Non-Born–Oppenheimer calculations of the pure vibrational spectrum of HeH+

Capturing Correlation Effects in Positron Binding to Atoms and Molecules

A major challenge in contemporary electronic structure theory involves the development of methods to describe in a balanced manner the contribution of correlation effects to energy differences. This challenge can be even greater for multicomponent systems containing more than one type of quantum particle. In the present work, we describe a flexible code for carrying out self-consistent field and configuration interaction (CI) calculations on multicomponent systems and use it to generate trial wave functions for use in diffusion Monte Carlo (DMC) calculations of the positron affinity of Be, Be2, Be4, Mg, CS2, and benzene. The resulting positron affinities (PAs) are in good agreement with the best values from the literature.

HeH+ under Spatial Confinement

In the present study, the influence of spatial confinement on the bond length as well as dipole moment, polarizability and (hyper)polarizabilities of HeH+ ion was analyzed. The effect of spatial confinement was modelled by cylindrically symmetric harmonic oscillator potential, that can be used to mimic high pressure conditions. Based on the conducted research it was found that the spatial confinement significantly affects the investigated properties. Increasing the confinement strength leads to a substantial decrease of their values. This work may be of particular interest for astrochemistry as HeH+ is believed to be the first compound to form in the Universe.

Structure, energetics, and spectroscopy of the chromophores of HHe+n, H2He+n, and He+n clusters and their deuterated isotopologues

The linear molecular ions H₂He⁺, HHe+2, and He+3 are the central units (chromophores) of certain He-solvated complexes of the H₂He+n, HHe+n, and He+n families, respectively. These are complexes which do exist, according to mass-spectrometry studies, up to very high n values. Apparently, for some of the H₂He+n and He+n complexes, the linear symmetric tetratomic H₂He+2 and the diatomic He+2 cations, respectively, may also be the central units. In this study, definitive structures, relative energies, zero-point vibrational energies, and (an)harmonic vibrational fundamentals, and, in some cases, overtones and combination bands, are established mostly for the triatomic chromophores. The study is also extended to the deuterated isotopologues D₂He⁺, DHe+2, and D₂He+2. To facilitate and improve the electronic-structure computations performed, new atom-centered, fixed-exponent, Gaussian-type basis sets called MAX, with X = T(3), Q(4), P(5), and H(6), are designed for the H and He atoms. The focal-point-analysis (FPA) technique is employed to determine definitive relative energies with tight uncertainties for reactions involving the molecular ions. The FPA results determined include the 0 K proton and deuteron affinities of the ⁴He atom, 14 875(9) cm^-1 [177.95(11) kJ mol^-1] and 15 229(8) cm^-1 [182.18(10) kJ mol^-1], respectively, the dissociation energies of the He+2 → He⁺ + He, HHe+2 → HHe⁺ + He, and He+3 → He+2 + He reactions, 19 099(13) cm^-1 [228.48(16) kJ mol^-1], 3948(7) cm^-1 [47.23(8) kJ mol^-1], and 1401(12) cm^-1 [16.76(14) kJ mol^-1], respectively, the dissociation energy of the DHe+2 → DHe⁺ + He reaction, 4033(6) cm^-1 [48.25(7) kJ mol^-1], the isomerization energy between the two linear isomers of the [H, He, He]⁺ system, 3828(40) cm^-1 [45.79(48) kJ mol^-1], and the dissociation energies of the H₂He⁺ → H+2 + He and the H₂He+2 → H₂He⁺ + He reactions, 1789(4) cm^-1 [21.40(5) kJ mol^-1] and 435(6) cm^-1 [5.20(7) kJ mol^-1], respectively. The FPA estimates of the first dissociation energy of D₂He⁺ and D₂He+2 are 1986(4) cm^-1 [23.76(5) kJ mol^-1] and 474(5) cm^-1 [5.67(6) kJ mol^-1], respectively. Determining the vibrational fundamentals of the triatomic chromophores with second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) techniques, both built around the Eckart-Watson Hamiltonian, proved unusually challenging. For the species studied, VPT2 has difficulties yielding dependable results, in some cases even for the fundamentals of the H-containing molecular cations, while carefully executed VCI computations yield considerably improved spectroscopic results. In a few cases unusually large anharmonic corrections to the fundamentals, on the order of 15% of the harmonic value, have been observed.

HeH+ Collisions with H2: Rotationally Inelastic Cross Sections and Rate Coefficients from Quantum Dynamics at Interstellar Temperatures

We report for the first time an accurate ab initio potential energy surface for the HeH⁺–H₂ system in four dimensions (4D) treating both diatomic species as rigid rotors. The computed ab initio potential energy point values are fitted using an artificial neural network method and used in quantum close coupling calculations for different initial states of both rotors, in their ground electronic states, over a range of collision energies. The state-to-state cross section results are used to compute the rate coefficients over a range of temperatures relevant to interstellar conditions. By comparing the four dimensional quantum results with those obtained by a reduced-dimensions approach that treats the H₂ molecule as an averaged, nonrotating target, it is shown that the reduced dimensionality results are in good accord with the four dimensional results as long as the HeH⁺ molecule is not initially rotationally excited. By further comparing the present rate coefficients with those for HeH⁺–H and for HeH⁺–He, we demonstrate that H₂ molecules are the most effective collision partners in inducing rotational excitation in HeH⁺ cation at interstellar temperatures. The rotationally inelastic rates involving o-H₂ and p-H₂ excitations are also obtained and they turn out to be, as in previous systems, orders of magnitude smaller than those involving the cation. The results for the H₂ molecular partner clearly indicate its large energy-transfer efficiency to the HeH⁺ system, thereby confirming its expected importance within the kinetics networks involving HeH⁺ in interstellar environments.

