Vibronic Contributions Research Articles

Effects of Excited State−Excited State Configurational Mixing on Emission Bandshape Variations in Ruthenium−Bipyridine Complexes

The 77 K emission spectra of 21 [Ru(L) 4bpy] ( m+ ) complexes for which the Ru/bpy metal-to-ligand-charge-transfer ( (3)MLCT) excited-state energies vary from 12 500 to 18 500 cm (-1) have vibronic contributions to their bandshapes that implicate excited-state distortions in low frequency ( lf; hnu lf < 1000 cm (-1)), largely metal-ligand vibrational modes which most likely result from configurational mixing between the (3)MLCT and a higher energy metal centered ( (3)LF) excited state. The amplitudes of the lf vibronic contributions are often comparable to, or sometimes greater than those of medium frequency ( mf; hnu mf > 1000 cm (-1)), largely bipyridine (bpy) vibrational modes, and for the [Ru(bpy) 3] (2+) and [Ru(NH 3) 4bpy] (2+) complexes they are consistent with previously reported resonance-Raman (rR) parameters. However, far smaller lf vibronic amplitudes in the rR parameters have been reported for [Os(bpy) 3 ] (2+), and this leads to a group frequency approach for interpreting the 77 K emission bandshapes of [Ru(L) 4bpy] ( m+ ) complexes with the vibronic contributions from mf vibrational modes referenced to the [Os(bpy) 3] (2+) rR parameters (OB3 model) and the envelope of lf vibronic components represented by a "progression" in an "equivalent" single vibrational mode ( lf1 model). The lf1 model is referenced to rR parameters reported for [Ru(NH 3) 4bpy] (2+). The observation of lf vibronic components indicates that the MLCT excited-state potential energy surfaces of Ru-bpy complexes are distorted by LF/MLCT excited-state/excited-state configurational mixing, but the emission spectra only probe the region near the (3)MLCT potential energy minimum, and the mixing can lead to larger distortions elsewhere with potential photochemical implications: (a) such distortions may labilize the (3)MLCT excited state; and (b) the lf vibrational modes may contribute to a temperature dependent pathway for nonradiative relaxation.

Effective method for the computation of optical spectra of large molecules at finite temperature including the Duschinsky and Herzberg–Teller effect: The Qx band of porphyrin as a case study

The authors extend their recent method for the computation of vibrationally resolved optical spectra of large molecules, including both the Duschinsky rotation and the effect of finite temperature in the framework of the Franck-Condon (FC) approximation, to deal with the more general case of the Herzberg-Teller (HT) model, where also the linear dependence of the transition dipole moment on the nuclear coordinates is taken into account. This generalization allows us to investigate weak and vibronically allowed transitions by far extending the range of application of the method. The calculation of the spectra of sizable molecules is computationally demanding because of the huge number of final vibrational states that must be taken into account, and the inclusion of HT terms further increases the computational burden. The method presented here automatically selects the relevant vibronic contributions to the spectrum, independent of their frequency, and it is able to provide fully converged spectra with a modest computational requirement. The effectiveness of the method is illustrated by computing the HT absorption and fluorescence Q(x) spectra of free-base porphyrin both at T=0 K and at room temperature, performing for the first time an exact treatment of vibrations in harmonic approximation. Q(x) spectra are compared to experiments and FC/HT interferences are analyzed in detail.

Quantum Mechanical Computations and Spectroscopy: From Small Rigid Molecules in the Gas Phase to Large Flexible Molecules in Solution

