Sequential Hydrogen Tunneling in o-Tolylmethylene.

o-Tolylmethylene 1 is a metastable triplet carbene that rearranges to o-xylylene 2 even at temperatures as low as 2.7 K via [1,4] H atom tunneling. Electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) spectroscopical techniques were used to identify two conformers of 1 (anti and syn) in noble gas matrices and in frozen organic solutions. Conformer-specific kinetic measurements revealed that the rate constants for the rearrangements of the anti and syn conformers of 1 are very similar. However, the orbital alignment in the syn conformer is less favorable for the hydrogen transfer reaction than the orbital configuration in the anti conformer. Our spectroscopic and quantum chemical investigations indicate that anti 1 and syn 1 rapidly interconvert via efficient quantum tunneling forming a rotational pre-equilibrium. The subsequent second tunneling reaction, the [1,4] H migration from anti 1 to 2, is rate-limiting for the formation of 2. We here present an efficient strategy for the study of such tunneling equilibria.

Heavy-Atom Tunneling in Semibullvalenes: How Driving Force, Substituents, and Environment Influence the Tunneling Rates.

Invited for the cover of this issue are the groups of Elsa Sanchez-Garcia and Wolfram Sander at the Universität Duisburg-Essen and the Ruhr-Universität Bochum. The image depicts the ideas skillfully visualized by Markus Henkel on the shift in equilibrium induced by isotopic labelling. Read the full text of the article at 10.1002/chem.202001202.

Heavy-Atom Tunneling in Semibullvalenes: How Driving Force, Substituents, and Environment Influence the Tunneling Rates.

The Cope rearrangement of selectively deuterated isotopomers of 1,5-dimethylsemibullvalene 2 a and 3,7-dicyano-1,5-dimethylsemibullvalene 2 b were studied in cryogenic matrices. In both semibullvalenes the Cope rearrangement is governed by heavy-atom tunneling. The driving force for the rearrangements is the small difference in the zero-point vibrational energies of the isotopomers. To evaluate the effect of the driving force on the tunneling probability in 2 a and 2 b, two different pairs of isotopomers were studied for each of the semibullvalenes. The reaction rates for the rearrangement of 2 b in cryogenic matrices were found to be smaller than the ones of 2 a under similar conditions, whereas differences in the driving force do not influence the rates. Small curvature tunneling (SCT) calculations suggest that the reduced tunneling rate of 2 b compared to that of 2 a results from a change in the shape of the potential energy barrier. The tunneling probability of the semibullvalenes strongly depends on the matrix environment; however, for 2 a in a qualitatively different way than for 2 b.

DFT/MRCI assessment of the excited-state interplay in a coumarin-schiff Mg2+ fluorescent sensor.

Fluorescent sensors with selectivity and sensitivity to metal ions are an active field in supramolecular chemistry for biochemical, analytical, and environmental problems. Mg2+ is one of the most abundant divalent ions in the cell, and it plays a critical role in many biological processes. Coumarin-based sensors are widely used as desirable fluorophore and binding moieties showing a remarkable sensitivity and fluorometric enhancement for Mg2+ . In this work, density functional theory/multireference configuration interaction (DFT/MRCI) calculations were performed in order to understand the sensing behavior of the organic fluorescent sensor 7-hydroxy-4-methyl-8-((2-(pyridin-2-yl)hydrazono)methyl)-2H-chromen-2-one (PyHC) in ethanol to solvated Mg2+ ions. The computed optical properties reproduce well-reported experimental data. Our results suggest that after photoexcitation of the free PyHC, a photo-induced electron transfer (PET) mechanism may compete with the fluorescence decay to the ground state. In contrast, this PET channel is no longer available in the complex with Mg2+ making the emissive decay more efficient. © 2019 Wiley Periodicals, Inc.

Evolution of the Optical Gap in the Acene Series: Undecacene.

Undecacene, the largest member of the acene family, was photogenerated in a polymer matrix under cryogenic conditions from a precursor with two α-diketone bridges. The electronic absorption of undecacene extends into the NIR region, but the spectrum is dominated by two strong absorptions in the UV/Vis range. The HOMO-LUMO transition is continuously shifted to lower energies as the number of rings of the acene increases (E vs. 1/N, N=number of rings), which is in line with the strong electron correlation calculated by DFT/MRCI.

Quantum-Chemical Studies on Excitation Energy Transfer Processes in BODIPY-Based Donor-Acceptor Systems.

