Elastic constants of molecular crystals in the pair-potential rigid-molecule approximation

Pavlides, P.; Pugh, D.

doi:10.1080/00268979100100071

Cited by 6 publications

(5 citation statements)

References 14 publications

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“…The elastic constant matrix 38 was then calculated from the second derivatives, 33 using the analytic expressions relating the Taylor expansion of the energy density to the stiffness constants. [39][40][41] Thus, the calculated elastic constants correspond to the stress-free crystal structure in the classical 0 K state.…”

Section: Methodsmentioning

confidence: 99%

“…The symmetry was subsequently relaxed to the appropriate subgroup if the second derivative (Hessian) matrix had any negative eigenvalues. The elastic constant matrix was then calculated from the second derivatives, using the analytic expressions relating the Taylor expansion of the energy density to the stiffness constants. − Thus, the calculated elastic constants correspond to the stress-free crystal structure in the classical 0 K state.…”

Section: Methodsmentioning

confidence: 99%

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The Prediction, Morphology, and Mechanical Properties of the Polymorphs of Paracetamol

2001

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The analgesic drug paracetamol (acetaminophen) has two reported metastable polymorphs, one with better tableting properties than the stable form, and another which remains uncharacterized. We have therefore performed a systematic crystal structure prediction search for minima in the lattice energy of crystalline paracetamol. The stable monoclinic form is found as the global lattice-energy minimum, but there are at least a dozen energetically feasible structures found, including the well-characterized metastable orthorhombic phase. Hence, we require additional criteria to reduce the number of hypothetical crystal structures that can be considered as potential polymorphs. For this purpose the elastic properties and vapor growth morphology of the known and predicted structures have been estimated using second-derivative analysis and the attachment-energy model. These inexpensive calculations give reasonable agreement with the available experimental data for the known polymorphs. Some of the hypothetical structures are predicted to have a low growth rate and plate-like morphology, and so are unlikely to be observed. Another is only marginally mechanically stable. Thus, this first consideration of such properties in a crystal-structure prediction study appears to reduce the number of predicted polymorphs while leaving a few candidates for the uncharacterized form.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

The Prediction, Morphology, and Mechanical Properties of the Polymorphs of Paracetamol

2001

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“…Several methodologies have been used to calculate elastic constants from the second derivatives of the potential energy surface at the classical, 0 K structure. These methods include full lattice dynamic calculations, which involve extracting wave velocities from calculated phonon dispersion curves and relating these to the elastic constants, − the numerical application of axial and shear strains, and analytic expressions directly relating second derivatives of the potential energy hypersurface to the elastic constant matrix. − We have incorporated the analytic method for rigid molecular crystals modeled by atom−atom interactions into the crystal structure modeling program DMAREL, thus enabling the use of highly accurate, anisotropic electrostatic models in elastic constant calculations.…”

Section: Methods and Computational Detailsmentioning

confidence: 99%

Elastic Constant Calculations for Molecular Organic Crystals

Day

Price

Leslie

2000

Crystal Growth & Design

109

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Elastic constants of a set of molecular organic crystals have been calculated within the crystal modeling program DMAREL, which was developed to allow the use of highly accurate, anisotropic atom-atom potentials. A set of six molecular crystals (durene, m-dinitrobenzene, the form of resorcinol, pentaerythritol, urea, and hexamethylenetetramine) has been chosen to sample a range of intermolecular interactions and crystal symmetries. The sensitivity of such calculations to variations in empirical repulsion-dispersion parameters and the electrostatic model is determined and discussed relative to the other errors in the theoretical model and typical experimental uncertainties. We find that model potentials whose functional form has been simplified often reproduce crystal structures and lattice energies adequately but perform poorly when used to calculate elastic constants. This is because more theoretically justified potentials are required to satisfactorily model the curvature at the equilibrium geometries. The rigid-molecule approximation can result in exaggerated elastic constants, and the neglect of thermal effects also leads to significant overestimation of the stiffness constants.

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“…(a) Fix the shape of molecular units, as in the rigid molecule approximation [67][68][69][70][71][72], so that molecules are not deformed during calculation of the dependence of energy on the lattice constants.…”

Section: A Method: Thermal Expansion From Ab Initio Energy Calculationsmentioning

confidence: 99%

“…II A) to calculate the thermal expansion coefficients in molecular solids. We fix (a) the shape (as in the rigid-molecule approximation) [67][68][69][70][71][72] and (b) the orientation of BH 4 − anions; we also fix (c) the direct lattice coordinates of the ionic centers of masses. (If BH 4 is not precisely symmetric, we can approximate the BH 4 center of mass by the position of the B nucleus.)…”

Section: B Application To Libhmentioning

confidence: 99%

Anisotropic thermal expansion in molecular solids: Theory and experiment onLiBH4

2014

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We propose a reliable and efficient computational method for predicting elastic and thermal expansion properties in crystals, particularly complex anisotropic molecular solids, and we apply it to the room-temperature orthorhombic P nma phase of LiBH 4. Using density-functional theory, we find thermal expansion coefficients at finite temperature, and we confirm them by temperature-dependent, in situ x-ray diffraction measurements. We also consider the effects of volume and pressure, as well as energy barriers for BH 4 − rotations and collective motions. Our combined study validates the theory and provides a better understanding of the structural behavior of LiBH 4 .

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Elastic constants of molecular crystals in the pair-potential rigid-molecule approximation

Cited by 6 publications

References 14 publications

The Prediction, Morphology, and Mechanical Properties of the Polymorphs of Paracetamol

The Prediction, Morphology, and Mechanical Properties of the Polymorphs of Paracetamol

Elastic Constant Calculations for Molecular Organic Crystals

Anisotropic thermal expansion in molecular solids: Theory and experiment onLiBH4

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