Born Oppenheimer Potential Research Articles

Elastic collision properties of ultracold calcium atoms

The s-wave scattering lengths are obtained for all stable isotope combinations of Ca atoms and those values are very sensitive to small changes of the reduced mass. These results rely on a recent measurement of the 40Ca–40Ca scattering length in a Bose condensate of 40Ca and making small corrections to a Born–Oppenheimer potential that reproduces all known spectroscopic data. We find that the 42Ca isotope has a scattering length of 417.5a0 and, thus, can be Bose condensed. The large interisotope scattering length between 43Ca and 42Ca indicates that sympathetic cooling of 43Ca by 42Ca atoms will be effective, and 43Ca–42Ca can also be used to study isotopic Bose–Fermi mixtures. We also predict a d-wave shape resonance for collisions of fermionic 43Ca atoms in different spin components.

Force-field functor theory: classical force-fields which reproduce equilibrium quantum distributions

Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.

Variational calculations for the hydrogen-antihydrogen system with a mass-scaled Born-Oppenheimer potential

Abstract The problem of proton-antiproton motion in the H-$\bar H$ system is investigated by means of the variational method. We introduce a modified nuclear interaction through mass-scaling of the Born-Oppenheimer potential. This improved treatment of the interaction includes the nondivergent part of the otherwise divergent adiabatic correction and shows the correct threshold behaviour. Using this potential we calculate the vibrational energy levels with angular momentum 0 and 1 and the corresponding nuclear wave functions, as well as the S-wave scattering length. We obtain a full set of all bound states together with a large number of discretized continuum states that might be utilized in variational four-body calculations. The results of our calculations gives an indication of resonance states in the hydrogen-antihydrogen system.

Quantum Wave-Packet Dynamics in Spin-Coupled Vibronic States

Extending the Shin-Metiu two-electron Hamiltonian, we construct a new Hamiltonian with effective singlet-triplet couplings. The Born-Oppenheimer electronic potentials and couplings are obtained for different parameters, and the laser-free dynamics is calculated with the full Hamiltonian and in the adiabatic limit. We compare the dynamics of the system using nuclear wave packets for different numbers of Born-Oppenheimer potentials and vibronic wave packets on a full 3-dimensional (two electron coordinates plus one nuclear coordinate) grid. Using strong fields, we show that it is possible to dynamically lock the spin state of the system by decoupling the singlet-triplet transition via a nonresonant dynamic Stark effect in the adiabatic limit. Although a similar spin-locking mechanism is observed in the dynamics of vibronic wave packets, multiphoton ionization cannot be neglected leading to the breakdown of the control scheme.

Dissociation dynamics of diatomic molecules in intense laser fields: A scheme for the selection of relevant adiabatic potential curves

We investigated the nuclear dynamics of diatomic molecular ions in intense laser fields by analyzing their fragment kinetic-energy release (KER) spectra as a function of the pump-probe delay $\ensuremath{\tau}$. Within the Born-Oppenheimer (BO) approximation, we calculated ab initio adiabatic potential-energy curves and their electric dipole couplings, using the quantum chemistry code gamess. By comparing simulated KER spectra as a function of either $\ensuremath{\tau}$ or the vibrational quantum-beat frequency for the nuclear dynamics on both individual and dipole-coupled BO potential curves with measured spectra, we developed a scheme for identifying electronic states that are relevant for the dissociation dynamics. We applied this scheme to investigate the nuclear dynamics in O${}_{2}$${}^{+}$ ions that are produced by ionization of neutral O${}_{2}$ molecules in an ultrashort infrared (IR) pump pulse and dissociate due to the dipole coupling of molecular potential curves in a delayed IR probe laser field.

Effects of adiabatic, relativistic, and quantum electrodynamics interactions on the pair potential and thermophysical properties of helium

