The newtonian limit of hermitian gravity

We construct the gauge invariant potentials of Hermitian Gravity [1] and derive the linearized equations of motion they obey. A comparison reveals a striking similarity to the Bardeen potentials of general relativity. We then consider the response to a point particle source, and discuss in what sense the solutions of Hermitian Gravity reduce to the Newtonian potentials. In a rather intriguing way, the Hermitian Gravity solutions exhibit a generalized reciprocity symmetry originally proposed by Born in the 1930s. Finally, we consider the trajectories of massive and massless particles under the influence of a potential. The theory correctly reproduces the Newtonian limit in three dimensions and the nonrelativistic acceleration equation. However, it differs from the light deflection calculated in linearized general relativity by 25 %. While the specific complexification of general relativity by extension to Hermitian spaces performed here does not agree with experiment, it does possess useful properties for quantization and is well-behaved around singularities as described in [1]. Another form of complex general relativity may very well agree with experimental data.     

ESI‐MS/MS of expanded porphyrins: a look into their structure and aromaticity

Electrospray mass spectrometry/mass spectrometry was used to investigate the gas‐phase properties of protonated expanded porphyrins, in order to correlate those with their structure and conformation. We have selected five expanded meso‐pentafluorophenyl porphyrins, respectively, a pair of oxidized/reduced fused pentaphyrins (22 and 24 π electrons), a pair of oxidized/reduced regular hexaphyrins (26 and 28 π electrons) and a regular doubly N‐fused hexaphyrin (28 π electrons). The gas‐phase behavior of the protonated species of oxidized and reduced expanded porphyrins is different. The oxidized species (aromatic Hückel systems) fragment more extensively, mainly by the loss of two HF molecules. The reduced species (Möbius aromatic or Möbius‐like aromatic systems) fragment less than their oxidized counterparts because of their increased flexibility. The protonated regular doubly fused hexaphyrin (non‐aromatic Hückel system) shows the least fragmentation even at higher collision energies. In general, cyclization through losses of HF molecules decreases from the aromatic Hückel systems to Möbius aromatic or Möbius‐like aromatic systems to non‐aromatic Hückel systems and is related to an increase in conformational distortion. Copyright © 2016 John Wiley & Sons, Ltd.     

Complexation of divalent metal ions with diols in the presence of anion auxiliary ligands: zinc-induced oxidation of ethylene glycol to glycolaldehyde by consecutive hydride ion and proton shifts

Ternary complexes of the type AH???M(2+)???L(-) (AH?=?diol, including diethylene and triethylene glycol, M?=?Ca, Mn, Fe, Co, Ni, Cu and Zn and auxiliary anion ligand L(-) =?CH(3)COO(-), HCOO(-) and Cl(-)) have been generated in the gas phase by MALDI and ESI, and their dissociation characteristics have been obtained. Use of the auxiliary ligands enables the complexation of AH with the divalent metal ion without AH becoming deprotonated, although A(-)???M(2+) is often also generated in the ion source or after MS/MS. For M?=?Ca, dissociation occurs to AH?+?M(2+)???L(-) and/or to A(-)???M(2+) + LH, the latter being produced from the H-shifted isomer A(-) ???M(2+)???LH. For a given ligand L(-), the intensity ratio of these processes can be interpreted (barring reverse energy barriers) in terms of the quantity PA(A(-)) - Ca(aff) (A(-)), where PA is the proton affinity and Ca(aff) is the calcium ion affinity. Deuterium labeling shows that the complex ion HOCH(2)CH(2) OH???Zn(2+)???(-)OOCCH(3), in addition to losing acetic acid (60 Da), also eliminates glycolaldehyde (HOCH(2)CH=O, also 60 Da); it is proposed that these reactions commence with a hydride ion shift to produce the ion-dipole complex HOCH(2)CHOH(+)??? HZnOOCCH(3), which then undergoes proton transfer and dissociation to HOCH(2)CH=O?+?HZn(+)???O?=?C(OH)CH(3). In this reaction, ethylene glycol is oxidized by consecutive hydride ion and proton shifts. A minor process leads to loss of the isomeric species HOCH=CHOH.     

Complexation of divalent metal ions with diols in the presence of anion auxiliary ligands: zinc‐induced oxidation of ethylene glycol to glycolaldehyde by consecutive hydride ion and proton shifts

Ternary complexes of the type AH???M²⁺???L^– (AH = diol, including diethylene and triethylene glycol, M = Ca, Mn, Fe, Co, Ni, Cu and Zn and auxiliary anion ligand L^– = CH₃COO^–, HCOO^– and Cl^–) have been generated in the gas phase by MALDI and ESI, and their dissociation characteristics have been obtained. Use of the auxiliary ligands enables the complexation of AH with the divalent metal ion without AH becoming deprotonated, although A^–???M²⁺ is often also generated in the ion source or after MS/MS. For M = Ca, dissociation occurs to AH + M²⁺???L^– and/or to A^–???M²⁺ + LH, the latter being produced from the H‐shifted isomer A^–???M²⁺???LH. For a given ligand L^–, the intensity ratio of these processes can be interpreted (barring reverse energy barriers) in terms of the quantity PA(A^–) – Ca_aff(A^–), where PA is the proton affinity and Ca_aff is the calcium ion affinity. Deuterium labeling shows that the complex ion HOCH₂CH₂OH???Zn²⁺???^–OOCCH₃, in addition to losing acetic acid (60 Da), also eliminates glycolaldehyde (HOCH₂CH=O, also 60 Da); it is proposed that these reactions commence with a hydride ion shift to produce the ion–dipole complex HOCH₂CHOH⁺??? HZnOOCCH₃, which then undergoes proton transfer and dissociation to HOCH₂CH=O + HZn⁺???O = C(OH)CH₃. In this reaction, ethylene glycol is oxidized by consecutive hydride ion and proton shifts. A minor process leads to loss of the isomeric species HOCH=CHOH. Copyright © 2012 John Wiley & Sons, Ltd.     

