Born Oppenheimer Potential Research Articles

Tetraquarks at large M and large N

We study tetraquarks in large N QCD with heavy quarks, in the domain where non-relativistic quantum mechanics offers an adequate approximation. Within the regime of validity of the Born-Oppenheimer approximation, we systematically study and explicitly construct tetraquark states. At leading order in the 1/N expansion, the bound spectrum consists of free mesons, while the 1/N corrections give rise to a Born-Oppenheimer potential that can bind the mesons into tetraquarks. We find two different types of tetraquarks, each endowed with distinct color-spatial wavefunctions. These states arise in the presence of an O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(N) mass hierarchy between the quarks and the antiquarks. We provide a quantitative argument indicating that only for such a hierarchy is the ground state of the system a tetraquark. We discuss what the extrapolation of our results to realistic values of the parameters may imply for the QCD tetraquark states.

Model-independent predictions for decays of double-heavy hadrons into pairs of heavy hadrons

Double-heavy hadrons can decay into pairs of heavy hadrons through transitions from confining Born-Oppenheimer potentials to heavy-hadron-pair potentials with the same Born-Oppenheimer quantum numbers. The states of the double-heavy hadron are constrained by a Born-Oppenheimer exclusion principle from the identical heavy quarks. The states of a pair of identical heavy hadrons are constrained by exclusion principles from identical particles. The transitions are also constrained by conservation of angular momentum and parity. From these constraints, we derive model-independent selection rules for decays of double-heavy hadrons into pairs of heavy hadrons. The coupling potentials are expressed as sums of products of Born-Oppenheimer transition amplitudes and angular-momentum coefficients. If there is a single dominant Born-Oppenheimer transition amplitude, it factors out of the coupling potentials between double-heavy hadrons in the same Born-Oppenheimer multiplet and pairs of heavy hadrons in specific heavy-quark-spin-symmetry multiplets and out of the corresponding partial decay rates. As examples, we discuss the Born-Oppenheimer potentials and multiplets for conventional double-heavy baryons and for double-heavy tetraquark mesons. We also discuss the relative partial decay rates for conventional double-heavy baryons into pairs of heavy hadrons. Published by the American Physical Society 2024

Born-Oppenheimer potentials for SU(3) gauge theory

We develop parametrizations of eight of the lowest Born-Oppenheimer potentials for quarkonium hybrid mesons as functions of the separation r of the static quark and antiquark sources. The parameters are determined by fitting results calculated using pure SU(3) lattice gauge theory. The parametrizations have the correct limiting behavior at small r, where the potentials form multiplets associated with gluelumps. They have the correct limiting behavior at large r, where the potentials form multiplets associated with excitations of a relativistic string. There is a narrow avoided crossing in the small-r region between two potentials with the same Born-Oppenheimer quantum numbers. Published by the American Physical Society 2024

Model-independent predictions for decays of hidden-heavy hadrons into pairs of heavy hadrons

Hidden-heavy hadrons can decay into pairs of heavy hadrons through transitions from confining Born-Oppenheimer potentials to hadron-pair potentials with the same Born-Oppenheimer quantum numbers. The transitions are also constrained by conservation of angular momentum and parity. From these constraints, we derive model-independent selection rules for decays of hidden-heavy hadrons into pairs of heavy hadrons. The coupling potentials are expressed as sums of products of Born-Oppenheimer transition amplitudes and angular-momentum coefficients. If there is a single dominant Born-Oppenheimer transition amplitude, it factors out of the coupling potentials between hidden-heavy hadrons in the same Born-Oppenheimer multiplet and pairs of heavy hadrons in specific heavy-quark-spin-symmetry doublets. If furthermore the kinetic energies of the heavy hadrons are much larger than their spin splittings, we obtain analytic expressions for the relative partial decay rates in terms of Wigner 6j and 9j symbols. We consider in detail the decays of quarkonia and quarkonium hybrids into the lightest heavy-meson pairs. For quarkonia, our model-independent selection rules and relative partial decay rates agree with previous results from quark-pair-creation models in simple cases and give stronger results in other cases. For quarkonium hybrids, we find disagreement even in simple cases. Published by the American Physical Society 2024