The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs. For other separations, the relative uncertainties are up to an order of magnitude larger (and obviously still larger near R = 4.8 bohrs where the potential crosses zero) and are dominated by the uncertainties of the nonrelativistic BO component. These estimates also include the contributions from the neglected relativistic and QED terms proportional to the fourth and higher powers of the fine-structure constant α. To obtain such high accuracy, it was necessary to employ explicitly correlated Gaussian expansions containing up to 2400 terms for smaller R (all R in the case of a QED component) and optimized orbital bases up to the cardinal number X = 7 for larger R. Near-exact asymptotic constants were used to describe the large-R behavior of all components. The fitted potential, exhibiting the minimum of -10.996 ± 0.004 K at R = 5.608 0 ± 0.000 1 bohr, was used to determine properties of the very weakly bound (4)He(2) dimer and thermophysical properties of gaseous helium. It is shown that the Casimir-Polder retardation effect, increasing the dimer size by about 2 Å relative to the nonrelativistic BO value, is almost completely accounted for by the inclusion of the Breit-interaction and the Araki-Sucher contributions to the potential, of the order α(2) and α(3), respectively. The remaining retardation effect, of the order of α(4) and higher, is practically negligible for the bound state, but is important for the thermophysical properties of helium. Such properties computed from our potential have uncertainties that are generally significantly smaller (sometimes by nearly two orders of magnitude) than those of the most accurate measurements and can be used to establish new metrology standards based on properties of low-density helium.

Nonadiabatic investigations of ro-vibrational frequencies within the systems , H2, and prospects for : use of distance-dependent effective masses

For small hydrogenic systems the discrepancy between theoretical and experimental studies of ro-vibrational spectra is mostly related to the neglect of adiabatic and non-adiabatic effects on the ro-vibrational eigenvalues. In the case of and its isotopomers, detailed investigations of low lying ro-vibrational excitations have been performed. Using gaussian geminals an absolute accuracy of the Born–Oppenheimer potential energy surface (PES) by ∼0.02 cm−1 was reached. Of similar quality are calculations of relativistic effects and diagonal adiabatic contributions. Non-adiabaticity can be simulated by using atomic masses for vibrational motion and nuclear masses for rotational motion, so that the deviation to experiment can be reduced to a few hundredths of a wavenumber. Recently, a rigorous non-adiabatic theory in terms of a single potential energy surface had been developed and was tested numerically for and H2. Within this new non-adiabatic theory distance-dependent effective nuclear masses have to be used. Our main interest is to use these new ideas for taking into account the effects of non-adiabaticity on the ro-vibrational spectrum of and its isotopomers. Within a perturbative approach we investigate the influence of the operator of nuclear kinetic energy of a triatomic molecule on the electronic wave function. For the asymptotic arrangement of a nearly separated atom–diatomic system we can calculate numerically with high accuracy the distance-dependent effective nuclear masses for and H2. The kinetic energy operator for a triatomic molecule describing ro-vibrational motion has many different terms, where different effective masses have to be taken into account. Within the present work for , the distance-dependent effective mass for the diatomic motion part, using Jacobi coordinates, will be presented.

Laser-controlled vibrational heating and cooling of oriented H+2 molecules

We investigate the control of the vibrational dynamics in the hydrogen molecular ion H+2 using strong femto-second infrared control-laser pulses. For our three-dimensional calculations, we use infrared laser pulses of 800 nm wavelength, 6 fs pulse duration and a peak intensity between 1012 and 1015 W cm−2. For laser electric fields aligned along the molecular axis, we numerically solve the full vibronic Schrödinger equation and compare our results with a model calculation that only includes the nuclear motion on the two lowest coupled adiabatic Born–Oppenheimer potential curves. The initial vibrational wave packet is launched with the ionization of the parent H2 molecule in the pump pulse. Precise timing between pump- and control-laser pulses allows for the direct manipulation of the final bound vibrational-state composition and dissociation dynamics of the ion. We show that significant enhancement of the occupation of particular stationary vibrational-state contributions can be achieved for laser intensities below the onset of strong ionization (≈1014 W cm−2). In addition, we find that this vibrational selectivity strongly depends on the delay time but not on the intensity of the control pulse. The relative stationary vibrational-state contributions and the shape of the vibrating wave packet depend sensitively on the control-pulse delay time, and the overall amplitude of the final vibrational wave packet depends on the intensity of the control pulse.

Born-Oppenheimer potential for HeH+

We demonstrate high accuracy calculations for the HeH$^+$ molecule using newly developed analytic formulas for two-center two-electron integrals with exponential functions. The Born-Oppenheimer potential for the ground electronic $^1\Sigma^+$ state is obtained in the range of 0.1 -- 60 au with precision of about $10^{-12}$ au. As an example at the equilibrium distance $r=1.463\,283$ au the Born-Oppenheimer potential amounts to $-2.978\,708\,310\,771(1)$. Obtained results lay the ground for theoretical predictions in HeH$^+$ with spectroscopic precision.

