Born-Oppenheimer Potential Energy Curves Research Articles

Born–Oppenheimer potential energy curves of NaK from the optimised atomic basis sets

The article presents adiabatic potential energy curves of the ground and excited electronic states for the diatomic NaK molecule. The calculations were made using the ab initio computational methods to include electron correlation. The studied molecule was calculated as the effective two-electron problem, in which only the valence electrons of the molecule are explicitly taken into account. The remaining electrons with atomic nuclei are described with appropriate, energy-consistent relativistic pseudopotentials. Additionally, a bespoke basis set, generated and optimised for both ground and excited electronic states of the NaK system was developed. The spectroscopic parameters of the calculated potential energy curves were determined and compared with the available experimental and theoretical results. The compliance of the obtained results, despite slight differences, is very satisfactory.

Benchmark calculations of ro-vibrational spectrum of HeH − and its isotopologues

Benchmark variational calculations of the Born–Oppenheimer potential energy curve (PEC) performed with explicitly correlated all-electron Gaussian functions with shifted centers are presented. The PEC energies include the leading relativistic and quantum-electrodynamics corrections and the first-order corrections due to adiabatic effects. The PEC is used to calculate the ro-vibrational spectra for HeH− and its isotopologues. The results show that these systems are marginally stable and have two to four bound vibrational levels and, for each vibrational level, a few bound rotational levels lying below the dissociation threshold. This indicates a possibility of detecting the HeH− anion in the laboratory and, perhaps, even in the interstellar space.

Calculating potential energy curves with fixed-node diffusion Monte Carlo: CO and N2.

This study reports on the prospect for the routine use of Quantum Monte Carlo (QMC) for the electronic structure problem, applying fixed-node Diffusion Monte Carlo (DMC) to generate highly accurate Born-Oppenheimer potential energy curves (PECs) for small molecular systems. The singlet ground electronic states of CO and N2 were used as test cases. The PECs obtained by DMC employing multiconfigurational trial wavefunctions were compared with those obtained by conventional high-accuracy electronic structure methods such as multireference configuration interaction and/or the best available empirical spectroscopic curves. The goal was to test whether a straightforward procedure using available QMC codes could be applied robustly and reliably. Results obtained with DMC codes were found to be in close agreement with the benchmark PECs, and the n3 scaling with the number of electrons (compared with n7 or worse for conventional high-accuracy quantum chemistry) could be advantageous depending on the system size. Due to a large pre-factor in the scaling, for the small systems tested here, it is currently still much more computationally intensive to compute PECs with QMC. Nevertheless, QMC algorithms are particularly well-suited to large-scale parallelization and are therefore likely to become more relevant for future massively parallel hardware architectures.

Rotation-vibration spectra for ground state of NaH and its isotopes with explicitly multireference configuration interaction method

High-level ab initiocalculations utilizing explicitly correlatedmulti-reference configuration interaction method (MRCI-F12), considering Davidson modification(Q), core-valence correlation correction(CV) and scalar relativistic correction(SR), were per- formed to compute the Born-Oppenheimer potential energy curve (PEC) of the ground state X 1 S + of NaH. On the base of the PEC, we obtained vibrational and rotational energy levels information of the ground state X 1 S + . The vibrational and rotational spectroscopic constants of X 1 S + were compared with the available experimental val- ues. We also report rotation-vibration spectra of the ground state for the isotopes of NaH, NaD and NaT molecules. The equilibrium internuclear distances Re and dissoci- ation energies De were calculated to be 1.8865u Aand 15823.29cm 1 for the ground state X 1 S + of NaH, which are in good agreement with the experimental results of 1.8859u A and 15815±5cm 1 .

A self-consistent GW approach to the van der Waals potential for a helium dimer.

van der Waals interaction between two helium (He) atoms is studied by calculating the total energy as a function of the He-He distance within the self-consistent GW approximation, which is expected to behave correctly in the long wavelength limit. In the Born-Oppenheimer (BO) approximation, the pair potential curve has its minimum value at 2.87 Å, which is somewhat larger than the local density approximation result, 2.40 Å, and is closer to previous quantum chemistry results. The expectation value for the interatomic distance, calculated by solving the Schrödinger equation for the two nuclei problem using the BO potential energy curve, is 30 Å, which is smaller but of the same order as previous experimental and theoretical results.

