On the excess-energy dependence of radiationless decay rate constants

The results of calculations of the dependence of the radiationless rate constant on the excess of excitation energy within the two-electronic states model under the weak coupling and statistical limits are presented. It is assumed that the exact molecular states for a given electronic configuration are global in character containing equal contributions from all degenerated vibrational levels at a given excitation energy due to intramolecular vibrational relaxation (IVR). The results of calculations indicate an important role of the low-frequency vibrational modes, the potential energy surfaces of which cross between the two electronic states involved into the radiationless process. The sharp increase of the rate constant is predicted for the excitation energy below the diabatic crossing point, followed by saturation at higher energies. The calculated rate constants for the T₁→S₀ intersystem crossing in pyrazine and benzene are in good agreement with experimental observations. Some comments concerning the “channel-three” phenomenon in benzene are presented.     

Application of adiabatic theory of vibrational predissociation to T-shaped triatomic van der Waals' molecules

An expression for the rate constant of the vibrational predissociation (VPD) of T-shaped triatomic van der Waals' (vdW) molecules is derived on the basis of the adiabatic separation between the high-frequency intramolecular and low-frequency vdW modes. The intramolecular and vdW modes are assumed to be characterized by the Morse-type interaction potentials. The dependence of the VPD line width on the intramolecular vibrational quantum number of a T-Shaped I₂-He vdW molecule is calculated by using the expression derived. The magnitudes of the calculated VPD line width are of the same order as those of the experimental. It is shown that the Condon approximation is insufficient and the non-Condon treatment is necessary to evaluate quantitatively the VPD rate constant within the adiabatic theory.     

Efficient calculation of Franck–Condon factors and vibronic couplings in polyatomics

We present a technique for the calculation of Franck–Condon factors and other integrals between vibronic wave functions belonging to different electronic states. The technique is well suited for the determination of the nonadiabatic or spin‐orbit couplings related to radiationless decays in polyatomics. Rigorous or approximate partitions of the internal coordinate space are exploited to achieve better efficiency and/or to go beyond the harmonic approximation. The technique is tested by computing the Internal Conversion and InterSystem Crossing rates of (CH₃)₃CNO in its ¹(n→π*) state. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 968–975, 2001     

Lifetime measurements of two-photon excited vibronic levels in the low pressure limit: naphthalene

Single vibronic lifetimes of two-photon excited states are measured in the low pressure limit for naphthalene. The two-photon spectrum, besides yielding new states in S₁, is also free of the interference from the neighborhood of the S₂, known from one-photon experiments, and hence unperturbed lifetimes can be measured to higher excess energies. The overall pattern of lifetimes with excess energy including both one-photon and two-photon states shows that the vibronic structure is subordinate to an overall monotonic decrease, much as found earlier for β-naphthylamine. This indicates, at least for naphthalene, that radiationless processes into triplets are dominated by Franck—Condon factors and not by vibronic inductions and promoting modes.     

Nuclear coordinate dependence of electronic matrix elements for radiationless transitions

The nuclear coordinate dependence of the electronic matrix elements for radiationless transitions (in the weak coupling limit) is investigated by the use of a Q-centroid approximation. This approach bears a similarity to the familiar r-centroid method in diatomic spectroscopy, but has a wholy different physical character. Because the Q-centroid for electronic relaxation is obtained as an average with density of states weighted Franck—Condon factors, it is not restricted to geometries near the equilibrium position of the initial electronic state as it is in the case of radiative transitions (in the weak coupling limit). For totally symmetric vibrations, it is shown that the Q-centroids for poor accepting modes are in the vicinity of the equilibrium positions for this vibration, while those for good accepting modes tend towards the surface crossing along those vibrational modes. Thus, in the case of dominant accepting modes, the electronic matrix element reflects a Teller surface crossing mechanism for electronic relaxation, even though the density of states weighted Franck—Condon factors reflect a tunnelling mechanism. For non-totally symmetric vibrations, Q-centroids may be large or small independent of their accepting mode capabilities. Thus, coupling mechanisms, which are “forbidden” at the equilibrium geometry in aromatic hydrocarbons, may become allowed and even dominant because of very distorted Q-centroid configurations. This leads to another possible reason for the absence of observation of a vibration that is clearly assignable as a promoting mode in the single vibronic level fluorescence studies of benzene-like molecules. The results underscore previous warnings as to the enormous errors incurred by using the Condon approximation for the nuclear coordinate dependent energy denominators that appear in the electronic matrix elements.     

