On the Fluorescence Properties and Nonradiative Transitions in Medium-Sized All-Trans Polyenes.

The nonadiabatic photodynamics of all-trans linear polyenes with N = 4-8 conjugated double bonds is studied from an electronic structure perspective. Excitation energies and stationary points for the 1Bu and 2Ag singlet states have been computed by using the state-average complete active space (SA-CASSCF) method and its second-order perturbation theory variant (MS-CASPT2). The dependence of the two low-lying excited states on the "chain length" N has been elucidated. In addition, the 1Bu-2Ag crossing seam has been mapped out in a suitable two-dimensional coordinate space and its minimum within the subspace has been determined. This minimum is found to increase substantially and monotonously in energy with increasing N. This increase is discussed and interpreted in relation to the fluorescence properties of these systems. In particular, it allows to understand the crossover from S1(2Ag) fluorescence for smaller N to S2(1Bu) (or dual) fluorescence for larger N.

Photodissociation dynamics and UV absorption spectrum of acetone oxide (CH3)2COO.

The photodynamics and B1A' ← X1A' absorption spectrum of acetone oxide, (CH3)2COO, are studied theoretically from first principles. The underlying adiabatic potential energy curves (and surfaces) are computed by a second-order multireference perturbation theory method and diabatized using a diabatization by ansatz scheme. To confirm the results, for selected geometries EOM-CCSD and XMS-RS2C calculations were also performed. The dynamical calculation rests on the multi-configuration time-dependent Hartree wavepacket propagation method. The experimental absorption spectrum is reproduced satisfactorily. This result serves to validate the Hamiltonian model built within the quasi-diabatic representation. Contrary to the smallest Criegee intermediate, CH2OO, it is found that the vibronic coupling between the B and C states of (CH3)2COO plays an essential role in reproducing the experimental absorption spectrum. Time-dependent electronic populations reveal a faster decay than for the smaller system CH2OO. This is interpreted in terms of the stronger coupling between the B and C states in the larger system leading to a shorter lifetime for the B state than in CH2OO.

Correlated quantum treatment of the photodissociation dynamics of formaldehyde oxide CH2OO.

An extended theoretical analysis of the photodissociation of the smallest Criegee intermediate CH2OO following excitation to the B state is presented. It relies on explicitly correlated multireference electronic wavefunctions combined with a quantum dynamical treatment for two interacting (B-C) electronic states and three coupled nuclear degrees of freedom. The 3D model relies on PESs along the O-O and C-O stretching as well as C-O-O bending modes for the two lowest excited states with A' symmetry, and is sufficiently accurate to reproduce the experimental B1A'-X1A' absorption spectrum, especially at the low-energy range to unprecedented accuracy. The existence of a deep well (∼0.4 eV) on the (diabatic) B state causes a considerable amount of the wavepacket to be reflected by the B state well, which can explain the vibronic structures appearing in the long wavelength range of 360-470 nm of the spectrum. The main progression appearing in the energy range from 360 to 470 nm is assigned to the O-O stretching mode while finer details are affected by couplings to the C-O stretching and C-O-O bending modes. The weakly avoided crossing between the B-state and C-state potential energy surfaces appearing near 3.1 eV excitation energy (for RS2-F12 method) causes considerable disturbance in the vibronic fine structure of the bands. The description of the latter is quite strongly affected by the type of electron correlation treatment adopted, either fully variational (MRCI type) or perturbation theoretic (RS2 type). The results give novel insight into the complex interactions governing that intriguing process.

Excited state dynamics of the s-trans-1, 3-butadiene cation: An ab initio quantum dynamical analysis.

The excited state dynamics of the s-trans-1,3-butadiene cation, focusing on the second and third bands of the photoelectron spectrum, have been investigated using a fully quantal approach, for the first time. The five lowest electronic states X2Bg, A2Au, B2Ag, C2Bu, and D2Ag considering the six vibrational modes S3, S5, S13, S17, S19, and S20 were taken into account in the nuclear quantum dynamical investigation. The potential energy curves have been calculated along these coordinates for the five lowest electronic states using the RS2C method. Our simulations indicate a moderately fast population transfer from the A2Au and B2Ag to the X2Bg state, taking place on a time scale of 70-80 fs. Furthermore, the computed second and third bands of the photoelectron spectrum are in good agreement with the corresponding experimental ones. Our calculation identifies the symmetric stretching of the central C-C bond S5 and the symmetric C-C-C bending S13 to be the main progression modes of the second and third bands of the photoelectron spectrum of (cationic) s-trans-1,3-butadiene.

Vibronic Coupling and Excitation Transfer in Hydrogen-Bonded Molecular Dimers: A Quantum Dynamical Analysis.

A brief pedagogic rederivation is given of basic exciton coupling theory, taking the nuclear coordinates to be fixed. This is then extended to take variations of these coordinates into account by adopting suitable multimode coupling models and extracting the transfer of excitation energy from the populations of the locally excited states. The dynamical problem thus defined is solved numerically in a fully quantal manner. Two doubly hydrogen bonded dimers of (hetero)aromatic systems are selected as representative cases whose electronic excitation spectra have been analyzed previously based on ab initio data, and good agreement with experiment has been found. The numerical calculations of the electronic populations reveal a complex time dependence of the excitation transfer that is far from being oscillatory or exponential. For localized excitation, the short-time behavior can be understood in terms of the quenched excitonic energy splitting, while for delocalized excitation a complex time dependence with rapidly changing features results. Some of these can be interpreted in terms of the vibronic structure of the excitation spectra. The importance of the quenched excitonic splitting for the short-time behavior of the excitation energy transfer is emphasized.

Nonadiabatic photodynamics and UV absorption spectrum of all-trans-octatetraene.

The short-time molecular quantum dynamics of all-trans-octatetraene after electronic excitation to the first bright valence state is theoretically investigated. A semiempirical approach of a multireference configuration interaction based on density functional theory, the so called hybrid DFT/MRCI, in both its original and redesigned formulations, is used for treating the electronic part of the problem. The nuclear kinetic part is defined with the help of symmetry-adapted internal coordinates also suitable for a large amplitude displacement. By incorporating ten in-plane and two out-of-plane nuclear degrees of freedom in the underlying Hamiltonian, the results of the time evolution of the excited wave packet are discussed. We show that the population transfer between the two coupled low-lying states in all-trans-octatetraene occurs in a 100-200 fs time regime. The calculated UV absorption spectra describe the main vibronic features correctly except for the band associated with the single-bond stretching motion which lacks intensity. The possible products of the photoisomerization in terms of symmetry-adapted coordinates are also discussed.

Excitonic Splitting and Vibronic Coupling Analysis of the m-Cyanophenol Dimer.

The S1/S2 splitting of the m-cyanophenol dimer, (mCP)2 and the delocalization of its excitonically coupled S1/S2 states are investigated by mass-selective two-color resonant two-photon ionization and dispersed fluorescence spectroscopy, complemented by a theoretical vibronic coupling analysis based on correlated ab initio calculations at the approximate coupled cluster CC2 and SCS-CC2 levels. The calculations predict three close-lying ground-state minima of (mCP)2: The lowest is slightly Z-shaped (Ci-symmetric); the second-lowest is <5 cm-1 higher and planar (C2h). The vibrational ground state is probably delocalized over both minima. The S0 → S1 transition of (mCP)2 is electric-dipole allowed (Ag → Au), while the S0 → S2 transition is forbidden (Ag → Ag). Breaking the inversion symmetry by 12C/13C- or H/D-substitution renders the S0 → S2 transition partially allowed; the excitonic contribution to the S1/S2 splitting is Δexc = 7.3 cm-1. Additional isotope-dependent contributions arise from the changes of the m-cyanophenol zero-point vibrational energy upon electronic excitation, which are Δiso(12C/13C) = 3.3 cm-1 and Δiso(H/D) = 6.8 cm-1. Only partial localization of the exciton occurs in the 12C/13C and H/D substituted heterodimers. The SCS-CC2 calculated excitonic splitting is Δel = 179 cm-1; when multiplying this with the vibronic quenching factor Γvibronexp = 0.043, we obtain an exciton splitting Δvibronexp = 7.7 cm-1, which agrees very well with the experimental Δexc = 7.3 cm-1. The semiclassical exciton hopping times range from 3.2 ps in (mCP)2 to 5.7 ps in the heterodimer (mCP-h)·(mCP-d). A multimode vibronic coupling analysis is performed encompassing all the vibronic levels of the coupled S1/S2 states from the v = 0 level to 600 cm-1 above. Both linear and quadratic vibronic coupling schemes were investigated to simulate the S0 → S1/S2 vibronic spectra; those calculated with the latter scheme agree better with experiment.

Theoretical analysis of the S2←S0 vibronic spectrum of the 2-pyridone dimer.

The interplay between excitonic and vibronic coupling in hydrogen-bonded molecular dimers leads to complex spectral structures and other intriguing phenomena such as a quenching of the excitonic energy splitting. We recently extended our analysis from that of the quenching mechanism to the theoretical investigation of the complete vibronic spectrum for the ortho-cyanophenol dimer. We now apply the same approach to the vibronic spectrum of the 2-pyridone dimer and discuss the assignment of vibronic lines to gain insight into the underlying coupling mechanism. This is based on potential energy surfaces obtained at the RI-CC2/aug-cc-pVTZ level. They are used for the dynamical analysis in the framework of a multi-mode vibronic coupling approach. The theoretical results based on the quadratic vibronic coupling model are found to be in good agreement with the experimental resonant two-photon ionization spectrum.

Analysis of the S2←S0 vibronic spectrum of the ortho-cyanophenol dimer using a multimode vibronic coupling approach.

The S2←S0 vibronic spectrum of the ortho-cyanophenol dimer (oCP)2 is analyzed in a joint experimental and theoretical investigation. Vibronic excitation energies up to 750 cm(-1) are covered, which extends our previous analysis of the quenching of the excitonic splitting in this and related species [Kopec et al., J. Chem. Phys. 137, 184312 (2012)]. As we demonstrate, this necessitates an extension of the coupling model. Accordingly, we compute the potential energy surfaces of the ortho-cyanophenol dimer (oCP)2 along all relevant normal modes using the approximate second-order coupled cluster method RI-CC2 and extract the corresponding coupling constants using the linear and quadratic vibronic coupling scheme. These serve as the basis to calculate the vibronic spectrum. The theoretical results are found to be in good agreement with the experimental highly resolved resonant two-photon ionization spectrum. This allows to interpret key features of the excitonic and vibronic interactions in terms of nodal patterns of the underlying vibronic wave functions.

Photoelectron spectrum and dynamics of the uracil cation.

The photoelectron spectrum of uracil and the molecular dynamics of its radical cation are investigated using the multiconfigurational time-dependent Hartree (MCTDH) method. For this aim, the vibronic coupling model Hamiltonian is used including up to ten important a' modes. Moreover, to account for coupling through conical intersections between states of different symmetry in the system, coupling constants of two a″ modes are taken into account. The parameters used in the model are obtained by fitting to ab inito data obtained with extensive EOM-IP-CCSD calculations. The first four cationic states were investigated, which are either of A″ (hole in a π orbital) or A' (hole in a nO orbital) symmetry. The results of the wavepacket propagations were used to calculate the corresponding photoelectron spectrum and compare to the experimental spectrum. The MCTDH simulations reproduce the experimental spectrum well. The dynamics starting from the D2 and D3 ionic states show a fast relaxation to the cationic ground state often involving direct D2-D0 or D3-D1 transitions.

