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ANT 2023 is a program for quasiclassical and semiclassical trajectories, both single-surface trajectories for which the Born-Oppenheimer approximation is valid and multi-surface calculations with electronic state changes, i.e., for electronically adiabatic and electronically nonadiabatic trajectories. There are several methods available for multisurface problems: surface hopping with or without time uncertainty and with or without decoherence, semiclassical Ehrenfest, self-consistent decay of mixing, and coherent switching with decay of mixing (CSDM). The potential surface for single-surface problems may be an analytic potential function supplied by the user, or one may use direct dynamics. To use the adiabatic representation (i.e., electronically adiabatic basis functions) for electronically nonadiabatic dynamics, the user may either provide the adiabatic surfaces and nonadiabatic couplings by direct dynamics, or the program may calculate them from diabatic surfaces and diabatic couplings, which are usually analytic. One can also use analytic fits to the surfaces and couplings to carry out calculations entirely in the diabatic representation. The curvature-driven approximation is available as an option for use with CSDM and trajectory surface hopping. The ANT 2023 program is especially recommended for calculations with analytic potential energy surfaces and couplings because of its high efficiency for such calculations. Program Title: ANT 2023 , revision B CPC Library link to program files: https://doi.org/10.17632/gr74wwckcp.1 Developer's repository link: https://doi.org/10.5281/zenodo.10011563 Licensing Provisions: Apache-2.0 Programming language : Fortran 90 Interfaces to other programs : For direct dynamics, the code has well tested interfaces to the Gaussian 09 [1], Gaussian 16 [2], MOPACmn [3], and Molpro [4] electronic structure codes. The interfaces are included, but these electronic structure programs must be obtained separately. Users may also provide their own interfaces to other electronic structure programs. [1] M. J. Frisch et al. Gaussian 09, Gaussian, Inc., Wallingford CT, 2016. [2] M. J. Frisch et al., Gaussian 16, Gaussian, Inc., Wallingford CT, 2016. [3] J. J. P. Stewart et al., MOPAC 5.022mn, University of Minnesota, Minneapolis, MN, 2015; Zenodo. https://doi.org/10.5281/zenodo.8153079 [4] H.-J. Werner et al., J. Chem. Phys. 152 (2020) 144107. Nature of problem : classical, quasiclassical, or semiclassical molecular dynamics for electronically adiabatic or electronically nonadiabatic collisions and unimolecular processes of atoms, molecules, and clusters Solution method : The program integrates the classical or semiclassical equations of motion for the motion of the nuclei. ANT 2023 can use anharmonic initial-state selection for initial states of diatomics or harmonic initial-state selection for general polyatomics. The equations of motion for electronically adiabatic processes are Hamilton's equations with potential energy functions corresponding to the Born-Oppenheimer approximation. The equations of motion for electronically nonadiabatic processes (non-Born-Oppenheimer processes) include trajectory surface hopping (fewest switches with or without time uncertainty and with or without decoherence) or several possible mean-field methods, including the semiclassical Ehrenfest method (also called the time-dependent Hartree method), self-consistent decay of mixing, and coherent switching with decay of mixing. Electronically nonadiabatic processes may be treated using either the adiabatic representation or a diabatic representation, and the potential surfaces and couplings may be obtained from analytic fits in a user-supplied subroutine or by direct dynamics, which involves requesting energies, gradients, and couplings as needed from a quantum chemistry electronic structure program. In the adiabatic representation, the coupling may be nonadiabatic coupling vectors (based on gradients of electronic wave functions), time-derivative couplings (based on overlaps of electronic wave functions), or curvature-driven couplings (based on the curvatures of the adiabatic potential energy surfaces). Additional comments : The ANT 2023 program authors are Y. Shu, L. Zhang, J. Zheng, Z. H. Li, A. W. Jasper, D. A. Bonhommeau, R. Valero, R. Meana-Pañeda, S. L. Mielke, Z. Varga, and D. G. Truhlar [5]; the authors of the article [6] describing ANT 2023 are Y. Shu, L. Zhang, and D. G. Truhlar. References : [1] M. J. Frisch et al. Gaussian 09, Gaussian, Inc., Wallingford CT, 2016. [2] M. J. Frisch et al., Gaussian 16, Gaussian, Inc., Wallingford CT, 2016. [3] J. J. P. Stewart et al., MOPAC 5.022mn, University of Minnesota, Minneapolis, MN, 2015; Zenodo. https://doi.org/10.5281/zenodo.8153079 [4] H.-J. Werner et al., J. Chem. Phys. 152 (2020) 144107. [5] Y. Shu, L. Zhang, J. Zheng, Z. H. Li, A. W. Jasper, D. A. Bonhommeau, R. Valero, R. Meana-Pañeda, S. L. Mielke, Z. Varga, & D. G. Truhlar. (2023). ANT 2023: A Program for Adiabatic and Nonadiabatic Trajectories (Version 2023). Zenodo. https://doi.org/10.5281/zenodo.10011563 [6] Y. Shu, L. Zhang, & D. G. Truhlar. Computer Physics Communications, to be published. [ABSTRACT FROM AUTHOR]

