Quantum geochemistry

lt;p>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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Erscheinungsdatum	10.05.2024
Reihe/Serie	Springer Geochemistry
Zusatzinfo	Illustrationen
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Naturwissenschaften ► Geowissenschaften ► Geologie
Schlagworte	Gaussian basis sets • Harmonic oscillator • isotopic fractionation • Lattice geometry • Quantum Mechanical Hamiltonian • Schrödinger equation
ISBN-10	3-031-21836-1 / 3031218361
ISBN-13	978-3-031-21836-1 / 9783031218361
Zustand	Neuware

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