Coupled-Channels Quantum Theory of Electronic Flux Density in Electronically Adiabatic Processes: Application to the Hydrogen Molecule Ion

The aim of the present contribution is to provide a framework for analyzing and visualizing the correlated many-electron dynamics of molecular systems, where an explicitly time-dependent electronic wave packet is represented as a linear combination of N -electron wave functions. The central quantity of interest is the electronic flux density, which contains all information about the transient electronic density, the associated phase, and their temporal evolution. It is computed from the associated one-electron operator by reducing the multi-determinantal, many-electron wave packet using the Slater-Condon rules. Here, we introduce a general tool for post-processing multi-determinant configuration-interaction wave functions obtained at various levels of theory. It is tailored to extract directly the data from the output of standard quantum chemistry packages using atom-centered Gaussian-type basis functions. The procedure is implemented in the open-source Python program detCI@ORBKIT, which shares and builds upon the modular design of our recently published post-processing toolbox [J. Comput. Chem. 37 (2016) 1511]. The new procedure is applied to ultrafast charge migration processes in different molecular systems, demonstrating its broad applicability.Convergence of the N -electron dynamics with respect to the electronic structure theory level and basis set size is investigated. This provides an assessment of the robustness of qualitative and quantitative statements that can be made concerning dynamical features observed in charge migration simulations.

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“…As the electronic states are real‐valued, the diagonal terms

j_{λ λ} true(r, t true)

, that is, the adiabatic flux density, vanish. The same argument holds for all matrix elements in eq.…”

Section: Computational Procedures and Theorymentioning

confidence: 99%

An open‐source framework for analyzing N‐electron dynamics. I. Multideterminantal wave functions

2017

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“…Vibrational reversals ofj R ðR; tÞ are predicted in Refs. [7,24,25] as a consequence of wave packet interference-here this is revealed by high resolution pump-probe spectroscopy. The cartoon in the very bottom of Fig.…”

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confidence: 98%

Nuclear Fluxes in Diatomic Molecules Deduced from Pump-Probe Spectra with Spatiotemporal Resolutions down to 5 pm and 200 asec

2013

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When molecules move, their nuclei flow. The corresponding quantum observable, i.e., the nuclear flux density, was introduced by Schrödinger in 1926, but until now, it has not been measured. Here the first experimental results are deduced from high-resolution pump-probe measurements of the time-dependent nuclear densities in a vibrating diatomic molecule or molecular ion. The nuclear densities are converted to flux densities by means of the continuity equation. The flux densities are much more sensitive to time-dependent quantum effects than the densities. Applications to the sodium molecule and the deuterium molecular ion unravel four new effects; e.g., at the turns from bond stretch to compression, the flux of the nuclei exhibits multiple changes of directions, from small to large bond lengths, a phenomenon that we call the "quantum accordion."

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“…10 The expression in eq 16 for the intramolecular contribution to the EFD can be reached by an alternate pathway. Instead of fixing the NCM at the origin of the laboratory coordinate frame we assume that the observer rides on the NCM, where his point of observation (x′) is related to that (x) of an observer in the laboratory frame by…”

Section: Quasi-classical Formulas For the Electron Flux Density mentioning

confidence: 99%

“…In this spirit we have developed a "coupled-channels" theory 9 and tried it on the oriented hydrogen molecule ion (H 2 + ) vibrating in the electronic ground state, 10 which is the only system for which highly accurate ("exact") maps of ⟨j e (x,t)⟩ are available. 4 For this simplest of all molecules the coupled-channels theory gives an EFD strictly parallel with the internuclear axis that agrees very well with the parallel component of the "exact" EFD.…”

Section: Introductionmentioning

confidence: 99%

Quasi-Classical Theory of Electronic Flux Density in Electronically Adiabatic Molecular Processes

Diestler

2012

J. Phys. Chem. A

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The standard Born-Oppenheimer (BO) description of electronically adiabatic molecular processes predicts a vanishing electronic flux density (EFD). A previously proposed "coupled-channels" theory permits the extraction of the EFD from the BO wave function for one-electron diatomic systems, but attempts at generalization to many-electron polyatomic systems are frustrated by technical barriers. An alternative "quasi-classical" approach, which eliminates the explicit quantum dynamics of the electrons within a classical framework, yet retains the quantum character of the nuclear motion, appears capable of yielding EFDs for arbitrarily complex systems. Quasi-classical formulas for the EFD in simple systems agree with corresponding coupled-channels formulas. Results of the application of the new quasi-classical formula for the EFD to a model triatomic system indicate the potential of the quasi-classical scheme to elucidate the dynamical role of electrons in electronically adiabatic processes in more complex multiparticle systems.

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Coupled-Channels Quantum Theory of Electronic Flux Density in Electronically Adiabatic Processes: Application to the Hydrogen Molecule Ion

Cited by 27 publications

References 17 publications

An open‐source framework for analyzing N‐electron dynamics. I. Multideterminantal wave functions

An open‐source framework for analyzing N‐electron dynamics. I. Multideterminantal wave functions

Nuclear Fluxes in Diatomic Molecules Deduced from Pump-Probe Spectra with Spatiotemporal Resolutions down to 5 pm and 200 asec

Quasi-Classical Theory of Electronic Flux Density in Electronically Adiabatic Molecular Processes

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