Manifestation of the vibronic analogue of the Fermi resonance in quasi-line spectra of porphyrins: Experiment and theoretical analysis

The quasi-line low-temperature (4.2 K) fluorescence excitation spectra of two porphyrins, meso-tetraazaporphin and meso-tetrapropylporphin introduced into an n-octane matrix are measured in the range of the S ₀ → S ₂ electronic transition. A characteristic feature of these spectra is that a conglomerate of quasi-lines—a structured complex band—is observed instead of one 0–0 quasi-line of the S ₀ → S ₂ transition. In this band, the intensity distributions for the two main types of impurity centers considerably differ from each other. The occurrence of such conglomerates is interpreted as a result of nonadiabatic electronic-vibrational interactions between vibronic S ₂ and S ₁ states (the complex vibronic analogue of the Fermi resonance). The frequencies and intensities of individual transitions determined from the deconvolution of complex conglomerates are used as the initial data for solving the inverse spectroscopic problem: the determination of the unperturbed electronic and vibrational levels of states involved in the resonance and the electronic-vibrational interaction matrix elements between them. This problem is solved with a method developed previously. The energy intervals between the S ₂ and S ₁ electronic levels of the two main types of impurity centers formed by molecules of a given porphyrin in the crystal matrix are found to significantly differ from each other (～100 cm^?1). At the same time, the energies of the unperturbed vibrational states of the S ₁ electronic level partcipating in the resonance are very close to each other for these two types of impurity centers.     

Finite and infinite dynamical systems of identical interacting particles

A dynamical system of infinite volume and of infinite number of identical interacting particles occupying energy levels has been constructed as the limit of an infinite sequence of finite, equivalent systems of increasing size and particle number. Systems both in equilibrium and in non-equilibrium state (designated S_∞=limS_k, , respectively, k=1,2,…) were investigated. The main results are:(i) The values in the T-limit (thermodynamic limit) of the physical quantities characterizing these systems are determined.(ii) The time evolution process both in and in systems is governed by the non-linear rate equations with common initial conditions p_i(t₀), where p_i(t)=n_i(t)/N are the occupation probabilities at time t. The time evolution process in the and systems is the same. The asymptotic approach to the equilibrium state is proved.(iii) For the case of the equilibrium state, the Boltzmann probability distribution p_i is given by the equation −lnp_i+a+e_ib=0 common to S_k and S_∞ systems with the same value of a and b. The term a=β⁻¹a_e, where a_e is the free energy per particle, and .(iv) The conditions for the equivalence of the systems being in equilibrium and also of the ones in non-equilibrium are stated.     

Fluorescence and fluorescence excitation spectra of jet-cooled carbazole

The fluorescence excitation spectra of jet-cooled carbazole molecules at vibrational temperatures of 55 and 80 K and the fluorescence spectrum of these molecules excited by radiation at the frequency of a pure electronic transition are measured. As the vibrational temperature increases, the excitation spectra exhibit a series of lines of the same symmetry, which are caused by the interaction of the active vibration with a subensemble of optically inactive vibrations. The final symmetry of the totally and nontotally symmetric vibrations is determined from the shape of the rotational contours of the lines of vibronic transitions. The values of a decrease in the frequency of the nontotally symmetric vibrations in the first excited electronic state S ₁ due to their interaction with the electronic state S ₂ are calculated to be up to 100 cm^?1. The frequencies of the pure electronic transitions in the absorption and fluorescence spectra coincide with each other and are equal to 30809 cm^?1, the frequencies of vibrations in the ground state S ₀ exceeding the frequencies of the corresponding vibrations in the excited state S ₁. The degree of polarization of the integral fluorescence is determined for a series of vibronic transitions of the a ₁ and b ₂ final symmetry that are observed in the fluorescence excitation spectra, and the contribution of the intensity with the borrowed polarization θ_⊥ to the integral fluorescence is calculated. It is found that the intensity θ_⊥ is higher for the transitions of the b ₂ symmetry and can reach ≈50%.     