Doubly heavy dibaryons as seen by string theory

We propose the stringy description of the system consisting of two heavy and four light quarks in the case of two light flavors of equal mass. As an application, we consider the three low-lying Born-Oppenheimer potentials as a function of the heavy quark separation. Our analysis shows that the ground state potential is described in terms of both hadroquarkonia and hadronic molecules. A connected string configuration makes the dominant contribution to the potential of an excited state at small separations, and for separations larger than 0.1 fm, it exhibits the diquark-diquark-diquark structure [Qq][Qq][qq]. For better understanding the quark organization inside the system, we introduce several critical separations related to the processes of string reconnection, breaking and junction annihilation. We also discuss the simplest string configurations including the five-string junctions and their implications for the system, in particular the emergence of composite quark objects different from diquarks and the process of junction fusion. Published by the American Physical Society 2024

Stress and heat flux via automatic differentiation.

Machine-learning potentials provide computationally efficient and accurate approximations of the Born-Oppenheimer potential energy surface. This potential determines many materials properties and simulation techniques usually require its gradients, in particular forces and stress for molecular dynamics, and heat flux for thermal transport properties. Recently developed potentials feature high body order and can include equivariant semi-local interactions through message-passing mechanisms. Due to their complex functional forms, they rely on automatic differentiation (AD), overcoming the need for manual implementations or finite-difference schemes to evaluate gradients. This study discusses how to use AD to efficiently obtain forces, stress, and heat flux for such potentials, and provides a model-independent implementation. The method is tested on the Lennard-Jones potential, and then applied to predict cohesive properties and thermal conductivity of tin selenide using an equivariant message-passing neural network potential.

Shadow Molecular Dynamics and Atomic Cluster Expansions for Flexible Charge Models.

A shadow molecular dynamics scheme for flexible charge models is presented where the shadow Born-Oppenheimer potential is derived from a coarse-grained approximation of range-separated density functional theory. The interatomic potential, including the atomic electronegativities and the charge-independent short-range part of the potential and force terms, is modeled by the linear atomic cluster expansion (ACE), which provides a computationally efficient alternative to many machine learning methods. The shadow molecular dynamics scheme is based on extended Lagrangian (XL) Born-Oppenheimer molecular dynamics (BOMD) [Eur. Phys. J. B 2021, 94, 164]. XL-BOMD provides stable dynamics while avoiding the costly computational overhead associated with solving an all-to-all system of equations, which normally is required to determine the relaxed electronic ground state prior to each force evaluation. To demonstrate the proposed shadow molecular dynamics scheme for flexible charge models using atomic cluster expansion, we emulate the dynamics generated from self-consistent charge density functional tight-binding (SCC-DFTB) theory using a second-order charge equilibration (QEq) model. The charge-independent potentials and electronegativities of the QEq model are trained for a supercell of uranium oxide (UO2) and a molecular system of liquid water. The combined ACE+XL-QEq molecular dynamics simulations are stable over a wide range of temperatures both for the oxide and for the molecular systems and provide a precise sampling of the Born-Oppenheimer potential energy surfaces. Accurate ground Coulomb energies are produced by the ACE-based electronegativity model during an NVE simulation of UO2, predicted to be within 1 meV of those from SCC-DFTB on average during comparable simulations.

Hibridon: A program suite for time-independent non-reactive quantum scattering calculations