POTLIB is a library of global and semiglobal potential energy surface subprograms. The library currently features 410 entries, including both single-state entries and multi-state entries. When one calls the routine of a single-state entry, it returns the ground-electronic-state adiabatic potential energy surface at the input geometry. In addition, some entries also return the gradient of the surface. When one calls a multi-state entry, it returns a diabatic potential energy matrix (DPEM). If the entry also has the gradient of the DPEM, one can compute adiabatic surfaces, their gradients, and the nonadiabatic coupling vectors (NACs) from the DPEM and its gradient by diagonalization. Some but not all the routines conform to one of a set of standard interfaces. The goal is to facilitate chemical dynamics research by collecting and disseminating a comprehensive collection of state-of-the-art potential energy routines (developed by a wide, international group of researchers) with systematic and well-defined interfaces for use with chemical dynamics programs. Systems in the library include CHArO 2 , CHN 2 O+, CH 2 O, CH 2 O 2 , CH 3 N 2 , CH 3 O, CH 4 , CH 4 Br, CH 4 Cl, CH 4 F, CH 4 O, CH 4 OCl, CH 4 OF, CH 4 OH, CH 5 , CH 5 + , CH 5 N, CH 5 O 2 , CH 8 O 2 , C 2 H 2 N 2 O, C 2 H 2 O, C 2 H 4 N, C 2 H 4 O 4 , C 2 H 6 Cl, C 2 H 6 F, C 2 H 6 H, C 2 H 6 O, C 2 H 6 OH, C 2 H 7 , C 2 O 2 , C 3 H 4 O 2 , C 3 H 7 NO, C 6 H 6 O, C 6 H 6 S, C 7 H8S, HBrCl, HCl 2 , HF 2 , HI 2 , HLiF, HNaF, HO 2 , HO 3 , HOBr, HSiO, H 2 Br, H 2 ClO, H 2 F, H 2 F 2 , H 2 FO, H 2 Na, H 2 O, H 2 O 2 , H 2 OBr, H 3 , H 3 Cl, H 3 ClN, H 3 ClO, H 3 N, H 3 O, H 3 O 2 , H 3 + , H 3 S, H 4 ClSi, H 4 N, H 4 NO, H 4 O 2 , H 5 GeO, H 5 Si, H 7 + , Al m H n , Al n , ArNO, K 2 Rb 2 , NO 2 , N 2 O, N 2 O 2 , N 3 , N 4 , O 3 , and O 4. Program title: PotLib 2023 CPC Library link to program files: https://doi.org/10.17632/chxxhnnt4p.1 Licensing provisions: Apache 2.0 Programming language: Fortran Does the new version supersede the previous version?: Yes Journal references of previous versions: Comput. Phys. Comm. 144 (2002) 169–187 [1]; Erratum: Comput. Phys. Comm. 156 (2004) 319–32. Nature of problem: Within the Born–Oppenheimer approximation, the electronically adiabatic interactions of atoms and molecules can be represented by a potential energy surface (PES) that depends on the geometry of the reacting species [2-4]. An electronically nonadiabatic system can be approximately described by a diabatic potential energy matrix (DPEM) that also depends on molecular geometry [5,6]. The library contains Fortran subroutines of PESs and DPEMs for reactive and non-reactive systems. Solution method: The user can incorporate a PES, DPEM, or PES set from a DPEM into a chemical dynamics computer code to supply the needed potential or potentials and optionally the gradients (forces) and surface couplings. Summary of revisions: The new version includes many more potentials than the original version of the library. [1] R.J. Duchovic, Y.L. Volobuev, G.C. Lynch, T.C. Allison, J.C. Corchado, D.G. Truhlar, A.F. Wagner, B.C. Garrett, Comput. Phys. Commun. 144 (2002) 169-187. [2] C.A. Parr, D.G. Truhlar, J. Phys. Chem. 75 (1971) 1844-1860. [3] D.G. Truhlar, R. Steckler, M.S. Gordon, Chem. Rev. 87 (1987) 217-236. [4] T.V. Albu, J. Espinosa-García, D.G. Truhlar, Chem. Rev. 107 (2007) 5101-5132. [5] B.C. Garrett, D.G. Truhlar, Theor. Chem. Adv. Perspect. 6A (1981) 215-289. [6] Y. Shu, Z. Varga, S. Kanchanakungwankul, L. Zhang, D.G. Truhlar, J. Phys. Chem. A 126 (2022) 992-1018. [ABSTRACT FROM AUTHOR]

Molecular high-order harmonic generation from the H2+ ion driven by spatial inhomogeneous fields consisting of the chirped pulse and a terahertz pulse has been theoretically investigated by numerically solving the non-Born-Oppenheimer time-dependent Schrödinger equation. It shows that with the introduction of the chirp as well as the spatial inhomogeneity of the pulse, not only the harmonic cutoff is remarkably extended, but also the single short quantum path is selected to contribute to the harmonic spectra. Moreover, through investigation the effects of the laser and the molecular parameters on the inhomogeneous harmonic generation, we found 1.92- and 3.3-dB enhanced fields for the chirp-free and chirped inhomogeneous pulses, respectively. Isotopic effect shows that intense harmonics can be generated from the lighter molecule. Furthermore, with the enhancement of the initial vibrational state and by properly adding a terahertz controlling pulse, the harmonic yield is enhanced by almost five orders of magnitude compared with the initial single chirped case. As a result, a 362-eV supercontinuum (which corresponds to a 4.0-dB laser field enhancement) with five orders of magnitude improvement is obtained. Finally, by properly superposing the harmonics, a series of intense extreme ultraviolet pulses with durations from 22 to 52 as can be produced. [ABSTRACT FROM AUTHOR]

The electron-nuclei interaction affects the intemuclear motion in slow ion-atom collisions, which in turn affects theoretical results for the cross sections of various collision processes. The results are especially sensitive to the details of the intemuclear dynamics in the presence of a strong isotope effect on the cross sections, as is the case, e.g., for the charge transfer in low-energy collisions of He2+ with H, D, and T. By considering this system as an example, we show that intemuclear trajectories defined by the Born-Oppenheimer (BO) potential in the entrance collision channel, which effectively accounts for the electron-nuclei interaction, are in much better agreement with trajectories obtained in the ab initio electron-nuclear dynamics approach [R. Cabrera-Trujillo et al., Phys. Rev. A 83, 012715 (2011)] than the corresponding Coulomb trajectories. We also show that the use of the BO trajectory instead of the Coulomb trajectory in the calculations of the charge-transfer cross sections within the adiabatic approach improves the agreement of the results with ab initio calculations. [ABSTRACT FROM AUTHOR]

