The Dynamics of Intramolecular Excited State Relaxation of <Emphasis Type="Italic">N</Emphasis>-Anthryl Substituted Pyridinium Cations

N-(1-Anthryl)-2,4,6-trimethyl-pyridinium (I), N-(2-anthryl)-2,4,6-trimethyl-pyridinium (II) and 10-(1-anthryl)-1,2,3,4,5,6,7,8-octahydro-acridinium cations (III) with anomalously high fluorescence Stokes shift have been investigated. Fluorescence kinetics analysis at various temperatures showed that in the range 293–77 K, the radiative deactivation rate constants (k_f) increase by 5.5 to 30 times. The low-temperature time-resolved emission spectra of I–III were found to be consistent with the model: A A^* B^* where A^* is the local excited twisted form and B^* is the relaxed more planar, bent conformer of the molecule. The rate constants of the excited relaxed state formation (k₁) and back reaction (k_–1) of compounds studied were estimated.     

Out-of-equilibrium quantum field dynamics in external fields

The quantum dynamics of the symmetry-broken λ(Φ ²)² scalar-field theory in the presence of an homogeneous external field is investigated in the large-N limit. We consider an initial thermal state of temperature T for a constant external field J. A subsequent sign flip of the external field, J→ - J, gives rise to an out-of-equilibrium nonperturbative quantum field dynamics. We review here the dynamics for the symmetry-broken λ(Φ ²)² scalar N component field theory in the large-N limit, with particular stress in the comparison between the results when the initial temperature is zero and when it is finite. The presence of a finite temperature modifies the dynamical effective potential for the expectation value, and also makes that the transition between the two regimes of the early dynamics occurs for lower values of the external field. The two regimes are characterized by the presence or absence of a temporal trapping close to the metastable equilibrium position of the potential. In the cases when the trapping occurs it is shorter for larger initial temperatures.     

Spectroscopic Studies of Fluorescent Dye <Emphasis Type="Italic">N</Emphasis>, <Emphasis Type="Italic">N</Emphasis>′- bis(2-hydroxy-5-methyl-benzylidene)-1,2-ethanediamine and its DNA Complex in Solution

Absorption and fluorescence emission properties of an N-salicylideneamine fluorescent dye molecule N, N-bis(2-hydroxy-5-methylbenzylidene)-1,2-ethanediamine (1) have been studied in three typical solvents—2-methylbutane, ethanol, dimethyl sulphoxide (DMSO), and its DNA complex in methanol/H₂O mixed solvent. The normal absorption band of 1 is observed in both aprotic and protic solvents and has been assigned to the l a transition in the enol form of 1. The long-wavelength absorption band of 1, which is caused by the formation of a cis-keto species in the ground state, is absent in aprotic solvents, but is observable in protic ones. Normal fluorescence emission from the excited enol state of 1 is obtained only when the normal absorption band is excited, while the excited-state intramolecular proton transfer (ESIPT) emissions from both cis- and trans-keto species are recorded in all cases, being acceptable for the variation of the relative emission intensities. A preliminary spectroscopic study of the 1–DNA complex indicates an intercalation-binding mode, the convincing supporting evidence being the enhanced ESIPT fluorescence intensity of 1 when complexed with DNA. Finally, a universal energy-state diagram is given to interpret the experimental results.     

The exclusive reaction of pion quasi-elastic knockout from nucleon <Emphasis Type="Italic">p(e,e′ π)B</Emphasis> to various states of the final baryon-spectator <Emphasis Type="Italic">B</Emphasis> and the quark models for the pion cloud of nucleon

The pion momentum distributions (MDs) in four channels of virtual decay p→B+π, B = N, Δ, N _1/2-(1535), N _1/2+(1440) are calculated in two models, the microscopic model of ³ P ₀ scalar q−q fluctuation with the pion as a composite q−q-system and the chiral semi-microscopic model of πq interaction with the pion as a structureless Goldstone boson. The results of the above models are similar for the baryon states B = N, Δ, N _1/2-(1535) but are rather different for the Roper resonance N _1/2+(1440) which corresponds to excitation of two oscillator quanta in the nucleon. The experimental investigation of pion MDs by means of the reaction of quasi-elastic knockout of pion by an electron of a few GeV energy p(e, e′ π)B may be very suitable for Jefferson Laboratory, Virginia (JLab).     