Characterization of Molecular Breakup by Very Intense Femtosecond XUV Laser Pulses.

We study the breakup of H2+ exposed to superintense, femtosecond laser pulses with frequencies greater than that corresponding to the ionization potential. By solving the time-dependent Schrödinger equation in an extensive field parameter range, it is revealed that highly nonresonant dissociation channels can dominate over ionization. By considering field-dressed Born-Oppenheimer potential energy curves in the reference frame following a free electron in the field, we propose a simple physical model that characterizes this dissociation mechanism. The model is used to predict control of vibrational excitation, magnitude of the dissociation yields, and nuclear kinetic energy release spectra. Finally, the joint energy spectrum for the ionization process illustrates the energy sharing between the electron and the nuclei and the correlation between ionization and dissociation processes.

Interaction of Ag(5s) and Ag(5p) with noble gas atoms

We investigate the interaction of ground and excited states of silver atom with all the noble gases, including helium. Born-Oppenheimer potential energy curves are calculated with quantum chemical techniques and spin-orbit effects in the excited states are included. We compare with experimentally available spectroscopic data, as well as previous calculations. The assignment of vibrational levels in the one experiment we compare with, may have to shift up by one unit.

Chemistry in high-frequency strong laser fields: the story of HeS molecule

The laser-induced stabilisation of atoms producing new chemical species has been evidenced before in the case of helium atoms in high-frequency strong laser fields producing quasi-stable dimers with a strong chemical bond. In the current work, it is shown that the laser-dressed orbitals of helium atoms retain their atomic character, for feasible laser parameters. Namely, the laser-dressed electron density of helium atom peaks at the atomic position. Yet, because of light-induced polarisation two other smaller peaks are obtained at the two classical turning points of the electronic quiver motion. The situation is remarkably different for the case of many-electron atoms such as sulphur. The laser-dressed electron density does not peak at the atomic nucleus (as in the case of helium in laser fields), but maximises at the two classical turning points of the electronic quiver motion that is induced by the high-frequency strong laser field. In the presence of high-frequency strong linear polarised laser field sulphur atoms and helium atoms interact to produce a strong chemical bond which is three orders of magnitude stronger than conventional chemical bonds and the laser-dressed bond in helium dimer. Moreover, as we show here, by varying the quiver length parameter of the laser field and the inter-nuclear distance, the structure of HeS changes from one isomer to another, as evidenced by the double minima in the laser-dressed Born–Oppenheimer potential energy curves.

Radiative association of He+2revisited

Aims. Rate coefficients for spontaneous and stimulated radiative association of the He + molecular ion are presented as a function of temperature, considering the association with rotational-vibrational states of the ground X electronic state from the continuum states of the lowest three excited A,C ,a ndE electronic states. Methods. The rate coefficients are obtained from the cross sections for radiative association, which are calculated by solving the Schrodinger equation for bound and continuum states supported by the corresponding Born-Oppenheimer potential energy curves. Results. The rate coefficients for the A → X spontaneous process are in excellent agreement with previous calculations. For temperatures up to about 10000 K, the spontaneous C → X and E → X processes are dominant, exceeding the A → X rate coefficient by several orders of magnitude. Stimulation of the radiative association by black-body radiation has significant influence only on the A → X process at temperatures below 1000 K. The black-body radiation temperature would have to be well above 50000 K in order to have any noticeable effect on the C → X and E → X processes.

Potential energy curves for the interaction of Ag($\mathbf {5}{\bm s}$5s) and Ag($\mathbf {5}{\bm p}$5p) with noble gas atoms

We investigate the interaction of ground and excited states of a silver atom with noble gases (NG), including helium. Born-Oppenheimer potential energy curves are calculated with quantum chemistry methods and spin-orbit effects in the excited states are included by assuming a spin-orbit splitting independent of the internuclear distance. We compare our results with experimentally available spectroscopic data, as well as with previous calculations. Because of strong spin-orbit interactions, excited Ag-NG potential energy curves cannot be fitted to Morse-like potentials. We find that the labeling of the observed vibrational levels has to be shifted by one unit.

