Multi-temperature X-ray Diffraction Research Articles

Refinement of multiconformer ensemble models from multi-temperature X-ray diffraction data.

Conformational ensembles underlie all protein functions. Thus, acquiring atomic-level ensemble models that accurately represent conformational heterogeneity is vital to deepen our understanding of how proteins work. Modeling ensemble information from X-ray diffraction data has been challenging, as traditional cryo-crystallography restricts conformational variability while minimizing radiation damage. Recent advances have enabled the collection of high quality diffraction data at ambient temperatures, revealing innate conformational heterogeneity and temperature-driven changes. Here, we used diffraction datasets for Proteinase K collected at temperatures ranging from 313 to 363K to provide a tutorial for the refinement of multiconformer ensemble models. Integrating automated sampling and refinement tools with manual adjustments, we obtained multiconformer models that describe alternative backbone and sidechain conformations, their relative occupancies, and interconnections between conformers. Our models revealed extensive and diverse conformational changes across temperature, including increased bound peptide ligand occupancies, different Ca2+ binding site configurations and altered rotameric distributions. These insights emphasize the value and need for multiconformer model refinement to extract ensemble information from diffraction data and to understand ensemble-function relationships.

Multi-temperature X-ray diffraction study of a reversible structural phase transition in the high-temperature polymorph of Ce2Rh2Ga compound

A recently investigated HT-Ce2Rh2Ga was found to exhibit a magnetic phase transition at 128.5 K. A comprehensive multi-temperature investigation in the 85–400 K temperature range showed that the compound undergoes a structural phase transition as well. Upon cooling below 123.2 K its crystal symmetry changes from Cmce to C2/m being accompanied by non-merohedral twinning. Both structural transformations are reversible with a small hysteresis furthermore. The temperature of the structural phase transition was detected by anomalies in temperature dependences of unit cell dimensions, interatomic distances, and atomic displacement parameters. Negative thermal expansion along the c-axis was revealed in the range 92.7–170 K. When cooled to 200 K, Ce and Rh atoms converge to a distance sufficient for structural changes to become qualitative. Upon further cooling to 145 K, this interaction affects positions of all the atoms in the structure, leading to anisotropy of earlier equivalent interatomic distances and a sharp anomalous increase in atomic displacement parameters, the dynamics of which deviates more and more from the theoretical dependences in the Einstein and Debye approximations.

X-ray diffraction data as a source of the vibrational free-energy contribution in polymorphic systems.

In this contribution we attempt to answer a general question: can X-ray diffraction data combined with theoretical computations be a source of information about the thermodynamic properties of a given system? Newly collected sets of high-quality multi-temperature single-crystal X-ray diffraction data and complementary periodic DFT calculations of vibrational frequencies and normal mode vectors at the Γ point on the yellow and white polymorphs of di-methyl 3,6-di-chloro-2,5-di-hydroxy-terephthalate are combined using two different approaches, aiming to obtain thermodynamic properties for the two compounds. The first approach uses low-frequency normal modes extracted from multi-temperature X-ray diffraction data (normal coordinate analysis), while the other uses DFT-calculated low-frequency normal mode in the refinement of the same data (normal mode refinement). Thermodynamic data from the literature [Yang et al. (1989), Acta Cryst. B45, 312-323] and new periodic ab initio DFT supercell calculations are used as a reference point. Both approaches tested in this work capture the most essential features of the systems: the polymorphs are enantiotropically related, with the yellow form being the thermodynamically stable system at low temperature, and the white form at higher temperatures. However, the inferred phase transition temperature varies between different approaches. Thanks to the application of unconventional methods of X-ray data refinement and analysis, it was additionally found that, in the case of the yellow polymorph, anharmonicity is an important issue. By discussing contributions from low- and high-frequency modes to the vibrational entropy and enthalpy, the importance of high-frequency modes is highlighted. The analysis shows that larger anisotropic displacement parameters are not always related to the polymorph with the higher vibrational entropy contribution.

