Molecular momentum distributions and compton profiles. Effects of bonding on some small molecules

Roux, Monique; Epstein, Irving R.

doi:10.1016/0009-2614(73)80328-8

Cited by 26 publications

(5 citation statements)

References 24 publications

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“…The addition of the virial ratio to the energy to produce the index J({E, VR}) destroys the correlation mentioned above rendering this latter index useless for all purposes except for the determination of the ability of an orbital to predict a correct virial ratio. Contrary to the suggestion of Epstein and co-workers [3] there is no evidence that a virial ratio different from unity is a result of imbalance between the accuracy of position and momentum space properties for an orbital. Note that in many past papers the Clementi 5 1s STO expansions 19 and 19a have been used as essentially HF orbitals.…”

Section: J I I E )contrasting

confidence: 66%

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Basis set quality. II. Information theoretic appraisal of various s‐ orbitals

Simas

Thakkar

Smith

1983

Int J of Quantum Chemistry

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The expectation values ( r k ) ( -2 s k 5 4 , k = lo), values of the charge density p ( r ) at selected points, and coefficients in the MacLaurin expansion of p ( r ) are used to test the quality of 71 orbital basis sets used for the atomic helium Hartree-Fock problem. These tests in position space are complementary to the momentum space tests previously carried out [Int. J. Quantum Chem. 21, 419 (1982)l. Information theoretic measures with respect to either or both position and momentum space properties are subsequently defined and the orbitals are ranked accordingly. These measures indicate that, for a given orbital, momentum space properties are more poorly predicted than position space ones. Moreover an improvement in the virial ratio does not necessarily lead to a more balanced orbital with respect to position and momentum space properties. Basis sets containing Slater-type orbitals are again found to be rather accurate. The exponentially damped rational function is confirmed to be the outstanding two-parameter unconventional orbital.

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Section: J I I E )contrasting

confidence: 66%

“…(3) Does the deviation of the virial ratio VR = -T/E from unity reflect an imbalance in the predictive ability of the orbital with respect to position and momentum properties as has been previously suggested by Epstein and coworkers [3] …”

Section: Introductionmentioning

confidence: 92%

Basis set quality. II. Information theoretic appraisal of various s‐ orbitals

Simas

Thakkar

Smith

1983

Int J of Quantum Chemistry

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“…This simple argument explains why the Compton profile of metallic iron in figure 7 is broader than the free-atom profile; the larger variance represents the cohesive energy. Roux and Epstein (1973) suggested that the departure from virial equality can be used as a measure of the quality of a model's momentum representation. This test often exposes inadequacies in the calculation of n ( p ) .…”

Section: The Virial Theorem and Cohesionmentioning

confidence: 99%

“…This approach was investigated theoretically by Epstein (1970) and Epstein and Lipscomb (1970) for hydrocarbons and boron hydrides. Their LMO calculations questioned the universality of bond transfer but the comprehensive work of first Epstein (1973) and then Smith and Whangbo (1974) did much to establish the advantages of interpreting chemical bonding from a momentum viewpoint (see also 0 2.2). This area has been recently reviewed by Williams and Thomas (1983).…”

Section: The Early Development Of Compton Scatteringmentioning

confidence: 99%

Compton scattering and electron momentum determination

Cooper¹

1985

Rep. Prog. Phys.

561

308

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When radiation is Compton-scattered the emerging beam is Doppler-broadened because of the motion of the target electrons. An analysis of this broadened lineshapethe Compton profile-provides detailed information about the electron momentum distribution in the scatterer. The technique is particularly sensitive to the behaviour of the slower moving outer electrons involved in bonding in condensed matter and can be used to test their quantum-mechanical description.The review begins with a brief survey of the historical development of the subject to within a decade of the present. The behaviour of quantum systems, from a momentum viewpoint, is explained and the conditions under which the scattering experiment can be interpreted directly in terms of electron momentum density are discussed. The experimental techniques with y rays, x-rays and electron beams are compared. Finally, recent results on insulators and conductors are surveyed and the extent to which they challenge conventional assumptions of band theory is critically reviewed. Scattering angle (deg ) Figure 2. ( a ) The degradation in photon energy upon Compton scattering through the angular range 0-180" for a selection of initial energies: A, 662 keV, I3'Cs; B, 412 keV, ' 9 8 A~; C, 159 keV, "' Te"' ; D, 60 keV, Am. The curves are determined from equation (1.2) of the text. Note that at high incident energies back-scattering is an effective energy loss mechanism. In the limit as uI+co, w2 drops to tmc'. ( b ) The Klein-Nishina cross section in units of ( e 2 / m c 2 ) 2 (see text: equation (1.3)) as a function of scattering angle for the same incident energies as in ( a ) above. Note that at low energies the cross section loses its forward/backward asymmetry and approaches the classical Thomson expression. 24 I earliest direct evidence for the validity of Fermi-Dirac as opposed to Maxwell-Boltzmann statistics for the electron gas. Relationship between electron momenta and line broadeningThe interpretation of the Compton lineshape, usually referred to as the Compton profile, is wittingly or unwittingly based upon an impulse approximation. DuMond and Jauncey pretended that they were seeing scattering from free but moving electrons. If their assumption is to be appropriate to electrons bound in atoms, molecules, etc, the collision between photon and electron must be impulsive. The other electrons are mere spectators when the interaction is extremely brief; they cannot relax to take account of the hole left by the recoiling electron until it has completely escaped from the system. In other words, the potential seen by the target electron is the same immediately before and immediately after the interaction: the potential energy term will therefore cancel in the conservation of energy equation. In this sense the collision occurs between a photon and an individual electron which appears to be moving but unbound. DuMond ( 1933) likened the Doppler-broadening process to the reflection The early development of Compton scatteringDespite the fact that both the energy shif...

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“…Similarly, because the low momentum values provide a small contribution to the overall energy balance, and because Jc(0) and Jv(0) are depending mainly on these momenta, their convergence is relatively slow. The kinetic energy of the valence orbital energies and their kinetic parts induces a relatively poor convergence of the Virial ratio, which is rather unfavorable, as the Virial measures the balance between the qualities of the orbitals and their energetical properties [24].…”

Section: The Orbital Energies E (~+ ' ) Are Calculated [Eq (Ll)] Fmentioning

confidence: 99%

Variation–iteration method in momentum space: Determination of Hartree–Fock atomic orbitals

Windt¹,

Defranceschi²,

Dehalle

1993

Int J of Quantum Chemistry

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A method using the Svartholm iterative procedure to solve atomic Hartree-Fock equations in momentum space is defined and applied to the ground states of Be and B'. The calculated atomic orbital properties follow a monotonic and stable convergence, but with rates of convergence depending on each property. The evolution of the orbitals during the iterations is explained by the combined actions of the variational principle, the Svartholm iterative procedure, and the momentum space representation. 0

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Molecular momentum distributions and compton profiles. Effects of bonding on some small molecules

Cited by 26 publications

References 24 publications

Basis set quality. II. Information theoretic appraisal of various s‐ orbitals

Basis set quality. II. Information theoretic appraisal of various s‐ orbitals

Compton scattering and electron momentum determination

Variation–iteration method in momentum space: Determination of Hartree–Fock atomic orbitals

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