High-order-harmonic generation (HHG) for the H2+ molecule in a 3-fs, 800-nm few-cycle Gaussian laser pulse combined with a static field is investigated by solving the one-dimensional electronic and one-dimensional nuclear time-dependent Schrödinger equation within the non-Born-Oppenheimer approximation. The spatial distribution in HHG is demonstrated and the results present the recombination process of the electron with the two nuclei, respectively. The spatial distribution of the HHG spectra shows that there is little possibility of the recombination of the electron with the nuclei around the origin z = 0 a.u. and equilibrium internuclear positions z = ±1.3 a.u. This characteristic is irrelevant to laser parameters and is only attributed to the molecular structure. Furthermore, we investigate the time-dependent electron-nuclear wave packet and ionization probability to further explain the underlying physical mechanism. [ABSTRACT FROM AUTHOR]

We examine the residual current to investigate the conversion efficiency from the few-cycle laser pulse into the terahertz radiation of H2+ by solving the time-dependent Schrödinger equation in the non-Born-Oppenheimer approach. It is found that the nuclear motion and high vibrational states will improve the optical-to-terahertz conversion efficiency significantly, while with the increasing of the laser intensity, ionization saturation will suppress the effects of moving nuclei. Moreover, based on the dependence of the residual current on the delay time of the nuclear vibration, we conclude that the terahertz signal may serve as a tool to probe the nuclear dynamics. [ABSTRACT FROM AUTHOR]

We introduce the electron-nucleus mean-field configuration-interaction (EN-MFCI) approach. It consists in building an effective Hamiltonian for the electrons taking into account a mean field due to the nuclear motion and, conversely, in building an effective Hamiltonian for the nuclear motion taking into account a mean field due to the electrons. The eigenvalue problems of these Hamiltonians are solved in basis sets giving partial eigensolutions for the active degrees of freedom (DOF's), that is to say, either for the electrons or for nuclear motion. The process can be iterated or electron and nuclear motion DOF's can be contracted in a CI calculation. In the EN-MFCI reduction of the molecular Schrödinger equation to an electronic and a nuclear problem, the electronic wave functions do not depend parametrically upon nuclear coordinates. So, it is different from traditional adiabatic methods. Furthermore, when contracting electronic and nuclear functions, a direct product basis set is built in contrast with methods which treat electrons and nuclei on the same footing, but where electron-nucleus explicitly correlated coordinates are used. Also, the EN-MFCI approach can make use of the partition of molecular DOF's into translational, rotational, and internal DOF's. As a result, there is no need to eliminate translations and rotations from the calculation, and the convergence of vibrational levels is facilitated by the use of appropriate internal coordinates. The method is illustrated on diatomic molecules. [ABSTRACT FROM AUTHOR]

We investigate the characteristic effects of nuclear motion on attosecond transient-absorption spectra in molecules by calculating the spectrum for different model systems. Two models of the hydrogen molecular ion are considered: one where the internuclear separation is fixed, and one where the nuclei are free to vibrate. The spectra for the fixed nuclei model are similar to atomic spectra reported elsewhere, while the spectra obtained in the model including nuclear motion are very different and dominated by extremely broad absorption features. These broad absorption features are analyzed and their relation to molecular dissociation investigated. The study of the hydrogen molecular ion validates an approach based on the Born-Oppenheimer approximation and a finite electronic basis. This latter approach is then used to study the three-dimensional hydrogen molecule including nuclear vibration. The spectrum obtained from H2 is compared to the result of a fixed-nuclei calculation. In the attosecond transient-absorption spectra of H2 including nuclear motion we find a rich absorption structure corresponding to population of different vibrational states in the molecule, while the fixed-nuclei spectra again are very similar to atomic spectra. We find that light-induced structures at well-defined energies reported in atomic systems are also present in our fixed nuclei molecular spectra, but suppressed in the H2+ and H2 spectra with moving nuclei. We show that the signatures of light-induced structures are closely related to the nuclear dynamics of the system through the shapes and relative arrangement of the Born-Oppenheimer potential-energy curves. [ABSTRACT FROM AUTHOR]

We study the two-body and three-body bound states in ultracold atomic mixtures with one of the atoms subjected to an isotropic spin-orbit (SO) coupling. We consider a system of two identical fermions interacting with one SO-coupled atom. It is found that there can exist two types of three-body bound states, Efimov trimers and universal trimers. The Efimov trimers are energetically less favored by the SO coupling, which will finally merge into the atom-dimer threshold as increasing the SO-coupling strength. Nevertheless, these trimers exhibit a discrete scaling law incorporating the SO-coupling effect. On the other hand, the universal trimers are more favored by the SO coupling. They can be induced at negative i-wave scattering lengths and with smaller mass ratios than those without SO coupling. These results are obtained by both the Born-Oppenheimer approximation and exact solutions from three-body equations. [ABSTRACT FROM AUTHOR]

We study tunneling ionization in a one-dimensional three-body model of a molecule, treating both electronic and nuclear degrees of freedom exactly. In a recent paper [Phys. Rev. Lett. 111, 153003 (2013)] it was demonstrated using a finite-range potential that the Born-Oppenheimer approximation breaks down for fields weaker than a critical field FBO when describing tunneling ionization of molecules, but works for stronger fields. It was also demonstrated that the weak-field asymptotic theory allows for an accurate description in this weak-field limit. In the present paper, we consider a potential with a Coulomb tail and nonzero dipole moment, modeling polar molecules. Our study shows that the conclusions of the aforementioned paper also hold for this potential. [ABSTRACT FROM AUTHOR]

We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a p-wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum I = ±1 whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.03404 for identical bosons and 2.41421 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum. [ABSTRACT FROM AUTHOR]

High-order-harmonic generation (HHG) spectra have been calculated for H2+ molecules aligned parallel to the polarization of the laser field. We make use of the Jacobi coordinates and neglect the rotation of the nuclei. The remaining time-dependent Schrödinger equation is three dimensional in spatial coordinates, one of them being the internuclear separation and the other two describing the electronic motion. The problem is solved using the accurate and efficient time-dependent generalized pseudospectral method in prolate spheroidal coordinates for the electronic coordinates and Fourier grid method for the internuclear separation. Laser pulses with a carrier wavelength of 800 nm, a duration of ten optical cycles, and a peak intensity of 2 × 1014 W/cm² have been used in the calculations. Our HHG spectra, which incorporate the effect of nuclear vibration, generally exhibit a significant deviation from those calculated for the fixed internuclear separations. The low-energy regions of the spectra, however, resemble those for the nuclei fixed at larger separations, while the high-energy regions are closer to those for the nuclei fixed at smaller internuclear distances. The dynamics of the nuclear vibrational wave packet is also obtained and analyzed. [ABSTRACT FROM AUTHOR]