Renormalizations and Operator Expansion in σ-Model

The operator expansion (OPE) is studied for the Green function n(0) n(x)) at x² → 0 (n(x) is the dynamical field of σ-model) in the framework of the two-dimensional σ-model with the O(N) symmetry group at large N. As a preliminary step we formulate the ronormalization scheme which permits introduction of an arbitrary intermediate scale μ² in the framework of 1/N expansion and discuss factorization (separation) of small (p < μ ) and large (p > μ ) momentum region. It is shown that definition of composite local operators and coefficient functions figuring in OPE is unambiguous only in the leading order in 1/N expansion when dominant are the solutions with exrtemum of action. Corrections of order f(μ²)/N (here /(μ²) is the effective interaction constant at the point μ²) in composite operators and coefficient functions essentially depend on factorization method of high and low momentum regions. It is shown also that contributions to the power corrections of order m²x²/(μ²)/N in the Green function (here m is the dynamical mass-scale factor in σ-model) arise simultaneously from two sources: from the mean vacuum value of the composite operator n ∂²n and from the hard particle contributions in the coefficient function of unite operator. Due to the analogy between σ-model and QCD the obtained result indicates theoretical limitations to the sum rule method in QCD.     

D2O‐catalyzed proton transfer selectivity of 4 different NH protons in the same molecule

When N‐benzyl‐N′‐methylacetamidinium hydrochloride (pKa=11.8) is dissolved in D₂O/DCl(1 M), an equilibrium of 2 54:46 stereoisomers in an ~2:1 =(R)N^δ+H(D) D/H ratio is formed. Therefore, 2 R =N‐benzyl (E and Z) and 2 R =N‐methyl (E and Z) groups attached to the corresponding H(D) (Z and E) for a total of 8 ¹H‐NMR signals are observed. Consequently, their rates of H and D transfer to D₂O can be measured by means of the ¹H‐NMR broadness (line shape) of the =(R )N^δ+H doublets and =(R )N^δ+D broad singlets. Acidity selectivity is observed for both processes. In fact, the relative proton and deuterium transfer rates follow the acidity order: =(PhCH₂)N^δ+‐H(E) > =(PhCH₂)N^δ+‐H(Z) > =(Me)N^δ+‐H(E) > =(Me)N^δ+‐H(Z). Proton transfer rates are in the range of 8 to 0.5 s^‐1 with α = .92. This tendency is independently supported by the observed experimental chemical shift deuterium isotopic perturbation. The rate‐limiting step for proton exchange is the breaking of the hydrogen bond due to the fast amidine reprotonation (~10¹¹ s). =(R)N^δ+D/=(R)N^δ+H equilibration is reached at ~80 s, and it can be measured by the relative =(R) N^δ+H versus =(R) N^δ+D signal integrations. The equilibrium of the 4 =(R)N^δ+H(D) centers is shifted toward deuterium, but they are further shifted in the more basic centers. Equilibrium is completely shifted toward D in the 4 centers when OD^? contributes with the exchange process at pD > 3.     

Exact Analytical Solution of the Schrödinger Equation for an N-Identical Body-Force System

A mathematical method is presented for solving the Schr?dinger equation for a system of identical body forces. The N-body forces are more easily introduced and treated within the hyperspherical harmonics. The problem of the N-body potential has been used at the level of both classical and quantum mechanics. The hypercentral interacting potential is assumed to depend on the hyperradius x = (ξ₁² + ξ₂² + ⋯ + ξ_N−1²)^1/2 only, where ξ₁,ξ₂,…,ξ_N−1 are Jacobi relative coordinates which are functions of N-particle relative positions r₁₂,r₂₃,…,r_N1. The problem of the harmonic oscillator and the Coulomb-type potential has been widely studied in different contexts. Using the N-body potential V(x) = ax² + bx − (c/x) as an example, and assuming an ansatz for the eigenfunction, an exact analytical solution of the Schr?dinger equation for an N-body system in three dimensions is obtained. This method is also applicable to some other types of potentials for N-identical interacting particles.     

