The rovibrational electric dipole transitions in the ground electronic state of the HD molecule are studied. A simple, yet rigorous formula is derived for the transition rates in terms of the electric dipole moment function $D(R)$, which is calculated in a wide range of $R$. Our numerical results for transition rates are in moderate agreement with experiments and previous calculations, but are at least an order of magnitude more accurate.
We present an accurate theoretical determination of rovibrational energy levels of the hydrogen molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation, obtained within nonadiabatic perturbation theory, including the mixed nonadiabatic-relativistic effects. Quantum electrodynamic corrections in the leading $α^5\,m$ and the next-to-leading $α^6\,m$ orders, as well as finite nuclear size effect, are also taken into account but within the Born-Oppenheimer approximation only. Final results for the transition wavel…
We report results of a theoretical investigation of hyperfine interactions in two homonuclear isotopologues of the hydrogen molecule: H$_{2}$ and D$_{2}$. We present a set of hyperfine coupling constants: spin-rotation, spin-spin dipole and, in the case of the D$_{2}$ molecule, electric quadrupole coupling constants for all bound states of the two isotopologues in their ground electronic $X^{1}Σ^{+}_{g}$ state. We provide a list of positions and intensities of 220 997 hyperfine components of 16 079 rovibrational quadrupole transitions of the O, Q and S branches. The positions and intensities o…
Rovibrational structure and electric dipole moments of the AcOCH$_3$+ ion
St. Petersburg State University（圣彼得堡国立大学）；Petersburg Nuclear Physics Institute named by B.P. Konstantinov of National Research Centre（国家研究中心孔斯坦丁诺夫圣彼得堡核物理研究所）
Controlling rovibrational state populations of polar molecules in inhomogeneous electric fields of the Stark deceleration: molecular dynamics and quantum chemistry simulations
In this work we discuss the rotational structure of Rydberg molecules. We calculate the complete wave function in a laboratory fixed frame and derive the transition matrix elements for the pho- toassociation of free ground state atoms. We discuss the implications for the excitation of different rotational states as well as the shape of the angular nuclear wave function. We find a rather com- plex shape and unintuitive coupling strengths, depending on the angular momenta coupling that are relevant for the states. This work explains the different steps to calculate the wave functions and the tra…
A general algorithm for computing the quadrupole-hyperfine effects in the rovibrational spectra of polyatomic molecules is presented for the case of ammonia (NH$_3$). The method extends the general variational approach TROVE by adding the extra term in the Hamiltonian that describes the nuclear quadrupole coupling, with no inherent limitation on the number of quadrupolar nuclei in a molecule. We applied the new approach to compute the nitrogen-nuclear-quadrupole hyperfine structure in the rovibrational spectrum of NH$_3$. These results agree very well with recent experimental spectroscopic dat…
We report a direct measurement of the 0-1 R(0) vibrational transition frequency in ground-state hydrogen deuteride (HD) using infrared-ultraviolet double resonance spectroscopy in a molecular beam. Ground-state molecules are vibrationally excited using a frequency comb referenced continuous-wave infrared laser, and the excited molecules are detected via state-selective ionization with a pulsed ultraviolet laser. We determine an absolute transition frequency of 111 448 815 477(13) kHz. The 0.12 parts-per-billion (ppb) uncertainty is limited primarily by the residual first-order Doppler shift.
The rovibrational kinetic energy for an arbitrary number of rigid molecules is computed. The result has the same general form as the kinetic energy in the molecular rovibrational Hamiltonian, although certain quantities are augmented to account for the rotational energy of the monomers. No specific choices of internal coordinates or body frame are made in order to accommodate the large variety of such conventions. However, special attention is paid to how key quantities transform when these conventions are changed. An example system is explicitly analysed as an illustration of the formalism.