Evidence of Low-Temperature Phase Transition in Tetracene–Tetracyanoquinodimethane Complex

Multitemperature X-ray diffraction and vibrational spectroscopic studies of tetracene–tetracyanoquinodimethane (TCNQ) charge transfer cocrystals have revealed the existence of a reversible phase transition in the temperature interval 150–200 K. It was shown that a new monoclinic polymorph of the cocrystal exists above that temperature range, with a structure that is very similar to the one previously described in the literature as being triclinic. The crystal structures of the two polymorphs were also calculated with periodic density functional theory quantum chemical calculations, and their geometries were compared to the experimental ones. The degree of charge transfer in both polymorphs was characterized using alteration in the bond lengths of the TCNQ molecule and frequency shifts obtained from vibrational spectroscopy data.

Vibrational smearing of the electron density as function of the strength and directionality of interatomic interactions: nonvalent interactions of a nitro group within an island-type crystal [Fe(NO)2(SC6H4NO2)

We consider the static and dynamic characteristics of interatomic bonding in the region of nonvalent interactions of a nitro group in the crystal of complex [Fe(NO)2(SC6H4NO2)]2. Based on results obtained by modeling vibrations within the framework of the density functional theory and those of multitemperature X-ray diffraction studies, a purely vibrational nature of the abnormally large atomic displacement ellipsoid of one of the O atoms of the nitro group was revealed and a model for the influence of peculiar features of intermolecular bonding on the observed dynamics was suggested. Using topological analysis of the experimental electron density function, we studied the nature of nonvalent intermolecular interactions of the nitro group and evaluated their strength and directionality in the equilibrium state. The dependence of the “pseudodegeneracy” region of atom—atom interaction on the nature of the interaction revealed and a method for determining the vibrational smearing of interactions was suggested, which allows one to analyze the stability of the connectivity graph of the crystal.

Thermodynamic parameters of the pedal motion in the crystal structures of two bromomethylated azobenzenes

Differences in the thermodynamic parameters of the central N-atoms' pedal motion in two bromomethylated azobenzenes were determined by multi-temperature X-ray diffraction, and rationalized by packing studies.

Methodical aspects of experimental studies for the relationship of static and dynamic features of crystal structure: application of various atomic scattering factors to study the vibrational characteristics of molecular crystals

The X-ray diffraction studies of one of chloroacetic acid polymorphs with two independent molecules in the unit cell made it possible to test different methods for description of the electron density distribution anisotropy (independent atom model, multipole refinement, and "invarioms") when refining the atomic displacement parameters to reveal subtle distinctions of vibrational characteristics of independent molecule. It was shown that features of molecular motion, derived by modeling of matrices of mean-squared displacement amplitudes against multitemperature X-ray diffraction data using the independent atom model and approach of "invarioms," are qualitatively the same, while their relationship with the static characteristics of the crystal structure of chloroacetic acid can be explained using topological analysis of the charge density distribution and ONIOM quantum chemical calculations. The total energy of intermolecular interactions of one of the independent molecules, whose geometry is less favorable in the isolated state, is higher, which is consistent with a lower contribution of the intermolecular vibration mode is its low-frequency vibrations.

Conjugation effects in a para-nitroaniline molecule and its structural non-rigidity

A thorough investigation of the spatial and electronic structures of p-nitroaniline using the precision X-ray diffraction analysis and quantum chemical calculations in the framework of the “Atoms in Molecules” theory revealed that the conjugation of functional groups with the benzene ring is small and amino group flattening in crystal compared to the gas phase is caused by the inductive effects. The structure non-rigidity of the nitro group was observed, which appears as its dynamic disordering confirming that the conjugation with the benzene ring is energetically unfavorable compared to the intrinsic conjugation effects. In case of the amino group, only the static temperature-independent disorder as a superposition of two non-planar configurations can be proposed according to the results of normal coordinate analysis by the simulation of mean-square amplitude matrixes using multi-temperature X-ray diffraction data.