CrRb: A molecule with large magnetic and electric dipole moments

We report calculations of Born-Oppenheimer potential energy curves of the chromium-rubidium heteronuclear molecule 52Cr-87Rb, and the long-range dispersion coefficient for the interaction between ground state Cr and Rb atoms. Our calculated van der Waals coefficient (C6=1770 a.u.) has an expected error of 3%. The ground state 6Sigma+ molecule at its equilibrium separation has a permanent electric dipole moment of de (Re=3.34 A) = 2.90 D. We investigate the hyperfine and dipolar collisions between trapped Cr and Rb atoms, finding elastic to inelastic cross section ratio of 100-1000.

Quasi-diabatic decoupling of Born-Oppenheimer potential energy curves for adsorbate-metal surface systems

We have applied the open-system treatment, recently developed by the authors, to a simple adsorbate-metal surface model potential. The open-system treatment is found to give a quasi-diabatic representation where the adsorbate electronic states cross the metal ones in the manifold consisting of the Born-Oppenheimer potential energy curves of the whole system. On the obtained quasi-diabatic curves, one can effectively follow time propagation of a nuclear wave packet. The computed propagation has revealed that the formation of a metastable adsorbate leads to the coherent vibrational motion of the neutral adsorbate as well as the desorption induced by electronic transitions.

Pressure broadening and shift ofHe(23P0,1,2)−He(23S)lines

The collisional broadening and shift of metastable helium fine-structure lines are calculated within the impact approximation. Ab initio Born-Oppenheimer potential energy curves correlating to $\mathrm{He}(1{}^{1}{S}_{0})$ and $\mathrm{He}(2{}^{3}{P}_{j})$ atomic levels are obtained using the configuration interaction valence bond method and combined with semiempirically calculated van der Waals interaction terms between these atoms to also study j-specific and j-changing collisions. A long-range van der Waals potential well exists in the ${}^{3}{\ensuremath{\Pi}}_{u}$ potential correlated to the $\mathrm{He}(1{}^{1}{S}_{0})+\mathrm{He}(2{}^{3}{P}_{j})$ limit, whose influence on the scattering phase shift is assessed. At $T=310\mathrm{K},$ the broadening and shift parameters are practically j independent and have average values of 12.60 and 1.87 MHz/Torr, respectively. The j-changing collisions have cross sections roughly five times smaller than the j-specific cross sections.

Spectroscopic and electric properties of NaH and NaD: Extrapolation to the complete basis set limit

We report accurate spectroscopic and electric properties for the ground electronic state of NaH and NaD from first principles electronic structure calculations at the coupled cluster singles-and-doubles with noniterative inclusion of connected triples [CCSD(T)] level of theory. A NaH/NaD Born–Oppenheimer potential energy curve is defined by extrapolating CCSD(T) ab initio energies to the complete basis set limit. Potential energy curves obtained using different basis sets and different basis set extrapolation schemes are compared to experimentally determined curves. When compared to experiment, basis set extrapolation yields a potential energy curve that results in highly accurate rotational and vibrational spectroscopic data for both NaH and NaD. An extensive set of spectroscopic parameters are tabulated. Electric properties are computed from CCSD(T) finite-field energies that have been extrapolated to the complete basis set limit. Dipole moment and dipole polarizability curves are reported. These quantities are vibrationally averaged for comparison with experimental values when they become available. Rovibrational transition matrix elements and vibrational lifetimes are also computed.

Helium-Antihydrogen Interaction: The Born-Oppenheimer Potential Energy Curve

The interaction of atomic antihydrogen with helium has been studied within the Born-Oppenheimer approximation. The linear combination of explicitly correlated Gaussian functions was used as the ansatz for the wave function of light particles. The potential energy curve with the minimum at 3.63 bohr and the barrier at 2.42 bohr has been obtained.

