Scaled in Cartesian Coordinates Ab Initio Molecular Force Fields of DNA Bases: Application to Canonical Pairs

The model of Regularized Quantum Mechanical Force Field (RQMFF) was applied to the joint treatment of ab initio and experimental vibrational data of the four primary nucleobases using a new algorithm based on the scaling procedure in Cartesian coordinates. The matrix of scaling factors in Cartesian coordinates for the considered molecules includes diagonal elements for all atoms of the molecule and off-diagonal elements for bonded atoms and for some non-bonded atoms (1–3 and some 1–4 interactions). The choice of the model is based on the results of the second-order perturbation analysis of the Fock matrix for uncoupled interactions using the Natural Bond Orbital (NBO) analysis. The scaling factors obtained within this model as a result of solving the inverse problem (regularized Cartesian scale factors) of adenine, cytosine, guanine, and thymine molecules were used to correct the Hessians of the canonical base pairs: adenine–thymine and cytosine–guanine. The proposed procedure is based on the block structure of the scaling matrix for molecular entities with non-covalent interactions, as in the case of DNA base pairs. It allows avoiding introducing internal coordinates (or coordinates of symmetry, local symmetry, etc.) when scaling the force field of a compound of a complex structure with non-covalent H-bonds.

Терагерцовая спектроскопия магнитоэлектрика HoAl-=SUB=-3-=/SUB=-(BO-=SUB=-3-=/SUB=-)-=SUB=-4-=/SUB=-

Experimental and theoretical study of submillimeter (terahertz) spectroscopic and magnetic properties of the rare-earth aluminum borate HoAl3(BO3)4 were performed at temperatures 3–300 K. In the transmittance spectra a number of resonance lines were detected at frequencies 2–35 cm–1 for different radiation polarizations. These modes were identified as transitions between the lower levels of the ground multiplet of the Ho3+ ion split by the crystal field, including both transitions from the ground state to the excited ones and transitions between the excited states. The established excitation conditions of the observed modes and the simulation of the spectra made it possible to separate the magnetic and electric dipole transitions and to determine the energies of the corresponding states, their symmetry, and the matrix elements of the transitions. Low-frequency lines that do not fit into the established picture of the electron states of Ho3+ were also found; these lines, apparently, correspond to the ions with the distorted by defects local symmetry of the crystal field.

All Structures Great and Small: Nanoscale Modulations in Nematic Liquid Crystals

The nature of the nanoscale structural organization in modulated nematic phases formed by molecules having a nonlinear molecular architecture is a central issue in contemporary liquid crystal research. Nevertheless, the elucidation of the molecular organization is incomplete and poorly understood. One attempt to explain nanoscale phenomena merely “shrinks down” established macroscopic continuum elasticity modeling. That explanation initially (and mistakenly) identified the low temperature nematic phase (NX), first observed in symmetric mesogenic dimers of the CB-n-CB series with an odd number of methylene spacers (n), as a twist–bend nematic (NTB). We show that the NX is unrelated to any of the elastic deformations (bend, splay, twist) stipulated by the continuum elasticity theory of nematics. Results from molecular theory and computer simulations are used to illuminate the local symmetry and physical origins of the nanoscale modulations in the NX phase, a spontaneously chiral and locally polar nematic. We emphasize and contrast the differences between the NX and theoretically conceivable nematics exhibiting spontaneous modulations of the elastic modes by presenting a coherent formulation of one-dimensionally modulated nematics based on the Frank–Oseen elasticity theory. The conditions for the appearance of nematic phases presenting true elastic modulations of the twist–bend, splay–bend, etc., combinations are discussed and shown to clearly exclude identifications with the nanoscale-modulated nematics observed experimentally, e.g., the NX phase. The latter modulation derives from packing constraints associated with nonlinear molecules—a chiral, locally-polar structural organization indicative of a new type of nematic phase.

Recurrent Generalization of F-Polynomials for Virtual Knots and Links

F-polynomials for virtual knots were defined by Kaur, Prabhakar and Vesnin in 2018 using flat virtual knot invariants. These polynomials naturally generalize Kauffman’s affine index polynomial and use smoothing in the classical crossing of a virtual knot diagram. In this paper, we introduce weight functions for ordered orientable virtual and flat virtual links. A flat virtual link is an equivalence class of virtual links with respect to a local symmetry changing a type of classical crossing in a diagram. By considering three types of smoothing in classical crossings of a virtual link diagram and suitable weight functions, there is provided a recurrent construction for new invariants. It is demonstrated by explicit examples that newly defined polynomial invariants are stronger than F-polynomials.

Time-space duality in 2D quantum gravity

An important task faced by all approaches of quantum gravity is to incorporate superpositions and quantify quantum uncertainties of spacetime causal relations. We address this task in 2D. By identifying a global Z2 symmetry of 1+1D quantum gravity, we show that gravitational path integral configurations come in equal amplitude pairs with timelike and spacelike relations exchanged. As a consequence, any two points are equally probable to be timelike and spacelike separated in a universe without boundary conditions. In the context of simplicial quantum gravity we identify a local symmetry of the action which shows that even with boundary conditions causal uncertainties are generically present. Depending on the boundary conditions, causal uncertainties can still be large and even maximal.

