Nonradiative deactivation of the lowest excited triplet state of the dibenzo-<Emphasis Type="Italic">p</Emphasis>-dioxin molecule

In the nonadiabatic approximation, we study how intramolecular interactions affect the nonradiative energy degradation T ₁ ^s ↝ S ₀ of triplet sublevels s of the lowest triplet state of the dibenzo-p-dioxin molecule. We consider the role played in the degradation by the shape of promoting high- and low-frequency vibrational modes and by spin-orbit interactions separately in the carbon backbone of the molecule and in heteroatoms (oxygen). We find that σ-electrons of oxygen that correspond to the lone pair and to valence electrons play different roles in the nonadiabatic interaction.     

Nonradiative deactivation of the lowest triplet state of tetrachlorodibenzo-p-dioxin

In the nonadiabatic approximation, we have studied how the shape of promoting out-of-plane vibrational modes and vibronically induced spin-orbit interactions in structural elements of the 2,3,7,8-tetrachlorodibenzo-p-dioxin molecule affect the energy degradation rate constants K _dg ^s of triplet T ₁ ^s sublevels.     

The role played by some factors of intramolecular interaction in nonradiative deactivation of the lowest triplet state of octachlorodibenzo-p-dioxin

We have studied how intramolecular interactions, such as vibronically induced spin-orbit (VISO) and nonadiabatic interactions, which are governed by different structural elements of the octachlorodibenzo-p-dioxin (OCDD) molecule, affect the deactivation of its lowest triplet state. In the nonadiabatic approximation, taking into account out-of-plane vibrational modes as promoting ones, we have estimated the values of rate constant K _dg ^s of the nonradiative energy deactivation of in-plane triplet sublevels (s = z, y) of the triplet state of the OCDD molecule.     

Effect of molecular structural elements of chloro-substituted derivatives of naphthalene on intramolecular interactions, which determine T1 ? S0 nonradiative transition

By calculating the matrix elements of operators of adiabatic and nonadiabatic interactions, which determine the process T ₁ ^S ↝ S ₀ in molecules of naphthalene and its 1,4- and 2,3-dichloro-substituted derivatives, we study how various factors of intramolecular interactions affect this process. The effects of α and β chlorine substituents on spin-orbit (SO) interactions in the carbon backbone of the molecule and in its chlorine atoms, where the compensation effect of SO interactions was revealed, are separated. It is found that high-frequency out-of-plane promoting modes (corresponding to vibrations of CCH groups) differently affect SO interactions in the carbon backbone of molecules and in chlorine atoms.     

Model and calculation of rate constants of nonradiative <Emphasis Type="Italic">T-S</Emphasis> intersystem conversion: Test by example of naphthalene and its chlorine derivatives

For in-plane spin states (s = z, y), the rate constants K _dg ^s of the nonradiative energy degradation T ₁ ⇝ S ₀ of the lowest triplet T ₁ state of naphthalene (NPH) and its dichloro-substituted derivatives at positions 1,4- and 2,3- of the molecule (1,4-NPH and 2,3-NPH) are calculated. A simple model is proposed for calculations that is based on the nonadiabatic approximation and uses all the out-of-plane vibrational modes of the molecule as promoting vibrational modes. As a result of calculations, the dependences of the rate constants K _dg and K _dg ^s on the positions of chlorine atoms in the molecule are obtained, which are consistent with the known data of magnetooptical measurements. The inversion of the ratio K _dg ^z : K _dg ^y in the 1,4-NPH and 2,3-NPH molecules is established.     

The effect of a heavy atom on the nonradiative intersystem crossing transition between ππ<Superscript>*</Superscript> excited states

The effect of a heavy atom on the rate of the nonradiative intersystem crossing transition S ₁(ππ^*) ? T(ππ^*) in molecules of polychlorinated dioxins and dibenzofuran is theoretically studied in the approximation of spin-orbit and nonadiabatic interactions coupling electronic states.     

Role of structural elements of chloronaphthalene molecules in spin-orbit coupling: Phosphorescence

The dipole moments (P ^s ) of the T ₁ ^S → S ₀ transition from the triplet sublevels s = z, y, x, which are determined by the spin-orbit (SO) coupling, are studied for a series of mono- and dichloro derivatives of naphthalene. Based on the model calculations, the effects of different factors (SO coupling in individual chlorine atoms occupying the α and β positions in the molecule, SO coupling in the carbon backbone of the molecule, and the compensation effect caused by the interference of SO interactions in individual structural elements of the molecule) on P ^s are differentiated and discussed.     

