Lithium Hydride Molecule Research Articles

Molecular Structure Theory without the Born-Oppenheimer Approximation: Rotationless Vibrational States of LiH.

Low-lying rotationless states of the lithium hydride molecule are studied in the framework of the variational method without assuming the Born-Oppenheimer (BO) approximation. Highly accurate solutions to the six-particle (two nuclei and four electrons) Schrödinger equation are obtained by means of expanding the wave functions of the considered states in terms of many thousands of all-particle explicitly correlated Gausssians. The basis functions are optimized independently for each state using the analytic energy gradient with respect to the nonlinear parameters. The non-BO wave functions obtained in the calculations are used to evaluate the leading-order relativistic and quantum electrodynamics energy corrections in the framework of the perturbation theory. The geometric structure of the molecule in the ground and excited states is discussed based on the analysis of the nucleus-nucleus correlation functions. The non-BO energies and structural parameters obtained of this work are compared with the most accurate BO results currently available.

Dirac particles with screened Kratzer–Hulthen plus ring-shaped potential in noncompact extra dimensions

To describe the four fundamental interactions observed in the universe, we used the Dirac equation containing an interaction of the screened Kratzer and the Hulthen potential with a ring-shaped term. We study the energy spectra of spin-[Formula: see text] particles in noncompact extra dimensions. The polar and angular parts of the N-dimensional Dirac equation are solved using the Nikiforov–Uvarov method. The transcendental energy equation and the associated two components spinor wavefunctions of the spin-[Formula: see text] particles are obtained. Moreover, we obtained the nonrelativistic limit of our results by mean of a specific mapping. Some special cases of the proposed potential have been discussed, and their corresponding eigenvalue energies were determined. Finally, we proposed that our results can be used in many branches of physics, to investigate scenarios in extra dimensions where spin-[Formula: see text] particles are involved. To test the reliability of our model, we computed the numerical values of the energy spectra of lithium hydride and hydrogen chloride diatomic molecules using a special case of the proposed potential. The energy spectra are calculated for different quantum numbers [Formula: see text] at different values of the dimensionality of the space. The results of this research are overall in good agreement with the theoretical studies of similar investigation.

Quantum description of magnetocaloric effect, thermo-magnetic properties and energy spectra of LiH, TiH, and ScH diatomic molecules under the influence of magnetic and Aharonov-Bohm (AB) flux fields with Deng-Fan-Screened Coulomb potential model

Quantum description of the isothermal and adiabatic magnetocaloric effect (MCE), thermomagnetic properties, and energy spectra of three diatomic molecules, namely: lithium hydride (LiH), titanium hydride (TiH), and scandium hydride (ScH), was examined with Deng-Fan-Screened Coulomb Potential using the Greene-Aldrich approximation to the centrifugal term. The numerical solutions of the proposed potential with and without the magnetic and AB flux fields obtained reveal that the combined impacts of the magnetic and AB flux fields completely remove the degeneracy of the energy spectra and control the behaviour of the MCE by acting as a regulating factor to cool or heat the MCE. Also, the proposed potential reduces to three exceptional cases, and the thermomagnetic plots obtained for the analysed dimer molecules agreed perfectly with previous work. This research has the potential to be applied in molecular physics and MCE studies for a variety of molecules.

Molecular Energy Landscapes of Hardware-Efficient Ansätze in Quantum Computing.

Rapid advances in quantum computing have opened up new opportunities for solving the central electronic structure problem in computational chemistry. In the noisy intermediate-scale quantum (NISQ) era, where qubit coherence times are limited, it is essential to exploit quantum algorithms with sufficiently short quantum circuits to maximize qubit efficiency. The procedural construction of hardware-efficient ansätze provides one approach to design such circuits. However, refining the accuracy of the global minimum by increasing circuit depth may lead to a proliferation of local minima that hinders global optimization. To investigate this phenomenon, we explore the energy landscapes of hardware-efficient circuits to identify ground-state energies of the hydrogen, lithium hydride, and beryllium hydride molecules. We also propose a simple dimensionality reduction procedure that reduces quantum gate depth while retaining high accuracy for the global minimum, simplifying the energy landscape, and hence speeding up optimization from both software and hardware perspectives.

