arXiv subjects

Robert Moszynski

Publications and source records attributed to Robert Moszynski.

At least 19 recordsLinked to original sources

arXiv2026

Creation and precise spectroscopy of $^{86}$Sr$_2$ halo molecules

We report on the creation of $^{86}$Sr$_2$ molecules in the halo state and neighboring weakly bound states. Efficient molecule production via one-photon photoassociation relies on sufficient wavefunction overlap between the target vibrational states in the electronic excited- and ground-state potentials. Using Autler-Townes spectroscopy, transition strengths are measured to identify optimal pathways for production of weakly bound molecules. Vibrational splittings for the three least-bound vibrational states are measured, and dominant systematic uncertainties are evaluated with uncertainties below 100 Hz. From these splittings, absolute binding energies for these weakly bound vibrational states are determined. The results pave the way to a molecular isotope shift measurement with Sr$_2$.

physics.atom-ph↗

arXiv2023

F-12 density matrices and cumulants from the explicitly connected coupled-cluster theory

We present the expansion to the expectation value coupled cluster theory (XCC) to the wavefunctions that include the inter electronic distances $r_{12}$ explicitly. We have extended our algebraic manipulation code \paldus to deal with the rems arising in the CC-F12 theory. We present the full working expressions for the one-electron density matrix (1RDM) and cumulant of the two-electron density matrix ($\lambda$-2RDM) in the framework of XCC-F12 theory. We discuss the possible approximations the expressions.

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

Molecular properties from the explicitly connected expressions of the response functions within the coupled-cluster theory

We review the methods based on expectation value coupled cluster formalism - a common framework for the derivation of properties: the ground-state average value of an observable, cumulants of the second-order reduced density matrices, polarization propagator, quadratic response function, and transition probabilities. We discuss the approximations and give examples of the most important numerical results.

physics.chem-ph↗

arXiv2020

Laser-induced electron diffraction of the ultrafast umbrella motion in ammonia

Visualizing molecular transformations in real-time requires a structural retrieval method with {\AA}ngstr\"om spatial and femtosecond temporal atomic resolution. Imaging of hydrogen-containing molecules additionally requires an imaging method that is sensitive to the atomic positions of hydrogen nuclei, with most methods possessing relatively low sensitivity to hydrogen scattering. Laser-induced electron diffraction (LIED) is a table top technique that can image ultrafast structural changes of gas-phase polyatomic molecules with sub-{\AA}ngstr\"om and femtosecond spatiotemporal resolution together with relatively high sensitivity to hydrogen scattering. Here, we image the umbrella motion of an isolated ammonia molecule (NH$_3$) following its strong field ionization. Upon ionization of a neutral ammonia molecule, the ammonia cation (NH$_3^+$) undergoes an ultrafast geometrical transformation from a pyramidal ($\Phi_{HNH} = 107 ^\circ$) to planar ($\Phi_{HNH}=120^\circ$) structure in approximately 8 femtoseconds. Using LIED, we retrieve a near-planar ($\Phi_{HNH}=117 \pm 5^\circ$) field-dressed NH$_3^+$ molecular structure $7.8-9.8$ femtoseconds after ionization. Our measured field-dressed NH$_3^+$ structure is in excellent agreement with our calculated equilibrium field dressed structure using quantum chemical ab initio calculations.

physics.chem-ph↗

arXiv2020

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

We report state-of-the-art ab initio calculations of the potential energy curve for the $a^3\Sigma_u^+$ 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$, $D_0$, $\omega_e$ 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↗

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

Imaging an isolated water molecule using a single electron wave packet

Observing changes in molecular structure requires atomic-scale {\AA}ngstrom and femtosecond spatio-temporal resolution. We use the Fourier transform (FT) variant of laser-induced electron diffraction (LIED), FT-LIED, to directly retrieve the molecular structure of ${\rm H_2O^+}$ with picometre and femtosecond resolution without a priori knowledge of the molecular structure nor the use of retrieval algorithms or ab initio calculations. We identify a symmetrically stretched ${\rm H_2O^+}$ field-dressed structure that is most likely in the ground electronic state. We subsequently study the nuclear response of an isolated water molecule to an external laser field at four different field strengths. We show that upon increasing the laser field strength from 2.5 to 3.8 V/{\AA}, the O-H bond is further stretched and the molecule slightly bends. The observed ultrafast structural changes lead to an increase in the dipole moment of water and, in turn, a stronger dipole interaction between the nuclear framework of the molecule and the intense laser field. Our results provide important insights into the coupling of the nuclear framework to a laser field as the molecular geometry of ${\rm H_2O^+}$ is altered in the presence of an external field.

