Non-Linear vibration of an elastic string

Equations proposed in previous work on the non-linear motion of a string show a basic disagreement, which is here traced to an assumption about the longitudinal displacement u. It is shown that it is neither necessary nor justifiable to assume that u is zero; and also that the velocity of propagation of u disturbances in a string is different from that in an infinite medium, although this difference is usually negligible. After formulating the exact equations of motion for the string, a systematic procedure is described for obtaining approximations to these equations to any order, making only the assumption that the strain in the material of the string is small. The lowest order equations in this scheme are non-linear, and are used to describe the response of a string near resonance. Finally, it is shown that in the absence of damping, planar motion of a string is always unstable at sufficiently high amplitudes, the critical amplitude falling to zero at the natural frequency and its subharmonics. The effect of slight damping on this instability is also discussed.

4-(5-Phenyl-1,2,4-triazolo[3,4-a]isoquinolin--yl)benzonitrile

In the title molecule, C23H14N4, the triazoloisoquinoline ring system is nearly planar, with an r.m.s. deviation of 0.038 (2) angstrom and a maximum deviation of -0.030 (2) angstrom from the mean plane of the triazole ring C atom which is bonded to the benzene ring. The benzene and phenyl rings are twisted by 57.65 (8) and 53.60 (9)degrees, respectively, with respect to the mean plane of the triazoloisoquinoline ring system. In the crystal structure, molecules are linked by weak aromatic pi-pi interactions [centroid-centroid distance = 3.8074 (12) angstrom]. In addition, the crystal structure exhibits a nonclassical intermolecular C-H center dot center dot center dot N hydrogen bond.

3-(4-Chlorophenyl)-5-phenyl-1,2,4-triazolo[3,4-a]isoquinoline

In the title molecule, C22H14ClN3, the triazoloisoquinoline ring system is approximately planar, with an r.m.s. deviation of 0.033 (2) angstrom and a maximum departure from the mean plane of 0.062 (1) angstrom for the triazole ring C atom, bonded to the benzene ring. The benzene and phenyl rings are twisted by 57.02 (6) and 62.16 (6)degrees, respectively, to the mean plane of the triazoloisoquinoline ring system. The molecule is stabilized by a weak intramolecular pi-pi interaction [centroid-centroid distance = 3.7089 (10) angstrom] between the benzene and phenyl rings. In the crystal structure, weak intermolecular C-H center dot center dot center dot N hydrogen bonds and C-H center dot center dot center dot pi interactions link the molecules.

(2E)-3-(4-Bromophenyl)-1-(2-methyl-4phenyl-3-quinolyl)prop-2-en-1-one

The conformation about the ethene bond [1.316 (3) angstrom] in the title compound, C25H18BrNO, is E. The quinoline ring forms dihedral angles of 67.21 (10) and 71.68 (10)degrees with the benzene and bromo-substituted benzene rings, respectively. High-lighting the non-planar arrangement of aromatic rings, the dihedral angle formed between the benzene rings is 58.57 (12)degrees.

1-[(2-Chloro-3-quinolyl)methyl]indoline-2,3-dione

In the title compound, C18H11ClN2O2, the isatin and 2-chloro-3-methylquinoline units are both almost planar, with r.m.s.deviations of 0.0075 and 0.0086 angstrom, respectively, and the dihedral angle between the mean planes of the two units is 83.13 (7)degrees. In the crystal, a weak intermolecular C-H center dot center dot center dot O interaction links the molecules into chains along the c axis.

Studies on the conformation of amino acids XII. Energy calculations on prolyl residue