Spectroscopic characterization of structural isomers of naphthalene: 1-Phenyl-1-butyn-3-ene

Laser induced fluorescence (LIF), single vibronic level dispersed fluorescence (DFL) spectra, and high resolution rotationally resolved scans of the S₀–S₁ transition of the C₁₀H₈ isomer 1-phenyl-1-butyn-3-ene have been recorded under jet-cooled conditions. The S₀–S₁ origin of PAV at 34 922 cm⁻¹ is very weak. A vibronic band located 464.0 above the origin, assigned as 30¹₀, dominates the LIF excitation spectrum, with intensity arising from vibronic coupling with the S₂ state. High resolution scans of the S₀–S₁ origin and 30¹₀ vibronic bands determine that the former is a 65:35 a:b hybrid band, while 30¹₀ is a pure a-type band, confirming the role for vibronic coupling and identifying the coupled state as the S₂ state. DFL spectra of all vibronic bands in the first 800 cm⁻¹ of the spectrum were recorded. A near-complete assignment of the vibronic structure in both S₀ and S₁ states is obtained. Herzberg–Teller vibronic coupling is carried by two vibrations, ν₂₈ and ν₃₀, involving in-plane deformations of the vinylacetylene side chain, leading to Duschinsky mixing evident in the intensities of transitions in excitation and DFL spectra. Extensive Duschinsky mixing is also present among the lowest five out-of-plane vibrational modes, involving motion of the side chain. Comparison with the results of DFT B3LYP and TDDFT calculations with a 6-311+G(d,p) basis set confirm and strengthen the assignments.     

Gauge-fixing conditions and natural decompositions of Yang-Mills fields

A general method of constructing canonical decompositions of Yang-Mills fields is presented. The gauge dependence is concentrated to a minimal set of variables which parametrize the group space of the gauge group. The decompositions fall into different classes for different boundary conditions and are characterized by a specific connection to gauge-fixing conditions which are consistent with these boundary conditions. All classes connected to gauge-fixing conditions on the field strength E_aⁱ yield local decompositions generalizing a similar decomposition given by Goldstone and Jackiw for SU(2) Yang-Mills. All classes connected to gauge-fixing conditions. which also involve A_aⁱ yield non-local decompositions in space. Explicit canonical decompositions are given for those classes which are connected to the Coulomb and axial gauges as well as the gauges of the form B_a^b_kE_b^k = 0, where B_a^b_k are constants.     

A disordered ising model with internal degrees of freedom

A solvable Ising-system withnn-interactions as a basic system is considered. This system is assumed to undergo a phase transition so that the thermal quantityq=Σ _i> ₀ ² /N, which is not necessarily the order parameter of the basic system, is different from zero (q≠0) forT _c. The whole system consists of the basis {S _i} and an equal number of additional spins η _i which are coupled linearly with the basic spinsS _i through an exchange constantJ _i which is distributed at random. The pairs of spinsS _i ?η _i can be interpreted as clusters with an internal degree of freedom. The specific heat Δc and the susceptibility Δ_χ of the internal degree of freedom can be separated exactly and show typical spin glass properties: the specific heat Δc is an analytic function over the whole temperature range and the susceptibility Δ_χ shows a cusp at the transition temperatureT _c of the basic system.     

Functional properties of quantum logics

A quantum logic is defined as a setL of functions from the set of all statesS into [0, 1] satisfying the orthogonality postulate: for any sequencea ₁,a ₂, ... of members ofL satisfyinga _i+a _j≤1 fori≠j there isb∈L such thatb+a ₁+a ₂+...=1. Every logicL is in a natural way an orthomodular σ-orthocomplemented partially ordered set (L, ≤, ′) with members ofS inducing a full set of measures onL. It is shown that a logicL is quite full if and only if (L,≤,′) is isomorphic to an orthocomplemented set lattice of subsets ofS. Sufficient conditions are given in order that a quite full logic be representable in the set of projection quadratic formsf(u)=(Pu, u) on a complex Hilbert space, or in the set of trace functionsf(A)=Trace (AP) generated by projectionsP, where the domain off is the set of non-negative self-adjoint trace operators of trace 1 in a complex Hilbert space.     

