Properties of atoms in molecules: Atoms under pressure

Bader, R. F. W.; Austen, Maggie A.

doi:10.1063/1.474769

Cited by 85 publications

(58 citation statements)

References 35 publications

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“…[37] Every bound atom is under pressure, the equilibrium pressure being determined by the condition that T(A) = ÀE(A). Atoms under pressure resulting from the application of an external constraining force that holds the system in an non-equilibrium geometry, must according to the virial theorem, exhibit a kinetic energy T(A) in excess of ÀE(A), the disparity increasing with increasing pressure.…”

Section: Applying the Quantum Mechanics Of An Open Systemmentioning

confidence: 99%

Pauli Repulsions Exist Only in the Eye of the Beholder

Bader

2006

Chemistry A European J

252

173

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This paper presents a rebuttal to the preceding paper in this issue entitled "Hydrogen-Hydrogen Bonding in Planar Biphenyl, Predicted by Atoms-In-Molecules Theory, Does Not Exist". The arguments presented therein are based on an arbitrary partitioning of the energy into contributions from physically unrealizable states of the system. The response given here is presented in terms of the Feynman, Ehrenfest, and virial theorems of quantum mechanics and the observable properties of a system. A reader is thus free to choose between subjectivity or physics.

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Section: Applying the Quantum Mechanics Of An Open Systemmentioning

confidence: 99%

Pauli Repulsions Exist Only in the Eye of the Beholder

Bader

2006

Chemistry A European J

252

173

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“…SettingĜ r Á p as the generator in Eq. (8), yields the atomic statement of the virial theorem, the theorem that enables one to de®ne the electronic energy of an open system and the pressure acting on it [32]. The eect of this transformation is to induce a scaling of the electronic coordinate r by the factor f e e and the eect of U Ã (e) on the state vector yields a properly normalized function with the coordinate r scaled by f. If q¢(r) denotes the transformed density viewed as a function of r, then Ñq¢(r) fÑ¢q(r¢) and the zero-¯ux surface is transformed into another surface of zero-¯ux.…”

Section: From Boundary Variations To Generators Of Physical Changementioning

confidence: 99%

The zero-flux surface and the topological and quantum definitions of an atom in a molecule

Bader

2001

Theoretical Chemistry Accounts: Theory, Computation, and Modeli

103

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The partitioning of a charge distribution by surfaces exhibiting a local zero¯ux in the gradient vector ®eld of the electron density leads to an exhaustive and disjoint division of the system into a set of mono-nuclear regions or atoms, provided the only local attractors present in the system are isolated nuclear attractors and the electronic energy is less than that required to produce the plasma state. The existence of non-isolated attractors, whose limited occurrence is con®ned primarily to excited state charge distributions of one-electron systems, is shown to be readily encompassed within the topological theory of molecular structure, a theory whose purpose is to relate a system's properties to the observed topology of its density distribution. The zeroux surface serves as the necessary boundary condition for the application of Schwinger's principle of stationary action to de®ne the physics of an atom in a molecule as an open system. Schwinger's principle requires the use of a special class of trial functions: those whose variation is to be equated to the action of smooth, continuous changes in the coordinates of the physical system caused by the action of generators of in®nitesimal transformations, the very requirement needed to ensure the applicability of the zero-¯ux surface condition as the de®ning constraint of an open system. The zero-¯ux surfaceThe quantum theory of atoms in molecules [1] is widely employed in the study of the experimentally measured and theoretically determined properties of molecules and crystals, as exempli®ed in a recent review by Spackman describing its application to the analysis of charge densities obtained from X-ray studies [2]. Within this theory, an atom is de®ned as a open system, one that is bounded by a surface S(r s ) of local zero¯ux in the gradient vector ®eld of the electron density q(r), as given in Eq. (1):where n(r) is a unit vector normal to the surface at r. At the meeting on`Chemical Bonding' in La Colle-surLoup France, my talk emphasized that the adoption of the quantum theory of atoms in molecules requires the replacement of the model of structure that imparts an existence to a bond separate from the atoms it links ± the ball and stick model or its orbital equivalents of atomic and overlap contributions ± with the concept of bonding between atoms; two atoms are bonded if they share an interatomic surface and are thus linked by a bond path. It was emphasized that the quantum mechanics of a proper open system not only enables one to de®ne the properties of atoms that are bonded to one another thereby assessing their degree of interaction, but provides, in addition, a characterization of the interaction through the theorems that govern the local behavior of the electron density [3]. This paper takes the opportunity to review and to consider in more detail the topological and mathematical implications of the zero-¯ux surface and its role in establishing the quantum mechanics of an open system, a move prompted in part in response to questions raised at the meeting...