Interpretation of structural properties and dynamic behavior of molecules in solution is of fundamental importance to understand their stability, chemical reactivity, and catalytic action. While information can be gained, in principle, by a variety of spectroscopic techniques, the interpretation of the rich indirect information that can be inferred from the analysis of experimental spectra is seldom straightforward because of the subtle interplay of several different effects, whose specific role is not easy to separate and evaluate. In such a complex scenario, theoretical studies can be very helpful at two different levels: (i) supporting and complementing experimental results to determine the structure of the target molecule starting from its spectral properties; (ii) dissecting and evaluating the role of different effects in determining the observed spectroscopic properties. This is the reason why computational spectroscopy is rapidly evolving from a highly specialized research field into a versatile and widespread tool for the assignment of experimental spectra and their interpretation in terms of chemical physical effects. In such a situation, it becomes important that both computationally and experimentally oriented chemists are aware that new methodological advances and integrated computational strategies are available, providing reliable estimates of fundamental spectral parameters not only for relatively small molecules in the gas phase but also for large and flexible molecules in condensed phases. In this Account, we review the most significant methodological contributions from our research group in this field, and by exploiting some recent results of their application to the computation of IR, UV-vis, NMR, and EPR spectral parameters, we discuss the microscopic mechanisms underlying solvent and vibrational effects on the spectral parameters. After reporting some recent achievements for the study of excited states by first principle quantum mechanical approaches, we focus on the treatment of environmental effects by means of mixed discrete-continuum solvent models and on effective methods for computing vibronic contributions to the spectra. We then discuss some new developments, mainly based on time-dependent approaches, allowing us to go beyond the determination of spectroscopic parameters toward the simulation of line widths and shapes. Although further developments are surely needed to improve the accuracy and effectiveness of several items in the proposed approach, we try to show that the first important steps toward a direct comparison between the results obtained in vitro and those obtained in silico have been made, making easier fruitful crossovers among experiments, computations and theoretical models, which would be decisive for a deeper understanding of the spectral behavior associated with complex systems and processes.

Eu 3 + as a probe for rare-earth dopant site structure in nano-glass-ceramics

Eu 3 + -doped transparent nano-glass-ceramics, 32(SiO2)9(AlO1.5)31.5(CdF2)18.5(PbF2)5.5(ZnF2):3.5(EuF3)mol %, have been prepared aiming at the investigation of the site structure of the Eu3+ rare-earth dopant. In this nano-glass-ceramic host, other rare-earth dopants, such as Er3+, Tm3+, Ho3+, and Dy3+, also have served as a dopant; however the Eu3+ ion is a preferably sensitive probe for a rare-earth dopant site structure due to its unique purely magnetic and purely electric dipole moment optical transitions involving the nondegenerate excited D50 and ground F70 states. The splitting in the respective emission and absorption spectra in the crystalline field of the nano-glass-ceramics and its parent glass has been studied. It has been concluded that the major site of the rare-earth dopant in the nano-glass-ceramics is nearly cubic, with an orthorhombic distortion according to the sequence Oh→D4h→D2h, and the majority of the rare-earth dopants substitute onto the Pb2+ site in the PbF2 nanocrystals embedded in the glass network. A vibronic contribution to the strength of the D50→F72 electric dipole moment transition has been found and the respective dominating contributing vibration mode has been proposed to be and to change as a2u→b1u→au, according to lowering the site symmetry in a sequence Oh→D4h→D2h.

Vibronic induced one- and two-photon absorption in a charge-transfer stilbene derivate

Both the electronic and the vibronic contributions to one- and two-photon absorption of a D-pi-D charge-transfer molecule (4-dimethylamino-4'-methyl-trans stilbene) are studied by means of density functional response theory combined with a linear coupling model. Vibronic profiles of the first four excited states are fully explored. The dominating vibrational modes for both Franck-Condon and Herzberg-Teller contributions are identified. The Franck-Condon contribution dominates the spectra of first, second, and fourth excited states. The Herzberg-Teller contribution is on the other hand of comparable size for the third excited state, where its inclusion leads to a blueshift with respect to the vertical transition. A similar vibronic coupling behavior is found for both one- and two-photon absorptions.

Effective method to compute vibrationally resolved optical spectra of large molecules at finite temperature in the gas phase and in solution

The authors present a new method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky rotation of the normal modes and the effect of thermal excitation. The method automatically selects the relevant vibronic contributions to the spectrum, independently of their frequency, and it is able to provide fully converged spectra with moderate computational times, both in vacuo and in solution. By describing the electronic states in the frame of the density functional theory and its time-dependent extension, they computed the room temperature absorption spectra of coumarin C153 and trans-stilbene in cyclohexane and the phosphorescence spectrum of porphyrazine in gas phase, showing that the method is fast and efficient. The comparison with experiment for trans-stilbene and coumarin C153 is very satisfactory, confirming the progress made toward a reliable method for the computation and interpretation for the optical spectra of large molecules.

Effective method to compute Franck-Condon integrals for optical spectra of large molecules in solution

The authors present a new method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky [Acta Physicochim. URSS 7, 551 (1937)] rotation of the normal modes. The method automatically selects the relevant vibronic contributions to the spectrum, independent of their frequency, and it is able to provide fully converged spectra with a quite modest computational time, both in vacuo and in condensed phase. Starting from the rigorous time-dependent expression they discuss indeed in which limits the spectrum of a molecule embedded in a solvent, described as a polarizable continuum, can be computed in a time-independent formalism, defining both nonequilibrium and equilibrium limits. In these cases the polarizable continuum model provides a suitable description of the solvent field. By computing the absorption spectra of anthracene in gas phase and of coumarin C153 in gas phase and cyclohexane, and the phosphorescence spectrum of the unsubstituted coumarin in ethanol they show that the method is fast and efficient.