Low-lying states of trinuclear mixed-valence cluster: [Fe3S4]0

Low-lying energy states of the [Fe₃S₄]⁰ cluster have been calculated by taking into account the double exchange, superexchange and vibronic interaction. It was found that the adiabatic potential of the excited state withS=0 corresponds to the full delocalization of the “excess” charge. From the analysis of experimental data of Mössbauer spectroscopy and the temperature dependence of the magnetic susceptibility the double exchange parametert≥4000 cm^?1 and the vibronic interaction parameter λ₂/2k cm^?1 have been estimated.     

离子有限拉摩半径效应对低频漂移波本征模的影响

本文指出,对于S_y≡k_y²ρ_i²≥1的短波模,通常所用的漂移波本征方程是不自洽的,由此而得出“普适模是稳定的”结论也是不恰当的。我们在弱剪切条件(L_s/r_n>>[2T_im_i/Tm_e]^1/2)下导出了适合S_y≥1的方程,并讨论了其近似表式。在最低级近似下(主要是忽略k′ρ_i²项),证明了不存在γ≥0的不稳定模式。考虑一级修正项后,尚不能得出确定的结论。 关键词：     

Why are formaldehyde and (possibly) propynal nonplanar in their S1(π1, n) electronic states?

Abnormally low frequencies observed for the out-of-plane vibration (b₁) of the $\text{A}\text{?}{}^1\text{A}{}_2$ electronic state of formaldehyde (H₂CO) and for the analogous carbonyl hydrogen vibration (a″) of $\text{A}\text{?}{}^1\text{A″}$ propynal (HCCCHO) are modeled by means of two-state calculations of vibronic coupling with higher singlet states, ¹B₂ and ¹A′, respectively. In each case, the active vibration is the out-of-plane hydrogen motion. The same vibronic calculations reproduce also the large positive anharmonicities of the active vibrations in the $\text{A}\text{?}\text{(π}{}^1\text{, n)}$ states; for H₂CO the calculated vibrational spacing alternates as observed, consistent with the known nonplanar structure, while in propynal the calculated spacing increases regularly, thus predicting an effectively planar structure. The nonplanarity of H₂CO is caused mainly by a vibronic coupling constant nearly twice that of propynal. The H₂CO coupling constant is near the value estimated independently by means of the intensity “borrowed” by the S₁-S₀ transition from the much stronger S₂-S₀ transition. Brief consideration is given to analogous vibrational levels of the ¹A₂ state of H₂CS and of the ³A₂ state of D₂CO in the vibronic context of this paper.     

Mode-selective internal conversion of perylene

We observed fluorescence excitation spectra and dispersed fluorescence spectra for single vibronic level excitation of jet-cooled perylene-h ₁₂ and perylene-d ₁₂, and carefully examined the vibrational structures of the S₀ ¹ A _g and S₁ ¹ B _2u states. We performed vibronic assignments on the basis of the results of ab initio calculation, and found that the vibrational energies in the S₁ state are very similar to those in the S₀ state, indicating that the potential energy curves are not changed much upon electronic excitation. We conclude that the small structural change is the main cause of its slow radiationless transition and high fluorescence quantum yield at the zero-vibrational level in the S₁ state. It has been already reported that the lifetime of perylene is remarkably short at specific vibrational levels in the S₁ state. Here, we show that the mode-selective nonradiative process is internal conversion (IC) to the S₀ state, and the ν₁₆(a _g ) in-plane ring deforming vibration is the promoting (doorway) mode in the S₁ state which enhances vibronic coupling with the high-vibrational level (b _2u ) of the S₀ state.     

On the invariants of the complex Ginzburg-Landau equation

Using Lie group theory, both the invariants and the similarity variables of the complex Ginzburg—Landau equation V_xx = a(V_t + bV) + cV|V|^2kwherea,b,c?Iandk?I are constructed.     

The Phosphorescence Excitation Spectrum of Jet-Cooled Xanthione in the Region of the T1←S0 and S1←S0 Absorption Transitions

The ³A₂(nπ*)→¹A₁X (T₁→S₀) phosphorescence excitation spectrum of jet-cooled xanthione was investigated in the region 14 920-17 600 cm⁻¹. The structure observed is shown to be due to the T₁←S₀ absorption and an assignment in terms of the vibronic structure of that band is proposed. A previous assignment of the S₁←S₀ origin is considered in detail and the transition involved is shown to be most probably due to absorption of a vibronic triplet state T_1z,ν7. An alternative but tentative assignment of the S_1,0←S_0,0 transition is suggested. Comparison is made with previous spectroscopic and theoretical work on the molecule and its congeners, 4H-pyran-4-thione and 4H-1-benzopyran-4-thione.     