NMR Studies of Crowded Diels–Alder Adducts of Phencyclone with N‐(2,6‐Dialkylphenyl)maleimides. Hindered Rotations and Magnetic Anisotropy

Abstract

Phencyclone, 1, reacted with N‐(2,6‐dimethylphenyl)maleimide, 2a; with N‐(2,6‐diethylphenyl)maleimide, 2b; and with N‐(2,6‐diisopropylphenyl)maleimide, 2c, respectively, to yield the corresponding Diels–Alder adducts, 3a–c. The adducts were extensively characterized by NMR (7 T) at ambient temperatures using one‐ and two‐dimensional (1D and 2D) proton and carbon‐13 techniques for assignments. Slow exchange limit (SEL) spectra were observed, demonstrating slow rotations on the NMR timescales, for the unsubstituted bridgehead phenyl groups [C(sp³)–C(aryl sp²) bond rotations] and for the 2,6‐dialkylphenyl groups [N(sp²)–C(aryl sp²) bond rotations]. Substantial magnetic anisotropic shifts were seen in the adducts. For example, in the N‐(2,6‐dialkylphenyl) moieties of the adducts, one of the alkyl groups is directed “into” the adduct cavity, toward the phenanthrenoid portion, and these “inner” alkyl proton NMR signals were shifted upfield. Thus, in CDCl₃, the “inner” methyl of adduct 3a exhibits a proton resonance at ?0.13 ppm, upfield of tetramethylsilane (TMS); the “inner” ethyl group signals from 3b appear at 0.026 ppm (CH₂, quartet), and ?0.21 ppm (CH₃, triplet); and the “inner” isopropyl group from 3c is seen at ?0.06 ppm (methine, approx. septet) and ?0.39 ppm (CH₃, doublet). Proton NMR of the crude N‐(2,6‐dialkylphenyl)maleamic acids (used as precursors of the maleimides, 2a–c) exhibited two sets of AB quartet signals, suggesting possible conformers from hindered rotation in the amide groups about the HN–C?O bonds.     

Reflectance fluctuations in an absorbing random waveguide

We study the statistics of the reflectance (the ratio of reflected and incident intensities) of an N-mode disordered waveguide with weak absorption g per mean free path. Two distinct regimes are identified. The regime γ N ²≫1 shows universal fluctuations. With increasing length L of the waveguide, the variance of the reflectance changes from the value 2/15N ², characteristic for universal conductance fluctuations in disordered wires, to another value 1/8N ², characteristic for chaotic cavities. The weak-localization correction to the average reflectance performs a similar crossover from the value 1/3N to 1/4N. In the regime γ N ²≫1, the large-L distribution of the reflectance R becomes very wide and asymmetric, P(R)∝(1−R)⁻² for R≪1−γN. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 4, 289–293 (25 August 1996) Published in English in the original Russian journal. Edited by J. R. Anderson.     

