Anisotropic displacement parameters for molecular crystals from periodic Hartree–Fock and density functional theory calculations

Abstract

Fully periodic Hartree-Fock and density functional theory calculations have been used to compute the anisotropic displacement parameters (ADPs) of molecular crystals at different temperatures by using the CRYSTAL code. Crystalline urea was adopted as a benchmark system to investigate the dependence on basis set and Hamiltonian. The results were compared with ADPs derived from neutron diffraction experiments. The approach can estimate the internal ADPs, corresponding to the contributions of high-frequency intramolecular vibrations, and for these internal contributions the results are almost independent of the basis set and Hamiltonian. Much larger variations and discrepancies from neutron diffraction experiments are seen for the external, low-frequency modes, which become dominant at higher temperatures. The approach was then tested on benzene and urotropine. Finally, ADPs of l-alanine were predicted at the B3LYP/6-31G(d,p) level of theory. The total ADPs, including low-frequency external modes, are underestimated, but can be brought into good agreement with the experimental ADPs by introducing a Grü neisen parameter, which partly accounts for anharmonicity of the potential energy surface, but likely also contains contributions from other deficiencies of the calculations.

Raman spectroscopic features of the neutral vacancy in diamond from ab initio quantum-mechanical calculations

“…ADPs offer a convenient way to rationalize such atomic motions; for a given temperature, an ellipsoid is associated with each atom, which provides information on the probability of finding that atom displaced from the equilibrium position. A 3 Â 3 Cartesian matrix representation of the atomic ADPs can be given, according to 47,48 …”

Thermal properties of molecular crystals through dispersion-corrected quasi-harmonic ab initio calculations: the case of urea

“…[10][11][12][13][14][15][16][17][18] However, once a reliable and balanced description of the various chemical interactions has been achieved by means of any of the above-mentioned quantum-chemical methods, the extension of their applicability to more complex properties of technological and industrial relevance, which would greatly increase their predictiveness, such as mechanical, elastic, optical and thermodynamic responses, [19][20][21][22] has to be performed. Apart from the intrinsic high degree of complexity of the required theoretical techniques and algorithms, the main difficulty here is represented by the fact that most of those properties are largely affected by thermal effects, [23][24][25] even at room temperature, such as zero-point energy, harmonic and anharmonic thermal nuclear motion, thermal lattice expansion, etc.…”

Validation of convolution approximation to the thermal-average electron density

“…It is to be emphasized that our analysis is restricted to internal (intra-molecular) vibrations of relatively high frequencies and thus low amplitudes. The inclusion of external modes (translation and rotation within the molecular mean field model [42]) or acoustic modes (within lattice dynamics [43]) is most likely to further demolish characteristic features of the static topology. A more general conclusion is that smearing the theoretical ED to compare it with the experimental ED deserves more attention than it has received during the most recent X-ray charge density era.…”