In this work we develop tools that enable the study of nonadiabatic effects with variational and diffusion Monte Carlo methods. We introduce a highly accurate wave-function ansatz for electron-ion systems that can involve a combination of both clamped ions and quantum nuclei. We explicitly calculate the ground-state energies of H2, LiH, H20, and FHF using fixed-node quantum Monte Carlo with wave-function nodes that explicitly depend on the ion positions. The obtained energies implicitly include the effects arising from quantum nuclei and electron-nucleus coupling. We compare our results to the best theoretical and experimental results available and find excellent agreement. [ABSTRACT FROM AUTHOR]

The properties of the electronic ground state of the polar and paramagnetic europium-S-state-atom molecules have been investigated. Ab initio techniques have been applied to compute the potential energy curves for the europium-alkali-metal-atom, EuX (X = Li, Na, K, Rb, Cs), europium-alkaline-earth-metal-atom, Euk (Y = Be, Mg, Ca, Sr, Ba), and europium-ytterbium, EuYb, molecules in the Born-Oppenheimer approximation for the highspin electronic ground state. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), was employed and the scalar relativistic effects within the small-core energy-consistent pseudopotentials were included. The permanent electric dipole moments and static electric dipole polarizabilities were computed. The leading long-range coefficients describing the dispersion interaction between atoms at large internuclear distances C(, are also reported. The EuK, EuRb, and EuCs molecules are examples of species possessing both large electric and magnetic dipole moments making them potentially interesting candidates for ultracold many-body quantum simulations when confined in an optical lattice in combined electric and magnetic fields. [ABSTRACT FROM AUTHOR]

Many of the XYZ mesons discovered in the last decade can be identified as bound states in Born-Oppenheimer (B-O) potentials for a heavy quark and antiquark. They include quarkonium hybrids, which are bound states in excited flavor-singlet B-0 potentials, and quarkonium tetraquarks, which are bound states in flavor-nonsinglet B-0 potentials. We present simple parametrizations of the deepest flavorsinglet B-0 potentials. We infer the deepest flavor-nonsinglet B-0 potentials from lattice QCD calculations of static adjoint mesons. Selection rules for hadronic transitions are used to identify XYZ mesons that are candidates for ground-state energy levels in the B-0 potentials for charmonium hybrids and tetraquarks. The energies of the lowest-energy charmonium hybrids are predicted by using the results of lattice QCD calculations to calculate the energy splittings between the ground states of different B-0 potentials and using the Schrodinger equation to determine the splittings between energy levels within a B-0 potential. [ABSTRACT FROM AUTHOR]

The static and dynamic electric multipolar polarizabilities and second hyperpolarizabilities of the H2+, D2+, and HD+ molecular ions in the ground and first excited states are calculated nonrelativistically using explicitly correlated Hylleraas basis sets. The calculations are fully nonadiabatic; the Born-Oppenheimer approximation is not used. Comparisons are made with published theoretical and experimental results, where available. In our approach, no derivatives of energy functions nor derivatives of response functions are needed. In particular, we make contact with earlier calculations in the Born-Oppenheimer calculation where polarizabilities were decomposed into electronic, vibrational, and rotational contributions and where hyperpolarizabilities were determined from derivatives of energy functions. We find that the static hyperpolarizability for the ground state of HD+ is seven orders of magnitude larger than the corresponding dipole polarizability. For the dipole polarizability of HD+ in the first excited state the high precision of the present method facilitates treatment of a near cancellation between two terms. For applications to laser spectroscopy of trapped ions we find tune-out and magic wavelengths for the HD+ ion in a laser field. In addition, we also calculate the first few leading terms for long-range interactions of a hydrogen molecular ion and a ground state H, He, or Li atom. [ABSTRACT FROM AUTHOR]

Within the Born-Oppenheimer approximation, we build a multichannel model to simulate the dissociation of H2+ in strong laser fields. Two applications of this model are presented: first, orthogonally polarized UV and infrared pulses are used to dissociate H2+ into 2pπu and 3dπg states, whose superposition results in asymmetric electron localization after the dissociation; second, two orthogonally polarized UV pulses are introduced to trigger competing Rabi oscillations among 1sσg, 2pσu, 3dσg and 2pπu states. This study shows the dissociation of H2+ can be steered into selected electronic states with controllable probabilities with state-of-the-art laser technologies. [ABSTRACT FROM AUTHOR]

We compare and contrast the wide Feshbach resonances and the corresponding weakly bound states in the lowest scattering channels of ultracold 6Li and 7Li. We use high-precision measurements of binding energies and scattering properties to determine interaction potentials that incorporate non-Born-Oppenheimer terms to account for the failure of mass scaling between 6Li and 7Li. Correction terms are needed for both the singlet and the triplet potential curves. The universal formula relating binding energy to scattering length is not accurate for either system. The 6Li resonance is open-channel-dominated and the van der Waals formula of Gao [J. Phys. B 37, 4273 (2004)] gives accurate results for the binding energies across much of the resonance width. The 7Li resonance, by contrast, is weakly closed-channel-dominated and a coupled-channel treatment of the binding energies is required. Plotting the binding energies in universal van der Waals form helps illustrate subtle differences between the experimental results and different theoretical forms near the resonance pole. [ABSTRACT FROM AUTHOR]

The energy spectrum, atom-dimer scattering length, and atom-trimer scattering length for systems of three and four ultracold atoms with δ-function interactions in one dimension are presented as a function of the relative mass ratio of the interacting atoms. The Born-Oppenheimer approach is used to treat three-body ("HHL") systems of one light and two heavy atoms, as well as four-body ("HHHL") systems of one light and three heavy atoms. Zero-range interactions of arbitrary strength are assumed between different atoms, but the heavy atoms are assumed to be noninteracting among themselves. Fermionic and bosonic heavy atoms with both positive and negative parity are considered. [ABSTRACT FROM AUTHOR]

