arXiv subjects

Michał Lesiuk

Publications and source records attributed to Michał Lesiuk.

At least 19 recordsLinked to original sources

arXiv2026

Uncertainty prediction in composite quantum chemistry approaches

In this work, we consider the problem of uncertainty estimation of the results obtained through theoretical calculations using a composite quantum chemistry scheme. Each component of the composite scheme carries its own individual uncertainty, originating principally from a finite size of the basis set used in the calculations. Of practical interest is the total uncertainty, i.e. the uncertainty of the sum of all components. We first show that the conventional error propagation rules that treat each component as a statistically uncorrelated variable are not well-justified in practice. To remedy this, we propose a method of estimating the total uncertainty of the composite scheme which does not rely on the assumption that the components are independent. It is formulated as a series of random walks with different starting values that represent the uncertainty of each component of the composite scheme. This method is first applied to two example composite schemes for the water dimer and the nitrogen molecule that illustrate its most salient features and allow for a deeper analysis. Next, the method is tested for a larger set of interaction energies from the S66 dataset for which trustworthy reference data are available and the error can be assessed unambiguously. It is shown that the method provides reliable and reasonably tight uncertainty estimates at an arbitrary predefined confidence level required in a given application. While the focus of the paper is on composite schemes, we believe that the general idea can be useful more broadly in computational chemistry and physics.

physics.chem-ph↗

arXiv2026

Determination of fundamental properties of nitrogen from first principles. I. Atomic polarizabilities and long-range dispersion coefficients

This work is the first in a series of papers in which we perform theoretical calculations of various fundamental properties of nitrogen relevant for gas thermometry experiments. In this part we focus on the properties of nitrogen atom, namely dynamic polarizabilities and dispersion coefficients that describe interaction between two nitrogen atoms at large internuclear separations. These quantities are calculated using a composite scheme based on coupled cluster and full configuration interaction methods and large Gaussian basis sets optimized specifically for the purposes of this work. The dispersion coefficients, $C_n$ with $n=6,8,10$, are obtained using Casimir--Polder formulas by numerical integration over dipole, quadrupole, and octuple polarizabilities for imaginary frequencies represented analytically by Padé approximants. Special attention is paid to careful error control and uncertainty estimation of the calculated quantities.

physics.chem-ph↗

arXiv2026

Determination of fundamental properties of nitrogen from first principles. II. Potential energy curve and spectroscopic properties of N$_2$

This work is the second part of the series devoted to first-principles determination of the fundamental properties of nitrogen. In this part, we calculate the potential energy curve for the electronic ground state of N$_2$. The potential is divided into three components: short-, medium-, and long-range, and a different computational protocol is applied to each component, based on a composite coupled cluster approach, genuine multireference methods, and asymptotic expansion of the interaction energy. A particular focus is on the short-range part, as the accuracy of this component is critical from the point of view of metrological applications, including the temperature dependence of many properties of nitrogen gas. Uncertainties of the theoretical data, originating both from basis set incompleteness and applied theoretical method, are rigorously analyzed and provided at $2σ$ level, i.e. expanded ($k=2$) uncertainties. The developed potential energy curve is used to calculate the spectroscopic parameters of the N$_2$ ground state and the results are compared with the available theoretical and experimental data.

physics.chem-ph↗

arXiv2026

Determination of fundamental properties of nitrogen from first principles. III. Temperature and frequency dependence of the molecular polarizability and magnetic susceptibility

This work is the third part of the series of papers that focus on the theoretical determination of the properties of nitrogen that are relevant in metrology. Here we present first-principles calculations of the temperature and frequency dependence of the molecular polarizability and magnetic susceptibility of the nitrogen molecule (N$_2$). The purely electronic contributions to the static polarizability, Cauchy coefficients (up to sixth order), and isotropic magnetic susceptibility are computed over a range of internuclear distances using a robust composite scheme combining several electronic structure methods. The temperature dependence, evaluated from $50$~K to $2000$~K, is determined using two independent methods: rovibrational averaging and path integral Monte Carlo (PIMC). The polarizabilities obtained from theory agree with the recent high-precision thermometry measurements, wherever the latter are available, but are significantly less accurate. However, the main usefulness of the theoretical data revolves around combining it with the available experimental results to generate semi-empirical estimates of various quantities that have never been measured thus far. As an example, we determine highly accurate semi-empirical estimates of the static polarizability at key reference temperatures, $α_0(T)=11.735\,962$~a.u.\ at $T=303$~K and $α_0(T)=11.735\,585$~a.u.\ at $T=273.16$~K. Furthermore, we report theoretical values for the magnetic susceptibility, highlighting the importance of the paramagnetic contribution, and address a significant discrepancy with the experimental data for this quantity.

