Lattice-dynamical evaluation of temperature factors for aromatic hydrocarbons, including internal molecular motion: a straightforward systematic procedure

Gramaccioli, C. M.; Filippini, G.; Simonetta, M.

doi:10.1107/s0567739482000734

Cited by 14 publications

(9 citation statements)

References 32 publications

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“…These substances are the same which have been treated in a previous work by Gramaccioli, Filippini & Simonetta (1982;here onwards GFS), where the contributions of internal and external modes to the temperature factors were considered separately.…”

Section: Applications and Discussionmentioning

confidence: 99%

“…The procedure of the calculations which are performed on such a basis is essentially the same as for the rigid body, which is a well known particular case (see, for instance, Cochran & Pawley, 1964;Pawley, 1967Pawley, , 1968Pawley, , 1972aWillis & Pryor, 1975). For calculating normal coordinates, the method proposed by Gwinn (1971) has proven to be the most practical, as we have already shown (Gramaccioli, Filippini & Simonetta, 1982).…”

Section: Methods Of Calculationmentioning

confidence: 99%

“…When the latter is obtained from W with a restricted basis, the contributions of the highest internal frequency modes should be added (see for instance Gramaccioli, Filippini & Simonetta, 1982).…”

Section: Methods Of Calculationmentioning

confidence: 99%

“…Even the so-called 'rigid bodies ', i.e. the molecules which look as such from a least-squares fit of temperature factors, are not necessarily rigid: this applies especially to the motion of the external H atoms (Johnson, 1970a;Scheringer, 1972a;Gramaccioli, Filippini & Simonetta, 1982).…”

Section: Introductionmentioning

confidence: 99%

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Lattice-dynamical evaluation of temperature factors in non-rigid molecular crystals: a first application to aromatic hydrocarbons

Gramaccioli¹,

Filippini²

1983

Acta Cryst Sect A

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Evaluation of temperature factors from a harmonic lattice-dynamical theory of molecular crystals has been applied to some aromatic hydrocarbons in the non-rigid case: i.e. mixing of lattice vibrations with the lowestfrequency internal modes. The calculations start from known atomic coordinates, unit-cell parameters and symmetry operations, using Cail fano-Neto potentials for in-plane modes, Williams IVa potentials for intermolecular interactions, and an overall value of 0.9 nN A for any twisting around C-C bonds. Molecular motions inside the crystal are described on the basis of normal coordinates of the isolated molecule, by applying Gwinn's method. For some molecules (benzene and naphthalene) the rigid-body approximation is adequate for the carbon-atom framework, and practically no coupling occurs between the lattice vibrations and the internal motion. For anthracene and phenanthrene, there are differences between rigid-body and non-rigid estimates of temperature factors. Molecular vibration tensors T, L, and S can be calculated, and also a general molecular displacement matrix (tensor). including even the internal modes (W), which permits extension of the rigid-body analysis to non-rigid molecules.

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Section: Applications and Discussionmentioning

confidence: 99%

Section: Methods Of Calculationmentioning

confidence: 99%

Section: Methods Of Calculationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lattice-dynamical evaluation of temperature factors in non-rigid molecular crystals: a first application to aromatic hydrocarbons

Gramaccioli¹,

Filippini²

1983

Acta Cryst Sect A

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“…Empirical 6-exp atom-atom potential-energy models proved to be very reliable (Pertsin & Kitaigorodsky, 1987). The method has recently been applied to silicates (Pilati, Bianchi & Gramaccioli, 1990), and the effects of molecular non-rigidity have also been considered (Gramaccioli, Filippini & Simonetta, 1982;Gramaccioli & Filippini, 1983;Filippini, 1990).…”

Section: Introductionmentioning

confidence: 99%

A test of chlorine and fluorine nonbonded potential functions with lattice-dynamical calculations

Munoz¹,

Criado²

1992

Acta Crystallogr Sect B

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Atombewegungen in Molekülkristallen aus Beugungsmessungen

1988

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VorbemerkungenBei modernen Rantgen-oder Neutronenbeugungsexperimenten im Bereich kleiner Moiekule wird meistens angenommen, daB die Wahrscheinlichkeitsdichtefunktion (probability density function, pdf) jedes einzelnen Atoms als GauB-Funktion dargestellt werden kann. Fiir eine Dimension gilt Gleichung (I), wobei u2 das zweite Moment der pdf ist (manchmal als Varianz oder Dispersion bezeichnet). Die entsprechende dreidimensionale Gleichung ergibt sich damit analog [GI. Komponenten (xI, x2, xj), und U-I ist die Inverse der symmetrischen Matrix U der zweiten Momente. Fur diese pdfs sind die Oberflichen gleicher Wahrscheinlichkeit Ellipsoide, und fur das zweite Moment u2 in einer willkiirlichen Richtung n(nl,n2,n3) gilt u 2 = n T U n ; u2 entspricht der mittleren quadratischen Auslenkungsamplitude (mean-square displacement amplitude, MSDA) in der Richtung nI2'. Es mu13 betont werden, daR diese pdfs nicht diejenigen Funktionen sind, die die Elektronendichte der stationlren Atome beschreiben ; vielmehr geben sie wieder, wie diese Elektronendichte durch die Abweichung des tatsachlichen Kristalls vom idealen, perfekt periodischen Gitter verschmiert wird (Abb. 2). Dieser Mangel an Periodizitat fiihrt zu einer gewissen Unscharfe in den Kernlagen. Im

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Lattice-dynamical evaluation of temperature factors for aromatic hydrocarbons, including internal molecular motion: a straightforward systematic procedure

Abstract: As a part of a systematic project of evaluating temperature factors for molecular crystals in a harmonic approximation,

Cited by 14 publications

References 32 publications

Lattice-dynamical evaluation of temperature factors in non-rigid molecular crystals: a first application to aromatic hydrocarbons

Lattice-dynamical evaluation of temperature factors in non-rigid molecular crystals: a first application to aromatic hydrocarbons

A test of chlorine and fluorine nonbonded potential functions with lattice-dynamical calculations

Atombewegungen in Molekülkristallen aus Beugungsmessungen

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