Spin—orbit and vibronic perturbations on the chiroptical spectra of dissymmetric pseudo-tetragonal metal complexes

The influence of spin—orbit and vibronic interactions upon the chiroptical properties of nearly degenerate dd transitions in metal complexes of pseudo-tetragonal symmetry is investigated. A model system is considered in which three nearly degenerate dd excited states are coupled via both spinorbit and vibronic interactions. Vibronic interactions among the three nearly degenerate dd electronic states are assumed to arise from a pseudo-Jahn—Teller (PJT) mechanism involving three different vibrational modes (each nontotally symmetric in the point group of the undistorted model system).A vibronic hamiltonian is constructed (for the excited states of the model system) which includes linear coupling terms in each of the three PJT-active vibrational modes as well as a linear coupling term in one totally symmetric mode of the system and a spin—orbit interaction term. Wavefunctions and eigenvalues for the spin—orbit/vibronic perturbed excited states. of the model system are obtained by diagonalizing this hamiltonian in a basis constructed of uncoupled vibrational and electronic (orbital and spin) wavefunctions.Rotatory strengths associated with transitions to vibronic levels of the perturbed system are calculated and “rotatory strength spectra” are computed assuming gaussian shaped vibronic spectral components. Calculations are carried out for a number of vibronic and spin—orbit coupling parameters and for various splitting energies between the interacting electronic states. The calculated results suggest that chiroptical spectra associated with transitions to a set of nearly degenerate dd excited states of a chiral transition metal complex cannot be interpreted directly without some consideration of the effects introduced by spin—orbit and vibronic perturbations. These perturbations can lead to substantial alterations in the sign patterns and intensity distributions of rotatory strength among vibronic levels derived from the interacting electronic states and it is generally not valid to assign specific features in the observed circular dichroism spectra to transitions between states with well-defined electronic (orbital and spin) identities.Our theoretical model is conservative with respect to the total (or net) rotatory strength associated with transitions to levels derived from the three interacting electronic states; the vibronic and spin—orbit coupling operators are operative only within this set of states. That is, the total (or net) rotatory strength associated with these transitions remains invariant to the vibronic and spin—orbit coupling parameters of the model.     

Influence du couplage vibronique sur le paramagnétisme d'un complexe cubique dans l'état électronique2T2

A study of temperature dependence of the paramagnetism of cubic complexes in a² T ₂ electronic state is reported. It is necessary to introduce four parameters: the spin-orbit coupling coefficientλ, the vibronic coupling parameterκ, the frequency ?ω_? of the twofold degenerate modes of vibration and the covalence parameterk. The perturbations due to the spin-orbit coupling and the vibronic coupling are both diagonalized using the vibronic functions in the Born-Oppenheimer approximation as basis set; the Zeeman perturbation is then diagonalized using the new vibronic functions as basis set. It is shown that the smaller the absolute value of the parameter \(\varrho = \frac{3}{{2\hbar \omega _\varepsilon }}\) , the greater the influence of the vibronic coupling on the temperature dependence of the paramagnetism. This influence is similar to that of the covalence but is not identical.     

Molecular design for high-spin molecules in view of vibronic couplings

A high-spin ground state is possible if a molecule has degenerate or pseudo-degenerate frontier orbitals. Since strong vibronic couplings, or electron-vibration interactions give rise to reduce the degeneracy or pseudo degeneracy, a lower-spin state is the ground state in such a molecule. Therefore small vibronic couplings are desirable for designing molecules with a high-spin ground state. Vibronic coupling constants of derivatives of m-phenylene diamine are evaluated. The calculated results are analyzed based on vibronic coupling density which enables us to control the vibronic coupling constants. Based on the vibronic coupling density analysis, we succeed in recovering the high-spin ground state from the closed-shell singlet ground state of a methoxy derivative of m-phenylene diamine by introducing an appropriate substituent.     

Nuclear Coordinate dependence of electronic transition moments in orbitally forbidden transitions: A new interpretation of deuterium isotope effects

The nuclear coordinate dependence of electronic transtion moments has been investigated for the purpose of finding new interpretations of deuterium isotope effects on spectral intensities and radiative decay rates in orbitally forbidden electronic transitions. By using “AO following nuclei” wavefunctions as the building block for the electronic wavefunction in the adiabatic BO vibronic wavefunction, the spin-free hamiltonian is diagonalized to generate eigenfunctions and eigen-energies. It is found that the electronic transtion moments based on these eigenfunctions show dependences upon the vibrational modes which are not directly involved in vibronic coupling. This leads to interpretations of the deuterium isotope effects in T₁ → S₀ radiative transitions of aromatic hydrocarbons and S₀ → S₁ absorption in pyrazine which are not based on the conventional Herzberg—Teller or non-BO coupling.     

