Influence of a strong magnetic field on the hydrogen molecular ion using B-spline-type basis-sets

Abstract

As an improvement on our previous work [J. Phys. B: At. Mol. Opt. Phys. 45 085101 (2012)], an accurate method combining the spheroidal coordinates and B-spline basis is applied to study the ground state 1σ g and low excited states 1σ u , 1π g,u , 1δ g,u , 2σ g of the H + 2 in magnetic fields ranging from 10 9 Gs (1 Gs = 10 −4 T) to 4.414 × 10 13 Gs. Comparing the one-center method used in our previous work, the present method has a higher precision with a shorter computing time. Equilibrium distances of the states of the H + 2 in strong magnetic fields were found to be accurate to 3∼5 significant digits (s.d.) and the total energies 6∼11 s.d., even for some antibonding state, such as 1π g , which is difficult for the one-center method to give reliable results while the field strength is B ≥ 10 13 Gs. For the large disagreement in previous works, such as the equilibrium distances of the 1π g state at B = 10 9 Gs, the present data may be used as a reference. Further, the potential energy curves (PECs) and the electronic probability density distributions (EPDDs) of the bound states 1σ g , 1π u , 1δ g and antibonding states 1σ u , 1π g , 1δ u for B = 1, 10, 100, 1000 a.u. (atomic unit) are compared, so that the different influences of the magnetic fields on the chemical bonds of the bound states and antibonding states are discussed in detail.

Efficient solver for time-dependent Schrödinger equation with interaction between atoms and strong laser field*

“…[15] To solve this problem, Patchkovskii et al have proposed a parallel method, [18] and achieved the spa-tial derivatives of the radial coordinate by using the finitedifference method (FDM), which leads to an increase in the grids for the larger sized problem, [17] and finally significantly increasing the amount of computation in the case of higher accuracy. [19] Guan et al solved TDSE of two-electron quantum system in spherical coordinates efficiently based on the finite-element (FE) discrete-variable-representation (DVR) and Short-Iteration-Lanczos (SIL) propagator, [20] because the FE-DVR can offer higher computing accuracy [21] and make the Hamiltonian matrix very sparse, whose effects are similar to those provided by the B-spline [22,23] and sine-DVR, [24] and the efficiency of the wave function evolution strongly relies on the sparsity of the Hamiltonian matrix for the SIL propagator. [25] The most ideal structure of the Hamiltonian matrix is expected to have diagonal or similarly sparse elements for the SIL propagator.…”