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Open AccessArticle

Gauge-Invariant Formulation of Time-Dependent Configuration Interaction Singles Method

Department of Nuclear Engineering and Management, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Photon Science Center, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Author to whom correspondence should be addressed.
Appl. Sci. 2018, 8(3), 433;
Received: 31 January 2018 / Revised: 6 March 2018 / Accepted: 8 March 2018 / Published: 13 March 2018
(This article belongs to the Special Issue Attosecond Science and Technology: Principles and Applications)
PDF [606 KB, uploaded 15 March 2018]


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. View Full-Text
Keywords: high-harmonic generation; Attosecond science; TDCIS high-harmonic generation; Attosecond science; TDCIS

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Sato, T.; Teramura, T.; Ishikawa, K.L. Gauge-Invariant Formulation of Time-Dependent Configuration Interaction Singles Method. Appl. Sci. 2018, 8, 433.

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