Translational Effects on Electronic and Nuclear Ring Currents

Barth, Ingo

doi:10.1021/jp305318s

Cited by 4 publications

(6 citation statements)

References 33 publications

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“…(We note that the role of translation of the NCM in the laboratory frame has been previously investigated. 69,70 ) Thus, the electronic population density (EPD) is r e;NCM ðx; tÞ ¼ CðtÞ…”

Section: Population Densities and Flux Densitiesmentioning

confidence: 99%

“…is the flux density of nucleus a with respect to nucleus b, which is determined accurately in the BOA (see eqn (70)). [Note that the term ''coupled-channels'' in the present context refers simply to the form of the EFD, i.e., the difference between contributions of channel a (defined as ''internal'' atom a ''colliding'' with nucleus b) and channel b (internal atom b colliding with nucleus a) to the EFD, as seen in eqn (78); this coupled-channels theory of the EFD is an approximation to the traditional quantum-dynamical description of collisions.]…”

Section: The Triumphs and The Defeat Of The Born-oppenheimer Approxim...mentioning

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.

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: Population Densities and Flux Densitiesmentioning

confidence: 99%

Section: The Triumphs and The Defeat Of The Born-oppenheimer Approxim...mentioning

confidence: 99%

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

Bredtmann

Diestler

et al. 2015

Phys. Chem. Chem. Phys.

123

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“…Furthermore, one expects that in the rotational states with zero or nonzero magnetic quantum numbers ( M = 0 or M ≠ 0), there are zero or nonzero ring currents about the rotation axis of the system; i.e., the azimuthal component of the flux density in the center-of-mass frame is zero or nonzero, respectively. The angular dependencies should be similar to those of electronic and nuclear flux densities in atoms. , To investigate corresponding symmetry properties, one has to use analytical expressions for the inverse functions of eqs and , i.e., Ψ(Ψ′,Θ′,ϕ,θ) and Θ(Ψ′,Θ′,ϕ,θ), and the Wigner D -matrices appearing in exact stationary wave functions …”

Section: Discussionmentioning

confidence: 99%

“…Although the translation of the closed many-body system is introduced in the laboratory frame, its wave function completely disappears in the center-of-mass frame, in which the point of origin is the center of mass of all particles and not the specific center of mass, e.g., nuclear center of mass that leads to the additional mass-polarization term in the Hamiltonian. − In general, the probability and flux densities in the laboratory frame with nonspherical wave function for the translation cannot be isotropic. Translational effects on prealigned electronic and nuclear ring currents in hydrogen-like systems (i.e., not in the rotational ground state of the system) have been already investigated, where ring currents can be induced by a circularly polarized laser pulse . A simplified analysis for the system with spherical wave function for the translation could be carried out and it would lead to the isotropic distribution of the probability and flux densities in the laboratory frame, if the corresponding densities in the center-of-mass frame are isotropic.…”

Section: Introductionmentioning

confidence: 99%

Probability and Flux Densities in the Center-of-Mass Frame

Barth

2018

J. Phys. Chem. A

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For an arbitrary nonstationary wave function of a nonrelativistic closed many-body system consisting of arbitrary interacting particles, the general expressions for the time-dependent one-particle probability and flux densities in the center-of-mass frame without applying Born-Oppenheimer approximation are obtained. Even the wave function for the translation is additionally introduced; it disappears in the center-of-mass frame automatically. It is shown that for the rotational ground state the time-dependent probability and flux densities of an arbitrary particle in the center-of-mass frame are isotropic. It means that the angular dependence is absent but these densities depend on radius and time. More importantly, it is shown that the angular components of the time-dependent flux density vanish. With these statements, one can calculate the radial component of the radius- and time-dependent electronic flux density within the Born-Oppenheimer approximation via the continuity equation. Application of this theory to the pulsating or exploding "quantum bubble" of the vibrating or dissociating Na molecule in the rotational ground state, respectively, is found elsewhere in this issue.

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“…Furthermore, we assume that the molecule does not rotate and that its nuclear center of mass is fixed at the origin. Effects of translations have been discussed in refs and .…”

Section: Applications To Cenfs During Cope Rearrangement Of Semibullv...mentioning

confidence: 99%

Concerted Electronic and Nuclear Fluxes During Coherent Tunnelling in Asymmetric Double-Well Potentials

Bredtmann¹,

Manz

Zhao³

2016

J. Phys. Chem. A

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The quantum theory of concerted electronic and nuclear fluxes (CENFs) during coherent periodic tunnelling from reactants (R) to products (P) and back to R in molecules with asymmetric double-well potentials is developed. The results are deduced from the solution of the time-dependent Schrödinger equation as a coherent superposition of two eigenstates; here, these are the two states of the lowest tunnelling doublet. This allows the periodic time evolutions of the resulting electronic and nuclear probability densities (EPDs and NPDs) as well as the CENFs to be expressed in terms of simple sinusodial functions. These analytical results reveal various phenomena during coherent tunnelling in asymmetric double-well potentials, e.g., all EPDs and NPDs as well as all CENFs are synchronous. Distortion of the symmetric reference to a system with an asymmetric double-well potential breaks the spatial symmetry of the EPDs and NPDs, but, surprisingly, the symmetry of the CENFs is conserved. Exemplary application to the Cope rearrangement of semibullvalene shows that tunnelling of the ideal symmetric system can be suppressed by asymmetries induced by rather small external electric fields. The amplitude for the half tunnelling, half nontunnelling border is as low as 0.218 × 10(-8) V/cm. At the same time, the delocalized eigenstates of the symmetric reference, which can be regarded as Schrödinger's cat-type states representing R and P with equal probabilities, get localized at one or the other minima of the asymmetric double-well potential, representing either R or P.

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Translational Effects on Electronic and Nuclear Ring Currents

Cited by 4 publications

References 33 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

Probability and Flux Densities in the Center-of-Mass Frame

Concerted Electronic and Nuclear Fluxes During Coherent Tunnelling in Asymmetric Double-Well Potentials

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