arXiv subjects

Michał Lesiuk

Publications and source records attributed to Michał Lesiuk.

At least 37 records · Page 2Linked to original sources

arXiv2022

A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation

A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrödinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one- or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from $5 \times 10^{13}\:\rm W/cm^2$ to $5 \times 10^{14}\:\rm W/cm^2$. We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.

physics.chem-ph↗

arXiv2022

Quintic-scaling rank-reduced coupled cluster theory with single and double excitations

We consider the rank-reduced coupled-cluster theory with single and double excitations (RR-CCSD) introduced recently [Parrish \emph{et al.}, J. Chem. Phys. {\bf 150}, 164118 (2019)]. The main feature of this method is the decomposed form of the doubly-excited amplitudes which are expanded in the basis of largest magnitude eigenvectors of the MP2 or MP3 amplitudes. This approach enables a substantial compression of the amplitudes with only minor loss of accuracy. However, the formal scaling of the computational costs with the system size ($N$) is unaffected in comparison with the conventional CCSD theory ($\propto N^6$) due to presence of some terms quadratic in the amplitudes. We show how to solve this problem, exploiting the fact that their effective rank increases only linearly with the system size and reduce the scaling of the RR-CCSD iterations down to the level of $N^5$. This is combined with an iterative method of finding dominant eigenpairs of the MP2 or MP3 amplitudes which eliminates the necessity to perform the complete diagonalization. Next, we consider the evaluation of the perturbative corrections to the CCSD energies resulting from triply excited configurations. The triply-excited amplitudes present in the CCSD(T) method are decomposed to the Tucker-3 format using the higher-order orthogonal iteration (HOOI) procedure. This enables to compute the energy correction due to triple excitations non-iteratively with $N^6$ cost. The accuracy of the resulting rank-reduced CCSD(T) method is studied both for total and relative correlation energies of a diverse set of molecules. Accuracy levels better than 99.9\% can be achieved with a substantial reduction of the computational costs. Concerning the computational timings, break-even point between the rank-reduced and conventional CCSD implementations occurs for systems with about $30-40$ active electrons.

physics.chem-ph↗

arXiv2022

Near-exact CCSDT energetics from rank-reduced formalism supplemented by non-iterative corrections

We introduce a non-iterative energy correction, added on top of the rank-reduced coupled-cluster method with single, double, and triple substitutions, that accounts for excitations excluded from the parent triple excitation subspace. The formula for the correction is derived by employing the coupled-cluster Lagrangian formalism with an additional assumption that the parent excitation subspace is closed under the action of the Fock operator. Owning to the rank-reduced form of the triple excitation amplitudes tensor, the computational cost of evaluating the correction scales as $N^7$ with the system size, $N$. The accuracy and computational efficiency of the proposed method is assessed both for total and relative correlation energies. We show that the non-iterative correction can fulfill two separate roles. If an accuracy level of a fraction of kJ/mol is sufficient for a given system the correction significantly reduces the dimension of the parent triple excitation subspace needed in the iterative part of the calculations. Simultaneously, it enables to reproduce the exact CCSDT results to an accuracy level below 0.1 kJ/mol with a larger, yet still reasonable, dimension of the parent excitation subspace. This typically can be achieved at a computational cost only several times larger than required for the CCSD(T) method. The proposed method retains black-box features of the single-reference coupled-cluster theory; the dimension of the parent excitation subspace remains the only additional parameter that has to be specified.

physics.chem-ph↗

arXiv2021

Spin-orbit coupling matrix elements from the explicitly connected expressions of the response functions within the coupled-cluster theory

In this work we present a coupled cluster based approach to the computation of the spin orbit coupling matrix elements. The working expressions are derived from the quadratic response function with the coupled cluster parametrization, using the auxiliary excitation operator S. Systematic approximations are proposed with the CCSD and CC3 levels of theory. The new method is tested by computing lifetimes of several electronic states of Ca, Sr and Ba atoms, with Gaussian and Slater basis sets. The results are compared with available theoretical and experimental data.

physics.chem-ph↗

arXiv2021

Theoretical determination of polarizability and magnetic susceptibility of neon

We report theoretical determination of the dipole polarizability of the neon atom, including its frequency dependence. Corrections for the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size effects are taken into account. We obtain the value $α_0=2.66080(36)$ for the static polarizability, and $α_2=2.850(7)$ and $α_4=4.932(14)$ for the first two polarizability dispersion coefficients (Cauchy moments); all values are in atomic units (a.u.). In the case of static polarizability, our result agrees with the best experimental determination [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)], but our estimated uncertainty is significantly larger. For the dispersion coefficients, the results obtained in this work appear to be the most accurate to date overall compared to published theoretical and experimental data. We also calculated the static magnetic susceptibility of the neon atom, needed to obtain the refractive index of gaseous neon. Our result, $χ_0 = -8.484(19) \cdot 10^{-5}$ a.u., is about 9% larger in absolute value than the recommended experimental value [CRC Handbook of Chemistry and Physics, CRC Press, 2019, p. 4-145].