Excitonic splittings in molecular dimers: why static ab initio calculations cannot match them.

After decades of research on molecular excitons, only few molecular dimers are available on which exciton and vibronic coupling theories can be rigorously tested. In centrosymmetric H-bonded dimers consisting of identical (hetero)aromatic chromophores, the monomer electronic transition dipole moment vectors subtract or add, yielding S0 → S1 and S0 → S2 transitions that are symmetry-forbidden or -allowed, respectively. Symmetry breaking by 12C/13C or H/D isotopic substitution renders the forbidden transition weakly allowed. The excitonic coupling (Davydov splitting) can then be measured between the S0 → S1 and S0 → S2 vibrationless bands. We discuss the mass-specific excitonic spectra of five H-bonded dimers that are supersonically cooled to a few K and investigated using two-color resonant two-photon ionization spectroscopy. The excitonic splittings Δcalc predicted by ab initio methods are 5-25 times larger than the experimental excitonic splittings Δexp. The purely electronic ab initio splittings need to be reduced ("quenched"), reflecting the coupling of the electronic transition to the optically active vibrations of the monomers. The so-called quenching factors Γ < 1 can be determined from experiment (Γexp) and/or calculation (Γcalc). The vibronically quenched splittings Γ·Δcalc are found to nicely reproduce the experimental exciton splittings.

Excited state dynamics in SO2. III. An ab initio quantum study of single- and multi-photon ionization.

We present an ab initio quantum study of the photoelectron spectra of sulfur dioxide, based on wavepacket propagations on manifolds of ionic, and excited/Rydberg states. We obtain excellent agreement for two different cases. First, the one photon ionization case where we can reproduce all details of the experimental spectrum and demonstrate the influence of the conical intersection between two of the ionic states. Then the multiphoton ionization regime, in which the dynamics of the wave packet on the two lowest singlet states is directly mapped in the spectra via a pump-probe scheme, as proposed in the experimental companion paper [I. Wilkinson et al., J. Chem. Phys. 140, 204301 (2014)].

Direct observation of spin-forbidden transitions through the use of suitably polarized light.

The study of excited triplet states of a molecular system is a difficult task because accessing them involves forbidden transitions from the singlet ground state. Nevertheless, absorption spectra of many molecules present, at low energies, the weak fingerprint of these triplet states. At higher energies this information is usually masked by the intense signal of the singlet states. Here we show, for the specific case of the sulphur dioxide molecule, that the combined use of polarized light and molecular alignment can enhance the triplet part of the spectrum, even making it the only absorption process.

Communication: Theoretical prediction of the importance of the (3)B2 state in the dynamics of sulfur dioxide.

Even though the sulfur dioxide molecule has been extensively studied over the last decades, its photo-excitation dynamics is still unclear, due to its complexity, combining conical intersections, and spin-orbit coupling between a manifold of states. We present a comprehensive ab initio study of the intersystem crossing of the molecule in the low energy domain, based on a wave-packet propagation on the manifold of the lowest singlet and triplet states. Furthermore, spin-orbit couplings are evaluated on a geometry-dependent grid, and diabatized along with the different conical intersections. Our results show for the first time the primordial role of the triplet (3)B2 state and furthermore predict novel interference patterns due to the different intersystem crossing channels induced by the spin-orbit couplings and the shapes of the different potential energy surfaces. These give new insight into the coupled singlet-triplet dynamics of SO2.

Are ß-H eliminations or alkene insertions feasible elementary steps in catalytic cycles involving gold(I) alkyl species or gold(I) hydrides?

The ß-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 ß-H-elimination, indicates that the pathway for the observed decomposition at 180 °C is not a ß-H-elimination. According to the calculations, the latter should not occur at temperatures below 200 °C. The microscopic reverse of the ß-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.

Ab initio quantum study of the photodynamics and absorption spectrum for the coupled 1(1)A2 and 1(1)B1 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).

