Vibrational spectroscopy of tolane; Coriolis coupling between Raman-active modes of g symmetry

ABSTRACT

Vibrational spectroscopy of tolane (diphenylacetylene), which has 66 normal modes, has been advanced. Anharmonic wavenumber predictions were made with the quartic potential energy surface obtained with B3LYP/cc-pVTZ model and the second-order perturbation theory (VPT2). Infrared (IR) intensity and Raman activities were computed at the harmonic level. The IR spectrum of the crystal and Raman spectra of the liquid and the crystal tolane were newly recorded. The lingering problem of an excess of polarised Raman bands at wavenumbers appropriate for fundamentals, other than a_g modes, has now been attributed to Coriolis coupling within modes of g symmetry species. Consequently, D_2h point symmetry group has been confirmed for a planar tolane molecule. Assignments for almost all fundamentals of tolane are now secure. The assignment for ν₃₂ remains questionable. Remaining unassigned fundamentals are: ν₃₄ and ν₃₅, which, as a_u symmetry species, are IR- and Raman-inactive transitions, and ν₅₉(b_2u), which is predicted to have a very low wavenumber.     

Instability of the lowest triplet state of benzene under environmental perturbations : zero-field splitting and radiative properties of the spin components

Coupling is considered between the lower ³ B _1u and ³ E _1u states of benzene under the combined influence of substituents and the crystal field. A model is derived in which the value of the E.S.R. parameter E, the orientation of the zero-field axes relative to the molecular frame and the radiative properties of the upper two spin components of the lowest triplet state are interpreted in terms of an electronic wavefunction.

With the model the reduced intensity of the 0-0 band relative to the 8₁ ⁰ band in the phosphorescence spectra of a number of benzene-like systems is explained. Further the radiative properties of the zero-field spin components of toluene in a benzene host are interpreted; in this system the angle between the in-plane zero-field axes and the molecular axes appears to be 74° (±6°).     

NMR 1 J(HD) coupling in HD as a function of interatomic distance in the presence of an external magnetic field

A theoretical study has been made of the dependence of the ¹ J(HD) coupling in HD on the interatomic distance R in the presence of a static uniform magnetic field B ₀. The behaviour of all coupling terms arising from Ramsey's magnetic electron-nucleus interactions, Fermicontact (FC), spin-dipolar (SD) and paramagnetic (PSO) and diamagnetic (DSO) spin-orbital interactions is analysed qualitatively for large R. It is concluded that the PSO, DSO and SD terms become negligibly small as R increases. Detailed calculations were carried out for the FC term following two different approaches: detailed full CI calculations within a non-perturbative approach; and explicit diagonalization of the Hamiltonian operator restricted to the subspace spanned by the ¹Σ⁺;_g and the ³Σ⁺;_u states. Within the approximations considered, the FC term of ¹ J(HD) is found to be independent of B ₀ and to increase by several orders of magnitude, in agreement with previous results by Bacskay, G. B., 1995, Chem. Phys. Lett., 242, 507, until a critical distance R(B ₀) is reached, beyond which it almost vanishes. The quenching of the coupling at R(B ₀) is due to the splitting of the ³Σ⁺;_u state in the presence of the field B ₀. The stronger the field the shorter is R(B ₀).     

用铁磁共振方法同时测定单晶外延膜的Ku和K1

本文导出了兼具沿晶面法向感生单轴各向异性(K_u)和立方磁晶各向异性(K₁)的任一晶面沿任一方向的薄膜共振场公式,从而提出了同时测定K_u和K₁的一种方法。以(111)晶面为例,给出了具体方法和实验结果。     

Calculation of potential energy curves for Rb2 including relativistic effects

All-electron relativistic calculations have been performed on the Rb₂ molecule. The molecular orbitals are optimized within a spin-free no-pair Hamiltonian formalism and spin-orbit coupling is treated using quasi-degenerate perturbation theory. Potential curves of the ground state and several excited states are calculated, and the spectroscopic constants T _e, D _e, R _e and ω_e are in good agreement with experimental values. The spin-orbit splittings at the 5p and 6p asymptotic limits are found to be underestimated by about 30%. Large perturbations in the spectra from the 1¹Σ⁺ _u(A) state are predicted due to an avoided crossing with a 1 ³Π_ub state caused by spin-orbit interaction. The predissociation dynamics of the 2 ¹Π_uC and 3 ¹Π_uD states is discussed. The calculations support the observation that a (1) ³ Δ_u state causes the fast predissociation of the ^{3 1}Π_uD state but rule out the (2)³Σ⁺ _u state as causing the slow predissociation at the lower part of the 3 ¹Π_uD potential energy curve.     