physics.atom-ph↗

arXiv2021

Potential energy curve for the $a^3Σ_u^+$ state of lithium dimer with Slater-type orbitals

We report state-of-the-art ab initio calculations of the potential energy curve for the $a^3Σ_u^+$ state of the lithium dimer conducted to achieve spectroscopic accuracy ($<$1cm$^{-1}$) without any prior adjustment to fit the corresponding experimental data. The nonrelativistic clamped-nuclei component of the interaction energy is calculated with a composite method involving six-electron coupled cluster and full configuration interaction theories combined with basis sets of Slater-type orbitals ranging in quality from double- to sextuple-zeta. To go beyond the nonrelativistic Born-Oppenheimer picture we include both the leading-order relativistic and adiabatic corrections, and find both of these effects to be non-negligible within the present accuracy standards. The potential energy curve developed by us allowed to calculate molecular parameters ($D_e$, $D_0$, $ω_e$ etc.) for this system, as well as the corresponding vibrational energy levels, with an error of only a few tenths of a wavenumber ($0.2-0.4\,$cm$^{-1}$). We also report an ab initio value for the scattering length of two $^2S$ lithium atoms which determines the stability of the related Bose-Einstein condensate.

physics.chem-ph↗

arXiv2020

Symphony on Strong Field Approximation

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the "simple man's models" which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include High-Harmonic Generation, Above-Threshold Ionization, and Non-Sequential Multielectron Ionization. "Simple man's models" provide, both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation, and the motivation for the powerful analytic approximations generally known as the Strong Field Approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach SFA is a method to solve the TDSE using a systematic perturbation theory in a part of the Hamiltonian describing continuum-continuum transitions in the presence of the laser field. In this review we focus on recent applications of SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom. The main novel part of the presented theory concerns generalizations of SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between Electron Impact Ionization (EII) and Resonant Excitation with Subsequent Ionization (RESI); (ii) time-dependent treatment in the single active electron (SAE) approximation of "large" molecules and targets which are themselves undergoing dynamics during the HHG or ATI process. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields.

quant-ph↗

arXiv2020

Second virial coefficients for helium-4 and helium-3 from accurate relativistic interaction potential

The second virial coefficient and the second acoustic virial coefficient for helium-4 and helium-3 are computed for a wide range of temperatures (0.5 - 1000K) using a highly accurate nonrelativistic interaction potential [M. Przybytek et al., Phys. Rev. Lett. 119, 123401 (2017)] and recalculated relativistic and quantum-electrodynamic components. The effects of the long-range retardation and of the nonadiabatic coupling of the nuclear and electronic motion are also taken into account. The results of our calculations represent at least fivefold improvement in accuracy compared to the previous ab initio work. The computed virial coefficients agree well with the most accurate recent measurements but have significantly smaller uncertainty.

physics.chem-ph↗

arXiv2020

A straightforward a posteriori method for reduction of density-fitting error in coupled-cluster calculations

We present a simple method for \emph{a posteriori} removal of a significant fraction of the density-fitting error from the calculated total coupled-cluster energies. The method treats the difference between the exact and density-fitted integrals as a perturbation, and simplified response-like equations allow to calculate improved amplitudes and the corresponding energy correction. The proposed method is tested at the coupled-cluster singles and doubles level of theory for a diverse set of moderately-sized molecules. On average, error reductions by a factor of approximately ten and twenty are observed in double-zeta and triple-zeta basis sets, respectively. Similar reductions are observed in calculations of interaction energies of several model complexes. The computational cost of the procedure is small in comparison with the preceding coupled-cluster iterations. The applicability of the method is not limited to the density-fitting approximation; in principle, it can be used in conjunction with an arbitrary decomposition scheme of the electron repulsion integrals.

physics.chem-ph↗

arXiv2019

Implementation of the full CCSDT electronic structure model with tensor decompositions

