Mode-Selective Promotion and Isotope Effects of Concerted Double-Hydrogen Tunneling in Porphycene Embedded in Superfluid Helium Nanodroplets

Nuclear Quantum Effects in Proton or Hydrogen Transfer

Proton or hydrogen transfers, basic chemical reactions, proceed either by thermally activated barrier crossing or via tunneling. Studies of molecules undergoing single or double proton or hydrogen transfer in the ground or excited electronic state reveal that tunneling can dominate under conditions usually considered to favor the thermal process. Moreover, the tunneling probability strongly varies for excitation of certain vibrational modes, which changes the effective barrier and/or proton transfer distance. When the reaction is fast compared to vibrational relaxation, the mode selectivity can still be maintained for molecules in solutions at 293 K. These observations point to dangers of relating the calculated minimum energy paths and the associated barriers to the experimentally obtained activation energies. The multidimensional character of the reaction coordinate is obvious; it can dramatically change for slowly and rapidly relaxing environments. We postulate that the hydrogen bond definition should be extended by specifically including the role of molecular vibrations.

Coupling between tautomerism and radiationless deactivation in porphycenes

Quantum yields of fluorescence of porphycenes – porphyrin isomers – can vary by orders of magnitude, even for very similar derivatives, such as meso-dimethyl- vs. meso-tetramethylporphycene. In weakly emitting porphycenes the fluorescence intensity strongly depends on viscosity and can be recovered by placing a molecule in a rigid environment. We postulate that the efficient nonradiative deactivation is due to the quantum effect, delocalization of the inner protons. The delocalization, which increases with the strength of intramolecular hydrogen bonds may induce structural changes that lead to distortion from planarity and, as a result, efficient S0 ← S1 internal conversion. The effect seems to be general, as indicated by good correlation between the quantum yield of fluorescence and the distance between H-bonded nitrogen atoms, the latter being a reliable measure of hydrogen bonding strength. Based on the available photophysical and X-ray data, such correlation was found so far for over 20 differently substituted porphycenes.

Spectroscopic investigation of photophysics and tautomerism of amino- and nitroporphycenes

Parent, unsubstituted porphycene and its two derivatives: 2,7,12,17-tetra-n-propylporphycene and 2,7,12,17-tetra-t-butylporphycene were substituted at the meso position with amino and nitro groups. These two families of porphycenes were characterized in detail with respect to their spectral, photophysical, and tautomeric properties. Two trans tautomers of similar energies coexist in the ground electronic state, but only one form dominates in the lowest excited singlet state. Absorption, magnetic circular dichroism (MCD), and emission anisotropy combined with quantum-chemical calculations led to the assignment of S₁ and S₂ transitions in both tautomers. Compared with the parent porphycene, the S₁-S₂ energy gap significantly increases; for one tautomeric form, the effect is twice as large as for the other. Both amino- and nitroporphycenes emit single fluorescence; previously reported dual emission of aminoporphycenes is attributed to a degradation product. Introduction of bulky t-butyl groups leads to a huge decrease in fluorescence intensity; this effect, arising from the interaction of the meso substituent with the adjacent t-butyl moiety, is particularly strong in the nitro derivative.

Determination of concerted or stepwise mechanism of hydrogen tunneling from isotope effects: Departure between experiment and theory

Isotope substitution is an important experimental technique that offers deep insight into reaction mechanisms, as the measured kinetic isotope effects (KIEs) can be directly compared with theory. For multiple proton transfer processes, there are two types of mechanisms: stepwise transfer and concerted transfer. The Bell-Limbach model provides a simple theory to determine whether the proton transfer mechanism is stepwise or concerted from KIEs. Recent STM experiments have studied the proton switching process in water tetramers on NaCl(001). Theoretical studies predict that this process occurs via a concerted mechanism, however, the experimental KIEs resemble the Bell-Limbach model for stepwise tunneling, raising question on the underlying mechanism or the validity of the model. We study this system using ab initio instanton theory, and in addition to thermal rates, we also considered microcanonical rates, as well as tunneling splittings. Instanton theory predicts a concerted mechanism, and the KIEs for tunneling rates (both thermal and microcanonical) upon deuteration are consistent with the Bell-Limbach model for concerted tunneling, but could not explain the experiments. For tunneling splittings, partial and full deuteration changes the size of it in a similar fashion to how it changes the rates. We further examined the Bell-Limbach model in another system, porphycene, which has both stepwise and concerted tunneling pathways. The KIEs predicted by instanton theory are again consistent with the Bell-Limbach model. This study highlights differences between KIEs in stepwise and concerted tunneling, and the discrepancy between theory and recent STM experiments. New theory/experiments are desired to settle this problem.