Intramolecular heavy atom effect on the polarization of phosphorescence of phenylacetylene

Phosphorescence spectra, both unpolarized quasilinear in a Shpolskii matrix and polarized in a rigid glass matrix, have been measured for seven monohalogen ring substituted phenylacetylenes. The vibrational analyses indicate the presence of two subspectra, labelled I and II. Subspectrum I involves transitions from T₁ to totally symmetric vibrational levels of S₀ while Subspectrum II refers to transitions from T₁ to b₁ (out-of- plane) vibrational levels of S₀. In the parent phenylacetylene, 90% of the intensity is attributed to subspectrum I; in the halo derivatives, the percentage of subspectrum II increases with mass of halogen. The polarization results show an enhancement of 0,0 in plane polarization contributions with heavy atom. Subspectrum I's out-of-plane polarized contribution is accounted for by T₁ mixing with σπ states, while the in plane polarized part is rationalized by direct spin-orbit coupling with ππ¹ states via three-center integrals and by 2nd order Herzberg-Teller spin-orbit coupling. Subspectrum II arises from 1st order Herzberg-Teller spin-orbit coupling.     

Roles played by an oxygen atom and out-of-plane high-frequency vibrational modes of a dibenzofuran molecule in the nonradiative deactivation of the lowest triplet state

We have studied the deactivation of the triplet sublevels s = z, y, and x of the lowest triplet state T ₁ ^s of the dibenzofuran molecule, which is determined by radiative (dipole) and nonradiative (degradation) transitions with the rate constants K _rad ^s and K _dg ^s . The main attention is paid to the nonradiative transitions T ₁ ^s ? S ₀ from the in-plane spin states (s = z, y), which are determined by the intramolecular interaction along the coordinates of out-of-plane vibrational modes. The roles played by the many-electron atom (oxygen) and high-frequency out-of-plane vibrational modes in the intramolecular interaction have been evaluated theoretically. Estimates of K _dg ^s based on three known approaches (three models) that describe the nonradiative transition in the approximation of adiabatic and nonadiabatic interactions are presented.     

Effect of the vibronically induced spin-orbit coupling of electronic ππ* states on nonradiative intersystem crossing: Anthracene

It is theoretically found that nonradiative S-T intersystem crossing S ₁ ? T _m in anthracene involves transitions from the S ₁(¹ B _1u ) state to the triplet T ₁(³ B _1u ) and T ₂(³ B _3g ) states, which are allowed in the model of vibronically induced spin-orbit (VISO) interactions and are forbidden in the model of direct spin-orbit (SO) interactions. The rate constants K _ST of the nonradiative transitions are estimated in the approximation of VISO interactions taking into account all the out-of-plane vibrational modes. It is shown that, at a small increase in the energy of the T ₂ state, which eliminates this state from the S-T intersystem crossing process, the rate constant K _ST decreases by three orders of magnitude. For different orbital symmetry combinations of the S and T states, for which the S-T intersystem crossing is allowed in the model of SO interactions and in the model of VISO interactions, the quantities (U _VISO)², which correspond to the squared perturbation matrix element of the coupling state, are calculated. These quantities are compared with the quantities (U _SO)² calculated by other researchers in the model of SO interactions. This comparison shows that, even in hydrocarbon molecules that do not contain heavy atoms, (U _VISO)² can exceed (U _SO)² by one to two orders of magnitude.     

Effect of a heavy atom in the S 1(ππ*) ↝ T 1(ππ*) nonradiative transition. 9,10-Dichloroanthracene

The rate constant K _ST for the nonradiative intersystem crossing transition S ₁(¹ B _1u ) ? T ₁(³ B _1u ) (I) in 9,10-dichloroanthracene (DClA) is calculated in terms of the model of vibronic-induced spin-orbit (VISO) interactions. The magnitude fluorescence quantum yield ?_fl is estimated. Comparison of K _ST(I) and ?_fl for DClA with the corresponding values obtained earlier for anthracene (AC), where K _ST is governed by the conversion channels (I) and S ₁(¹ B _1u ) ? T ₂(³ B _3g ) (II), shows that the theoretical estimates reflect the anomalous heavyatom effect in these molecules in accordance with the experimental (literature) data. The cause for this effect is revealed. The influence of different factors on the K _ST(I) constant and on the ratio of its components K _ST ^s (where s denotes the z and y spin-sublevels) is established for DClA. These factors are the magnitude of the spin-orbit coupling parameter in a chlorine atom, the change, as compared to AC (in the same conversion channel (I)) of the distribution of electrons in the carbon core of the DClA molecule, and the change in the form of out-of-plane vibrational modes involved in VISO interactions.     