BODIPY-based excitation energy transfer (EET) cassettes are experimentally extensively studied and serve as excellent model systems for the investigation of photophysical processes, since they occur in any photosynthetic system and in organic photovoltaics. In the present work, the EET rates in five BODIPY-based EET cassettes in which anthracene serves as the donor have been determined, employing the monomer transition density approach (MTD) and the ideal dipole approximation (IDA). To this end, a new computer program has been devised that calculates the direct and exchange contributions to the excitonic coupling (EC) matrix element from transition density matrices generated by a combined density functional and multireference configuration interaction (DFT/MRCI) calculation for the monomers. EET rates have been calculated according to Fermi's Golden Rule from the EC and the spectral overlap, which was obtained from the calculated vibrationally resolved emission and absorption spectra of donor and acceptor, respectively. We find that the direct contribution to the EC matrix element is dominant in the studied EET cassettes. Furthermore, we show that the contribution of the molecular linker to the EET rate cannot be neglected. In our best fragment model, the molecular linker is attached to the donor moiety. For cassettes in which the transition dipole moments of donor and acceptor are oriented in parallel manner, our results confirm the experimental findings reported by Kim et al. [J. Phys. Chem. A 2006, 110, 20-27]. In cassettes with a perpendicular orientation of the donor and acceptor transition dipole moments, dynamic effects turn out to be important.

Thermal and solvent effects on the triplet formation in cinnoline.

Cinnoline (1,2-diazanaphthalene) is of particular interest among the diazanaphthalenes. Its triplet quantum yield upon photoexcitation depends strongly on the temperature and the solvent environment. At the beginning of this study, the properties of the lowest triplet electronic state were not understood either. To elucidate the photophysics of cinnoline, we implemented algorithms based on the time-dependent approach for calculating intersystem crossing rates and one-photon spectra of thermally equilibrated vibronic levels. Our quantum chemical investigations reveal that the triplet formation in hydrocarbon solutions at low temperatures is an El-Sayed forbidden process. At higher temperatures and in hydroxylic solutions an additional El-Sayed allowed channel opens up, increasing the intersystem crossing rate substantially. Furthermore, we have solved the old puzzle concerning the character of the lowest triplet state of cinnoline. In the gas phase the electronic structure has mainly nπ* character with additional contributions from ππ* configurations since the nuclear arrangement in the pyridazine ring is not planar. In hydroxylic solvents, the electronic structure of the T1 state is altered. The simulation of the triplet emission shows that the experimentally observed phosphorescence of cinnoline in ethanol most certainly stems from the (3)(ππ*) emission.

Ultrafast deactivation mechanism of the excited singlet in the light-induced spin crossover of [Fe(2,2'-bipyridine)3]2+.

The mechanism of the light-induced spin crossover of the [Fe(bpy)3](2+) complex (bpy=2,2'-bipyridine) has been studied by combining accurate electronic-structure calculations and time-dependent approaches to calculate intersystem-crossing rates. We investigate how the initially excited metal-to-ligand charge transfer (MLCT) singlet state deactivates to the final metastable high-spin state. Although ultrafast X-ray free-electron spectroscopy has established that the total timescale of this process is on the order of a few tenths of a picosecond, the details of the mechanisms still remain unclear. We determine all the intermediate electronic states along the pathway from low spin to high spin and give estimates for the deactivation times of the different stages. The calculations result in a total deactivation time on the same order of magnitude as the experimentally determined rate and indicate that the complex can reach the final high-spin state by means of different deactivation channels. The optically populated excited singlet state rapidly decays to a triplet state with an Fe d(6)(t(2g)(5)e(g)(1)) configuration either directly or by means of a triplet MLCT state. This triplet ligand-field state could in principle decay directly to the final quintet state, but a much faster channel is provided by internal conversion to a lower-lying triplet state and subsequent intersystem crossing to the high-spin state. The deactivation rate to the low-spin ground state is much smaller, which is in line with the large quantum yield reported for the process.

On-the-fly semiclassical study of internal conversion rates of formaldehyde.

Internal conversion is an inherently quantum mechanical process. To date, "ab initio" computation of internal conversion rates was limited to harmonic based approximations. These are questionable since the typical transition to the ground electronic state occurs at energies which are far from the harmonic limit. It is thus of interest to study the applicability of the Semiclassical Initial Value Representation (SCIVR) approach which is in principle amenable to "on the fly" studies even with "many" degrees of freedom. In this work we apply the Herman-Kluk-SCIVR methodology to compute the internal conversion rates for formaldehyde for a variety of initial vibronic states. The SCIVR computation gives reasonable agreement with experiment, while the harmonic approximation typically gives rates that are too high.

