comput Chem 32:1775–1784

    Article  CAS  Google Scholar 

  • De La Pierre M, Nöel Y, Mustapha S, Meyer A, D’Arco Ph, Dovesi R (2013) The infrared vibrational spectrum of andradite–grossular solid solutions. A quantum-mechanical simulation. Am Mineral 98:966–976

    Article  CAS  Google Scholar 

  • Demichelis R, Civalleri B, D’Arco Ph, Dovesi R (2010a) Performance of 12 DFT functionals in the study of crystal systems: \(\text{ Al }_2 \text{ SiO }_5\) orthosilicates and Al hydroxides as a case study. Int J Quantum Chem 110:2260–2273

    Article  CAS  Google Scholar 

  • Demichelis R, Civalleri B, Ferrabone M, Dovesi R (2010b) On the performance of eleven DFT functionals in the description of the vibrational properties of aluminosilicates. Int J Quantum Chem 110:406–415

    Article  CAS  Google Scholar 

  • Dirac PAM (1930a) The principles of quantum mechanics. Clarendon Press, Oxford

    Google Scholar 

  • Dirac PAM (1930b) Note on exchange phenomena in the Thomas atom. Math Proc Camb Philos Soc 26:376–385

    Article  CAS  Google Scholar 

  • Dovesi R, Pisani C, Roetti C, Silvi B (1987) The electronic structure of \(\alpha \)-quartz: a periodic Hartree–Fock calculation. J Chem Phys 86:6967–6971

    Article  CAS  Google Scholar 

  • Dovesi R, Erba A, Orlando R, Zicovich-Wilson CM, Civalleri B, Maschio L, Rerat M, Casassa S, Baima J, Salustro S, Kirtman B (2018) Quantum mechanical condensed matter simulations with CRYSTAL. WIREs Comput Mol Sci 8:e1360

    Article  CAS  Google Scholar 

  • Einstein A (1905) On the electrodynamics of moving bodies. Ann Phys 17:891–921

    Article  Google Scholar 

  • Erba A, Mahmoud A, Belmonte D, Dovesi R (2014) High pressure elastic properties of minerals from ab initio simulations: the case of pyrope, grossular and andradite silicate garnets. J Chem Phys 140:124703

    Article  CAS  Google Scholar 

  • Frost DJ (2008) The upper mantle and transition zone. Elements 4:171–176

    Article  CAS  Google Scholar 

  • Gatti C (2015) Chemical bonding in crystals: new directions. Z Kristallogr 220:399–457

    Google Scholar 

  • Gibbs GV, Downs JW, Boisen MB (1994) The elusive SiO bond. In: Heaney PJ, Prewitt CT, Gibbs GV (eds) MSA reviews in mineralogy, Silica, vol 29, pp 331–368

  • Gibbs GV, Boisen Jr MB, Beverly LL, Rosso KM (2001) A computational quantum chemical study of the bonded interactions in Earth materials and structurally and chemically related molecules. In: Cygan RT, Kubicky JD (eds) MSA reviews in mineralogy and geochemistry, molecular modeling theory: application in the geosciences, vol 42, pp 345–381

  • Gibbs GV, Jayatilaka D, Spackman MA, Cox DF, Rosso KM (2006) Si–O bonded interactions in silicate crystals and molecules: a comparison. J Phys Chem A 110:12678–12683

    Article  CAS  Google Scholar 

  • Gibbs GV, Downs RT, Cox DF, Ross NL, Boisen MB, Rosso KM (2008a) Shared and closed-shell O–O interactions in silicates. J Phys Chem A 112:3693–3699

    Article  CAS  Google Scholar 

  • Gibbs GV, Downs RT, Cox DF, Ross NL, Prewitt CT, Rosso KM, Lippmann T, Kirfel A (2008b) Bonded interactions and the crystal chemistry of minerals: a review. Zeits Krist 223:1–40

    CAS  Google Scholar 

  • Gibbs GV, Ross NL, Cox DF, Rosso KM (2014) Insights into the crystal chemistry of Earth materials rendered by electron density distributions: Pauling’s rules revisited. Am Mineral 99:1071–1084

    Article  Google Scholar 

  • Gillespie RJ, Robinson EA (1996) Electron domains and the VSEPR model of molecular geometry. Angew Chem Int Ed Engl 35:495–514

    Article  CAS  Google Scholar 

  • Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev B 136:B864–B871

    Article  Google Scholar 

  • Koch W, Holthausen MC (2000) A chemists guide to density functional theory. Wiley-VCH, Weinheim