General transformation expressions of the second-order non-adiabatic Hamiltonian of the atomic nuclei, including the kinetic-energy correction terms, are derived upon the change from laboratory-fixed Cartesian coordinates to general curvilinear coordinate systems commonly used in rovibrational computations. The kinetic-energy or so-called "mass-correction" tensor elements are computed with the stochastic variational method and floating explicitly correlated Gaussian functions for the H$_2^+$ molecular ion in its ground electronic state. (Further numerical applications for the $^4$He$_2^+$ mole…
The leading nonadiabatic corrections to rovibrational levels of a diatomic molecule are expressed in terms of three functions of internuclear distance: corrections to the adiabatic potential, the effective nuclear mass, and the effective moment of inertia. The resulting radial Schrödinger equation for nuclear motion is solved numerically yielding accurate nonadiabatic energies for all rovibrational levels of H$_2$ molecule in excellent agreement with previous calculations by Wolniewicz.
We present a new method for the generation of rotationally and vibrationally state-selected, translationally cold molecular ions in ion traps. Our technique is based on the state-selective threshold photoionization of neutral molecules followed by sympathetic cooling of the resulting ions with laser-cooled calcium ions. Using N$_2^+$ ions as a test system, we achieve > 90 % selectivity in the preparation of the ground rovibrational level and state lifetimes on the order of 15 minutes limited by collisions with background-gas molecules. The technique can be employed to produce a wide range of a…
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 …
The spectrum of triatomic molecules with close rovibrational opposite parity levels is sensitive to the $\mathcal{P}$,$\mathcal{T}$-odd effects. This makes them a convenient platform for the experimental search of a new physics. Among the promising candidates one may distinguish the YbOH as a non-radioactive compound with a heavy atom. The energy gap between levels of opposite parity, $l$-doubling, is of a great interest as it determines the electric field strength required for the full polarization of the molecule. Likewise, the influence of the bending and stretching modes on the sensitiviti…
The dicarbon molecular anion is currently of interest as a candidate for laser cooling due to its electronic structure and favorable branching ratios to the ground electronic and vibrational states. Helium has been proposed as a buffer gas to cool the molecule's internal motion. We calculate the cross sections and corresponding rates for rovibrational inelastic collisions of the dicarbon anion with He, and also with Ne and Ar, on three-dimensional ab initio potential energy surfaces using quantum scattering theory. The rates for vibrational quenching with He and Ne are very small and are simil…
Quantum state-resolved spectroscopy was recently achieved for C60 molecules when cooled by buffer gas collisions and probed with a midinfrared frequency comb. This rovibrational quantum state resolution for the largest molecule on record is facilitated by the remarkable symmetry and rigidity of C60, which also present new opportunities and challenges to explore energy transfer between quantum states in this many-atom system. Here we combine state-specific optical pumping, buffer gas collisions, and ultrasensitive intracavity nonlinear spectroscopy to initiate and probe the rotation-vibration e…
Analytic consideration of the Bohr-Oppenheimer (BO) approximation for diatomic molecules is proposed: accurate analytic interpolation for potential curve consistent with its rovibrational spectra is found. It is shown that in the Bohr-Oppenheimer approximation for four lowest electronic states $1sσ_g$ and $2pσ_u$, $2p π_u$ and $3d π_g$ of H$_2^+$, the ground state X$^2Σ^+$ of HeH and the two lowest states $^1Σ^+_g$ and $^3Σ^+_u$ of H$_2$, the potential curves can be analytically interpolated in full range of internuclear distances $R$ with not less than {4-5-6} figures. Approximation based on …
An analytical representation for the potential energy curve for the ground state $X^1Σ^+$ of the hydrogen fluoride molecule (HF) is presented in the frame of the Born-Oppenheimer approximation. The analytical expression for the potential energy curve is based in a two point Padé approximant which correctly reproduces the asymptotic behaviors at small $R\rightarrow 0$ and large $R\rightarrow\infty$ internuclear distances, obtaining not less than 4-5 s.d. when compared with experimental results. The rovibrational spectra of the diatomic molecule HF is calculated by solving the Schrödinger equati…
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 calculate…
