Far infrared spectra of solid molecular nitrogen

This paper reports the observation of the far infrared absorption spectrum of a single crystal of N₂, measured over absorption paths of 4 cm (lengthwise) and 2 cm (across the crystal). The crystal chamber, with quartz windows, was immersed in a flow of cold helium gas. The spectrum from 20 to 120 cm^–1 was recorded in the liquid phase, the-phase, and over the full temperature range of the-phase (35.6–2.0 K) with a Fourier transform spectrometer. The spectral resolution, which was not instrument-limited, and the large path allowed the observation of more detailed multiphonon-transition structure in the spectrum of the-phase than has previously been observed.     

HeI-Photoelektronen-Spektrum von Cl-NSO

The ultraviolet photoelectron spectrum of the N-chlorothionylimide molecule (Cl-NSO) has been obtained and analyzed. The spectrum is interpreted by comparison with the known spectra of the parent compounds H-NSO, SO₂ and the related molecules Cl-NCO and H-NCO as well as with the aid ofab initio SCF-calculations in terms of ionization from the eight highest filled valence molecular orbitals in this molecule.

     

PAN和PPN的HeI光电子能谱（PES）

给出了两个重要的大气污染化合物PAN和PPN的紫外光电子能谱（PES）。为了 指认PES谱,对两个分子实施了HF和OVGF方法的理论计算,并给出了它们各自的优 化几何构型、PES谱低电离能区的两个分离（PAN）为11.42 eV和12.07 eV;PPN为 11.08 eV和11.79 eV）被归于分子中主要体现“NO_2”基团贡献的最高占有分子轨 道（HOMO）和次最高占有分子轨道（SHOMO）电子电离作用结果。而PPN的第一电离 能11.08 eV低于PAN的11.42 eV,是由于PPN分子中增加的“CH_2”基团电子的给予 作用,这为PPN应具有较大的生物毒性提供合理的解释。     

Fourier transform IR spectrum and photoreactivity of the C3O2:HCl complex isolated in solid argon

IR spectroscopy was coupled with the matrix isolation technique to study the molecular complex formed between C₃O₂ and HCl and its photodissociation. The vibrational frequencies of the complex were compared with those of HCl and C₃O₂ monomers. For C₃O₂, a bent structure was characterized in the solid environment.

The vibrational frequencies were calculated in the 4000–400 cm⁻¹ range using an ab initio method at the MP2/6-31G** level for the most stable complex; these frequencies describe the hydrogen interaction with the central carbon atom of C₃O₂ (T complex). The measured shifts between the vibrational mode frequencies of the complex and monomers were in good agreement with the calculated values.

Broad-band UV irradiation ( > 230 nm) of the T complex leads preferentially to ketene chloride and carbon monoxide. Ketene chloride formation can be explained by the reaction between HCl and the carbene C₂O, which results from photo-dissociation at the C=CO bond of C₃O₂.     

Construction of Spatiotemporal-Coupling Optimal Low-Dimensional Dynamical Systems for Compressible Navier-Stokes Equations; [可压缩 Navier-Stokes 方程的时空耦合优化低维动力系统建模方法]北大核心CSCD

For the low-dimensional dynamical system model to study dynamics properties of Navier-Stokes equations, it is very important that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. However, to date, there is no universal approach to ensure this purpose for general problems. Herein, it is found that any low-dimensional model based on spatial bases, such as proper orthogonal decomposition bases, optimal spatial bases, and other classical spatial bases, is not predictable, i.e., the error increases with the time evolution of the flow field. With the theoretical framework for building optimal dynamical systems and the new concept of spatiotemporal-coupling spectrum expansion, the low-dimensional model for compressible Navier-Stokes equations was constructed to approximate the numerical solution to large-eddy simulation equations, and the numerical results and novel time evolution of spatiotemporal-coupling bases were given. The entire field error is typically below 10−2%, and the average error at each grid point is below 10−8%. The spatiotemporal-coupling optimal low-dimensional dynamical systems can ensure that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. Therefore, characteristic dynamics properties of spatiotemporal-coupling optimal low-dimensional dynamical systems are the same as those of real flow. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

ON THE ESSENTIAL SPECTRUM OF PSEUDODIFFERENTIAL OPERATORS （Ⅱ）

This paper coutinues the studies of the essential spectrum of nonsemi-bounded pseudodifferential operators. The author improves the results in [5] in some sense. For the relativistic Schrodinger operator,√(-Δ+m^2)+v(x),complete results are obtained.     

Absence of absolutely continuous spectrum of Floquet operators

The spectrum of the Floquet operator associated with time-periodic perturbations of discrete Hamiltonians is considered. If the gap between successive eigenvalues _j of the unperturbed Hamiltonian grows as _j - _j-1 j and the multiplicity of _j grows asj with >0 asj tends to infinity, then the corresponding Floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough.     

Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

AM1 study of photoelectron spectra.

The -orbital structure of the monomeric form of the 2,2,4,6-tetrachloro-2,2-dihydro-1,5,2-diazaphosphorinine has been studied by photoelectron spectroscopy and using quantum-chemical calculations by the semiempirical AM1 method. It has been concluded that the electronic and energy characteristics of four higher -MOs (frontier and three next orbitals) of this compound may be interpreted in terms of semipolar bonds formed by three atoms (C, P, and N). For describing two low-lying -MOs of the ⁴,⁵-phosphorine studied, it is necessary to take into account the --interaction.For Part 8, see Ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 827–831, April, 1996.     

含吲哚核端基多甲川菁染料的合成及性能

我们曾合成了具有桥环的硫三碳菁及多甲川苯乙烯菁,并测定了光学性能。本文报道吲哚环为端基的桥链三碳菁和四甲川苯乙烯菁的合成及在有机溶剂中电子吸收光谱及溶解性能的测定。所用仪器同前,7种多甲川菁染料的合成反应如下: