Horst Köppel

Vibronic coupling effects in the photoelectron spectrum of ethylene

The vibrational structure of the first band in the photoelectron spectrum of ethylene is calculated taking into account the vibronic coupling between the ground state and first excited state of the ion. The vibronic Hamiltonian describes linear coupling to the totally symmetric vibrational modes ν1–ν3 as well as to the non‐totally symmetric torsional mode ν4. The energies and coupling constants entering the calculation are computed by ab initio Hartree–Fock and many‐body methods. Qualitative agreement between the theoretical and the experimental spectrum is found. By slightly readjusting some of the parameters, the experimental spectrum can be reproduced accurately. It turns out that nonadiabatic and intensity borrowing effects are small. The vibronic coupling results mainly in a pronounced anharmonicity of the adiabatic potential energy surface. In particular, a nonplanar equilibrium geometry is found for the ionic ground state, the equilibrium torsional angle being ∼25°. Although the corrections to the ...

Multistate vibronic interactions in the benzene radical cation. I. Electronic structure calculations

The multistate vibronic interactions in the benzene radical cation are investigated theoretically, employing the framework of a linear vibronic coupling scheme. The five lowest electronic states are included in the treatment; in view of the degeneracy of some states, this amounts to eight coupled potential energy surfaces. Different types of ab initio calculations have been performed for the system parameters and been found to be in good mutual agreement, thus supporting each other. The calculations reveal a whole sequence of low-energy conical intersections between the potential energy surfaces of different states. Their importance for the nuclear dynamics in this prototypical organic radical cation is pointed out. Wave-packet dynamical simulations for these coupled potential energy surfaces will be presented in the following paper (Paper II).

Geometric phase effects and wave packet dynamics on intersecting potential energy surfaces

The impact of the geometric phase on the time evolution of quantum‐mechanical wave packets is studied theoretically. Two model systems of coupled electronic potential energy surfaces are compared. One of them, the well‐known E×e Jahn–Teller system, comprises two conically intersecting surfaces, and the dynamics is subject to the geometric phase. The other system, describing the (E+A)×e Pseudo‐Jahn–Teller effect, comprises three intersecting surfaces and the dynamics is not subject to a geometric phase. Apart from the geometric phase, the coupling to the upper surface is verified to be negligible for low‐energy wave packet motion. Still, the geometric phase leads to a pronounced difference of low‐energy wave packet dynamics in both systems. Most significant is the phenomenon of destructive self‐interference of the two parts of the wave packet that encircle the conical intersection on opposite sides. The importance of the resulting different shape of the wave packet for a fs pump‐probe spectrum is pointed out.

Are β‐H‐Eliminations or Alkene Insertions Feasible Elementary Steps in Catalytic Cycles Involving Gold(I) Alkyl Species or Gold(I) Hydrides?

The β-H-elimination in the (iPr)AuEt complex and its microscopic reverse, the insertion of ethene into (iPr)AuH, were investigated in a combined experimental and computational study. Our DFT-D3 calculations predict free-energy barriers of 49.7 and 36.4 kcal mol(-1) for the elimination and insertion process, respectively, which permit an estimation of the rate constants for these reactions according to classical transition-state theory. The elimination/insertion pathway is found to involve a high-energy ethene hydride species and is not significantly affected by continuum solvent effects. The high barriers found in the theoretical study were then confirmed experimentally by measuring decomposition temperatures for several different (iPr)Au(I) -alkyl complexes which, with a slow decomposition at 180 °C, are significantly higher than those of other transition-metal alkyl complexes. In addition, at the same temperature, the decomposition of (iPr)AuPh and (iPr)AuMe, both of which cannot undergo β-H-elimination, indicates that the pathway for the observed decomposition at 180 °C is not a β-H-elimination. According to the calculations, the latter should not occur at temperatures below 200 °C. The microscopic reverse of the β-H-elimination, the insertion of ethene into the (iPr)AuH could neither be observed at pressures up to 8 bar at RT nor at 1 bar at 80 °C. The same is true for the strain-activated norbornene.

Barrier recrossing in the vinylidene–acetylene isomerization reaction: A five-dimensional ab initio quantum dynamical investigation

The spectroscopy and dynamics of the vinylidene–acetylene isomerization reaction are studied theoretically. Based on a new ab initio potential energy surface, the nuclear dynamics is followed by grid methods and wave packet propagation techniques. All five planar degrees of freedom are included in the calculation, for all three different isotopomers. The experimental photoelectron spectra by Lineberger and co-workers are very well reproduced; upon a small adjustment of the calculated anionic equilibrium geometry the agreement becomes excellent. The vinylidene survival probability for broadband photodetachment exhibits three different time regimes, the longest of which points towards an unusual stability of this reactive intermediate. The latter finding is corroborated by the calculated state-specific lifetimes which exceed previous estimates in the literature by ∼3 orders of magnitude. These findings are found to be reconfirmed when taking the discrete level structure of vibrationally highly excited acety...