Explicit algebraic expressions for the expansion of the vibrational matrix elements in series of matrix elements on the wave functions of the ground vibrational state have been obtained for arbitrary sufficiently differentiable functions of the internuclear distance, arbitrary values v and v', and the potential curves whose ladder operators can be constructed. A diagram technique have been developed for it that consists in: 1) the numeration of the matrix elements by points of the 2D diagram with coordinates (l, k), 2) the drawing arrows between points of this diagram corresponding to the acti…
An algebraic model taking into account the influence of the molecular rotation on the wave functions of vibrational-rotational states of the diatomic molecule using the formalism of the ladder operators and an expansion in a small parameter characterizing the vibrational-rotational interaction have been proposed for the potentials whose the creation and annihilation operators can be constructed. Expressions for the expansion of the wave function of the vibrational-rotational states in a set of wave functions of the rotationless vibrational states have been obtained of the second order in the p…
C$_3$P$^-$ is analogous to the known interstellar anion C$_3$N$^-$ with phosphorus replacing the nitrogen in a simple step down the periodic table. In this work, it is shown that C$_3$P$^-$ is likely to possess a dipole-bound excited state. It has been hypothesized and observationally supported that dipole-bound excited states are an avenue through which anions could be formed in the interstellar medium. Additionally, C$_3$P$^-$ has a valence excited state that may lead to further stabilization of this molecule, and C$_3$P$^-$ has a larger dipole moment than neutral C$_3$P ($\sim 6$ D vs. $\si…
A general variational approach for computing the rovibrational dynamics of polyatomic molecules in the presence of external electric fields is presented. Highly accurate, full-dimensional variational calculations provide a basis of field-free rovibrational states for evaluating the rovibrational matrix elements of high-rank Cartesian tensor operators, and for solving the time-dependent Schrödinger equation. The effect of the external electric field is treated as a multipole moment expansion truncated at the second hyperpolarizability interaction term. Our fully numerical and computationally ef…
Electron-impact vi->vf vibrational excitations cross sections, involving rovibrationally excited N_{2}(v_{i}, J) and NO(v_{i}, J) molecules (fixed J), are calculated for collisions occurring through the nitrogen resonant electronic state N_{2}^{-} (X ^{2}Π_{g}), and the three resonant states of nitric oxide NO^{-}(^{3}Σ^{-},^{1} Δ,^{1} Σ^{+}). Complete sets of cross sections have been obtained for all possible transitions involving 68 vibrational levels of N2(X ^{1}Σ^{+}_{g}) and 55 levels of NO(X ^{2}Π), for the incident electron energy between 0.1 and 10 eV. In order to study the rotational …
We demonstrate coherent microwave control of rotational and hyperfine states of trapped, ultracold, and chemically stable $^{23}$Na$^{40}$K molecules. Starting with all molecules in the absolute rovibrational and hyperfine ground state, we study rotational transitions in combined magnetic and electric fields and explain the rich hyperfine structure. Following the transfer of the entire molecular ensemble into a single hyperfine level of the first rotationally excited state, $J{=}1$, we observe collisional lifetimes of more than $3\, \rm s$, comparable to those in the rovibrational ground state…
We present a general variational approach for computing the laser-induced rovibrational dynamics of molecules taking into account the hyperfine effects of the nuclear quadrupole coupling. The method combines the general variational approach TROVE, which provides accurate rovibrational hyperfine energies and wave functions for arbitrary molecules, with the variational method RichMol, designed for generalized simulations of the rovibrational dynamics in the presence of external electric fields. We investigate the effect of the nuclear quadrupole coupling on the short-pulse laser alignment of a p…
We present a perturbative method for ab initio calculations of rotational and rovibrational effective Hamiltonians of both rigid and non-rigid molecules. Our approach is based on a curvilinear implementation of second order vibrational Møller-Plesset perturbation theory (VMP2) extended to include rotational effects via a second order contact transformation. Though more expensive, this approach is significantly more accurate than standard second order vibrational perturbation theory (VPT2) for systems that are poorly described to zeroth order by rectilinear normal mode harmonic oscillators. We …
Ultracold polar and magnetic ${}^{23}$Na${}^6$Li molecules in the rovibrational ground state of the lowest triplet $a^3Σ^+$ electronic state have been recently produced. Here, we calculate the electronic and rovibrational structure of these 14-electron molecules with spectroscopic accuracy ($<0.5\,$cm$^{-1}$) using state-of-the-art ab initio methods of quantum chemistry. We employ the hierarchy of the coupled-cluster wave functions and Gaussian basis sets extrapolated to the complete basis set limit. We show that the inclusion of higher-level excitations, core-electron correlation, relativisti…
