arXiv subjects

Robert Moszynski

Publications and source records attributed to Robert Moszynski.

At least 37 records · Page 2Linked to original sources

arXiv2015

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↗

arXiv2015

Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. II. Neumann expansion of the exchange integrals

In this paper we consider calculation of two-centre exchange integrals over Slater-type orbitals (STOs). We apply the Neumann expansion of the Coulomb interaction potential and consider calculation of all basic quantities which appear in the resulting expression. Analytical closed-form equations for all auxiliary quantities have already been known but they suffer from large digital erosion when some of the parameters are large or small. We derive two differential equations which are obeyed by the most difficult basic integrals. Taking them as a starting point, useful series expansions for small parameter values or asymptotic expansions for large parameter values are systematically derived. The resulting novel expansions replace the corresponding analytical expressions when the latter introduce significant cancellations. Additionally, we reconsider numerical integration of some necessary quantities and present a new way to calculate the integrand with a controlled precision. All proposed methods are combined to lead to a general, stable algorithm. We perform extensive numerical tests of the introduced expressions to verify their validity and usefulness. Advances reported here provide methodology to compute two-electron exchange integrals over STOs for a broad range of the nonlinear parameters and large angular momenta.

quant-ph↗

arXiv2014

Transition properties from the Hermitian formulation of the coupled cluster polarization propagator

Theory of one-electron transition density matrices has been formulated within the time-independent coupled cluster method for the polarization propagator [R. Moszynski, P. S. Żuchowski, and B. Jeziorski, Coll. Czech. Chem. Commun. {\bf 70}, 1109 (2005)]. Working expressions have been obtained and implemented with the coupled cluster method limited to single, double, and linear triple excitations (CC3). Selected dipole and quadrupole transition probabilities of the alkali earth atoms, computed with the new transition density matrices are compared to the experimental data. Good agreement between theory and experiment is found. The results obtained with the new approach are of the same quality as the results obtained with the linear response coupled cluster theory (LRCC). The one-electron density matrices for the ground state in the CC3 approximation have also been implemented. The dipole moments for a few representative diatomic molecules have been computed with several variants of the new approach, and the results are discussed to choose the approximation with the best balance between the accuracy and computational efficiency.

physics.chem-ph↗

arXiv2014

Controlling magnetic Feshbach resonances in polar open-shell molecules with non-resonant light

Magnetically tunable Feshbach resonances for polar paramagnetic ground-state diatomics are too narrow to allow for magnetoassociation starting from trapped, ultracold atoms. We show that non-resonant light can be used to engineer the Feshbach resonances in their position and width. For non-resonant field strengths of the order of $10^9\,$W/cm$^2$, we find the width to be increased by three orders of magnitude, reaching a few Gauss. This opens the way for producing ultracold molecules with sizeable electric and magnetic dipole moments and thus for many-body quantum simulations with such particles.

physics.atom-ph↗

arXiv2013

Chemical reactions of ultracold alkali-metal dimers in the lowest-energy $^3Σ$ state

We show that the interaction of polar alkali dimers in the quintet spin state leads to the formation of a deeply bound reaction complex. The reaction complex can decompose adiabatically into homonuclear alkali dimers (for all molecules except KRb) and into alkali trimers (for all molecules). We show that there are no barriers for these chemical reactions. This means that all alkali dimers in the $a^3Σ^+$ state are chemically unstable at ultracold temperature, and the use of an optical lattice to segregate the molecules and suppress losses may be necessary. In addition, we calculate the minimum energy path for the chemical reactions of alkali hydrides. We find that the reaction of two molecules is accelerated by a strong attraction between the alkali atoms, leading to a barrierless process that produces hydrogen atoms with large kinetic energy. We discuss the unique features of the chemical reactions of ultracold alkali dimers in the $a^3Σ^+$ electronic state.

physics.atom-ph↗

arXiv2013

Femtosecond two-photon photoassociation of hot magnesium atoms: A quantum dynamical study using thermal random phase wavefunctions

Two-photon photoassociation of hot magnesium atoms by femtosecond laser pulses, creating electronically excited magnesium dimer molecules, is studied from first principles, combining \textit{ab initio} quantum chemistry and molecular quantum dynamics. This theoretical framework allows for rationalizing the generation of molecular rovibrational coherence from thermally hot atoms [L. Rybak \textit{et al.}, Phys. Rev. Lett. {\bf 107}, 273001 (2011)]. Random phase thermal wave functions are employed to model the thermal ensemble of hot colliding atoms. Comparing two different choices of basis functions, random phase wavefunctions built from eigenstates are found to have the fastest convergence for the photoassociation yield. The interaction of the colliding atoms with a femtosecond laser pulse is modeled non-perturbatively to account for strong-field effects.