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 $X^1\Sigma_g^+$ 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↗

arXiv2018

Imaging the Renner-Teller effect using laser-induced electron diffraction

Structural information on electronically excited neutral molecules can be indirectly retrieved, largely through pump-probe and rotational spectroscopy measurements with the aid of calculations. Here, we demonstrate the direct structural retrieval of neutral carbonyl disulfide (CS$_2$) in the B$^1$B$_2$ excited electronic state using laser-induced electron diffraction (LIED). We unambiguously identify the ultrafast symmetric stretching and bending of the field-dressed neutral CS$_2$ molecule with combined picometer and attosecond resolution using intrapulse pump-probe excitation and measurement. We invoke the Renner-Teller effect to populate the B$^1$B$_2$ excited state in neutral CS$_2$, leading to bending and stretching of the molecule. Our results demonstrate the sensitivity of LIED in retrieving the geometric structure of CS$_2$, which is known to appear as a two-center scatterer.

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↗

arXiv2017

Combining Slater-type orbitals and effective core potentials

We present a general methodology to evaluate matrix elements of the effective core potentials (ECPs) within one-electron basis set of Slater-type orbitals (STOs). The scheme is based on translation of individual STO distributions in the framework of Barnett-Coulson method. We discuss different types of integrals which naturally appear and reduce them to few basic quantities which can be calculated recursively or purely numerically. Additionally, we consider evaluation of the STOs matrix elements involving the core polarisation potentials (CPP) and effective spin-orbit potentials. Construction of the STOs basis sets designed specifically for use with ECPs is discussed and differences in comparison with all-electron basis sets are briefly summarised. We verify the validity of the present approach by calculating excitation energies, static dipole polarisabilities and valence orbital energies for the alkaline earth metals (Ca, Sr, Ba). Finally, we evaluate interaction energies, permanent dipole moments and ionisation energies for barium and strontium hydrides, and compare them with the best available experimental and theoretical data.

physics.chem-ph↗

arXiv2016

Transition moments between excited electronic states from the Hermitian formulation of the coupled cluster quadratic response function

We introduce a new method for the computation of the transition moments between the excited electronic states based on the expectation value formalism of the coupled cluster theory [B. Jeziorski and R. Moszynski, Int. J. Quant. Chem. 48, 161 (1993)]. The working expressions of the new method solely employ the coupled cluster amplitudes. In the approximation adopted in the present paper the cluster expansion is limited to single, double, and linear triple excitations. The computed dipole transition probabilities for the singlet-singlet and triplet-triplet transitions in alkali earth atoms agree well with the available theoretical and experimental data. In contrast to the existing coupled cluster response theory, the matrix elements obtained by using our approach satisfy the Hermitian symmetry even if the excitations in the cluster operator are truncated. As a part of the numerical evidence for the new method, we report calculations of the transition moments between the excited triplet states which have not yet been reported in the literature within the coupled cluster theory. Slater-type basis sets constructed according to the correlation-consistency principle are used in our calculations.

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↗

arXiv2014

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↗

arXiv2014

Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. III. Case study of the beryllium dimer

In this paper we present results of ab-initio calculations for the beryllium dimer with basis set of Slater-type orbitals (STOs). Nonrelativistic interaction energy of the system is determined using the frozen-core full configuration interaction calculations combined with high-level coupled cluster correction for inner-shell effects. Newly developed STOs basis sets, ranging in quality from double to sextuple zeta, are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order ${\alpha}^2$ are calculated perturbatively by using the Breit-Pauli Hamiltonian and are found to be significant. We also estimate the leading-order QED effects. Influence of the adiabatic correction is found to be negligible. Finally, the interaction energy of the beryllium dimer is determined to be 929.0$\,\pm\,$1.9 $cm^{-1}$, in a very good agreement with the recent experimental value. The results presented here appear to be the most accurate ab-initio calculations for the beryllium dimer available in the literature up to date and probably also one of the most accurate calculations for molecular systems containing more than four electrons.

physics.chem-ph↗

arXiv2014

Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. I. Coulomb and hybrid integrals

In this paper, which constitutes the first part of the series, we consider calculation of two-centre Coulomb and hybrid integrals over Slater-type orbitals (STOs). General formulae for these integrals are derived with no restrictions on the values of the quantum numbers and nonlinear parameters. Direct integration over the coordinates of one of the electrons leaves us with the set of overlap-like integrals which are evaluated by using two distinct methods. The first one is based on the transformation to the ellipsoidal coordinates system and the second utilises a recursive scheme for consecutive increase of the angular momenta in the integrand. In both methods simple one-dimensional numerical integrations are used in order to avoid severe digital erosion connected with the straightforward use of the alternative analytical formulae. It is discussed that the numerical integration does not introduce a large computational overhead since the integrands are well-behaved functions, calculated recursively with decent speed. Special attention is paid to the numerical stability of the algorithms. Applicability of the resulting scheme over a large range of the nonlinear parameters is tested on examples of the most difficult integrals appearing in the actual calculations including at most 7i-type functions (l=6).

quant-ph↗