From Synchronous to Sequential Double Proton Transfer: Quantum Dynamics Simulations for the Model Porphine

Accardi, Antonio; Barth, Ingo; Kühn, Oliver; Manz, J.

doi:10.1021/jp103435d

Cited by 26 publications

(46 citation statements)

References 54 publications

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“…Theoretical studies related to those of primary concern in this perspective deal with, for example, purely nuclear fluxes during chemical reactions [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] or purely electronic fluxes during adiabatic [23][24][25][26][27][28][29] and diabatic [30][31][32][33][34][35][36][37][38] processes (e.g., electronic ring currents in degenerate electronic excited states [23][24][25] or electronic fluxes during diabatic reactions; [30][31][32][33][34][35][36][37][38] see also ref. [39][40][41].…”

Section: Timm Bredtmannmentioning

confidence: 99%

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Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes

Bredtmann

Diestler

et al. 2015

Phys. Chem. Chem. Phys.

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123

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An elementary molecular process can be characterized by the flow of particles (i.e., electrons and nuclei) that compose the system. The flow, in turn, is quantitatively described by the flux (i.e., the time-sequence of maps of the rate of flow of particles though specified surfaces of observation) or, in more detail, by the flux density. The quantum theory of concerted electronic and nuclear fluxes (CENFs) associated with electronically adiabatic intramolecular processes is presented. In particular, it is emphasized how the electronic continuity equation can be employed to circumvent the failure of the Born-Oppenheimer approximation, which always predicts a vanishing electronic flux density (EFD). It is also shown that all CENFs accompanying coherent tunnelling between equivalent "reactant" and "product" configurations of isolated molecules are synchronous. The theory is applied to three systems of increasing complexity. The first application is to vibrating, aligned H2(+)((2)Σg(+)), or vibrating and dissociating H2(+)((2)Σg(+), J = 0, M = 0). The EFD maps manifest a rich and surprising structure in this simplest of systems; for example, they show that the EFD is not necessarily synchronous with the nuclear flux density and can alternate in direction several times over the length of the molecule. The second application is to coherent tunnelling isomerization in the model inorganic system B4, in which all CENFs are synchronous. The contributions of core and valence electrons to the EFD are separately computed and it is found that core electrons flow with the nuclei, whereas the valence electrons flow obliquely to the core electrons in distinctive patterns. The third application is to the Cope rearrangement of semibullvalene, which also involves coherent tunnelling. An especially interesting discovery is that the so-called "pericyclic" electrons do not behave in the manner typically portrayed by the traditional Lewis structures with appended arrows. Indeed, it is found that only about 3 pericyclic electrons flow, in contrast to the 6 predicted by the Lewis picture. It is remarkable that the time scales of these three processes vary by 18 orders of magnitude: femtoseconds (H2(+)((2)Σg(+))); picoseconds (B4); kilosceconds (semibullvalene). It is emphasized that results presented herein are appearing in the literature for the first time.

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Section: Timm Bredtmannmentioning

confidence: 99%

“…That C given by eqn (15) solves the internal Schrödinger equation can be seen by its direct substitution into eqn (10b). We emphasize that, in general, C is complex.…”

Section: Wave Functionsmentioning

confidence: 99%

Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes

Bredtmann

Diestler

et al. 2015

Phys. Chem. Chem. Phys.

Self Cite

123

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“…Letter the reactant (the details on how this initial state can be experimentally achieved can be read in ref 33). The mean energy of the initial state is 4.885 eV, well above the values of the barriers TS (0.600 eV), and also the saddle point SP2, (1.069 eV), so we do not expect remarkable tunneling effects during the first forward reaction.…”

Section: The Journal Of Physical Chemistry Lettersmentioning

confidence: 84%

Conditional Born–Oppenheimer Dynamics: Quantum Dynamics Simulations for the Model Porphine

