The toroid antenna as a conditioner of electromagnetic fields into (low energy) gauge fields

Treatment of the radiated field from a toroid antenna as two A fields in resonance or a field, and the toroid as a field radiator, results in the prediction of (i) omnidirectional radiation patterns (with small indentations at the poles), and (ii) periodic resonances in the driving conditions. These predictions have been confirmed experimentally, giving validity to the fundamental nature of this topological and group theory understanding of the first order determinants of electromagnetic field dynamics. Resonant gauge () fields are produced by a toroid radiator as either propagating or standing waves. In the case of a torus with a single winding, an alternating current driver will produce a series of nonmeasurable A vector potential resonances, which overlap and combine into measurable phase factor or gauge field, , waves. Such waves, although generated on a toroidal-solenoidal structure of nonsimple topology, are yet spherical waves – either standing spherical waves, or propagating spherical waves. The topological constraints of electromagnetic fields mapped to a torus driven by single or double wiring are described. It is shown that such mapping results in group symmetries higher than U(1), e.g., SU(2), and that electromagnetic activity is affected by such mapping, being determined by the symmetry forms. Underpinning these symmetry forms are topological conservation laws. The toroid antenna exhibits a series of low and high impedances and permits a U(1) to SU(2) mapping of e.m. fields over a fiber bundle, as well as a mapping of rational and real numbers to complex numbers (in S³ for the nonresonant condition) and quaternions (in S⁴ for the resonant condition). When in resonance, the singly-wound and the doubly-wound (caduceous) torus emits radiation in SU(2)/Z₂ form. The fields emitted for the resonantly driven toroid are alternatively self-dual and anti-self-dual (i.e., instanton solutions to the Maxwell equations of S⁴). In resonance, the singly wound and the doubly wound torus produce fields which are both multiply connected, and of SU(2)/Z₂ form (homeomorphic to S³), as well as simply connected, and of SU(2) from (homeomorphic to S⁴). This study has implications far beyond the immediate subject. If the conventional theory of electromagnetism, i.e., Maxwell's theory, which is of U(1) symmetry form, is but the simplest local theory of electromagnetism, then those pursuing a unified field theory may wish to consider as a candidate field for unification not only this simple local theory, but other forms of conditioned electromagnetism. As is shown here, other such forms can be either force fields or gauge fields of higher group symmetry, e.g., SU(2) and above.     

H2CCC光谱性质的从头算研究

采用全活化空间自洽场方法(CASSCF)在C2v对称性和ANO-S基组水平下, 研究了H2CCC自由基及其阴阳离子的基态和低激发态性质. 为了进一步考虑动态电子相关效应, 采用多组态二级微扰理论(CASPT2)获得了更加精确的能量值. 计算得到X1A1 → 1A2, X1A1 → 1B1和X1A1 → 21A1在159.0, 216.5和476.4 kJ/mol处的激发可分别归因于π(b2)→π*(b1), n(a1)→π*(b1)和π(b1)→π*(b1)的跃迁, 理论波长与紫外吸收光谱得到的实验数据一致. 计算得到的电子亲和势与实验值也非常接近.     

C6H5N光谱性质的多组态二级微扰理论研究

采用全活化空间自洽场方法(CASSCF)在C2v对称性和6-31g(d,p) 基组水平下, 研究了C6H5N自由基及其阴阳离子的基态和低激发态性质. 为了进一步考察动态电子相关效应, 采用多组态二级微扰理论(CASPT2)获得更加精确的能量值. 计算得到13A2→13A1和13A2→13B2在4303.1和4212.2 kJ/mol处的激发可分别归因于π(b1)→ny和π(a2)→ny的跃迁, 而13A2→13B1和13A2→11B1在2634.9和2700.4 kJ/mol处的激发具有nx→π*(a2)和π(a2)→nx的混合跃迁特征, 理论波长与紫外吸收光谱得到的实验数据一致. 计算得到的电离能与实验值也非常接近.     

