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In this work, we propose an efficient and accurate computational method to evaluate the many-potential α(Zα)n≥3 vacuum polarization density of hydrogen-like atoms within the finite-basis approximation of the Dirac equation. To prove the performance of our computational method, we choose to work with the one-electron 23892U atom. In summary, we find that compliance with charge conjugation symmetry is a priori required to obtain physical results that are in line with our knowledge of the analytical problem. We also note that the final numerical results are found to be in excellent agreement with previous formal analytical (and numerical) evaluations that are limited to a few simple nuclear distribution models. Our technique can be efficiently implemented and evaluated in codes that solve the radial Dirac equation in the finite basis set framework and allows the use of arbitrary (radial) nuclear charge distribution. The obtained numerical results of the nonperturbative vacuum polarization density automatically account for the extended nuclear size effect. This method is hence of special importance for atomic Dirac problems whose analytical Green's functions expressions are not at hand or have relatively complicated analytical forms. Furthermore, we propose a vacuum polarization density formula that forces compliance with charge conjugation symmetry and can be used in cases where the relativistic basis violates this symmetry, as is the case in most relativistic basis set programs. In addition, we have shown that vector components of the vacuum polarization four-current vanish in the case where the Dirac Hamiltonian is symmetric under time-reversal symmetry.

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A method for highly accurate calculations of atomic electric quadrupole moments (EQM) is presented, using relativistic general-excitation-rank configuration interaction wave functions based on Dirac spinors. Application to the clock transition states of the thulium atom employing up to full Quadruple excitations for the atomic wave function yields a final value of Qzz(2F7/2)=0.07+0.07−0.00 a.u., establishing that the thulium electronic ground state has an exceptionally small EQM. A detailed analysis of this result is presented which has implications for EQMs of other atoms with unpaired f electrons.

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In this study, we present a complete set of electron scattering cross-sections from 1-Methyl-5-Nitroimidazole (1M5NI) molecules for impact energies ranging from 0.1 to 1000 eV. This information is relevant to evaluate the potential role of 1M5NI as a molecular radiosensitizers. The total electron scattering cross-sections (TCS) that we previously measured with a magnetically confined electron transmission apparatus were considered as the reference values for the present analysis. Elastic scattering cross-sections were calculated by means of two different schemes: The Schwinger multichannel (SMC) method for the lower energies (below 15 eV) and the independent atom model-based screening-corrected additivity rule with interferences (IAM-SCARI) for higher energies (above 15 eV). The latter was also applied to calculate the total ionization cross-sections, which were complemented with experimental values of the induced cationic fragmentation by electron impact. Double differential ionization cross-sections were measured with a reaction microscope multi-particle coincidence spectrometer. Using a momentum imaging spectrometer, direct measurements of the anion fragment yields and kinetic energies by the dissociative electron attachment are also presented. Cross-sections for the other inelastic channels were derived with a self-consistent procedure by sampling their values at a given energy to ensure that the sum of the cross-sections of all the scattering processes available at that energy coincides with the corresponding TCS. This cross-section data set is ready to be used for modelling electron-induced radiation damage at the molecular level to biologically relevant media containing 1M5NI as a potential radiosensitizer. Nonetheless, a proper evaluation of its radiosensitizing effects would require further radiobiological experiments.

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We introduce \textsc{qcmath}, a user-friendly quantum chemistry software tailored for electronic structure calculations, implemented using the Wolfram Mathematica language and available at \url{}. This software, designed with accessibility in mind, takes advantage of the symbolic capabilities intrinsic to Mathematica. Its primary goal is to provide a supportive environment for newcomers to the field of quantum chemistry, enabling them to easily conceptualize, develop, and test their own ideas. The functionalities of \textsc{qcmath} encompass a broad spectrum of methods, catering to both ground- and excited-state calculations. We provide a comprehensive overview of these capabilities, complemented by essential theoretical insights. To facilitate ease of use, we offer an exhaustive blueprint of the software's architecture. Furthermore, we provide users with comprehensive guides, addressing both the operational aspects and the more intricate programming facets of \textsc{qcmath}.

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Hierarchy configuration interaction (hCI) has been recently introduced as an alternative configuration interaction (CI) route combining excitation degree and seniority number, which showed to efficiently recover both dynamic and static correlations for closed-shell molecular systems [\href{}{\textit{J.~Phys.~Chem.~Lett.}~\textbf{2022}, \textit{13}, 4342}]. Here, we generalize hCI for an arbitrary reference determinant, allowing calculations for radicals and for excited states in a state-specific way. We gauge this route against excitation-based CI (eCI) and seniority-based CI (sCI) by evaluating how different ground-state properties of radicals converge to the full CI limit. We find that hCI outperforms or matches eCI, whereas sCI is far less accurate, in line with previous observations for closed-shell molecules. Employing the second-order Epstein-Nesbet perturbation theory as a correction significantly accelerates the convergence of hCI and eCI. We further explore various hCI and sCI models to calculate excitation energies of closed- and open-shell systems. Our results underline that both the choice of the reference determinant and the set of orbitals drive the fine balance between correlation of ground and excited states. State-specific hCI2 and higher order models perform similarly to their eCI counterparts, whereas lower orders of hCI deliver poor results. In turn, sCI1 produces decent excitation energies for radicals, encouraging the development of related seniority-based coupled cluster methods.

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Electron correlation Density functional theory Basis sets Relativistic quantum chemistry Dispersion coefficients Quantum Monte Carlo ALGORITHM 3315Fm Atomic processes Argile Configuration interaction CP violation Chimie quantique BIOMOLECULAR HOMOCHIRALITY Configuration Interaction Ground states 3115bw Valence bond 3115ag AROMATIC-MOLECULES Polarizabilities Numerical calculations A posteriori Localization Ab initio calculation Brown dwarfs Ion Coupled cluster Carbon Nanotubes 3115aj AB-INITIO CALCULATION Béryllium Azide Anion Atrazine Single-core optimization Diffusion Monte Carlo Quantum Chemistry 3115vj CP Violation Parity violation 3470+e 3115am Wave functions Atomic and molecular structure and dynamics 3115ae Diatomic molecules Quantum chemistry Biodegradation Pesticides Metabolites Clustering Molecular modeling Environmental fate Partial least squares COMPUTATION Dipole Electron electric moment BSM physics Hyperfine structure Auto-énergie Pesticide Coupled cluster calculations Large systems Perturbation theory BENZENE MOLECULE Line formation CIPSI Xenon Corrélation électronique Relativistic corrections Dirac equation Abiotic degradation Boys Anderson mechanism A priori Localization Petascale Range separation CHEMICAL-SHIFTS Argon Time reversal violation Parallel speedup Excited states États excités Molecular properties Electron electric dipole moment Benchmarks Aimantation Molecular descriptors Benzene Atoms 3115vn Acrolein Atomic data Atrazine-cations complexes QSAR Time-dependent density-functional theory Spin-orbit interactions Configuration interactions Analytic gradient New physics Relativistic quantum mechanics Mécanique quantique relativiste Atom Beyond Standard Model AB-INITIO CLUSTERS


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