Electron spin resonance in the photo-excited triplet state of free base porphin in a single crystal of n-octane

E.S.R. experiments have been performed on the lowest triplet state of free base porphin (H₂P) in a n-octane single crystal at 1·3 K. The results demonstrate that the large majority of guest molecules occur in two orientations. While the molecules in these two orientations are coplanar, they have their N-H H-N axes at right angles. The fine structure results show that the two molecular orientations have zero-field splittings that differ by a few per cent in magnitude. Further, the 65 cm^-1 doublet separation which appears in the fluorescence spectrum of H₂P is related to the occurrence of these two orientations.

Resolved hyperfine structure is obtained for the two in-plane canonical orientations of the magnetic field and also when the field bisects the angle between these two directions. From an analysis of the fine structure and hyperfine structure results it is established that the zero-field splitting pattern is described by the parameters (average over the two orientations) the x axis is taken along the N-H H-N direction and z is the out-of-plane axis. From a computer simulation of the hyperfine structure it further follows that this structure is dominated by a high spin density at the methine carbons; with the coupling constants of the C-H fragment proposed by Hirota et al. the methine density is found to be ρ_m = 0·163.

In order to interpret the experimental results the zero-field splitting parameters and spin density distribution have been calculated for the lower triplet states of H₂P on the basis of a set of PPP-SCF-MO-CI calculations. From these calculations it follows that the lowest triplet state must correspond to the excitation e_g ←a _2u in Gouterman's four-orbital model. In terms of the D _2h symmetry of the H₂P molecule the assignment is ³ B _2u (b _3g ←b _1u ). For this assignment the calculations yield .     

Spin relaxation of triplet pyrene in a crystal and in a glass

We have investigated the EPR spectral lines of the photo-excited triplet state of pyrene-d-10 both in a fluorene single crystal and an ethanol glass matrix. In the crystal we have measured the width, shape and saturation parameters, λ′, a and B _{1/2 ^u} , of the ΔM = 1 lines from both sites in the cleavage plane, Y-Z, at 193 K and along the principal directions, X, Y, Z, between 143 K and 300 K. In the glass the same parameters have been measured for the six resonances of the absorption derivative at 77 K. We have used a general deconvolution procedure to extract the unresolved inhomogeneous and homogeneous broadenings, ΔB _G and ΔB _L ≡ 1/γT ₂, and the spin-lattice relaxation rate, T ₁ ^-1, from λ′, a and B _{1/2 ^u} for the different types of resonances. The use of Fourier-series expansions permits optimal utilization of the data and resolution of the terms of different symmetries for these quantities. The application of the method of moments, using assumed spin densities, permits the demonstration that the main contribution to the constant term of ΔB _G, but only a small part of its anisotropy, originates from the intramolecular hyperfine interactions. As T ₂ and T ₁ are of the same order of magnitude, we have assumed the same mechanism, i.e. modulation of the fine-structure tensor D, for both relaxation effects. A first-order semi-classical treatment leads to partial agreement between the main features of the calculated and observed orientation dependences if one assumes strongly anisotropic librations coupled to large modulations of D. This is consistent with the maximal libration amplitudes estimated from the differences between the D tensors measured in the crystal and in the glass. Variations with temperature are attributed to a competition between the increase of modulation amplitudes and decrease of correlation time with heating.     

Magnetism in a UNi2/3Rh1/3Al single crystal

We report a magnetization, magnetostriction, electrical resistivity, specific heat and neutron scattering study of a UNi_2/3Rh_1/3Al single crystal, a solid solution of an antiferromagnet UNiAl and a ferromagnet URhAl. The huge uniaxial magnetic anisotropy confining the principal magnetic response to the c axis in the parent compounds persists also for the solid solution. The magnetization curve at 1.6 K has a pronounced S shape with an inflection at 12 T. The temperature dependence of magnetic susceptibility exhibits a maximum around 10 K and is magnetic history dependent at lower temperatures where the resistivity increases linearly with decreasing temperature. The low-temperature ρ(T) anomaly is removed in a magnetic field applied along c, which yields a large negative magnetoresistance amounting to m46 zin 14T (at 2 K). The C/T values exhibit a minimum around 12 K and below 8 K they become nearly constant (about 250 mJ mol^?1 K^?2), which is strongly affected by magnetic fields. Neutron scattering data confirm a non-magnetic ground state of UNi_2/3Rh_1/3Al. The bulk properties at low temperatures are tentatively attributed to the freezing of U magnetic moments with antiferromagnetic correlations. The additional intensities detected on top of nuclear reflections in neutron diffraction in a magnetic field applied along c are found to be proportional to the field-induced magnetization, which reflects field-induced ferromagnetic coupling of U magnetic moments. This scenario is corroborated also by finding low-temperature magnetostriction data that also scale with the square of magnetization.     

