Abstract The equilibrium carbon-carbon (C-C) bond lengths in π -electron hydrocarbons are very sensitive to the electronic ground-state characteristic. In recent two papers by Stolarczyk and Krygowski (J Phys Org Chem, 34:e4154,e4153, 2021) a simple quantum approach, Augmented Hückel Molecular Orbital (AugHMO) model, is proposed for qualitative, as well quantitative, study of this phenomenon. s...

We develop a random batch Ewald (RBE) method for molecular dynamics simulations of particle systems with long-range Coulomb interactions, which achieves an $O(N)$ complexity in each step simulating $N$-body systems. The RBE is based on the splitting kernel “minibatch” type technique introduced to speed up summation Fourier series part splitting. Importance sampling employed reduce induced force...

The interaction between two stiff parallel DNA molecules is discussed using linear Debye-Hückel screening theory with and without inclusion of the dielectric discontinuity at the DNA surface, taking into account the helical symmetry of DNA. The pair potential furthermore includes the amount and distribution of counterions adsorbed on the DNA surface. The interaction does not only depend on the ...

A theoretical analysis of Coulomb systems on lattices in general dimensions is presented. The thermodynamics is developed using Debye–Hückel theory with ion-pairing and dipole–ion solvation, specific calculations being performed for three-dimensional lattices. As for continuum electrolytes, low-density results for simple cubic ~sc!, body-centered cubic ~bcc!, and face-centered cubic ~fcc! latti...

Systems of charged particles on anisotropic three-dimensional lattices are investigated theoretically using Debye–Hückel theory. It is found that the thermodynamics of these systems strongly depends on the degree of anisotropy. For weakly anisotropic simple cubic lattices, the results indicate the existence of order–disorder phase transitions and a tricritical point, while the possibility of lo...

The ring-current aromaticity of the bicalicene molecule arises, in spite of the 16 π carbon perimeter, from strong local diatropic circulations on the two pentagonal rings, as shown by current-density maps computed at the ipsocentric RHF/6-311G** and DFT/6-311G** levels of theory. Conjugated-circuit models cannot capture this pattern of circulation as it arises from 'ionic' contributions in a v...

Figure S1. Density of states (DOS) for the periodic structures of TiO2 anatase (a), phenyl-acac-TiO2 (b), and 3-acac-pyran-2-one-TiO2 (c), calculated at the extended Hückel level. The filled black lines in (b)-(c) are the projected DOS of the dye chromophores. The blue arrows point to the electronic states with a predominant contribution of HOMO, and the red arrows point to the electronic state...

The irreducible bases in the icosahedral group space are calculated explicitly by reducing the regular representation. The symmetry adapted bases of the system with I or Ih symmetry can be calculated easily and generally by applying those irreducible bases to wavefunctions of the system, if they are not vanishing. As examples, the submatrices of the Hückel Hamiltonians for Carbon-60 and Carbon-...

We study the phase behavior of solutions consisting of positive and negative ions of valence z to which a third ionic species of valence Z > z is added. Using a discretized Debye-Hückel theory, we analyze the phase behavior of such systems for different values of the ratio Z̄ ≡ Z/z. We find, for Z̄ > 1.934, a three-phase coexistence region and, for Z̄ > 2, a closed (reentrant) coexistence loop at ...