Temperature dependence of the thermodynamic parameters of cobalt(II) clathrochelate: X-ray diffraction and calorimetric characteristics of the low temperature structural phase transition

The temperature dependence of heat capacity of the polycrystalline sample of cobalt(II) clathrochelate in a range of 6–300 K is studied. Based on the smoothed dependence C p(T), the entropy and enthalpy values in a temperature range of 8–300 K and their standard values at 298.15 K are calculated. In the C p(T) curve in a range of 50–70 K, a process is recorded whose entropy and enthalpy are 1.2 J·(K·mol−1) and 68 J·mol−1 respectively. A comparison of the results with the data of a multitemperature X-ray diffraction study makes it possible to attribute this process to the structural phase transition.

Temperature dependence of one-dimensional hydrogen bonding in morpholinium hydrogen chloranilate studied by 35Cl nuclear quadrupole resonance and multi-temperature X-ray diffraction

The temperature dependence of (35)Cl NQR frequencies and the spin-lattice relaxation times T(1) has been measured in the wide temperature range of 4.2-420 K for morpholinium hydrogen chloranilate in which a one-dimensional O-HO hydrogen-bonded molecular chain of hydrogen chloranilate ions is formed. An anomalous temperature dependence of the NQR frequencies was analyzed to deduce a drastic temperature variation of the electronic state of the hydrogen-bonded molecular chain. The hydrogen atom distribution in the OHO hydrogen bond is discussed from the results of NQR as well as multi-temperature X-ray diffraction. Above ca. 330 K, the T(1) showed a steep decrease with an activation energy of ca. 70 kJ mol(-1) and with an isotope ratio (37)Cl T(1)/(35)Cl T(1) = 0.97 ± 0.2. The orientational change of the z axis of electric field gradient tensor in conjunction with the hydrogen transfer between adjacent hydrogen chloranilate ions is suggested as a possible relaxation mechanism.

Elucidating Negative Thermal Expansion in MOF-5

Multi-temperature X-ray diffraction studies show that twisting, rotation, and libration cause negative thermal expansion (NTE) of the nanoporous metal−organic framework MOF-5, Zn4O(1,4-benzenedicarboxylate)3. The near-linear lattice contraction is quantified in the temperature range 80−500 K using synchrotron powder X-ray diffraction. Vibrational motions causing the abnormal expansion behavior are evidenced by shortening of certain interatomic distances with increasing temperature according to single-crystal X-ray diffraction on a guest-free crystal over a broad temperature range. Detailed analysis of the atomic positional and displacement parameters suggests two contributions to cause the effect: (1) local twisting and vibrational motion of the carboxylate groups and (2) concerted transverse vibration of the linear linkers. The vibrational mechanism is confirmed by calculations of the dynamics in a molecular fragment of the framework.

Hydrogen bonding in 1,2-diazine–chloranilic acid (2 : 1) studied by a 14N nuclear quadrupole coupling tensor and multi-temperature X-ray diffraction

Protons involved in the H-bond system in 1,2-diazine-chloranilic acid (2 : 1) are assumed to be in jumping motion in the double-minimum potential corresponding to the two extreme electronic states of O-H...N and O-...H-N+. 14N nuclear quadrupole coupling constants were determined by 1H-14N nuclear quadrupole double resonance. Assuming that the observed coupling constants are result of a fast exchange of the two extreme electronic states, the coupling constants for each state were estimated by use of the equilibrium populations of the two extreme states determined from multi-temperature X-ray single-crystal diffraction. It was suggested that not only the population but also the electron distribution of the extreme electronic states itself changes with temperature.

