The Spectrum of the Molecular Eigenstates of Pyrazine and the Reconstruction of Decays of Rotational States of the  1B3u (0–0) Transition of Pyrazine

Meer, B. J. van der; Jonkman, Harry T.; Kommandeur, Jan

doi:10.1155/lc.2.77

Cited by 42 publications

(5 citation statements)

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“…The molecular eigenstate spectra of pyrazine belonging to the 0−0 band of the S 0 → S 1 transition have been precisely examined first by van der Meer et al with an ultrahigh-resolution of ∼10 MHz, and the energies and intensities of the spectra belonging to the P(1) transition are given for the 12 strongest states. The same group showed that it is possible to relate the spectra observed for the P(1) transition to the S−T mixed states composed of a zero-order singlet state with J’ = 0 and 11 zero-order triplet states by a trial-and-error method, which are denoted by |S〉 and {|T j 〉} in eq 3 . Lawrance and Knight reanalyzed the data by using a more elegant deconvolution procedure, and {|T j 〉} located at −2821.5, −2495.4, −1380.5, −518.7, −340.9, −304.1, −90.7, −8.8, 436.7, 619.7, and 816.3 MHz were shown to interact with the S 1 origin with J’ = 0 with the coupling strengths of 289.3, 228.4, 287.0, 84.0, 53.8, 75.9, 129.5, 127.5, 422.7, 79.0, and 56.0 MHz, respectively.…”

Section: Magnetic Field Effects On Fluorescencementioning

confidence: 99%

Magnetic Field Effects on Fluorescence in Isolated Molecules with the Intermediate Level Structure of Singlet−Triplet Mixed States

Ohta

1996

J. Phys. Chem.

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A review is presented of external magnetic field effects on the fluorescence of isolated molecules which exhibit the intermediate level structure composed of singlet−triplet mixed states. Fluorescence intensity (quantum yield), decay profile (lifetime), and polarization are well affected by an external magnetic field, even when fluorescence is considered to be emitted from a diamagnetic singlet state. Effects of molecular rotation, molecular vibration, methyl internal rotation, and deuterium substitution are observed in magnetic field effects on fluorescence, and these effects are interpreted in terms of the level density of the triplet states coupled to a singlet state. It is also shown how intramolecular vibrational energy redistribution and dissociation via triplet states are related to the field dependence of fluorescence.

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Section: Magnetic Field Effects On Fluorescencementioning

confidence: 99%

Magnetic Field Effects on Fluorescence in Isolated Molecules with the Intermediate Level Structure of Singlet−Triplet Mixed States

Ohta

1996

J. Phys. Chem.

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“…Необходимо отметить, что обратная задача выглядит достаточно необычно и первоначально для ее решения применялся метод проб и ошибок [2,22] (с использованием данных для молекул нафталина и пиразина соответственно). Критерием подгонки параметров A m и B m служило совпадение интенсивностей рассчитанного и наблюдаемого спектров.…”

Section: постановка задачиunclassified

“…В табл. 2 наши результаты сравнены с данными расчетов на основе методов проб и ошибок [22] и функции Грина [27]. Как видно, значения A m и B m с точностью до двух знаков после десятичной точки совпадают во всех методах.…”

Section: расчеты матричных элементов a M и B M для молекул порфиринов и пиразинаunclassified

“…, 11) с электронным состоянием S 1 молекулы пиразина (все в 10 −2 cm −1 ) Экспериментально значения E k определяются с точностью до двух знаков после десяточной точки, последний знак для величин Am и Bm следует считать лишним. Он приведен только для сравнения с данными расчетов[22] и[27].…”

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Решение Обратной Задачи Для Сложного Вибронного Аналога Резонанса Ферми На Основе Плоских Вращений Якоби

Кузьмицкий¹

2020

Журнал Технической Физики

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Based on algebraic methods, we have found an accurate solution for the inverse task for the vibronic analogue of the complex Fermi resonance, i.e. the determination from the spectral data (energies Ek and transition intensities Ik of the observed conglomerate of lines, k = 1, 2, ..., n; n > 2) energies of the «dark» states Am and the matrix elements of their coupling Bm with the «bright» state. The algorithm consists of two stages. At the first stage, the Jacobi plane rotations are used to construct an orthogonal similarity transformation matrix X, for which the elements of the first row obey the requirement (X1k)^2 = Ik, which corresponds to that fact that there is only one non-perturbed «bright» state. At the second stage, the quantities Am and Bm are obtained after solving the eigenvalue problem for block of «dark» states of the matrix Xdiag({Ek})X-1.

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“…1). The spectral deconvolution problem seems quite unusual, and to solve it initially the trial-and-error method was applied (for naphthalene [8,19], pyrazine [20]). In [21][22][23][24] the inverse problem in question was solved using the formalism of the Green's function, and later, for the case of discrete " dark" states, the method of direct-coupling model was formulated [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

DOORWAY models in the inverse problem for a complex vibronic analogue of the fermi resonance

Kuzmitsky

2022

Optics and Spectroscopy

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We solve the inverse problem for the complex Fermi resonance or its vibronic analogue, and to this end we use the matrix XEXt, where E=diag(\Ek\) is a diagonal matrix, Ek are the energies of the observed "conglomerate" of lines, and the intensities of these lines Ik determine the first row of the matrix X, (X1k)2=Ik k=1,2,...,n,n≥3. Hamiltonian matrix of the direct model, HDIR, whose parameters are the energies of pre-diagonalized "dark" states, Ai, and the matrix elements of their coupling to the "bright" state, Bi, (i=1,2,...,n-1), is obtained after the diagonalization of the XEXt block, which belongs to the "dark" states. We show that Hamiltonian matrix with the single doorway state (DW), HDW1, can be obtained from the matrices HDIR or XEXt by first step of the Householder triangularization, i.e. by similarity transformation with a reflection matrix constructed by quantities Bi or Di=(XEXt)1,i+1. For the energy of the first DW1 state, g1, and the matrix element of its coupling to the "bright" state, w1, the use of the Householder transformation gives: g1=Sigman-1i=1B2iAi/(Sigman-1j=1B2j)= Sigmank=1E3kIk/Sigmanl=1E2lIl, |w1|=(Sigman-1i=1B2i)1/2= Sigmank=1E2kIk)1/2. In similar way, using the Householder transformation, the Hamiltonians for the models with several doorway states, HDW2,HDW3,...,HDW(n-1), are successively obtained. The Hamiltonian of the DW(n-2) model is represented by a symmetric tridiagonal matrix HDW(n-1), its diagonal elements gi determine the energies of the DW1-,DW2-,...,DW(n-1) states, and the off-diagonal elements wi determine the corresponding coupling between them. Keywords: vibronic coupling, complex vibronic analogue of the Fermi resonance, inverse problem, Householder transformation, doorway models.

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The Spectrum of the Molecular Eigenstates of Pyrazine and the Reconstruction of Decays of Rotational States of the ¹B_3u (0–0) Transition of Pyrazine

Cited by 42 publications

References 3 publications

Magnetic Field Effects on Fluorescence in Isolated Molecules with the Intermediate Level Structure of Singlet−Triplet Mixed States

Magnetic Field Effects on Fluorescence in Isolated Molecules with the Intermediate Level Structure of Singlet−Triplet Mixed States

Решение Обратной Задачи Для Сложного Вибронного Аналога Резонанса Ферми На Основе Плоских Вращений Якоби

DOORWAY models in the inverse problem for a complex vibronic analogue of the fermi resonance

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