arXiv subjects

Stanislav Komorovsky

Publications and source records attributed to Stanislav Komorovsky.

6 recordsLinked to original sources

arXiv2026

Biquaternion Algebra with Bilinear Multiplication: A General, Elegant, and Computationally Advantageous Framework for Relativistic Electronic Structure Calculations on CPUs and GPUs

Quaternion algebra provides a natural representation of time-reversal-symmetric matrix structures in relativistic electronic-structure theory, whereas complementary time-reversal-antisymmetric structures extend this representation to complex quaternions, or biquaternions. Here, we explicitly exploit biquaternion algebra for fundamental objects, including operators, kinetically and magnetically balanced basis functions, and their expectation values, within a unified framework encompassing real, complex, and real quaternion subalgebras as special cases. To realize this framework computationally, we have developed HMATLIB, a biquaternion matrix library implemented within the ReSpect package for pure CPU and hybrid CPU/GPU execution. A key development is a bilinear algorithm for matrix-valued biquaternion multiplication that reduces the number of real matrix--matrix multiplications from 64 to 24 compared with the conventional component-wise approach, while the biquaternion representation effectively doubles the maximum accessible matrix dimension under the same 32-bit indexing constraint. Numerical benchmarks on modern CPU and GPU architectures demonstrate that the biquaternion formulation consistently outperforms its isomorphic complex-algebra counterpart. For the largest matrices reported, hybrid CPU/GPU execution accelerates bilinear matrix multiplication by approximately 5-8 times over pure CPU execution and matrix diagonalization by approximately 12 and 61 times relative to CPU oneAPI MKL and NVHPC OpenBLAS, respectively. These results establish biquaternion algebra as a general and computationally advantageous framework for modern relativistic electronic-structure calculations.

physics.chem-ph↗

arXiv2025

X2C Hamiltonian Models in ReSpect: Bridging Accuracy and Efficiency

Since its inception, the ReSpect program has been evolving to provide powerful tools for simulating spectroscopic processes and exploring emerging research areas, all while incorporating relativistic effects, particularly spin-orbit interactions, in a fully variational manner. Recent developments have focused on exact two-component (X2C) Hamiltonian models that go beyond the standard one-electron X2C approach by incorporating two-electron picture-change corrections. This paper presents the theoretical foundations of two distinct atomic mean-field X2C models, amfX2C and extended eamfX2C, which offer computationally efficient and accurate alternatives to fully relativistic four-component methods. These models enable simulations of complex phenomena, such as time-resolved pump-probe spectroscopies and cavity-modified molecular properties, which would otherwise be computationally prohibitive. ReSpect continues to evolve, providing state-of-the-art quantum chemical methods and post-processing tools, all available free of charge through our website, www.respectprogram.org, to support researchers exploring relativistic effects across various scientific disciplines.

physics.chem-ph↗

arXiv2024

Hyperfine rovibrational states of H$_3^+$ in a weak external magnetic field

Rovibrational energies, wave functions, and Raman transition moments are reported for the lowest-energy states of the H$_3^+$ molecular ion including the magnetic couplings of the proton spins and molecular rotation in the presence of a weak external magnetic field. The rovibrational-hyperfine-Zeeman Hamiltonian matrix is constructed and diagonalized using the rovibrational eigenstates and the proton spin functions. The developed methodology can be used to compute hyperfine-Zeeman effects also for higher-energy rovibrational excitations of H$_3^+$ and other polyatomic molecules. These developments will guide future experiments extending quantum logic spectroscopy to polyatomic systems.

physics.chem-ph↗

arXiv2023

The existence and unambiguity of the principal axis system of the EPR tensors

Although the role of the electron paramagnetic resonance (EPR) g-tensor and hyperfine coupling tensor in the EPR effective spin Hamiltonian is discussed extensively in many textbooks, certain aspects of the theory are missing. In this text we will cover those gaps and thus provide a comprehensive theory about the existence of principal axes of the EPR tensors. However, an important observation is that both g- and a-tensors have two sets of principal axes -- one in the real and one in the fictitious spin space -- and, in fact, are not tensors. Moreover, we present arguments based on the group theory why only eigenvalues of the G-tensor, $\mb{G} = \mb{g}\mb{g}^{\!\mathsf{T}}$, and the sign of the determinant of the g-tensor are observable quantities (an analogical situation also holds for the hyperfine coupling tensor). We keep the number of assumptions to a minimum and thus the theory is applicable in the framework of the Dirac--Coulomb--Breit Hamiltonian and for any spatial symmetry of the system.

quant-ph↗

arXiv2023

Exact two-component TDDFT with simple two-electron picture-change corrections: X-ray absorption spectra near L- and M-edges of four-component quality at two-component cost

X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter with high spatial and elemental sensitivity. However, the theoretical modelling of XAS is a challenging task since XAS spectra feature a fine structure due to scalar (SC) and spin-orbit (SO) relativistic effects, in particular near L and M absorption edges. While full four-component (4c) calculations of XAS are nowadays feasible, there is still interest in developing approximate relativistic methods that enable XAS calculations at the two-component (2c) level while maintaining the accuracy of the parent 4c approach. In this article we present theoretical and numerical insights into two simple yet accurate 2c approaches based on an (extended) atomic mean-field exact two-component Hamiltonian framework, (e)amfX2C, for the calculation of XAS using linear eigenvalue and damped-response time-dependent density functional theory (TDDFT). In contrast to the commonly used one-electron X2C (1eX2C) Hamiltonian, both amfX2C and eamfX2C account for the SC and SO two-electron and exchange-correlation picture-change (PC) effects that arise from the X2C transformation. As we demonstrate on L- and M-edge XAS spectra of transition metal and actinide compounds, the absence of PC corrections in the 1eX2C approximation results in a substantial overestimatation of SO splittings, whereas (e)amfX2C Hamiltonians reproduce all essential spectral features such as shape, position, and SO splitting of the 4c references in excellent agreement, while offering significant computational savings. Therefore, the (e)amfX2C PC correction models presented here constitute reliable relativistic 2c quantum-chemical approaches for modelling XAS.

physics.chem-ph↗

arXiv2016

New quantum number for the many-electron Dirac-Coulomb Hamiltonian

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this work, we examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We show that the square of many-electron operator $\mathcal{K}_+$, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator $\mathcal{K}$, the $\mathcal{K}^2_+$ has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We demonstrate that $\mathcal{K}_+$ is connected to $\mathcal{K}$ through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call $\mathcal{K}_+$ the generator of the many-electron TR symmetry. By diagonalizing the operator $\mathcal{K}^2_+$ in the basis of Kramers-restricted Slater determinants, we introduce the relativistic variant of configuration state functions (CSF), denoted as Kramers CSF. A new quantum number associated with $\mathcal{K}^2_+$ has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree--Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain.

quant-ph↗