The 2000 Å absorption system of the benzene single crystal in polarized light

The 2000 Å absorption system in the benzene single crystal is investigated at liquid nitrogen temperature. The analysis of the polarized spectra recorded along b and c in (100) plates appears to be not in favour of the assignment of the π* └π system to an upper state of B _1u symmetry, and it is not in contrast with the hypothesis of a ¹ E _2g upper state.

The first band in the system, located at 46 565 cm^-1, and totally polarized along c, is discussed in terms either of an out-of-plane false origin of the ¹ E _2g └¹ A _1g system, or of a new transition lying between the first two well known π-systems of benzene, possibly of π* └σ type.     

Anisotropy of the upper critical field and specific heat in V3Si — a superconductor with cubic symmetry

The specific heat of a V₃Si single crystal (T _c=17 K, H _c2=20 T) in magnetic fields up to 8 T isinvestigated experimentally for three orientations of the field relative to the crystallographic directions — H∥〈001〉, H∥〈110〉, and H∥〈111〉. Both the upper critical magnetic field and the specific heat of the mixed state are observed to depend on the orientation of the magnetic field relative to the crystallographic directions (anisotropy): The critical field reaches its maximum value and the specific heat its minimum value in a field along the 〈001〉 direction. The anisotropy scale in both phenomena increases as the magnetic field and reaches 3% in a 6 T field. The interrelationship of the upper critical field anisotropy and the specific-heat anisotropy in type-II superconductors is studied. It is shown that the anisotropy of the specific heat in the mixed state in weak fields can serve as a criterion for nontrivial pairing. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 26–29 (10 January 1999)     

The probabilities of triplet-singlet transitions in aromatic hydrocarbons and ketones

Calculations have been performed on the probabilities of triplet-singlet transitions in benzene and acetone in connection with the decay times of the phosphorescence. The transition probability was determined from the extent to which excited singlet states are mixed with the triplet state. The assumption that in benzene the phosphorescent state has ³ B_2u properties—so that the ¹ B_1u singlet state is mixed with it-—yields the best agreement with the experimental data. In the case of acetone the phosphorescence was considered as a triplet-singlet transition in which only the electrons of the CO group are involved. In both cases the agreement with experiment is as satisfactory as in other calculations on transition probabilities, the figures for the decay times being 190 and 7 seconds for benzene and 7·8 and 0·6 milliseconds for acetone. The ratio of the calculated decay times is in good agreement with the experimental result (2·4×10⁴ and 1·2×1O⁴).     

Electron states in quantum-dot and antidot arrays placed in a strong magnetic field

Quantum electronic states in a dot (antidot) array in the presence of a dc magnetic field are studied. A new method of numerical calculation of the electron spectrum and wave functions in a two-dimensional periodic potential and perpendicular magnetic field is proposed. The magnetic-subband energies, density of electron states, and electron density |ψ(x,y)|², as well as the amplitude of the potential, and lattice period and degree of anisotropy for different magnetic fields have been found. The calculations were performed for quantum dots in the In_0.2Ga_0.8As-GaAs and GaAs-Al_0.3Ga_0,7As systems. The rearrangement of the spectrum with variation of magnetic field and with transition from the tight-binding to weak-binding approximation is studied (ω _c is the cyclotron frequency, and V ₀ is the periodic-potential amplitude). The calculations show that the two-dimensional lattices epitaxially grown presently on semiconductor surfaces permit observation of quantum effects associated with rearrangement of the spectrum (electron transport and optical absorption) in magnetic fields H⩽1 MG. Fiz. Tverd. Tela (St. Petersburg) 40, 1134–1139 (June 1998)     

Calculation of the Normal Vibrations of Benzene in the First Singlet Electron-Excited State 1 B 2u

Using the CIS/6-311+G^** method, the normal vibrations of the benzene molecule in the first singlet electron-excited state ¹ B _2u have been calculated. The algorithm of calculation of the force field in dependent coordinates by the method of generalized inversion is described. A method of autoscaling in dependent natural coordinates is suggested. For six groups of natural coordinates scaling factors have been obtained, the use of which has led to agreement between the calculated and experimental frequencies of the vibrations of benzene. The frequencies of the B _1u -symmetry-type vibrations, for which there is no experimental assignment, have been calculated. The problem of selection of the force field in dependent coordinates is discussed.     

Structural stability and mechanical properties of Be3N2 under high pressure

Abstract

A theoretical investigations on the structural stability and mechanical properties of Be₃N₂ crystallising in α and β phases was performed using first-principles calculations based on density functional theory. The obtained ground state structure and mechanical properties are in excellent agreement with the available experimental and theoretical data. A full elastic tensor and crystal anisotropy of Be₃N₂ in two phases are determined in the wide pressure range. Results indicated that the two phases of Be₃N₂ are mechanically stable and strongly pressure dependent in the range of pressure from 0 to 80 GPa. The superior mechanical properties show that the two phases of Be₃N₂ are potential candidate structures to be the hard material. And the α-Be₃N₂ has better mechanical properties than β-Be₃N₂. By the calculated B/G ratio, it is predicted that both phases are intrinsically brittleness and strongly prone to ductility when the pressure is above 65.6 and 68.5 GPa, respectively. Additionally, the pressure-induced elastic anisotropy analysis indicates that the elastically anisotropic of Be₃N₂ in both phases is strengthening with increasing pressure, and strongly dependent on the propagation direction.     