NMR Studies of Hindered Rotation and Magnetic Anisotropy: The Diels–Alder Adducts of Phencyclone with N‐Phenylmaleimide and N‐(2‐Trifluoromethylphenyl)maleimide. Ab Initio Calculations for Optimized Structures

Abstract

N‐Phenylmaleimide, 2, and N‐(2‐trifluoromethylphenyl)maleimide, 3, were separately added to phencyclone, 1, to yield the corresponding phencyclone Diels–Alder adducts, 4 and 5. The resulting adducts (and some precursors) have been characterized by one‐ and two‐dimensional ¹H and ¹³C NMR at 300 and 75 MHz, and by ¹⁹F NMR at 282 MHz, at ambient temperatures. The NMR data are consistent, for both adducts, with: (a) hindered rotation of the bridgehead unsubstituted phenyl groups about the C(sp²)–C(sp³) bonds, based on slow exchange limit (SEL) spectra and (b) endo adduct configuration based on magnetic anisotropic effects in the ¹H NMR. The NMR spectra of the phencyclone adduct, 4, of N‐phenylmaleimide, indicate free rotation on the NMR timescales (fast exchange limit, FEL spectra) about the N‐phenyl bond. The spectra for the adduct, 5, of N‐(2‐trifluoromethylphenyl)maleimide are interpreted as consistent with SEL regimes, for the N‐aryl rotations, with a single rotamer present in which the trifluoromethyl group is directed “out of” the adduct cavity, and away from the phenanthrenoid moiety. This conclusion is based, in part, on NMR data suggesting the apparent slow N‐aryl bond rotation in a pair of atropisomers corresponding to the acetic acid addition products from the N‐(2‐trifluoromethylphenyl)maleimide. Evidence of magnetic anisotropic effects due to the phenanthrenoid moiety and proximal carbonyls is discussed. ¹H, ¹³C, and ¹⁹F assignments are presented and interpreted. Molecular modeling calculations at the Hartree–Fock level, 6‐31G* basis set, were performed to provide geometry optimizations for energy‐minimized structures of selected compounds.     

Theoretical studies of three-dimensional potential energy surfaces using neural networks and rotational spectra of the Ar–N2 complex

ABSTRACT

A new three-dimensional potential energy surface (PES) of the Ar–N₂ van der Waals complex is constructed using the neural network method based on ab initio data points at the CCSD(T) level. The aug-cc-pVQZ basis set is employed for all atoms with midbond functions. The vibrationally averaged PES V₀₀ is characterised by a global T-shaped minimum which occurs at R = 3.715 Å, θ = 90.0° with a well depth of 98.779 cm^?1. Based on our three-dimensional PES, bound-state calculations are performed for three isotopomers of Ar–¹⁴N₂, Ar–¹⁵N₂, and Ar–¹⁴N¹⁵N, and several intermolecular vibrational states are assigned by analysing the wavefunctions. Moreover, the averaged structural parameters are calculated and the pure rotational transition frequencies with J = 0--6 are predicted. The spectroscopic constants are determined by fitting the rotational energy levels. The theoretical results are in good agreement with experimental data and this work gives more accurate results than those determined previously for the Ar–N₂ complex.     

Magnetic phases in UNi<Subscript>2</Subscript>Si<Subscript>2</Subscript>

The tetragonal compound UNi₂Si₂ exhibits in zero magnetic field three different antiferromagnetic phases belowT _N =124 K. They are formed by ferromagnetic basal planes, which are antiferromagnetically coupled along thec-axis with the propagation vectorq=(0, 0, q _z ). Two additional order-order magnetic phase transitions are observed below T _N , namely atT ₁=108 K and T ₂=40 K in zero magnetic field. All three phases exhibit strong uniaxial anisotropy confining the U moments to a direction parallel to the c-axis. UNi₂Si₂ single crystals were studied in detail by measuring bulk thermodynamic properties, such as thermal expansion, resistivity, susceptibility, and specific heat. A microscopic study using neutron diffraction was performed in magnetic fields up to 14.5 T parallel to the c-axis, and a complex magnetic phase diagram has been determined. Here, we present the analysis of specific-heat data measured in magnetic fields up to 14 T compared with the results of the neutron-diffraction study and with other thermodynamic properties of UNi₂Si₂.     