Hibridon is a program package to solve the close-coupled equations which occur in the time independent quantum treatment of inelastic atomic and molecular collisions. Gas-phase scattering, photodissociation, collisions of atoms and/or molecules with flat surfaces, and bound states of weakly-bound complexes can be treated. From calculation of the S matrix, integral and differential cross sections, stereodynamic (alignment and steric asymmetry) cross sections, as well as more specialized quantities, such as transport and tensor cross sections, and cross sections between hyperfine levels, and photodissociation amplitudes can be obtained. The program is capable of treating closed-shell systems where the nuclear motion takes place on a single Born-Oppenheimer potential as well as open-shell systems for which the nuclear motion can evolve on several coupled electronic (Born-Oppenheimer) potentials. Program summaryProgram Title: HibridonCPC Library link to program files:https://doi.org/10.17632/sk9zcvz8vs.1Developer's repository link:https://doi.org/10.5281/zenodo.7551616Licensing provisions: GPLv3Programming language: Fortran 90External routines/libraries: LAPACK, BLASNature of problem: Solution of the time-independent Schrödinger equation for the inelastic scattering of atoms and molecules, for the photodissociation of molecules, and for the ro-vibrational motion of weakly bound molecular complexes.Solution method: The scattering wavefunction is expanded in a set of internal states of the system, constructed as direct products of the internal states of one (or both) fragments and angular functions which describe the rotation of one collision partner about the other. The Schrödinger equation for the nuclear motion is solved by determining the expansion coefficients as a function of the interparticle separation starting from the short-range classically forbidden region outwards to the asymptotic region. The S matrix is given by the asymptotic behavior of the wavefunction. Integral and differential cross sections, as well as other scattering and photodissociation quantities are calculated from the S matrix.

Many-Body Effects in Aqueous Systems: Synergies Between Interaction Analysis Techniques and Force Field Development

Interaction analysis techniques, including the many-body expansion (MBE), symmetry-adapted perturbation theory, and energy decomposition analysis, allow for an intuitive understanding of complex molecular interactions. We review these methods by first providing a historical context for the study of many-body interactions and discussing how nonadditivities emerge from Hamiltonians containing strictly pairwise-additive interactions. We then elaborate on the synergy between these interaction analysis techniques and the development of advanced force fields aimed at accurately reproducing the Born-Oppenheimer potential energy surface. In particular, we focus on ab initio-based force fields that aim to explicitly reproduce many-body terms and are fitted to high-level electronic structure results. These force fields generally incorporate many-body effects through (a) parameterization of distributed multipoles, (b) explicit fitting of the MBE, (c) inclusion of many-atom features in a neural network, and (d) coarse-graining of many-body terms into an effective two-body term. We also discuss the emerging use of the MBE to improve the accuracy and speed of ab initio molecular dynamics.

Shadow energy functionals and potentials in Born-Oppenheimer molecular dynamics.

In Born-Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born-Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born-Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born-Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born-Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original "zeroth-level" shadow energy functionals and potentials used in extended Lagrangian BOMD [Niklasson, Eur. Phys. J. B 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree-Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

Interference-induced anisotropy in a two-dimensional dark-state optical lattice

We describe a two-dimensional optical lattice for ultracold atoms with spatial features below the diffraction limit created by a bichromatic optical standing wave. At every point in space these fields couple the internal atomic states in a three-level Lambda coupling configuration. Adiabatically following the local wavefunction of the resulting dark state yields a spatially uniform Born-Oppenheimer potential augmented by geometric scalar and vector potentials appearing due to spatially rapid changes of the wavefunction. Depending on system parameters, we find that the geometric scalar potential can interpolate from a 2D analogue of the Kronig-Penney lattice, to an array of tubes with a zig-zag shaped barrier. The geometric vector potential induces a spatially periodic effective magnetic field (the Berry's curvature) that can be tuned to cause destructive interference between neighboring tubes, thereby decoupling them at a critical point in parameter space. We numerically investigate the energy spectrum including decay from the excited state, and find that the adiabatic approximation is sound for strong coupling strengths, leading to negligible loss in the dark state manifold. Furthermore, the spectrum is well-described by a non-Hermitian tight binding model with on-site losses, and hopping characterized by both loss and, surprisingly, gain.