On the theoretical problems in constructing interactions involving higher-spin massless particles

It is shown that a gauge theory of self-interacting massless spin-3 particles which is analogous to Yang-Mills or the theory of gravity does not exist. A way out may be the existence of an interacting infinite family of massless particles of various spins. The first-order interactions which are possible between such particles show a remarkable structure. This is established by explicit construction. Detailed results are obtained for the possible algebraic structures which one may obtain for gauge theories which are induced from the gauge invariance of free lagrangians.     

Gas phase ion chemistry of methyl acetate,methyl propanoate and their enolic tautomers. An experimental approach

From a combination of isotopic substitution, time-resolved measurements and sequential collision experiments, it was proposed that whereas ionized methyl acetate prior to fragmentation rearranges largely into \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 \mathop {\rm C}\limits^ + ({\rm OH}){\rm O}\mathop {\rm C}\limits^{\rm .} {\rm H}_2 $\end{document}, in contrast, methyl propanoate molecular ions isomerize into \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^. {\rm H}_2 {\rm CH}_2 \mathop {\rm C}\limits^ + ({\rm OH}){\rm OCH}_3 $\end{document}. Metastably fragmenting methyl acetate molecular ions are known predominantly to form H₂?OH together with \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 - \mathop {\rm C}\limits^ + = {\rm O} $\end{document}, whereas ionized methyl propanoate largely yields H₃CO˙ together with \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 {\rm CH}_2 - \mathop {\rm C}\limits^ + = {\rm O} $\end{document}. The observations were explained in terms of the participation of different distonic molecular ions. The enol form of ionized methyl acetate generates substantially more H₃CO˙ in admixture with H₂?OH than the keto tautomer. This is ascribed to the rearrangement of the enol ion to the keto form being partially rate determining, which results in a wider range of internal energies among metastably fragmenting enol ions. Extensive ab initio calculations at a high level of theory would be required to establish detailed reaction mechanisms.     

Double collision experiments

A variety of double collision experiments, whereby fast species undergo collisional interactions in two distinct regions of a mass spectrometer, are described. These include two-stage charge reversal of negative ions, two-stage double electron transfer from targets to cations, neutralization-reionization experiments as well as delayed analysis of organic cations formed in a one-step charge reversal of anions. Experiments have been performed on a number of systems of current interest in gas-phase ion chemistry. It is concluded that autoelectron detachment of benzyl anions leads to benzyl radicals, whereas the collisionally induced electron detachment produces a mixture of benzyl and tropyl radicals. By contrast, electron detachment from [H₃CNH]^? is not a metastable process and occurs only after excitation to produce H₃CNH˙ radicals, which do not rearrange into the thermodynamically more stable H₂CNH₂˙. It is shown that in the double electron transfer reactions H⁺ + Xe→H˙ + Xe⁺˙ and H˙ + Xe→H^? + Xe⁺˙, excited states are produced. From double collision experiments on methyl formate ions, it is concluded that the non-decomposing ions have undergone rearrangement on the time-scale of 10 μs into the distonic isomer, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm H} - \mathop {\rm C}\limits^ + ({\rm OH}){\rm O}\mathop {\rm C}\limits^. {\rm H}_2 $\end{document}. Finally, it is shown that short-lived (<0.2 μs) [H₂, C, N]⁺ ions generated by charge-reversal of [H₂CN]^? have the [H₂CN]⁺ structure, whereas most of the long-lived (10 μs) ions have the [HCNH]⁺ structure.     

On the mechanism of isomerization in the esters of some α,β-unsaturated carboxylic acids—II

The effect of a phenyl group on the mechanisms of isomerization in the ionized methyl esters of simple α,β-unsaturated acids (methyl acrylate and related compounds) has been investigated with the aid of deuterium labelling as well as information from mass analysed ion kinetic energy spectra and first field free region metastable peak shapes. Substitution of a hydrogen atom of the O? CH₃ group by a phenyl group (benzyl acrylate and homologues) greatly enhances the rate of [ester] → [acid] isomerizations (loss of H₂O and COOH˙). It is inferred that this is due to an accelerating effect of the phenyl group on the first and the third steps (ring opening of the key intermediate ion which has the structure of the ionized enol form of γ-butyrolactone) of the reaction whose mechanism is basically the same as that in methyl acrylate. A phenyl group present at the α- or β-position of the vinylic double bond appears to suppress the [ester] → [acid] isomerization in some compounds by promoting other reactions or opening up a new reaction pathway, i.e. the loss of CH₂O from ionized methyl atropate for which mechanisms are proposed.