Acetylation makes the difference: a joint experimental and theoretical study on low-lying electronically excited states of 9H-adenine and 9-acetyladenine.

Vibronic spectra of 9H-adenine, 9-acetyladenine and several alkyladenines have been recorded by resonant two-photon ionization spectroscopy of the laser-desorbed molecules, entrained in a molecular beam. While adenine and the alkyladenines exhibit similar electronic spectra, 9-acetyladenine behaves considerably different. Theoretical absorption spectra of 9H-adenine and 9-acetyladenine were calculated using the combined density functional theory/multi-reference configuration interaction approach and using second order coupled cluster theory, in order to explain striking differences in the experimental spectra. The major differences between the 9H-adenine and the 9-acetyladenine absorption spectra can be traced back to the different configurations, which contribute to the excitations, both of the lowest ππ* and the nπ* states. While the excitations in 9H-adenine are localized in the chromophore, they show considerable charge transfer character from the chromophore to the acetyl group in the case of 9-acetyladenine.

Ground and electronically excited singlet-state structures of 5-fluoroindole deduced from rotationally resolved electronic spectroscopy and ab initio theory.

The structure and electronic properties of the electronic ground state and the lowest excited singlet state (S(1)) of 5-fluoroindole (5FI) were determined by using rotationally resolved spectroscopy of the vibration-less electronic origin of 5FI. From the parameters of the axis reorientation Hamiltonian, the absolute orientation of the transition dipole moment in the molecular frame was determined and the character of the excited state was identified as L(b).

The structure of 5-cyanoindole in the ground and the lowest electronically excited singlet states, deduced from rotationally resolved electronic spectroscopy and ab initio theory.

The structure and electronic properties of the electronic ground and the lowest excited singlet states of 5-cyanoindole (5CI) were determined using rotationally resolved spectroscopy of the vibrationless electronic origin of 5CI. In contrast to most other indole derivatives, the lowest excited state of 5CI is determined to be of L(a) character. The conventional approximate coupled cluster singles and doubles model (CC2) fails to describe the geometry of the excited state correctly. Nevertheless, scaling the spin components of equal and opposite spins within the CC2 model as proposed by Hellweg et al. (Phys. Chem. Chem. Phys., 2008, 10, 1159) resulted in very good geometry parameters for the excited state.

Photophysical and quantum chemical study on a J-aggregate forming perylene bisimide monomer.

Perylene bisimides (PBIs) are excellent dyes and versatile building blocks for supramolecular structures. Only recently have PBIs been shown to depict absorption characteristics of J-aggregates. We apply electronic structure calculations and femtosecond pump-probe spectroscopy to the monomeric, bay-substituted building-block of a PBI aggregate in dichloromethane to investigate its electronically excited states in order to provide the ingredients for the description of excitons in the aggregates and their annihilation processes. The PBI S(1)←S(0) absorption spectrum and the S(1)→S(0) emission spectrum have been assigned based on time-dependent Density Functional Theory calculations for the geometry-optimized electronic ground state and excited state structures in the gas phase. The monomeric absorption spectrum contains a strong transition at 580 nm and a broad shoulder between 575-500 nm, both features are attributed to a vibrational progression with an effective vibrational mode of 1415 cm(-1) whose major contributing vibrational normal modes are breathing modes of the perylene body. The effective vibrational mode of the emission spectrum is characterized by a frequency of 1369 cm(-1), whose major contributing vibrational normal modes are characterized by perylene and phenol (bay-substituent) CH bendings. The S(n)←S(1) excited state absorption spectrum is assigned based on Multi-Reference Configuration Interaction methodology. Here, we identify three transitions which give rise to two broad experimental features, one being located between 500 and 600 nm and the other one ranging from 650 to 750 nm.

Time-dependent approaches for the calculation of intersystem crossing rates.