Ultralong-range polyatomic Rydberg molecules formed by a polar perturber

The internal electric field of a Rydberg atom electron can bind a polar molecule to form a giant ultralong-range stable polyatomic molecule. Such molecules not only share their properties with Rydberg atoms (such as long lifetimes and large sizes) but they also possess huge permanent electric dipole moments and in addition allow for coherent control of the polar molecule orientation. In this work, we include additional Rydberg manifolds which couple to the nearly degenerate set of Rydberg states employed in the previous work (S T Rittenhouse and H R Sadeghpour 2010 Phys. Rev. Lett. 104 243002). The coupling of a set of (n + 3)s Rydberg states with the n(l > 2) nearly degenerate Rydberg manifolds in alkali metal atoms leads to pronounced avoided crossings in the Born–Oppenheimer potentials. Ultimately, these avoided crossings enable the formation of the giant polyatomic Rydberg molecules with standard two-photon laser photoassociation techniques.

Dynamical features of interference phenomena in the presence of entanglement

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.

Charge exchange in collisions of beryllium with its ion

Close-coupling calculations of the resonance and near resonance charge exchange in ion-atom collisions of Be at low and intermediate energies are presented. Accurate ab initio calculations are carried out of the Born-Oppenheimer potentials and the non-adiabatic couplings that are due to the finite nuclear masses and drive the near resonance charge exchange. We show that the near resonance charge exchange cross section follows Wigner's threshold law of inelastic processes for energies below 10(-8) eV and that the zero temperature rate constant for it is 4.5 × 10(-10) cm(3) s(-1). At collision energies much larger than the isotope shift of the ionization potentials of the atoms, we show that the near resonance charge exchange process is equivalent to the resonance charge exchange with cross sections having a logarithmic dependence. We also investigate the perturbation to the charge exchange process due to the non-adiabatic interaction to an electronic excited state. We show that the influence is negligible at low temperatures and still small at intermediate energies despite the presence of resonances.

Franck–Condon factors for molecule–ion reactions of [formula omitted] and its isotopomers

An existing, systematic, fundamental database of Franck–Condon factors and transition probabilities for all isotopomers of the hydrogen molecule (H 2, D 2, T 2, HD, HT, and DT) has been extended for reactions which connect the molecule with its ion H 2 + ( v ) (or the corresponding ion of the specific isotopomer). The most recent Born–Oppenheimer potential curves were used to calculate the vibrational eigenvalues and eigenfunctions, from which the Franck–Condon factors were obtained by convolution. The accuracy of the results has been assessed and a comparison with results available in the literature was performed.

Born-Oppenheimer potential forH2

The Born-Oppenheimer potential for the $^1\Sigma_g^+$ state of H$_2$ is obtained in the range of 0.1 -- 20 au, using analytic formulas and recursion relations for two-center two-electron integrals with exponential functions. For small distances James-Coolidge basis is used, while for large distances the Heitler-London functions with arbitrary polynomial in electron variables. In the whole range of internuclear distance about $10^{-15}$ precision is achieved, as an example at the equilibrium distance $r=1.4011$ au the Born-Oppenheimer potential amounts to $-1.174\,475\,931\,400\,216\,7(3)$. Results for the exchange energy verify the formula of Herring and Flicker [Phys. Rev. {\bf 134}, A362 (1964)] for the large internuclear distance asymptotics. The presented analytic approach to Slater integrals opens a window for the high precision calculations in an arbitrary diatomic molecule.

Electronic–geometric coupling in model reactive system

The equilibria in triatomic (collinear) reactive system are examined. The linear-response treatment of adjustments in the molecular electronic and geometrical degrees-of-freedom, determined from the chemical-potential (electronegativity) equalization principle, are predicted using the previously proposed analytical representation of the chemical hardness matrix in atomic resolution. The system relaxation is determined from the joint electronic–nuclear Hessian in the electron-following representation, defined by the corresponding second partials of the system Born–Oppenheimer potential. It includes the diagonal blocks of the electronic hardness tensor and geometric force constants, as well as the off-diagonal blocks of the nuclear Fukui function indices, which determine the coupling between the molecular electronic and geometrical structures. The latter are explicitly modelled using the canonical hardness tensor of the constituent atoms. This combined treatment explicitly accounts for the mutual coupling between the system charge distribution and its geometry. The molecular compliant descriptors, which determine the system minimum-energy coordinates, can be also generated using the inverse, electron-preceding representation.