Observations concerning light promoted electronic delocalization in covalently linked transition metal complexes

The emission spectral band shapes of several polypyridine-ligand (PP) bridged bis-ruthenium(II) complexes imply that Ru(II)/Ru(III) electronic coupling is weaker in their lowest energy metal to ligand charge transfer (MLCT) excited states than in their corresponding mixed valence ground states. In general, the amplitudes of the vibronic contributions to emission band shapes decrease markedly with the excited state-ground state energy differences, and it is expected that complexes with degenerate, or mixed valence excited states will have very weak vibronic side bands if configurational mixing of the degenerate MLCT excited states is substantial. However, the bimetallic PP-bridged ruthenium complexes emit at significantly lower energy than their monometallic analogs, but the vibronic contributions to their 77 K emission spectra are very similar to those of their monometallic complexes analogs. This indicates that the mixed valence excited states of the bimetallic complexes are electronically localized.

Probes of the Metal-to-Ligand Charge-Transfer Excited States in Ruthenium-Am(m)ine-Bipyridine Complexes: The Effects of NH/ND and CH/CD Isotopic Substitution on the 77 K Luminescence

The effects of ligand perdeuteration on the metal-to-ligand charge-transfer (MLCT) excited-state emission properties at 77 K are described for several [Ru(L)(4)bpy](2+) complexes in which the emission process is nominally [uIII,bpy-] --> [RuII,bpy]. The perdeuteration of the 2,2'-bipyridine (bpy) ligand is found to increase the zero-point energy differences between the ground states and MLCT excited states by amounts that vary from 0 +/- 10 to 70 +/- 10 cm(-1) depending on the ligands L. This indicates that there are some vibrational modes with smaller force constants in the excited states than in the ground states for most of these complexes. These blue shifts increase approximately as the energy difference between the excited and ground states decreases, but they are otherwise not strongly correlated with the number of bipyridine ligands in the complex. Careful comparisons of the [Ru(L)(4)(d(8)-bpy)](2+) and [Ru(L)(4)(h(8)-bpy](2+) emission spectra are used to resolve the very weak vibronic contributions of the C-H stretching modes as the composite contributions of the corresponding vibrational reorganizational energies. The largest of these, 25 +/- 10 cm(-1), is found for the complexes with L = py or bpy/2 and smaller when L = NH(3). Perdeuteration of the am(m)ine ligands (NH(3), en, or [14]aneN(4)) has no significant effect on the zero-point energy difference, and the contributions of the NH stretching vibrational modes to the emission band shape are too weak to resolve. Ligand perdeuteration does increase the excited-state lifetimes by a factor that is roughly proportional to the excited-state-ground-state energy difference, even though the CH and NH vibrational reorganizational energies are too small for nuclear tunneling involving these modes to dominate the relaxation process. It is proposed that metal-ligand skeletal vibrational modes and configurational mixing between metal-centered, bpy-ligand-centered, and MLCT excited states are important in determining the zero-point energy differences, while a large number of different combinations of relatively low-frequency vibrational modes must contribute to the nonradiative relaxation of the MLCT excited states.

Emission band shape probes of the mixed-valence excited state properties of polypyridyl-bridged bis-ruthenium(II) complexes

The absorption spectra and emission spectral band shapes of several polypyridine-ligand (PP) bridged bis-ruthenium(II) complexes imply that the Ru(II)/Ru(III) electronic coupling is weak in their lowest energy metal to ligand charge transfer (MLCT) excited states. Many of these PP-bridging ligands contain pyrazine moieties and the weak electronic coupling of the excited states contrasts to the strong electronic coupling inferred for the correlated mixed-valence ground states. Although the bimetallic complexes emit at significantly lower energy than their monometallic analogs, the vibronic contributions to their 77 K emission spectra are much stronger than expected based on comparison to the monometallic analogs (around twofold in some complexes) and this feature is characteristic of bimetallic complexes in which the mixed-valence excited states are electronically localized. The weaker excited state than ground state donor/acceptor electronic coupling in this class of complexes is attributed to PP-mediated super-exchange coupling in which the mediating orbital of the bridging ligand (PP-LUMO) is partly occupied in the MLCT excited states, but is unoccupied in the ground states; therefore, the vertical Ru(III)-PP − (MLCT) energy is larger and the mixing coefficient smaller in these excited states than is found for Ru(II)-PP in the corresponding ground states.