The first s-Rydberg transitions of ethyl bromide and ethyl iodide as related to the corresponding methyl halides

The transitions observed in the first s-Rydberg region of the spectra of ethyl bromide, ethyl bromide-d₅, and ethyl iodide are reported and assigned. The assignments are made by examining the effect of symmetry reduction from C_3v to C_s on the observed electronic states and vibrational modes of the corresponding methyl halide spectrum. The calculated spectra obtained in this way give good agreement with the observed spectra. These resulting assignments are discussed in terms of a competition between spin-orbit coupling and hyper-conjugation.     

Exchange interactions in a trigonal chromium (III) pair

The theory of exchange interactions in the excited state of a trigonal chromium(III) pair which occurs in Cs₃Cr₂Cl₉, and first nearest neighbours in ruby, is extended to the singly excited ² T ₁, ² T ₂ and ² E(t ₂ ³) pair states. The multiplet splitting is described by an effective hamiltonian which includes trigonal field, spin-orbit coupling, first-order Zeeman effect and bilinear and biquadratic exchange. Previous calculations on the important single-ion intensity mechanism for ² E pair states are incorrect. The corrected electric dipoles for ² E and also for ² T ₁ and ² T ₂ pair states are presented.     

Electronic and vibrational spectroscopy of the low-lying states of potassium mono-sulphide KS,and comparison in the series of MS (M = Li,Na, K,Rb, Cs)

ABSTRACT

Potential energy curves (PECs) of the lowest electronic states of the potassium mono-sulphide KS have been determined with highly correlated ab initio calculations, using internally contracted multi reference interaction configuration methods including Davidson correction (MRCI?+?Q) with and without considering spin-orbit effects. For the three low-lying bound states, we report a set of spectroscopic parameters including equilibrium distances, dissociation energies, vibrational and rotational constants. The effects of spin-orbit-induced changes on these parameters are also discussed. An analysis of the properties of the three bound states, X²Π, 1²Σ⁺ and 2²Π, illustrates the common characteristics of the whole series of compounds in the MS family (M?=?Li, Na, K, Rb, Cs). Indeed, the shapes of the PECs of these bound states are strongly affected by the interactions between the two ionic states, ²Σ⁺ and ²Π, correlating at large internuclear separations (R_MS) to the first ionic dissociation limit [M⁺?+?S^?] and the electronic states correlating to the three/four lowest dissociation limits. The spectroscopy of these low-lying electronic states and the lifetime of their vibrational levels are thus affected by the spin-orbit interactions which are mainly related to the S atom and consequently common to all alkali-metal mono-sulphides.     

Radiative deactivation of the lowest triplet state of dibenzo-<Emphasis Type="Italic">p</Emphasis>-dioxine

A theoretical evaluation of the dipole moments of vibronic transitions (which are governed by vibronic spin-orbit interactions) was carried out for dibenzo-p-dioxin molecules. On the basis of the comparison of the obtained results with the data on the distribution of line intensities in a fine-structure phosphorescence spectrum of dibenzo-p-dioxin at 4.2 K, it is inferred that radiative deactivation of the lowest triplet state T ₁ (ππ*) occurs from one of the triplet sublevels. For the molecules of dibenzo-p-dioxin and one of the isomers of tetrachlorodibenzo-p-dioxin, the effect of the form of vibrational modes and individual constants of the spin-orbit coupling in O and Cl atoms on vibronic spin-orbit interactions is discussed.     

Unravelling overlaps and torsion-facilitated coupling using two-dimensional laser-induced fluorescence

Two-dimensional laser-induced fluorescence (2D-LIF) spectroscopy is employed to identify contributions to fluorescence excitation spectra that arise from both overlapping bands and coupling between zero-order states (ZOSs). Evidence is found for the role of torsional motion in facilitating the coupling between vibrations that particularly involves the lowest-wavenumber out-of-plane vibrational modes. The experiments are carried out on jet-cooled p-fluorotoluene, where the molecules are initially in the lowest two torsional levels. Here we concentrate on the 390–420?cm^?1 features in the S₁?←?S₀ excitation spectrum, assigning the features seen in the 2D-LIF spectrum, aided by separate dispersed fluorescence spectra. The 2D-LIF spectra allow the overlapping contributions to be cleanly separated, including some that arise from vibrational-torsional coupling. Various coupling routes open up because of the different symmetries of the lowest two torsional modes; these combine with the vibrational symmetry to provide new symmetry-allowed vibration-torsion (‘vibtor’) interactions, and the role of the excited m?=?1 torsional level is found to be significant.     