Numerically stable inversion approach to construct Kohn-Sham potentials for given electron densities within a Gaussian basis set framework.

We present a Kohn-Sham (KS) inversion approach to construct KS exchange-correlation potentials corresponding to given electron densities. This method is based on an iterative procedure using linear response to update potentials. All involved quantities, i.e., orbitals, potentials, and response functions, are represented by Gaussian basis functions. In contrast to previous KS inversion methods relying on Gaussian basis sets, the method presented here is numerically stable even for standard basis sets from basis set libraries due to a preprocessing of the auxiliary basis used to represent an exchange-correlation charge density that generates the exchange-correlation potential. The new KS inversion method is applied to reference densities of various atoms and molecules obtained by full configuration interaction or CCSD(T) (coupled cluster singles doubles perturbative triples). The considered examples encompass cases known to be difficult, such as stretched hydrogen or lithium hydride molecules or the beryllium isoelectronic series. For the stretched hydrogen molecule, potentials of benchmark quality are obtained by employing large basis sets. For the carbon monoxide molecule, we show that the correlation potential from the random phase approximation (RPA) is in excellent qualitative and quantitative agreement with the correlation potential from the KS inversion of a CCSD(T) reference density. This indicates that RPA correlation potentials, in contrast to those from semi-local density-functionals, resemble the exact correlation potential. Besides providing exchange-correlation potentials for benchmark purposes, the proposed KS inversion method may be used in density-partition-based quantum embedding and in subsystem density-functional methods because it combines numerical stability with computational efficiency.

Variational quantum eigensolver for dynamic correlation functions

Recent practical approaches for the use of current generation noisy quantum devices in the simulation of quantum many-body problems have been dominated by the use of a variational quantum eigensolver (VQE). These coupled quantum-classical algorithms leverage the ability to perform many repeated measurements to avoid the currently prohibitive gate depths often required for exact quantum algorithms, with the restriction of a parameterized circuit to describe the states of interest. In this work, we show how the calculation of zero-temperature dynamic correlation functions defining the linear response characteristics of quantum systems can also be recast into a modified VQE algorithm, which can be incorporated into the current variational quantum infrastructure. This allows for these important physical expectation values describing the dynamics of the system to be directly converged on the frequency axis, and they approach exactness over all frequencies as the flexibility of the parameterization increases. The frequency resolution hence does not explicitly scale with gate depth, which is approximately twice as deep as a ground state VQE. We apply the method to compute the single-particle Green's function of ab initio dihydrogen and lithium hydride molecules, and demonstrate the use of a practical active space embedding approach to extend to larger systems. While currently limited by the fidelity of two-qubit gates, whose number is increased compared to the ground state algorithm on current devices, we believe the approach shows potential for the extraction of frequency dynamics of correlated systems on near-term quantum processors.

Quantum simulation of the ground-state Stark effect in small molecules: a case study using IBM Q

As quantum computing approaches its first commercial implementations, quantum simulation emerges as a potentially ground-breaking technology for several domains, including biology and chemistry. However, taking advantage of quantum algorithms in quantum chemistry raises a number of theoretical and practical challenges at different levels, from the conception to its actual execution. We go through such challenges in a case study of a quantum simulation for the hydrogen (H $$_2$$ ) and lithium hydride (LiH) molecules, at an actual commercially available quantum computer, the IBM Q. The former molecule has always been a playground for testing approximate calculation methods in quantum chemistry, while the latter is just a little bit more complex, lacking the mirror symmetry of the former. Using the variational quantum eigensolver method, we study the molecule’s ground state energy versus interatomic distance, under the action of stationary electric fields (Stark effect). Additionally, we review the necessary calculations of the matrix elements of the second quantization Hamiltonian encompassing the extra terms concerning the action of electric fields, using STO-LG-type atomic orbitals to build the minimal basis sets.

