Protein-ligand structure and electronic coupling of photoinduced charge-separated state: 9,10-anthraquinone-1-sulfonate bound to human serum albumin

To elucidate how the protein-ligand docking structure affects electronic interactions in the electron-transfer process, we have analyzed time-resolved electron paramagnetic resonance spectra of photoinduced charge-separated (CS) states generated by light excitation of 9,10-anthraquinone-1-sulfonate (AQ1S(-)) bound to human serum albumin at a hydrophobic drug-binding region. The spectra have been explained in terms of the triplet-triplet electron spin polarization transfer model to determine both the geometries and the exchange couplings of the CS states of AQ1S(2-?)-histidine-242 radical cation (H242(+?)) and AQ1S(2-?)-tryptophan-214 radical cation (W214(+?)). For the CS state of the former, it has been revealed that, due to the orthogonal relationship between the singly occupied molecular orbitals of AQ1S(2-?) and H242(+?), the electronic coupling (5.4 cm(-1)) is very weak, contributing to the prevention of energy-wasting charge recombination, even at a contact edge-to-edge separation.     

Electron transfer in bis(hydrazines), a critical test for application of the Marcus model

Electron transfer in the cations of bis(hydrazines), bridged by six different π‐systems (compounds 1–6) is studied using ab initio and density functional theory (DFT) methods. Due to ionization from an antibonding combination of the lone‐pair orbitals of the nitrogens in one of the hydrazine units, conjugation is introduced in the N? N bond of that unit. This leads to a shortening of the N? N bond distance and an increase of the planarity around the nitrogens. Due to steric hindrance, this causes an increase of the angle, called φ, between the lone‐pair orbital on the nitrogen attached to the bridge and the p‐orbital on the adjacent bridge carbon for the ionized unit in the charge localized, relaxed state of the molecule. This angle controls the magnitude of the electronic coupling. In the fully delocalized symmetric transition state of the ion, however, this angle is low for both units, due to the fact that the conjugation introduced at the ionized hydrazine unit is now shared between both units. An extended π‐system is formed including the orbitals of the hydrazine units and the bridge, which leads to a large electronic coupling. The electronic coupling derived by optical methods, corresponding to the structure of the relaxed, asymmetric cation with a large φ for the ionized unit, appears to be much smaller. We believe this is due to an approximate cosine dependence on φ of the coupling. The calculations carried out support these conclusions. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 655–664, 2001     

Electronic couplings and on-site energies for hole transfer in DNA: systematic quantum mechanical/molecular dynamic study

The electron hole transfer (HT) properties of DNA are substantially affected by thermal fluctuations of the pi stack structure. Depending on the mutual position of neighboring nucleobases, electronic coupling V may change by several orders of magnitude. In the present paper, we report the results of systematic QM/molecular dynamic (MD) calculations of the electronic couplings and on-site energies for the hole transfer. Based on 15 ns MD trajectories for several DNA oligomers, we calculate the average coupling squares V(2) and the energies of basepair triplets XG(+)Y and XA(+)Y, where X, Y=G, A, T, and C. For each of the 32 systems, 15,000 conformations separated by 1 ps are considered. The three-state generalized Mulliken-Hush method is used to derive electronic couplings for HT between neighboring basepairs. The adiabatic energies and dipole moment matrix elements are computed within the INDO/S method. We compare the rms values of V with the couplings estimated for the idealized B-DNA structure and show that in several important cases the couplings calculated for the idealized B-DNA structure are considerably underestimated. The rms values for intrastrand couplings G-G, A-A, G-A, and A-G are found to be similar, approximately 0.07 eV, while the interstrand couplings are quite different. The energies of hole states G(+) and A(+) in the stack depend on the nature of the neighboring pairs. The XG(+)Y are by 0.5 eV more stable than XA(+)Y. The thermal fluctuations of the DNA structure facilitate the HT process from guanine to adenine. The tabulated couplings and on-site energies can be used as reference parameters in theoretical and computational studies of HT processes in DNA.     