Effect of diffusion on gain saturation in gas lasers

A theoretical model is developed to account for the effect of diffusion on gain saturation in gas lasers. It is shown that the effect can be characterized by the functionK(k ₂ a, k ₂ b), which depends on pressure, temperature, radius of the beama, and the radius of the cylindrical cavityb. It is concluded that diffusion can be very effective whenk ₂ a is small andb is several times larger thana.     

Universality Limits of a Reproducing Kernel for a Half-Line Schrödinger Operator and Clock Behavior of Eigenvalues

We extend some recent results of Lubinsky, Levin, Simon, and Totik from measures with compact support to spectral measures of Schrödinger operators on the half-line. In particular, we define a reproducing kernel S _L for Schrödinger operators and we use it to study the fine spacing of eigenvalues in a box of the half-line Schrödinger operator with perturbed periodic potential. We show that if solutions u(ξ, x) are bounded in x by ${e^{\epsilon x}}We extend some recent results of Lubinsky, Levin, Simon, and Totik from measures with compact support to spectral measures of Schr?dinger operators on the half-line. In particular, we define a reproducing kernel S _L for Schr?dinger operators and we use it to study the fine spacing of eigenvalues in a box of the half-line Schr?dinger operator with perturbed periodic potential. We show that if solutions u(ξ, x) are bounded in x by e^ex{e^{\epsilon x}} uniformly for ξ near the spectrum in an average sense and the spectral measure is positive and absolutely continuous in a bounded interval I in the interior of the spectrum with x₀ ? I{\xi_0\in I}, then uniformly in I,

