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arXiv:1301.1723 · Molecular Physics

Study of dipole moments of LiSr and KRb molecules by quantum Monte Carlo methods

Shi Guo, Michal Bajdich, Luboš Mitáš, PETER J. REYNOLDS

Published Jun 18, 2013• 9 citations
arXivHTMLPDF

Abstract

Heteronuclear dimers are of significant interest to experiments seeking to exploit ultracold polar molecules in a number of novel ways, including precision measurement, quantum computing and quantum simulation. We calculate highly accurate Born–Oppenheimer total energies and electric dipole moments as a function of internuclear separation for two such dimers, LiSr and KRb. We apply fully correlated, high-accuracy quantum Monte Carlo methods for evaluating these molecular properties in a many-body framework. We use small-core effective potentials combined with multi-reference Slater–Jastrow trial wave functions to provide accurate nodes for the fixed-node diffusion Monte Carlo method. For reference and comparison, we calculate the same properties with Hartree–Fock and with restricted Configuration Interaction methods, and carefully assess the impact of the recovered many-body correlations on the calculated quantities. For LiSr, we find a highly non-linear dipole moment curve, which may make this molecule’s dipole moment tunable through vibrational state control.

DOI
10.1080/00268976.2013.788741

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Heteronuclear dimers are of significant interest to experiments seeking to exploit ultracold polar molecules in a number of novel ways, including precision measurement, quantum computing and quantum simulation. We calculate highly accurate Born–Oppenheimer total energies and electric dipole moments as a function of internuclear separation for two such dimers, LiSr and KRb. We apply fully correlated, high-accuracy quantum Monte Carlo methods for evaluating these molecular properties in a many-body framework. We use small-core effective potentials combined with multi-reference Slater–Jastrow trial wave functions to provide accurate nodes for the fixed-node diffusion Monte Carlo method. For reference and comparison, we calculate the same properties with Hartree–Fock and with restricted Configuration Interaction methods, and carefully assess the impact of the recovered many-body correlations on the calculated quantities. For LiSr, we find a highly non-linear dipole moment curve, which may make this molecule’s dipole moment tunable through vibrational state control.
The relativistic configuration interaction valence-bond method has been used to calculate permanent and transition electric dipole moments of the KRb heteronuclear molecule as a function of internuclear separation. The permanent dipole moment of the ground-state $X{}^{1}{\ensuremath{\Sigma}}^{+}$ potential is found to be 0.30(2) ea0{\mathrm{ea}}_{0}ea0​ at the equilibrium internuclear separation with excess negative charge on the potassium atom. For the $a{}^{3}{\ensuremath{\Sigma}}^{+}$ potential the dipole moment is an order of smaller magnitude (1 ${\mathrm{ea}}_{0}=8.47835{10}^{\ensuremath{-}30}\mathrm{Cm}).$ In addition, we calculate transition dipole moments between the two ground-state and excited-state potentials that dissociate to the K(4s)+Rb(5p)\mathrm{K}(4s)+\mathrm{Rb}(5p)K(4s)+Rb(5p) limits. Using this data we propose a way to produce singlet $X{}^{1}{\ensuremath{\Sigma}}^{+}$ KRb molecules by a two-photon Raman process starting from an ultracold mixture of doubly spin-polarized ground state K and Rb atoms. This Raman process is only allowed due to relativistic spin-orbit couplings and the absence of gerade-ungerade selection rules in heteronuclear dimers.
The rapid development of experimental techniques to produce ultracold alkali molecules opens the ways to manipulate them and to control their dynamics using external electric fields. A prerequisite quantity for such studies is the knowledge of their static dipole polarizability. In this paper, we computed the variations with internuclear distance and with vibrational index of the static dipole polarizability components of all homonuclear alkali dimers including Fr(2), and of all heteronuclear alkali dimers involving Li to Cs, in their electronic ground state and in their lowest triplet state. We use the same quantum chemistry approach as in our work on dipole moments [Aymar and Dulieu, J. Chem. Phys. 122, 204302 (2005)], based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective potentials for core polarization. Polarizabilities are extracted from electronic energies using the finite-field method. For the heaviest species Rb(2), Cs(2), and Fr(2) and for all heteronuclear alkali dimers, such results are presented for the first time. The accuracy of our results on atomic and molecular static dipole polarizabilities is discussed by comparing our values with the few available experimental data and elaborate calculations. We found that for all alkali pairs, the parallel and perpendicular components of the ground state polarizabilities at the equilibrium distance R(e) scale as (R(e))(3), which can be related to a simple electrostatic model of an ellipsoidal charge distribution. Prospects for possible alignment and orientation effects with these molecules in forthcoming experiments are discussed.