Ab inito study on triplet excitation energy transfer in photosynthetic light-harvesting complexes

We have studied the triplet energy transfer (TET) for photosynthetic light-harvesting complexes, the bacterial light-harvesting complex II (LH2) of Rhodospirillum molischianum and Rhodopseudomonas acidophila, and the peridinin-chlorophyll a protein (PCP) from Amphidinium carterae. The electronic coupling factor was calculated with the recently developed fragment spin difference scheme (You and Hsu, J. Chem. Phys. 2010, 133, 074105), which is a general computational scheme that yields the overall coupling under the Hamiltonian employed. The TET rates were estimated based on the couplings obtained. For all light-harvesting complexes studied, there exist nanosecond triplet energy transfer from the chlorophylls to the carotenoids. This result supports a direct triplet quenching mechanism for the photoprotection function of carotenoids. The TET rates are similar for a broad range of carotenoid triplet state energy, which implies a general and robust TET quenching role for carotenoids in photosynthesis. This result is also consistent with the weak dependence of TET kinetics on the type or the number of π conjugation lengths in the carotenoids and their analogues reported in the literature. We have also explored the possibility of forming triplet excitons in these complexes. In B850 of LH2 or the peridinin cluster in PCP, it is unlikely to have triplet exciton since the energy differences of any two neighboring molecules are likely to be much larger than their TET couplings. Our results provide theoretical limits to the possible photophysics in the light-harvesting complexes.     

What governs the charge transfer in DNA? The role of DNA conformation and environment

Charge transfer in DNA has received much attention in the last few years due to its role in oxidative damage and repair in DNA and also due to possible applications of DNA in nanoelectronics. Despite intense experimental and theoretical efforts, the mechanism underlying long-range hole transport is still unresolved. This is in particular due to the sensitive dependence of charge transfer on the complex structure and dynamics of DNA and the interaction with the solvent, which could not be addressed adequately in the modeling approaches up to now. In this work, we study the factors governing hole transfer in detail, using a DFT-based fragment-orbital method, which allows to compute the charge transfer parameters along multinanosecond molecular dynamics simulations. Environmental effects are captured using a hybrid quantum mechanics-molecular mechanics (QM/MM) coupling scheme. This methodology allows to analyze several factors responsible for charge transfer in DNA in detail. The fluctuation of counterions, strongly counterbalanced by the surrounding water, leads to large oscillations of onsite energies, which govern the energetics of hole propagation along the DNA strand. In contrast, the electronic couplings depend only on DNA conformation and are not affected by the solvent. In particular, the onsite energies are strongly correlated between neighboring nucleobases, indicating that a conformational-gating type of mechanism may be induced by the collective environmental degrees of freedom.     

On the conjugation length for oligo(ethynylnaphthalene)-based molecular rods

The synthesis is described for a small series of oligomers built from (2, 3, 4 or 6) ethynyl-naphthalene repeat units and end-capped with solubilising 1,2,3-tris-dodecyloxy-benzene groups. These compounds absorb in the near-UV region and exhibit strong fluorescence in both fluid solution and a glassy matrix at 77 K. The spectral profiles are fully consistent with a structurally heterogeneous ground state becoming more planar upon excitation and with the low-temperature glass further stabilising the co-planar orientation. The absorption and fluorescence maxima move towards lower energy with increasing number of repeat units and there is a corresponding increase in the Huang-Rhys factor for the radiative process. The non-radiative rate constants also depend on molecular length and are well explained in terms of the energy-gap law. In contrast, very weak phosphorescence is observed at 77 K for which the peak maximum and lifetime remain insensitive to the number of naphthalene units. The triplet lifetimes recorded at ambient temperature are also independent of the molecular length but the triplet-triplet absorption spectra change throughout the series. These results are discussed in terms of the degree of electronic coupling between adjacent repeat units for each of the relevant excited states. During these studies it was noted that the rate of intersystem crossing to the triplet manifold is but weakly affected by heavy-atom perturbers. A non-fluorescent complex is formed between iodoethane and the molecular rod but the corresponding bimolecular process occurs at well below the diffusion-controlled limit. This behaviour is considered in terms of spin-orbit coupling between the excited states and takes account of the differing conjugation lengths.     