Pressure effect on the structural and electronic properties of CuInS2

The pressure dependence of the bond length and energy gap in chalcopyrite CuInS₂ between 0 and 40 GPa has been investigated using pseudopotentials plane-wave method within the generalized gradient approximation for the exchange-correlation potential. We found that the bond length decreases as the pressure increases. Also, the energy gap of CuInS2 expands as the pressure increases with a rate of 10.693 meV/GPa. The linear pressure coefficient calculated is approximately half the reported experimental value of 23 meV/GPA. Our calculated bulk modulus of 68.7 GPa is in good agreement with the available experimental and theoretical values. The present calculations show that the d-electrons of Cu ions are one of the important factors that dominate the contributions to the I-VI bonds and the energy gap in CuInS₂.     

On the distorted wave approximation for chemical reactions

Various procedures for constructing transition amplitudes for chemical reactions in the distorted wave approximation are demonstrated. Calculations are performed for the collinear reaction H+H₂(ν = 0) → H₂(ν = 0) + H at low energies. Comparison is made with exact results after unitarization is invoked through (1) exponential unitarization and (2) the Condon approximation. In the threshold region the Condon approximation gives quite reasonable agreement with exact results.     

Complex Franck—Condon overlap integral in nonradiative decays

Considering the nuclear coordinate (Q) dependence of the electronic energy denominator appearing in the virbonic coupling matrix element, a complex Franck—Condon overlap integral which is needed in order to evaluate the nonradiative decay rate constant not only in the weak coupling but also in the strong coupling case is derived. The real part of the overlap integral plays an important role in the weak coupling case. The imaginary part is originated from the potential energy surface crossing regions and, consequently, contributes to the nonradiative decay rate constant in the strong coupling case. When the Q-dependence of the electronic energy denominator is neglected, the complex overlap integral leads to the results ontained by using the usual Herzberg—Teller expansion method. It is shown that the complex integral is expressed by the optical Franck—Condon overlap integral multiplied by a correction factor when the nonradiative decay from the vibrationless state is considered.     

Quantum dynamics of vibration–vibration energy transfer for vibrationally excited HF colliding with H2

The rate constants for H₂–HF energy transfer processes, especially for those in vibrationally excited states, are very demanding in astrophysics and chemical laser engineering, especially for those in vibrationally excited states. Based on our recent potential energy surface, we used the coupled-states approximation including the nearest neighboring Coriolis couplings with energy-based local basis set to perform dynamics calculation for the H₂–HF energy transfer system. Rate constants for vibrational transitions (1; 3) → (0; 4), (1; 3) → (2; 2), and (0; 3) → (1; 2) were obtained. For state-to-state rate constants, transitions that have no internal angular momentum gap dominate at high temperatures. The vibrational-resolved rate constant for (1; 3) → (0; 4) initially decreases and then increases with the temperature, while those for (1; 3) → (2; 2), and (0; 3) → (1; 2) transitions monotonically increase. The calculated rate constants are in good agreement with the available experimental results. These dynamical data can be further applied to the numerical simulation of hydrogen fluoride chemical laser. © 2018 Wiley Periodicals, Inc.     

Geometries and energies of the excited states of pyridazine studied by sac and sac CI calculations

The geometries and energies of the ground and excited states of pyridazine are calculated by an ab initio calculation which includes electron correlation. It is found that electron correlation plays an essential role in determining the geometries of the excited states. The optimized geometry of the T₁ state as well as that of the ground state are planar. On the other hand, the force constant along the twisted mode of the NN bond in the T₁ state is much smaller than that in the ground state. It is suggested that this distorted potential produces a large Franck-Condon factor between the T₁ and S₀ states, which leads to a very large radiationless decay rate constant of the T₁ state. The location of the S₂ origin is discussed on the basis of the present results.     