We discuss the importance of the fermion nodes for the quantum Monte Carlo (QMC) methods and find two cases of the exact nodes. We describe the structure of the generalized pairing wave functions in Pfaffian antisymmetric form and demonstrate their equivalency with certain class of configuration interaction wave functions. We present the QMC calculations of a model fermion system at unitary limit. We find the system to have the energy of E=0.425Efree and the condensate fraction of α=0.48. Further we also perform the QMC calculations of the potential energy surface and the electric dipole moment along that surface of the LiSr molecule. We estimate the vibrationally averaged dipole moment to be 〈D〉ν=0=−0.4(2).
In this study, we investigate the structure of the polar alkali-metal-atom--strontium diatomic molecules as possible candidates for the realization of samples of ultracold polar molecular species not yet investigated experimentally. Using a quantum chemistry approach based on effective core potentials and core polarization potentials, we model these systems as effective three-valence-electron systems, allowing for calculation of electronic properties with full configuration interaction. The potential curve and the permanent dipole moment of the ${}^{2}{\ensuremath{\Sigma}}^{+}$ ground state are determined as functions of the internuclear distance for LiSr, NaSr, KSr, RbSr, and CsSr molecules. These molecules are found to exhibit a significant permanent dipole moment, though smaller than those of the alkali-metal-atom--Rb molecules.
We perform a systematic investigation of the electronic properties of the (2)Σ(+) ground state of Li-alkaline-earth dimers. These molecules are proposed as possible candidates for quantum simulation of lattice-spin models. We apply powerful quantum chemistry coupled-cluster method and large basis sets to calculate potential energies and permanent dipole moments for the LiBe, LiMg, LiCa, LiSr, and LiYb molecules. Agreement of calculated molecular constants with existing experimental data is better than or equal to 8%. Our results reveal a surprising irregularity in the dissociation energy and bond length with an increase in the reduced mass of the molecule. At the same time, the permanent dipole moment at the equilibrium separation has the smallest value between 0.01 a.u. and 0.1 a.u. for the heaviest (LiSr and LiYb) molecules and increases to 1.4 a.u. for the lightest (LiBe), where 1 a.u. is one atomic unit of dipole moment. We consider our study of the (2)Σ(+) molecules a first step towards a comprehensive analysis of their interactions in an optical trap.
Quantum chemistry is a useful tool that provides insight into the properties and behavior of chemical systems. Modern software packages have made quantum chemistry methods more easily accessible, and the continued increase in available computational resources has allowed them to be applied to larger systems at higher levels of theory. Two significant problems that the field faces are the high computational complexity of high-level methods and the shift toward parallelism in high performance computing architectures. This work examines the treatment of weakly interacting molecular systems with the fixed-node diffusion Monte Carlo (DMC) method. DMC and other quantum Monte Carlo (QMC) methods offer a possible solution to both of the aforementioned problems: they can produce near-exact results with a lower scaling (with respect to problem size) than other similarly-accurate methods, and they are inherently parallel, so there is little additional cost associated with distributing the work of a single QMC calculation across a large number of processing units. The only error in DMC that is not systematically improvable is the constraint of a fixed nodal surface of the many-particle wave function of the system being studied. There are many cases in which a single Slater determinant trial function is sufficient to obtain accurate results, but there are others in which more sophisticated multi-determinant trial functions are necessary. Furthermore, it is non-trivial to generate nodal surfaces of similar quality for isolated and interacting molecules, so cancellation of errors is not guaranteed. We examine the use of different single- and multi-determinant trial functions in DMC calculations on small chemical systems with the goal of further understanding how to construct appropriate trial functions for molecules and clusters.