Identification of unavoided crossings in nonadiabatic photoexcited dynamics involving multiple electronic states in polyatomic conjugated molecules

Radiationless transitions between electronic excited states in polyatomic molecules take place through unavoided crossings of the potential energy surfaces with substantial non-adiabatic coupling between the respective adiabatic states. While the extent in time of these couplings are large enough, these transitions can be reasonably well simulated through quantum transitions using trajectory surface hopping-like methods. In addition, complex molecular systems may have multiple "trivial" unavoided crossings between noninteracting states. In these cases, the non-adiabatic couplings are described as sharp peaks strongly localized in time. Therefore, their modeling is commonly subjected to the identification of regions close to the particular instantaneous nuclear configurations for which the energy surfaces actually cross each other. Here, we present a novel procedure to identify and treat these regions of unavoided crossings between non-interacting states using the so-called Min-Cost algorithm. The method differentiates between unavoided crossings between interacting states (simulated by quantum hops), and trivial unavoided crossings between non-interacting states (detected by tracking the states in time with Min-Cost procedure). We discuss its implementation within our recently developed non-adiabatic excited state molecular dynamics framework. Fragments of two- and four-ring linear polyphenylene ethynylene chromophore units at various separations have been used as a representative molecular system to test the algorithm. Our results enable us to distinguish and analyze the main features of these different types of radiationless transitions the molecular system undertakes during internal conversion.     

Conformational study of halogen- and hydrogen-substituted polythionylphosphazenes using density functional theory method

The structure and conformational stability of polythionylphosphazenes is investigated by modeling single polymer chains with small mimics. The model compounds are composed of repeat units of the corresponding polythionylphosphazenes. Two of the model compounds have hydrogens and two have chlorines as substituents on phosphorus atoms. The substituents on sulfur may be either fluorine or chlorine. Fully geometry-optimized structures and energies of the stable conformations involving rotations around the P? N bond near the sulfur are obtained using the density functional theory method. The structural and conformational analyses indicate that the rotation around the N? P bond leads to variations in the bond lengths, the SNP bond angle openings, as well as couplings between dihedral angles in different conformations in all model compounds. In addition, the conformational analysis suggests that the minima on the conformational potential energy surface in these compounds may be located in the vicinity of the following values of the NP? NS dihedral angle: -50°, 90° (or 60°), 180°, and 240°. It was found that the values of the conformational energy differences range between less than 1 to 5 kcal/mol. A comparison is made between the structural results obtained using the density functional theory and the ab initio molecular orbital theory for the global minimum structures. © 1995 John Wiley & Sons, Inc.     

Use of U-shaped donor-bridge-acceptor molecules to study electron tunneling through nonbonded contacts

A systematic determination of electronic coupling matrix elements in U-shaped molecules is demonstrated. The unique architecture of these systems allows for the determination of the electronic coupling through a pendant molecular moiety that resides between the donor and acceptor groups; this moiety quantifies the efficiency of electron tunneling through nonbonded contacts. Experimental electron-transfer rate constants and reaction free energies are used to calibrate a molecular-based model that describes the solvation energy. This approach makes it possible to experimentally determine electronic couplings and compare them with computational values.     

Theoretical characterization of charge transport in chromia (alpha-Cr2O3)

Transport of conduction electrons and holes through the lattice of alpha-Cr2O3 (chromia) is modeled as a valence alternation of chromium cations using ab initio electronic structure calculations and electron-transfer theory. In the context of the small polaron model, a cluster approach was used to compute quantities controlling the mobility of localized electrons and holes, i.e., the reorganization energy and the electronic coupling matrix element that enter Marcus' theory. The calculation of the electronic coupling followed the generalized Mulliken-Hush approach using the complete active space self-consistent-field (CASSCF) method and the quasidiabatic method. Our findings indicate that hole mobility is more than three orders of magnitude larger than electron mobility in both (001) and [001] lattice directions. The difference arises mainly from the larger internal reorganization energy calculated for electron-transport relative to hole-transport processes while electronic couplings have similar magnitudes. The much larger hole mobility versus electron mobility in alpha-Cr2O3 is in contrast to similar hole and electron mobilities in hematite alpha-Fe2O3 previously calculated. Our calculations also indicate that the electronic coupling for all charge-transfer processes of interest is smaller than for the corresponding processes in hematite. This variation is attributed to the weaker interaction between the metal 3d states and the O(2p) states in chromia than in hematite, leading to a smaller overlap between the charge-transfer donor and acceptor wave functions and smaller superexchange coupling in chromia. Nevertheless, the weaker coupling in chromia is still sufficiently large to suggest that charge-transport processes in chromia are adiabatic in nature. The electronic coupling is found to depend on both the superexchange interaction through the bridging oxygen atoms and the d-shell electron-spin coupling within the Cr-Cr donor-acceptor pair, while the reorganization energy is essentially independent of the electron-spin coupling.     