    Google Scholar 

  • Lacivita V, Erba A, Dovesi R, D’Arco Ph (2014) Elasticity of grossular–andradite solid solution: an ab initio investigation. Phys Chem Chem Phys 16:15331–15338

    Article  CAS  Google Scholar 

  • Lee C, Yang W, Parr RG (1988) Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785–789

    Article  CAS  Google Scholar 

  • Maschio L, Ferrabone M, Meyer A, Garza J, Dovesi R (2011) The infrared spectrum of spessartine \(\text{ Mn }_3 \text{ Al }_2 \text{ Si }_3 \text{ O }_{12}\): an ab initio all electron simulation with five different functionals (LDA, PBE, PBESOL, B3LYP and PBE0. Chem Phys Lett 501:612–618

    Article  CAS  Google Scholar 

  • Matsui M, Higo Y, Okamoto Y, Irifune T, Funakoshi K (2012) Simultaneous sound velocity and density measurements of NaCl at high temperatures and pressures: application as a primary pressure standard. Am Mineral 97:1670–1675

    Article  CAS  Google Scholar 

  • McWeeny R (1992) Methods of molecular quantum mechanics. Academic Press, London

    Google Scholar 

  • Merli M, Pavese A (2018) Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids. Acta Crystallogr A 74:102–111

    Article  CAS  Google Scholar 

  • Murri M, Mazzucchelli ML, Campomenosi N, Korsakov AV, Prencipe M, Mihailova BD, Scambelluri M, Angel RJ, Alvaro M (2018) Raman elastic geobarometry for anisotropic minerals inclusions. Am Mineral. https://doi.org/10.2138/am-2018-6625CCBY (in press)

  • Nestola F, Prencipe M, Nimis P, Sgreva N, Perrit SH, Chinn IL, Zaffiro G (2018) Toward a robust elastic geobarometry of kyanite inclusions in eclogitic diamonds. J Geophys Res 123:6411–6423

    CAS  Google Scholar 

  • Noel Y, Catti M, D’Arco Ph, Dovesi R (2006) The vibrational frequencies of forsterite \(\text{ Mg }_2 \text{ SiO }_4\); an all-electron ab initio study with the CRYSTAL code. Phys Chem Miner 33:383–393

    Article  CAS  Google Scholar 

  • Oganov AR, Glass CW (2006) Crystal structure prediction using ab initio evolutionary techniques: principles and applications. J Chem Phys 124:244704

    Article  CAS  Google Scholar 

  • Oganov AR, Lyakhov AO, Valle M (2011) How evolutionary crystal structure prediction works—and why. Acc Chem Res 44:227–237

    Article  CAS  Google Scholar 

  • Ogilvie JF, Wang FYH (1991) Does \({\text{ He }_2}\) exist? J Chin Chem Soc 38:425–427

    Article  CAS  Google Scholar 

  • Ottonello G, Civalleri B, Ganguly J, Perger WF, Belmonte D, Zuccolini MV (2010a) Thermo-chemical and thermo-physical properties of the high-pressure phase anhydrous B (\(\text{ Mg }_{14} \text{ Si }_5\text{ O }_{24}\)): an ab-initio all-electron investigation. Am Mineral 95:563–573

    Article  CAS  Google Scholar 

  • Ottonello G, Zuccolini MV, Belmonte D (2010b) The vibrational behavior of silica clusters at the glass transition: ab initio calculations and thermodynamic implications. J Chem Phys 133:104508

    Article  CAS  Google Scholar 

  • Ottonello G, Attene M, Ameglio D, Belmonte D, Zuccolini MV, Natali M (2013) Thermodynamic investigation of the CaO–Al\(_2\)O\(_3\)–SiO\(_2\) system at high P and T through polymer chemistry and convex-hull techniques. Chem Geol 346:81–92

    Article  CAS  Google Scholar 

  • Pascale F, Zicovich-Wilson CM, Orlando R, Roetti C, Ugliengo P, Dovesi R (2005) Vibration frequencies of \(\text{ Mg }_3\text{ Al }_2\text{ Si }_3\text{ O }_{12}\) pyrope. An ab initio study with the CRYSTAL code. J Phys Chem B 109:6146–6152

    Article  CAS  Google Scholar 

  • Perdew JP (1986) Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys Rev B 33:8822–8824

    Article  CAS  Google Scholar 

  • Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868

    Article  CAS  Google Scholar 

  • Pisani C, Dovesi R (1980) Exact exchange Hartree–Fock calculations for periodic systems. I. Illustration of the method. Int J Quantum Chem 17:501–516