We report a complete implementation of the coupled-cluster method with single, double, and triple excitations (CCSDT) where tensor decompositions are used to reduce its scaling and overall computational costs. For the decomposition of the electron repulsion integrals the standard density fitting (or Cholesky decomposition) format is used. The coupled-cluster single and double amplitudes are treated conventionally, and for the triple amplitudes tensor we employ the Tucker-3 compression formula, $t_{ijk}^{abc} \approx t_{XYZ} \,U^X_{ai}\,U^Y_{bj} \,U^Z_{ck}$. The auxiliary quantities $U^X_{ai}$ come from singular value decomposition (SVD) of an approximate triple amplitudes tensor based on perturbation theory. The efficiency of the proposed method relies on an observation that the dimension of the "compressed" tensor $t_{XYZ}$ sufficient to deliver a constant relative accuracy of the correlation energy grows only linearly with the size of the system, $N$. This fact, combined with proper factorization of the coupled-cluster equations, leads to practically $N^6$ scaling of the computational costs of the proposed method, as illustrated numerically for linear alkanes with increasing chain length. This constitutes a considerable improvement over the $N^8$ scaling of the conventional (uncompressed) CCSDT theory. The accuracy of the proposed method is verified by benchmark calculations of total and relative energies for several small molecular systems and comparison with the exact CCSDT method. The accuracy levels of 1 kJ/mol are easily achievable with reasonable SVD subspace size, and even more demanding levels of accuracy can be reached with a considerable reduction of the computational costs. Extensions of the proposed method to include higher excitations are briefly discussed, along with possible strategies of reducing other residual errors.

physics.chem-ph↗

arXiv2019

Theoretical description of the ionization processes with a discrete basis set representation of the electronic continuum

In this work we present a new method of approximating the continuum wavefunctions with a discrete basis set. This method aims to be at least compatible with other well known methods of the electronic structure theory to describe processes in the electronic continuum. As an example of the application we present the results of the calculations of the photoionization cross sections for the hydrogen atom and hydrogen molecule and for the helium atom. We also obtained the photoelectron angular distribution for the hydrogen molecule. The agreement of our results with the experimental data is very good in the energy range from the ionization threshold up to photon energies of about 60 eV.

physics.chem-ph↗

arXiv2019

Complete basis set extrapolation of electronic correlation energies using the Riemann zeta function

In this communication we present a method of complete basis set (CBS) extrapolation of correlation energies obtained with a systematic sequence of one-electron basis sets. Instead of fitting the finite-basis results with a certain functional form, we perform analytic re-summation of the missing contributions coming from higher angular momenta, $l$. The assumption that they vanish asymptotically as an inverse power of $l$ leads to an expression for the CBS limit given in terms of the Riemann zeta function. This result is turned into an extrapolation method that is very easy to use and requires no "empirical" parameters to be optimized. The performance of the proposed method is assessed by comparing the results with accurate reference data obtained with explicitly correlated theories and with results obtained with standard extrapolation schemes. On average, the errors of the zeta-function extrapolation are several times smaller compared with the conventional schemes employing the same number of points. A recipe for estimation of the residual extrapolation error is also proposed.

physics.chem-ph↗

arXiv2019

Size consistency and counterpoise correction in explicitly correlated calculations of interaction energies and interaction-induced properties

Explicitly correlated calculations of interaction energies with wave functions that include all interparticle distances have suffered so far from the lack of size-consistency resulting from the difficulty to define monomer energies corresponding to the applied dimer basis. As a consequence it has not been possible to obtain interaction energies vanishing at infinite intermonomer distance $R$. This has dramatically reduced the accuracy of calculations at distances where the error in the dimer energy was comparable with the interaction energy itself. The same problem occurs in calculations of interaction-induced properties. In this communication we show how to circumvent this difficulty and obtain interaction energies or interaction-induced properties that vanish at large $R$. This is achieved by relaxing the Pauli principle in the diagonalization of the Hamiltonian of noninteracting monomers. The basis functions used for this diagonalization belong to the representation of the permutation group of the dimer induced by the product of representations appropriate for the monomer spin states. Nonlinear parameters of the basis set are optimized only for the dimer in the Pauli-allowed sector of the Hilbert space. In this way, one obtains $R$-dependent energy of noninteracting monomers and the corresponding interaction energy includes a counterpoise correction for the basis set superposition error. The efficiency of this procedure is demonstrated for the interaction of two hydrogen atoms where accurate reference data are known.