Analysis and predictions of the vibronic spectrum of the ethynyl radical C2H by ab initio methods

A purely ab initio study of the vibronic structure of the C₂H spectrum in the region up to 7000 cm^?1, which is complicated by the coupling of theX ²Σ⁺ andA ² II systems, is presented. The potential surfaces for the three lowest-lying electronic states 1² A′, 2² A′ and 1² A″ correlating withX ²Σ⁺ andA ² II at the linear molecular geometry are calculated for the various geometrical distortions by means of the multireference configuration interaction (MRD-CI) method. These adiabatic surfaces are transformed into suitable diabatic counterparts. An approach is developed for a simultaneous treatment of three electronic states coupled via the bending and C-C stretching vibrations. Spin-orbit splitting of the vibronic levels and the vibronically averaged values for the hyperfine coupling constants are computed. The results obtained in this study enable a reliable explanation of the available experimental findings of the C₂H spectrum and predict a number of features to be verified by future experiments.     

Absorption in regio-regular poly(3-hexyl)thiophene thin films: Fermi resonances,interband coupling and disorder

Absorption in conjugated polymer aggregates is studied theoretically, taking into account excitonic (intermolecular) coupling, exciton–phonon (EP) coupling and site-energy disorder, all treated on equal footing within a generalized Holstein Hamiltonian with numerically generated eigenmodes and energies. The analysis deals primarily with the weak excitonic coupling regime, which for polymers, corresponds to J₀ ? 0.4ω₀ where J₀ is the nearest neighbor excitonic coupling and ω₀ (≈1400 cm⁻¹) is the frequency of the ring breathing/stretching mode coupled to the molecular electronic transition with Huang–Rhys factor, λ² ≈ 1. Disorder is characterized by a Gaussian distribution of molecular transition frequencies of width σ. Absorption spectra are calculated under the two-particle approximation (TPA) as well as the less accurate, but computationally more efficient single-particle approximation (SPA). Fermi resonances (FRs) arise due to the coupling between the optically allowed single-particle states (vibronic excitons) and the dark two-particle states. In the motional narrowing limit FRs are clearly resolved. Further increases in σ cause the FRs to merge into a single peak for each vibronic band. At this point the SPA becomes accurate for the entire spectrum. The SPA also provides the basis for simplified analytical expressions for the peak intensity ratios, from which the free exciton bandwidth, W, can be determined. Analytical expressions are also obtained for the peak-positions within the vibronic progression. Application to regio-regular poly(3-hexyl)thiophene films shows the exciton bandwidth, W, to be in the range 0.8ω₀–ω₀. The model also accounts for the irregular peak spacings observed in experiment.     

Theoretical study of the static Jahn-Teller effect—I. Two-mode vibronic coupling in octahedral halocomplexes with doubly degenerate electronic states

A two-mode E_g-(a_1g+e_g) vibronic coupling is analyzed for octahedral systems. Analytic formula for the adiabatic potential surface (APS) is obtained considering quadratic vibronic terms and anharmonicities of normal vibrations as well. Potential constants, viz. five elastic force constants and three vibronic constants, are evaluated from the numerical map of the APS applying the non-linear regression analysis. Numerical values are obtained for hexahalocomplexes on the CNDO/INDO level of total energy calculations.     

On the calculation of vibronic coupling matrix elements

The non-diagonal matrix elements in the adiabatic Born-Oppenheimer approximation are considered. The effect of the Q-dependence of the electronic energy denominator is calculated explicitly for an arbitrary initial and final state. It is shown that the inclusion of this effect does not change the relative values of the coupling matrix elements for different initial vibronic states.     