quant-ph↗

arXiv2013

On the large interelectronic distance behavior of the correlation factor for explicitly correlated wave functions

In currently most popular explicitly correlated electronic structure theories the dependence of the wave function on the interelectronic distance rij is built via the correlation factor f(rij). While the short-distance behavior of this factor is well understood, little is known about the form of f(rij) at large rij. In this work we investigate the optimal form of f(r12) on the example of the helium atom and helium-like ions and several well-motivated models of the wave function. Using the Rayleigh-Ritz variational principle we derive a differential equation for f(r12) and solve it using numerical propagation or analytic asymptotic expansion techniques. We found that for every model under consideration, f(r12) behaves at large r12 as r12^ρ exp(B r12) and obtained simple analytic expressions for the system dependent values of ρ and B. For the ground state of the helium-like ions the value of B is positive, so that f(r12) diverges as r12 tends to infinity. The numerical propagation confirms this result. When the Hartree-Fock orbitals, multiplied by the correlation factor, are expanded in terms of Slater functions r^n exp(-βr), the numerical propagation reveals a minimum in f(r12) with depth increasing with N. For the lowest triplet state B is negative. Employing our analytical findings, we propose a new 'range-separated' form of the correlation factor with the short- and long-range r12 regimes approximated by appropriate asymptotic formulas connected by a switching function. Exemplary calculations show that this new form of f(r12) performs somewhat better than the correlation factors used thus far in the standard R12 or F12 theories.

quant-ph↗

arXiv2013

Interatomic potentials, electric properties, and spectroscopy of the ground and excited states of the Rb_2 molecule: Ab initio calculations and effect of a non-resonant field

We formulate the theory for a diatomic molecule in a spatially degenerate electronic state interacting with a non-resonant laser field and investigate its rovibrational structure in the presence of the field. We report on \textit{ab initio} calculations employing the double electron attachment intermediate Hamiltonian Fock space coupled cluster method restricted to single and double excitations for all electronic states of the Rb$_2$ molecule up to $5s+5d$ dissociation limit of about 26.000$\,$cm$^{-1}$. In order to correctly predict the spectroscopic behavior of Rb$_2$, we have also calculated the electric transition dipole moments, non-adiabatic coupling and spin-orbit coupling matrix elements, and static dipole polarizabilities, using the multireference configuration interaction method. When a molecule is exposed to strong non-resonant light, its rovibrational levels get hybridized. We study the spectroscopic signatures of this effect for transitions between the X$^1Σ_g^+$ electronic ground state and the A$^1Σ_u^+$ and b$^3Π_u$ excited state manifold. The latter is characterized by strong perturbations due to the spin-orbit interaction. We find that for non-resonant field strengths of the order $10^9$W/cm$^2$, the spin-orbit interaction and coupling to the non-resonant field become comparable. The non-resonant field can then be used to control the singlet-triplet character of a rovibrational level.

physics.atom-ph↗

arXiv2013

Optical Kerr and Cotton-Mouton effects in atomic gases: a quantum-statistical study

Theory of the birefringence of the refractive index in atomic diamagnetic dilute gases in the presence of static electric (optical Kerr effect) and magnetic (Cotton-Mouton effect) fields is formulated. Quantum-statistical expressions for the second Kerr and Cotton-Mouton virial coefficients, valid both in the low and high temperature regimes, are derived. It is shown that both virial coefficients can rigorously be related to the difference of the fourth derivatives of the thermodynamic (pressure) virial coefficient with respect to the strength of the non-resonant optical fields with parallel and perpendicular polarizations and with respect to the external static (electric or magnetic) field. Semiclassical expansions of the Kerr and Cotton-Mouton coefficients are also considered, and quantum corrections up to and including the second order are derived. Calculations of the second Kerr and Cotton-Mouton virial coefficients of the helium-4 gas at various temperatures are reported. The role of the quantum-mechanical effects and the convergence properties of the semiclassical expansions are discussed. Theoretical results are compared with the available experimental data.

physics.atom-ph↗

arXiv2012

Optimized production of ultracold ground-state molecules: Stabilization employing potentials with ion-pair character and strong spin-orbit coupling