Double Proton Transfer Across a Table: The Formic Acid Dimer-Fluorobenzene Complex

Proton transfer via tunneling is a fundamental quantum‐mechanical phenomenon. We report rotational spectroscopy measurements of this process in the complex of the formic acid dimer with fluorobenzene. The assignment of the spectrum indicates that this complex exists in the form of a π–π stacked structure. Each rotational transition of the parent isotopologue exhibits splitting. Isotopic substitution experiments show that the spectral splitting results from double‐proton transfer tunneling in the formic acid dimer. Presence of fluorobenzene as a neighboring molecule does not quench the double proton transfer in the formic acid dimer but decreases its tunneling splitting from 341(3) MHz to 267.608(1) MHz. Calculations suggest that the presence of the weakly bounded fluorobenzene does not influence the activation energy of the proton transfer. The fluorobenzene is reoriented with respect to the formic acid dimer during the course of the reaction, slowing down the proton transfer motion.

2 + 2 Can Make Nearly a Thousand! Comparison of Di- and Tetra-Meso-Alkyl-Substituted Porphycenes

Two porphycenes, substituted at the meso positions with two and four methyl groups, respectively, reveal similar absorption spectra, but their photophysical properties are completely different. 9,20-dimethylporphycene emits fluorescence with about 20% quantum yield, independent of the solvent. In contrast, fluorescence of 9,10,19,20-tetramethylporphycene is extremely weak in nonviscous solvents, but it can be recovered by placing the chromophore in a rigid environment. We propose a model that explains these differences, based on calculations and structural analogies with other extremely weakly emitting derivatives, dibenzo[cde,mno]porphycenes. The efficient S₁ deactivation involves delocalization of two inner cavity protons coupled with proton translocation toward a high-energy cis tautomer. The latter process leads to distortion from planarity. The probability of deactivation increases with the strength of the intramolecular NH···N hydrogen bonds. The model also explains the observation of biexponential fluorescence decay in weakly emitting porphycenes. It can be extended to other derivatives, in particular, the asymmetrically substituted ones. We also point to the possibility of using specific porphycenes as viscosity sensors, in particular, when working in single molecule regime.

Influence of local microenvironment on the double hydrogen transfer in porphycene

We performed time-resolved transient absorption and fluorescence anisotropy measurements in order to study tautomerization of porphycene in rigid polymer matrices at cryogenic temperatures. Studies were carried out in poly(methyl methacrylate) (PMMA), poly(vinyl butyral) (PVB), and poly(vinyl alcohol) (PVA). The results prove that in all studied media hydrogen tunnelling plays a significant role in the double hydrogen transfer which becomes very sensitive to properties of the environment below approx. 150 K. We also demonstrate that there exist two populations of porphycene molecules in rigid media: "hydrogen-transferring" molecules, in which tautomerization occurs on time scales below 1 ns and "frozen" molecules in which double hydrogen transfer is too slow to be monitored with nanosecond techniques. The number of "frozen" molecules increases when the sample is cooled. We explain this effect by interactions of guest molecules with a rigid host matrix which disturbs symmetry of porphycene and hinders tunnelling. Temperature dependence of the number of hydrogen-transferring molecules suggests that the factor which restores the symmetry of the double-minimum potential well in porphycene are intermolecular vibrations localized in separated regions of the amorphous polymer.

Elucidating the Nuclear Quantum Dynamics of Intramolecular Double Hydrogen Transfer in Porphycene

