The multi-configurational time-dependent Hartree approach

Meyer, Heinz‐Dieter; Manthe, Uwe; Cederbaum, L. S.

doi:10.1016/0009-2614(90)87014-i

Cited by 1,859 publications

(1,573 citation statements)

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“…The same Coulomb force, however, acts repulsively between the electrons. This electron-electron interaction represents a major challenge in the understanding and modelling of atomic and molecular states, their structure and in particular their dynamics 2,3,14 . Here, we focus on the 1 P sp 2,n+ series 15 of doubly-excited states in helium below the N = 2 ionization threshold.…”

mentioning

confidence: 99%

Reconstruction and control of a time-dependent two-electron wave packet

Ott

Kaldun

Argenti

et al. 2014

Nature

268

218

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Esta es la versión de autor del artículo publicado en: This is an author produced version of a paper published in: The concerted motion of two or more bound electrons governs atomic 1 and molecular 2,3 non-equilibrium processes and chemical reactions. It is thus a long-standing scientific dream to measure and control the dynamics of two bound and correlated electrons in the quantum regime. At least two active electrons and a nucleus are required to address such quantum three-body problem 4 for which analytical solutions do not exist, a condition that is met in the helium atom. While attosecond dynamics were previously observed for singleactive electron/hole cases 5-7 , such time-resolved observation of two-electron motion thus far remained an unaccomplished challenge. Here, we measure a 1.2-femtosecond quantum beat among low-lying doubly-excited states in helium and use it to reconstruct a correlated two-electron wave packet. Our experimental method combines attosecond transientabsorption spectroscopy 5,7-9 at unprecedented high spectral resolution (20 meV s.d. near 60 eV) with an intensity-tuneable visible laser field to couple 10-12 the quantum states from the weak-field to the strong-coupling regime. Employing the Fano resonance as a phasesensitive quantum interferometer 13 , we demonstrate the coherent control of two correlated electrons, which form the basis of most covalent molecular bonds in nature. As we show, such multi-dimensional spectroscopy experiments provide benchmark data for testing fundamental few-body quantum-dynamics theory. They also light a route for site-specific measurement and control of metastable electronic transition states that are at the heart of fundamental reactions in chemistry and biology.Electrons are bound to atoms and molecules by the Coulomb force of the nuclei. Moving between atoms, they form the basis of the molecular bond. The same Coulomb force, however, acts repulsively between the electrons. This electron-electron interaction represents a major challenge in the understanding and modelling of atomic and molecular states, their structure and in particular their dynamics 2,3,14 . Here, we focus on the 1 P sp 2,n+ series 15 of doubly-excited states in helium below the N = 2 ionization threshold. They are excited by a single-photon transition from the 1 S 1s 2 ground state by the promotion of both electrons to at least principal quantum number n = 2. The states autoionize due to electron-electron interaction and their spectroscopic signature manifests as asymmetric non-Lorentzian line shapes. The latter were first observed in the 1930s 16 and attributed 17 , by Ugo Fano, to the quantum interference of bound states with the continuum to which they are coupled (Fig. 1c,d). The coupling is described by the configuration interaction V CI with the single-ionization continuum |1s,p, where one electron is in the 1s ground state and the other one is in the continuum with kinetic energy . The magnitude of V CI determines the lifetimes of the transiently bound states. In our case,...

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mentioning

confidence: 99%

Reconstruction and control of a time-dependent two-electron wave packet

Ott

Kaldun

Argenti

et al. 2014

Nature

268

218

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“…In this, neither the electrons nor the nuclei were in a stationary state [20][21][22]. The multiconfiguration time-dependent Hartree (MCTDH) method [35,36] was applied to solve the time-dependent nuclear Schrödinger equation within a two-electronic-state coupled representation. The potential energy surfaces and R-dependent dipole moments occurring in the radiative coupling terms were taken from…”

Section: Resultsmentioning

confidence: 99%

Monitoring the Birth of an Electronic Wavepacket in a Molecule with Attosecond Time-Resolved Photoelectron Spectroscopy

et al. 2014

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“…with T = − 1 2 ∆ , yields a system of coupled ordinary and partial differential equations for the coefficients a = (a J ) J and orbitals φ = (φ j ) j , rigorously derived in [2,23] under the implicit assumption that a sufficiently regular solution exists:…”

Section: Of 16mentioning

confidence: 99%

“…The method chosen to make the linear electronic Schrödinger equation (1.1) tractable for numerical computation, is the multi-configuration time-dependent Hartree-Fock method, MCTDHF [5,13,14,25,29,30], which is closely related to the MCTDH method in quantum molecular dynamics [2,3,4,23,24].…”

Section: Introductionmentioning

confidence: 99%

Variational-splitting time integration of the multi-configuration time-dependent Hartree-Fock equations in electron dynamics

Koch

Lubich

2010

IMA Journal of Numerical Analysis

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We discuss the numerical approximation of the solution to the multi-configuration time-dependent Hartree-Fock (MCTDHF) equations in quantum dynamics. The MCTDHF method approximates the high-dimensional wave function of the time-dependent electronic Schrödinger equation by an antisymmetric linear combination of products of functions depending only on three-dimensional spatial coordinates. The equations of motion, obtained via the Dirac-Frenkel time-dependent variational principle, consist of a coupled system of three-dimensional nonlinear partial differential equations and ordinary differential equations. We investigate the convergence properties of a time integrator based on a splitting of the Hamiltonian directly in the variational principle. First-order convergence in the H 1 Sobolev norm and second-order convergence in the L 2 norm are established under a solution regularity of H 2 . As a prerequisite, we show that the MCTDHF equations have a solution in this Sobolev space if the initial data has such regularity.

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The multi-configurational time-dependent Hartree approach

Cited by 1,859 publications

References 17 publications

Reconstruction and control of a time-dependent two-electron wave packet

Reconstruction and control of a time-dependent two-electron wave packet

Monitoring the Birth of an Electronic Wavepacket in a Molecule with Attosecond Time-Resolved Photoelectron Spectroscopy

Variational-splitting time integration of the multi-configuration time-dependent Hartree-Fock equations in electron dynamics

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