arXiv subjects

Jakub Lang

Publications and source records attributed to Jakub Lang.

13 recordsLinked to original sources

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 Pad\'e 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 $2\sigma$ 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, $\alpha_0(T)=11.735\,962$~a.u.\ at $T=303$~K and $\alpha_0(T)=11.735\,585$~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↗

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↗

arXiv2024

Path-integral calculation of the third dielectric virial coefficient of helium based on ab initio three-body polarizability and dipole surfaces

We develop a surface for the electric dipole moment of three interacting helium atoms and use it, together with state-of-the-art potential and polarizability surfaces, to compute the third dielectric virial coefficient, $C_\varepsilon$, for both $^4$He and $^3$He isotopes. Our results agree with previously published data computed using an approximated form for the three-body polarizability, and are extended to the low-temperature regime by including exchange effects. Additionally, the uncertainty of $C_\varepsilon$ is rigorously determined for the first time by propagating the uncertainties of the potential and polarizability surfaces; this uncertainty is much larger than the contribution from the dipole-moment surface to $C_\varepsilon$. Our results compare reasonably well with the limited experimental data. The first-principles values of $C_ε$ computed in this work will enhance the accuracy of primary temperature and pressure metrology based on measurements of the dielectric constant of helium.

physics.chem-ph↗

arXiv2024

Thermophysical properties of argon gas from improved two-body interaction potential

A new ab initio interaction potential for the electronic ground state of the argon dimer has been developed. The new potential uses previously calculated accurate Born--Oppenheimer potential while significantly improving the description of relativistic effects by including the two-electron Darwin and orbit-orbit corrections. Moreover, retardation of the electromagnetic interactions is taken into account in the long-range part of the potential and leading-order quantum electrodynamics correction is calculated. Spectroscopic properties of the argon dimer such as positions of vibrational levels, bond-dissociation energy, and rotational and centrifugal-distortion constants are reported. We show that the inclusion of the two-electron relativistic terms results in a destabilization of the previously discovered weakly bound ninth vibrational state. Finally, thermophysical properties of the argon gas including pressure and acoustic virial coefficients, as well as transport properties -- viscosity and thermal conductivity -- are evaluated using the new potential. For the thermophysical properties, the obtained ab initio values are somewhat less accurate than the most recent experimental results. However, the opposite is true for the transport properties, where the theoretical results calculated in this work have significantly smaller uncertainties than the data derived from measurements.

physics.chem-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

Three-body potential and third virial coefficients for helium including relativistic and nuclear-motion effects

The non-additive three-body interaction potential for helium was computed using the coupled-cluster theory and the full configuration interaction method. The obtained potential comprises an improved nonrelativistic Born--Oppenheimer energy and the leading relativistic and nuclear-motion corrections. The mean absolute uncertainty of our calculations due to the incompleteness of the orbital basis set was determined employing complete-basis-set extrapolation techniques and was found to be 1.2%. For three helium atoms forming an equilateral triangle with the side length of 5.6~bohr our three-body potential amounts to $-$90.6~mK, with an estimated uncertainty of 0.5~mK. An analytic function, developed to accurately fit the computed three-body interaction energies, was chosen to correctly describe the asymptotic behavior of the three-body potential for trimer configurations corresponding to both the three-atomic and the atom-diatom fragmentation channels. For large triangles with sides $r_{12}$, $r_{23}$, and $r_{31}$, the potential takes correctly into account all angular terms decaying as $r_{12}^{-l} r_{23}^{-m} r_{31}^{-n}$ with $l+m+n \le 14$ for the nonrelativistic Born--Oppenheimer energy and $l+m+n \le 9$ for the post-Born--Oppenheimer corrections. We also developed a short-range analytic function describing the local behavior of the total uncertainty of the computed three-body interaction energies. Using both fits we calculated the third pressure and acoustic virial coefficients for helium and their uncertainties for a wide range of temperatures. The results of these calculations were compared with available experimental data and with previous theoretical determinations. The estimated uncertainties of present calculations are 3-5 times smaller than those reported in the best previous work.

