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Erschienen in:
From Quantum Theory to Computational Chemistry. A Brief Account of Developments Kapitel lesen Erstes Kapitel lesen

2012 | OriginalPaper | Buchkapitel

The Position of the Clamped Nuclei Electronic Hamiltonian in Quantum Mechanics

verfasst von : Brian Sutcliffe, R. Guy Woolley

Erschienen in: Handbook of Computational Chemistry

Verlag: Springer Netherlands

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Abstract

Arguments are advanced to support the view that at present it is not possible to derive molecular structure from the full quantum mechanical Coulomb Hamiltonian associated with a given molecular formula that is customarily regarded as representing the molecule in terms of its constituent electrons and nuclei. However molecular structure may be identified provided that some additional chemically motivated assumptions that lead to the clamped nuclei Hamiltonian are added to the quantum mechanical account.

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Vorheriges Kapitel From Quantum Theory to Computational Chemistry. A Brief Account of Developments
Nächstes Kapitel Remarks on Wave Function Theory and Methods
Fußnoten
1
The work was completed in 1944 and was actually received by the journal in October 1948.
 
2
An elementary example is afforded by the momentum operator \(\hat{p} = -i\hslash d/dq\), which is Hermitian on an appropriately defined class of \({L}^{2}\) functions \(\phi (q)\); for these functions it is self-adjoint on \(-\infty \leq q \leq +\infty \) but this property is lost if either of the \(\infty \) limits is replaced by any finite value a – see, for example, Thirring (1981).
 
3
Some specifics of the implementation of permutational and rotational symmetry in quantum mechanics are discussed in section “The Symmetries of the Clamped Nuclei Electronic Hamiltonian.”
 
4
A similar requirement must be placed on the denominator in Eq. 12 of Kutzelnigg (2007) for the equation to provide a secure definition.
 
5
This means that the permutation and its inverse are always in the same class. A group with this property is said to be an ambivalent group.
 
6
By “constant” here is meant simply that the elements of the matrix are not themselves dependent on the variables.
 
7
It is sometimes convenient to think of the nuclear positions as defining a particular embedding for the basis vectors or coordinate frame.
 
8
Notice that in this approximation the mass of the nucleus is of no consequence, only the charge matters.
 
9
The operator in this form is clearly only possible for finite groups but similar operators are constructible for most infinite groups of interest.
 
10
The Coulomb Hamiltonian for the electrons and nuclei specified by the molecular formula.
 
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Metadaten
Titel
The Position of the Clamped Nuclei Electronic Hamiltonian in Quantum Mechanics
verfasst von
Brian Sutcliffe
R. Guy Woolley
Copyright-Jahr
2012
Verlag
Springer Netherlands
Buch
Handbook of Computational Chemistry

Print ISBN: 978-94-007-0710-8

Electronic ISBN: 978-94-007-0711-5

Copyright-Jahr: 2012

DOI
https://doi.org/10.1007/978-94-007-0711-5_2

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