Albareda

Bofill

Tavernelli

et al. 2015

J. Phys. Chem. Lett.

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We report a new theoretical approach to solve adiabatic quantum molecular dynamics halfway between wave function and trajectory-based methods. The evolution of a N-body nuclear wave function moving on a 3N-dimensional Born− Oppenheimer potential-energy hyper-surface is rewritten in terms of single-nuclei wave functions evolving nonunitarily on a 3-dimensional potential-energy surface that depends parametrically on the configuration of an ensemble of generally defined trajectories. The scheme is exact and, together with the use of trajectory-based statistical techniques, can be exploited to circumvent the calculation and storage of many-body quantities (e.g., wave function and potential-energy surface) whose size scales exponentially with the number of nuclear degrees of freedom. As a proof of concept, we present numerical simulations of a 2-dimensional model porphine where switching from concerted to sequential double proton transfer (and back) is induced quantum mechanically. O n the basis of the Born−Huang expansion of the molecular wave function, 1 an exact description of adiabatic molecular dynamics requires the propagation of a nuclear wavepacket on the ground-state Born−Oppenheimer potential-energy surface (gs-BOPES). This propagation scheme is, somehow, computationally doubly prohibitive. Besides the computational burden associated with the propagation of the (many-body) nuclear wave function, the calculation of the gs-BOPES constitutes, per se, a time-independent problem that grows exponentially with the number of electrons and nuclei. In this respect, two main classes of computational methods have emerged depending on whether the knowledge of the gs-BOPES is required in the full configuration space, that is, fullquantum methods, 2,3 or only at certain reduced number of points, namely trajectory-based or direct methods.4,5 While methods for computing the energy of any configuration of nuclei have become quicker and more accurate, full-quantum dynamics calculations still become rapidly unfeasible for large molecules. Alternatively, direct dynamics notably reduce the computational cost of the simulations by avoiding partially, sometimes completely, the calculation of the full gs-BOPES (this can be done, for instance, by the use of reaction-path Hamiltonians 6,7 ). Nuclear quantum effects, however, can be hardly included systematically in this second class of methods. Up to date, only quantum-trajectory methods have the particularity of being able to describe all nuclear quantum effects (just as full-quantum methods) and being on-the-fly simultaneously.8−11 Unfortunately, these methods have serious problems in dealing with the so-called quantum potential, which gathers, by definition, all quantum information on the system. The mathematical structure of the quantum potential depends on the inverse of the quantum probability density, and thus, its manipulation entails serious instability problems. 12−14We report here an exact theoretical approach to solve adiabatic quantum molecular dynamics based o...

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“…Nonvanishing electronic and nuclear current densities occur not only in nonstationary states, corresponding to electron circulations, 1−5 molecular vibrations, 6 motors, 7 pseudorotations, 8,9 rotations, torsions, 10 isomerizations, proton transfers, 11,12 pericyclic rearrangements, 13,14 or chemical reactions 15−17 but also in stationary states. 18,19 The existence of stationary current densities is guaranteed in electronic degenerate states of atoms, ions, 20, 21 and linear 22,23 or ring-shaped molecules 24 or in nuclear degenerate states of pseudorotating molecules.…”

Section: Introductionmentioning

confidence: 99%

Translational Effects on Electronic and Nuclear Ring Currents

Barth

2012

J. Phys. Chem. A

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In previous works, it was predicted that electronic and nuclear ring currents in degenerate excited states of atomic and molecular systems persist after the end of driven circularly polarized atto- or femtosecond laser pulses on relatively long time scales, often on pico- or nanosecond time scales, before spontaneous emission occurs. Although this conclusion is true in the center of mass frame, it is not true in the laboratory frame, where the translation has to be considered. In this theoretical work, the analytic formulas for the ring current densities, electric ring currents, mean ring current radii, and induced magnetic fields at the ring center, depending on the translational wavepacket widths, are derived. It shows that the ring currents and the corresponding induced magnetic fields in the laboratory frame persist on shorter timecales due to spreading of translational wavepackets. The electronic ring currents in 2p(±) orbitals of the hydrogen-like systems decay on the femtosecond time scale, but the corresponding nuclear ring currents with giant induced magnetic fields (for example up to 0.54 MT for (7)Li(2+)) and very small mean ring current radii on the femtometer scale decay on the very short, zeptosecond time scale, according to the Heisenberg uncertainty principle. The theory is also applied to ring currents in many-electron atoms and ions as well as to nuclear ring currents in pseudorotating molecules. For example, in the first triply degenerate pseudorotational states |v(1)l(±1)> of the tetrahedral molecule OsH(4), the ring currents of the heavy central nucleus Os decay on the attosecond time scale.

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From Synchronous to Sequential Double Proton Transfer: Quantum Dynamics Simulations for the Model Porphine

Cited by 26 publications

References 54 publications

Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes

Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes

Conditional Born–Oppenheimer Dynamics: Quantum Dynamics Simulations for the Model Porphine

Translational Effects on Electronic and Nuclear Ring Currents

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