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Quantum Geochemistry

verfasst von: Giulio Armando Ottonello

Verlag: Springer International Publishing

Buchreihe : Springer Geochemistry

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Principles

Frontmatter

Chapter 1. Particles and Waves

Abstract

This short chapter is intended to give an introductory appraisal of some fundamental concepts of Wave Mechanics which are at the base of the Quantum procedures.

Giulio Armando Ottonello

Chapter 2. The Schrödinger Equation

Abstract

In this chapter, we enter in more detail in the significance of a wave function, when this is associated to a “free particle” or to a particle subjected to external constraints.

Giulio Armando Ottonello

Chapter 3. The Harmonic Oscillator

Abstract

After a short premise on the mathematical implications arising from the adoption of the harmonic oscillator in the wave-mechanical interpretation of the vibrational energy (i.e. the significance of “singularities” and the need for a “normalization”), we look, in some detail, at the “form” of the potential well (“sampled”, as we will see later, but not determined by the vibrational motion).

Giulio Armando Ottonello

Chapter 4. The Uncertainty Principle

Abstract

There is nowadays a somewhat disturbing attitude to emphasize the apparently magic aspects of Quantum Mechanics. Heisenberg’s uncertainty principle is among the most quoted ones.

Giulio Armando Ottonello

Chapter 5. The Hydrogen Atom

Abstract

The quantum mechanical treatment of the hydrogen atom is central in the development of Quantum Chemistry, from the comprehension of the spectral series (the Balmer series of hydrogen was the first one expressed through a simple formula) to that of the atomic structure under the hydrogen-like approximation (i.e. one electron occupying progressively orbits of higher energy in all possible configurations).

Giulio Armando Ottonello

Chapter 6. Many-Electron Atoms

Abstract

The quantum mechanical treatment of atomic energies received a strong impulse by the powerful analysis of the multiplets due to Slater (1929).

Giulio Armando Ottonello

Chapter 7. Molecules

Abstract

In these short notes we encounter first the conceptually simplest molecule, the H₂⁺ ion, i.e. a single electron rotating about two nuclear centers, and we move then toward a more complex case: the H₂ molecule.

Giulio Armando Ottonello

Chapter 8. 3D and 2D Periodic Structures

Abstract

Again, in this chapter, we encounter many fundamental concepts such as the Metric Tensor, the Reciprocal Lattice.

Giulio Armando Ottonello

Methods

Frontmatter

Chapter 9. Molecular Orbitals in the HF Theory

Abstract

The passage from atomic orbitals (AOs) to Molecular Orbitals (MOs) is not so simple as it could appear at first glance. The best sentence apt to resume the task is, in my opinion, that one expressed long ago by Roothan: “The basic concept of the Molecular Orbital method is to find approximate electronic wave functions for a molecule by assigning to each electron a one-electron wave function which in general extends over the whole molecule”.

Giulio Armando Ottonello

Chapter 10. DFT Functionals

Abstract

The Density Functional Theory is at the core of all modern ways of computing accurate electron energies under all aggregation states of the matter.

Giulio Armando Ottonello

Chapter 11. Electron Correlation Methods

Abstract

This chapter is essentially an introductory treatment of the advanced procedures apt to solve molecular equilibrium structures and to characterize at best their ground state energy and the energy of excited states as well: the Mølller Plesset (MP) Perturbation theory and the Configuration Interaction (CI) procedures.

Giulio Armando Ottonello

Chapter 12. Quantum Mechanical Wave Functions

Abstract

We have seen in the initial parts of this book that a wave may be defined as a disturbance in some physical system which is periodic in both space and time.

Giulio Armando Ottonello

Chapter 13. Ab Initio Molecular Dynamics

Abstract

Although in some way promoted by Ehrenfest almost one century ago (Ehrenfest 1927), Ab Initio Molecular Dynamics (AIMD) developed massively only in the eighties of the last century, under the influx of a seminal work of Car and Parrinello (1985).

Giulio Armando Ottonello

Chapter 14. Electron Delocalization Indices

Abstract

Electron delocalization/localization is related to the two-electron, or pair, density, which is the simplest quantity that describes the correlated motion of a pair of electrons (Bader and Stephens, 1974; Poater et al., 2005).

Giulio Armando Ottonello

Chapter 15. Nuclear Magnetic Resonance

Abstract

Nuclear Magnetic Resonance (NMR) is an extensively adopted experimental procedure in Geochemistry.

Giulio Armando Ottonello

Applications

Frontmatter

Chapter 16. Atmospheric Gases

Giulio Armando Ottonello

Chapter 17. Volcanic Gases

Abstract

The atomic composition of volcanic gases is conveniently described by the C–O–H–S system, since these four atoms concur to form almost all the gaseous molecules associated with magmas. The major molecular species present in volcanic gases.

Giulio Armando Ottonello

Chapter 18. Aqueous Solutions

Abstract

The importance of aqueous solutions in geochemistry may be appreciated if we recall that two-thirds of our planet is covered by water and that waters of various salinities help to determine the volcanic and metamorphic processes in the Earth’s upper mantle and crust.

Giulio Armando Ottonello

Chapter 19. Silicate Melts

Abstract

We have already seen that, like other fused salts, silicate melts too are ionic liquids (Sect. 16.3.4). In an ionic melt, coulombic forces between charges of opposite sign lead to relative short-distance ordering of ions, with anions surrounded by cations and vice versa. The probability of finding a cation replacing an anion in such ordering is effectively zero.

Giulio Armando Ottonello

Chapter 20. Crystals

Abstract

The treatment of natural crystals cannot be very comprehensive, for obvious reasons, and I limit myself to some rock-forming minerals and to some phases of peculiar interest in Geochemistry and Cosmochemistry, that received the dedicated attention of Quantum Chemists.

Giulio Armando Ottonello

Backmatter

Titel: Quantum Geochemistry
verfasst von: Giulio Armando Ottonello
Verlag: Springer International Publishing
Electronic ISBN: 978-3-031-21837-8
Print ISBN: 978-3-031-21836-1
DOI: https://doi.org/10.1007/978-3-031-21837-8

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