    Article  CAS  Google Scholar 

  • Pisani C, Maschio L, Casassa S, Halo M, Schütz M, Usvyat D (2008) Periodic local MP2 method for the study of electronic correlation in crystals: theory and preliminary applications. J Comput Chem 29:2113–2124

    Article  CAS  Google Scholar 

  • Prencipe M (2002) Ab initio Hartree–Fock study and charge density analysis of beryl \((\text{ Al }_4\text{ Be }_6 \text{ Si }_{12} \text{ O }_{36})\). Phys Chem Miner 29:552–561

    Article  CAS  Google Scholar 

  • Prencipe M, Nestola F (2005) Quantum-mechanical modeling of minerals at high pressures. The role of the Hamiltonian in a case study: the beryl \((\text{ Al }_4 \text{ Be }_6 \text{ Si }_{12} \text{ O }_{36})\). Phys Chem Miner 32:471–479

    Article  CAS  Google Scholar 

  • Prencipe M, Nestola F (2007) Minerals at high pressure. Mechanics of compression from quantum mechanical calculations in a case study: the beryl \((\text{ Al }_4 \text{ Be }_6 \text{ Si }_{12} \text{ O }_{36})\). Phys Chem Miner 34:37–52

    Article  CAS  Google Scholar 

  • Prencipe M, Zupan A, Dovesi R, Aprà E, Saunders VR (1995) Ab initio study of the structural properties of LiF, NaF, KF, LiCl, NaCl, and KCl. Phys Rev B 51:3391–3396

    Article  CAS  Google Scholar 

  • Prencipe M, Tribaudino M, Nestola F (2003) Charge-density analysis of spodumene \((\text{ LiAlSi }_2 \text{ O }_6)\), from ab initio Hartree–Fock calculations. Phys Chem Miner 30:606–614

    Article  CAS  Google Scholar 

  • Prencipe M, Pascale F, Zicovich-Wilson CM, Saunders VR, Orlando R, Dovesi R (2004) The vibrational spectrum of calcite (\(\text{ CaCO }_3\)): an ab initio quantum-mechanical calculation. Phys Chem Miner 31:559–564

    Article  CAS  Google Scholar 

  • Prencipe M, Noel Y, Civalleri B, Roetti C, Dovesi R (2006) Quantum-mechanical calculation of the vibrational spectrum of beryl (\(\text{ Al }_4 \text{ Be }_6 \text{ Si }_{12} \text{ O }_{36}\)) at the \(\varGamma \) point. Phys Chem Miner 33:519–532

    Article  CAS  Google Scholar 

  • Prencipe M, Noel Y, Bruno M, Dovesi R (2009) The vibrational spectrum of lizardite-1\(T\) [\(\text{ Mg }_3 \text{ Si }_2 \text{ O }_5(\text{ OH })_4\)] at the \(\varGamma \) point: a contribution from an ab initio periodic B3LYP calculation. Am Mineral 94:986–994

    Article  CAS  Google Scholar 

  • Prencipe M, Scanavino I, Nestola F, Merlini M, Civalleri B, Bruno M, Dovesi R (2011) High-pressure thermo-elastic properties of beryl \((\text{ Al }_4\text{ Be }_6 \text{ Si }_{12} \text{ O }_{36})\) from ab initio calculations, and observations about the source of thermal expansion. Phys Chem Miner 38:223–239

    Article  CAS  Google Scholar 

  • Prencipe M, Mantovani L, Tribaudino M, Bersani D, Lottici PP (2012) The Raman spectrum of diopside: a comparison between ab initio calculated and experimentally measured frequencies. Eur J Mineral 24:457–464

    Article  CAS  Google Scholar 

  • Prencipe M, Maschio L, Kirtman B, Salustro S, Erba A, Dovesi R (2014a) Raman spectrum of \(\text{ NaAlSi }_2 \text{ O }_6 \text{ jadeite }\). A quantum mechanical simulation. J Raman Spectrosc 45:703–709

    Article  CAS  Google Scholar 

  • Prencipe M, Bruno M, Nestola F, De La Pierre M, Nimis P (2014b) Toward an accurate ab initio estimation of compressibility and thermal expansion of diamond in the [0, 3000 K] temperature and [0, 30 GPa] pressures ranges, at the hybrid HF/DFT theoretical level. Am Mineral 99:1147–1154

    Article  Google Scholar 

  • Sakurai JJ, Napolitano J (2014) Modern quantum mechanics, 2nd edn. Pearson, Harlow

