Comments on matter collineations of plane symmetric, cylindrically symmetric and spherically symmetric spacetimes

Comments are made on some recently published papers on matter collineations of plane symmetric, cylindrically symmetric and spherically symmetric spacetimes

Toward Reliable Modeling of S-nitrosothiol Chemistry: Structure and Properties of Methyl Thionitrite (CH3SNO), an S-nitrosocysteine Model

Methyl thionitrite CH3SNO is an important model of S-nitrosated cysteine aminoacid residue (CysNO), a ubiquitous biological S-nitrosothiol (RSNO) involved in numerous physiological processes. As such, CH3SNO can provide insights into the intrinsic properties of the —SNO group in CysNO, in particular, its weak and labile S—N bond. Here, we report an ab initio computational investigation of the structure and properties of CH3SNO using a composite Feller-Peterson-Dixon scheme based on the explicitly correlated coupled cluster with single, double, and perturbative triple excitations calculations extrapolated to the complete basis set limit, CCSD(T)-F12/CBS, with a number of additive corrections for the effects of quadruple excitations, core-valence correlation, scalar-relativistic and spin-orbit effects, as well as harmonic zero-point vibrational energy with an anharmonicity correction. These calculations suggest that the S—N bond in CH3SNO is significantly elongated (1.814 Å) and has low stretching frequency and dissociation energy values, νS—N = 387 cm−1 and D0 = 32.4 kcal/mol. At the same time, the S—N bond has a sizable rotation barrier, △ role= presentation style= display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 20px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px 2px 0px 0px; margin: 0px; position: relative; \u3e△△E0≠ role= presentation style= display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 12px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px 2px 0px 0px; margin: 0px; position: relative; \u3e≠≠ = 12.7 kcal/mol, so CH3SNO exists as a cis- or trans-conformer, the latter slightly higher in energy, △ role= presentation style= display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 20px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px 2px 0px 0px; margin: 0px; position: relative; \u3e△△E0 = 1.2 kcal/mol. The S—N bond properties are consistent with the antagonistic nature of CH3SNO, whose resonance representation requires two chemically opposite (antagonistic) resonance structures, CH3—S+=N—O−and CH3—S−/NO+, which can be probed using external electric fields and quantified using the natural resonance theory approach (NRT). The calculated S—N bond properties slowly converge with the level of correlation treatment, with the recently developed distinguished cluster with single and double excitations approximation (DCSD-F12) performing significantly better than the coupled cluster with single and double excitations (CCSD-F12), although still inferior to the CCSD(T)-F12 method that includes perturbative triple excitations. Double-hybrid density functional theory (DFT) calculations with mPW2PLYPD/def2-TZVPPD reproduce well the geometry, vibrational frequencies, and the S—N bond rotational barrier in CH3SNO, while hybrid DFT calculations with PBE0/def2-TZVPPD give a better S—N bond dissociation energy

On the definition of matter collineations

It is shown that when the stress-energy tensor of a spacetime is diagonal and is written in the mixed form, its collineations admit infinite dimensional Lie algebras except possibly in the case when the tensor depends on all the spacetime coordinates. The result can be extended for more general second rank tensors

Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights

Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields

Electrostatic Point Charge Fitting as an Inverse Problem: Revealing the Underlying Ill-Conditioning

Atom-centered point charge model of the molecular electrostatics---a major workhorse of the atomistic biomolecular simulations---is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. Here, to reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem, and construct an analytically soluble model with the point charges spherically arranged according to Lebedev quadrature naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field

Weyl collineations that are not curvature collineations

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel". Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality".Comment: 9 page

Conformal Ricci collineations of static spherically symmetric spacetimes

Conformal Ricci collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating conformal Ricci collineations is found when the Ricci tensor is non-degenerate, in which case the number of independent conformal Ricci collineations is \emph{fifteen}; the maximum number for 4-dimensional manifolds. In the degenerate case it is found that the static spherically symmetric spacetimes always have an infinite number of conformal Ricci collineations. Some examples are provided which admit non-trivial conformal Ricci collineations, and perfect fluid source of the matter

Photochemical Electrocyclic Ring Closure and Leaving Group Expulsion from N-(9-oxothioxanthenyl)Benzothiophene Carboxamides

N-(9-Oxothioxanthenyl)benzothiophene carboxamides bearing leaving groups (LG− = Cl−, PhS−, HS−, PhCH2S−) at the C-3 position of the benzothiophene ring system photochemically cyclize with nearly quantitative release of the leaving group, LG−. The LG− photoexpulsions can be conducted with 390 nm light or with a sunlamp. Solubility in 75% aqueous CH3CN is achieved by introducing a carboxylate group at the C-6 position of the benzothiophene ring. The carboxylate and methyl ester derivatives regiospecifically cyclize at the more hindered C-1 position of the thioxanthone ring. Otherwise, the photocyclization favors the C-3 position of the thioxanthone. Quantum yields for reaction are 0.01–0.04, depending on LG− basicity. Electronic structure calculations for the triplet excited state show that excitation transfer occurs from the thioxanthone to the benzothiophene ring. Subsequent cyclization in the triplet excited state is energetically favourable and initially generates the triplet excited state of the zwitterionic species. Expulsion of LG− is thought to occur once this species converts to the closed shell ground state

Structure, Stability, and Substituent Effects in Aromatic \u3cem\u3eS\u3c/em\u3e-Nitrosothiols: The Crucial Effect of a Cascading Negative Hyperconjugation/Conjugation Interaction

Aromatic S-nitrosothiols (RSNOs) are of significant interest as potential donors of nitric oxide and related biologically active molecules. Here, we address a number of poorly understood properties of these species via a detailed density functional theory and the natural bond orbital (NBO) investigation of the parent PhSNO molecule. We find that the characteristic perpendicular orientation of the −SNO group relative to the phenyl ring is determined by a combination of the steric factors and the donor–acceptor interactions including, in particular, a cascading orbital interaction involving electron delocalization from the oxygen lone pair to the σ-antibonding S–N orbital and then to the π*-aromatic orbitals, an unusual negative hyperconjugation/conjugation long-range delocalization pattern. These interactions, which are also responsible for the relative weakness of the S–N bond in PhSNO and the modulation of −SNO group properties in substituted aromatic RSNOs, can be interpreted as a resonance stabilization of the ionic resonance component RS–/NO+ of the RSNO electronic structure by the aromatic ring, similar to the resonance stabilization of PhS– anion. These insights into the chemistry and structure–property relationships in aromatic RSNOs can provide an important theoretical foundation for rational design of new RSNOs for biomedical applications