Ground State Potential Curves Research Articles

Chemically Accurate Potential Curves for H2 Molecules Using Explicitly Correlated Qubit-ADAPT.

With the recent advances in the development of devices capable of performing quantum computations, a growing interest in finding near-term applications has emerged in many areas of science. In the era of nonfault tolerant quantum devices, algorithms that only require comparably short circuits accompanied by high repetition rates are considered to be a promising approach for assisting classical machines with finding a solution on computationally hard problems. The ADAPT approach previously introduced in Nat. Commun. 10, 3007 (2019) extends the class of variational quantum eigensolver algorithms with dynamically growing ansätze in order to find approximations to the ground and excited state energies of molecules. In this work, the ADAPT algorithm has been combined with a first-quantized formulation for the hydrogen molecule in the Born-Oppenheimer approximation, employing the explicitly correlated basis functions introduced in J. Chem. Phys. 43, 2429 (1965). By the virtue of their explicit electronic correlation properties, it is shown in classically performed simulations that chemical accuracy (<1.6 mHa) can be reached for ground and excited state potential curves using reasonably short circuits.

HF, DF, TF: approximating potential curves, calculating rovibrational states

A simple analytical expression for the potential energy curve for the ground state X 1Σ+ of the hydrogen fluoride molecule HF obtained in the framework of the Born–Oppenheimer approximation is proposed. This analytical expression for the potential energy curve is based in the two point Padé approximation, which correctly reproduces the asymptotic behavior at small R → 0 and large R → ∞ internuclear distances, and position and depth of potential well, leading to the accuracy of 4–5 decimal digits when compared with experimental data. The rovibrational spectra of the diatomic molecule HF is calculated by solving the Schrödinger equation for nuclear motion using the Lagrange-mesh method. The ground state X 1Σ+ contains 21 vibrational states (ν, 0) and 724 rovibrational states (ν, L) with maximal angular momentum equal to 55. The change of reduced mass in the Schrödinger equation for nuclear motion allows us to obtain the rovibrational spectrum of the ground state potential curve of the deuterium fluoride DF (contains 29 vibrational states (ν, 0) and 1377 rovibrational states (ν, L)) and tritium fluoride TF (contains 35 vibrational states (ν, 0) and 1967 rovibrational states (ν, L)) with maximal angular momenta 76 and 92, respectively. Entire rovibrational spectra is presented for the HF molecule and its two isotopologues DF and TF.

Application of the coupled-cluster CC(P;Q) approaches to the magnesium dimer

ABSTRACTSeveral coupled-cluster approaches with an approximate treatment of connected triply or quadruply excited clusters, including the CCSD(T), , and CR-CC(2,3) corrections to CCSD, the active-space CCSDt and CCSDTq methods, and the CC(t;3) and CC(q;4) corrections to CCSDt and CCSDTq derived using the CC(P;Q) framework, and their CCSDT and CCSDTQ parents are applied to the ground-state potential curve and vibrational term values of the magnesium dimer. The correlation-consistent aug-cc-pV(n+d)Z and aug-cc-pwCVnZ ( and Q) basis sets are used. Among the noniterative triples corrections to CCSD, the CR-CC(2,3) approach performs the best, but, in analogy to the previously studied beryllium dimer [I. Magoulas et al., J. Phys. Chem. A 122, 1350 (2018)], the CC(t;3) and CC(q;4) methods outperform other employed approaches in reproducing the CCSDT and CCSDTQ data. Composite calculations combining the nearly all-electron CCSDT and valence CC(q;4) and CCSDTQ computations reproduce the experimentally resolved part of the vibrational spectrum of to within ∼1 when the vibrational spacings are examined, while predicting five extra vibrational states near the dissociation threshold, which have not been experimentally resolved. The corresponding binding energies and equilibrium bond lengths are within a few and 0.01 Å from their experimentally derived values.