A local Gaussian Processes method for fitting potential surfaces that obviates the need to invert large matrices

In order to compute a vibrational spectrum, one often wishes to start with a set of ab initio Born–Oppenheimer potential values at points, called fitting points, and interpolate or fit to find values of the potential at quadrature or collocation points. It is common to do this once to build a potential energy surface (PES). Once the PES is known, it can be evaluated at any point in configuration space. Gaussian Process (GP) is frequently being used to make a PES. As is the case in other interpolation methods, to use GP one must store and invert a matrix whose size is the number of fitting points. The matrix is sometimes large enough that approximations are introduced to reduce the cost of the calculation. We show that is possible to use many local Gaussian Process fits rather than one global fit. Retaining only local Gaussians and the associated points works well despite the fact that other Gaussians have tails with significant amplitude in the local region. We demonstrate that from the potential values obtained from the local fits it is possible to compute accurate energy levels of formaldehyde. In one calculation, potential values were obtained with N=120,000 fitting points by inverting matrices of size less than m=400. The local idea reduces the cost from N3 to T(m3+N), where T is the number of desired potential points.

Vibronic interactions in trilobite and butterfly Rydberg molecules

Ultralong-range Rydberg molecules provide an exciting testbed for molecular physics at exaggerated scales. In the so-called trilobite and butterfly Rydberg molecules, the Born-Oppenheimer approximation can fail due to strong nonadiabatic couplings arising from the combination of radial oscillations and rapid energy variations in the adiabatic potential energy curves. We utilize an accurate coupled-channel treatment of the vibronic system to observe the breakdown of Born-Oppenheimer physics, such as nonadiabatic trapping and decay of molecular states found near pronounced avoided crossings in the adiabatic potential curves. Even for vibrational states localized far away from avoided crossings, a single-channel model is quantitatively sufficient only after including the diagonal nonadiabatic corrections to the Born-Oppenheimer potentials. Our results indicate the importance of including nonadiabatic physics in the description of ultralong-range Rydberg molecules and in the interpretation of measured vibronic spectra.

QQqqq¯ quark system, compact pentaquark, and gauge/string duality

For the case of two light flavors we propose the stringy description of the system consisting of two heavy and three light quarks, with the aim of exploring the quark organization inside the system and its low-lying Born-Oppenheimer potentials as a function of the heavy quark separation. Our analysis reveals several critical separations related to the processes of string reconnection, breaking and junction annihilation. We find that a compact pentaquark configuration makes the dominant contribution to the potential of the first excited state at small separations, and for separations larger than $0.1\,\text{fm}$, the antiquark-diquark-diquark structure emerges. Moreover, it turns out that the length scale of string junction annihilation is the same as that for the $QQ\bar q\bar q$ system. We also discuss the relation to the potential of the $QQq$ system and some relations among the masses of hadrons in the heavy quark limit.

Reaction of N+ Ion with H2, HD, and D2 at Low Temperatures: Experimental Study of the Pathway to Deuterated Nitrogen-containing Molecules in the Interstellar Medium

This work is motivated by many observations of nitrogen hydrides including their isotopologues in the interstellar space. We studied the formation of NH+ and ND+ ions in the nearly thermoneutral hydrogen abstraction reactions of N+ ions with H2, HD, and D2 at temperatures from 300 K down to 15 K using a variable-temperature 22-pole radio frequency ion trap. For the reaction of N+ with HD, the branching ratios for production of ND+ and NH+ ions were also determined. The activation energies of all four reaction channels were determined from the temperature dependencies of the measured reaction rate coefficients. Under the assumption of no energy barriers on the reaction paths, we derive the vibrationless energy change (i.e., the difference of equilibrium Born–Oppenheimer potential energies of products and reactants) in the reactions as ΔE e = (103 ± 3) meV.

Toward a stringy description for the QQ¯qq¯ -quark system

For the case of two light flavors we propose the stringy description of the system made of one heavy and one light quark-antiquark pair, with the aim of exploring the two lower-lying Born-Oppenheimer potentials as a function of a separation of the heavy quark-antiquark pair. Our analysis reveals three critical separations related to the processes of string reconnection, breaking and junction annihilation. In particular, for the ground state potential only the process of string reconnection matters. We find that a tetraquark state makes the dominant contribution to the potential of the first excited state at small separations, and this is the big difference with the $QQ\bar q\bar q$-quark system where it does so to the ground state potential. Another big difference is the emergence of the full diquark picture $[Qq][\bar Q\bar q]$ rather than the partial picture $QQ[\bar q\bar q]$ for the tetraquark state. On the other hand, the scales of string junction annihilation, below which the systems can be thought of mainly as the compact tetraquarks, are very close for both cases and become almost the same if the phenomenological rule $E_{QQ}=\frac{1}{2} E_{Q\bar Q}$ holds. The same is also true for the screening lengths whose values are in agreement with lattice QCD.

