Comparison of approximate methods for computation of the concerted adiabatic electronic and nuclear fluxes in aligned H2+(2

Photoionization of Oriented HD(1Σ+) Yields Vibrating HD+(2Σ+) with Charge Breathing and Small Charge Transfer

“…We briefly summarize the methods that have been developed in the previous works, , which allow us to calculate eigenfunctions and eigenvalues of the Hamiltonian . First, the position vector of the electron r is written in spherical polar coordinates ( r , θ, ϕ) and the molecular Hamiltonian is transformed into Ĥ = prefix− ℏ 2 2 μ normaln normald 2 normald R 2 + e 2 4 π ε 0 R − ℏ 2 2 μ normale [ 1 r 2 ∂ ∂ r true( r 2 ∂ ∂ r true) ] + L̂ 2 2 μ normale r 2 − e 2 4 π ε 0 ∑ l = 0 ∞ r normalp < l r normalp > …”

“…It should be pointed out that eigenfunctions calculated via eq are only valid for states with symmetry 2 Σ + . We remark that our eigenfunctions can, in principle, be constructed following a Born–Huang expansion, which includes nonadiabatic couplings by increasing systematically the number of the BO wavefunctions employed as a basis set . Nevertheless, we have experienced a very slow convergence in obtaining accurate electron flux density through a Born–Huang expansion.…”

“…We remark that our eigenfunctions can, in principle, be constructed following a Born−Huang expansion, which includes nonadiabatic couplings by increasing systematically the number of the BO wavefunctions employed as a basis set. 36 Nevertheless, we have experienced a very slow convergence in obtaining accurate electron flux density through a Born− Huang expansion. In this work, we have used the mass ratios 36 it is expected that these energy errors would affect the probability density and flux density for time propagation beyond ∼1000 fs, as it has been tested using the continuity equation ∂ t ρ + ∇•j = 0 as witness.…”

“…36 Nevertheless, we have experienced a very slow convergence in obtaining accurate electron flux density through a Born− Huang expansion. In this work, we have used the mass ratios 36 it is expected that these energy errors would affect the probability density and flux density for time propagation beyond ∼1000 fs, as it has been tested using the continuity equation ∂ t ρ + ∇•j = 0 as witness.…”

“…4,28−35 Since the BO approximation yields a zero electronic flux density, one has to appeal for frameworks beyond the BO approximation, which inevitably leads to take into account electronic excited states. 10,36 Therefore the question if charge migration also takes place arises, despite the energy separation of the vibronic bound states precludes significant electronic motion in the attosecond time scale. To solve this conundrum, we revisit the field-free dynamics of the HD + ( 2 Σ + ) ion following the ionization of the HD( 1 Σ + ) molecule.…”