A quantum electrodynamics (QED) correction surface for the simplest polyatomic and polyelectronic system H3+ is computed using an approximate procedure. This surface is used to calculate the shifts to vibration-rotation energy levels due to QED; such shifts have a magnitude of up to 0.25 cm-1 for vibrational levels up to 15 000 cm-1 and are expected to have an accuracy of about 0.02 cm-1. Combining our H3+ QED correction surface with existing highly accurate Born-Oppenheimer, relativistic, and adiabatic components suggests that deviations of the resulting ah initio energy levels from observed ones are largely due to nonadiabatic effects. [ABSTRACT FROM AUTHOR]

In this work we present very accurate quantum-mechanical calculations of all bound pure vibrational states of the HD+ ion performed without the Born-Oppenheimer (BO) approximation. All three particles forming the system are treated on equal footing. The approach involves separating the center-of-mass motion from the laboratory-frame nonrelativistic Hamiltonian and expending the wave function of each considered state in terms of all-particle explicitly correlated Gaussian functions. The Gaussian exponential parameters are variationally optimized with the aid of the analytical energy gradient calculated with respect to these parameters. For each state the leading relativistic corrections are calculated as expectation values of the corresponding operators with the non-BO wave function of the state. The non-BO approach allows us to directly describe the charge asymmetry in HD+ which is due to the nuclear-mass asymmetry. The effect increases with the vibrational excitation and affects the values of the relativistic corrections. This phenomenon is the focus of the present study. [ABSTRACT FROM AUTHOR]

Our work is devoted to developing a general approach for nonpenetrating Rydberg states of polar molecules. We propose a method to estimate the accuracy of calculation of their wave functions and quantum defects. Basing on this method we estimate the accuracy of Born-Oppenheimer (BO) and inverse Born-Oppenheimer (IBO) approximations for these states. This estimation enables us to determine the space and energy regions where BO and IBO approximations are valid. It depends on the interplay between I coupling (due to dipole potential of the core) and I uncoupling (due to rotation the core). Next we consider the intermediate region where both BO and IBO are not valid. For this intermediate region we propose a modification of Fano's multichannel quantum defect theory to match BO and IBO wave functions and show that it gives more reliable results. They are demonstrated on the example of SO molecule. [ABSTRACT FROM AUTHOR]

A method for calculating the oscillator strengths for rovibrational transitions of a diatomic system within an approach that is not based on the Born-Oppenheimer (BO) approximation is presented. The non-BO wave functions representing the bound states of the system are expanded in terms of explicitly correlated Gaussian functions. The method is applied to calculate oscillator strengths for the HD+ ion for transitions between rotationless vibrational states and vibrational states which are rotationally singly excited. The effect of the asymmetry of the HD+ charge distribution on the oscillator strengths and on the lifetimes of the states is elucidated. [ABSTRACT FROM AUTHOR]

We report the development of a direct variational method for calculating the first rotational excited state of diatomic molecules with s electrons where the Born-Oppenheimer approximation is not assumed. The method employs all-particle explicitly correlated Gaussian basis functions. The exponential parameters of the Gaussians are optimized with the aid of an analytically calculated energy gradient determined with respect to these parameters. The method is tested in calculations of the ortho-para spin isomerization of the hydrogen molecule in its all-bound vibrational states. [ABSTRACT FROM AUTHOR]

A general approach to evaluation of two-center two-electron exponential integrals with arbitrary parameters is presented. The results for the Born-Oppenheimer potential for various excited states of molecular hydrogen with Kolos-Wolniewicz functions are obtained with precision exceeding previous values by about three orders of magnitude. [ABSTRACT FROM AUTHOR]

Total and partial cross sections for breakup of the ground rovibronic state of H+² by photon impact are calculated using the exact nonadiabatic nonrelativistic Hamiltonian without approximation. The converged results span six orders of magnitude. The breakup cross section is divided into dissociative excitation and dissociative ionization. The dissociative excitation channels are divided into contributions from principal quantum numbers 1-4. For dissociative ionization, the fully differential cross section is calculated using a formally exact expression. These results are compared with approximate expressions. The Born-Oppenheimer expression for the dissociative ionization amplitude is shown to be deficient near onset. A Born-Oppenheimer approximation to the final state is shown to give accurate results for the sharing of kinetic energy between the electronic and the internuclear degrees of freedom--the doubly differential cross section. To accurately calculate the triply differential cross section, including the angular behavior, it is shown that nonadiabatic wave functions for both initial and final states are required at low electron energies. [ABSTRACT FROM AUTHOR]

The properties of the electronic ground state of the polar and paramagnetic chromium-closed-shell-atom molecules have been investigated. State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the chromium-alkaline-earth-metal-atom, CrX (X = Be, Mg, Ca, Sr, Ba), and chromium-ytterbium, CrYb, molecules in the Born-Oppenheimer approximation for the high-spin X7£+ electronic ground state. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), was employed and the scalar relativistic effects within the Douglas-Kroll-Hess Hamiltonian or energy-consistent pseudopotentials were included. The permanent electric dipole moments and static electric dipole polarizabilities were computed. The leading long-range coefficients describing the dispersion interaction between the atoms at large interatomic distances C6 are also reported. The molecules under investigation are examples of species possessing both large magnetic and electric dipole moments making them potentially interesting candidates for ultracold many-body physics studies. [ABSTRACT FROM AUTHOR]

We introduce and analyze several low-dimensional scattering systems that exhibit geometric phase phenomena. The systems are fully solvable and we compare accurate solutions of them with those obtained in a Born-Oppenheimer projection approximation. We illustrate how geometric magnetism manifests in them, and explore the relationship between solutions obtained in the diabatic and adiabatic pictures. We provide an example, involving a neutral atom dressed by an external field, in which the system mimics the behavior of a charged particle that interacts with, and is scattered by, a ferromagnetic material. We also introduce a similar system that exhibits Aharonov-Bohm scattering. We propose possible practical applications. We provide a theoretical approach that underscores universality in the appearance of geometric gauge forces. We do not insist on degeneracies in the adiabatic Hamiltonian, and we posit that the emergence of geometric gauge forces is a consequence of symmetry breaking in the latter. [ABSTRACT FROM AUTHOR]