We present three formulas for calculating intersystem crossing rates in the Condon approximation to the golden rule by means of a time-dependent approach: an expression using the full time correlation function which is exact for harmonic oscillators, a second-order cumulant expansion, and a short-time approximation of this expression. While the exact expression and the cumulant expansion require numerical integration of the time correlation function, the integration of the short-time expansion can be performed analytically. To ensure convergence in the presence of large oscillations of the correlation function, we use a Gaussian damping function. The strengths and weaknesses of these approaches as well as the dependence of the results on the choice of the technical parameters of the time integration are assessed on four test examples, i.e., the nonradiative S(1) ⇝ T(1) transitions in thymine, phenalenone, flavone, and porphyrin. The obtained rate constants are compared with previous results of a time-independent approach. Very good agreement between the literature values and the integrals over the full time correlation functions are observed. Furthermore, the comparison suggests that the cumulant expansion approximates the exact expression very well while allowing the interval of the time integration to be significantly shorter. In cases with sufficiently high vibrational density of states also the short-time approximation yields rates in good agreement with the results of the exact formula. A great advantage of the time-dependent approach over the time-independent approach is its excellent computational efficiency making it the method of choice in cases of large energy gaps, large numbers of normal modes, and high densities of final vibrational states.

Renormalization of the frozen Gaussian approximation to the quantum propagator.

The frozen Gaussian approximation to the quantum propagator may be a viable method for obtaining "on the fly" quantum dynamical information on systems with many degrees of freedom. However, it has two severe limitations, it rapidly loses normalization and one needs to know the Gaussian averaged potential, hence it is not a purely local theory in the force field. These limitations are in principle remedied by using the Herman-Kluk (HK) form for the semiclassical propagator. The HK propagator approximately conserves unitarity for relatively long times and depends only locally on the bare potential and its second derivatives. However, the HK propagator involves a much more expensive computation due to the need for evaluating the monodromy matrix elements. In this paper, we (a) derive a new formula for the normalization integral based on a prefactor free HK propagator which is amenable to "on the fly" computations; (b) show that a frozen Gaussian version of the normalization integral is not readily computable "on the fly"; (c) provide a new insight into how the HK prefactor leads to approximate unitarity; and (d) how one may construct a prefactor free approximation which combines the advantages of the frozen Gaussian and the HK propagators. The theoretical developments are backed by numerical examples on a Morse oscillator and a quartic double well potential.

Vibronic coupling in indole: I. Theoretical description of the 1La-1Lb interaction and the electronic spectrum.

The properties of the three lowest singlet electronic states (ground, (1)L(b), and (1)L(a) states) of indole (C(8)H(7)N) have been calculated with second-order approximate coupled-cluster theory (CC2) within the resolution-of-the-identity approximation. Refined electronic energies at the CC2 optimized structures and transition dipole moments were calculated using a density functional theory multi-reference configuration-interaction (DFT/MRCI) approach. Structures, energies, and dipole moments are reported for all three states and compared to experimental values. From the optimized structures and calculated transition dipole moments, we predict that pure (1)L(b) bands will have positive signs for both the axis reorientation angle theta(T) and the angle theta of the transition dipole moment with respect to the inertial a axis. For (1)L(a) bands the signs of both angles will be reversed. Vibronically coupled bands can exhibit opposite signs for theta and theta(T). The absorption and emission spectra of indole are calculated based on the Franck-Condon Herzberg-Teller approximation using numerical transition dipole moment derivatives at the DFT/MRCI level of theory. Implications for the experimentally observed vibronic spectra are discussed. Predictions are made for rotationally resolved spectra of various rovibronic bands. A conical intersection, connecting the (1)L(b) and (1)L(a) states, which can be accessed to varying extents via different Herzberg-Teller active modes is found approximately 2000 cm(-1) above the (1)L(b) minimum.

Vibronic coupling in indole: II. Investigation of the 1La-1Lb interaction using rotationally resolved electronic spectroscopy.

High-resolution electronic spectra of indole (C(8)H(7)N) and their detailed analysis are reported. Thirteen low-lying vibronic bands--from the electronic origin transition at 35,231.4 cm(-1) up to 1000 cm(-1) above--are recorded with rotational resolution. Besides inertial parameters and inertial defects these spectra yield detailed information, for each individual band, on the transition-dipole-moment orientations in the molecular inertial frame as well as on the reorientation of that inertial frame upon electronic excitation. The natural lifetimes of the individual vibronic states have also been determined. Strongly varying orientations of the transition-dipole-moments, unexpected positive inertial defects, and decreasing lifetimes, which are only partly related to increased excitation energy, are observed. These results are clear indications of the interaction of the two lowest electronically excited singlet states ((1)L(b) and (1)L(a)). Our experimental findings are strongly supported by, and in excellent agreement with, the theoretical description of the interaction of the two electronic states described in the preceding paper. These results provide clear evidence for strong vibronic coupling of the two electronic states (1)L(b) and (1)L(a) and for the energetic location of the (1)L(a)-state more than 1000 cm(-1) above the (1)L(b) vibrationless state.