H[formula omitted], HeH and H[formula omitted]: Approximating potential curves, calculating rovibrational states

Analytic consideration of the Bohr–Oppenheimer (BO) potential curves for diatomic molecules is proposed: accurate analytic interpolation for a potential curve consistent with its rovibrational spectra is found.It is shown that in the BO approximation for four lowest electronic states 1sσg and 2pσu, 2pπu and 3dπg of H2+, the ground state X2Σ+ of HeH and the two lowest states 1Σg+ and 3Σu+ of H2, the potential curves can be analytically interpolated in full range of internuclear distances R with not less than 4–5–6 s.d. Approximation based on matching the Laurant-type expansion at small R and a combination of the multipole expansion with one-instanton type contribution at large distances R is given by two-point Padé approximant. The position of minimum, when exists, is predicted within 1% or better.For the molecular ion H2+ in the Lagrange mesh method, the spectra of vibrational, rotational and rovibrational states (ν,L) associated with 1sσg and 2pσu, 2pπu and 3dπg potential curves are calculated. In general, it coincides with spectra found via numerical solution of the Schrödinger equation (when available) within six s.d. It is shown that 1sσg curve contains 19 vibrational states (ν,0), while 2pσu curve contains a single one (0,0) and 2pπu state contains 12 vibrational states (ν,0). In general, 1sσg electronic curve contains 420 rovibrational states, which increases up to 423 when we are beyond BO approximation. For the state 2pσu the total number of rovibrational states (all with ν=0) is equal to 3, within or beyond Bohr–Oppenheimer approximation. As for the state 2pπu within the Bohr–Oppenheimer approximation the total number of the rovibrational bound states is equal to 284. The state 3dπg is repulsive, no rovibrational state is found.It is confirmed in Lagrange mesh formalism the statement that the ground state potential curve of the heteronuclear molecule HeH does not support rovibrational states.Accurate analytical expression for the potential curves of the hydrogen molecule H2 for the states 1Σg+ and 3Σu+ is presented. The ground state 1Σg+ contains 15 vibrational states (ν,0),ν=0–14. In general, this state supports 301 rovibrational states. The potential curve of the state 3Σu+ has a shallow minimum: it does not support any rovibrational state, it is repulsive.

A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves.

The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorski-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an effective Hamiltonian may be built, allowing for the dressing of the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI. Such a formulation accounts then for the coupling between the static and dynamic correlation effects. With our new definition of zeroth-order energies, these two approaches are strictly size-extensive provided that local orbitals are used, as numerically illustrated here and formally demonstrated in the Appendix. Also, the present formalism allows for the factorization of all double excitation operators, just as in internally contracted approaches, strongly reducing the computational cost of these two approaches with respect to other determinant-based perturbation theories. The accuracy of these methods has been investigated on ground-state potential curves up to full dissociation limits for a set of six molecules involving single, double, and triple bond breaking together with an excited state calculation. The spectroscopic constants obtained with the present methods are found to be in very good agreement with the full configuration interaction results. As the present formalism does not use any parameter or numerically unstable operation, the curves obtained with the two methods are smooth all along the dissociation path.

Controversial electronic structures and energies of Fe2, Fe 2 (+), and Fe 2 (-) resolved by RASPT2 calculations.

The diatomic molecule Fe2 was investigated using restricted active space second-order perturbation theory (RASPT2). This molecule is very challenging to study computationally because predictions about the ground state and excited states depend sensitively on the choice of the quantum chemical method. For Fe2 we show that one needs to go beyond a full-valence active space in order to achieve even qualitative agreement with experiment for the dissociation energy, and we also obtain a smooth ground-state potential curve. In addition we report the first multireference study of Fe 2 (+), for which we predict an (8)Σu (-) ground state, which was not predicted by previous computational studies. By using an active space large enough to remove the most serious deficiencies of previous theoretical work and by explicitly investigating the interpretations of previous experimental results, this study elucidates previous difficulties and provides - for the first time - a qualitatively correct treatment of Fe2, Fe 2 (+), and Fe 2 (-). Moreover, this study represents a record in terms of the number or active electrons and active orbitals in the active space, namely 16 electrons in 28 orbitals. Conventional CASPT2 calculations can be performed with at most 16 electrons in 16 orbitals. We were able to overcome this limit by using the RASPT2 formalism.

