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We report calculations of the high harmonic generation spectra of the C\textsubscript{60} fullerene molecule, employing a diverse set of real-time time-dependent quantum chemical methods. All methodologies involve expanding the propagated electronic wavefunction in bases consisting of the ground and singly excited time-independent eigenstates obtained through the solution of the corresponding linear-response equations. We identify the correlation and exchange effect in the spectra by comparing the results from methods relying on the Hartree-Fock reference determinant with those obtained using approaches based on the density functional theory with different exchange-correlation functionals. The effect of the full random phase approximation treatment of the excited electronic states is also analyzed and compared with the configuration interaction singles and the Tamm-Dancoff approximation. We also showcase that the real-time extension of the semiempirical method INDO/S can be effectively applied for an approximate description of laser-driven dynamics in large systems., Comment: 50 pages, 9 figures

We report calculations of the high-order harmonic spectra of few-atomic clusters of two noble gases, helium and krypton, subjected to laser pulses of intensities above $10^{13}$ W/cm\textsuperscript{2}. We employ a fully \textit{ab intio} framework, namely the real-time time-dependent configuration interaction singles coupled to a discrete Gaussian basis set. Our model reproduces the observed higher than quadratic dependence between the high-order harmonic yield and the number of atoms, and the obtained value of the enhancement rate is in quantitative agreement with experimental results. We suggest a mechanism responsible for the high-order harmonic enhancement, according to which, after the tunneling ionization, the residual ion polarizes the electron densities of surrounding atoms in the cluster, which leads to increased electron-electron repulsion during the recollision. The proposed mechanism is not only fully consistent with both our calculations and the experimental data, but can also explain the limitations of previous theoretical studies on high-order harmonic generation in clusters., Comment: 15 pages, 7 figures

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.

Time-dependent quantum chemical methods coupled to Gaussian basis sets are gaining popularity in modeling the electron dynamics of atoms and molecules interacting with intense laser fields. Two approaches most widely used for this purpose, the real-time time-dependent configuration interaction singles and the real-time time-dependent density functional theory, both have their limitations, so the development of more accurate yet computationally efficient time-dependent methods is still in demand. In this work we explore the applicability of the real-time time-dependent configuration interaction singles and doubles (RT-TDCISD) in modeling strong field phenomena. Since the main drawback of RT-TDCISD is its unfavourable scaling, we develop several algorithms for reducing the effective propagation space by selecting these CISD eigenstates that should have dominant contribution to the time-evolution of the wavefunction. We test them by performing calculations of the high harmonic spectra of the H\textsubscript{2} molecule. We find out that the laser-driven electron dynamics is mostly realized in a very small subspace of eigenstates dominated by single excitations, that constitutes about one percent of the whole CISD eigenspectrum. Therefore, by properly selecting this subspace one can reduce the dimension of the propagation equation by two orders of magnitude without affecting the time-resolved observables., Comment: 24 pages in single column, 5 figures

In this paper, we investigate the effects of full electronic correlation on the high harmonic generation in the helium atom subjected to laser pulses of extremely high intensity. To do this, we perform real-time propagations of the helium atom wavefunction using quantum chemistry methods coupled to Gaussian basis sets. The calculations are done within the real-time time-dependent configuration interaction framework, at two levels of theory: time-dependent configuration interation with single excitations (TD-CIS, uncorrelated method) and time-dependent full configuration interaction (TD-FCI, fully correlated method), and analyse obtained HHG spectra. The electronic wavefunction is expanded in Dunning basis sets supplemented with functions adapted to describing highly excited continuum states. We also compare the TD-CI results with grid-based propagations of the helium atom within the single-active-electron approximation. Our results show when including the dynamical electron correlation, a noticeable improvement to the description of HHG can be achieved, in terms of e.g. a more constant intensity in the lower energy part of the harmonic plateau. However, such effects can be captured only if the basis set used suffices to reproduce the most basic features, such as the HHG cutoff position, at the uncorrelated level of theory., Comment: 14 pages, 2 figures

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., Comment: 18 pages, 9 tabels

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., Comment: 35 pages, 1 figure

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.

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 Schr\"odinger 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., Comment: Minor changes in Sec. 1, 2 and 3

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.

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.

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.

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagiello\'nski, 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 Schr\"odinger 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., Comment: We dedicate this work to the memory of Bertrand Carr\'e, who passed away in March 2018 at the age of 60. This Accepted Manuscript is available under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/3.0/)

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.