Line shapes in electronic absorption spectra. Phenanthrene

The 3000 Å, (¹B₂ ← ¹A₁), absorption system of phenanthrene in durene crystals at 4°K illustrates an electronic transition, which is subject to near-resonance vibronic perturbations whose effect is intermediate to both the small (sparse intermediate) and large molecule (statistical) limits. Both broad (300 cm^?1) and narrow (10 cm^?1) lines are evident. A model is proposed which incorporates both these features by fast allowing for a consideration of the interaction between a small number of discrete levels, those associated with the largest coupling, followed by a treatment of the broadening of these levels through interaction with the remaining near continuum of states of the lower electronic state. Thus, one and the same electronic state provides both a sparse and dense manifold of levels. An important result of the model is that in terms of absorption intensities all the lines emerge with the same heights but differ in widths. When the intensities are summed with respect to energies this aspect is obscured. This approach has been shown to satisfactorily reproduce many of the features of the ¹B₂ absorption spectra of phenanthrene and phenanthrene-d₁₀. The ¹B₂ absorption systems have also been measured in the vapour phase and fine structure attributable to vibronic coupling and sequence band development are discussed.     

Manifestation of intramolecular vibrational energy redistribution on electronic relaxation in large molecules

Some universal characteristics are discussed of the decay lifetimes and fluorescence quantum yields from the S₁ manifold of large molecules, which originate from the coupling between intrastate vibrational energy redistribution and interstate electronic relaxation. The time-resolved total fluorescence decay from the S₁ state of jet-cooled 9-cyanoanthracene exhibits non-exponential decay in the energy range E_v= 1200–1740 cm⁻¹ above the S₁ origin, which does not originate from dephasing but rather manifests the effects of intrastate intermediate level structure for vibrational energy redistribution on intersystem crossing.     

Inverse deuterium isotope effect in the intersystem crossing of diphenylcarbene

The singlet-to-triplet intersystem crossing rate (k_st) of diphenylcarbene (DPC) is found to exhibit an inverse isotope effect in various solvents. An off-resonance coupling model between the initial singlet state and a sparse triplet vibronic manifold accounts for k_ST showing both an inverse isotope effect in a given solvent as well as an inverse energy gap effect in a solvent series.     

Vibronic coupling effects in the highly resolved optical spectra of 1,3-perinaphthadiyl,a molecule with a triplet ground state

Quasilinear spectra of 1,3-perinaphthadiyl have been obtained in n-pentane and n-hexane by photolysis of cyclopropanoacenaphthylene. The spectra of the biradical display a large absorption-emission asymmetry, which is discussed in terms of vibronic coupling. Our analysis indicates that the two lowest excited electronic states are separated by less than 250cm⁻¹. The results of open shell PPP and CNDO/S calculations with various CI bases are given and compared with experimental data.     

Vibronic coupling in benzene cation and anion: vibronic coupling and frontier electron density in Jahn-Teller molecules

Vibronic coupling constants of Jahn-Teller molecules, benzene radical cation and anion, are computed as matrix elements of the electronic part of the vibronic coupling operator using the electronic wave functions calculated by generalized restricted Hartree-Fock and state-averaged complete active space self-consistent-field methods. The calculated vibronic coupling constants for benzene cation agree well with the experimental and theoretical values. Vibronic coupling density analysis, which illustrates the local properties of the coupling, is performed in order to explain the order of magnitude of the coupling constant from view of the electronic and vibrational structures. This analysis reveals that the couplings of the e2g2 and e2g3 modes in which the large displacements locate on C-C bonds are strong in the cation. On the other hand, they are greatly weakened in the anion because of the decrease of electron density in the region of the C-C bonds, which originates from the antibonding nature of the singly occupied molecular orbital of the anion. However, the difference of the electronic structure has a little influence on the vibronic coupling of the e2g4 mode. These results indicate that the vibronic coupling depends not only on the direction of the nuclear displacement but also on the frontier electron density.     

A new spin-specific mechanism of attractive vibronic interaction

An interesting new type of spin-specific vibronic coupling is found. The non-adiabatic coupling induces an effective attractive interaction which softens the orginal repulsive interaction between a pair of electrons. The relation with the Cooper pair of superconducting electrons is discussed.     

Electronic transitions and vibronic coupling in neptunyl compounds

The low-lying electronic transitions of the neptunyl (NpO(2)(2+)) ion are characterized as either charge transfer (CT) or intra- 5f. Comparison of these classes of electronic transitions reveals significantly different photophysical properties, especially in vibronic coupling. An empirical model developed for analyses of uranyl CT vibronic transitions is used here to simulate the absorption (excitation) spectra of neptunyl in two compounds of different chemical compositions and structural symmetries. Analyses reveal that CT vibronic coupling in neptunyl has the same characteristics as that in typical uranyl analogues. The primary profile of the CT spectra is similar for neptunyl respectively with respect to chloride- and oxide-neptunium bonding interactions. On the other hand, vibronic coupling to the CT transitions is significantly different from that of f-f transitions, even within a given neptunyl compound. Electronic energy levels, vibronic coupling strength, and frequencies of various vibration modes were evaluated for transitions to the excited states of different origins in the region from 8000 cm(-1) to 21000 cm(-1) for two neptunyl compounds.     