On the existence of a natural common gauge-origin for the calculation of magnetic properties of atoms and molecules via gaugeless basis sets

It is proven that, within the conventional approach using a common origin and gaugeless basis sets for the calculation of atomic magnetizability and Larmor current density induced by an external magnetic field, the natural gauge origin coincides with the nucleus. Recipes for defining an optimal gauge origin for the calculation of magnetizability and magnetic shielding at the nuclei of a molecule are given. Within the common origin approach, the paramagnetic contributions to the components of magnetic tensors of a molecule are represented by a minimum number of non-vanishing parameters if the gauge origin is chosen at a point characterized by the total molecular symmetry, e.g., the center of electronic charge for magnetizabilities. It is shown that total values of diagonal components of the magnetic shielding tensor σ(I) at a nucleus I in a molecule, as well as separate diamagnetic σ(dI) and paramagnetic σ(pI) contributions, calculated via the common origin method, are origin independent for a number of local point group symmetries. The diagonal components (and the average value) of σ(I) depend on the gauge origin only for nuclear site symmetries C(1), C(s), C(n), C(nv), n = 2, 3.... Group-theoretical methods show interesting features, e.g., for S(4) local symmetry, in a coordinate transformation, the paramagnetic contribution to the zz component and to the trace of the shielding tensor is origin independent, whereas the xx and yy components mix into one another, in such a way that their sum remains constant.     

Topological effects for nonsymmetrical configurations: the C2H+2 as a case study

During the last decade the study of topological effects formed by molecular systems became a routine but it was always carried out for configurations that were limited by symmetry conditions. To be more specific this applied to the Jahn-Teller (JT) effect formed by molecular configurations of planar symmetry [see, e.g., Baer et al., Faraday Discuss. 127, 337 (2004)] and the Renner-Teller effect formed by configurations of axial symmetry [see, e.g., Halasz et al., J. Chem. Phys. 126, 154309 (2007)]. In this article we consider for the first time molecular configurations that avoid any symmetry conditions or, in other words, are characterized by the C(1) point group. We report on a detailed study of topological effects formed by such a molecular system. The study concentrates on both, the two-state (Abelian) case and the multistate (non-Abelian) case. It is shown that the theory that was originally developed to treat topological effects due the JT intersection and also applies for the study of topological effects in the most general case. The study is accompanied with numerical results.     

Magnetic susceptibility of alkali-tetracyanoquinodimethane salts and extended Hubbard models with bond order and charge density wave phases

The molar spin susceptibilities χ(T) of Na-tetracyanoquinodimethane (TCNQ), K-TCNQ, and Rb-TCNQ(II) are fit quantitatively to 450 K in terms of half-filled bands of three one-dimensional Hubbard models with extended interactions using exact results for finite systems. All three models have bond order wave (BOW) and charge density wave (CDW) phases with boundary V = V(c)(U) for nearest-neighbor interaction V and on-site repulsion U. At high T, all three salts have regular stacks of TCNQ(-) anion radicals. The χ(T) fits place Na and K in the CDW phase and Rb(II) in the BOW phase with V ≈ V(c). The Na and K salts have dimerized stacks at T < T(d) while Rb(II) has regular stacks at 100 K. The χ(T) analysis extends to dimerized stacks and to dimerization fluctuations in Rb(II). The three models yield consistent values of U, V, and transfer integrals t for closely related TCNQ(-) stacks. Model parameters based on χ(T) are smaller than those from optical data that in turn are considerably reduced by electronic polarization from quantum chemical calculation of U, V, and t of adjacent TCNQ(-) ions. The χ(T) analysis shows that fully relaxed states have reduced model parameters compared to optical or vibration spectra of dimerized or regular TCNQ(-) stacks.     