The favoured conformations of the prolyl residue have been obtained by calculating their potential energies arising from bond-angle strain, torsion-angle strain, non-bonded and electrostatic interatomic energies. In addition to the five membered ring, the peptide unit at the amino end (with ω = 180°) and the C′ atom at the carboxyl end have been taken into account. It is found that there are two local minima in the configurational space of the parameters defining the conformation, as is actually observed-one (denoted by B) with Cγ displaced on the same side as C′, which is lower in energy than the other (denoted by A) with Cγ displaced on the opposite side of C′. The other four atoms Cδ, N, Cα, Cβ are nearly in a plane. The conformations of minimum energy (for both A and B) have bond angles very close to the mean observed values while the torsion angles are well within the range observed in various structures for each type. Taking into account the fact that the influence of neighbouring molecules in a crystal structure may make the conformation of a molecule different from the minimal one, the ranges of the conformational parameters for which the energy is within 0.6 kcal/mole above the minimum value (called the "most probable range") and within 1.2 kcal/mole (called the "probable range") have been determined. The ranges thus obtained, agree well with observation, and most of the observed data lie within the most probable ranges, although differing appreciably from the conformation of minimum energy. The study has been extended, in a limited way, to the conformation of the ring in the amino acid proline. Since the nitrogen is tetrahedral in this (as contrasted with being planar in the prolyl residue), it is found that any one of the five atoms can be out of plane (either way), with the other four lying nearly in a plane. These correspond to low energy conformations (up to 1.2 kcal/mole above the minimum). One such example, in which the Cα atom is out of plane is known for dl-proline · HCl. It is also shown that in these calculations energies due to bond length distortions can be neglected to a good degree of approximation, provided the 'best' values of the bond lengths for the particular compound are used in the theoretical calculations.

Raman spectrum of triglycine selenate (G3Se), [(NH2CH2COOH)3 H2SeO4]

The Raman spectrum of a single crystal of triglycine selenate G3Se which is ferroelectric below 22° C. has been photographed using λ 2537 excitation. 42 Raman lines have been recorded of which 6 belong to the lattice spectrum, 3 are due to NH...O oscillations and the remaining 33 are due to internal oscillations of the ions of glycine and SeO4--. There is a close similarity between the spectrum of triglycine selenate and the spectrum of its isomorph, triglycine sulphate, the frequency shifts due to the SO4-- ion being replaced by the frequency shifts due to the SeO4-- ion. The existence of glycine in the zwitterion form in the structure of G3Se is substantiated by the appearance in the Raman spectrum of lines which are attributable to NH3+ groups and COO- groups. The appearance of the additional C-H line at 2982 cm.-1 in the spectrum of triglycine selenate which is absent in the spectrum of α-glycine indicates the existence of planar monoprotonated glycine also in the structure, as indicated by X-ray studies.

Aspects of tautomerism. Part III. A new dimerisation reaction of pseudo-acid chlorides

Pseudo-acid chlorides of five 4′-substituted o-benzoylbenzoic acids are converted into a mixture of dilactones with sodium iodide in acetone. The meso-isomer is always formed to a larger extent than the (±)-mixture. These results imply that the radicals involved are not planar.

Nitrosation of N,N′-ethylenebis-(acetylacetoneimine) complexes of copper (II) and nickel(II) and characterization of the products

Isonitroso derivatives of copper(II) and nickel(II) complexes of N,N′-ethylenebis(acetylacetoneimine) have been prepared by nitrosation of the respective complexes using nitric oxide as well as nitrite ion. The condensation of isonitrosoacetylacetone in the presence and in the absence of nickel(II) has been investigated. The i.r. and electronic spectra and magnetic moment of the nickel(II) and copper(II) complexes have been studied. The nature of bonding of the ligand to the metal ion is discussed. The complexes have planar structures.

Methyl 1-methyl-1H-1,2,3-triazole-4-carboxylate

The title molecule, C5H7N3O2, has an almost planar conformation, with a maximum deviation of 0.043 (3) angstrom, except for the methyl H atoms. In the crystal structure, intermolecular C-H center dot center dot center dot O hydrogen bonds link the molecules into layers parallel to the bc plane. Intermolecular pi-pi stacking interactions [centroid-centroid distances = 3.685 (2) and 3.697 (2) angstrom] are observed between the parallel triazole rings.

Nickel(II) complexes of 1-benzyl-2-phenylbenzimidazole

Nickel(II) complexes of 1-benzyl-2-phenylbenzimidazole (BPBI) of the general formula [Ni(BPBI)2X2](X=Cl-, Br-, NCS- or NO3-) have been prepared and their magnetic moments, i.r. and electronic spectra studied. [Ni(BPBI)2Cl2] has a pseudotetrahedral structure while [Ni(BPBI)2 Br2] exists as square planar and speudotetrahedral isomers. [Ni(BPBI)2I2] and [NI(BPBI)2(NCS)2] have square planar stereochemistry. The nitrato complex [Ni(BPBI)2(NO)3)2] exists in two different octahedral modifications in the solid state.

