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The electronic properties in particular the occupation number of 5f electrons and the valence state of Am ions in americium trichloride (AmCl3) are studied by using density functional theory (DFT) merged with dynamical mean‐field theory (DMFT). We find that j = 5/2, j = 7/2 manifolds both are in the insulating regimes, resulting in the semiconducting band gap of about 0.837 eV, together with the weak Am 5f‐conduction electrons hybridization and the localized 5f‐derived spectra feature in the vicinity of the Fermi level. The weighted summation for the occupation probabilities of 5fn (n = 3–7) atomic configurations suggests that 5f electrons have the inter‐configuration fluctuation with an average occupation number of 5f electrons n5f ~ 5.182, corresponding to the valence state of Am3.818+ in AmCl3. The 5fn‐mixing‐driven inter‐configuration fluctuation might originate from the complicated quantum mechanics processes such as the dual nature of 5f electrons and the flexible electronic configuration of Am ions. Finally, the so‐called quasiparticle band structure is also predicted. [ABSTRACT FROM AUTHOR]

Based on quadratic and linear polynomial interpolation approximations and the Crank-Nicolson technique, a new second-order difference approximation method of the Caputo fractional derivative of order α ∈ (1 , 2) is proposed. This method is different from the known second-order methods, which is called the L 2- 1 σ Crank-Nicolson method in this paper. Using the L 2- 1 σ Crank-Nicolson method of the Caputo fractional derivative, a fully discrete L 2- 1 σ Crank-Nicolson difference method for two-dimensional time-fractional wave equations with variable coefficients is developed. The unconditional stability and convergence of the method are rigorously proved. The optimal error estimates in the discrete L 2 -norm and H 1 -norm are obtained under a relatively weak regularity condition. The error estimates show that the method has the second-order convergence in both time and space for all α ∈ (1 , 2). In order to overcome the loss of the temporal convergence order caused by the stronger singularity of the exact solution at the initial time, a nonuniform L 2- 1 σ Crank-Nicolson difference method is also developed on a class of general nonuniform time meshes. Numerical results confirm the theoretical convergence result. The effectiveness of the nonuniform method for non-smooth solutions with the stronger singularity at the initial time is tested on a class of initially graded time meshes. [ABSTRACT FROM AUTHOR]