Feshbach resonances and transition rates for cold homonuclear collisions betweenK39andK41atoms

We report results from close-coupling calculations for homonuclear ultracold collisions between potassium atoms, using the most up-to-date Born-Oppenheimer potential curves. The present study includes both of the bosonic isotopes $^{39}\mathrm{K}$ and $^{41}\mathrm{K}$. The $s$-wave scattering lengths as functions of the magnetic field strength for collisions between atoms in identical and different hyperfine states are obtained. Several Feshbach resonances are located and characterized for both isotopes. Comparison with experiments, where such data are available, show excellent agreement. We also study weakly bound molecular states of the ${\mathrm{K}}_{2}$ molecule in close relation to the calculated Feshbach resonances. Another objective of the present work is to study inelastic collisions in which the hyperfine states of the colliding atoms are changed. From this type of calculation we obtain transition rates as functions of the magnetic field strength. Finally, we discuss how such transition rates might be of importance for experimental work.

Electronic spin-flipping collisions of hydrogen atoms

We present a unified multichannel approach to calculate electron spin-exchange and spin-flipping transition cross sections for collisions of H with H, H with T, and T with T. We use the theory to calculate the hyperfine quenching cross sections for collision energies that range from $1$ mK to thermal temperatures. We show that spin-flipping transitions are induced by the splitting of the $b {}^{3}{\ensuremath{\Sigma}}_{u}$ Born-Oppenheimer potential via the long-range magnetic interactions among electrons. We find that the spin-flipping cross sections in the tritium dimer are about a magnitude larger than that predicted by mass scaling the H-H cross sections. For the former, we show that the spin-exchange cross sections are several magnitudes larger, at cold temperatures, than that of the hydrogen system. We compare the results of the multichannel approach with those obtained using approximate methods such as the degenerate internal-state, the elastic, and Born approximations and discuss their respective range of validity.

Symmetry breaking in the cyclic C3C2H radical

We have employed high-level coupled cluster methods including connected triple excitations to study the possibility of symmetry-breaking in the (2)B(2) ground state of the c-C(3)C(2)H radical. Specifically, we find that spin-restricted open-shell Hartree-Fock (ROHF) reference orbitals yield a C(2v) structure, whereas spin-unrestricted Hartree-Fock (UHF) and Brueckner orbitals lead to a symmetry-broken C(s) minimum-energy geometry. Equation-of-motion coupled cluster singles and doubles method for ionized states yields a C(s) structure with a double-zeta basis set, but not with a triple-zeta basis set. Through a detailed analysis of the orbital instability/near-instability behavior of each type of Hartree-Fock reference, we have determined that the UHF reference wave function is more reliable than the ROHF reference in this case and that the Born-Oppenheimer potential surface for c-C(3)C(2)H exhibits a symmetry broken C(s) global minimum. This result is supported by excited-state computations, which indicate that a second-order (pseudo) Jahn-Teller interaction is responsible for the symmetry-breaking.

Dependence of the scattering length for hydrogen atoms on effective mass

The possibility that the non-adiabatic correction to the scattering length of a pair of hydrogen atoms interacting via the ground state molecular potential, X1Σg +, of H2 could be made by replacing the mass of each nucleus by a different effective mass is explored. The Born-Oppenheimer potential with adiabatic, relativistic and radiative corrections is used in calculations of the scattering lengths and the mass-dependent shifts of the rotationless vibrational levels with fixed and varying effective masses. The shifts are compared with established values and it is demonstrated that the semi-classical formula for the scattering length accounts well for the effect of changing the mass. A perturbing potential that is equivalent to a change in mass is derived and it is compared to a published local non-adiabatic potential.

Ab-initio determination of Bose-Hubbard parameters for two ultracold atoms in an optical lattice

We calculate numerically the exact energy spectrum of the six-dimensional problem of two interacting Bosons in a three-well optical lattice. The particles interact via a full Born-Oppenheimer potential which can be adapted to model the behavior of the s-wave scattering length at Feshbach resonances. By adjusting the parameters of the corresponding Bose-Hubbard (BH) Hamiltonian the deviation between the numerical energy spectrum and the BH spectrum is minimized. This defines the optimal BH parameter set which we compare to the standard parameters of the BH model. The range of validity of the BH model with these parameter sets is examined, and an improved analytical prediction of the interaction parameter is introduced. Furthermore, the extended BH model and implications due to the energy dependence of the scattering length and couplings to higher Bloch bands at a Feshbach resonance are discussed.