We discuss the production of ultracold molecules in their electronic ground state by photoassociation employing electronically excited states with ion-pair character and strong spin-orbit interaction. A short photoassociation laser pulse drives a non-resonant three-photon transition for alkali atoms colliding in their lowest triplet state. The excited state wave packet is transferred to the ground electronic state by a second laser pulse, driving a resonant two-photon transition. After analyzing the transition matrix elements governing the stabilization step, we discuss the efficiency of population transfer using transform-limited and linearly chirped laser pulses. Finally, we employ optimal control theory to find the most efficient stabilization pathways. We find that the stabilization efficiency can be increased by one and two orders of magnitude for linearly chirped and optimally shaped laser pulses, respectively.

physics.atom-ph↗

arXiv2012

Analytical two-center integrals over Slater geminal functions

We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analysed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the usefulness and correctness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the exp(-γr12) term in the master integral.

quant-ph↗

arXiv2012

Rovibrational dynamics of the strontium molecule in the A^1Σ_u^+, c^3Π_u, and a^3Σ_u^+ manifold from state-of-the-art ab initio calculations

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the electronic states in the A^1Σ_u^+, c^3Π_u, and a^3Σ_u^+ manifold of the strontium dimer, the spin-orbit and nonadiabatic coupling matrix elements between the states in the manifold, and the electric transition dipole moment from the ground X^1Σ_g^+ to the nonrelativistic and relativistic states in the A+c+a manifold. The potential energy curves and transition moments were obtained with the linear response (equation of motion) coupled cluster method limited to single, double, and linear triple excitations for the potentials and limited to single and double excitations for the transition moments. The spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction method limited to single and double excitations. Our results for the nonrelativistic and relativistic (spin-orbit coupled) potentials deviate substantially from recent ab initio calculations. The potential energy curve for the spectroscopically active (1)0_u^+ state is in quantitative agreement with the empirical potential fitted to high-resolution Fourier transform spectra [A. Stein, H. Knoeckel, and E. Tiemann, Eur. Phys. J. D 64, 227 (2011)]. The computed ab initio points were fitted to physically sound analytical expressions, and used in converged coupled channel calculations of the rovibrational energy levels in the A+c+a manifold and line strengths for the A^1Σ_u^+ <-- X^1Σ_g^+ transitions. Positions and lifetimes of quasi-bound Feshbach resonances lying above the ^1S + ^3P_1 dissociation limit were also obtained. Our results reproduce (semi)quantitatively the experimental data observed thus far. Predictions for on-going and future experiments are also reported.

physics.chem-ph↗

arXiv2012

Formation of deeply bound ultracold Sr_2 molecules by photoassociation near the ^1S + ^3P_1 intercombination line

We predict feasibility of the photoassociative formation of Sr_2 molecules in arbitrary vibrational levels of the electronic ground state based on state-of-the-art ab initio calculations. Key is the strong spin-orbit interaction between the c^3Π_u, A^1Σ_u^+ and B^1Σ_u^+ states. It creates not only an effective dipole moment allowing free-to-bound transitions near the ^1S + ^3P_1 intercombination line but also facilitates bound-to-bound transitions via resonantly coupled excited state rovibrational levels to deeply bound rovibrational levels of the ground X^1Σ_g^+ potential, with v" as low as v"=6. The spin-orbit interaction is responsible for both optical pathways. Therefore, those excited state levels that have the largest bound-to-bound transition moments to deeply bound ground state levels also exhibit a sufficient photoassociation probability, comparable to that of the lowest weakly bound excited state level previously observed by Zelevinsky et al. [Phys. Rev. Lett. 96, 203201 (2006)]. Our study paves the way for an efficient photoassociative production of Sr_2 molecules in ground state levels suitable for experiments testing the electron-to-proton mass ratio.

physics.atom-ph↗

arXiv2011

Generating Molecular Rovibrational Coherence by Two-Photon Femtosecond Photoassociation of Thermally Hot Atoms

The formation of diatomic molecules with rotational and vibrational coherence is demonstrated experimentally in free-to-bound two-photon femtosecond photoassociation of hot atoms. In a thermal gas at a temperature of 1000 K, pairs of magnesium atoms, colliding in their electronic ground state, are excited into coherent superpositions of bound rovibrational levels in an electronically excited state. The rovibrational coherence is probed by a time-delayed third photon, resulting in quantum beats in the UV fluorescence. A comprehensive theoretical model based on ab initio calculations rationalizes the generation of coherence by Franck-Condon filtering of collision energies and partial waves, quantifying it in terms of an increase in quantum purity of the thermal ensemble. Our results open the way to coherent control of a binary reaction.