We address the double hydrogen transfer (DHT) dynamics of the porphycene molecule, a complex paradigmatic system in which the making and breaking of H-bonds in a highly anharmonic potential energy surface require a quantum mechanical treatment not only of the electrons but also of the nuclei. We combine density functional theory calculations, employing hybrid functionals and van der Waals corrections, with recently proposed and optimized path-integral ring-polymer methods for the approximation of quantum vibrational spectra and reaction rates. Our full-dimensional ring-polymer instanton simulations show that below 100 K the concerted DHT tunneling pathway dominates but between 100 and 300 K there is a competition between concerted and stepwise pathways when nuclear quantum effects are included. We obtain ground-state reaction rates of 2.19 × 10¹¹ s^–1 at 150 K and 0.63 × 10¹¹ s^–1 at 100 K, in good agreement with experiment. We also reproduce the puzzling N–H stretching band of porphycene with very good accuracy from thermostated ring-polymer molecular dynamics simulations. The position and line shape of this peak, centered at around 2600 cm^–1 and spanning 750 cm^–1, stem from a combination of very strong H-bonds, the coupling to low-frequency modes, and the access to cis-like isomeric conformations, which cannot be appropriately captured with classical-nuclei dynamics. These results verify the appropriateness of our general theoretical approach and provide a framework for a deeper physical understanding of hydrogen transfer dynamics in complex systems.

Supersonic jet spectroscopy of parent hemiporphycene: Structural assignment and vibrational analysis for S0 and S1 electronic states

Hemiporphycene (HPc), a constitutional isomer of porphyrin, is studied under supersonic expansion conditions by means of laser-induced fluorescence, visible-visible hole-burning experiments, single vibronic level fluorescence techniques, and quantum chemical calculations. Only one trans form of jet-cooled HPc is observed, in contrast to solution studies that evidence a mixture of two trans tautomeric forms separated in energy by ∼1 kcal/mol. Reliable structural assignment is provided by simulating absorption and emission patterns at the density functional theory and time-dependent density functional theory levels of theory. The vibronic spectra are nicely reproduced for both electronic ground and lowest excited singlet states for the most stable trans form. In contrast to another porphyrin isomer, porphycene (Pc), no tunneling or photo-induced hydrogen transfer is detected. The lower symmetry of HPc compared with Pc and the concomitant non-equivalent positions of the inner-cavity nitrogen atoms result in a non-symmetric double minimum potential for tautomerization, larger energy barrier, and a longer tunneling distance, with the average intramolecular hydrogen bond length larger in HPc than in Pc. HPc readily forms hydrates that show red-shifted absorption relative to the bare molecule.

Unusual effects in single molecule tautomerization: hemiporphycene

Temporal evolution of the fluorescence spectra of individual hemiporphycene molecules reveals unusual double hydrogen transfer reaction dynamics.

Non-typical fluorescence studies of excited and ground state proton and hydrogen transfer

Fluorescence studies of tautomerization have been carried out for various systems that exhibit single and double proton or hydrogen translocation in various environments, such as liquid and solid condensed phases, ultracold supersonic jets, and finally, polymer matrices with single emitters. We focus on less explored areas of application of fluorescence for tautomerization studies, using porphycene, a porphyrin isomer, as an example. Fluorescence anisotropy techniques allow investigations of self-exchange reactions, where the reactant and product are formally identical. Excitation with polarized light makes it possible to monitor tautomerization in single molecules and to detect their three-dimensional orientation. Analysis of fluorescence from single vibronic levels of jet-isolated porphycene not only demonstrates coherent tunneling of two internal protons, but also indicates that the process is vibrational mode-specific. Next, we present bifunctional proton donor-acceptor systems, molecules that are able, depending on the environment, to undergo excited state single intramolecular or double intermolecular proton transfer. For molecules that have donor and acceptor groups located in separate moieties linked by a single bond, excited state tautomerization can be coupled to mutual twisting of the two subunits.

Spectroscopic and microscopic investigations of tautomerization in porphycenes: condensed phases, supersonic jets, and single molecule studies

Tautomerization of porphycene, coherent in supersonic jets and a rate process in solutions, can be controlled for single molecules on surfaces.

Non-classical effects in proton or hydrogen transfer

Results of thorough investigations of tautomerism in the ground and excited electronic states performed for various organic molecules under different regimes: condensed phases, isolated and single molecules, with a special emphasis on porphycene, a porphyrin isomer, demonstrate that, in order to precisely describe the proton/hydrogen transfer path, one has to explicitly consider tunneling. Tautomerization is a multidimensional process, controlled by excitation of specific vibrational modes. Vibrational excitation can both enhance or hinder the reaction. The role of specific vibrational modes can now be assessed, even at the level of single molecules.