We develop the quantum theory of a scalar field on loop quantum cosmology Bianchi I geometry. In particular, by considering only the single modes of the field, the evolution equation is derived from the quantum scalar constraint: it is shown that the same equation can be obtained from quantum field theory on a "classical" effective geometry. We then study the dependence of this effective space-time on the wave vector of the modes (which could in principle generate a deformation in local Lorentz symmetry), by analyzing the dispersion relation for propagation of the test field on the resulting geometry. We show that when we disregard the backreaction no Lorentz violation is present, despite the effective metric being different than the classical Bianchi I. Furthermore, a preliminary analysis of the correction due to inclusion of backreaction is briefly discussed in the context of Born-Oppenheimer approximation. [ABSTRACT FROM AUTHOR]

We use a £2-discretization technique for solving the time-dependent Schrödinger equation for H+2 interacting with a short vuv laser pulse, in the Born-Oppenheimer approximation. The calculations include the electronic three-dimensional and vibrational one-dimensional motions. In this approach, we use the prolate spheroidal coordinate system to describe the electronic functions and a basis of Laguerre and Legendre functions [Phys. Rev. A 71, 053407 (2005)]. The vibrational motion is treated by using a basis of Sturmian functions. We consider the problem of two-photon dissociation of H+2 with photons ranging from 0.32 to 0.4 a.u corresponding to wavelengths from 143 to 114 nm. The initial vibrational wave paeket results from a vertical (Franck-Condon) transition from the H2 ground state towards a superposition of vibrational states in the lsog electronic state of H+2. The effects of various types of nuclear interference on the population of the dissociative channels 2sσg and 3dσg are discussed in detail. In addition, we show that for 0.32-a.u. photon energy, the interference effects in the 3dσg channel whose existence has been demonstrated previously [Phys. Rev. Lett. 102, 123001 (2009)] can be observed in the total kinetic energy release spectrum. [ABSTRACT FROM AUTHOR]

The electroprotonic ground-state wave function of CH3OH is calculated beyond the Born-Oppenheimer (BO) approximation using multiconfiguration wave-function theory for a system composed of electrons and protons. A CH3OH molecule is treated as a quasidiatomic molecule in which orbitals for both electrons and protons are described in a laboratory fixed cylindrical coordinate system with C and O atoms being fixed on the z axis. The probability density of the four protons shows that the C atom is surrounded by three protons and the O atom by one proton, and that the dihedral angle of the O-H bond axis with respect to one of the C-H bond axes becomes 180°, exhibiting appropriately the conformational correlation between the two functional groups. The optimized spatial configuration of the protons was found to be in good agreement with that obtained by the standard BO-based electronic structure calculation. The non-BO electroprotonic wave functions introduced here afford the basis for describing ultrafast hydrogen migration in hydrocarbon molecules in an intense laser field. [ABSTRACT FROM AUTHOR]

A scheme is proposed to generate isolated attosecond pulses in the water window driven by a multicycle 2400-nm midinfrared laser field with moderate intensity interacting with H2+ molecules. Single attosecond pulses are achieved due to the charge resonance-enhanced ionization and nuclear motion by the numerical solutions of a non-Born-Oppenheimer time-dependent Schrödinger equation. Thus, the single attosecond pulse generation provides insight into the nuclear dynamics. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the implementation of a generalized approach for calculating quantum defects in high Rydberg states of polar molecules with an account for the dipole moment of the molecular core and l uncoupling of the Rydberg electron. Adiabatic (Born-Oppenheimer) and nonadiabatic (inverse Born-Oppenheimer) regions of the spectrum are considered. The nonadiabatic case with a nonzero projection of the core momentum on the core axis is considered and is illustrated by the example of the SO molecule. [ABSTRACT FROM AUTHOR]

We study few-body problems in mixed dimensions where two or three heavy atoms are trapped individually in parallel one-dimensional tubes or two-dimensional disks and a single light atom travels freely in three dimensions. Using the Born-Oppenheimer approximation, we find three- and four-body bound states for a broad parameter region. Specifically, the existence of trimer and tetramer states persists to the negative scattering length regime, where no two-body bound state is present. As pointed out by Y. Nishida in an earlier work [Phys. Rev. A 82, 011605(R) (2010)], these few-body bound states are stable against three-body recombination due to geometric separation. In addition, we find that the binding energy of the ground trimer and tetramer state reaches its maximum value when the scattering lengths are comparable to the separation between the low-dimensional traps. [ABSTRACT FROM AUTHOR]

The dissociation dynamics of HD+ molecules is studied theoretically by numerically solving the time-dependent Schrödinger equation in which the molecular vibrational and rotational degrees of freedom are included. Based on the Born-Oppenheimer approximation, the ground 1sσ8 state and the excited 2pσu state are taken into account, corresponding to two dissociative channels HD+ → D + H+ and HD+ → H + D+, respectively. Two dissociative nuclear wave packets overlap and interfere after excited by two ultrashort laser pulses. The interference patterns can be controlled by varying the laser parameters and the dissociation probabilities are demonstrated for different laser fields. The kinetic energy-dependent distributions of the fragments are calculated using an asymptotic-flow expression in the momentum space. The branching ratio D+/(H+ + D+), as a function of the delay time and the relative phase between two laser pulses, is also discussed. [ABSTRACT FROM AUTHOR]