The Characterization of the High-Frequency Vibronic Contributions to the 77 K Emission Spectra of Ruthenium−Am(m)ine−Bipyridyl Complexes, Their Attenuation with Decreasing Energy Gaps, and the Implications of Strong Electronic Coupling for Inverted-Region Electron Transfer

The 77 K emission spectra of a series of [Ru(Am)6-2n(bpy)n]2+ complexes (n = 1-3) have been determined in order to evaluate the effects of appreciable excited state (e)/ground state (g) configurational mixing on the properties of simple electron-transfer systems. The principal focus is on the vibronic contributions, and the correlated distortions of the bipyridine ligand in the emitting MLCT excited state. To address the issues that are involved, the emission band shape at 77 K is interpreted as the sum of a fundamental component, corresponding to the {e,0'} --> {g,0} transition, and progressions in the ground-state vibrational modes that correlate with the excited-state distortion. Literature values of the vibrational parameters determined from the resonance-Raman (rR) for [Ru(NH3)4bpy]2+ and [Ru(bpy)3]2+ are used to model the emission spectra and to evaluate the spectral analysis. The Gaussian fundamental component with an energy Ef and bandwidth Deltanu1/2 is deconvoluted from the observed emission spectrum. The first-, second-, and third-order terms in the progressions of the vibrational modes that contribute to the band shape are evaluated as the sums of Gaussian-shaped contributions of width Deltanu1/2. The fundamental and the rR parameters give an excellent fit of the observed emission spectrum of [Ru(NH3)4bpy]2+, but not as good for the [Ru(bpy)3]2+ emission spectrum probably because the Franck-Condon excited state probed by the rR is different in symmetry from the emitting MLCT excited state. Variations in vibronic contributions for the series of complexes are evaluated in terms of reorganizational energy profiles (emreps, Lambdax) derived from the observed spectra, and modeled using the rR parameters. This modeling demonstrates that most of the intensity of the vibronic envelopes obtained from the frozen solution emission spectra arises from the overlapping of first-order vibronic contributions of significant bandwidth with additional convoluted contributions of higher order vibronic terms. The emrep amplitudes of these complexes have their maxima at about 1500 cm(-1) in frozen solution, and Lambdax(max) decreases systematically by approximately 2-fold as Ef decreases from 17,220 for [Ru(bpy)3]2+ to 12,040 cm(-1) for [Ru(NH3)4bpy]2+ through the series of complexes. Corrections for higher order contributions and bandwidth differences based on the modeling with rR parameters indicate that the variations in Lambdax(max) imply somewhat larger decreases in first-order bpy vibrational reorganizational energies. The large attenuation of vibrational reorganizational energies of the [Ru(Am)6-2n(bpy)n]2+ complexes contrasts with the apparent similarity of reorganizational energy amplitudes for the absorption and emission of [Ru(NH3)4bpy]2+. These observations are consistent with increasing and very substantial excited-state/ground-state configurational mixing and decreasing excited-state distortion as Ef decreases, but more severe attenuation for singlet/singlet than triplet/singlet mixing (alphage > alphaeg for the configurational mixing coefficients at the ground-state and excited-state potential energy minima, respectively); it is inferred that 0.18 > or = alphage2 > or = 0.09 for [Ru(bpy)3]2+ and 0.37 > or = alphage2 > or = 0.18 for [Ru(NH3)4bpy]2+ in DMSO/water glasses, where the ranges are based on models that there is or is not a spin restriction on configurational mixing (alphage > alphaeg and alphage = alphaeg), respectively, for these complexes.

On the hyperfine coupling in tetragonal copper(II) complexes

The vibronic effect on the hyperfine coupling (HFC) parameters in tetragonal copper(II) complexes was studied. The parameters of the vibronic contributions from the \(3d_{_z 2}\)- and 4s-AOs of the Cu2+ ion to the ground-state function were estimated. The anomalous behavior of the isotropic HFC was analyzed in terms of the static model with consideration of the vibronic coupling. The static and vibronic contributions to the anisotropic portions of the components of the HFC tensor were estimated.