physics.chem-ph↗

arXiv2026

On the effective rank of canonical polyadic decomposition of electron repulsion integrals

In this paper, we study the effective rank of the canonical polyadic decomposition applied to the electron repulsion integrals, ubiquitous in quantum chemistry. We demonstrate, both mathematically and numerically, that in general the effective rank of this decomposition cannot grow linearly as a function of the system size. Moreover, we derive a lower bound for the effective rank in the form $\propto N_{\mathrm{AO}}^2/\log_2^7 N_{\mathrm{AO}}$, where $N_{\mathrm{AO}}$ is the number of atomic orbitals in the molecule, under mild conditions imposed on the decomposition threshold $ε$. As a result, while a subquadratic growth of the CPD rank is not excluded, a linear relationship between the rank and $N_{\mathrm{AO}}$ cannot hold universally. The implications of these findings for the use of the canonical polyadic format to represent electron repulsion integrals in quantum chemistry are analyzed.

physics.chem-ph↗

arXiv2025

Rank-reduced equation-of-motion coupled cluster formalism with full inclusion of triple excitations

In this work we describe the rank-reduced variant of the equation-of-motion coupled cluster theory with complete inclusion of single, double, and triple excitations. The advantage of the proposed formalism in comparison with the canonical theory stems from the application of Tucker decomposition format to the ground- and excited-states triply-excited amplitudes tensors. By exploiting the linear scaling of the dimension of the decomposed amplitudes with respect to the system size $N$, one can reduce the computational cost of the method to the level of $N^6$ and storage requirements to $N^4$. While in practice the proposed rank-reduced formalism introduces an error, we show that it is several times smaller than the inherent error of the parent theory with the proposed default settings for a wide range of problems. Higher level of accuracy can be achieved by increasing the value of a single parameter present in this formulation, recovering the canonical method in an appropriate limit. We illustrate the accuracy and performance of the proposed method by calculations for a group of molecules with excited states of different character -- from dominated by single excitations with respect to the reference determinant to states with moderate and large contribution of double and higher excitations. We report calculations of potential energy curves and related spectroscopic parameters for the first four singlet excited states of magnesium dimer, as well as the potential energy curve for the excited state of charge-transfer character in the NH$_3$-F$_2$ complex as a function of intermolecular separation.

physics.chem-ph↗

arXiv2025

Estimating complete basis set extrapolation error through random walk

We propose a method of estimating the uncertainty of a result obtained through extrapolation to the complete basis set limit. The method is based on an ensemble of random walks which simulate all possible extrapolation outcomes that could have been obtained if results from larger basis sets had been available. The results assembled from a large collection of random walks can be then analyzed statistically, providing a route for uncertainty prediction at a confidence level required in a particular application. The method is free of empirical parameters and compatible with any extrapolation scheme. The proposed technique is tested in a series of numerical trials by comparing the determined confidence intervals with reliable reference data. We demonstrate that the predicted error bounds are reliable, tight, yet conservative at the same time.

physics.data-an↗

arXiv2025

Complete Active Space Iterative Coupled Cluster Theory

In this work, we investigate the possibility of improving multireference-driven coupled cluster (CC) approaches with an algorithm that iteratively combines complete active space (CAS) calculations with tailored CC and externally corrected CC. This is accomplished by establishing a feedback loop between the CC and CAS parts of a calculation through similarity transformation of the Hamiltonian with those CC amplitudes that are not encompassed by the active space. We denote this approach the complete active space iterative coupled cluster (CASiCC) ansatz. We investigate its efficiency and accuracy in the singles and doubles approximation by studying the prototypical molecules H4, H8, H2O, and N2. Our results demonstrate that CASiCC systematically improves on the single-reference CCSD and the ecCCSD methods across entire potential energy curves, while retaining modest computational costs. However, the tailored coupled cluster method shows superior performance in the strong correlation regime suggesting that its accuracy is based on error compensation. We find that the iterative version of externally corrected and tailored coupled cluster methods converge to the same results.