physics.chem-ph↗

arXiv2018

Ab initio potential energy curve for the ground state of beryllium dimer

This work concerns \emph{ab initio} calculations of the complete potential energy curve and spectroscopic constants for the ground state $X^1Σ_g^+$ of the beryllium dimer, Be$_2$. High accuracy and reliability of the results is one of the primary goals of the paper. To this end we apply large basis sets of Slater-type orbitals combined with high-level electronic structure methods including triple and quadruple excitations. The effects of the relativity are also fully accounted for in the theoretical description. For the first time the leading-order quantum electrodynamics effects are fully incorporated for a many-electron molecule. Influence of the finite nuclear mass corrections (post-Born-Oppenheimer effects) turns out to be completely negligible for this system. The predicted well-depth ($D_e=934.5\pm2.5\,\mbox{cm}^{-1}$) and the dissociation energy ($D_0=808.0\,\mbox{cm}^{-1}$) are in a very good agreement with the most recent experimental data. We confirm the existence of the weakly bound twelfth vibrational level [Patkowski et al., Science 326, 1382 (2009)] and predict that it lies just about 0.5 $\mbox{cm}^{-1}$ below the onset of the continuum.

physics.chem-ph↗

arXiv2017

Calculation of Araki-Sucher correction for many-electron systems

In this paper we consider the evaluation of the Araki-Sucher correction for arbitrary many-electron atomic and molecular systems. This contribution appears in the leading order quantum electrodynamics corrections to the energy of a bound state. The conventional one-electron basis set of Gaussian-type orbitals (GTOs) is adopted; this leads to two-electron matrix elements which are evaluated with help of generalised the McMurchie-Davidson scheme. We also consider the convergence of the results towards the complete basis set. A rigorous analytic result for the convergence rate is obtained and verified by comparing with independent numerical values for the helium atom. Finally, we present a selection of numerical examples and compare our results with the available reference data for small systems. In contrast with other methods used for the evaluation of the Araki-Sucher correction, our method is not restricted to few-electron atoms or molecules. This is illustrated by calculations for several many-electron atoms and molecules.

physics.chem-ph↗

arXiv2015

Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment

We employ \textit{ab initio} methods of quantum chemistry to investigate spin-1/2 fermions interacting via a two-body contact potential in a one-dimensional harmonic trap. The convergence of the total energy with the size of the one-particle basis set is analytically investigated for the two-body problem and the same form of the convergence formula is numerically confirmed to be valid for the many-body case. Benchmark calculations for two to six fermions with the full configuration interaction method equivalent to the exact diagonalization approach, and the coupled cluster method including single, double, triple, and quadruple excitations are presented. The convergence of the correlation energy with the level of excitations included in the coupled cluster model is analyzed. The range of the interaction strength for which single-reference coupled cluster methods work is examined. Next, the coupled cluster method restricted to single, double, and noniterative triple excitations, CCSD(T), is employed to study a two-component Fermi gas composed of 6 to 80 atoms in a one-dimensional harmonic trap. The density profiles of trapped atomic clouds are also reported. Finally, a comparison with experimental results for few-fermion systems is presented. Upcoming possible applications and extensions of the presented approach are discussed.

cond-mat.quant-gas↗

arXiv2015

Crossover between few and many fermions in a harmonic trap

The properties of a balanced two-component Fermi gas in a one-dimensional harmonic trap are studied by means of the coupled cluster method. For few fermions we recover the results of exact diagonalization, yet with this method we are able to study much larger systems. We compute the energy, the chemical potential, the pairing gap, and the density profile of the trapped clouds, smoothly mapping the crossover between the few-body and many-body limits. The energy is found to converge surprisingly rapidly to the many-body result for every value of the interaction strength. Many more particles are instead needed to give rise to the non-analytic behavior of the pairing gap, and to smoothen the pronounced even-odd oscillations of the chemical potential induced by the shell structure of the trap.

cond-mat.quant-gas↗

arXiv2015

Calculation of the molecular integrals with the range-separated correlation factor

Explicitly correlated quantum chemical calculations require calculations of five types of molecular integrals beyond the standard electron repulsion integrals. We present a novel scheme, which utilises general ideas of the McMurchie-Davidson technique, to compute these integrals when the so-called \range-separated" correlation factor is used. This correlation factor combines the well-known short range behaviour, resulting from the electronic cusp condition, with the exact long-range asymptotics found for the helium atom [M. Lesiuk, B. Jeziorski, and R. Moszynski, J. Chem. Phys. $\textbf{139}$, 134102 (2013)]. Almost all steps of the presented procedure are formulated recursively, so that an efficient implementation and control of the precision are possible. Additionally, the present formulation is very flexible and general, and it allows for use of an arbitrary correlation factor in the electronic structure calculations with minor or no changes.

physics.chem-ph↗