Spectra and time-dependent dynamics of H3 near the conical intersection in the (2p)1E′ ground electronic manifold

We report on the spectra and dynamics of H3 near the conical intersection in its (2p)1E′ ground electronic manifold. The time-dependent wave packet approach and the double many-body expansion (DMBE) potential energy surface (PES) are employed for this purpose. We use Jacobi coordinates (R,r,γ) and employ the fast Fourier transform method for R and r, and the discrete variable representation method for γ, in conjunction with the split-operator formalism to describe the evolution of the wave packet (WP) in space and time, respectively. While the main focus of the present work is to explicitly reveal the effects of nonadiabatic coupling between the two sheets of the DMBE PES, companion calculations are also carried out to investigate the dynamics on the uncoupled upper and lower adiabatic sheets, both in two and three dimensions (for total angular momentum J=0). A set of pseudospectra is calculated by Fourier transforming the time autocorrelation function of suitably chosen Gaussian wave packets located init...

Vibrational quenching of excitonic splittings in H-bonded molecular dimers: The electronic Davydov splittings cannot match experiment

The S(1)/S(2) state exciton splittings of symmetric doubly hydrogen-bonded gas-phase dimers provide spectroscopic benchmarks for the excited-state electronic couplings between UV chromophores. These have important implications for electronic energy transfer in multichromophoric systems ranging from photosynthetic light-harvesting antennae to photosynthetic reaction centers, conjugated polymers, molecular crystals, and nucleic acids. We provide laser spectroscopic data on the S(1)/S(2) excitonic splitting Δ(exp) of the doubly H-bonded o-cyanophenol (oCP) dimer and compare to the splittings of the dimers of (2-aminopyridine)(2), [(2AP)(2)], (2-pyridone)(2), [(2PY)(2)], (benzoic acid)(2), [(BZA)(2)], and (benzonitrile)(2), [(BN)(2)]. The experimental S(1)/S(2) excitonic splittings are Δ(exp) = 16.4 cm(-1) for (oCP)(2), 11.5 cm(-1) for (2AP)(2), 43.5 cm(-1) for (2PY)(2), and <1 cm(-1) for (BZA)(2). In contrast, the vertical S(1)/S(2) energy gaps Δ(calc) calculated by the approximate second-order coupled cluster (CC2) method for the same dimers are 10-40 times larger than the Δ(exp) values. The qualitative failure of this and other ab initio methods to reproduce the exciton splitting Δ(exp) arises from the Born-Oppenheimer (BO) approximation, which implicitly assumes the strong-coupling case and cannot be employed to evaluate excitonic splittings of systems that are in the weak-coupling limit. Given typical H-bond distances and oscillator strengths, the majority of H-bonded dimers lie in the weak-coupling limit. In this case, the monomer electronic-vibrational coupling upon electronic excitation must be accounted for; the excitonic splittings arise between the vibronic (and not the electronic) transitions. The discrepancy between the BO-based splittings Δ(calc) and the much smaller experimental Δ(exp) values is resolved by taking into account the quenching of the BO splitting by the intramolecular vibronic coupling in the monomer S(1) ← S(0) excitation. The vibrational quenching factors Γ for the five dimers (oCP)(2), (2AP)(2), (2AP)(2), (BN)(2), and (BZA)(2) lie in the range Γ = 0.03-0.2. The quenched excitonic splittings Γ[middle dot]Δ(calc) are found to be in very good agreement with the observed splittings Δ(exp). The vibrational quenching approach predicts reliable Δ(exp) values for the investigated dimers, confirms the importance of vibrational quenching of the electronic Davydov splittings, and provides a sound basis for predicting realistic exciton splittings in multichromophoric systems.

Ab initio quantum study of the photodynamics and absorption spectrum for the coupled 11A2 and 11B1 states of SO2

The nonadiabatic photoinduced dynamics occurring in the coupled 1(1)A(2) and 1(1)B(1) excited states of SO(2) is investigated using ab initio quantum dynamical methods. To this end, large scale calculations of the potential energy surfaces have been carried out at the multireference configuration interaction level. All vibrational degrees of freedom of the molecule are considered in the potential energy surface calculations and the quantum dynamical treatment. To deal with the symmetry-allowed conical intersection which occurs between the potential energy surfaces, we use the diabatic picture in the framework of regularized diabatic states. Wave-packet propagation on the coupled surfaces was performed and allowed to reproduce with good accuracy the complex absorption band observed experimentally in the 29,000-42,000 cm(-1) range. This provides a basis for a subsequent theoretical treatment of the high order harmonic spectra of SO(2).

Mechanism of visible-light photoisomerization of a rhenium(I) carbonyl-diimine complex

The mechanism of photoisomerization of a Re(I) carbonyl-diimine complex under visible-light irradiation is deciphered by means of ab initio calculations. By highlighting the key role of triplet states as well as spin-orbit and vibronic couplings, we provide a clear picture of this complicated multi-step process.

Hierarchy of effective modes for the dynamics through conical intersections in macrosystems

An extension of the effective-mode theory for the short-time dynamics through conical intersections in macrosystems [L. S. Cederbaum et al., Phys. Rev. Lett. 94, 113003 (2005)] is proposed. The macrosystem, containing a vast number of nuclear degrees of freedom (modes), is decomposed into a system part and an environment part. Only three effective modes are needed-together with the systems modes-to accurately calculate low resolution spectra and the short-time dynamics of the entire macrosystem. Here, the authors propose an iterative scheme to construct a hierarchy of additional triplets of effective modes. This naturally extends the effective-mode formulation. By taking into account more and more triplets, the dynamics are accurately predicted for longer and longer times, and more resolved spectra can be calculated. Numerical examples are presented, computed using various numbers of additional effective modes.