\fracSL(x0 + a/L, x0 + b/L)SL(x0, x0)? \fracsin(pr(x0)(a - b))pr(x0)(a - b),\frac{S_L(\xi_0 + a/L, \xi_0 + b/L)}{S_L(\xi_0, \xi_0)}\rightarrow \frac{\sin(\pi\rho(\xi_0)(a - b))}{\pi\rho(\xi_0)(a - b)},      16. Anisotropic thermopower of the organic metal, β-(BEDT-TTF)2I3      K. Mortensen  J.M. Williams  H.H. Wang 《Solid State Communications》1985,56(1):105-110 Thermopower of the ambient pressure organic superconductor β-(BEDT-TTF)2I3 has been studied. Measurements performed on, respectively, crystals of needle formed morphology and on flake-like crystals with hexagon shape showed equal thermopower results. S was measured along the a-axis as well as along the b′-axis. Marked anisotropy is observed in the entire temperature region studied. The temperature dependence, as represented by dS/dT, is, however, nearly isotropic. On the basis of an analysis of anisotropic thermopower we attribute the isotropic part of S to a term depending on the bond-properties and the anisotropic part of S to the scattering mechanism. The analysis yields transfer integrals of the order of 0.12 eV along both a- and b′-axes.      17. ESR millimeter-band spectroscopy of magnetic ordering in the low-dimensional magnet CuGeO3      S. V. Demishev  A. V. Semeno  N. E. Sluchanko  N. A. Samarin  A. N. Vasil’ev  L. I. Leonyuk 《Journal of Experimental and Theoretical Physics》1997,85(5):943-948 Resonant absorption of microwaves in CuGeO3 single crystals in a frequency band of 40 to 120 GHz, in magnetic field B⩽15 T, at temperatures ranging between 0.5 and 300 K, and in the configuration B∥a has been investigated. Several absorption lines (S 0, S a, and S b) whose parameters strongly depend on temperature have been detected close to ESR. The temperature dependence of the total absorption in the main line S 0 with the Landé g-factor g 0=2.154 at temperatures above the spin-Peierls transition temperature is in good agreement with Bonner and Fisher’s theoretical prediction for a one-dimensional Heisenberg spin chain. In addition to the main resonance, a resonance of smaller amplitude, S a, with the g-factor g a=2.72 has been detected at temperatures ranging down to a characteristic temperature T≃1 K, below which the amplitude of this feature drops to zero. A radical restructuring of the magnetoabsorption spectrum occurs at the temperature of the spin-Peierls transition T SP≈14 K. At T<12 K new features emerge in the spectrum, namely, a broad absorption line overlapping with the narrow lines S 0 and S a, and a line S b with g b=1.83, which is not detected at temperatures above T SP. An analysis of amplitudes and total absorption of ESR lines as functions of temperature has shown that the temperature range below 1 K is anomalous, which may be caused by an additional ordering in the CuGeO3 magnetic subsystem at low temperatures. Zh. éksp. Teor. Fiz. 112, 1727–1738 (November 1997)      18. Vibronic-spin-orbit coupling in octachlorodibenzo-p-dioxin      E. A. Gastilovich  V. G. Klimenko  N. V. Korol’kova  S. A. Serov 《Optics and Spectroscopy》2002,93(5):682-689 The dipole moments of vibronic transitions P 0R caused by vibronic-spin-orbit coupling along the coordinates of out-of-plane vibration modes R (to which the most intense vibronic lines of the fine-structure phosphorescence spectrum correspond) were calculated for the 3 B 1u (π π*) → S 0 electronic transition in an octachlorodibenzo-p-dioxin molecule. The dependence of distribution (P 0R )2 over R on the constant of spin-orbit coupling ?A in different atomic groups (A = C, O, α-Cl, and β-Cl) of the molecule is ascertained. The contribution of these atomic groups (related to ?A) to the value of P 0R i for the transitions from various triplet i-sublevels of the electronic state is determined. The obtained results about the different effect of the α-Cl and β-Cl atoms on the vibronic P 0R i and pure electronic transition dipole moments are discussed in connection with experimental data on the weak influence of the amount of chlorine atoms in polychlorinated dioxins on the phosphorescence decay time.      19. Theoretical Analysis of the Fluorescence Spectra of 7-Azaindole and Its Tautomer      G. N. Ten  O. E. Glukhova  M. M. Slepchenkov  V. I. Baranov 《Optics and Spectroscopy》2016,120(3):359-366 The electronic—vibrational fluorescence spectra of the first, S0 → 1Lb, and second, S0 → 1La, electronic transitions of 7-azaindole and its tautomer for an isolated state have been calculated. Specific features of structural changes in 7-azaindole and its tautomer upon electronic excitation are determined. Vibrational spectra are assigned for the ground state, and the vibrational structure of fluorescence spectra is interpreted. It is shown that the intensity redistribution between the 6a and 6b oscillations, which is observed in the fluorescence spectrum of the S0 → 1Lb transition in 7-azaindole, can be explained as a result of intensity borrowing (according to the Herzberg—Teller mechanism) from the 1La state.      20. Assignments of visible absorption of s-tetrazine vapor      K.K. Innes  L.A. Franks  A.J. Merer  G.K. Vemulapalli  T. Cassen  J. Lowry 《Journal of Molecular Spectroscopy》1977,66(3):465-477 A detailed vibrational analysis of the 5515 Å absorption of s-tetrazine (tetra-azabenzene) vapor is attempted. More than 80% of the total intensity of the system can be accounted for by band assignments to a single allowed electronic transition, 1B3u-1Ag. The only progression-forming vibration in absorption in ν6a. Three progressions in ν′6a account for all intense cold bands. Isotopic shifts of bands lead to convincing assignments of the two excited-state vibrations upon which ν6a progressions are based, namely ν6b and ν8a. It is shown that in all probability the antisymmetric mode ν6b is prominent because of vibrational (Fermi) resonance rather than because of vibronic interactions.

Anisotropic thermopower of the organic metal, β-(BEDT-TTF)2I3

Thermopower of the ambient pressure organic superconductor β-(BEDT-TTF)₂I₃ has been studied. Measurements performed on, respectively, crystals of needle formed morphology and on flake-like crystals with hexagon shape showed equal thermopower results. S was measured along the a-axis as well as along the b′-axis. Marked anisotropy is observed in the entire temperature region studied. The temperature dependence, as represented by dS/dT, is, however, nearly isotropic. On the basis of an analysis of anisotropic thermopower we attribute the isotropic part of S to a term depending on the bond-properties and the anisotropic part of S to the scattering mechanism. The analysis yields transfer integrals of the order of 0.12 eV along both a- and b′-axes.     