The Berry phase, which was discovered more than two decades ago, provides very deep insight into the geometric structure of quantum mechanics. Its classical counterpart, Hannay's angle, is defined if closed curves of action variables return to the same curves in phase space after a time evolution. In this paper we study the Berry phase and Hannay's angle in a quantum-classical hybrid system under the Born-Oppenheimer approximation. By the term quantum-classical hybrid system, we mean a composite system consists of a quantum subsystem and a classical subsystem. The effects of subsystem-subsystem couplings on the Berry phase and Hannay's angle are explored. The results show that the Berry phase has been changed sharply by the couplings, whereas the couplings have a small effect on the Hannay's angle. [ABSTRACT FROM AUTHOR]

The structure of {a±,a±,b∓}-type Coulombic systems is characterized by the effective ground-state density of the a-type particles, computed via nonrelativistic quantum mechanics without introduction of the Born-Oppenheimer approximation. A structural transition is observed when varying the relative mass of the a- and b-type particles, e.g., between atomic H- and molecular H2+. The particle-density profile indicates a molecular-type behavior for the positronium ion, Ps-. [ABSTRACT FROM AUTHOR]

A strongly interacting, and entangling, heavy nonrecoiling external particle effects a significant change of the environment. Described locally, the corresponding entanglement event is a generalized electric Aharonov-Bohm effect, which differs from the original one in a crucial way. We propose a gedanken interference experiment. The predicted shift of the interference pattern is due to a self-induced or "private" potential difference experienced while the particle is in vacuum. We show that all nontrivial Born-Oppenheimer potentials are "private" potentials. We apply the Born-Oppenheimer approximation to interference states. Using our approach, we calculate the relative phase of the external heavy particle as well as its uncertainty throughout an interference experiment or entanglement event. We thus complement the Born-Oppenheimer approximation for interference states. [ABSTRACT FROM AUTHOR]

We propose a feasible scheme to cool down a mechanical resonator (MR) in a three-mirror cavity optomechanical system with controllable external optical driving fields. Under the Born-Oppenheimer approximation, the whole dynamics of the mechanical resonator and cavities is reduced to that of a time-dependent harmonic oscillator, whose effective frequency can be controlled through the optical driving fields. The fast cooling of the MR can be realized by controlling the amplitude of the optical driving fields. Significantly, we further show that the ground-state cooling may be achieved via the three-mirror cavity optomechanical system without the resolved sideband condition. [ABSTRACT FROM AUTHOR]

First and second derivative of the nonadiabatic coupling between the several ¹Σ+ adiabatic states of the KH molecule considered from accurate diabatic and adiabatic data have been evaluated. Such derivatives of the electronic wave function are determined through a numerical differentiation of the rotational matrix connecting the diabatic and adiabatic representations. The first as well as the second derivative present many peaks related to ionic-neutral and neutral-neutral coupling between the ¹Σ+ states. Such radial coupling has been exploited to calculate the first adiabatic correction, which corresponds to the diagonal term of the second derivative divided by the reduced mass, for the ground and some excited states of the KH molecule. The second adiabatic correction has been determined using the virial theorem. The first adiabatic correction was added to the adiabatic potential energy curves to redetermine the corrected spectroscopic constants and vibrational energy levels. The vibrational shift, which is the difference between the corrected and the adiabatic levels, has been calculated for X, A, C, and D ¹Σ+ states of the KH molecule. A shift of some 10 cm-1 is observed for some vibrational levels showing the breakdown of the Born-Oppenheimer approximation. [ABSTRACT FROM AUTHOR]

All 18 bound pure vibrational levels of the HD molecule have been calculated within the framework that does not assume the Born-Oppenheimer (BO) approximation. The nonrelativistic energies of the states have been corrected for the relativistic effects of the order of α² (where a is the fine structure constant), calculated using the perturbation theory with the nonrelativistic non-BO wave functions being the zero-order approximation. The calculations were performed by expanding the non-BO wave functions in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance and by performing extensive optimization of the Gaussian nonlinear parameters. Up to 10 000 basis functions were used for each state. [ABSTRACT FROM AUTHOR]

State-of-the-art ab initio techniques have been applied to compute the potential energy curves of the (BaRb)+ molecular ion in the Born-Oppenheimer approximation for the singlet and triplet states dissociating into the ground-state ¹S Rb+ ion and the Ba atom in the ground ¹S state or the lowest singlet or triplet D excited states, and for the singlet and triplet states dissociating into the ground-state ²S Rb atom and the ground-state ²S Ba+ ion. The ground-state potential energy was obtained with the coupled-cluster method restricted to single, double, and nonperturbative triple excitations. The first triplet states in the Σ, Π, and Δ symmetries were computed with the restricted open-shell coupled-cluster method restricted to single, double, and nonperturbative triple excitations. All other excited-state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles, doubles, and linear triples framework. The long-range coefficients describing the electrostatic, induction, and dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments governing the X ¹Σ → ¹Π transitions 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. [ABSTRACT FROM AUTHOR]

The quantum dynamics of two distant H atoms excited by ultrashort and spatially shaped laser pulses is studied by the numerical solution of the non-Born-Oppenheimer time-dependent Schrödinger equation within a three-dimensional (3D) model, including the internuclear distance R and the two z coordinates of the electrons z1 and z2. The two one-dimensional (1D) H atoms, A and B, are assumed to be initially in their ground states with a large (but otherwise arbitrary) internuclear separation of R=100 a.u. (5.29 nm). Two types of a spatial envelope of a laser field linearly polarized along the z axis are considered: (i) a broad Gaussian envelope, such that atom A is excited by the laser field predominantly, and (ii) a narrow envelope, such that practically only atom A is excited by the laser field. With the laser carrier frequency ω=1.0 a.u. and the pulse duration tp=5 fs, in both cases an efficient energy transfer from atom A to atom B has been found. The ionization of atom B achieved mostly after the end of the laser pulse is close to or even higher than that of atom A. It is shown that with a narrow spatial envelope of the laser field, the underlying mechanisms of the energy transfer from A to B and the ionization of B are the Coulomb attraction of the laser driven electron by the proton of atom B and a short-range Coulomb repulsion of the two electrons when their wave functions significantly overlap in the domain of atom B. In the case of a broad Gaussian spatial envelope of the laser field, the opposite process also occurs, but with smaller probability: the energy is transferred from the weakly excited atom B to atom A, and the ionization of atom A is also induced by the electron-electron repulsion in the domain of atom A due to a strong overlap of the electronic wave functions. [ABSTRACT FROM AUTHOR]