红宝石吸收宽带的强度

红宝石晶体中Cr³⁺与六个近邻O^2-组成一个有严重畸变的正八面体,因而高阶奇晶场与一阶奇晶场有相同的数量级。由于红宝石中Cr³⁺的格位近似保持C_3v对称,T_2u型的高阶场非常小,可以忽略,但T_1u,A_2u型高阶晶场对红宝石吸收谱强度则原则上不能予以忽视,对于Y带和U^⊥带,高阶场有显著贡献,但对U^‖带,所产生的强度非常小。本文考虑了格点奇对称振动对U,Y带强度的贡献,发现U^‖带主要是奇振动与电子耦合产生的吸收谱。由此出发,讨论了红宝石宽带振子强度、带形等问题,得到了与实验相符合的结果。     

Ferromagnetic resonance in a uniaxial magnetic film subjected to magnetic biasing along its hard axis

The precession dynamics of the magnetization of a film with an in-plane uniaxial anisotropy is analyzed in the spectrum of ferromagnetic resonance corresponding to magnetic biasing along the hard axis of the film. An additional resonance peak is revealed near magnetic anisotropy field H _u . This peak is related to the appearance of angular bistability due to the presence of two symmetric angular equilibrium positions in field H < H _u .     

Symmetry analysis of the interplay between local moment anisotropies and propagation vectors in the borocarbides

Representational analysis is used to examine the interplay between Fermi surface nesting and local moment effects in the formation of the magnetically ordered states of the rare-earth nickel borocarbides, RNi₂B₂C. We derive compatibility tables for the propagation wavevector k, the local moment anisotropy and the ordered moment direction μ _k for materials with this tetragonal crystal structure. The magnetic structures observed in the rare-earth nickel borocarbides are discussed in this context.     

Nuclear relaxation and motional anisotropy of liquid s-triazine

The dynamic structure of liquid s-triazine has been studied by analysing the deuterium and nitrogen-14 quadrupolar relaxation data of d ₃-s-triazine.

The molecular motions are markedly anisotropic with: (a) fast, large angle jump, inertial type in-plane motions of almost zero activation enthalpy and large negative activation entropy; (b) comparatively slow, small angle jump, rotational diffusion type, out of plane motions of higher activation enthalpy and small activation entropy. Comparison of the data on the dynamic behaviour of pyridine [3] and benzene [4] with the present ones on s-triazine leads to a general picture of molecular motions of planar hexagonal rotors in the liquid state (at atmospheric pressure). The behaviour of pyridine, which has a dipole moment departs somewhat from the more similar (and more anisotropic) behaviour of benzene and s-triazine. These results also support our previous finding of motional anisotropy in liquid pyridine [3].

A pictorial representation of the motional anisotropy in benzene, pyridine and s-triazine is giving using motional ellipsoids whose axes lengths are proportional to the diffusion constants.     

Molecular dynamics calculation of the dielectric constant

Molecular dynamics (MD) simulations of an isolated dipolar system (made of Stockmayer molecules) has been performed. A two dimensional system has been adopted, using a ‘2-D electrostatics’ dipolar interaction.

The isolated system was a disc in vacuo. The autocorrelation function (ACF) of the moment of the disc was extracted from our runs, together with the ACF of the moment of a small inner disc (‘microscopic’ or ‘multimolecular’ ACF). Comparison of these two ACF has allowed us to compute the response function of the annulus between the two discs. The behaviour of the latter was that predicted by the theory of Fatuzzo and Mason. It is thus shown, for the first time, that one can obtain, by numerical simulation of a few hundred molecules, reliable values of the complex permittivity of highly polar fluids, despite the long range character of the dipolar interaction.

Its behaviour is surprisingly realistic when compared with that of real 3-D polar liquids.

Monomolecular ACF have also been extracted from the MD runs. They recall that of the Itinerant Oscillator model, the long time behaviour of <u(0). u(t)> being diffusive, but shorter-lived than that of the multimolecular ACF. Compared to the free rotation, the monomolecular orientational correlation time dt (u(0). u(t)> cannot be explained quantitatively using the theory of dielectric friction derived from the Onsager reaction field. Finally a comparison between this monomolecular correlation time and the multimolecular one is made: Models linking the ratio of these two times to the Kirkwood g _K factor are examined.