physics.chem-ph↗

arXiv2023

Hilbert space multireference coupled clusters tailored by matrix product states

The DMRG method, despite its favorable scaling, it is in practice not suitable for computations of dynamic correlation. Several approaches to include that in post-DMRG methods exist; in our group we focused on the tailored-CC (TCC) approach. This method works well in many situations, however, in exactly degenerate cases (with two or more determinants of equal weight), it exhibits a bias towards the reference determinant representing the Fermi vacuum. Although in some cases it is possible to use a compensation scheme to avoid this bias for energy differences, as we did in a previous work on the singlet-triplet gap in the tetramethylenethane (TME) molecule, it is certainly a drawback. In order to overcome the single-reference bias of the TCC method, we have developed a Hilbert-space multireference version of tailored CC, which can treat several determinants on an equal footing. We have employed a multireference analysis of the DMRG wave function in the matrix product state form to get the active amplitudes for each reference determinant and their constant contribution to the effective Hamiltonian. We have implemented and compared the performance of three Hilbert-space MRCC variants - the state universal one, and the Brillouin-Wigner and Mukherjee's state specific ones. We have assessed these approaches on the cyclobutadiene and tetramethylenethane (TME) molecules, which are both diradicals with exactly degenerate determinants at a certain geometry. Two DMRG active spaces have been selected based on orbital entropies, while the MRCC active space comprised the HOMO and LUMO orbitals needed for description of the diradical. We have also investigated the sensitivity of the results on orbital rotation of the HOMO-LUMO pair, as it is well known that Hilbert-space MRCC methods are not invariant to such transformations.

physics.chem-ph↗

arXiv2022

Collision-induced three-body polarizability of helium

We present first-principles theoretical determination of the three-body polarizability and the third dielectric virial coefficient of helium. Coupled-cluster theory and the full configuration interaction procedure were used to perform required electronic structure calculations. The mean absolute relative uncertainty of the trace of the three-body polarizability tensor, resulting from the incompleteness of orbital basis set, was determined using extrapolation techniques. Additional uncertainty due to approximate treatment of triple and the neglect of higher excitations was estimated using full configuration interaction calculations. An analytic function was developed to describe the behavior of the polarizability and its asymptotic decay to three-atomic and atom-diatom fragmentation channels. We also developed an analytic function describing the local behavior of the total uncertainty of our calculations. Using both fits we calculated the third dielectric virial coefficient and its uncertainty using the classical and semiclassical Feynman-Hibbs approaches. The results of our calculations were compared with available experimental data and with recent Path-Integral Monte Carlo (PIMC) calculations employing the so-called superposition approximation of the three-body polarizability. For temperatures above 200 K we observed significant discrepancy between the classical results obtained using either the superposition approximation or the ab initio computed polarizability. The theoretical data reported in this work eliminate the main accuracy bottleneck of the development of optical pressure standard and are expected to facilitate further progress in the field of quantum thermal metrology

physics.chem-ph↗

arXiv2020

Ground State of the Fe(II)-porphyrin Model System Corresponds to the Quintet State: A DFT and DMRG-based Tailored CC Study

Fe(II)-porphyrins (FeP) play an important role in many reactions relevant to material science and biological processes, due to their closely lying spin states. However, this small energetic separation also makes it challenging to establish the correct spin state ordering. Although the prevalent opinion is that these systems posses the triplet ground state, the recent experiment on Fe(II)-phthalocyanine under conditions matching those of an isolated molecule points toward the quintet ground state. We present a thorough study of FeP model by means of the density functional theory and density matrix renormalization group based tailored coupled clusters, in which we address all previously discussed correlation effects. We examine the importance of geometrical parameters, the Fe-N distances in particular, and conclude that the system possesses the quintet ground state, which is in our calculations well-separated from the triplet state.

physics.chem-ph↗

arXiv2020

Near-linear Scaling in DMRG-based Tailored Coupled Clusters: An Implementation of DLPNO-TCCSD and DLPNO-TCCSD(T)

We present a new implementation of DMRG-based tailored coupled clusters method (TCCSD), which employs the domain-based local pair natural orbital approach (DLPNO-TCCSD). Compared to the previous LPNO version of the method, the new implementation is more accurate, offers more favorable scaling and provides more consistent behavior across the variety of systems. On top of the singles and doubles, we include the perturbative triples correction (T), which is able to retrieve even more dynamic correlation. The methods were tested on three systems: tetramethyleneethane, oxo-Mn(Salen) and Iron(II)-porphyrin model. The first two were revisited to assess the performance with respect to LPNO-TCCSD. For oxo-Mn(Salen), we retrieved between 99.8-99.9% of the total canonical correlation energy which is the improvement of 0.2% over the LPNO version in less than 63% of the total LPNO runtime. Similar results were obtained for Iron(II)-porphyrin. When the perturbative triples correction was employed, irrespective of the active space size or system, the obtained energy differences between two spin states were within the chemical accuracy of 1 kcal/mol using the default DLPNO settings.

physics.chem-ph↗