Vibronic Contributions to Charge Transport Across Molecular Junctions

We report low-temperature charge transport measurements of metal−molecule−metal junctions. Studies on insulating alkyl and π-conjugated molecular wires provide experimental insight into the coupling between tunnel charge carriers and molecular vibrations in molecular electronic systems. By comparison with other vibrational spectroscopy studies and density functional theory calculations, the observed vibrational peaks have been assigned to longitudinal modes of the molecules.

Vibronic Coupling between Soret and Higher Energy Excited States in Iron(II) Porphyrins: Raman Excitation Profiles of A2g Modes in the Soret Region

Resonance Raman spectra were observed for heme proteins and iron(II) porphyrins including ferrous-CO and ferrous-isocyanide derivatives of cytochrome P450cam, a synthetic iron(II) porphyrin complex having a thiolate axial ligand, ferrous-isocyanide derivative of myoglobin, and synthetic iron(II) porphyrin complexes having either an imidazole or a sulfide axial ligand. Among them, the former three were found to be a hyperporphyrin, giving red and blue Soret absorption bands, whereas others were normal porphyrins giving a single Soret band. When Raman scattering was excited within the Soret region, an anomalously polarized (ap) Raman line, which was assignable to the O19 mode belonging to the A2g species, was observed at 153786 cm -1 for all these compounds. Both the synthetic iron(II) porphyrins having the imidazole and sulfide ligands also showed another ap Raman line at 1230 cm -1 , which was assigned to O26 of A2g symmetry. Raman excitation profiles of the O19 and O26 modes showed a maximum that was displaced from the 0-0 component of the Soret or red Soret band toward higher frequencies by the frequency of the corresponding mode, indicating the 0-1 component. Although Raman lines of these modes were also observed upon excitation at the 0-0 component, they were significantly more intense at the 0-1 component. These results, together with nonadiabatic theories about vibronic contribution to Raman intensity, indicated the presence of vibronic coupling between the Soret (or red Soret) excited state and some other electronic excited state(s) located in the blue of the Soret band. The present study hence demonstrates that lower occupied orbitals other than those described in the ordinary four-orbital model and its extended form, which is applicable to the hyperporphyrins, contribute to the Soret (or red Soret) excited states.

Vibronic contributions to resonant NLO responses: two-photon absorption in push–pull chromophores

Two-photon absorption (TPA) spectra of push–pull chromophores are described in terms of a two-state model accounting for electron-vibration coupling. Vibrations have two main effects in TPA spectra. The most obvious one is the appearance of a vibrational structure in the spectrum; in this respect we find large Herzberg–Teller (HT) contributions. The second effect was not recognized so far: vibrational states contribute a new channel to TPA process, that shows up with a blue-shift and a distortion of the spectrum.

Electronic and Vibronic Contributions to the Band Splitting in Optical Spectra of Heme Proteins

We have employed Rayleigh−Schrodinger perturbation theory to obtain a simple quantum mechanical model to simulate the influence of asymmetric distortions on the optical spectra of metalporphyrins. The model is based on Gouterman's classical four orbital model and considers group theoretical restriction for the interactions between different electronic states. In heme proteins, asymmetric distortions of the porphyrin macrocycle are induced by axial ligands, asymmetric peripheral substituents, and the anisotropic protein environment. They give rise to electronic and vibronic perturbations, which cause additional mixing between vibronic states and, for B1g-type perturbations, also, a split of the Q and B states, which are 2-fold degenerated in symmetric porphyrins exhibiting a D4h symmetry. To compare our calculations with experimentally observed splits of the Q band in the spectra of various ferrocytochrome c (Manas et al. J. Phys. Chem. B. 1999, 103, 6344) we estimated vibronic matrix elements from resonan...

First-principles investigation of the cooperative Jahn-Teller effect for octahedrally coordinated transition-metal ions

Fundamental aspects of the cooperative Jahn-Teller effect are investigated using density functional theory in the generalized gradient approximation. ${\mathrm{LiNiO}}_{2},$ ${\mathrm{LiMnO}}_{2},$ and ${\mathrm{LiCuO}}_{2}$ are chosen as candidate materials as they possess small, intermediate, and large cooperative Jahn-Teller distortions, respectively. The cooperative distortion is decomposed into the symmetrized-strain modes and $k=0$ optical phonons, revealing that only the ${E}_{g}$ and ${A}_{1g}$ strain modes and ${E}_{g}$ and ${A}_{1g}$ $k=0$ optical-phonon modes participate in the cooperative distortion. The first-principles results are then used to find values for the cooperative Jahn-Teller stabilization energy and the electron-strain and electron-phonon coupling. It is found that the dominant source of anisotropy arises from the third-order elastic contributions, rather than second-order vibronic contributions. Additionally, the importance of higher-order elastic coupling between the ${E}_{g}$ and ${A}_{1g}$ modes is identified, which effectively causes expansion of ${A}_{1g}$-type modes and allows for a larger ${E}_{g}$ distortion. Finally, the strain anisotropy induced by the antiferromagnetically ordered states is shown to cause a significant difference in the cooperative Jahn-Teller stabilization energy for the different orientations of the cooperative distortion.