Strong vibronic coupling effects in ionization spectra: The “mystery band” of butatriene

A theory of vibronic coupling in molecules is presented and applied to butatriene. The energies and coupling constants which enter the calculation are computed using ab initio Hartree—Fock and many-body methods. The influence of the energy splitting and the coupling constants on the calculated spectrum is discussed. It is definitely shown that the “mystery band” in the photoelectron spectrum of butatriene arises from the vibronic coupling between the electronic states ²B_3g and ²B_3u. To reproduce the experimental observations it is essential to include in the calculation both totally and non-totally symmetric vibrational 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.     

Asymmetric band profile of the Soret band of deoxymyoglobin is caused by electronic and vibronic perturbations of the heme group rather than by a doming deformation

We measured the Soret band of deoxymyoglobin (deoxyMb), myoglobin cyanide (MbCN), and aquo-metmyoglobin (all from horse heart) with absorption and circular dichroism (CD) spectroscopies. A clear non-coincidence was observed between the absorption and CD profiles of deoxyMb and MbCN, with the CD profiles red- and blueshifted with respect to the absorption band position, respectively. On the contrary, the CD and absorption profiles of aquametMb were nearly identical. The observed noncoincidence indicates a splitting of the excited B state due to heme-protein interactions. CD and absorption profiles of deoxyMb and MbCN were self-consistently analyzed by employing a perturbation approach for weak vibronic coupling as well as the relative intensities and depolarization ratios of seven bands in the respective resonance Raman spectra measured with B-band excitation. The respective B(y) component was found to dominate the observed Cotton effect of both myoglobin derivatives. The different signs of the noncoincidences between CD and absorption bands observed for deoxyMb and MbCN are due to different signs of the respective matrix elements of A(1g) electronic interstate coupling, which reflects an imbalance of Gouterman's 50:50 states. The splitting of the B band reflects contributions from electronic and vibronic perturbations of B(1g) symmetry. The results of our analysis suggest that the broad and asymmetric absorption band of deoxyMb results from this band splitting rather than from its dependence on heme doming. Thus, we are able to explain recent findings that the temperature dependences of CO rebinding to myoglobin and the Soret band profile are uncorrelated[Ormos et al., Proc. Natl. Acad. Sci U.S.A. 95, 6762 (1998)].     

Analysis of vibronic intensities in the phosphorescence spectrum of dimethylbenzaldehydes in durene

An attempt is reported to explain the main intensity patterns in the phosphorescence spectra of 2,4-, 2,5- and 3,4-dimethyl-benzaldehyde-1h₁ and -1d₁, observed previously. The analysis is based on CNDO and MINDO calculations of (transition) dipole moments, spin-orbit couplings, vibronic couplings, state energies, normal coordinates and vibrational frequencies. Where possible these quantities are empirically checked and corrected. Additional information, especially about the separation of the closely spaced T₁(³ππ^*) and T₂(³nπ^*) states, is obtained from phosphorescence excitation spectra reported here for all six isomers. The phosphorescence spectra consist of two components, an “allowed” component of ³ππ^* and a “forbidden” component of ³nπ^* symmetry. It is concluded that the allowed component is partly induced by the crystal field. The forbidden component is vibronically induced by out-of-plane vibrations among which the aldehydic CH(CD)-wag mode is the most active. The observed intensity patterns for this component are ascribed to interference between two mechanisms, one involving vibronic coupling between S₀ and S₁(¹nπ^*) and spin-orbit coupling between S₁ and T₁, the other involving vibronic coupling between T₁ and T₂ and spin-orbit coupling between S₀ and T₂. Within the groups of either 1h₁ or 1d₁ isomers, the main changes in the spectrum are shown to be due to the change in T₁–T₂ energy separation. The changes observed upon deuterium substitution in the aldehyde group involve, in addition to changes in the T₁–T₂ gap, changes in vibronic coupling due to normal-coordinate mixing. All these spectral changes are reproduced by calculations based on a mixture of theoretical and empirical input parameters, derived from, or at least consistent with, other observations, including excitation spectra, dipole moments and zero-field splittings. It is concluded that the mechanisms underlying these calculations offer a satisfactory explanation of the observed intensity patterns in the phosphorescence spectra of dimethylbenzaldehydes.