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.

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., Comment: submitted to Phys. Rev. A

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., Comment: submitted to Phys. Rev. A

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., Comment: 23 pages, 5 figures

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., Comment: 25 pages, 12 figures, 1 table

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., Comment: 6 pages, 4 figures

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.

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., Comment: submitted to Phys. Rev. A

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).

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.

The electronic structure of the (LiYb)$^+$ molecular ion is investigated with two variants of the coupled cluster method restricted to single, double, and noniterative or linear triple excitations. Potential energy curves for the ground and excited states, permanent and transition electric dipole movements, and long-range interaction coefficients $C_4$ and $C_6$ are reported. The data is subsequently employed in scattering calculations and photoassociation studies. Feshbach resonances are shown to be measurable despite the ion's micromotion in the Paul trap. Molecular ions can be formed in their singlet electronic ground state by one-photon photoassociation and in triplet states by two-photon photoassociation; and control of cold atom-ion chemistry based on Feshbach resonances should be feasible. Conditions for sympathetic cooling of an Yb$^+$ ion by an ultracold gas of Li atoms are found to be favorable in the temperature range of 10$\,$mK to 10$\,$nK; and further improvements using Feshbach resonances should be possible. Overall, these results suggest excellent prospects for building a quantum simulator with ultracold Yb$^+$ ions and Li atoms., Comment: 13 pages, 13 figures, 2 tables

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. \.Zuchowski, 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.

A detailed characterization of the interaction between the most abundant molecules in air is important for the understanding of a variety of phenomena in atmospherical science. A completely {\em ab initio} global potential energy surface (PES) for the O$_2(^3\Sigma^-_g)$ + N$_2(^1\Sigma^+_g)$ interaction is reported for the first time. It has been obtained with the symmetry-adapted perturbation theory utilizing a density functional description of monomers [SAPT(DFT)] extended to treat the interaction involving high-spin open-shell complexes. The computed interaction energies of the complex are in a good agreement with those obtained by using the spin-restricted coupled cluster methodology with singles, doubles and noniterative triple excitations [RCCSD(T)]. A spherical harmonics expansion containing a large number of terms due to the anisotropy of the interaction has been built from the {\em ab initio} data. The radial coefficients of the expansion are matched in the long range with the analytical functions based on the recent {\em ab initio} calculations of the electric properties of the monomers [M. Bartolomei et al., J. Comp. Chem., {\bf 32}, 279 (2011)]. The PES is tested against the second virial coefficient $B(T)$ data and the integral cross sections measured with rotationally hot effusive beams, leading in both cases to a very good agreement. The first bound states of the complex have been computed and relevant spectroscopic features of the interacting complex are reported. A comparison with a previous experimentally derived PES is also provided.

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 $a^3\Sigma^+$ 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 $a^3\Sigma^+$ electronic state., Comment: 4 pages, 3 figures, 4 tables

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.

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^{\rho} exp(B r12) and obtained simple analytic expressions for the system dependent values of {\rho} 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(-{\beta}r), 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., Comment: 42 pages, 5 figures, submitted to the Journal of Chemical Physics

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., Comment: 26 pages, 5 figures

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$^1\Sigma_g^+$ electronic ground state and the A$^1\Sigma_u^+$ and b$^3\Pi_u$ 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., Comment: 28 pages, 14 figures, 5 tables

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(-\gamma r12) term in the master integral., Comment: 28 pages, 0 figures, 7 tables

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., Comment: 14 pages, 10 figures

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^3\Pi_u, A^1\Sigma_u^+ and B^1\Sigma_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^1\Sigma_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., Comment: 11 pages, 10 figures

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the electronic states in the A^1\Sigma_u^+, c^3\Pi_u, and a^3\Sigma_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^1\Sigma_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^1\Sigma_u^+ <-- X^1\Sigma_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., Comment: Final version, accepted for publication in Journal of Chemical Physics

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.

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., Comment: Accepted in "Structural Chemistry"

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., Comment: 9 pages, 3 figures

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., Comment: final version, accepted for publication in Phys Rev Lett

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., Comment: 13 pages, 10 figures

State-of-the-art {\em ab initio} techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the ground state and first fifteen excited singlet and triplet states within the coupled-cluster framework. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments 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. 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. The electronic structure data was employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed $b^3\Sigma^+$, $a^3\Pi$, $A^1\Pi$, and $C^1\Pi$ states with subsequent efficient stabilization into the $v^{\prime\prime}=1$ vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from $v^{\prime\prime}=1$ to $v^{\prime\prime}=0$. Alternatively, photoassociation and stabilization to $v^{\prime\prime}=0$ can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds.