Energy-transfer quantum dynamics of HeH+ with He atoms: Rotationally inelastic cross sections and rate coefficients

Two different ab initio potential energy surfaces are employed to investigate the efficiency of the rotational excitation channels for the polar molecular ion HeH⁺ interacting with He atoms. We further use them to investigate the quantum dynamics of both the proton-exchange reaction and the purely rotational inelastic collisions over a broad range of temperatures. In current modeling studies, this cation is considered to be one of the possible cooling sources under early universe conditions after the recombination era and has recently been found to exist in the interstellar medium. The results from the present calculations are able to show the large efficiency of the state-changing channels involving rotational states of this cation. In fact, we find them to be similar in size and behavior to the inelastic and reaction rate coefficients obtained in previous studies, where H atoms were employed as projectiles. The same rotational excitation processes, occurring when free electrons are the collision partners of this cation, are also compared with the present findings. The relative importance of the reactive, proton-exchange channel and the purely inelastic channels is also analyzed and discussed. The rotational de-excitation processes are also investigated for the cooling kinetics of the present cation under cold trap conditions with He as the buffer gas. The implications of the present results for setting up more comprehensive numerical models to describe the chemical evolution networks in different environments are briefly discussed.

Accurate spectroscopic properties by diffusion quantum Monte Carlo calculations

The capability of Diffusion Quantum Monte Carlo (DMC) to produce high quality potential energy curve (PEC) was evaluated. H₂⁺, HeH⁺ and LiH PECs were built by all-electron fixed-node DMC calculations. Trial wave functions were obtained from Hartree-Fock (HF) (H₂⁺), MCSCF and CI (HeH⁺ and LiH) calculations multiplied by Jastrow factor. The quality of these generated PECs was analyzed throughout equilibrium distance, dissociation energy, vibrational energies and rovibrational spectroscopic constants (ω_e, ω_ex_e, ω_ey_e, α_e, γ_e and B_e). The Discrete Variable Representation (DVR) and the Dunham approaches were used to determine the rovibrational spectroscopic constants. The PECs and the aforementioned properties were also obtained by the following methods: MCSCF/aug-cc-pV5Z (LiH), CCSD(T)/aug-cc-pV5Z (HeH⁺ and LiH) and HF (H₂⁺ and HeH⁺) levels. The results of these DMC computations, specially the DMC-DVR procedure, are the most accurate among others DMC calculations available in the literature for these systems. They suggest that DMC can be used to achieve accurate PECs to produce spectroscopic properties with the same level of accuracy of theoretical benchmarks and experimental data of the literature.

Charge asymmetry in the rovibrationally excited HD molecule

The recently developed method for performing all-particle non-Born-Oppenheimer variational calculations on diatomic molecular systems excited to the first excited rotational state and simultaneously vibrationally excited is employed to study the charge asymmetry and the level lifetimes of the HD molecule. The method uses all-particle explicitly correlated Gaussian functions. The nonlinear parameters of the Gaussians are optimized with the aid of the analytical energy gradient determined with respect to these parameters.

Calculations of the ground states of BeH and BeH+ without the Born-Oppenheimer approximation

Non-Born-Oppenheimer variational calculations employing explicitly correlated Gaussian basis functions have been performed for the ground states of the beryllium monohydride molecule (BeH) and its ion (BeH+), as well as for the beryllium atom (Be) and its ion (Be+). An approach based on the analytical energy gradient calculated with respect to the Gaussian exponential parameters was employed. The calculated energies were used to determine the ionization potential of BeH and the dissociation energies of BeH and BeH+. Also, the generated wave functions were used to compute various expectation values, such as the average interparticle distances and the nucleus-nucleus correlation functions.

Relativistic corrections to the non-Born-Oppenheimer energies of the lowest singlet Rydberg states of He3 and He4

In this work the authors present an approach to calculate the leading-order relativistic corrections for ground and excited states of helium isotopomers. In the calculations they used variational wave functions expanded in terms of explicitly correlated Gaussians obtained without assuming the Born-Oppenheimer approximation.

Darwin and mass-velocity relativistic corrections in non-Born-Oppenheimer variational calculations

The Pauli approach to account for the mass-velocity and Darwin relativistic corrections has been applied to the formalism for quantum mechanical molecular calculations that does not assume the Born-Oppenheimer (BO) approximation regarding separability of the electronic and nuclear motions in molecular systems. The corrections are determined using the first order perturbation theory and are derived for the non-BO wave function of a diatomic system expressed in terms of explicitly correlated Gaussian functions with premultipliers in the form of even powers of the internuclear distance. As a numerical example we used calculations of the transition energies for pure vibrational states of the HD(+) ion.

Darwin and mass-velocity relativistic corrections in the non-Born-Oppenheimer calculations of pure vibrational states of H2

The Darwin and mass-velocity relativistic corrections have been calculated for all pure vibrational states of the H2 using the perturbation theory and very accurate variational wave functions obtained without assuming the Born-Oppenheimer (BO) approximation. Expansions in terms of explicitly correlated Gaussians with premultipliers in the form of even powers of the internuclear distance were used for the wave functions. With the inclusion of the two relativistic corrections to the non-BO energies the transition energies for the highest states agree more with the experimental results.

Convergence of experiment and theory on the pure vibrational spectrum of HeH(+)

Very accurate quantum mechanical calculations of the pure vibrational spectrum of the molecular ion are reported and compared with newly obtained pure vibrational transitions extracted from the available experimental data. The calculations are performed without assuming the Born-Oppenheimer approximation regarding separability of the nuclear and electronic motions and include the first order relativistic mass-velocity and Darwin corrections. For the two lowest transitions, whose experimental energies are established with the highest precision, the calculated and the experimental results show very good agreement.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.