Tunneling splitting in double-proton transfer: Direct diagonalization results for porphycene

Investigating proton tunneling dynamics in the time-dependent Schrödinger equation

Understanding the temporal evolution of the wave function in the proton tunneling reactions allows us to make theoretical predictions on the possible femtosecond spectroscopy patterns. However, the analytical solution of the time-dependent Schrödinger equation of complex molecules is challenging and requires a high computational cost. In this study, we solve the time-dependent Schrödinger equation using the Fourier grid Hamiltonian method, highlighting its simplicity of calculation, even for multidimensional tunneling reactions. The obtained model is applied to studying malonaldehyde's two-dimensional intramolecular proton tunneling, comparing the results with those obtained using other computational methods.

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.

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.

Hindered rotor tunneling splittings: an application of the two-dimensional non-separable method to benzyl alcohol and two of its fluorine derivatives

In this work we present a novel application of the two-dimensional non-separable (2D-NS) method to the calculation of torsional tunneling splittings in systems with two hindered internal rotors. This method could be considered an extension of one-dimensional methods for the case of compounds with two tops. The 2D-NS method includes coupling between torsions in the kinetic and potential energy. Specifically, it has been applied to benzyl alcohol (BA) and two of its fluorine derivatives: 3-fluorobenzyl alcohol (3FBA) and 4-fluorobenzyl alcohol (4FBA). These molecules present two torsions, i.e., about the -CH2OH (ϕ1) and -OH (ϕ2) groups. The electronic structure calculations to build the two-dimensional torsional potential energy surface were performed at the DF-LMP2-F12//DF-LMP2/cc-pVQZ level of theory. For BA and 4FBA the calculated ground-state vibrational level splittings are 429 and 453 MHz, respectively, in good agreement with the experimental values of 337.10 and 492.82 MHz, respectively. In these two cases there are four equivalent wells and the tunneling splitting is the result of transitions between the two closer minima along ϕ1. The analysis of the wavefunctions, as well as the previous experimental work on the system, supports this conclusion. For 3FBA the observed ground-state splitting is 0.82 MHz, whereas in this case the calculated value amounts only to 0.02 MHz. The 2D-NS method, through the analysis of the wavefunctions, shows that this tiny tunneling splitting occurs between the two most stable minima of the potential energy surface. Additionally, we predict that the first vibrationally excited tunneling splitting will also be small and exclusively due to the interconversion between the second lowest minima.

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.

Mode-Specific Tunneling Splittings for a Sequential Double-Hydrogen Transfer Case: An Accurate Quantum Mechanical Scheme

We present the first accurate quantum dynamics calculations of mode-specific tunneling splittings in a sequential double-hydrogen transfer process. This is achieved in the vinylidene-acetylene system, the simplest molecular system of this kind, and by large-scale parallel computations with an efficient theoretical scheme developed by us. In our scheme, basis functions are customized for the hydrogen transfer process; a 4-dimensional basis contraction strategy is combined with the preconditioned inexact spectral transform method; efficient parallel implementation is achieved. Mode-specific permutation tunneling splittings of vinylidene states are reported and tremendous mode-specific promotion effects are revealed; in particular, the CH2 rock mode enhances the ground-state splitting by a factor of 10(3). We find that the ground-state vinylidene has a reversible-isomerization time of 622 ps, much longer than all previous estimates. Our calculations also shed light on the importance of the deep intermediate well and vibrational excitation in the double-hydrogen transfer processes.