physics.chem-ph↗

arXiv2025

Another Angle on Benchmarking Noncovalent Interactions

For noncovalent interactions (NCIs), the CCSD(T) coupled cluster method is widely regarded as the `gold standard'. With localized orbital approximations, benchmarks for ever larger NCI complexes are being published; yet tantalizing evidence from quantum Monte Carlo (QMC) results appears to indicate that as the system size grows, CCSD(T) overbinds NCIs by progressively larger amounts, particularly when $π$-stacking is involved. Alas, post-CCSD(T) methods like CCSDT(Q) are cost-prohibitive, which requires us to consider alternative means of estimating post-CCSD(T) contributions. In this work, we take a step back by considering the evolution of the correlation energy with respect to the number of subunits for such $π$-stacked sequences as acene dimers and alkadiene dimers. We show it to be almost perfectly linear, and propose the slope of the line as a probe for the behavior of a given electron correlation method. By comparison with rank-reduced CCSDT(Q) results for benzene and naphthalene dimers, we show that while CCSD(T) does slightly overbind, it does not at the level suggested by the QMC results.

physics.chem-ph↗

arXiv2025

Non-iterative Triples for Transcorrelated Coupled Cluster Theory

We present an implementation of a perturbative triples correction for the coupled cluster ansatz including single and double excitations based on the transcorrelated Hamiltonian. Transcorrelation introduces explicit electron correlation in the electronic Hamiltonian through similarity transformation with a correlation factor. Due to this transformation, the transcorrelated Hamiltonian includes up to three-body couplings and becomes non-Hermitian. Since the conventional coupled cluster equations are solved by projection, it is well suited to harbor non-Hermitian Hamiltonians. The arising three-body operator, however, creates a huge memory bottleneck and increases the runtime scaling of the coupled cluster equations. As it has been shown that the three-body operator can be approximated, by expressing the Hamiltonian in the normal-ordered form, we investigate this approximation for the perturbative triples correction. Results are compared with a code-generation based transcorrelated coupled cluster implementation up to quadruple excitations.

physics.chem-ph↗

arXiv2024

Signatures of supermassive charged gravitinos in liquid scintillator detectors

In a previous work [K.A. Meissner and H. Nicolai, Eur. Phys. J. C {\bf 84}, 269 (2024)], two of the present authors have suggested possible experimental ways to search for stable supermassive particles with electric charges of $\cO(1)$ in upcoming underground experiments, in particular the new Jiangmen Underground Neutrino Observatory (JUNO) experiment. In the current paper, we present a detailed analysis of the specific signature of such gravitino-induced events for the JUNO detector and for upcoming liquid argon detectors like DUNE (Deep Underground Neutrino Experiment). The proposed method of detection relies on the ``glow'' produced by photons during the passage of such particles through the detector liquid, which would last for about a few to a few hundred microseconds depending on its velocity and the track. The cross sections for electronic excitation of the main component of the scintillator liquid, namely linear alkylbenzene (LAB), by the passing gravitino are evaluated using quantum-chemical methods. The results show that, if such particles exist, the resulting signals would lead to a unique and unmistakable signature, for which we present event simulations as they would be seen by the JUNO or DUNE photomultipliers. Our analysis brings together two very different research areas, namely fundamental particles physics and the search for a fundamental theory on the one hand, and methods of advanced quantum chemistry on the other.

hep-ph↗

arXiv2024

Rank-reduced equation-of-motion coupled cluster triples: an accurate and affordable way of calculating electronic excitation energies

