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https://www.selleckchem.com/products/phenol-red-sodium-salt.html Carbon nanotubes (CNTs) have a wide range of applications in nanotechnology engineering. This research aims to quantify the effect of wall vibration on n-decane molecules' diffusion in double-walled CNTs (DWNTs) with different diameters and determine the diffusion mechanisms behind it. Molecular dynamics simulations are performed to generate mass density profiles of confined n-decane molecules. The root mean square fluctuation and mean squared displacement analyses show that the confinement suppresses n-decane molecules' fluctuations. A self-diffusion coefficient of n-decane molecules in a 13.6 Å-diameter DWNT is the largest. However, the vibration enhancement of the n-decane molecules' diffusion in a 27.1 Å-diameter DWNT is 207%, more extensive than that in 13.6 Å-diameter and 10.8 Å-diameter DWNTs. The n-decane-CNT attractive interactions, extreme confinement, and surface friction affect the n-decane molecules' diffusion in CNTs with vibration.Single-reference methods such as Hartree-Fock-based coupled cluster theory are well known for their accuracy and efficiency for weakly correlated systems. For strongly correlated systems, more sophisticated methods are needed. Recent studies have revealed the potential of the antisymmetrized geminal power (AGP) as an excellent initial reference for the strong correlation problem. While these studies improved on AGP by linear correlators, we explore some non-linear exponential Ansätze in this paper. We investigate two approaches in particular. Similar to Wahlen-Strothman et al. [Phys. Rev. B 91, 041114(R) (2015)], we show that the similarity transformed Hamiltonian with a Hilbert-space Jastrow operator is summable to all orders and can be solved over AGP by projecting the Schrödinger equation. The second approach is based on approximating the unitary pair-hopper Ansatz recently proposed for application on a quantum computer. We report benchmark numerical calcula

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