A fast scheme to calculate electronic couplings between P3HT polymer units using diabatic orbitals for charge transfer dynamics simulations

We propose a fast and accurate calculation method to compute the electronic couplings between molecular units in a thiophene-ring-based polymer chain mimicking a real organic semiconducting polymer, poly(3-hexylthiophene). Through a unit block diabatization scheme, the method employed minimal number of diabatic orbitals to compute the site energies and electronic couplings, which were validated by comparing with benchmark density functional theory calculations. In addition, by using the obtained electronic couplings, a quantum dynamics simulation was carried out to propagate a hole initially localized in a thiophene-ring unit of the polymer chain. This work establishes a simple, efficient, and robust means for the simulation of electron or hole transfer processes in organic semiconducting materials, an important capability for study and understanding of the class of organic optoelectronic and photovoltaic materials. © 2018 Wiley Periodicals, Inc.     

First-principles calculation of electronic spectra of light-harvesting complex II

We report on a fully quantum chemical investigation of important structural and environmental effects on the site energies of chlorophyll pigments in green-plant light-harvesting complex II (LHC II). Among the tested factors are technical and structural aspects as well as effects of neighboring residues and exciton couplings in the chlorophyll network. By employing a subsystem time-dependent density functional theory (TDDFT) approach based on the frozen density embedding (FDE) method we are able to determine site energies and electronic couplings separately in a systematic way. This approach allows us to treat much larger systems in a quantum chemical way than would be feasible with a conventional density functional theory. Based on this method, we have simulated a series of mutagenesis experiments to investigate the effect of a lack of one pigment in the chlorophyll network on the excitation properties of the other pigments. From these calculations, we can conclude that conformational changes within the chlorophyll molecules, direct interactions with neighboring residues, and interactions with other chlorophyll pigments can lead to non-negligible changes in excitation energies. All of these factors are important when site energies shall be calculated with high accuracy. Moreover, the redistribution of the oscillator strengths due to exciton coupling has a large impact on the calculated absorption spectra. This indicates that modeling mutagenesis experiments requires us to consider the entire set of chlorophyll molecules in the wild type and in the mutant, rather than just considering the missing chlorophyll pigment. An analysis of the mixing of particular excitations and the coupling elements in the FDEc calculation indicates that some pigments in the chlorophyll network act as bridges which mediate the interaction between other pigments. These bridges are also supported by the calculations on the "mutants" lacking the bridging pigment.     

Control over charge separation in phthalocyanine-anthraquinone conjugates as a function of the aggregation status

We have prepared three isomeric donor-acceptor systems, in which two phthalocyanine (Pc) units have been attached to the 1-,5- (1a), 1-,8- (1b), or 2-,6- (1c) positions of a central anthraquinone (AQ) moiety, leading to packed (1b) or extended (1a and 1c) topologies. The electronic interactions between the donor and the acceptor in the ground state or in the excited states have been studied by different electrochemical and photophysical techniques. Due to the markedly different topologies, we have been able to modify these interactions at the intramolecular level and, by a proper choice of the solvent environment, at the intermolecular level within aggregates. In triad 1b, the ZnPc units are forced to pi-stack cofacially and out of the plane of the AQ ring. Consequently, this molecule shows strong inter-Pc interactions that give rise to intramolecular excitonic coupling but a relatively small electronic communication with the AQ acceptor through the vinyl spacers. On the contrary, the 1-,5- or 2-,6-connections of triads 1a and 1c allow for an efficient pi-conjugation between the active units that extends over the entire planar system. These two molecules tend to aggregate in aromatic solvents by pi-pi stacking, giving rise to J-type oligomers. Photoexcitation of the Pc units of 1a-c results in the formation of the Pc.+-AQ.- charge transfer state. We have demonstrated that the kinetics of these electron transfer reactions is greatly dependent on the aggregation status of the triads.     