Monte Carlo simulations of molecular clusters in nucleation

A better understanding of the limiting step in a first order phase transition, the nucleation process, is of major importance to a variety of scientific fields ranging from atmospheric sciences to nanotechnology and even to cosmology. This is due to the fact that in most phase transitions the new phase is separated from the mother phase by a free energy barrier. This barrier is crossed in a process called nucleation. Nowadays it is considered that a significant fraction of all atmospheric particles is produced by vapor-to liquid nucleation. In atmospheric sciences, as well as in other scientific fields, the theoretical treatment of nucleation is mostly based on a theory known as the Classical Nucleation Theory. However, the Classical Nucleation Theory is known to have only a limited success in predicting the rate at which vapor-to-liquid nucleation takes place at given conditions. This thesis studies the unary homogeneous vapor-to-liquid nucleation from a statistical mechanics viewpoint. We apply Monte Carlo simulations of molecular clusters to calculate the free energy barrier separating the vapor and liquid phases and compare our results against the laboratory measurements and Classical Nucleation Theory predictions. According to our results, the work of adding a monomer to a cluster in equilibrium vapour is accurately described by the liquid drop model applied by the Classical Nucleation Theory, once the clusters are larger than some threshold size. The threshold cluster sizes contain only a few or some tens of molecules depending on the interaction potential and temperature. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range, as predicted by the McGraw-Laaksonen scaling law. By calculating correction factors to Classical Nucleation Theory predictions for the nucleation barriers of argon and water, we show that the corrected predictions produce nucleation rates that are in good comparison with experiments. For the smallest clusters, the deviation between the simulation results and the liquid drop values are accurately modelled by the low order virial coefficients at modest temperatures and vapour densities, or in other words, in the validity range of the non-interacting cluster theory by Frenkel, Band and Bilj. Our results do not indicate a need for a size dependent replacement free energy correction. The results also indicate that Classical Nucleation Theory predicts the size of the critical cluster correctly. We also presents a new method for the calculation of the equilibrium vapour density, surface tension size dependence and planar surface tension directly from cluster simulations. We also show how the size dependence of the cluster surface tension in equimolar surface is a function of virial coefficients, a result confirmed by our cluster simulations.

1-[(2-Chloro-8-methylquinolin-3-yl)methyl]pyridin-2(1H)-one

In the title compound, C16H13ClN2O, the quinoline ring system is approximately planar [maximum deviation 0.021 (2) angstrom] and forms a dihedral angle of 85.93 (6)degrees with the pyridone ring. Intermolecular C-H center dot center dot center dot O hydrogen bonding, together with weak C-H center dot center dot center dot pi and pi-pi interactions [centroid-to-centroid distances 3.5533 (9) and 3.7793 (9) angstrom], characterize the crystal structure.

2-Chloro-8-methyl-3-[(pyrimidin-4-yloxy)methyl]quinoline

In the title compound, C15H12ClN3O, the quinoline ring system is essentially planar, with a maximum deviation of 0.017 (1) angstrom. The crystal packing is stabilized by pi-pi stacking interactions between the quinoline rings of adjacent molecule, with a centroid-centroid distance of 3.5913 (8) angstrom. Aweak C-H center dot center dot center dot pi contact is also observed between molecules.

5-(4-Chlorophenyl)-3-(2,4-dimethylthiazol-5-yl)-1,2,4-triazolo[3,4-a]isoquinoline

In the title molecule, C21H15ClN4S, the triazoloisoquinoline ring system is approximately planar, with an r.m.s. deviation of 0.054 (2) angstrom and a maximum deviation of 0.098 (2) angstrom from the mean plane for the triazole ring C atom that is bonded to the thiazole ring. The thiazole and benzene rings are twisted by 66.36 (7) and 56.32 (7)degrees respectively, with respect to the mean plane of the triazoloisoquinoline ring system. In the crystal structure, molecules are linked by intermolecular C-H center dot center dot center dot N interactions along the a axis. The molecular conformation is stabilized by a weak intramolecular pi-pi interaction involving the thiazole and benzene rings, with a centroid-centroid distance of 3.6546 (11) angstrom . In addition, two other intermolecular pi-pi stacking interactions are observed, between the triazole and benzene rings and between the dihydropyridine and benzene rings [centroid-centroid distances = 3.6489 (11) and 3.5967 (10) angstrom, respectively].