Magnetic circular and linear dichroism in cubic high spin d5 complex

Magneto-optical parameters useful for the interpretation of magnetic circular dichroism (MCD) and magnetic linear dichroism (MLD) spectra of high spin d⁵ complexes in tetrahedral or octahedral crystalline fields have been calculated. Two possible intensity borrowing mechanisms—one involving spin-orbit (s.o.) interaction of the ground sextet with the excited quartet states and the other involving the s.o. interaction of an excited charge transfer sextet with the excited quartet states—have been considered for electric dipole transitions in T_d symmetry and for magnetic dipole transitions in O_h symmetry. Of the numerous other mechanisms which may induce electric dipole oscillator strength in O_h symmetry complexes, eight (those in involving odd parity T _1u or T _2u states vibronically induced via t _1u or t _2u vibrational modes) have been investigated in detail. In each of these mechanisms, parameters have been calculated for transitions to all individual s.o. components of all excited quartet states. It is shown how the MCD and MLD techniques, if used in combination, may provide specific information on the mechanism of intensity borrowing and on the spectroscopic assignments of individual s.o. components.     

Effect of the orbital structure and symmetry of electronic states on nonradiative <Emphasis Type="Italic">S-T</Emphasis> intersystem crossing: Dibenzofuran

The nonradiative S-T intersystem crossing S ₁(ππ*) ? T ₁(ππ*) in dibenzofuran (DB(O)) molecules has been theoretically investigated within the model of vibronically induced spin-orbit (VISO) coupling of electronic states, where the vibronic perturbation takes into account all out-of-plane vibrational modes of a molecule. It is established that the S-T intersystem crossing S ₁(¹ A ₁) ? T ₁(³ B ₂) involves also the intermediate (T _m )T ₂(³ A ₁) and T ₃(³ B ₂) triplet states. The calculated rate constant K _ST = (4.5–4.7) × 10⁷s^?1 of the nonradiative transition is in agreement with the known experimental data. The manifestation of approximate (belonging to the D _2h group) symmetry of singlet and triplet molecular states in VISO couplings has been studied. An effect of the heavy (oxygen) atom of a DB(O) molecule on K _ST is established.     

Quantum theory of the magneto-optical effect and magnetization of Nd-substituted yttrium iron garnet

The magneto-optical and magnetic properties of Nd ³⁺ ions in Y ₃Fe ₅O ₁₂ garnet are analyzed by using quantum theory. In the spontaneous state, the magneto-optical effects originate mainly from the intra-ionic electric dipole transitions between the 4 f ³ and 4 f ²5d states split by the spin-orbit, crystal field, and superexchange interactions. For the excited configuration, the coupling scheme of Yanase is extended to the Nd ³⁺ ion. The magneto-optical resonance frequencies are mainly determined by the splitting of the 5d states induced by the crystal field. The theoretical results of both Nd magnetization and Faraday rotation are in good agreement with experiments. The observed Faraday rotation is proved to be of the paramagnetic type. Although the value of the magneto-optical resonance frequency derived from a macroscopic analysis is approximately confirmed by our theoretical study, a new assignment about the transitions associated with this resonance is unambiguously determined. The spin-orbit coupling of the ground configuration has a great influence on both the Faraday rotation and magnetization, but, unlike the theoretical results obtained in some metals and alloys, the relation between the Faraday rotation and the spin-orbit coupling strength is more complex than a linear one. The magnitude of the magneto-optical coefficient increases as the spin-orbit interaction strength of the ground configuration decreases when the strength is not very weak. Finally, the temperature dependence of the magneto-optical coefficient and the effect of the mixing of different ground-term multiplets induced by the crystal field are analyzed. Received 8 November 2000     

Photoinduced dynamics to photoluminescence in Ln3+ (Ln = Ce,Pr) doped β-NaYF4 nanocrystals computed in basis of non-collinear spin DFT with spin-orbit coupling

ABSTRACT

In this work, non-collinear spin DFT + U approaches with spin-orbit coupling (SOC) are applied to Ln³⁺ doped β-NaYF₄ (Ln = Ce, Pr) nanocrystals in Vienna ab initio Simulation Package taking into account unpaired spin configurations using the Perdew–Burke–Ernzerhof functional in a plane wave basis set. The calculated absorption spectra from non-collinear spin DFT + U approaches are compared with that from spin-polarised DFT + U approaches. The spectral difference indicates the importance of spin–flip transitions of Ln³⁺ ions. Suite of codes for nonadiabatic dynamics has been developed for 2-component spinor orbitals. On-the-fly nonadiabatic coupling calculations provide transition probabilities facilitated by nuclear motion. Relaxation rates of electrons and holes are calculated using Redfield theory in the reduced density matrix formalism cast in the basis of non-collinear spin DFT + U with SOC. The emission spectra are calculated using the time-integrated method along the excited state trajectories based on nonadiabatic couplings.