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…
A procedure for calculation of rotation-vibration states of medium sized molecules is presented. It combines the advantages of variational calculations and perturbation theory. The vibrational problem is solved by diagonalizing a Hamiltonian matrix, which is partitioned into two sub-blocks. The first, smaller sub-block includes matrix elements with the largest contribution to the energy levels targeted in the calculations. The second, larger sub-block comprises those basis states which have little effect on these energy levels. Numerical perturbation theory, implemented as a Jacobi rotation, i…
Characterising molecules for fundamental physics: an accurate spectroscopic model of methyltrioxorhenium derived from new infrared and millimetre-wave measurements
Precision spectroscopy of trapped HfF^+ will be used in a search for the permanent electric dipole moment of the electron (eEDM). While this dipole moment has yet to be observed, various extensions to the standard model of particle physics (such as supersymmetry) predict values that are close to the current limit. We present extensive survey spectroscopy of 19 bands covering nearly 5000 cm^(-1) using both frequency-comb and single-frequency laser velocity-modulation spectroscopy. We obtain high-precision rovibrational constants for eight electronic states including those that will be necessary…
$Q_{\rm int}$($T$), of the H$_2$$^{16}$O molecule is reported for temperatures between 0 and 6000 K. Determination of $Q_{\rm int}$($T$) is principally based on the direct summation technique involving all accurate experimental energy levels known for H$_2$$^{16}$O (almost 20~000 rovibrational energies including an almost complete list up to a relative energy of 7500 \cm), augmented with a less accurate but complete list of first-principles computed rovibrational energy levels up to the first dissociation limit, about 41~000 \cm\ (the latter list includes close to one million bound rovibration…
Strong magnetic fields have a large impact on the dynamics of molecules. In addition to the changes of the electronic structure, the nuclei are exposed to the Lorentz force with the magnetic field being screened by the electrons. In this work, we explore these effects using ab-initio molecular dynamics simulations based on an effective Hamiltonian calculated at the Hartree-Fock level of theory. To correctly include these non-conservative forces in the dynamics, we have designed a series of novel propagators that show both good efficiency and stability in test cases. As a first application, we …
We explore one-dimensional (1-D) samples of ultracold polar molecules with attractive dipole-dipole interactions and show the existence of a repulsive barrier due to a strong quadrupole interaction between molecules. This barrier can stabilize a gas of ultracold KRb molecules and even lead to long-range wells supporting bound states between molecules. The properties of these wells can be controlled by external electric fields, allowing the formation of long polymer-like chains of KRb, and studies of quantum phase transitions by varying the effective interaction between molecules. We discuss th…
We analyze the electric dipole moments (PDMs) and static electric dipole polarizabilities of the alkali--alkaline-earth (Alk-AlkE) dimers by employing finite-field coupled-cluster methods, both in the frameworks of non-relativistic and four-component spinfree relativistic theory. In order to carry out comparative analyses rigorously, we consider those Alk-AlkE molecules made out of the lightest to the medium-heavy constituent atoms (Alk: Li to Rb and AlkE: Be through Sr). We present behaviour of electron correlation effects as well as relativistic effects with the size of the molecules. Uncert…
Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets. This makes it a promising candidate for experimental study of the $\mathcal{P}$,$\mathcal{T}$-violation. Previous studies concentrated on the calculations for different geometries without the averaging over the rovibrational wave function and stressed the possibility that the dependence of the $\mathcal{P}$, $\mathcal{T}$ parameters on the bond angle may significantly alter the observed value. We obtain the rovibrational wave functions of RaOH in the ground electronic stat…
We use time-resolved direct frequency comb spectroscopy in the mid-infrared to obtain high-resolution rovibrational spectra of products produced from the OD+CO reaction. In this work, we present spectral analyses for isotopologues of the transient DOCO radicals from this reaction in the OD stretch region. The analyses were performed with aid of two different theoretical approaches based on both perturbation theory and variational calculations used for prediction of rovibrational spectra of polyatomic molecules. We discuss the advantages and challenges of our current approach for studying spect…