Measurement of long-range cross-correlation rates using a combination of single- and multiple-quantum NMR spectroscopy in one experiment

A method is described to determine long-range cross-correlations between the modulations of an anisotropic chemical shift (e.g., of a C' carbonyl carbon in a protein) and the fluctuations of a weak long-range dipolar interaction (e.g., in cross-correlation between the same C' carbonyl and the H(N) proton of the neighboring amide group). Such long-range correlations are difficult to measure because the corresponding long-range scalar couplings are so small that Redfield's secular approximation is often violated. The method, which combines features of single- and double-quantum NMR spectroscopy, allows one to cancel the effects of dominant short-range dipolar interactions (e.g., between the CSA of the amide nitrogen N and the dipolar coupling to its attached proton H(N)) and is designed so that the secular approximation is rescued even if the scalar coupling between the long-range dipolar coupling partners is very small. The cross-correlation rates thus determined in ubiquitin cover a wide range because of local motions and variations of the CSA tensors.     

Intermolecular coulomb couplings from ab initio electrostatic potentials: application to optical transitions of strongly coupled pigments in photosynthetic antennae and reaction centers

An accurate and numerically efficient method for the calculation of intermolecular Coulomb couplings between charge densities of electronic states and between transition densities of electronic excitations is presented. The coupling of transition densities yields the F?rster type excitation energy transfer coupling, and from the charge density coupling, a shift in molecular excitation energies results. Starting from an ab initio calculation of the charge and transition densities, atomic partial charges are determined such as to fit the resulting electrostatic potentials of the different states and the transition. The different intermolecular couplings are then obtained from the Coulomb couplings between the respective atomic partial charges. The excitation energy transfer couplings obtained in the present TrEsp (transition charge from electrostatic potential) method are compared with couplings obtained from the simple point-dipole and extended dipole approximations and with those from the ab initio transition density cube method of Krüger, Scholes, and Fleming. The present method is of the same accuracy as the latter but computationally more efficient. The method is applied to study strongly coupled pigments in the light-harvesting complexes of green sulfur bacteria (FMO), purple bacteria (LH2), and higher plants (LHC-II) and the "special pairs" of bacterial reaction centers and reaction centers of photosystems I and II. For the pigment dimers in the antennae, it is found that the mutual orientation of the pigments is optimized for maximum excitonic coupling. A driving force for this orientation is the Coulomb coupling between ground-state charge densities. In the case of excitonic couplings in the "special pairs", a breakdown of the point-dipole approximation is found for all three reaction centers, but the extended dipole approximation works surprisingly well, if the extent of the transition dipole is chosen larger than assumed previously. For the "special pairs", a large shift in local transition energies is found due to charge density coupling.     

Towards understanding of magnetic interactions within a series of tetrathiafulvalene-pi conjugated-verdazyl diradical cation system: a density functional theory study

The intramolecular magnetic exchange coupling constants (J) for a series of tetrathiafulvalene (TTF) and verdazyl diradical cations connected by a range of pi conjugated linkers have been investigated by means of methodology based on unrestricted density functional theory. The magnetic interaction between radicals is transmitted via pi-electron conjugation for all considered compounds. The calculation of J yields strong or medium ferromagnetic coupling interactions (in the range of 56 and 300 K) for diradical cations connected by linkers with an even number of carbon atoms that are able to provide a spin polarization pathway, while antiferromagnetic coupling is predicted when linkers with an odd number of carbon atoms are employed. The topological analysis of spin density distributions have been used to reveal the effects of the spin polarization on both linkers and spin carriers. The absence of heteroatoms that impede the spin polarization pathway, and the existence of a unique spin polarization path instead of several possible competitive routes are factors which contribute to large positive J values favoring ferromagnetic interactions between the two terminal pi-radicals. The magnitude of J depends strongly on the planarity of the molecular structure of the diradical cation since a more effective orbital overlap between the two pi-systems can be achieved. Hence, the dependence of J on the torsion angle (theta) of each spin carrier has been analyzed. In this respect, our findings show that this geometrical distortion reduces largely the calculated J values for ferromagnetic couplings, leading to weak antiferromagnetic interactions for a torsion angle of 90 degrees .     