ESR millimeter-band spectroscopy of magnetic ordering in the low-dimensional magnet CuGeO3

Resonant absorption of microwaves in CuGeO₃ single crystals in a frequency band of 40 to 120 GHz, in magnetic field B⩽15 T, at temperatures ranging between 0.5 and 300 K, and in the configuration B∥a has been investigated. Several absorption lines (S ₀, S _a, and S _b) whose parameters strongly depend on temperature have been detected close to ESR. The temperature dependence of the total absorption in the main line S ₀ with the Landé g-factor g ₀=2.154 at temperatures above the spin-Peierls transition temperature is in good agreement with Bonner and Fisher’s theoretical prediction for a one-dimensional Heisenberg spin chain. In addition to the main resonance, a resonance of smaller amplitude, S _a, with the g-factor g _a=2.72 has been detected at temperatures ranging down to a characteristic temperature T≃1 K, below which the amplitude of this feature drops to zero. A radical restructuring of the magnetoabsorption spectrum occurs at the temperature of the spin-Peierls transition T _SP≈14 K. At T<12 K new features emerge in the spectrum, namely, a broad absorption line overlapping with the narrow lines S ₀ and S _a, and a line S _b with g _b=1.83, which is not detected at temperatures above T _SP. An analysis of amplitudes and total absorption of ESR lines as functions of temperature has shown that the temperature range below 1 K is anomalous, which may be caused by an additional ordering in the CuGeO₃ magnetic subsystem at low temperatures. Zh. éksp. Teor. Fiz. 112, 1727–1738 (November 1997)     

Vibronic-spin-orbit coupling in octachlorodibenzo-p-dioxin

The dipole moments of vibronic transitions P _0R caused by vibronic-spin-orbit coupling along the coordinates of out-of-plane vibration modes R (to which the most intense vibronic lines of the fine-structure phosphorescence spectrum correspond) were calculated for the ³ B _1u (π π*) → S ₀ electronic transition in an octachlorodibenzo-p-dioxin molecule. The dependence of distribution (P _0R )² over R on the constant of spin-orbit coupling ?_A in different atomic groups (A = C, O, α-Cl, and β-Cl) of the molecule is ascertained. The contribution of these atomic groups (related to ?_A) to the value of P _0R ⁱ for the transitions from various triplet i-sublevels of the electronic state is determined. The obtained results about the different effect of the α-Cl and β-Cl atoms on the vibronic P _0R ⁱ and pure electronic transition dipole moments are discussed in connection with experimental data on the weak influence of the amount of chlorine atoms in polychlorinated dioxins on the phosphorescence decay time.     

Theoretical Analysis of the Fluorescence Spectra of 7-Azaindole and Its Tautomer

The electronic—vibrational fluorescence spectra of the first, S₀ → ¹L_b, and second, S₀ → ¹L_a, electronic transitions of 7-azaindole and its tautomer for an isolated state have been calculated. Specific features of structural changes in 7-azaindole and its tautomer upon electronic excitation are determined. Vibrational spectra are assigned for the ground state, and the vibrational structure of fluorescence spectra is interpreted. It is shown that the intensity redistribution between the 6a and 6b oscillations, which is observed in the fluorescence spectrum of the S₀ → ¹L_b transition in 7-azaindole, can be explained as a result of intensity borrowing (according to the Herzberg—Teller mechanism) from the ¹L_a state.     

Assignments of visible absorption of s-tetrazine vapor

A detailed vibrational analysis of the 5515 Å absorption of s-tetrazine (tetra-azabenzene) vapor is attempted. More than 80% of the total intensity of the system can be accounted for by band assignments to a single allowed electronic transition, ¹B_3u-¹A_g. The only progression-forming vibration in absorption in ν_6a. Three progressions in ν′_6a account for all intense cold bands. Isotopic shifts of bands lead to convincing assignments of the two excited-state vibrations upon which ν_6a progressions are based, namely ν_6b and ν_8a. It is shown that in all probability the antisymmetric mode ν_6b is prominent because of vibrational (Fermi) resonance rather than because of vibronic interactions.