S K-edge X-ray absorption studies of tetranuclear iron-sulfur clusters: mu-sulfide bonding and its contribution to electron delocalization.

X-ray absorption spectroscopy (XAS) at the sulfur ( approximately 2470 eV) and chlorine ( approximately 2822 eV) K-edges has been applied to a series of 4Fe-4S model complexes. These are compared to 2Fe-2S model complexes to obtain insight into the localized ground state in the mixed-valence dimer versus the delocalized ground state in the mixed-valence tetramer. The preedges of hypothetical delocalized mixed-valence dimers [Fe(2)S(2)](+) are estimated using trends from experimental data and density functional calculations, for comparison to the delocalized mixed-valence tetramer [Fe(4)S(4)](2+). The differences between these two mixed-valence sites are due to the change of the sulfide-bridging mode from micro(2) to micro(3). The terminal chloride and thiolate ligands are used as spectator ligands for the electron density of the iron center. From the intensity of the preedge, the covalency of the terminal ligands is found to increase in the tetramer as compared to the dimer. This is associated with a higher effective nuclear charge on the iron in the tetramer (derived from the energies of the preedge). The micro(3)-bridging sulfide in the tetramer has a reduced covalency per bond (39%) as compared to the micro(2)-bridging sulfide in the dimer (51%). A simple perturbation model is used to derive a quadratic dependence of the superexchange coupling constant J on the covalency of the metal ions with the bridging ligands. This relationship is used to estimate the superexchange contribution in the tetramer (J = -156 cm(-)(1)) as compared to the mixed-valence dimer (J = -360 cm(-)(1)). These results, combined with estimates for the double exchange and the vibronic coupling contributions of the dimer sub-site of the tetramer, lead to a delocalized S(t) = (9)/(2) spin ground state for the mixed-valence dimer in the tetramer. Thus, the decrease in the covalency, hence the superexchange pathway associated with changing the bridging mode of the sulfides from micro(2) to micro(3) on going from the dimer to the tetramer, significantly contributes to the delocalization of the excess electron over the dimer sub-site in the tetramer.

Electronic and vibronic contributions to two-photon absorption of molecules with multi-branched structures

The electronic and vibronic contributions to the two-photon absorption of a series molecules with multi-branched structures have been studied using ab initio response theory. The results indicate that the electronic coupling between different branches alone cannot explain the experimental finding of a strong enhancement of the two-photon absorption cross section over the single branch structure, whereas it is predicted that vibronic contributions can play an important role in this respect. It is shown that for multi-branched molecules the use of circularly polarized light can increase the two-photon absorption cross section by a factor of 1.5 over linearly polarized light excitation.

A comparative study of the pseudo Jahn–Teller instability of linear molecules Ag 3 and I 3 and their positive and negative ions

In confirmation of the general idea of pseudo Jahn–Teller origin of instability of high-symmetry configurations of polyatomic systems that determines their geometry, a series of six molecules, Ag 3 n and I 3 n, n=−1,0,+1, were investigated. The electronic structure of the ground state of all the six molecules in the linear configuration was calculated by the extended-Hückel method with atomic charge and electron configuration self-consistency, while the excited state energy levels and wavefunctions were estimated in the single transition approximation. Then, the orbital vibronic constants, bare force constants and the vibronic contribution of the appropriate excited states to the instability of the linear configuration were evaluated. The obtained results show that in both series, silver and iodine, the curvature of the adiabatic potential of the linear configuration, in the direction of the bending distortions, decreases from the negative ions to the neutral atoms to the positive ions and becomes negative in the latter two cases, thus explaining the origin of the experimentally observed geometries. The numerical data give a detailed insight into: (1) the origin of the linear→bent distortions as being due to the additional covalency created by the σ–π overlap in the bent configuration; (2) the specific excited states that contribute to this process of geometry formation; and (3) the difference between the silver and iodine series.