Linear and nonlinear optical susceptibilities for a novel borate oxide BaBiBO4: Theory and experiment

The linear and nonlinear optical susceptibilities for different tensor components of BaBiBO₄ single crystals have been calculated using the full-potential linear augmented plane wave method. The results of these calculations are verified by our measurements of linear and nonlinear optical properties using Nd-YAG laser at fundamental wavelength 1064 nm. The calculated energy gap is in a good agreement with experimental energy gap data obtained by optical absorption. We present results for the imaginary and real parts of the frequency-dependent dielectric constant. The calculated birefringence of BaBiBO₄ is positive in agreement with the experimental data. Calculations are reported for the frequency-dependent complex part of second-order nonlinear optical susceptibilities . The linear and nonlinear optical susceptibilities are scissors corrected to match the value of the energy gap from the local density approximation calculations with the experimental value. The second harmonic generation efficiency of this compound is about five times larger than KDP (KH₂PO₄). It is crucial that we have obtained a large anisotropy of the second-order susceptibilities for three main second-order tensor components both experimentally and theoretically. The possible origin of the obtained anisotropy is discussed within a framework of the energy band calculations.     

Excited state dynamics and spectroscopy of the 1A″ state of NSF vapor — comparisons with SO2

The fluorescence emission spectrum and analysis of NSF vapor is presented. Single vibronic level excitation near the S₁ origin gives rise to a 10 μs radiative decay. The fluorescence lifetime for excitation of levels with ? 4500 cm^?1 excess vibrational energy becomes controlled by a unimolecular radiationless process which is likely photodissociation; the dependence of this radiationless rate on energy and vibrational mode is investigated. The perturbations resulting from coupling of zero-order S₁ states with other vibronic levels which control the excited state dynamics of SO₂ are apparently not operative for NSF. Attempts are made to rationalize the grossly different dynamic behavior of the S₁ levels of these two otherwise very similar systems.     

Non-adiabatic unimolecular dissociation of polyatomic molecules. I. General theory

A golden-rule expression for the rate constant for unimolecular dissociation of a polyatomic molecule via a non-adiabatic process is expressed, in the harmonic oscillator approximation, in terms of a diatomic-like predissociation rate constant (k^diat), which contains all the electronic part of the dynamics of the process, and in terms of a product of (3N - 7) Frank—Condon factors. The influence of a difference in the equilibrium geometries of the initial and final electronic states is pointed out. A suitably averaged rate constant is defined, and it is shown that the shortcomings of the separable hamonic oscillator model can be usefully corrected by appropriate rate constant averaging, which allows for the effect of anharmonicity as well as for the non-separability and possibly poor choice of normal coordinates. The theory presented is suitable for calculating rate constants in cases where information regarding enery partitioning among fragments is not required.     

Photoisomerization through a “funnel” in polar and non-polar solvents

Fast radiationless deactivation S_e ∼→ S₀ of a photoexcited state through a “funnel” is discussed. The experimental rates of such transitions cannot be explained in general by a one-dimensional model considering only the angle of isomerization. Inclusion of the full number of degrees of freedom leads to a multi-dimensional intersection of the adiabatic potential energy surfaces U_e and U₀ in the region of the “funnel” where non-adiabatic interactions are strong and cause a fast electronic transition S_e ∼→ S₀. The rate constant of the isomerization reaction is found to be strongly related to the rate of rotational relaxation in the solvent and relaxation of the solvent orientational polarization.     