Ab initio X(1)0(+) ground state potential curves of Pb···RG dimers (RG = He, Ne, Ar) including spin-orbit effects. Simulation of diffusion coefficients.

CCSD(T) ground state potential curves of Pb···RG systems (RG = He, Ne and Ar) are presented and the importance of the inclusion of spin-orbit effects is discussed. The closed-shell character of the Pb atom at the two-component relativistic level of relativistic theory leads to shallower potential energy curves compared to scalar relativistic open-shell calculations. The pressure-independent cross-diffusion coefficients pD12 have been simulated using the extrapolated two-component CCSD(T) ground state potential curves. The diffusion coefficients from scattering theory are compared with simulations based on molecular dynamics (MD) using the velocity autocorrelation function (VACF) and the Einstein equation. A correction for the proper assessment of the uncertainty in the VACF is proposed. The acceleration of the MD simulation of Pb in RG diffusion is proposed utilizing the RG in Pb diffusion. The dU[TQ]Z/CCSD(T) potential curve of Pb···He (De = 8.667 cm(-1), re = 4.683 Å) supports only one vibrational level. The anharmonicity of this potential is compared to the potential of He···He which also supports only one vibrational level. The comparison is based on the mean square separations of the vibrational wave function.

Correcting the potential curve of the ground state of the KrXe molecule

The results of modelling the published VUV spectra of the gas-discharge plasma of a krypton/xenon mixture are used to propose and approve a correction of the ground-state potential curve of the KrXe molecule.

Relativistic effects in HgHe and HgXe CCSD(T) ground state potential curves. Low-density viscosity simulations of Hg:Xe mixture

The comparison of coupled cluster with single and double excitations and with perturbative correction of triple excitations [CCSD(T)] ground state potential curves of mercury with rare gases (RG): HgHe and HgXe, at several levels of theory is presented. The scalar relativistic (REL) effects and spin-orbit coupling effects in the ground state potential curves of these weakly bounded dimers are considered. The CCSD(T) ground state potential curves at the level of the Dirac-Coulomb Hamiltonian (DCH) are compared with CCSD(T) curves at the level of 4-component spin-free modified DCH, the scalar 2nd order Douglas-Kroll-Hess (DKH2) and the nonrelativistic (NR-LL) (Lévy-Leblond) Hamiltonian. In addition, London-Drude formula and SCF interaction energy curves are employed in the analysis of different contributions of REL effects in dissociation energies of HgRG and Hg(2) dimers. Moreover, the large anharmonicity of the HgHe ground state potential curve is highlighted. The computationally less demanding scalar DKH2 Hamiltonian is employed to calculate the HgXe, Hg(2) , and Xe(2) all electron CCSD(T) ground state potential curves in highly augmented quadruple zeta basis sets. These potential curves are used to simulate the shear viscosity of mercury, xenon, and mercury-xenon (Hg:Xe) mixture.

Accurate calculations of dissociation energies of weakly bonded He2 and Be2 molecules by MRCI method

The He2 and Be2 ground state potential curves have been calculated by extrapolating to an infinite basis BSSE corrected MRCI total energies obtained with large Gaussian basis sets, large reference configuration spaces, and pseudo-natural molecular orbitals. The calculated De = 11.0031 K and Re = 5.607 a.u. of He2 are in an excellent agreement with De = 11.006 ± 0.004 K and Re = 5.608 ± 0.012 a.u. obtained recently by SAPT with SM energy correction. The obtained Be2 non-relativistic De = 822 cm−1 and relativistically corrected De = 818 cm−1 are in a good agreement with experimental De = 790 ± 30 cm−1 and the value of 829 ± 64 cm−1 obtained recently by a quantum Monte Carlo method.