Molecular Opacity Calculations for Lithium Hydride at Low TemperatureSupported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300), the National Natural Science Foundation of China (Grant Nos. 11934004 and 11604052), and the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province, China (Grant No. 135409230).

The opacities of the lithium hydride molecule are calculated for temperatures of 300 K, 1000 K, 1500 K, and 2000 K, at a pressure of 10 atm, in which the contributions from the five low-lying electronic states are considered. The ab initio multi-reference single and double excitation configuration interaction (MRDCI) method is applied to compute the potential energy curves (PECs) of the 7LiH, including four 1 Σ + states and one 1 Π state, as well as the corresponding transition dipole moments between these states. The ro-vibrational energy levels are calculated based on the PECs obtained, together with the spectroscopic constants. In addition, the partition functions are also computed, and are provided at temperatures ranging from 10 K to 2000 K for 7LiH, 7LiD, 6LiH, and 6LiD.

Eigensolution, expectation values and thermodynamic properties of the screened Kratzer potential

Within the framework of non-relativistic quantum mechanics via the Nikiforov-Uvarov (NU) method, we obtained the energy eigenvalues and the corresponding normalized eigenfunctions of a newly proposed screened Kratzer potential for lithium hydride (LiH) and hydrogen chloride (HCl) diatomic molecules. With the help of the Hellman-Feynman theorem, the expressions for the expectation values of the square of inverse of position, $ r^{-2}$ , inverse of position, $ r^{-1}$ , kinetic energy, T , and square of momentum, $ p^2$ , and their respective numerical values for the selected diatomic molecules are presented. The vibrational partition function and other thermodynamic functions are also obtained in closed form for the diatomic molecules, using the energy eigenvalues. The results obtained clearly agree with the previously obtained results in the literature.

Variational quantum algorithms for discovering Hamiltonian spectra

Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developing algorithms to calculate the ground state energy of molecules on near-term quantum computers. However, calculating excited state energies has attracted comparatively less attention, and it is currently unclear what the optimal method is. We introduce a low depth, variational quantum algorithm to sequentially calculate the excited states of general Hamiltonians. Incorporating a recently proposed technique, we employ the low depth swap test to energetically penalise the ground state, and transform excited states into ground states of modified Hamiltonians. We use variational imaginary time evolution as a subroutine, which deterministically propagates towards the target eigenstate. We discuss how symmetry measurements can mitigate errors in the swap test step. We numerically test our algorithm on Hamiltonians which encode 3SAT optimisation problems of up to 18 qubits, and the electronic structure of the Lithium Hydride molecule. As our algorithm uses only low depth circuits and variational algorithms, it is suitable for use on near-term quantum hardware.

Time-Dependent Multicomponent Density Functional Theory for Coupled Electron-Positron Dynamics.

Electron-positron interactions have been utilized in various fields of science. Here we develop time-dependent multicomponent density functional theory to study the coupled electron-positron dynamics from first principles. We prove that there are coupled time-dependent single-particle equations that can provide the electron and positron density dynamics, and derive the formally exact expression for their effective potentials. Introducing the adiabatic local density approximation to time-dependent electron-positron correlation, we apply the theory to the dynamics of a positronic lithium hydride molecule under a laser field. We demonstrate the significance of the coupling between electronic and positronic motion by revealing the complex positron detachment mechanism and the suppression of electronic resonant excitation by the screening effect of the positron.