Structural and Spectroscopic Effects of Li+ Substitution for Na+ in LixNa1-xCaGd0.5Ho0.05Yb0.45(MoO4)3 Scheelite-Type Upconversion Phosphors

A set of new triple molybdates, LixNa1-xCaGd0.5(MoO4)3:Ho3+0.05/Yb3+0.45, was successfully manufactured by the microwave-accompanied sol–gel-based process (MAS). Yellow molybdate phosphors LixNa1-xCaGd0.5(MoO4)3:Ho3+0.05/Yb3+0.45 with variation of the LixNa1-x (x = 0, 0.05, 0.1, 0.2, 0.3) ratio under constant doping amounts of Ho3+ = 0.05 and Yb3+ = 0.45 were obtained, and the effect of Li+ on their spectroscopic features was investigated. The crystal structures of LixNa1-xCaGd0.5(MoO4)3:Ho3+0.05/Yb3+0.45 (x = 0, 0.05, 0.1, 0.2, 0.3) at room temperature were determined in space group I41/a by Rietveld analysis. Pure NaCaGd0.5Ho0.05Yb0.45(MoO4)3 has a scheelite-type structure with cell parameters a = 5.2077 (2) and c = 11.3657 (5) Å, V = 308.24 (3) Å3, Z = 4. In Li-doped samples, big cation sites are occupied by a mixture of (Li,Na,Gd,Ho,Yb) ions, and this provides a linear cell volume decrease with increasing Li doping level. The evaluated upconversion (UC) behavior and Raman spectroscopic results of the phosphors are discussed in detail. Under excitation at 980 nm, the phosphors provide yellow color emission based on the 5S2/5F4 → 5I8 green emission and the 5F5 → 5I8 red emission. The incorporated Li+ ions gave rise to local symmetry distortion (LSD) around the cations in the substituted crystalline structure by the Ho3+ and Yb3+ ions, and they further affected the UC transition probabilities in triple molybdates LixNa1-xCaGd0.5(MoO4)3:Ho3+0.05/Yb3+0.45. The complex UC intensity dependence on the Li content is explained by the specificity of unit cell distortion in a disordered large ion system within the scheelite crystal structure. The Raman spectra of LixNa1-xCaGd0.5(MoO4)3 doped with Ho3+ and Yb3+ ions were totally superimposed with the luminescence signal of Ho3+ ions in the range of Mo–O stretching vibrations, and increasing the Li+ content resulted in a change in the Ho3+ multiplet intensity. The individual chromaticity points (ICP) for the LiNaCaGd(MoO4)3:Ho3+,Yb3+ phosphors correspond to the equal-energy point in the standard CIE (Commission Internationale de L’Eclairage) coordinates.

How to Lay Bricks: Local-Global Alignment Predicts Preference for Shifted Tile Patterns

We examine the aesthetic characteristics of row tile patterns defined by repeating strips of polygons. In experiment 1 participants rated the perceived beauty of equilateral triangle, square and rectangular tilings presented at vertical and horizontal orientations. The tiles were shifted by one-fourth increments of a complete row cycle. Shifts that preserved global symmetry were liked the most. Local symmetry by itself did not predict ratings but tilings with a greater number of emergent features did. In a second experiment we presented row tiles using all types of three- and four-sided geometric figures: acute, obtuse, isosceles and right triangles, kites, parallelograms, a rhombus, trapezoid, and trapezium. Once again, local polygon symmetry did not predict responding but measures of correspondence between local and global levels did. In particular, number of aligned polygon symmetry axes and number of aligned polygon sides were significantly and positively correlated with beauty ratings. Preference was greater for more integrated tilings, possibly because they encourage the formation of gestalts and exploration within and across levels of spatial scale.

Synthesis and crystal structure of racemic (R*,R*)-2,2′-(1,4-phenylene)bis(3-phenyl-2,3,5,6-tetrahydro-4H-1,3-thiazin-4-one)

In the racemic title compound, C26H24N2O2S2, one of the thiazine rings shows a twisted boat conformation (Q = 0.743 Å, θ = 92.1°) and the other a half-chair puckering (Q = 0.669 Å, θ = 54.3°). The terminal phenyl rings are almost parallel to each other [dihedral angle 21.71 (10)°]. Both of these rings are orthogonal to the central phenyl ring, subtending a dihedral angle of about 78° in each case. The extended structure is consolidated by C—H...O and C—H...S hydrogen bonds as well as aromatic ring interactions of parallel-displaced and T-type. The molecule has approximate C2 local symmetry but this is not carried over to its three-dimensional structure or the intermolecular interactions.