In the present work we report an implementation of the rank-reduced equation-of-motion coupled cluster method with approximate triple excitations (RR-EOM-CC3). The proposed variant relies on tensor decomposition techniques in order to alleviate the high cost of computing and manipulating the triply-excited amplitudes. In the RR-EOM-CC3 method, both ground-state and excited-state triple-excitation amplitudes are compressed according to the Tucker-3 format. This enables to factorize the working equations such that the formal scaling of the method is reduced to $N^6$, where $N$ is the system size. An additional advantage of our method is the fact the accuracy can be strictly controlled by proper choice of two parameters defining sizes of triple-excitation subspaces in the Tucker decomposition for the ground and excited states. Optimal strategies of selecting these parameters are discussed. The developed method has been tested in a series of calculations of electronic excitation energies and compared to its canonical EOM-CC3 counterpart. Errors several times smaller than the inherent error of the canonical EOM-CC3 method (in comparison to FCI) are straightforward to achieve. This conclusion holds both for valence states dominated by single excitations and for states with pronounced doubly-excited character. Taking advantage of the decreased scaling, we demonstrate substantial computational costs reductions (in comparison with the canonical EOM-CC3) in the case of two large molecules -- L-proline and heptazine. This illustrates the usefulness of the RR-EOM-CC3 method for accurate determination of excitation energies of large molecules.

physics.chem-ph↗

arXiv2023

Relativistic treatment of diamagnetic susceptibility of helium

We report theoretical calculations of the diamagnetic susceptibility, $χ_0$, of helium atom. We determined the complete relativistic correction to $χ_0$ of the order of $α^4$, where $α$ is the fine structure constant, by including all $α^4$ terms originating from the Dirac and Breit equations for a helium atom in a static magnetic field. Finite nuclear mass corrections to $χ_0$ was also evaluated. To obtain very accurate results and reliable uncertainty estimates we used a sequence of explicitly correlated basis sets of fully optimized Slater geminals. We found that $χ_0=-2.119\,106(34)\cdot10^{-5}$ $a_0^3$ and $χ_0=-2.119\,400(34)\cdot10^{-5}$ $a_0^3$ for $^4$He and $^3$He isotopes, respectively, where $a_0$ is the Bohr radius and the uncertainties shown in the parentheses are due entirely to the very conservative estimate of the neglected QED corrections of the order of $α^5$. Our results are compared with the available experimental data and with previous, incomplete theoretical determinations of the $α^4$ contributions to the diamagnetic susceptibility of helium.

physics.atom-ph↗

arXiv2023

Atomic Bethe logarithm in the mean-field approximation

In this work we develop and implement a method for calculation of the Bethe logarithm for many-electron atoms. This quantity is required to evaluate the leading-order quantum electrodynamics correction to the energy and properties of atomic and molecular systems beyond the Dirac theory (the Lamb shift). The proposed formalism is based on the mean-field representation of the ground-state electronic wavefunction and of the response functions required in the Schwartz method [C. Schwartz, Phys. Rev. {\bf 123}, 1700 (1961)]. We discuss difficulties encountered in the calculations with the emphasis on the specific basis set requirements in the vicinity of the atomic nucleus. This problem is circumvented by introducing a modified basis set of exponential functions which are able to accurately represent the gradient of hydrogen-like orbitals. The Bethe logarithm is computed for ground electronic states of atoms from hydrogen to magnesium and, additionally, for argon. Whenever possible, the results are compared with the available reference data from the literature. In general, the mean-field approximation introduces a surprisingly small error in the calculated values, suggesting that the electron correlation effects are of minor importance in determination of the Bethe logarithm. Finally, we propose a robust scheme to evaluate the Lamb shift for arbitrary light molecular systems at little computational cost. As an illustration, the method is used to calculate Lamb shifts of the vibrational levels of the nitrogen molecule.

physics.atom-ph↗

arXiv2023

Diamagnetic susceptibility of neon and argon including leading relativistic effects

We report theoretical calculations of the static diamagnetic susceptibility, $χ_0$, of neon and argon atoms. The calculations were performed using a hierarchy coupled-cluster methods combined with application of both the Gaussian and Slater orbital basis sets. We included the complete relativistic correction of order of $α^4$, where $α$ is the fine structure constant, and obtained an estimate of the quantum electrodynamics (QED) contributions. The finite nuclear mass and size corrections were also considered but are found to be small. The final results are $χ_0=-8.4786(7)\cdot10^{-5}$ $a_0^3$ for the neon and $χ_0=-22.9545(32)\cdot10^{-5}$ $a_0^3$ for the argon atom, where $a_0$ is the Bohr radius. The uncertainties in the last digits, shown in the parentheses, are primarily due to the errors in the non-relativistic electronic wavefunction, as well as due to the neglected quantum electrodynamics corrections.