Spectroscopy and Tautomerization Studies of Porphycenes

Tautomerization in porphycenes, constitutional isomers of porphyrins, is strongly entangled with spectral and photophysical parameters. The intramolecular double hydrogen transfer occurring in the ground and electronically excited states leads to uncommon spectroscopic characteristics, such as depolarized emission, viscosity-dependent radiationless depopulation, and vibrational-mode-specific tunneling splittings. This review starts with documentation of the electronic spectra of porphycenes: Absorption and magnetic circular dichroism are discussed, together with their analysis based on the perimeter model. Next, photophysical characteristics are presented, setting the stage for the final part, which discusses the developments in research on tautomerism. Porphycenes have been studied in different experimental regimes: molecules in condensed phases, isolated in supersonic jets and helium nanodroplets, and, recently also on the level of single molecules investigated by optical and scanning probe microscopies. Because of the rich and detailed information obtained from these diverse investigations, porphycenes emerge as very good models for studying the complex, multidimensional phenomena involved in the process of intramolecular double hydrogen transfer.

Single molecule Raman spectra of porphycene isotopologues

Single molecule surface-enhanced resonance Raman scattering (SERRS) spectra have been obtained for the parent porphycene (Pc-d0) and its deuterated isotopologue (Pc-d12), located on gold and silver nanoparticles. Equal populations of "hot spots" by the two isotopologues are observed for 1 : 1 mixtures in a higher concentration range of the single molecule regime (5 × 10(-9) M). For decreasing concentrations, hot spots are preferentially populated by undeuterated molecules. This is interpreted as an indication of a lower surface diffusion coefficient of Pc-d12. The photostability of single Pc molecules placed on nanoparticles is strongly increased in comparison with polymer environments. Trans tautomeric species dominate the spectra, but the analysis of time traces reveals transient intermediates, possibly due to rare cis tautomeric forms.

Direct Observation of Photoinduced Tautomerization in Single Molecules at a Metal Surface

Molecular switches are of fundamental importance in nature, and light is an important stimulus to selectively drive the switching process. However, the local dynamics of a conformational change in these molecules remain far from being completely understood at the single-molecule level. Here, we report the direct observation of photoinduced tautomerization in single porphycene molecules on a Cu(111) surface by using a combination of low-temperature scanning tunneling microscopy and laser excitation in the near-infrared to ultraviolet regime. It is found that the thermodynamically stable trans configuration of porphycene can be converted to the metastable cis configuration in a unidirectional fashion by photoirradiation. The wavelength dependence of the tautomerization cross section exhibits a steep increase around 2 eV and demonstrates that excitation of the Cu d-band electrons and the resulting hot carriers play a dominant role in the photochemical process. Additionally, a pronounced isotope effect in the cross section (∼100) is observed when the transferred hydrogen atoms are substituted with deuterium, indicating a significant contribution of zero-point energy in the reaction. Combined with the study of inelastic tunneling electron-induced tautomerization with the STM, we propose that tautomerization occurs via excitation of molecular vibrations after photoexcitation. Interestingly, the observed cross section of ∼10(-19) cm(2) in the visible-ultraviolet region is much higher than that of previously studied molecular switches on a metal surface, for example, azobenzene derivatives (10(-23)-10(-22) cm(2)). Furthermore, we examined a local environmental impact on the photoinduced tautomerization by varying molecular density on the surface and find substantial changes in the cross section and quenching of the process due to the intermolecular interaction at high density.

Evidence for Dominant Role of Tunneling in Condensed Phases and at High Temperatures: Double Hydrogen Transfer in Porphycenes

Investigation of the double hydrogen transfer in porphycene, its 2,7,12,17-tetra-tert-butyl derivative, and their N-deuterated isotopologues revealed the dominant role of tunneling, even at room temperature in condensed phase. Ultrafast optical spectroscopy with polarized light employed in a wide range of temperatures allowed the identification and evaluation of contributions of two tunneling modes: vibrational ground-state tunneling, occurring from the zero vibrational level, and vibrationally activated, via a large amplitude, low-frequency mode. Good correspondence was found between the rates of incoherent tunneling occurring in condensed phase and the values estimated on the basis of tunneling splittings observed in molecules isolated in supersonic jets or helium nanodroplets. The results provide solid experimental insight into widely proposed quantum facets of ubiquitous hydrogen-transfer phenomena.