Non-abelian electrodynamics and the vacuumB (3)

By using an 0(3) gauge group, a non-Abelian theory of vacuum electrodynamics is developed in which the newly discovered longitudinal vacuum fieldsB ⁽³⁾ andi E ⁽³⁾ appear self-consistently with the usual plane wavesB ⁽¹⁾,B ⁽²⁾,E ⁽¹⁾, andE ⁽²⁾ in the circular basis (1), (2), (3), a complex representation of space. Using the charge quantization condition the vacuum Maxwell equations are given in the non-Abelian representation.     

一种新型的两态叠加多模Schrödinger猫态光场的等阶N次方Y压缩

本文根据量子力学的线性叠加原理,构造了由多模(即q模)相干态的相反态|{-Z_j}〉q及多模虚相干态|{Z_j}〉q这两者的线性叠加所组成的一种新型的多模Schrdinger猫态光场|Ψ⁽²⁾〉q,利用新近建立的多模压缩态理论,研究了态|Ψ⁽²⁾〉q的N次方Y压缩效应。结果发现:①当压缩阶数N=2p且p=2m(m=1,2,3,…,…)时,态|Ψ⁽²⁾〉q总是恒处于N-Y最小测不准态;②当压缩阶数N=2p且p=2m+1(m=0,1,2,3,…,…)时,如果各模的初始相位φ_j,态间的初始相位差θ_pq^(I)-θ_nq^(R)以及各单模相干态光场的平均光子数之总和 等满足一定的量子化条件,则态|Ψ⁽²⁾〉q可呈现出周期性变化的、任意阶的N次方Y压缩效应;③当压缩阶数N=2p′+1时,无论p′=2m(m=0,1,2,…,…)还是p′=2m+1(m=0,1,2,3,…,…),只要各模的初始相位φ_j满足一定的量子条件,则当两态叠加几率幅满足r_pq^(I)=r_nq^(R)时,态|Ψ⁽²⁾〉q就恒处于N-Y测不准态,始终不呈现N-Y最小测不准态和N次方Y压缩;而当r_pq^(I)≠r_nq^(R)时,态|Ψ⁽²⁾〉q始终不呈现N-Y测不准态、N-Y最小测不准态和N次方Y压缩效应。     

Infrared spectroscopy of closed s-shell gas-phase M+(N2O)n (M = Li,Al) ion-molecule complexes*

ABSTRACT

We present the results of a combined experimental and computational study of the structures of gas-phase M⁺(N₂O)_n (M?=?Li, Al) complexes. Infrared spectra were recorded in the region of the N₂O asymmetric (N?=?N) stretch using photodissociation spectroscopy employing the inert messenger technique. Unlike in our previous studies on M⁺(N₂O)_n (M?=?Cu, Ag, Au and M?=?Co, Rh, Ir) complexes, N– and O–bound isomers in this case are near isoenergetic and are not distinguished spectroscopically at this resolution. In the case of Li⁺ complexes, there is, however, evidence for the presence of bound N₂ moieties, indicating the presence of inserted, OLi⁺N₂(N₂O)_n–type structures. The weak N₂ band lies to the blue of the signature of molecularly N– and O–bound ligands and is well–reproduced in the simulated spectra of energetically low-lying structures computed from density functional theory. No such inserted isomers are observed in the case of Al⁺(N₂O)_n complexes whose infrared spectra can be understood on the basis of molecularly-bound N₂O ligands. The differences in M⁺(N₂O)_n structures observed for these closed–shell, ns², metal centres relative to other metal cations are discussed in terms of the likely bonding motifs.     

Parallel and automated library synthesis of 2-long alkyl chain benzoazoles and azole[4,5-<Emphasis Type="BoldItalic">b</Emphasis>]pyridines under microwave irradiation

Summary A versatile route to 40-membered library of 2-long alkyl chain substituted benzoazoles (1 and 2) and azole[4,5-b]pyridines (3 and 4) via microwave-assisted combinatorial synthesis was developed. The reactions were carried out in both monomode and multimode microwave oven. With the latter, all reactions were performed in high-throughput experimental settings consisting of an 8×5 combinatorial library designed to synthesize 40 compounds. Each step, from the addition of reagents to the recovery of final products, was automated. The microwave-assisted N-long chain alkylation reactions of 2-alkyl-1H-benzimidazole (1) and 2-alkyl-1H-benzimidazole[4,5-b] pyridines (3) were also studied.     