Search for Interstellar LiH in the Milky Way

Abstract We report the results of a sensitive search for the 443.952902 GHz transition of the lithium hydride (LiH) molecule toward two interstellar clouds in the Milky Way, W49N and Sgr B2 (Main), that has been carried out using the Atacama Pathfinder Experiment telescope. The results obtained toward W49N place an upper limit of on the LiH abundance, , in a foreground, diffuse molecular cloud along the sight line to W49N, corresponding to 0.5% of the solar system lithium abundance. Those obtained toward Sgr B2 (Main) place an abundance limit in the dense gas within the Sgr B2 cloud itself. These limits are considerably smaller that those implied by the tentative detection of LiH reported previously for the z = 0.685 absorber toward B0218+357.

Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method

We used a tool of conventional Nikiforov-Uvarov method to determine bound state solutions of Schrodinger equation with quantum interaction potential called Hulthen-Yukawa inversely quadratic potential (HYIQP). We obtained the energy eigenvalues and the total normalized wave function. We employed Hellmann-Feynman Theorem (HFT) to compute expectation valuesr-2,r-1,T, andp2for four different diatomic molecules: hydrogen molecule (H2), lithium hydride molecule (LiH), hydrogen chloride molecule (HCl), and carbon (II) oxide molecule. The resulting energy equation reduces to three well-known potentials which are as follows: Hulthen potential, Yukawa potential, and inversely quadratic potential. The bound state energies for Hulthen and Yukawa potentials agree with the result reported in existing literature. We obtained the numerical bound state energies of the expectation values by implementing MATLAB algorithm using experimentally determined spectroscopic constant for the different diatomic molecules. We developed mathematica programming to obtain wave function and probability density plots for different orbital angular quantum number.

Correlation effects in strong-field ionization of heteronuclear diatomic molecules

We develop a time-dependent theory to investigate electron dynamics and photoionization processes of diatomic molecules interacting with strong laser fields including electron-electron correlation effects. We combine the recently formulated time-dependent generalized-active-space configuration interaction theory [D. Hochstuhl and M. Bonitz, Phys. Rev. A 86, 053424 (2012); S. Bauch et al., Phys. Rev. A 90, 062508 (2014)] with a prolate spheroidal basis set including localized orbitals and continuum states to describe the bound electrons and the outgoing photoelectron. As an example, we study the strong-field ionization of the two-center four-electron lithium hydride molecule in different intensity regimes. By using single-cycle pulses, two orientations of the asymmetric heteronuclear molecule are investigated: Li-H, with the electrical field pointing from H to Li, and the opposite case of H-Li. The preferred orientation for ionization is determined and we find a transition from H-Li, for low intensity, to Li-H, for high intensity. The influence of electron correlations is studied at different levels of approximation, and we find a significant change in the preferred orientation. For certain intensity regimes, even an interchange of the preferred configuration is observed, relative to the uncorrelated simulations. Further insight is provided by detailed comparisons of photoelectron angular distributions with and without correlation effects taken into account.

A priori determination of the nodal surfaces of trial wavefunctions of lithium hydride molecule

A comparative analysis of geometric properties of the nodal surfaces of four-electron trial wave function for LiH molecule is performed within the framework of the Hartree—Fock approximation and the method of many-electron wave functions (MWF) developed by the authors. Unlike the MWF method, the Hartree—Fock approximation fails to include the dependence of the nodal surfaces of MWF on nuclear charges of atoms in molecules and on effects of correlated motion of electrons with antiparallel spins because the nodal surfaces are specified by the mathematical properties of Slater determinants rather than physically clear and more practically valuable algebraic products of electrostatic potential differences.

Electron scattering with LiH molecule including a realistic dipole potential

Various electron scattering processes are examined theoretically for the strongly polar lithium hydride molecule. We have introduced a realistic dipole potential to calculate rotational cross sections of LiH upon electron impact. From the ionization threshold onwards total cross sections for elastic and inelastic scattering are evaluated in the complex molecular potential, and total ionization cross sections are extracted by CSP-ic method developed in recent years. While most of the results are new some indirect comparisons are made to draw conclusions.