Renormalized one-loop theory of correlations in disordered diblock copolymers

A renormalized one-loop (ROL) theory developed in previous work [P. Grzywacz, J. Qin, and D. C. Morse, Phys. Rev E. 76, 061802 (2007)] is used to calculate corrections to the random phase approximation (RPA) for the structure factor S(q) in disordered diblock copolymer melts. Predictions are given for the peak intensity S(q?), peak position q?, and single-chain statistics for symmetric and asymmetric copolymers as functions of χ(e)N, where χ(e) is an effective Flory-Huggins interaction parameter and N is the degree of polymerization. The ROL and Fredrickson-Helfand (FH) theories are found to yield asymptotically equivalent results for the dependence of the peak intensity S(q?) upon χ(e)N for symmetric diblock copolymers in the limit of strong scattering, or large χ(e)N, but to yield qualitatively different predictions for symmetric copolymers far from the ODT and for asymmetric copolymers. The ROL theory predicts a suppression of S(q?) and a decrease of q? for large values of χ(e)N, relative to the RPA predictions, but an enhancement of S(q?) and an increase in q? for small χ(e)N. The decrease in q? near the ODT is shown to be unrelated to any change in single-chain statistics, and to be a result of inter-molecular correlations. Conversely, the predicted increase in q? at small values of χ(e)N is a direct result of non-Gaussian single-chain statistics.     

Modeling of the elementary step of chemical transformation of crystals: II. Application to decomposition of metal azides

The model set forth in Part I for analyzing the elementary chemical step (ECS) in the case of solid state reactions is applied to an examination of the thermal decomposition, photolysis, and radiolysis of metal azides. A comparison is made of various possible elementary chemical transformations of the structural units (SU) of the crystals of these salts. At the same time, correlations in orbital symmetry and spin are analyzed, and correlation diagrams (CD) that identify the electronic terms of the SU and the products of their transformation are constructed. On the basis of an analysis of the ECS, the mechanism of the chemical step of decomposition of the salts tested is formulated and an interpretation is given to various experimental data (composition and yield of products, catalysis and autocatalysis, effect of magnetic field, etc.).     

The excited state dipole moments of betaine pyridinium investigated by an innovative solvatochromic analysis and TDDFT calculations

This work reports on the solvatochromic properties of a simple heterocyclic betaine pyridinium, 2-(1-pyridinio)benzimidazolate (SBPa), having promising potentialities in non-linear optics. From advanced PCM-TDDFT calculations, the solvatochromism of SBPa was found to be unusual, involving two different electronic states for absorption (S(0)→ S(2)) and emission (S(1)→S'(0)). To account for this behavior, we developed an innovative physical treatment which consists in a non-linear fit of the solvatochromic data using the Bilot-Kawski theoretical model and visualizing the least-square coefficient χ(2) on a 2D map as a function of the solute polarizability and gas phase absorption energy. In parallel, Kamlet-Taft correlations were undertaken to select a propitious set of electrostatic solvents usable in this treatment. Protic solvents that lead to specific interactions and nonpolar solvents that favor dimerization processes were excluded. From a choice of aprotic solvents with sufficiently high polarity, 4 dipole moments μ(g)(S(0)) = +9.1 D, μ(e)(S(2)) = -1.5 D, μ(e)(S(1)) = 0 D and μ(g)(S'(0)) = +3.31 D were determined, the 3 former values being in close agreement with TDDFT values, although the solute polarizability values seem underestimated. Anyhow, disregarding this discrepancy, we evaluated the static hyperpolarizability to β(0) = -64 × 10(-30) esu from the solvatochromic data in close agreement with DFT calculations.     

A theoretical and structural investigation of thiocarbon anions

Density functional theory energies, geometries, and population analyses as well as nucleus-independent chemical shifts (NICS) have been used to investigate the structural and magnetic evidence for cyclic CnSn(2-) and CnSn (n = 3-6) electron delocalization. Localized molecular orbital contributions to NICS, computed by the individual gauge for localized orbitals method, dissect pi effects from the sigma single bonds and lone pair influences. CnSn(2-) (n = 3-5) structures in Dnh symmetry are minima. Their aromaticity decreases with increasing ring size. C3S3(2-) is both sigma and pi aromatic, while C4S4(2-) and C5S5(2-) are much less aromatic. NICS(0)pi, the C-C(pi) contribution to NICS(0) (i.e., at the ring center), decreases gradually with ring size. In contrast, cyclic C6S6(2-) prefers D2h symmetry due to the balance between aromaticity, strain energy, and the S-S bond energies and is as aromatic as benzene. The theoretical prediction that C6S6(6-) has D6h minima was confirmed by X-ray structure analysis. Comparisons between thiocarbons and oxocarbons based on dissected NICS analysis show that CnSn(2-) (n = 3-5) and C6S6(6-) are less aromatic in Dnh symmetry than their oxocarbon analogues.     

