We investigate the delocalization of operators in non-chaotic quantum systems whose interactions are encoded an underlying graph or network. In particular, we study how fast different sizes delocalize as network connectivity is varied. argue that these properties well captured by Krylov complexity and show, numerically, efficient large can only happen within sufficiently connected topologies. F...

In the present work, the structural and electronic properties, and conductivity of (5,5) and (6,6) Single Walled Carbon Nanotubes in the ground state have done by using the Hartree-Fock and density functional theory DFT-B3LYP/6-31G* level. Delocalization of charge density between the bonding or lone pair and antibonding orbitals calculated by NBO (natural bond orbital) analysis. These methods a...

We prove the existence of dynamical delocalization for random Landau Hamiltonians near each Landau level. Since typically there is dynamical localization at the edges of each disordered-broadened Landau band, this implies the existence of at least one dynamical mobility edge at each Landau band, namely a boundary point between the localization and delocalization regimes, which we prove to conve...

Density functional theory (DFT) is often used to determine the electronic and geometric structures of molecules. While studying alkynyl radicals, we discovered that DFT exchange-correlation (XC) functionals containing less than ∼22% Hartree-Fock (HF) exchange led to qualitatively different structures than those predicted from ab initio HF and post-HF calculations or DFT XCs containing 25% or mo...

The van der Waals interfaces of molecular donor/acceptor or graphene-like two-dimensional (2D) semiconductors are central to concepts and emerging technologies of light-electricity interconversion. Examples include, among others, solar cells, photodetectors, and light emitting diodes. A salient feature in both types of van der Waals interfaces is the poorly screened Coulomb potential that can g...

Delocalized, solvated electrons are a topic of much recent interest. We apply the electron delocalization range EDR(r;u) (J. Chem. Phys., 2014, 141, 144104) to quantify the extent to which a solvated electron at point r in a calculated wavefunction delocalizes over distance u. Calculations on electrons in one-dimensional model cavities illustrate fundamental properties of the EDR. Mean-field ca...

Enzymes use protein architectures to create highly specialized structural motifs that can greatly enhance the rates of complex chemical transformations. Here, we use experiments, combined with ab initio simulations that exactly include nuclear quantum effects, to show that a triad of strongly hydrogen-bonded tyrosine residues within the active site of the enzyme ketosteroid isomerase (KSI) faci...

The unusual aromatic stability of cyclic bicalicene has been suggested to come from a tetraionic structure, where positive and negative charges are located on the cyclopropene and cyclopentadiene rings, respectively. Energetic, magnetic, geometric and electron delocalization analysis performed on a series of bicalicene derivatives, incorporating different electron donating and withdrawing group...