Adiabatic Energies of Excited 1Σu States of the Hydrogen Molecule

Accurate Born–Oppenheimer potential energy curves and adiabatic corrections are computed for the six lowest 1Σu states of the hydrogen molecule. For the 41Σu–61Σu states adiabatic term values of the vibrational levels supported by the potentials and the corresponding rotational constants are given. For the outer potential well of the 61Σu state, Franck–Condon factors are listed for the possible transitions to the HH̄1Σg state.

Model studies of nonadiabatic dynamics

Mixed quantum-classical methods are applied to an increasingly challenging series of model problems, and their accuracy is examined. The models involve one light and one heavy degree of freedom, and exhibit substantial nonadiabatic behavior. In all of the models the coupling between the light and heavy particles is linear (harmonic). In addition, different external potentials are applied to the heavy particle only. The energies of the light particle quantum states, as a function of the position of the heavy particle, define a sequence of ground and excited Born–Oppenheimer potential energy curves. Because the light particle experiences a purely harmonic potential, the potential energy curves are parallel and equally spaced for all of the models. In addition, the nonadiabatic couplings among potential energy curves persist for all times due to the nonvanishing linear coupling between light and heavy particles. The model problems were used to test two strategies for carrying out mixed quantum-classical dynamics in systems involving nonadiabatic transitions: mean field and surface hopping. The model calculations reported here suggest that, in cases where linear couplings dominate, the mean field mixed quantum-classical method displays useful accuracy and is robust to the introduction of anharmonic heavy-particle interactions. The model calculations also reveal special situations in which the surface hopping approximation is inappropriate.

Correlation study of Franck-Condon barriers associated with electron self-exchange reactions with ionization potentials and electron affinities and experimental Born-Oppenheimer potentials

An accurate theoretical scheme for obtaining directly the Franck-Condon barrier associated with the electron self-exchange reaction from ionization potentials and electron affinities is presented. Applicability is tested using some diatomic molecular redox couples. The corresponding ionization potentials and electron affinities are obtained from the Born-Oppenheimer potential energy curves which are directly determined from the experimental vibration-rotational spectroscopic data. The Franck-Condon barriers are calculated for the electron self-exchange reactions and are also compared with those from other theoretical methods.

Double-Minimum Potential Energy Curves Resulting from Adiabatic Effects: The 4s3Σ+gand 4d3Σ+gStates of the Hydrogen Molecule

The Born–Oppenheimer potential energy curve and the adiabatic corrections for the 4sand 4d3Σ+gstates of the hydrogen molecule have been calculated for a wide range of internuclear distance using explicitly correlated wavefunctions in elliptic coordinates. It is shown that similarly to the 4sstate the 4dalso state exhibits a single-minimum potential energy curve in the BO approximation and a double-minimum potential energy curve in the adiabatic approximation. The energies of the vibrational levels and rotational constants for both states have been computed. As a result of the existence of the double-minimum potential energy curves, the sets of vibrational levels form two series of levels, each connecting with outer or inner minimum. Large and irregular discrepancies with experimental data have been found. This is partially a consequence of not applying the nonadiabatic corrections, which are expected to play an important role in this case.

The a3Σ +g State of the Hydrogen Molecule

The Born-Oppenheimer potential energy curve and the adiabatic corrections for the a 3Σ + g state of the hydrogen molecule have been recalculated for a wide range of internuclear distance using explicitly correlated wavefunctions in elliptic coordinates. The calculated potential energy curve is lower than the previous one by more than I cm −1. The energies of the vibrational levels and rotational constants for this state have been also computed. In addition, the nonadiabatic corrections have been estimated on the basis of an approximate Van Vleck formula. The estimated nonadiabatic shift for the lowest level of H 2 has been independently confirmed by comparing the nonadiabatic energy calculated by Bishop and Cheung with the adiabatic energy presented in this work. It is shown that by taking into account estimated nonadiabatic corrections as well as relativistic and radiative effects, excellent agreement with experiment is achieved.