The electronic spectrum and photodissociation of dinitrogen tetroxide (N(2)O(4)): Multireference configuration interaction studies

Multireference configuration interaction (MRCI) calculations were performed for vertical excitation energies and potential curves of N(2)O(4) in D(2h) symmetry using the TZVPP basis set with diffuse functions on the nitrogens. The strong absorption of N(2)O(4) around 185 nm is assigned to the transition from the ground state to 1?(1)B(1u) (σ(O)→σ(?) (N-N)) rather than 1?(1)B(2u) (π(O)→π(?) (NO(2) ),n→σ(?) (N-N)), as previously assumed. (N(2)O(4) is placed in the yz-plane, with N-N along z.) Transition to 1?(1)B(1u) is calculated to have an oscillator strength f=0.71 and is z-polarized, in agreement with the experimental observations. Another state, 2?(1)B(2u), lies close by, however, at a much lower f-value. The weak absorption around 340 nm is assigned to 1?(1)B(3u). Excitation to 1?(1)B(2u) is calculated at 227 nm. There is no clear assignment of a state for the observed shoulder around 260 nm. TD-DFT (time-dependent density functional theory) vertical excitation energies are close to MRCI values. MRCI singlet and triplet potential curves for the dissociation N(2)O(4)→2NO(2), combined with a table of NO(2) states correlating with those of N(2)O(4), indicate possible products of photodissociation at various wavelengths. The extensive literature on the photodissociation of N(2)O(4) is reviewed. DFT geometry optimizations have been performed on low-lying singlet and triplet states.     

First-principles Calculations of H2O Adsorption Reaction on the GaN（0001） Surface

The adsorption and decomposition of H2O on GaN（0001） surface have been explored employing density functional theory （DFT）. Two distinct adsorption features of H2O on GaN（0001） corresponding to molecular adsorption and H-OH dissociative adsorption are revealed by our calculations. The activities of the surface reactions of H2O on GaN（0001） surface are investigated. For the stepwise processes of H2O decomposition into H2 in gas phase and adsorbed O atom （H2O（g）→H2O（chem）→OH（chem） ＋ H（chem）→2H（chem） ＋ O（chem）→H2（g） ＋ O（chem））, the first and second steps are facile and can even occur at room temperature; while the last two have high barriers and thus are difficult to proceed, especially the fourth step is endothermic. In short, H2O adsorption and decomposition into H2 in gas phase and adsorbed O atom on GaN（0001） surface are exothermic by -43.98 kcal/mol.     

Modeling of the elementary step in the chemical transformation of crystals. I. Statement of the problem; description of the model

A model is proposed within the framework of activated-complex (AC) theory for analyzing the elementary chemical step (ECS) in the case of solid state reactions. By ECS is understood the synchronous restructuring (change in configuration, decomposition) of polyatomic structural units (SU) of the crystal or synchronous formation of new molecular groupings from poly- or monatomic SU. Simple physical observations lead to the conclusion that the ECS of solid state transformations does not have high molecularity. The mechanism which controls activation and deactivation is not directly considered. For activated SU that do not experience deactivation, it is suggested that interaction of these reacting SU with their surroundings in the crystal is constant throughout the course of the ECS. In conformity with this, an analysis of elementary steps of chemical transformation in crystals leads to an examination of the transformation of groupings composed of a small number of the SU of the crystal. A comparison of the ECS is carried out based on a comparison of the energies of activation (E_a) corresponding to the transformations. The E_a for various paths of transformation are evaluated by using the correlation diagram (CD) method. In a correlation analysis, experimental data for crystals should be used. Orbital symmetry and multiplicity of terms should be examined on the basis of specific quantum chemical analysis. The problem is formally reduced to a molecular one; however, the separable SU are bearers of properties of the crystal which are important for the ECS (enthalpy of formation, symmetry, electron composition, spectroscopic properties, etc.).     