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“…[1]. The surface integral ᐂ s (Ω) has been shown to be proportional to the pressure volume product for the atom Ω and it enables one to determine the pressure acting on an atom in any environment (25).…”

Section: S ω R) J R) N(r)mentioning

confidence: 99%

1997 Polanyi Award Lecture Why are there atoms in chemistry?

Bader¹

1998

Can. J. Chem.

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Dalton made a bold assumption in his atomic hypothesis by stating that atoms retained their mass and their identity in chemical combination. Its vindication had to await Rutherford's nuclear model of the atom. The continuing evolution of chemistry led to the realization that atoms exhibit not only a unique mass but also characteristic additive properties, thereby making it possible to recognize their presence in a molecule and to predict the molecule's static and reactive properties. The theoretical vindication of the model of a functional group as the carrier of chemical information had to await the work of Feynman and Schwinger. Their generalization of physics leads to a unique definition of an atom as an open quantum system and makes possible the renormalization that is required to account for the short-range nature of the forces that enable one to identify a given group in any environment. The lecture will demonstrate that the proper open systems predicted by the quantum action principle define the atom and that this definition accounts for the retention of an atom's chemical identity by enabling one to replace the quantum mechanical observables for force and energy with dressed, real space density distributions whose forms parallel the transferable topology of the electron density distribution.Résumé : Dalton, dans son hypothèse atomique, a posé un postulat audacieux lorsqu'il a affirmé que les atomes gardent leur masse et leur identité dans les combinaisons chimiques. Il a fallu attendre le développement du modèle de l'atome de Rutherford pour le justifier. L'évolution continuelle de la chimie a permis de réaliser que les atomes ne présentent pas uniquement une masse qui est spécifique, mais aussi des propriétés additives caractéristiques qui permettent de reconnaître leur présence dans une molécule et de prédire les propriétés statiques et réactives de la molécule. La justification théorique du modèle d'après lequel le groupe fonctionnel est porteur de l'information chimique a dû attendre les travaux de Feynman et Schwinger. Leur généralisation de la physique a conduit à une définition unique d'un atome d'après laquelle il s'agit d'un système quantique ouvert et elle permet la renormalisation requise pour tenir compte de la nature à courte portée des forces qui permettent d'identifier un groupe donné dans tous les environnements. Dans cette conférence, on démontrera que les systèmes ouverts appropriés prédits par le principe de l'action quantique permettent de définir l'atome et que cette définition permet de tenir compte de la rétention de l'identité chimique d'un atome en permettant de remplacer les données observables de la mécanique quantique pour la force et l'énergie par des distributions de densité d'espace réel dont les formes sont parallèles à la topologie transférable de la distribution de la densité électronique.

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Properties of atoms in molecules: Atoms under pressure

Cited by 85 publications

References 35 publications

Pauli Repulsions Exist Only in the Eye of the Beholder

Pauli Repulsions Exist Only in the Eye of the Beholder

The zero-flux surface and the topological and quantum definitions of an atom in a molecule

1997 Polanyi Award Lecture Why are there atoms in chemistry?

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