From Proton Disorder to Proton Migration: A Continuum in the Hydrogen Bond of a Proton Sponge in the Solid State

The crystal structure of the ionic complex of 1,8-bis(dimethylamino)naphthalene (DMAN) and 4,5-dichlorophthalic acid has been investigated using a multi-temperature X-ray diffraction approach. The two short intramolecular hydrogen bonds exhibit different behaviors, with the [O···H···O]- hydrogen bond appearing approximately centered throughout the experiment. The [N···H···N]+ hydrogen bond, on the other hand, exhibits a complicated temperature-dependent behavior, with disordered electron density being observed at lower temperatures, with apparent migration at higher temperatures. This continuum can be explained simply in terms of the changing local environment of the [N···H···N]+ hydrogen bond induced by lattice expansion. The related complex of DMAN with 3,4-furandicarboxylic acid shows no equivalent effects; this is consistent with the explanation proposed.

Designing Hydrogen Bonds with Temperature-Dependent Proton Disorder: The Effect of Crystal Environment

Two crystal structures, each containing a 4-dimethylaminobenzoic acid dimer (4-DABA), have been studied by multitemperature X-ray diffraction methods. In form I of pure 4-DABA, temperature-dependent proton disorder is observed. In the molecular complex with 3,5-dinitrobenzoic acid, no such disorder is observed in the 4-DABA dimer but is observed in the 3,5-dinitrobenzoic acid dimer. The effect of the crystal environment perturbing the local symmetry of apparently similar molecular structures is discussed in relation to this change in observed proton disorder.

Looking for structural phase transitions in the colossal magnetoresistive thiospinel FeCr 2S 4 by a multi-temperature single-crystal X-ray diffraction study

A multi-temperature X-ray diffraction study was performed on the colossal magnetoresistive thiospinel FeCr 2S 4 to find out if structural phase transitions are associated with the magnetic transitions of the two Fe and Cr sublattices. The temperature dependence of the cell parameters was carefully screened, and the crystal structure was determined at four different temperatures. The present X-ray diffraction experiment, the first performed on a single crystal, confirms that bulk FeCr 2S 4 is not subject to structural phase transformations in the temperature range 293–23 K. The occurrence of the forbidden (0 0 2) reflection and the non-stoichiometric sample composition are discussed.

Multitemperature X-ray diffraction analysis in the study of phase transitions, molecular dynamics and crystal disorder

Multitemperature X-ray diffraction analysis in the study of phase transitions, molecular dynamics and crystal disorder

Observation of 4f electron transfer from Ce to B6 in the Kondo crystal CeB6 and its mechanism by multi-temperature X-ray diffraction.

Electron density distributions (EDD) in CeB(6) were measured by X-ray diffraction at 100, 165, 230 and 298 K. Analysis with a weak-field model, in which the spin-orbit interaction dominates the energy splitting of the 4f levels, revealed that more 4f electrons were donated from Ce to B(6) at the lower temperature. Donated electrons localize around the B-B bonds connecting B(6) octahedra. The localized electrons and an expansion of the outermost 5p orbitals change the effective atomic potentials and enhance the anharmonic vibration (AHV) of constituent atoms at lower temperature. Enhanced AHV increases the entropy and makes the electron donation inevitable. Changes in crystal structure, EDD, electron configuration and AHV are found to be closely correlated with one another and the mechanism of the electron transfer in the Kondo crystal CeB(6) in the studied temperature range was elucidated. This is, to the authors' knowledge, the first multi-temperature measurement of EDD that elucidates a mechanism of change from the temperature dependence of the EDD. Parameters change consistently at all the temperatures except 298 K, at which the excited states Gamma(7) of the Ce 4f states have significant electron population. The thermal excitation to Gamma(7) levels expands the B(6) octahedra, since Gamma(7) has main lobes along <111> or from Ce to the centre of B(6) octahedra. The energy gap between the ground state Gamma(8) and Gamma(7) was calculated to be 470 K from the ratio of electron populations of both states. The present experiment opens the door to accurate X-ray EDD analyses of rare earth complexes.