We consider how trapped molecules can be sympathetically cooled by ultracold atoms. As a prototypical system, we study LiH molecules co-trapped with ultracold Li atoms. We calculate the elastic and inelastic collision cross sections of LiH + Li with the molecules initially in the ground state and in the first rotationally excited state. We then use these cross sections to simulate sympathetic cooling in a static electric trap, an ac electric trap, and a microwave trap. In the static trap we find that inelastic losses are too great for cooling to be feasible for this system. The ac and microwave traps confine ground-state molecules, and so inelastic losses are suppressed. However, collisions in the ac trap can take molecules from stable trajectories to unstable ones and so sympathetic cooling is accompanied by trap loss. In the microwave trap there are no such losses and sympathetic cooling should be possible., Comment: 9 pages, 10 figures, minor revisions following referee suggestions

Theory of long-range interactions between an atom in its ground S state and a linear molecule in a degenerate state with a non-zero projection of the electronic orbital angular momentum is presented. It is shown how the long-range coefficients can be related to the first and second-order molecular properties. The expressions for the long-range coefficients are written in terms of all components of the static and dynamic multipole polarizability tensor, including the nonadiagonal terms connecting states with the opposite projection of the electronic orbital angular momentum. It is also shown that for the interactions of molecules in excited states that are connected to the ground state by multipolar transition moments additional terms in the long-range induction energy appear. All these theoretical developments are illustrated with the numerical results for systems of interest for the sympathetic cooling experiments: interactions of the ground state Rb($^2$S) atom with CO($^3\Pi$), OH($^2\Pi$), NH($^1\Delta$), and CH($^2\Pi$) and of the ground state Li($^2$S) atom with CH($^2\Pi$)., Comment: 30 pages, 3 figures

State-of-the-art ab initio techniques have been applied to compute the potential energy surface for the lithium atom interacting with the lithium hydride molecule in the Born-Oppenheimer approximation. The interaction potential was obtained using a combination of the explicitly correlated unrestricted coupled-cluster method with single, double, and noniterative triple excitations [UCCSD(T)-F12] for the core-core and core-valence correlation and full configuration interaction for the valence-valence correlation. The potential energy surface has a global minimum 8743 cm^{-1} deep if the Li-H bond length is held fixed at the monomer equilibrium distance or 8825 cm^{-1} deep if it is allowed to vary. In order to evaluate the performance of the conventional CCSD(T) approach, calculations were carried out using correlation-consistent polarized valence X-tuple-zeta bases, with X ranging from 2 to 5. The contribution beyond the CCSD(T)-F12 model, obtained from full configuration interaction (FCI) calculations for the valence-valence correlation, was shown to be very small. At linear LiH-Li geometries the ground-state potential shows an avoided crossing with an ion-pair potential.Using both adiabatic and diabatic pictures we analyse the interaction between the two potential energy surfaces and its possible impact on the collisional dynamics. When the LiH bond is allowed to vary, a seam of conical intersections appears at C_{2v} geometries. At the linear LiH-Li geometry, the conical intersection is at a Li-H distance which is only slightly larger than the monomer equilibrium distance, but for nonlinear geometries it quickly shifts to Li-H distances that are well outside the classical turning points of the ground-state potential of LiH. Finally, the reaction channels for the exchange and insertion reactions are also analyzed., Comment: 38 pages, 9 figures

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$^1\Sigma \to ^1\Sigma, ^1\Pi$ 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., Comment: 41 pages, 10 figures, 4 tables

We propose an improved photoassociation scheme to produce ultracold molecules in their vibronic ground state for the generic case where non-adiabatic effects facilitating transfer to deeply bound levels are absent. Formation of molecules is achieved by short laser pulses in a Raman-like pump-dump process where an additional near-infrared laser field couples the excited state to an auxiliary state. The coupling due to the additional field effectively changes the shape of the excited state potential and allows for efficient population transfer to low-lying vibrational levels of the electronic ground state. Repetition of many pump-dump sequences together with collisional relaxation allows for accumulation of molecules in v=0., Comment: Phys. Rev. A, in press