Complementary version of fermion coupled coherent states method and gram–schmidt algorithm: Theory and applications for electronic states of and

Abstract

In our previous report, we introduced a new version of Fermion coupled coherent states method (FCCS) which was especially suited for simulating the first symmetric spatial electronic state of two-electron systems. In this manuscript, we report a complementary version for FCCS method to simulate both of the first symmetric and antisymmetric spatial electronic states of two-electron systems. Moreover, the Gram-Schmidt orthogonalization process is employed to reach the excited states of the system. We apply this FCCS method and the original coupled coherent state method to simulate the energy of different electronic states of H2 and H2+, respectively. The results for the energy of computed electronic states of H2 and H2+ show a pretty good consistency with the exact values. © 2017 Wiley Periodicals, Inc.

Static Coherent States Method: One- and Two-Electron Laser-Induced Systems with Classical Nuclear Dynamics

“…For two-electron systems, as the system is fermionic, the CSs grid should be constructed in such a way that the total wave function of the system becomes anti-symmetric [29,31,32]. For example, in the ground state of a two-electron system, as the spin wave function is anti-symmetric, the spatial wave function should be symmetric.…”

“…During the last two decades, a number of approaches have been developed to solve the TDSE for high-dimensional quantum systems in the presence of an ultra-short intense laser field on the basis of coherent states (CSs) and to investigate related phenomena [27][28][29][30][31][32]. CSs have many advantageous features.…”

“…The CCS method was originally developed to simulate systems with distinguishable particles. For simulating fermionic systems, two different versions of a fermion coupled coherent state (FCCS) method were introduced [29,31,32]. The first version of the FCCS method, which was introduced by Shalashilin et al, uses a Slater determinant to symmetrize the CCS equations [29].…”

“…The first version of the FCCS method, which was introduced by Shalashilin et al, uses a Slater determinant to symmetrize the CCS equations [29]. The second version of the FCCS method, introduced by Eidi et al [31,32], simplifies the process by (anti)symmetrizing the CSs grid, with all the governing equations the same as for the CCS method. However, the CCS method and its derivatives are essentially trajectory-guided.…”

“…In the SCS method, in contrast to the CCS method and other older methods that use an evolving gird of CSs [33][34][35][36], the CSs grid remains constant throughout the imaginary and real-time simulations. To simulate two-electron systems, the SCS method uses the same algorithm used in FCCS-II for symmetrizing the CSs grid [31,32].…”