Abstract
We propose a gauge-invariant formulation of the channel orbital-based time-dependent configuration interaction singles (TDCIS) method [Phys. Rev. A, 74, 043420 (2006)], one of the powerful ab initio methods to investigate electron dynamics in atoms and molecules subject to an external laser field. In the present formulation, we derive the equations of motion (EOMs) in the velocity gauge using gauge-transformed time-dependent, not fixed, orbitals that are equivalent to the conventional EOMs in the length gauge using fixed orbitals. The new velocity-gauge EOMs avoid the use of the length-gauge dipole operator, which diverges at large distance, and allows us to exploit computational advantages of the velocity-gauge treatment over the length-gauge one, e.g., a faster convergence in simulations with intense and long-wavelength lasers, and the feasibility of exterior complex scaling as an absorbing boundary. The reformulated TDCIS method is applied to an exactly solvable model of one-dimensional helium atom in an intense laser field to numerically demonstrate the gauge invariance. We also discuss the consistent method for evaluating the time derivative of an observable, which is relevant, e.g., in simulating high-harmonic generation.
Highlights
time-dependent configuration interaction singles (TDCIS) method, the time-dependent electronic wavefunction is given by the configuration interaction (CI) expansion, occ vir
This approach is guaranteed to be equivalent to the CI coefficient-based length gauge (LG) TDCIS, it brings no numerical gain over Equation (22), peculiarly including both E · r and A · p, and requiring extensive gauge transformation of all occupied and virtual orbitals
We numerically apply the channel orbital-based TDCIS method in the LG, velocity gauge (VG), and rotated velocity-gauge (rVG) to the 1D model Helium atom, using the computational code developed by modifying an existing time-dependent Hartree-Fock (TDHF) code used in our previous work [30,33,48]
Summary
Time-dependent configuration interaction singles (TDCIS) method is one of the powerful ab initio methods to investigate laser-driven electron dynamics in atoms and molecules [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. The channel orbital-based approach [2] has been applied only in the LG [1,2,14,15], and as shown below in this paper, the VG treatment with fixed orbitals is not very appropriate for applications to high-field phenomena This is a serious drawback, since for an efficient simulation of molecules, it is highly appreciated to take advantage of the velocity-gauge treatment, e.g., the feasibility of exterior complex scaling [43,44] as an absorbing boundary, to reduce the computational cost related to the number of grid points. The Hartree atomic units are used throughout unless otherwise noted
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