Pathway analysis of super-exchange electronic couplings in electron transfer reactions using a multi-configuration self-consistent field method

We present a novel pathway analysis of super-exchange electronic couplings in electron transfer reactions using localized molecular orbitals from multi-configuration self-consistent field (MCSCF) calculations. In our analysis, the electronic coupling and the tunneling pathways can be calculated in terms of the configuration interaction (CI) Hamiltonian matrix obtained from the localized MCSCF wave function. Making use of the occupation restricted multiple active spaces (ORMAS) method can effectively produce the donor, acceptor, and intermediate configuration state functions (CSFs) and CIs among these CSFs. In order to express the electronic coupling as a sum of individual tunneling pathways contributions, we employed two perturbative methods: L?wdin projection-iteration method and higher-order super-exchange method. We applied them to anion couplings of butane-1,4-diyl and pentane-1,5-diyl. The results were (1) the electronic couplings calculated from the two perturbative methods were in reasonable agreement with those from a non-perturbative method (one-half value of the energy difference between the ground and first excited states), (2) the main tunneling pathways consisted of a small number of lower-order super-exchange pathways where bonding, anti-bonding, or extra-valence-shell orbitals were used once or twice, and (3) the interference among a huge number of higher-order super-exchange pathways significantly contributed to the overall electronic coupling, whereas each of them contributed only fractionally. Our method can adequately take into account both effects of non-dynamical electron correlation and orbital relaxation. Comparing with the analyses based on the Koopmans' theorem (ignoring both effects) and the ORMAS-CIs from frozen localized reference orbitals (ignoring the effect of orbital relaxation), we discuss these effects.     

Sequence-controlled oligomers fold into nanosolenoids and impart unusual optical properties

Controlled syntheses give unique block oligomers with alternating flexible ethylene glycol and rigid perylenetetracarboxylic diimide (PDI) units. The number of rigid units vary from n=1 to 10. PDI units were stitched together by using efficient phosphoramidite chemistry. The resulting oligomers undergo folding in most solvents, including chloroform. In their ground state, these folded oligomers were characterized by using Fourier transform ion cyclotron resonance mass spectrometry (FTICR‐MS), NMR spectroscopy, and electronic absorption spectroscopy. FTICR‐MS revealed the exact masses of these sequence‐controlled oligomers, which confirmed the chemical composition and validated the synthetic strategy. The NMR neighboring ring‐current effect (NRE) indicates the formation of cofacial π stacks; the stacked aromatic rings have nearly coaxial alignment akin to a nanosoleniod. Nanosolenoidal shielding in π stacks causes all aromatic protons to shift upfield, whereas NOE in a cyclic hetero‐chromophoric dimer supports a rotated, cofacial π‐stacking orientation separated by about 3.5 Å. Electron–phonon coupling is much stronger than excitonic coupling in these self‐folded PDI oligomers; thus, Franck–Condon factors dictate the observed spectral features in visible spectra. The absorbance spectrum exhibits weak hypochromism due to π stacking with increasing stacking units n. Finally, ab initio calculations support the experimental observations, indicating 3.5 Å cofacial spacing in which one molecule is rotated 30° from the eclipsed orientation and higher oligomers can adopt, without a compensating energy penalty, either the right/left‐handed helices or the 1,3‐eclipsed structures. Both theory and experiments validate the nano‐π‐solenoids and their novel photophysical properties.     

Vibronic interactions and possible electron pairing in the photoinduced excited electronic States in molecular systems: a theoretical study

Electron-phonon interactions in the photoinduced excited electronic states in molecular systems such as phenanthrene-edge-type hydrocarbons are discussed and compared with those in the monoanions and cations. The complete phase patterns difference between the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) (the atomic orbitals between two neighboring carbon atoms combined in phase (out of phase) in the HOMO are combined out of phase (in phase) in the LUMO) are the main reason that the C-C stretching modes around 1500 cm(-1) afford much larger electron-phonon coupling constants in the excited electronic states than in the charged electronic states. The frequencies of the vibrational modes that play an essential role in the electron-phonon interactions for the excited electronic states are similar to those for the monoanions and cations in phenanthrene-edge-type hydrocarbons. Possible electron pairing and Bose-Einstein condensation in the photoinduced excited electronic states as well as those in the monoanions and cations in molecular systems such as phenanthrene-edge-type hydrocarbons are also discussed.     

E ⊗ ϵ Jahn–Teller anharmonic coupling for an octahedral system

The coupling between doubly degenerate electronic states and doubly degenerate vibrations is analyzed for an octahedral system on the basis of the introduction of an anharmonic Morse potential for the vibronic part. The vibrations are described by anharmonic coherent states and their linear coupling with the electronic states is considered. The matrix elements of the vibronic interaction are built and the energy levels corresponding to the interaction Hamiltonian derived. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002