Multilevel effect on ultrafast isotope-selective vibrational excitations: Quantum optimal control study

We demonstrate, using optimal control theory, that perfect isotope-selective molecular vibrational excitations on the ground-state potential curve in multilevel systems can be completed in much shorter time scales than those in two-level systems. We consider a gaseous isotopic mixture of cesium iodide ( 133CsI and 135CsI) and, using two-level and multilevel systems, try to obtain electric fields that drive different isotopes into different vibrational levels. As a result, we find that in multilevel systems isotope-selective excitation processes can be controlled much faster, which we call multilevel effect. It is likely that this effect makes use of the large isotope shifts of higher vibrational levels than the lowest two.

The ground-state potential curve of the beryllium dimer

The ground-state potential curve for the beryllium dimer is calculated using different methods. In the most accurate calculation a minimum of 0.9 kcal/mole is found at a distance of 4.9 a.u. Corrections for deficiencies in the basis set lead to a predicted well depth of 2.0 kcal/mole. Three classes of methods have been used—MCSCF, CI, and MBPT methods—and calculations were performed with two different basis sets. The largest basis set has 7s, 3p, and 2d contracted Gaussian functions where the 2d functions were optimized in the molecule. Nearly complete CI calculations with this basis set recovers 97% of the valence correlation energy. The main conclusion from the calculations with the different methods and basis sets is that it is necessary to compute practically all the valence shell correlation energy in order to obtain a reliable, qualitatively correct, potential curve for Be2. The best illustration of this point is that large MCSCF calculations with 1832 configurations, obtained from a complete distribution of 4 electrons in 20 orbitals, give qualitatively wrong potential curves. This is particularly remarkable since 98.8% of the valence correlation energy obtainable with the basis set is recovered.

Modification of atomic solids via electronic subsystem probed by spectroscopic methods

The role of electronic excitations in the modification of surface properties of atomic solids (AS) is considered using solid Kr as an example. The study is focused on the novel phenomenon found recently in AS: anomalous low temperature “post-desorption” (ALTpD) observed after irradiation of AS with low-energy electron beam. The experiments were performed employing cathodoluminescence (CL) method in combination with correlated in real time measurements of thermally stimulated luminescence (TSL), thermally stimulated exoelectron emission (TSEE) and detection of the “post-desorption” yield. Analysis of the yields correlation enabled us to verify a two-stage mechanism of the ALTpD: (i) thermally assisted release of electrons from their traps followed by (ii) intrinsic charge recombination resulting in “excimer dissociation” via radiative transition to a repulsive part of the ground state potential curve.

On relativistic effects in ground state potential curves of Zn2, Cd2, and Hg2 dimers. A CCSD(T) study

The ground state potential curves of the Zn2, Cd2, and Hg2 dimers calculated at different levels of theory are presented and compared with each other as well as with experimental and other theoretical studies. The calculations at the level of Dirac-Coulomb Hamiltonian (DCH), 4-component spin-free Hamiltonian, nonrelativistic Lévy-Leblond Hamiltonian and at the level of simple Coulombic correction to DCH are presented. The potential curves are calculated in an all-electron supermolecular approach including the correction to basis set superposition error (BSSE). Electron correlation is treated at the coupled cluster level including single and double excitations and noniterative triple corrections, CCSD(T). In addition, simulations of the temperature dependence of dynamic viscosities in the low-density limit using the obtained ground state potential curves are presented.