Calculating electron paramagnetic resonance g-matrices for triplet state molecules from multireference spin-orbit configuration interaction wave functions.

We present a way to calculate electron paramagnetic resonance (EPR) g-matrices from variationally optimized spin-orbit coupled wave functions. Our method constructs a triangular g-matrix from the matrix representation of the total electron magnetic moment in the basis of the spin-orbit coupled wave functions by means of a projection technique. Principal g-values are obtained in the standard fashion by forming from the triangular matrix g the tensor G=gg(t) and diagonalizing it. In principle, the scheme allows to calculate the spin-orbit orbital Zeeman cross term which usually gives the dominating contribution to the EPR g-shifts for any multiplicity. We have implemented this approach into a multireference spin-orbit configuration interaction (MRSOCI) program [M. Kleinschmidt et al., J. Chem. Phys. 124, 124101 (2006)]. Test applications are carried out for various triplet state sytems. The g-shifts of several of main group diatomics with X (3)Sigma(g)(-) ground state are investigated at the level of ab initio MRSOCI. We obtain perpendicular g-shifts which underestimate experimental Delta g(perpendicular) values from literature by approximately 13% on the average. For a set of organic triplet state molecules we employ the combined density functional theory/multireference configuration interaction (DFT/MRCI) technique [S. Grimme and M. Waletzke, J. Chem. Phys. 111, 5645 (1999)] to reduce the computational costs of the spin-free correlation problem. This approach yields principal g-values that match experiment well in many cases. Due to the small absolute g-shifts, a rigorous comparison will require the inclusion of first-order contributions such as the relativistic mass correction and gauge correction terms which have not been included here. For the triplet state dication trans-(CNSSS)(2)(2+) the principal g-shifts Delta g(a)=-0.3 ppt, Delta g(b)=17.5 ppt, and Delta g(c)=26.6 ppt are significantly larger and compare rather well to the experimental values Delta g(1)=-0.1+/-0.2 ppt, Delta g(2)=14.8+/-0.2 ppt, and Delta g(3)=24.8+/-0.1 ppt [A. Berces et al., Magn. Reson. Chem. 37, 353 (1999)]. In comparison to conventional truncated sum-over state techniques based on Rayleigh-Schrodinger perturbation theory, our new variational approach shows, in practice, robust and advantageous convergence characteristics with respect to the size of the many-particle basis set. We demonstrate that the DFT/MRSOCI technology is a very feasible means to compute reliable g-shifts for large organic triplet systems at low computational cost.

Semiclassical on-the-fly computation of the S(0)-->S(1) absorption spectrum of formaldehyde.

The anharmonic S(0)-->S(1) vibronic absorption spectrum of the formaldehyde molecule is computed on the fly using semiclassical dynamics. This first example of an on-the-fly semiclassical computation of a vibronic spectrum was achieved using a unit prefactor modified frozen Gaussian semiclassical propagator for the excited state. A sample of 6000 trajectories sufficed for obtaining a converged spectrum, which is in reasonable agreement with experiment. Similar agreement is not obtained when using a harmonic approximation for the spectrum, demonstrating the need for a full anharmonic computation. This first example provides a resolution of approximately 100 cm(-1). Potential ways of improving the methodology and obtaining higher resolution and accuracy are discussed.

High-resolution and dispersed fluorescence examination of vibronic bands of tryptamine: spectroscopic signatures for L(a)/L(b) mixing near a conical intersection.

The vibronic spectrum of tryptamine has been studied in a molecular beam up to an energy of 930 cm(-1) above the S(0)-S(1) electronic origin. Rotationally resolved electronic spectra reveal a rotation of the transition dipole moment direction from (1)L(b) to (1)L(a) beginning about 400 cm(-1) above the (1)L(b) origin. In this region, vibronic bands which appear as single bands at low resolution contain rotational structure from more than one vibronic transition. The number of these transitions closely tracks the total vibrational state density in the (1)L(b) electronic state as a function of internal energy. Dispersed fluorescence spectra show distinct spectroscopic signatures attributable to the (1)L(b) and (1)L(a) character of the mixed excited-state wave functions. The data set is used to extrapolate to a (1)L(a) origin about 400 cm(-1) above the (1)L(b) origin. DFT-MRCI calculations locate a conical intersection between these two states at about 900 cm(-1) above the L(a) origin, whose structure is located along a tuning coordinate which is close to a linear interpolation between the two excited-state geometries. Along the branching coordinate, there is no barrier from (1)L(a) to (1)L(b). A two-tier model for the vibronic coupling is proposed.