Interaction between LiH molecule and Li atom from state-of-the-art electronic structure calculations

State-of-the-art ab initio techniques have been applied to compute the potential energy surface for the lithium atom interacting with the lithium hydride molecule in the Born-Oppenheimer approximation. The interaction potential was obtained using a combination of the explicitly correlated unrestricted coupled-cluster method with single, double, and noniterative triple excitations [UCCSD(T)-F12] for the core-core and core-valence correlation and full configuration interaction for the valence-valence correlation. The potential energy surface has a global minimum 8743 cm(-1) deep if the Li-H bond length is held fixed at the monomer equilibrium distance or 8825 cm(-1) deep if it is allowed to vary. In order to evaluate the performance of the conventional CCSD(T) approach, calculations were carried out using correlation-consistent polarized valence X-tuple-zeta basis sets, with X ranging from 2 to 5, and a very large set of bond functions. Using simple two-point extrapolations based on the single-power laws X(-2) and X(-3) for the orbital basis sets, we were able to reproduce the CCSD(T)-F12 results for the characteristic points of the potential with an error of 0.49% at worst. The contribution beyond the CCSD(T)-F12 model, obtained from full configuration interaction calculations for the valence-valence correlation, was shown to be very small, and the error bars on the potential were estimated. At linear LiH-Li geometries, the ground-state potential shows an avoided crossing with an ion-pair potential. The energy difference between the ground-state and excited-state potentials at the avoided crossing is only 94 cm(-1). Using both adiabatic and diabatic pictures, we analyze the interaction between the two potential energy surfaces and its possible impact on the collisional dynamics. When the Li-H bond is allowed to vary, a seam of conical intersections appears at C(2v) geometries. At the linear LiH-Li geometry, the conical intersection is at a Li-H distance which is only slightly larger than the monomer equilibrium distance, but for nonlinear geometries it quickly shifts to Li-H distances that are well outside the classical turning points of the ground-state potential of LiH. This suggests that the conical intersection will have little impact on the dynamics of Li-LiH collisions at ultralow temperatures. Finally, the reaction channels for the exchange and insertion reactions are also analyzed and found to be unimportant for the dynamics.

Ab initio quantum Monte Carlo study of the positronic hydrogen cyanide molecule

Quantum Monte Carlo methods are used to investigate the binding of a positron to the hydrogen cyanide (HCN) and lithium hydride (LiH) molecules. Our value of the adiabatic positron affinity (PA) of LiH of 1.010(3) eV is very close to the best theoretical value of 1.005 eV, obtained from variational calculations using explicitly correlated Gaussian basis sets [K. Strasburger, J. Chem. Phys. 114, 00615 (2001)]. We have obtained a reliable estimate of 0.0378(48) eV for the PA of the HCN molecule, which is almost 20 times larger than that obtained at the Hartree-Fock level, and strongly supports the binding of a positron in the electrostatic field of the HCN molecule. Our results show the importance of correlation effects for describing weakly bound positronic molecular complexes.

Electronic extracule densities

The electronic extracule density is the probability density function for the centre of mass of an electron pair. The first calculations of the extracule density for atomic and molecular systems are reported. Extracule densities for the ground states of the helium, lithium, and beryllium atoms, and the hydrogen and lithium hydride molecules are displayed and analyzed.

Spectroscopic data for the LiH molecule from pseudopotential quantum Monte Carlo calculations

Quantum Monte Carlo and quantum chemistry techniques are used to investigate pseudopotential models of the lithium hydride (LiH) molecule. Interatomic potentials are calculated and tested by comparing with the experimental spectroscopic constants and well depth. Two recently developed pseudopotentials are tested, and the effects of introducing a Li core polarization potential are investigated. The calculations are sufficiently accurate to isolate the errors from the pseudopotentials and core polarization potential. Core-valence correlation and core relaxation are found to be important in determining the interatomic potential.