quant-ph↗

arXiv2011

Rovibrational interactions in linear triatomic molecules: a theoretical study in curvilinear vibrational coordinates

A variational solution to the rovibrational problem in curvilinear vibrational coordinates has been implemented and used to investigate the nuclear motions in several linear triatomic molecules, like HCN, OCS, and HCP. The dependence of the rovibrational energy levels on the rotational quantum numbers and the l-doubling has been studied. Two approximations to the rovibrational Hamiltonian have been examined, depending on the level of truncation of the potential energy operator. It turns out that truncation after the fifth order in the potential is sufficient to produce vibrational energies of high accuracy. An interesting feature of the present formulation of the problem in terms of the curvilinear vibrational coordinates is the explanation for the l-doubling of the rovibrational levels, which in this picture is interpreted as the result of the inequivalency of the average rotational constants in mutually perpendicular planes, rather than as the effect of the Coriolis-type interactions between the vibrational and rotational motions. The present theoretical results are compared with the available experimental data from high-resolution spectroscopy, as well as with other ab initio calculations.

physics.chem-ph↗

arXiv2011

Weak intermolecular interactions in gas-phase NMR

Gas-phase NMR spectra demonstrating the effect of weak intermolecular forces on the NMR shielding constants of the interacting species are reported. We analyse the interaction of the molecular hydrogen isotopomers with He, Ne, and Ar, and the interaction in the He-CO_2 dimer. The same effects are studied for all these systems in the ab initio calculations. The comparison of the experimental and computed shielding constants is shown to depend strongly on the treatment of the bulk susceptibility effects, which determine in practice the pressure dependence of the experimental values. Best agreement of the results is obtained when the bulk susceptibility correction in rare gas solvents is evaluated from the analysis of the He-rare gas interactions, and when the shielding of deuterium in D_2-rare gas systems is considered.

physics.chem-ph↗

arXiv2011

Cold collisions of an open-shell S-state atom with a ^2Pi molecule: N(^4S) colliding with OH in a magnetic field

We present quantum-theoretical studies of collisions between an open-shell S-state atom and a ^2Pi-state molecule in the presence of a magnetic field. We analyze the collisional Hamiltonian and discuss possible mechanisms for inelastic collisions in such systems. The theory is applied to the collisions of the nitrogen atom (^4S) with the OH molecule, with both collision partners initially in fully spin-stretched (magnetically trappable) states, assuming that the interaction takes place exclusively on the two high-spin (quintet) potential energy surfaces. The surfaces for the quintet states are obtained from spin-unrestricted coupled-cluster calculations with single, double, and noniterative triple excitations. We find substantial inelasticity, arising from strong couplings due to the anisotropy of the interaction potential and the anisotropic spin-spin dipolar interaction. The mechanism involving the dipolar interaction dominates for small magnetic field strengths and ultralow collision energies, while the mechanism involving the potential anisotropy prevails when the field strength is larger (above 100 G) or the collision energy is higher (above 1 mK). The numerical results suggest that sympathetic cooling of magnetically trapped OH by collisions with ultracold N atoms will not be successful at higher temperatures.

physics.chem-ph↗

arXiv2011

Sympathetic cooling of the Ba$^+$ ion by collisions with ultracold Rb atoms: theoretical prospects

State-of-the-art {\em ab initio} techniques have been applied to compute the potential energy curves of the (BaRb)$^+$ molecular ion in the Born-Oppenheimer approximation. The long-range coefficients describing the electrostatic, induction, and dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments governing the X$^1Σ\to ^1Σ, ^1Π$ have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Nonadiabatic radial and angular coupling matrix elements, as well as the spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. With these couplings, the spin-orbit coupled (relativistic) potential energy curves for the 0$^+$ and 1 states relevant for the running experiments have been obtained. Finally, relativistic transition moments and nonadiabatic coupling matrix elements were obtained from the nonrelativistic results and spin-orbit eigenvectors. The electronic structure input has been employed in the single channel scattering calculations of the collisional cross sections between the Ba$^+$ ion and Rb atom. Both nonrelativistic and relativistic potentials were used in these calculations. Our results show that the inelastic cross section corresponding to the charge transfer from the Rb atom to the Ba$^+$ ion is much smaller than the elastic one over a wide range of energies up to 1 mK. This suggests that sympathetic cooling of the Ba$^+$ ion by collisions with ultracold Rb atoms should be possible.

physics.atom-ph↗