Time-dependent renormalized-natural-orbital theory applied to laser-driven<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:math>

Hanusch, Adrian; Rapp, J.; Brics, M.; Bauer, Dieter

doi:10.1103/physreva.93.043414

Cited by 9 publications

(10 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where g mn (t) = m(t)|ĝ(t)|n(t) = i m(t)|ṅ(t) with an arbitrary hermitian operatorĝ(t). The sums in (12) are finite now and run over the N • orbitals considered in the numerical implementation, which span a truncated subspace. The operatorR(t) =1 − N• n=1 |n(t) n(t)| projects onto the orthogonal complement of that subspace.…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…In summary, there are three essential steps from the general EOM (12) to the EOM for RNOs being propagated in TDRNOT. First, a functional for γ 2,ijkl (t) is used, which for N = 2 is known exactly but for N > 2 needs to be approximated.…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…In order to solve (12) numerically an expression for γ 2,ijkl (t) and a convention for ĝ(t) need to be chosen. Regarding γ 2,ijkl (t), one approach is to expand the state in the same truncated orthonormal basis as γ1 (t) and γ2 (t),…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…To estimate the minimal number of spatial NOs or determinants required, one may take the first N spat • NOs with the highest ONs in (16), calculated from the exact TDSE wavefunction at the end of the laser pulse, to evaluate the observable of interest. Note that this corresponds to a hypothetical TDRNOT simulation without truncation error [9][10][11][12], i.e., with an infinite number of NOs taken into account for propagation, but only the dominating N spat indicates that SPDI is a very correlated process, and differential, correlated photoelectron momentum spectra are correlation-sensitive observables. It is interesting to investigate how many RNOs for TDRNOT (or determinants in MCTDHF) are necessary to describe SPDI.…”

Section: A Single-photon Double Ionizationmentioning

confidence: 99%

“…In this work, we employ SPDI as a demanding benchmark for the recently developed time-dependent renormalized-natural-orbital theory (TDRNOT) [8][9][10][11][12] and the widely known multi-configurational time-dependent Hartree-Fock (MCTDHF) [13][14][15]. We work out the connection between TDRNOT and MCTDHF and benchmark their performance with a 1D helium model atom, for which the time-dependent Schrödinger equation (TDSE) is still numerically exactly solvable.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Single-photon double ionization: renormalized-natural-orbital theory versus multi-configurational Hartree–Fock

Brics¹,

Rapp²,

Bauer³

2017

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

The N -particle wavefunction has too many dimensions for a direct time propagation of a many-body system according to the time-dependent Schrödinger equation (TDSE). On the other hand, time-dependent density functional theory (TDDFT) tells us that the single-particle density is, in principle, sufficient. However, a practicable equation of motion (EOM) for the accurate time evolution of the single-particle density is unknown. It is thus an obvious idea to propagate a quantity which is not as reduced as the single-particle density but less dimensional than the N -body wavefunction. Recently, we have introduced time-dependent renormalized-natural-orbital theory (TDRNOT). TDRNOT is based on the propagation of the eigenfunctions of the one-body reduced density matrix (1-RDM), the so-called natural orbitals. In this paper we demonstrate how TDRNOT is related to the multi-configurational time-dependent Hartree-Fock (MCTDHF) approach. We also compare the performance of MCTDHF and TDRNOT vs the TDSE for single-photon double ionization (SPDI) of a 1D helium model atom. SPDI is one of the effects where TDDFT does not work in practice, especially if one is interested in correlated photoelectron spectra, for which no explicit density functional is known.

show abstract

Section: Theoretical Methodsmentioning

confidence: 99%

Section: Theoretical Methodsmentioning

confidence: 99%

Section: Theoretical Methodsmentioning

confidence: 99%

Section: A Single-photon Double Ionizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Single-photon double ionization: renormalized-natural-orbital theory versus multi-configurational Hartree–Fock

Brics¹,

Rapp²,

Bauer³

2017

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

show abstract

Methods for the Simulation of Coupled Electronic and Nuclear Motion in Molecules Beyond the Born-Oppenheimer Approximation

Lötstedt

Katō

Yamanouchi

2019

Springer Series in Chemical Physics

View full text Add to dashboard Cite

Natural excitation orbitals from linear response theories: Time-dependent density functional theory, time-dependent Hartree-Fock, and time-dependent natural orbital functional theory

Meer

Gritsenko²,

Baerends³

2017

The Journal of Chemical Physics

View full text Add to dashboard Cite

Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In contrast, in a basis of natural orbitals (NOs) or Hartree-Fock orbitals, excitations often employ many orbitals and are accordingly hard to characterize. We demonstrate that it is possible in these cases to transform to natural excitation orbitals (NEOs) which resemble very closely the KS orbitals and afford the same simple description of excitations. The desired transformation has been obtained by diagonalization of a submatrix in the equations of linear response time-dependent 1-particle reduced density matrix functional theory (LR-TDDMFT) for the NO transformation, and that of a submatrix in the linear response time-dependent Hartree-Fock (LR-TDHF) equations for the transformation of HF orbitals. The corresponding submatrix is already diagonal in the KS basis in the LR-TDDFT equations. While the orbital shapes of the NEOs afford the characterization of the excitations as (mostly) simple orbital-to-orbital transitions, the orbital energies provide a fair estimate of excitation energies.

show abstract

Time-dependent renormalized-natural-orbital theory applied to laser-drivenH2+

Cited by 9 publications

References 50 publications

Single-photon double ionization: renormalized-natural-orbital theory versus multi-configurational Hartree–Fock

Single-photon double ionization: renormalized-natural-orbital theory versus multi-configurational Hartree–Fock

Methods for the Simulation of Coupled Electronic and Nuclear Motion in Molecules Beyond the Born-Oppenheimer Approximation

Natural excitation orbitals from linear response theories: Time-dependent density functional theory, time-dependent Hartree-Fock, and time-dependent natural orbital functional theory

Contact Info

Product

Resources

About