The dipole-bound excited state of the methylene nitrile anion (CH2CN-) has been suggested as a candidate carrier for a diffuse interstellar band (DIB) at 803.8 nm. Its corresponding radical has been detected in the interstellar medium (ISM), making the existence for the anion possible. This work applies state-of-the-art ab initio methods such as coupled cluster theory to reproduce accurately the electronic excitations for CH2CN- and the similar methylene enolate anion, CH2CHO-. This same approach has been employed to indicate that 19 other anions may possess electronically excited states, five…
A classical microscopic theory of rovibrational motion at high angular momenta in symmetrical non-linear molecules AB$_2$ is derived within the framework of small oscillations near the stationary states of a rotating molecule. The full-dimensional analysis including stretching vibrations has confirmed the existence of the bifurcation predicted previously by means of the rigid-bender model. The formation of fourfold energy clusters has already been experimentally verified for H$_2$Se and it has been demonstrated in fully-dimensional quantum mechanical calculations using the MORBID computer prog…
The efficiency of cavity sideband cooling of trapped molecules is theoretically investigated for the case where the IR transition between two rovibrational states is used as a cycling transition. The molecules are assumed to be trapped either by a radio-frequency or optical trapping potential, depending on whether they are charged or neutral, and confined inside a high-finesse optical resonator which enhances radiative emission into the cavity mode. Using realistic experimental parameters and COS as a representative molecular example, we show that in this setup cooling to the trap ground state…
We present a data-driven approach for the prediction of the electric dipole moment of diatomic molecules, which is one of the most relevant molecular properties. In particular, we apply Gaussian process regression to a novel dataset to show that dipole moments of diatomic molecules can be learned, and hence predicted, with a relative error <5%. The dataset contains the dipole moment of 162 diatomic molecules, the most exhaustive and unbiased dataset of dipole moments up to date. Our findings show that the dipole moment of diatomic molecules depends on atomic properties of the constituents atom…
Rothe's Method for Quantum Dynamics in Atoms and Molecules with Gaussian Wavepackets
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo（奥斯陆大学化学系希莱拉索量子分子科学中心）；Faculty of Chemistry, University of Warsaw（华沙大学化学学院）；Department of Chemistry and Biochemistry, University of Arizona（亚利桑那大学化学与生物化学系）
$Aims$: We revisit with new augmented accuracy the theoretical dynamics of basic isotope exchange reactions involved in the $^{12}$C/$^{13}$C, $^{16}$O/$^{18}$O, and $^{14}$N/$^{15}$N balance because these reactions have already been studied experimentally in great detail. $Methods$: Electronic structure methods were employed to explore potential energy surfaces, full-dimensional rovibrational calculations to compute rovibrational energy levels that are numerically exact, and chemical network models to estimate the abundance ratios under interstellar conditions. $Results$: New exothermicities,…
It is shown that the dipole moment of polar (water, methanol, formamide, acetone and acetonitrile) molecules in the neighborhood of a cation is increased primarily by polarization from the bare electrostatic charge of the cation, although the effective value of the latter is somewhat reduced by "back donation" of electrons from neighbouring polar molecules. In other words, the classical picture may be viewed as if a point charge slightly smaller than the nominal charge of the cation would be placed at the cation site. It was found that the geometrical arrangement of the polar molecules in the …
We report on the creation of an ultracold dipolar gas of fermionic $^{23}$Na$^{40}$K molecules in their absolute rovibrational and hyperfine ground state. Starting from weakly bound Feshbach molecules, we demonstrate hyperfine resolved two-photon transfer into the singlet ${\rm X}^1Σ^+ |v{=}0,J{=}0\rangle$ ground state, coherently bridging a binding energy difference of 0.65 eV via stimulated rapid adiabatic passage. The spin-polarized, nearly quantum degenerate molecular gas displays a lifetime longer than 2.5 s, highlighting NaK's stability against two-body chemical reactions. A homogeneous …
Based on fundamental symmetries, molecules cannot have a permanent electric dipole moment although it is commonly used in the literature to explain the different molecular spectra for heteronuclear and homonuclear molecules. Electric-dipole rotational and vibrational spectra can indeed be observed in heteronuclear molecules while they are missing in molecules with identical nuclei. I show that the missing spectral features can be explained as an effect of the exchange symmetry for identical particles.
