Molecular quasiparticle and excitation energies determine essentially the spectral characteristics measured in various spectroscopic experiments. Accurate prediction of these energies has been rather challenging for ground-state density functional methods, because the commonly adopted density function approximations suffer from delocalization error. In this work, by presuming a quantitative correspondence between the quasiparticle energies and the generalized Kohn–Sham orbital energies, and employing a previously developed global scaling correction approach, we achieve substantially improved prediction of molecular quasiparticle and excitation energies. In addition, we also extend our previous study on temporary anions in resonant states, which are associated with negative molecular electron affinities. The proposed approach does not require any explicit self-consistent field calculation on the excited-state species, and is thus highly efficient and convenient for practical purposes.

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Unit cell consistency (UCC) means that the physical properties or quantities of solids resulted from electronic structure calculations should not depend on the specific choice of the unit cell. The UCC of maximally localized wannier functions (MLWFs), a family of localized orbitals that are very useful in the theoretical characterization of solids, has scarcely been studied. In this work, we explore both analytically and numerically the UCC of MLWFs, and propose an explicit symmetry constraint on the unitary transformation matrices to ensure the UCC is rigorously preserved. Numerical calculations also demonstrate that without the symmetry constraint the MLWFs constructed in a supercell model may violate the UCC. This work thus provides useful guidance for the use of MLWFs in sophisticated solid-state systems and applications.

It has been an active research issue for many years to construct new bent functions. For k odd with gcd(n, k) = 1, and a ∈ F * 3 n , the function f (x) = T r(ax 3 k +1 2 √ 5; for the case of (n, k) = (5t + 4, 4t + 3) or (5t + 1, 4t + 1) with t ≥ 1, the number of trace terms is 8; and for the case of (n, k) = (7t + 6, 6t + 5) or (7t + 1, 6t + 1) with t ≥ 1, the number of trace terms is 21. As a byproduct, we find new classes of ternary bent functions with only 8 or 21 trace terms.

Impulsive noise is commonly present in many applications of actual communication networks, leading to algorithms based on the Gaussian model no longer being applicable. A robust parameter estimator of frequency-hopping (FH) signals suitable for various impulsive noise environments, referred to as ℓp-STFT, is proposed. The ℓp-STFT estimator replaces the ℓ2-norm by using the generalized version ℓp-norm where 1 < p < 2 for the derivation of the short-time Fourier transform (STFT) as an objective function. It combines impulsive noise processing with any time-frequency analysis algorithm based on STFT. Considering the accuracy of parameter estimation, the double-window spectrogram difference (DWSD) algorithm is used to illustrate the suitability of ℓp-STFT. Computer simulations are mainly conducted in α-stable noise to compare the performance of ℓp-STFT with STFT and fractional low-order STFT (FLOSTFT), Cauchy noise, and Gaussian mixture noise as supplements of different background noises to better demonstrate the robustness and accuracy of ℓp-STFT.