    Google Scholar 

  • Scanavino I, Prencipe M (2013) Ab-initio determination of high-pressure and high-temperature thermoelastic and thermodynamic properties of low-spin \((\text{ Mg }_{\text{1x }}\text{ Fe }_{\text{ x }})\text{ O }\) ferropericlase with \(x\) in the range [0.06, 0.59]. Am Mineral 98:1270–1278

    Article  CAS  Google Scholar 

  • Scanavino I, Belousov R, Prencipe M (2012) Ab initio quantum-mechanical study of the effects of the inclusion of iron on thermoelastic and thermodynamic properties of periclase (MgO). Phys Chem Miner 39:649–663

    Article  CAS  Google Scholar 

  • Schwinger J (1951) The theory of quantized fields. Phys Rev 82:914–927

    Article  Google Scholar 

  • Slater JC (1967) Quantum theory of molecules and solids, vol I. McGraw Hill, New York

    Google Scholar 

  • Stangarone C, Tribaudino M, Prencipe M, Lottici PP (2016) Raman modes in Pbca enstatite (\(\text{ Mg2Si }_2 \text{ O }_6\)): an assignment by quantum mechanical calculation to interpret experimental results. J Raman Spectrosc 47:1247–1258

    Article  CAS  Google Scholar 

  • Stangarone C, Bottger U, Bersani D, Tribaudino M, Prencipe M (2017) Ab initio simulations and experimental Raman spectra of \(\text{ Mg }_2\text{ SiO }_4\) forsterite to simulate Mars surface environmental conditions. J Raman Spectrosc 48:1528–1535

    Article  CAS  Google Scholar 

  • Stixrude L, Lithgow-Bertelloni C (2005) Thermodynamics of mantle minerals—I. Physical properties. Geophys J Int 162:610–632

    Article  Google Scholar 

  • Stixrude L, Lithgow-Bertelloni C (2011) Thermodynamics of mantle minerals—II. Phase equilibria. Geophys J Int 184:1180–1213

    Article  CAS  Google Scholar 

  • Tosoni S, Doll K, Ugliengo P (2006) Hydrogen bond in layered materials: structural and vibrational properties of kaolinite by a periodic B3LYP approach. Chem Mater 18:2135–2143

    Article  CAS  Google Scholar 

  • Trindle C, Shillady D (2008) Electronic structure modeling: connections between theory and software. CRC Press, Taylor & Francis Group, Boca Raton

    Book  Google Scholar 

  • Ungureanu CG, Prencipe M, Cossio R (2010) Ab initio quantum-mechanical calculation of \(\text{ CaCO }_3\) aragonite at high pressure: thermodynamic properties and comparison with experimental data. Eur J Mineral 22:693–701

    Article  CAS  Google Scholar 

  • Ungureanu CG, Cossio R, Prencipe M (2012) An Ab-initio assessment of thermo-elastic properties of CaCO\(_3\) polymorphs: calcite case. Calphad 37:25–33

    Article  CAS  Google Scholar 

  • Vosko SH, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can J Phys 58:1200–1211

    Article  CAS  Google Scholar 

  • Wu Z, Cohen RE (2006) More accurate generalized gradient approximation for solids. Phys Rev B 73:235116

    Article  CAS  Google Scholar 

  • Zucchini A, Prencipe M, Comodi P, Frondini F (2012) Ab initio study of cation disorder in dolomite. Calphad 38:177–184

    Article  CAS  Google Scholar 

  • Zucchini A, Prencipe M, Belmonte D, Comodi P (2017) Ab initio study of the dolomite to dolomite-II high-pressure phase transition. Eur J Mineral 29:227–238

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The Accademia dei Lincei must be acknowledged for offering me the opportunity to write this review. Gerald Gibbs must also be gratefully acknowledged for reviewing the manuscript, and for being one of the most important inspiring sources in my scientific career.

Author information

Authors and Affiliations

  1. Department of Earth Sciences, University of Torino, Via Valperga Caluso, 35, 10125, Turin, Italy

    Mauro Prencipe

Authors
  1. Mauro Prencipe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mauro Prencipe.

Additional information

The author Mauro Prencipe has been awarded with the 2018 Lincei Prize on Geosciences.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prencipe, M. Quantum mechanics in Earth sciences: a one-century-old story. Rend. Fis. Acc. Lincei 30, 239–259 (2019). https://doi.org/10.1007/s12210-018-0744-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12210-018-0744-1

Keywords

Search

Navigation