Why Are Selenouracils as Basic as but Stronger Acids than Uracil in the Gas Phase?

The gas‐phase basicity and acidity of 2‐selenouracil ( 2SU ), 4‐selenouracil ( 4SU ), and 2,4‐diselenouracil ( 24SU ) have been calculated at the B3LYP/6‐311+G(3df,2p) level of theory. Our results showed that all these compounds behave as bases of moderate strength in the gas phase. As was found for uracil and for the thiouracil analogues, the most basic site is the heteroatom at position 4, and only for 2SU is there a certain ambiguity in assigning the basic site. More importantly, with the only exception of 2SU , selenouracils are as basic as or slightly less basic than uracil, because the replacement of the oxygen atom at position 2 by a selenium atom leads to an increase of the electron delocalization inside the six‐membered ring, which decreases the intrinsic basicity of the heteroatom at position 4. As already reported for uracil and thiouracils, for selenouracils N1 is the most acidic site. However, selenouracils are predicted to be stronger acids than uracil. This acidity enhancement is essentially due to a specific stabilization of the anion when O is replaced by Se. Two factors are responsible for this stabilization: a significant aromatization of the ring upon deprotonation and a better dispersion of the excess electron density when the system contains third‐row atoms.     

Interaction of segmented polyurethanes and polyurethane-ureas with water

Sorption of water vapor by oligomeric homopolymers and triblock copolymers of ethylene oxide and propylene oxide, and by polyurethanes and polyurethane - ureas derived from them is discussed. While the sorption isotherms (plots of ψ₁ vs a₁, where ψ is he volume fraction of sorbed water and a₁ is activity) for most polymers investigated here are smooth and convex towards the abscissa, those found with polyurethane-ureas containing long hard blocks have a “toe” at low activities. The plots of a₁/ψ₁ vs a₁ are shown to facilitate the analysis of data and the interpretation in terms of the D'Arcy-Watt theory. Smooth isotherms are fitted by a simple equation with two parameters. The first is related to the limiting value, χ₀, (at ψ₁ → 0) of the χ parameter characterizing the polymer-water interaction. The dependences of χ₀ on the polymer composition (content of hard segments or oxyethylene units) can provide information on the interaction between hard and soft segments. The second parameter is used in the computation of parameters characterizing the clustering tendency of water molecules. This tendency depends mainly on the content of oxypropylene units but is also raised by urethane or urea groups, though not so much as by oxypropylene groups.     

Fractal MTW Zeolite Crystals: Hidden Dimensions in Nanoporous Materials

Screw dislocation structures in crystals are an origin of symmetry breaking in a wide range of dense‐phase crystals. Preparation of such analogous structures in framework‐phase crystals is of great importance in zeolites but is still a challenge. On the basis of crystal‐structure solving and model building, it was found that the two specific intergrowths in MTW zeolite produce this complex fractal and spiral structure. With the structurally determined parameters (spiral pitch h, screw angle θ, and spatial angle ψ) of Burgers circuit, the screw dislocation structure can be constructed by two different dimensional intergrowth sections. Thus the reported complexity of various dimensions in diverse crystals can be unified.     

Orbital magnetization in extended systems.