The problem of time is one of the most relevant open issues in canonical quantum gravity. Although there is a huge literature about this topic, a commonly accepted solution has not been found yet. Here, we focus on the semiclassical approach to the problem of time, that has the main goal of reproducing quantum field theory on a fixed Wentzel-Kramers-Brillouin (WKB) background accounting also for quantum gravity corrections. We analyze the different choices of the expansion parameter and discuss the problems arising in previous proposals, where a nonunitary evolution emerges as an effect of quantum gravity corrections. In this work, we develop a new approach to solve this problem by performing the WKB expansion with the introduction of the so-called kinematical action as a clock for quantum matter, that allows to recover a unitary dynamics. [ABSTRACT FROM AUTHOR]

We compute the composition of the bottomonium Υ(nS) states [including Υ(10860)] and the new Υ(10753) resonance reported by Belle in terms of quarkonium and meson-meson components. We use a recently developed novel approach utilizing lattice QCD string breaking potentials for the study of resonances. This approach is based on the diabatic extension of the Born-Oppenheimer approximation and the unitary emergent wave method and allows us to compute the poles of the S matrix. We focus on I=0 bottomonium S wave bound states and resonances, where the Schrödinger equation is a set of coupled differential equations. One of the channels corresponds to a confined heavy quark-antiquark pair ̄bb, and the others correspond to pairs of heavy-light mesons. In a previous study, only one meson-meson channel ̄B(*)B(*) was considered. Now, we also include the closed strangeness channel ̄B(*)sB(*)s, extending our formalism significantly to have a more realistic description of bottomonium. We confirm the new Belle resonance Υ(10753) as a dynamical meson-meson resonance with around 76% meson-meson content. Moreover, we identify Υ(4S) and Υ(10860) as states with both sizable quarkonium and meson-meson contents. With these results, we contribute to the clarification of ongoing controversies in the vector bottomonium spectrum. [ABSTRACT FROM AUTHOR]

We construct a quantum mechanical matrix model that is a dimensional reduction of N=1 super-Yang-Mills on S³×R. We do so by pulling back the set of left-invariant connections of the gauge bundle onto the real superspace, with the spatial R³ compactified to S³. We quantize the N=1 SU(2) matrix model in the weak-coupling limit g≪1, with g the dimensionless gauge coupling constant, using the Born-Oppenheimer approximation and find that different superselection sectors emerge for the effective gluon dynamics in this regime, reminiscent of different phases of the full quantum theory. We demonstrate that the Born-Oppenheimer quantization is indeed compatible with supersymmetry, albeit in a subtle manner. In fact, we can define effective supercharges that relate the different sectors of the matrix model's Hilbert space. These effective supercharges have a different definition in each phase of the theory. [ABSTRACT FROM AUTHOR]

We apply the diabatic formalism, first introduced in molecular physics, to the description of heavy-quark mesons. In this formalism the dynamics is completely described by a diabatic potential matrix whose elements can be derived from unquenched lattice QCD studies of string breaking. For energies far below the lowest open flavor meson-meson threshold, the resulting diabatic approach reduces to the well-known Born-Oppenheimer approximation where heavy-quark meson masses correspond to energy levels in an effective quark-antiquark potential. For energies close below or above that threshold, where the Born-Oppenheimer approximation fails, this approach provides a set of coupled Schrödinger equations incorporating meson-meson components nonperturbatively, i.e., beyond loop corrections. A spectral study of heavy mesons containing c̅c with masses below 4.1 GeV is carried out within this framework. From it a unified description of conventional as well as unconventional resonances comes out. [ABSTRACT FROM AUTHOR]

This paper focuses on tetraquarks containing one heavy quark and one heavy antiquark in the formal limit where the heavy quark masses go to infinity. It extends the theoretical framework developed for a tetraquark containing two heavy quarks based on semiclassical analysis and the Born-Oppenheimer approximation. It is shown that, for sufficiently small light quark masses, parametrically narrow q̅q'Q̅Q tetraquarks must exist in the formal limit of arbitrarily large heavy quark masses. The analysis is model independent; it requires no assumptions about the structure of the state or the mechanism of its decay beyond what can be deduced directly from QCD. The formal analysis here is only directly applicable to tetraquarks with large angular momentum and hence does not directly apply to experimentally observed tetraquark candidates. We also discuss the condition needed for a version of the analysis to apply for low angular momenta states. Whether this condition holds can be explored via lattice calculations. Current lattice calculations suggest that the condition is not met. If these preliminary calculations are confirmed, there are strong implications for the nature of the observed tetraquark resonances containing ̅cc or ̅bb pairs. It raises the possibility that the observed tetraquarks exist and are narrow not because the charm and bottom quarks are extremely heavy, but because they are sufficiently light. [ABSTRACT FROM AUTHOR]

In this paper we present in greater detail previous work on the Born-Oppenheimer approximation to treat the hydrogen bond of QCD, and add a similar treatment of doubly heavy baryons. Doubly heavy exotic resonances X and Z can be described as color molecules of two-quark lumps, the analogue of the H2 molecule, and doubly heavy baryons as the analog of the H2+ ion, except that the two heavy quarks attract each other. We compare our results with constituent quark model and lattice QCD calculations and find further evidence in support of this upgraded picture of compact tetraquarks and baryons. [ABSTRACT FROM AUTHOR]

In this paper we present in greater detail previous work on the Born-Oppenheimer approximation to treat the hydrogen bond of QCD, and add a similar treatment of doubly heavy baryons. Doubly heavy exotic resonances X and Z can be described as color molecules of two-quark lumps, the analogue of the H2 molecule, and doubly heavy baryons as the analog of the H2+ ion, except that the two heavy quarks attract each other. We compare our results with constituent quark model and lattice QCD calculations and find further evidence in support of this upgraded picture of compact tetraquarks and baryons. [ABSTRACT FROM AUTHOR]