arXiv subjects

Rafał Podeszwa

Publications and source records attributed to Rafał Podeszwa.

5 recordsLinked to original sources

arXiv2026

Elimination of angular dependency in the quantum three-body problem made easy

We present a systematic account of the separation of the angular degrees of freedom from the nonrelativistic Schrödinger equation for a three-body quantum system with arbitrary masses, charges, total angular momentum, and parity. The resulting reduced Schrödinger equation (RSE) for the partial-wave components, expressed as functions solely of the interparticle distances, is reported in a compact matrix operator form. The remnants of the angular dependence, essential for the hermiticity of the RSE and consequently the stability of variational computations, appear in the RSE formalism as additional angular factors, derived by expanding minimal bipolar harmonics into a basis of Wigner functions \texorpdfstring{$\mathcal{D}$}{D}. We validate the final form of the RSE by computing accurate energy levels for helium states using an explicitly correlated Hylleraas-type basis. This work serves as a self-contained reference for the RSE formulation, consolidating elements previously scattered throughout the literature, thereby offering a convenient foundation for further analytical and numerical studies of general three-body quantum systems.

physics.atom-ph↗

arXiv2023

ZZPolyCalc: An open-source code with fragment caching for determination of Zhang-Zhang polynomials of carbon nanostructures

Determination of topological invariants of graphene flakes, nanotubes, and fullerenes constitutes a challenging task due to its time-intensive nature and exponential scaling. The invariants can be organized in a form of a combinatorial polynomial commonly known as the Zhang-Zhang (ZZ) polynomial or the Clar covering polynomial. We report here a computer program, ZZPolyCalc, specifically designed to compute ZZ polynomials of large carbon nanostructures. The curse of exponential scaling is avoided for a broad class of nanostructures by employing a sophisticated bookkeeping algorithm, in which each fragment appearing in the recursive decomposition is stored in the cache repository of molecular fragments indexed by a hash of the corresponding adjacency matrix. Although exponential scaling persists for the remaining nanostructures, the computational time is reduced by a few orders of magnitude owing to efficient use of hash-based fragment bookkeeping. The provided benchmark timings show that ZZPolyCalc allows for treating much larger carbon nanostructures than previously envisioned.

physics.comp-ph↗

arXiv2005

Second-order electronic correlation effects in a one-dimensional metal

The Pariser-Parr-Pople (PPP) model of a single-band one-dimensional (1D) metal is studied at the Hartree-Fock level, and by using the second-order perturbation theory of the electronic correlation. The PPP model provides an extension of the Hubbard model by properly accounting for the long-range character of the electron-electron repulsion. Both finite and infinite version of the 1D-metal model are considered within the PPP and Hubbard approximations. Calculated are the second-order electronic-correlation corrections to the total energy, and to the electronic-energy bands. Our results for the PPP model of 1D metal show qualitative similarity to the coupled-cluster results for the 3D electron-gas model. The picture of the 1D-metal model that emerges from the present study provides a support for the hypothesis that the normal metallic state of the 1D metal is different from the ground state.

cond-mat.str-el↗

arXiv2005

Accurate interaction energies from perturbation theory based on Kohn-Sham model

The density-functional based symmetry-adapted perturbation theory [SAPT(DFT)] has been applied to the argon, krypton, and benzene dimers. It is shown that--at a small fraction of computational costs--SAPT(DFT) can provide similar accuracies for the interaction energies as high-level wave-function based methods with extrapolations to the complete basis set limits. This accuracy is significantly higher than that of any other DFT or DFT-based approaches proposed to date.

physics.chem-ph↗

arXiv2002

Multiple solutions of CCD equations for PPP model of benzene

To gain some insight into the structure and physical significance of the multiple solutions to the coupled-cluster doubles (CCD) equations corresponding to the Pariser-Parr-Pople (PPP) model of cyclic polyenes, complete solutions to the CCD equations for the A^{-}_{1g} states of benzene are obtained by means of the homotopy method. By varying the value of the resonance integral beta from -5.0 eV to -0.5 eV, we cover the so-called weakly, moderately, and strongly correlated regimes of the model. For each value of beta 230 CCD solutions are obtained. It turned out, however, that only for a few solutions a correspondence with some physical states can be established. It has also been demonstrated that, unlike for the standard methods of solving CCD equations, some of the multiple solutions to the CCD equations can be attained by means of the iterative process based on Pulay's direct inversion in the iterative subspace (DIIS) approach.

physics.chem-ph↗