第Ⅰ类两态叠加多模叠加态光场的非线性高阶压缩特性研究

本文在文献20的基础上进一步提出了多模辐射场的N-Y最小测不准态、N-H最小测不准态、N-Y压缩最小测不准态以及N-H压缩最小测不准态等的定义.构造了由多模(q模)相干态|{Z_j}>_q及其相反态|{-Z_j}>_q的线性叠加所组成的第Ⅰ类两态叠加多模叠加态光场|ψ₁⁽²⁾>_q,利用文献20新近提出的有关多模辐射场的两种非线性高阶压缩的定义,首次对态|ψ₁⁽²⁾>_q的N次方Y压缩及N次方H压缩效应进行了详细研究.结果表明,1)当N为偶数时,态|ψ₁⁽²⁾>_q恒处于N-Y最小测不准态;当N为奇数时,态|ψ₁⁽²⁾>_q在一定条件下可呈现出周期性变化的、任意阶的N次方Y压缩效应.2)当q·N为偶数时,态|ψ₁⁽²⁾>_q恒处于N-H最小测不准态;当q·N为奇数时,在另外的条件下,态|ψ₁⁽²⁾>_q则可呈现出周期性变化的、任意阶的N次方H压缩效应.3)N次方Y压缩及N次方H压缩效应的压缩深度与腔模总数q、压缩参数R_j以及压缩阶数N等非线性相关,后者与上述参量的非线性关联程度要比前者的更强.     

多模复共轭虚偶相干态光场的等阶N次方Y压缩与等阶N次方H压缩

本文利用新近建立的多模压缩态理论,详细研究了一种新型的多模复共轭虚偶相干态光场|Ψ_i,e^*(2)>_q的广义非线性等阶N次方Y压缩与等阶N次方H压缩特性.结果发现:1)当压缩阶数N为奇数时,态Ψ_i,e^*(2)>_q在一定条件下总可呈现出周期性变化的、任意阶的等阶N次方Y压缩效应;当腔模总数q与压缩阶数N两者之乘积q·N为奇数时,则在一定条件下态|Ψ_i,e^*(2)>_q又可呈现出周期性变化的、任意阶的等阶N次方H压缩效应.2)态|Ψ_i,e^*(2)>_q与多模偶相干态光场|Ψ_i,e^*(2)>_q与多模虚偶相干态光场|Ψ_i,e⁽²⁾>_q的压缩幅度、压缩条件和压缩特征等完全相同.这一结果再次从理论上证实了多模压缩光中的确存在着“相反压缩”和“压缩简并”这两类新的物理现象.     

Spherical harmonics and cartesian tensor scalar product expansions of the distribution function

On the basis of the expansion of the distribution function in a sum of the spherical harmonics, the distribution functionf(v, r, t) is expanded in a series of scalar products of two Cartesian tensors term by term, i.e. The tensors and ^(l) (l=2, 3) are constructed in dependence on the spherical harmonic expansion coefficients (the tensors and ^(l) (l=0, 1) have been constructed by Jancel and Kahan [3]). On the basis of the knowledge of the analytic form off ₂ andf ₃ the equations forf ₁ f ₂ andf ₃ for the case of the Boltzmann's equation are determined.Technická 2, Praha 6, Czechoslovakia.     

The energy level ordering in two-electron quantum dot spectra

The spectra of a two-electron quantum dot in a magnetic field of arbitrary strength is obtained by using the shifted 1/Nexpansion method. The level ordering as well as the transitions in the angular momenta of the quantum dot are studied. The dependence of the electron absorption spectra on the applied magnetic field is also calculated. Comparisons show that our results are in good agreement with the exact ones.