Radiative and nonradiative lifetimes in excited states of Ar,Kr and Xe atoms in a neon matrix

Synchrotron radiation with its intense continuum and its excellent time structure has been exploited for time resolved luminescence spectroscopy in the solid state. By selective excitation of n = 1, n′ = 2 exciton states of Xe, Kr and Ar atoms in a neon matrix we were able to identify the emitting states involved. Lifetimes within the cascade of radiative and radiationless relaxation between excited states as well as the radiative lifetimes for transitions to the ground state have been derived from the decay curves. Energy positions and radiative lifetimes of the emitting states correspond quite well with those of the free atoms. Radiative and radiationless relaxation processes take place within the manifold of excited states of the guest atoms. The rate constants for radiationless decay confirm an energy gap law. The order of the radiationless processes reaches in some cases extremely high values. Selection rules for spin and angular momentum are essential to understand the observed radiationless transition rates.     

Photoelectron spectrum of NO2−: SAC-CI gradient study of vibrational-rotational structures

Three-dimensional accurate potential energy surfaces around the local minima of NO₂⁻ and NO₂ were calculated with the SAC/SAC-CI analytical energy gradient method. Therefrom, the ionization photoelectron spectra of NO₂⁻, the equilibrium geometries and adiabatic electron affinity of NO₂, and the vibrational frequencies including harmonicity and anharmonicity of NO₂⁻ and NO₂ were obtained. The calculated electron affinity was in reasonable agreement with the experimental value. The SAC-CI photoelectron spectra of NO₂⁻ at 350 K and 700 K including the rotational effects were calculated using the Franck–Condon approximation. The theoretical spectra reproduced well the fine experimental photoelectron spectra observed by Ervin et al. (J. Phys. Chem. 1988, 92, 5405). The results showed that the ionizations from many vibrational excited states as well as the vibrational ground state are included in the experimental photoelectron spectra especially at 700 K and that the rotational effects are important to reproduce the experimental photoelectron spectra of both temperatures. The SAC/SAC-CI theoretical results supported the analyses of the spectra by Ervin et al., except that we could show some small contributions from the asymmetric-stretching mode of NO₂⁻. © 2018 Wiley Periodicals, Inc.     

Transition probabilities for the ionization of N2, O2, NO and CO molecules

Franck–Condon factors are presented for the normal and stable isotope-labelled N₂, O₂, NO and CO molecules for transitions to the observed ionized states by using the Rydberg–Klein–Rees (RKR ) potential energy curves of the various electronic states involved. It has been observed that for some transitions, the Franck–Condon factors based on the RKR potential energy curves differ appreciably from those based on the Morse potential function. The effect of isotopic substitution on the transition probabilities is also quite significant in a number of cases.     

Competition between intersystem crossing and internal conversion in isolated large molecules

The excess energy and deuteration dependence of the radiationless decay rate in “isolated” aromatic hydrocarbons (anthracene, 9,10-dimethylanthracene, phenanthrene and fluorene) suggest that S₁→S₀ internal conversion dominates over S₁→T intersystem crossing for molecules with very large excess vibrational energies.     

An accurate analytical formula for the van der Waals potentials of homonuclear rare-gas dimers with one adjustable parameter

In the present article, the Tang–Toennies–Yiu (TTY) potential model is modified by introducing one adjustable parameter. Then, the van der Waals potentials of He₂, Ne₂, Ar₂, Kr₂, and Xe₂ are calculated by this model with the adjustable parameter being determined by the well determined well depth D_e of these systems. Based on the derived potentials, the vibrational energy spacings of these systems are also calculated. It is shown that the present derived potentials and vibrational energy spacings agree well with experiment and other theoretical calculations. Finally, the normalization constant A in the asymptotic wave function of rare-gas atoms is estimated. The present derived normalization constant A is very close to the one by calculating the ratio between the Hartree–Fock function and the asymptotic wave function. The results confirm that absorbing the first-order polarization energy into the exchange energy expression is a well approximation for the present systems.     

Radiationless decay of the second excited singlet states of aromatic thiones: Experimental verification of the energy gap law

S₂ → S₀ fluorescence quantum yields and S₂ lifetimes of eight aromatic thiones in inert perfluoroalkane solutions at room temperature have been measured using picosecond laser techniques. Photostable, structurally rigid thiones undergo S₂ → S₁ internal conversion at rates consistent with the energy gap law of radiationless transitions. An average electronic coupling matrix element of 1.9 × 10² cm^?1 is found.