(4,4')-Bipyridine in vacuo and in solvents: a quantum chemical study of a prototypical floppy molecule from a molecular transport perspective.

We report results of quantum chemical calculations for the neutral and anionic species of (4,4')-bipyridine (44BPY), a prototypical molecule with a floppy degree of freedom, placed in vacuo and in solvents. In addition to equilibrium geometries and vibrational frequencies and spectra, we present adiabatic energy curves for the vibrational modes with significant intramolecular reorganization upon charge transfer. Special attention is paid to the floppy strongly anharmonic degree of freedom of 44BPY, which is related to the most salient structural feature, namely the twist angle θ between the two pyridine rings. The relevance of the present results for molecular transport will be emphasized. We show that the solvent acts as a selective gate electrode and propose a scissor operator to account for solvent effects on molecular transport. Our result on the conductance G vs. cos(2)θ is consistent with a significant transmission in perpendicular conformation indicated by previous microscopic analysis.

Multi-state vibronic interactions in the 1,2,3-trifluorobenzene radical cation.

The multi-state and multi-mode vibronic interactions between the five lowest electronic states of the title compound are investigated theoretically by an ab initio quantum dynamical approach. The well-established linear vibronic coupling scheme is adopted, augmented by quadratic coupling terms for the totally symmetric modes. The pertinent system parameters are obtained from outer valence Greens function and equation-of-motion coupled-cluster ab initio calculations. Large-scale quantum dynamical simulations are performed employing a powerful wavepacket propagation scheme. The band shapes and line structures (as far as available) of the experimental photoelectron spectra are well reproduced. Time-dependent electronic populations reveal ultrafast internal conversion processes and allow for important insight into the fluorescence properties of the radical cation. The relation to other fluoro derivatives of the benzene radical cation is discussed.

Vibrational quenching of excitonic splittings in H-bonded molecular dimers: adiabatic description and effective mode approximation.

The quenching of the excitonic splitting in hydrogen-bonded molecular dimers has been explained recently in terms of exciton coupling theory, involving Förster's degenerate perturbation theoretical approach [P. Ottiger, S. Leutwyler, and H. Köppel, J. Chem. Phys. 136, 174308 (2012)]. Here we provide an alternative explanation based on the properties of the adiabatic potential energy surfaces. In the proper limit, the lower of these surfaces exhibits a double-minimum shape, with an asymmetric distortion that destroys the geometric equivalence of the excitonically coupled monomers. An effective mode is introduced that exactly reproduces the energy gain and amount of distortion that occurs in a multi-dimensional normal coordinate space. This allows to describe the quenched exciton splitting as the energy difference of the two (S(1) and S(2)) vibronic band origins in a one-dimensional (rather than multi-dimensional) vibronic calculation. The agreement with the earlier result (based on Förster theory) is excellent for all five relevant cases studied. A simple rationale for the quenched exciton splitting as nonadiabatic tunneling splitting on the lower double-minimum potential energy surface is given.

Efficient computation of adiabatic electronic populations in multi-mode vibronic systems: theory, implementation, and application.

The effective-mode formalism developed earlier is applied to efficiently compute adiabatic electronic populations of multi-mode vibronic systems. Two different versions of the formalism are utilized. In the first one, the effective modes are used as new vibrational basis, and the time-dependent wave function as well as populations are calculated numerically exactly. In the second variant, the hierarchy-of-modes formalism is applied as an approximation scheme which leads to accurate results when including typically 7-10 members of the hierarchy. While in the first version, the propagation of the wave packet becomes numerically tedious, the computation of the adiabatic populations is rendered possible at all. Through the hierarchy-of-modes formalism, both the propagation as well as computation of adiabatic populations are speeded up by 1-3 orders of magnitude in typical cases. The formalism is applied to study the dynamics of pyrazine-type models for varying vibronic coupling strength and a (very) large number of bath modes.