While the orbital magnetic dipole moment of any finite sample is well-defined, it becomes ill-defined in the thermodynamic limit as a result of the unboundedness of the position operator. Effects due to surface currents and to bulk magnetization are not easily disentangled. The corresponding electrical problem, where surface charges and bulk polarization appear as entangled, was solved about a decade ago by the modern theory of polarization, based on a Berry phase. We follow a similar path here, making progress toward a bulk expression for the orbital magnetization in an insulator represented by a lattice-periodic Hamiltonian with broken time-reversal symmetry. We therefore limit ourselves to the case where the macroscopic (i.e. cell-averaged) magnetic field vanishes. We derive an expression for the contribution to the magnetization arising from the circulating currents internal to the bulk Wannier functions, and then transform to obtain a Brillouin zone integral involving the occupied Bloch orbitals. A version suitable for practical implementation in discretized reciprocal space is also derived, and the gauge invariance of both versions is explicitly shown. However, tests on a tight-binding model indicate the presence of additional edge currents, and it remains to be determined whether these can be related to the bulk band structure.     

A unified theory of spin 0 nuclear interactions

A Gauge Theory that contains the pion triplet as strong force quanta, a quantum theory of gravity and unifies the strong (nuclear) and gravitational interactions is proposed under a relaxation of the requirement of covariance for Lorentz boost transformations. A modified form of local gauge invariance in which the nucleon field phase is allowed to vary with each time point but not each space point leads to the introduction of a new compensatory field. The quanta of this field are massless spin 0 particles that propagate at the speed of light. They are interpreted as gravitons which mediate the Newtonian gravitational force. It is suggested that the universality of the interaction is linked with the conservation of mass. The associated equation of motion yields Newton's Inverse Square Law for the static case and, because of retardation of potentials, gives rise to a precession of planetary orbits. A qualitative indication of the energy loss observed in the binary pulsar PSR1913+16 within the Newtonian framework is also given. A modification of the Yang–Mills invariance is applied to nucleons. It requires the strong interaction between nucleons to be invariant under independent rotations of the isotopic spin at each time point but not each space point. This results in the introduction of a triplet of compensating fields having massless spin 0 quanta that are interpreted as massless pions. An SU(2)×U(1) theory combining isotopic spin and hypermass symmetries is then developed. Spontaneous Symmetry Breaking yields three massive particles (along with a Higgs particle) and one massless particle. The three massive particles have mass, spin and charge that identify them as pions, while the single massless spin 0 particle, which couples to the nucleons with a strength proportional to mass, is interpreted as the spin 0 graviton. The model provides a resolution of one of the outstanding puzzles of theoretical physics: why gravity is so much weaker than the other forces of nature.     

Two-boson Realizations of the Polynomial Angular Momentum Algebra and Some Applications

In this paper two kinds of two-boson realizations of the polynomial angular momentum algebra are obtained by generalizing the well known Jordan–Schwinger realizations of the SU(2) and SU(1,1) algebras. Especially, for the Higgs algebra, an unitary realization and two nonunitary realizations, together with the properties of their respective acting spaces are discussed in detail. Furthermore, similarity transformations, which connect the nonunitary realizations with the unitary ones, are gained by solving the corresponding unitarization equations. As applications, the dynamical symmetry of the Kepler system in a two-dimensional curved space is studied and phase operators of the Higgs algebra are constructed.     

Estimating the segregation strength of microphase‐separated diblock copolymers from the interfacial width

The ever‐growing catalog of monomers being incorporated into block polymers affords exceptional control over phase behavior and nanoscale structure. The segregation strength, χN, is the fundamental link between the molecular‐level detail and the thermodynamics. However, predicting phase behavior mandates at least one experimental measurement of χN for each pair of blocks. This typically requires access to the disordered state. We describe a method for estimating χN from small‐angle X‐ray scattering measurements of the interfacial width between lamellar microdomains, t_x, in the microphase‐separated melt. The segregation strength is determined by comparing t_x to self‐consistent field theory calculations of the intrinsic interfacial width, t_i, as a function of the mean‐field χN. The method is validated using a series of independent experimental measurements of t_x and χN, measured via the order–disorder transition temperature, T_ODT. The average absolute relative difference between χN calculated from t_x and the value calculated from T_ODT is a modest 11%. Corrections for nonplanarity of the interfaces are investigated but do not improve the agreement between the experiments and theory. Published 2019. This article is a U.S. Government work and is in the public domain in the USA. J. Polym. Sci., Part B: Polym. Phys. 2019 © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 932–940