Lithium Dimer Research Articles

Enthalpy, mean energy, entropy, and Gibbs free energy of lithium dimer under magnetic field

It is well known that the lithium diatomic molecule has important potential application in engineering, and industry. For this purpose, in this research, the thermal properties of the lithium diatomic molecule are theoretically calculated taking into account both an external magnetic field and Aharonov-Bohm (AB) flux. To this end, the interaction in the diatomic molecule is proposed as an improved Scarf ΙΙ potential model (ISPM). The Schrödinger equation is solved using an appropriate Pekeris-like approximation form for the centrifugal barrier and the energy spectrum and wave functions are obtained. Then, the partition function is obtained to study the thermal properties of the lithium dimer. The calculated thermal properties of 7Li2 (2 3Πg) in this work are mean energy, entropy, specific heat, enthalpy, and Gibbs free energy. Our theoretical results are also compared with the experimental data. The findings show that the obtained results are in good agreement with experimental data. Without considering the magnetic field and AB flux, the deviation of specific heat, Gibbs free energy, and enthalpy are 3.73%, 4.96%, and 5.31%, respectively. By considering the magnetic field and AB flux, we find that the deviation of the aforementioned properties are 1.91%, 2.04%, and 2.32%, respectively. Therefore, it is found that the external magnetic field and AB flux have great influences on the thermal properties of lithium.

Influence of an electric‐field on the topological stability of the neutral lithium dimer

AbstractIn this investigation, we seek to understand the role of non‐nuclear attractors (NNAs) of the neutral Li2 dimer subjected to an electric (±E) field that is directed parallel (±Ex) and perpendicular (±Ey) to the bond‐path. The ±Ex‐fields and ±Ey‐fields are separately applied to the Li2 molecular graph until the bond ruptures. The next generation quantum theory of atoms in molecules (NG‐QTAIM) interpretation of bonding was constructed with the stress tensor σ(r) eigenvectors on the Hessian of ρ(r) molecular graph. The asymmetry induced by both the ±Ey‐field and ±Ex‐field was detected in terms of the rotation of the orthogonal triad of stress tensor σ(r) eigenvectors {e1σ, e2σ, e3σ} relative to the Cartesian coordinate frame. The orthogonal triad of Hessian of ρ(r) eigenvectors {e1, e2, e3} however, were only able to detect rotation induced by the high degree of asymmetry present for bent bond‐paths induced by the ±Ey‐fields. Larger movement of the NNAs along the bond‐path correlated with greater bond critical point (BCP) bond metallicity ξ(rb). The effect of applying the ±Ex‐field was compared with unpublished results on neutral Li2 subject to a stretching distortion. The lack of NNA motion along the bond‐path for the stretching distortion correlated with a lower degree of bond metallicity ξ(rb). The stress tensor σ(r) eigenvectors have a unique ability to detect rotation relative to the Cartesian coordinate frame for high bond‐path symmetry occurring for the bond‐stretching distortion and application of the ±Ex‐field. Suggestions for future work are provided.

Morse potential specific heat with applications: an integral equations theory based

The specific heat in its molar form or mass form is a significant thermal property in the study of the thermal capacity of the described system. There are two basic methods for the determination of the molar specific heat capacity, one of them is the experimental procedure and the other is the theoretical procedure. The present study deals with finding a formula of the molar specific heat capacity using the theory of the integral equations for Morse interaction which is a very important potential for the study of the general oscillations in the quantum mechanics. We use the approximation (Mean-Spherical) for finding the total energy of the compositions described by Morse interaction. We find two formulas of the heat capacity, one at a constant pressure and the other at a constant volume. We conclude that the Morse molar specific heat is temperature dependent via the inverse square low with respect to temperature. Besides, we find that the Morse molar specific heat is proportional to the square of the Morse interaction well depth. Also, we find that the Morse molar specific heat depends on the particles’ diameter, the bond distance of Morse interaction, the width parameter of Morse interaction, and the volumetric density of the system. We apply the formula of the specific heat for finding the specific heat of the vibrational part for two dimer which are the lithium and caesium dimers and for the hydrogen fluoride, hydrogen chloride, nitrogen, and hydrogen molecules.

Ground-state potential energy functions and vibration-rotation energy levels of beryllium lithium and its cation.

The accurate ground-state potential energy functions of the beryllium lithium dimer, BeLi, and its cation, BeLi+ , have been determined from ab initio calculations using the multi-reference averaged coupled-pair functional (MR-ACPF) method in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. The importance of the electron correlation beyond the MR-ACPF level of approximation, scalar relativistic, and adiabatic effects was discussed. For BeLi+ , the similar calculation was performed using the single-reference coupled-cluster method, up to the CCSDTQ level of approximation. The vibration-rotation energy levels of the two species were predicted to near the "spectroscopic" accuracy. Strangely enough, the predicted vibrational term values do not compare well with the recent experimental data for either BeLi or BeLi+ , with discrepancies reaching as much as 20-60 cm-1 for highly excited vibrational levels.

