Conformational Analysis of [60]PCBM from DFT Simulations of Electronic Energies, Bond Strain and the 13C NMR Spectrum: Input Geometry Determination and Ester Bond Rotation Dynamics

With the aim of determining the best input geometry for DFT calculations of [60]PCBM, the geometry of 24 chemically possible [60]PCBM conformers were optimised and their electronic energies and average bond strains were determined. A DFT analysis of the relevant dihedral angles provided insights into the dynamical behaviour of the ester group through sterically restricted bond rotations. In addition, the 13C NMR spectra of the six better performing conformers were simulated and compared with an experiment. There is a close correlation between average bond strain, total electronic energy and mean absolute error of the simulated 13C NMR spectra of the ester carbons. The best overall candidate conformer for the input geometry had the C61-C4, C4-C3 and C3-C2 single bonds of the alkyl chain in syn, anti and anti arrangements, respectively, and had the C2-C1 and C1-O single bonds of the ester in syn and anti arrangements, respectively. This contrasts strikingly with most representations of PCBM in the literature, which depict all relevant bonds in anti arrangements.

Control of Chirality, Bond flexing and Anharmonicity in an Electric Field

We located ‘hidden’ S-character chirality in formally achiral glycine using a vector-based interpretation of the total electronic charge density distribution. We induced the formation of stereoisomers in glycine by the application of an electric field. Control of chirality was indicated from the proportionate response to a non-structurally distorting electric field. The bond-flexing was determined to be a measure of bond strain, which could be a factor of three lower or higher, depending on the direction of the electric field, than in the absence of the electric field. The bond-anharmonicity was found to be approximately independent of the electric field. We also compared the formally achiral glycine with the chiral molecules alanine and lactic acid, quantifying the preferences for the S and R stereoisomers. The proportional response of the chiral discrimination to the magnitude and direction of the applied electric field indicated use of the chirality discrimination as a molecular similarity measure.

X-ray diffraction study of distorted perovskites R(Co3/4Ti1/4)O3 (R = La, Pr, Nd, Sm, Eu, Gd, Dy, Ho)

The crystal structure and powder patterns were prepared for the distorted perovskite series R(Co3/4Ti1/4)O3 (R = La, Pr, Nd, Sm, Eu, Gd, Dy, Ho). The R(Co3/4Ti1/4)O3 members are isostructural with each other and are crystallized in the orthorhombic crystal system with space group Pnma, Z = 4. From R = La to Ho, the lattice parameters a range from 5.4614(3) to 5.5368(2) Å, b range from 7.7442(4) to 7.4859(2) Å, and c range from 5.5046(3) to 5.2170(2) Å. The unit-cell volumes, V which range from 232.81(2) to 216.237(11) Å3 follow the trend of “lanthanide contraction”. The structure distortion of these compounds is evidenced in the tilt angles θ, ϕ, and ω, which represent rotations of an octahedron about the pseudo-cubic perovskite [110]p, [001]p and [111]p axes. All three tilt angles increase across the lanthanide series (for R = La to R = Ho: θ increases from 8.34° to 17.00°, ϕ from 6.24° to 8.53°, and ω from 10.41° to 18.96°), indicating a greater octahedral distortion as the ionic radius of R3+ [r(R3+)] decreases. The bond valence sum values for the (Co/Ti) site and the R site of R(Co3/4Ti1/4)O3 reveal no significant bond strain in these compounds. X-ray diffraction patterns of the R(Co3/4Ti1/4)O3 samples were submitted to the Powder Diffraction File.

X-ray diffraction and density functional theory studies of R(Fe0.5Co0.5)O3 (R = Pr, Nd, Sm, Eu, Gd)

The structure of a series of lanthanide iron cobalt perovskite oxides, R(Fe0.5Co0.5)O3 (R = Pr, Nd, Sm, Eu, and Gd), have been investigated. The space group of these compounds was confirmed to be orthorhombic Pnma (No. 62), Z = 4. From Pr to Gd, the lattice parameter a varies from 5.466 35(13) Å to 5.507 10(13) Å, b from 7.7018(2) to 7.561 75(13) Å, c from 5.443 38(10) to 5.292 00(8) Å, and unit-cell volume V from 229.170(9) Å3 to 220.376(9) Å3, respectively. While the trend of V follows the trend of the lanthanide contraction, the lattice parameter “a” increases as the ionic radius r(R3+) decreases. X-ray diffraction (XRD) and transmission electron microscopy confirm that Fe and Co are disordered over the octahedral sites. The structure distortion of these compounds is evidenced in the tilt angles θ, ϕ, and ω, which represent rotations of an octahedron about the pseudocubic perovskite [110]p, [001]p, and [111]p axes. All three tilt angles increase across the lanthanide series (for R = Pr to R = Gd: θ increases from 12.3° to 15.2°, ϕ from 7.5° to 15.8°, and ω from 14.4° to 21.7°), indicating a greater octahedral distortion as r(R3+) decreases. The bond valence sum for the sixfold (Fe/Co) site and the eightfold R site of R(Fe0.5Co0.5)O3 reveal no significant bond strain. Density Functional Theory calculations for Pr(Fe0.5Co0.5)O3 support the disorder of Fe and Co and suggest that this compound to be a narrow band gap semiconductor. XRD patterns of the R(Fe0.5Co0.5)O3 samples were submitted to the Powder Diffraction File.

A new peridynamic formulation with shear deformation for elastic solid

We propose a new peridynamic formulation with shear deformation for linear elastic solid. The key idea lies in subtracting the rigid body rotation part from the total deformation. Based on the strain energy equivalence between classic local model and non-local model, the bond force vector is derived. A new damage rule of maximal deviatoric bond strain for elastic brittle fracture is proposed in order to account for both the tensile damage and shear damage. 2D and 3D numerical examples are tested to verify the accuracy of the current peridynamics. The new damage rule is applied to simulate the propagation of Mode I, II and III cracks.

Intramolecular multi-bond strain: the unrecognized side of the dichotomy of conjugated systems

Apart from the more familiar π-conjugation, there is also significant π–π repulsion which is a kind of unrecognized intramolecular strain and can be quantified with the linear B4H2 model system.