Quantum Geochemistry

ISBN-13: 9783031218361 / Angielski / Twarda / 2023 / 490 str.

Giulio Armando Ottonello

Opis

This book summarizes recent impressive improvements in the application of Quantum Mechanics, coupled with the significant increase in both speed and storage capabilities of modern computers, that allow to depict the energy and reactive properties of chemically complex materials through first principles and destroy the dogmatic assumption that the natural complexity cannot be modeled. It presents methods of Quantum Chemistry applied to various fields of geoscience. The book aims to convey to the audience, methods and procedures apt to obtain sound thermodynamic and thermo-physical data for earth’s materials under various aggregation states. The attention of this book focusses on the applicative aspects of the various procedures, with reference to the underlying theory.

Spis treści

Principles

 

1) Some recalls on Physical basis:

1-1)

roman";"="">       Statistical interpretation of a wave function

1-2) Effect of an external potential on the time-dependent and time-independent Schrödinger equation

1-3) 

The Quantum Mechanical Hamiltonian

1-4) The postulates of Quantum Mechanics (Operators and eigenvalue equations; Eigenvalue equations in vector space; The expectation value postulate; The uncertainty principle; Eigenfunction sets)

1-5)Probability density and Probability Current

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1-6)The Schrödinger equation in momentum space and generalized coordinates

1-7)  The Harmonic oscillator – general representation

px; margin-top: 0cm; margin-bottom: 0cm; margin-left: 70.9pt; text-indent: -52.9pt;">1-8)Thermal energy and nuclear motion

 

Methods

2) Gaussian Basis Sets (Exponents optimization; Polarized and diffuse functions)

3)  Plane waves (LDA; GGA; PWSCF; LAPW )

4)Pseudo-potentials

5) 

size: 14px;">Functionals

5-1)                Harthree-Fock (HF and electron correlation; Restricted HF, Restricted Open HF)

5-2)                Density Functionals (The Colle-Salvetti Theorem and the Lee-Yan-Parr approximation)

10pt; text-indent: -52.9pt;">5-3)                Hybrid functional (Local Density Approximation; General Gradient Approximation)

 

Generalities  about Observables

6) Thermodynamic parameters (to be expanded)

alibri , sans-ser^  7) Thermophysical parameters (to be expanded)

  8) Spectroscopic parameters (to be expanded)

 

Applications

 9)                  Gaseous species: The isolated gaseous molecule: elect

ron energy and zero-point energy; Electron-convention and Ion-Convention;         Adiabatic  vs Vertical IMolar Entropy and Molar Gibbs free energy of formation from the elements; Molar Volume; Dissociation energy of some geologically relevant gaseous species

10)                       &nbSolvation energy; Scaling from “absolute” to “conventional” magnitudes; Thermochemical cycles and the “Hydronium Ion” [H3O]+; Entropy of aqueous species; Basicity of acids: The Acetic Acid as an example; The pKa scale of organic and inorganic acids; The individual ionic activity coefficient in acqueous solutions of different ionic strenght; Thermodynamic properties of aqueous species with heavy atoms;

11) Silicate Melts: Silicate melts as dielectric media; Tetrahedral symmetry: the role of  sp3 hybridization; The effect of ad-ions on the orbital energy on oxygen centers: inner and external orbitals; Polymeric structures and the role of electron localization – electron delocalization in determining bond strength and medium range symmetry; Silicate melts as solvents: applications of The Scaled Particle Theory

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12)  Crystals

12-1) Lattice geometry (Translational symmetry; Unit Cell; Point Groups; Space Groups; Symmetry restrictions imposed by periodicity; Basis sets effect; HF for open shell crystals UHF for periodic systems)

ly: Calibri , sans-serif;">12-2) Periodic boundary conditions and Bloch functions (Density of states; Bond structure; Fermi Energy and Fermi Surface)

12-3)             Density of States, Bond Structure Fermi Energy and Fermi Surface

12-4)             Lattice Dynamics and Thermal Properties (Model Potential Functions; Harmonic Approximation; Born Matrix and Dispersion Relation; Experimental Methods and empirical fittings; Quantum Mechanical derivation of Force Constants)

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12-5)            Thermal stress and electron delocalization (Bader Analysis; Topological weaknesses; Thermally-induced bond-weakening; Buckenau assumption and RUM modes)   

12-6)             Observables (Total Energy and related Properties; The formation energy and other energy differences; The equilibrium geometry; EOS and Phase transitions; Bulk mod

ulus and elastic constants; Thermodynamic properties: energy quantization and phonons; Thermodynamic functions and Density of States; Quasi harmonic Model; Thermal expansion;; The asymmetric potential well: evidences from discrete static potential calculations; The Coulomb, repulsive and dispersive potentials;; Madelung Energy; Thermal energy and thermal expansion: the shift of the potential energy minimum; Surface Energy; Surfaces and Local Defect; One electron density matrix and related observables )

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13)                           Isotopomeric energy and isotopic fractionation 

13-1)              Nuclear mass and vibrational properties (Separative effect and equilibrium exchanges; Bigeleisen-Mayer approximation; Kieffer rules; The “Isotopic Hergodicity Principle”; Reaction Kinetics and isotope exchange; Diffusion induced Isotope fractionation.

13-2)              Nuclear Mass and Relativistic effects

001pt;tab-stops:0cm"> Calibri, sans-serif;">13-3)              Ab-initio Stable Isotopes (C-H-O-S)

13-4)              Ab-initio transition metals (Fe-Cu-Cr)

13-5)              Ab-initio Metallomics (Ca)

 

; margin-top: 0cm; margin-bottom: 0cm; margin-left: 21.3pt;">APPENDIX

1)                            Operators and eigenvalue equations (Self-adjoint form and Hermite equations; Properties of eigenfunctions; Eigenfunction expansions; Orthogonality of eigenfunctions; Adjoint operators and Hermitian symmetry)

2)                            Separation of differential equations

3)                            The metric tensor 

4)                            Reciprocal Lattice 

5)                            The Block Theorem

6); line-height: normal;" times="" new="" ro                            Plane waves

7)                            Gaussian Functions

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