Molecular dynamics of linear molecules in strong magnetic fields.

Molecular rotations and vibrations have been extensively studied by chemists for decades, both experimentally using spectroscopic methods and theoretically with the help of quantum chemistry. However, the theoretical investigation of molecular rotations and vibrations in strong magnetic fields requires computationally more demanding tools. As such, proper calculations of rotational and vibrational spectra were not feasible up until very recently. In this work, we present rotational and vibrational spectra for two small linear molecules, H2 and LiH, in strong magnetic fields. By treating the nuclei as classical particles, trajectories for rotations and vibrations are simulated from ab initio molecular dynamics. Born-Oppenheimer potential energy surfaces are calculated at the Hartree-Fock and MP2 levels of theory using London atomic orbitals to ensure gauge origin invariance. For the calculation of nuclear trajectories, a highly efficient Tajima propagator is introduced, incorporating the Berry curvature tensor accounting for the screening of nuclear charges.

Generalized quasiharmonic approximation via space group irreducible derivatives

The quasiharmonic approximation (QHA) is the simplest nontrivial approximation for interacting phonons under constant pressure, bringing the effects of anharmonicity into temperature-dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. Here we formulate the generalized QHA, providing a practical algorithm for computing the strain state and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second-order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate our approach by evaluating the temperature and pressure dependence of select elastic constants and the thermal expansion in thoria (${\mathrm{ThO}}_{2}$) using density functional theory with three exchange-correlation functionals. The QHA results are compared to our measurements of the elastic constant tensor using time-domain Brillouin scattering and inelastic neutron scattering. Our irreducible derivative approach simplifies the implementation of the generalized QHA, which will facilitate reproducible, data-driven applications.

Cavity-altered thermal isomerization rates and dynamical resonant localization in vibro-polaritonic chemistry

It has been experimentally demonstrated that reaction rates for molecules embedded in microfluidic optical cavities are altered when compared to rates observed under "ordinary" reaction conditions. However, precise mechanisms of how strong coupling of an optical cavity mode to molecular vibrations affects the reactivity and how resonance behavior emerges are still under dispute. In the present work, we approach these mechanistic issues from the perspective of a thermal model reaction, the inversion of ammonia along the umbrella mode, in the presence of a single-cavity mode of varying frequency and coupling strength. A topological analysis of the related cavity Born-Oppenheimer potential energy surface in combination with quantum mechanical and transition state theory rate calculations reveals two quantum effects, leading to decelerated reaction rates in qualitative agreement with experiments: the stiffening of quantized modes perpendicular to the reaction path at the transition state, which reduces the number of thermally accessible reaction channels, and the broadening of the barrier region, which attenuates tunneling. We find these two effects to be very robust in a fluctuating environment, causing statistical variations of potential parameters, such as the barrier height. Furthermore, by solving the time-dependent Schrödinger equation in the vibrational strong coupling regime, we identify a resonance behavior, in qualitative agreement with experimental and earlier theoretical work. The latter manifests as reduced reaction probability when the cavity frequency ωc is tuned resonant to a molecular reactant frequency. We find this effect to be based on the dynamical localization of the vibro-polaritonic wavepacket in the reactant well.

Born–Oppenheimer potentials for Π, Δ, and Φ states of the hydrogen molecule

We report on accurate variational calculations of the Born–Oppenheimer potential for excited states of the hydrogen molecule with , and Φ symmetries. The obtained potential energy curves reach the relative precision of or better along internuclear distances of 0.01–20 au. Calculations rely on the recursive evaluation of two-centre two-electron molecular integrals with exponential functions in arbitrary precision arithmetics. Our results for most of the states are the first-ever reported, and for the previously calculated states constitute an improvement by several orders of magnitude.