The ground state well depth position Rm of Van der Waals molecules and the spectral line shapes

As the ground state potential curve is strongly related to spectral line shapes, the minumum position of the ground state potential is obtained from the experiemental absorption profile k(Δ ν, T) at high density of the radiating atoms. The temperature dependence of the absorption processes of Hg and Cd lines 253.65 and 326.1 nm, respectively perturbed by inert gases (Xe, Kr, Ar and Ne) had been carefully studied over a wide spectral range. Using the point of the maximum temperature dependence Δ ν m in each case, we are able to calculate the position of the ground state potential R m using a simple formula.

Electron-impact fragmentation ofCl2−

A merged beam technique has been used to investigate the fragmentation of the ${\mathrm{Cl}}_{2}^{\ensuremath{-}}$ ion in collisions with electrons over an energy range of $0--200\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. We have measured absolute cross sections for detachment, detachment plus dissociation and dissociation processes. Over the energy range studied, the dominant breakup mechanism is dissociation. Dissociation is relatively enhanced in the ${e}^{\ensuremath{-}}+{\mathrm{Cl}}_{2}^{\ensuremath{-}}$ collision system due to the suppression of the normally dominant detachment process, as a result of the large difference between the equilibrium internuclear distances of the ${\mathrm{Cl}}_{2}$ and ${\mathrm{Cl}}_{2}^{\ensuremath{-}}$ ground state potential curves. A prominent structure is observed just above the threshold in the ${\mathrm{Cl}}^{\ensuremath{-}}+\mathrm{Cl}+{e}^{\ensuremath{-}}$ dissociation channel. It is proposed that the structure is a resonance associated with production and rapid decay of an excited state of the doubly charged ${\mathrm{Cl}}_{2}^{\ensuremath{-}}$ ion. A plausible mechanism for production of the di-anionic state based on an excitation plus capture process is suggested.

Bohr's 1913 molecular model revisited.

It is generally believed that the old quantum theory, as presented by Niels Bohr in 1913, fails when applied to few electron systems, such as the H(2) molecule. Here, we find previously undescribed solutions within the Bohr theory that describe the potential energy curve for the lowest singlet and triplet states of H(2) about as well as the early wave mechanical treatment of Heitler and London. We also develop an interpolation scheme that substantially improves the agreement with the exact ground-state potential curve of H(2) and provides a good description of more complicated molecules such as LiH, Li(2), BeH, and He(2).

Different ground-state potentials for the same ultracold-collision outcome

For ultracold strontium atoms colliding at 1 μK, we search for and determine a class of continuous deformations of the ground-state potential curve, under which scattering results are invariant. We search for these potential transformations by keeping track of the changes in the scattering length and photoassociation probabilities ( X 1 Σ g + → 1 Σ u + ) , as we systematically vary a suitable parametric description of the ground-state potential curve. Through a careful analysis of the numerical data thus obtained, we determine one-parameter transformations leaving the scattering matrix invariant. Moreover, we find that any two of these transformations are quadratically related.

High-intensity and ground-state influence on photoassociation line shapes of 88Sr

The photoassociation probabilities of a sample of ultracold strontium atoms at 1 μK, are analyzed under the systematically varied conditions of frequency detuning and laser intensities, and for different dispersion values of the ground state potential curve. At low intensities, different values of dispersion coefficient of the ground state potential can give the same line shape, but at high enough intensity this multiplicity is lifted and the revealed periodic behavior is broken. The intensity of the laser becomes a control knob in the laboratory and it can be used to make better determinations of the ground state potential energy curve.

Accurate asymptotic ground state potential curves of Cs $\mathsf{_2}$ from two-colour photoassociation

Over 100 high lying level energies of the lowest electronic states $X^1{\rm\Sigma}^ + _g$ and $a^3{\rm\Sigma}^ + _u$ in Cs2 are determined in a $\Lambda$ -like scheme two-colour photoassociation spectroscopy. The results are analyzed with a coupled channel model using an asymptotic approach, based on nodal lines. From this analysis we determine the long range dispersion coefficient C6 to 6846.2 $\pm$ 15.6 a.u. We also obtain the first experimental determination of the amplitude of the asymptotic exchange term.