physics.atom-ph↗

arXiv2023

First-principles calculation of the frequency-dependent dipole polarizability of argon

In this work we report state-of-the-art theoretical calculations of the dipole polarizability of the argon atom. Frequency dependence of the polarizability is taken into account by means of the dispersion coefficients (Cauchy coefficients) which is sufficient for experimentally relevant wavelengths below the first resonant frequency. In the proposed theoretical framework, all known physical effects including the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size corrections are accounted for. We obtained $α_0=11.0763(19)$ for the static polarizability and $α_2=27.976(15)$ and $α_4=95.02(11)$ for the second and fourth dispersion coefficients, respectively. The result obtained for the static polarizability agrees (within the estimated uncertainty) with the most recent experimental data [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)], but is less accurate. The dispersion coefficients determined in this work appear to be most accurate in the literature, improving by more than an order of magnitude upon previous estimates. By combining the experimentally determined value of the static polarizability with the dispersion coefficients from our calculations, the polarizability of argon can be calculated with accuracy of around $10\,$ppm for wavelengths above roughly $450\,$nm. This result is important from the point of view of quantum metrology, especially for a new pressure standard based on thermophysical properties of gaseous argon. Additionally, in this work we calculate the static magnetic susceptibility of argon which relates the refractive index of dilute argon gas with its pressure. While our results for this quantity are less accurate than in the case of the polarizability, they can provide, via Lorenz-Lorentz formula, the best available theoretical estimate of the refractive index of argon.

physics.chem-ph↗

arXiv2022

When gold is not enough: platinum standard of quantum chemistry with $N^7$ cost

In this paper we extend the rank-reduced coupled-cluster formalism to the calculation of non-iterative energy corrections due to quadruple excitations. There are two major components of the proposed formalism. The first is an approximate compression of the quadruple excitation amplitudes using the Tucker format. The second is a modified functional used for evaluation of the corrections which gives exactly the same results for the exact amplitudes, but is less susceptible to errors resulting from the aforementioned compression. We show, both theoretically and numerically, that the computational cost of the proposed method scales as the seventh power of the system size. Using reference results for a set of small molecules, the method is calibrated to deliver relative accuracy of a few percent in energy corrections. To illustrate the potential of the theory we calculate the isomerization energy of \emph{ortho}/\emph{meta} benzyne (C$_6$H$_4$) and the barrier height for the Cope rearrangement in bullvalene (C$_{10}$H$_{10}$). The method retains a near-black-box nature of the conventional coupled-cluster formalism and depends on only one additional parameter that controls the accuracy.

physics.chem-ph↗

arXiv2022

Explicitly correlated electronic structure calculations with transcorrelated matrix product operators

In this work, we present the first implementation of the transcorrelated electronic Hamiltonian in an optimization procedure for matrix product states by the density matrix renormalization group (DMRG) algorithm. In the transcorrelation ansatz, the electronic Hamiltonian is similarity-transformed with a Jastrow factor to describe the cusp in the wave function at electron-electron coalescence. As a result, the wave function is easier to approximate accurately with the conventional expansion in terms of one-particle basis functions and Slater determinants. The transcorrelated Hamiltonian in first quantization comprises up to three-body interactions, which we deal with in the standard way by applying robust density fitting to two- and three-body integrals entering the second-quantized representation of this Hamiltonian. The lack of hermiticity of the transcorrelated Hamiltonian is taken care of along the lines of the first work on transcorrelated DMRG [J. Chem. Phys. 153, 164115 (2020)] by encoding it as a matrix product operator and optimizing the corresponding ground state wave function with imaginary-time time-dependent DMRG. We demonstrate our quantum chemical transcorrelated DMRG approach at the example of several atoms and first-row diatomic molecules. We show that transcorrelation improves the convergence rate to the complete basis set limit in comparison to conventional DMRG. Moreover, we study extensions of our approach that aim at reducing the cost of handling the matrix product operator representation of the transcorrelated Hamiltonian.

physics.chem-ph↗