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Carbon in atomic, molecular and crystalline (3D and 2D) forms

E. L. Wolf

in Graphene: A New Paradigm in Condensed Matter and Device Physics

Published in print:
2013
Published Online:
January 2014
ISBN:
9780199645862
eISBN:
9780191767852
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199645862.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

The carbon atom is discussed in the Bohr and Schrödinger pictures. Radii and energies of core and valence states are estimated. Ionization levels of carbon are used to estimate properties at variable ... More


Covalent Compounds

Mark Ladd

in Bonding, Structure and Solid-State Chemistry

Published in print:
2016
Published Online:
May 2016
ISBN:
9780198729945
eISBN:
9780191818783
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198729945.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

Chapter 2 introduces the Planck quantum theory and the Schrödinger equation. Radial and angular functions are derived and atomic orbitals discussed. Molecular structure is discussed in terms of the ... More


Recap: Molecular Orbitals and Common Misconceptions

Jochen Autschbach

in Quantum Theory for Chemical Applications: From Basic Concepts to Advanced Topics

Published in print:
2020
Published Online:
February 2021
ISBN:
9780190920807
eISBN:
9780197508350
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190920807.003.0011
Subject:
Chemistry, Quantum and Theoretical Chemistry

This chapter recapitulates the series of approximations that lead to the commonly used description of the electronic structure of molecules in terms of molecular orbitals (MOs), which in turn are ... More


From Atomic Orbitals to Molecular Orbitals and Chemical Bonds

Jochen Autschbach

in Quantum Theory for Chemical Applications: From Basic Concepts to Advanced Topics

Published in print:
2020
Published Online:
February 2021
ISBN:
9780190920807
eISBN:
9780197508350
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190920807.003.0009
Subject:
Chemistry, Quantum and Theoretical Chemistry

It is shown how an aufbau principle for atoms arises from the Hartree-Fock (HF) treatment with increasing numbers of electrons. The Slater screening rules are introduced. The HF equations for general ... More


Large-Scale Algorithms

Delalleau Olivier, Bengio Yoshua, and Le Roux Nicolas

in Semi-Supervised Learning

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262033589
eISBN:
9780262255899
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262033589.003.0018
Subject:
Computer Science, Machine Learning

This chapter presents a subset selection method that can be used to reduce the original system to one of size m 〈〈 n. The idea is to solve for the labels of a subset S ⊂ X of only m points, while ... More


Vegetation indices

Nathalie Pettorelli

in The Normalized Difference Vegetation Index

Published in print:
2013
Published Online:
May 2015
ISBN:
9780199693160
eISBN:
9780191810145
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:osobl/9780199693160.003.0002
Subject:
Biology, Biodiversity / Conservation Biology

This chapter discusses the concept of vegetation indices and their role in ecological research and conservation. It reviews previous published indices, including the Normalized Difference Vegetation ... More


The Nearly Free Electron, OPW, Pseudopotential, and Tight Binding Methods

J. B. Ketterson

in The Physics of Solids

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198742906
eISBN:
9780191821523
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198742906.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the techniques used to calculate the wave functions and energy levels of Bloch electrons propagating in periodic solids, starting with the nearly-free electron (NFE) ... More


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