Multidimensional Hamiltonian for tunneling with position-dependent mass

A multidimensional Hamiltonian for tunneling is formulated, based on the mode with imaginary frequency of the transition state as a reaction coordinate. To prepare it for diagonalization, it is transformed into a lower-dimension Hamiltonian by incorporating modes that move faster than the tunneling into a coordinate-dependent kinetic energy operator, for which a Hermitian form is chosen and tested for stability of the eigenvalues. After transformation to a three-dimensional form, which includes two normal modes strongly coupled to the tunneling mode, this Hamiltonian is diagonalized in terms of a basis set of harmonic oscillator functions centered at the transition state. This involves a sparse matrix which is easily partially diagonalized to yield tunneling splittings for the zero-point level and the two fundamental levels of the coupled modes. The method is tested on the well-known benchmark molecule malonaldehyde and a deuterium isotopomer, for which these splittings have been measured. Satisfactory agreement with experiment results is obtained.

Calculations of Mode-Specific Tunneling of Double-Hydrogen Transfer in Porphycene Agree with and Illuminate Experiment

We report a theoretical study of mode-specific tunneling splittings in double-hydrogen transfer in trans-porphycene. We use a novel, mode-specific "Qim path method", in which the reaction coordinate is the imaginary-frequency normal mode of the saddle point separating the equivalent minima. The model considers all 108 normal modes and uses no adjustable parameters. The method gives the ground vibrational-state tunneling splitting, as well the increase in the splitting upon excitation of certain modes, in good agreement with experiment. Interpretation of these results is also transparent with this method. In addition, predictions are made for mode excitations not investigated experimentally. Results for d1 and d2 isotopolgues are also in agreement with experiment.

Thermally and vibrationally induced tautomerization of single porphycene molecules on a Cu(110) surface

We report the direct observation of intramolecular hydrogen atom transfer reactions (tautomerization) within a single porphycene molecule on a Cu(110) surface by scanning tunneling microscopy. It is found that the tautomerization can be induced via inelastic electron tunneling at 5 K. By measuring the bias-dependent tautomerization rate of isotope-substituted molecules, we can assign the scanning tunneling microscopy-induced tautomerization to the excitation of specific molecular vibrations. Furthermore, these vibrations appear as characteristic features in the dI/dV spectra measured over individual molecules. The vibrational modes that are associated with the tautomerization are identified by density functional theory calculations. At higher temperatures above ∼75  K, tautomerization is induced thermally and an activation barrier of about 168 meV is determined from an Arrhenius plot.

Double Hydrogen Transfer in Low Symmetry Porphycenes

The rate constants of intramolecular double hydrogen transfer have been determined for of tert-butyl-substituted porphycenes: 2-tert-butyl-, 2,7-di-tert-butyl-, 2,7,12-tri-tert-butyl-, and 2,7,12,17-tetra-tert-butylporphycene using femtosecond pump-probe polarization spectroscopy. The rates increase monotonically with the number of substituents. As is the case for other porphycenes studied so far, the tautomerization becomes slower after excitation to the lowest excited singlet state. The potential for the trans-trans self-exchange reaction is symmetrical in di- and tetra-tert-butyl substituted derivatives, but not for the singly and triply substituted ones. Our studies enabled determination of the relative populations of nonequivalent tautomers and thus of the equilibrium constants in S0 and S1 states, as well as estimation of ground and excited state activation energies for the tautomerization process.

The long and winding road to new porphycenes

We describe attempts — not always successful — made over the years to improve the efficiency of porphycene synthesis and to produce novel compounds, custom-designed for specific purposes. New porphycenes are reported, some of them obtained rather unexpectedly as by-products of the planned reactions. Structure and energy computations of possible tautomeric forms in porphycenes substituted by one, two, three, and four tert-butyl groups lead to predictions regarding the kinetics and mechanisms of intramolecular double hydrogen transfer. The occurrence of tautomerization in single molecules of tert-butylsubstituted porphycenes is demonstrated by using fluorescence polarization techniques.

Determination of the rotational diffusion tensor of porphycene by 13C and 1H spin relaxation methods

The longitudinal (13)C and (1)H relaxation rates were determined in porphycene in CD(2)Cl(2) solution. These data, augmented by (13)C{(1)H} NOE enhancements were numerically analyzed to evaluate the rotational diffusion tensor of the molecule and the vibrational correction for the one-bond (13)C-(1)H dipolar couplings. The (13)C and (1)H relaxation data seem to be consistent with each other, and the emerging picture of the rotational dynamics of porphycene compares well with the results that can be found in the literature.