The bond length of the improved Rosen Morse potential, applying for: Cesium, hydrogen, hydrogen fluoride, hydrogen chloride, lithium, and nitrogen molecules

One of the generalized vibrational potentials is the improved Rosen Morse potential (IRMP), which is used in vibrational interactions studies, especially, for the study of the vibrations of the diatomic systems or dimers. The IRMP interaction has three independent fitting parameters which are the bond equilibrium length of the IRMP, the energy well depth of the IRMP, and the range of the well of potential parameter. In this study, the principles of the integral equation theory of the simple fluids are employed with the boundary conditions for deriving a simple formula between the bond equilibrium length of the IRMP and the other two fitting parameters of the IRMP interaction. We investigate the relation between the bond equilibrium length of the IRMP interaction and the absolute temperature. We find that the bond equilibrium length of the IRMP interaction depends on the absolute temperature of the system, and increases slowly with the absolute temperature. Also, we find that the bond equilibrium length of the IRMP interaction depends on the diameter of the particles in the system, and also increases with the diameter of the particles for different temperature values and for different values of the depth of the IRMP well. We find that the bond equilibrium length of the IRMP interaction decreases when the depth of the IRMP well increases for different values of temperature, also we find that this bond length increases when the range of the well of the IRMP parameter increases for different values of temperature and for different values of the depth of the IRMP well. We apply our formula of the bond equilibrium length of the IRMP interaction for six different molecules and dimers, which are the caesium dimer (Cs2), the lithium dimer (Li2), the hydrogen chloride (HCl), the hydrogen fluoride (HF), the nitrogen molecule (N2), and the hydrogen molecule (H2). We find that, in general, the bond equilibrium length of the IRMP interaction for these molecules and dimers is between 0.9 Å and 7Å for a wide range of temperatures, and the largest value is for the caesium dimer and the lowest value is for the hydrogen fluoride molecule. The formula which we derive for the bond equilibrium length of the IRMP interaction can be applied further to a wide range of molecules and dimers.

An accurate potential model for the a3Σu+ state of the lithium dimer.

An accurate Tang-Toennies (TT) model potential is introduced to describe the interatomic potential of the lithium dimer in the a3Σu+ state. With only one well-known parameter, the ionization energy, the new model potential compares favorably with the experimentally fitted Morse/Long-range (MLR) potential of Dattani and Le Roy [J. Mol. Spectrosc., 2011, 268, 199] and is in excellent agreement with the state-of-the-art ab initio potential of Lesiuk et al. [Phys. Rev. A, 2020, 102, 062806]. With the known dispersion coefficients and the ionization energy, the new potential requires only two experimental parameters, namely the depth of the potential well De and its location Re. The new potential can be extended to the region of zero separation by the united atom limit.

Vibrational energies of some diatomic molecules for a modified and deformed potential

A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov–Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.

Ab initio calculation of the ground and first excited states of the lithium dimer

Based on a high level ab initio calculation which is carried out with the multireference configuration interaction method under the aug-cc-pVXZ (AVXZ) basis sets, X = T, Q, 5, the accurate potential energy curves (PECs) of the ground state and the first excited state of Li2 are constructed. By fitting the ab initio potential energy points with the Murrell–Sorbie potential function, the analytic potential energy functions (APEFs) are obtained. The molecular bond length at the equilibrium (R e ), the potential well depth (D e ), and the spectroscopic constants (B e , ω e , α e , and ω e χ e ) for the state and the state are deduced from the APEFs. The vibrational energy levels of the two electronic states are obtained by solving the time-independent Schrödinger equation with the Fourier grid Hamiltonian method. All the spectroscopic constants and the vibrational levels agree well with the experimental results. The Franck–Condon factors (FCFs) corresponding to the transitions from the vibrational level (v′ = 0) of the ground state to the vibrational levels (v″ = 0–74) of the first excited state have been calculated. The FCF for the vibronic transition of (v″ = 0) ←(v′ = 0) is the strongest. These PECs and corresponding spectroscopic constants provide reliable theoretical references to both the spectroscopic and the molecular dynamic studies of the Li2 dimer.

Ro-vibrational energies of cesium dimer and lithium dimer with molecular attractive potential

An approximate solution of the Schrӧdinger equation for a molecular attractive potential was obtained using the parametric Nikiforov–Uvarov method. The energy equation and the corresponding radial wave functions were calculated. The effects of the potential parameters on the energy eigenvalues were examined. The thermal properties under the molecular attractive potential were calculated and the behaviour of the thermal properties with the maximum quantum state (λ) and the temperature parameter (β) respectively, were studied. Using the molecular spectroscopic parameters, the Rydberg–Klein–Rees (RKR) of cesium dimer and lithium dimer were both obtained and compared with the experimental values. The RKR values of both cesium dimer and lithium dimer calculated aligned with the observed values. The deviation and average deviation of the RKR for each molecule were also calculated.

The change in the nature of bonding in the Li2 dimer under confinement

AbstractConfinement and pressure have profound effects on the electronic structure of atoms and molecules. In this work, we study the effects of a harmonic confinement on the electronic structure of the lithium dimer. To do this, we use quantum chemistry methods that include much of the electronic correlation (Coupled Cluster and CASSCF). The confinement induces a change, with respect to the free molecule, in the electronic configuration of Li2. There is a critical confinement value for which the ground state stops being the singlet and becomes the triplet . We also study changes in the bonding pattern. Li2 conserves the bonding pattern of the free molecule independently of the strength of confinement, as it is revealed by the electron localization function.

A Fock-operator complete active space self-consistent field (CAS-SCF) method combined with frozen-density embedding.

We report the implementation of a Fock-operator complete-active space self-consistent field (CAS-SCF) method combined with frozen-density embedding (FDE) into the KOALA quantum-chemistry program. The implementation is based on configuration interaction from an unrestricted reference determinant and is able to treat electronic configurations such as singlet, triplet, or quintet states embedded in a molecular environment. In order to account for possible spin polarization effects, the FDE contribution is extended to the unrestricted case. We assess the convergence obtained with the implementation at the example of a stretched lithium dimer with significant multi-reference character. The efficiency of the implementation enables the orbital optimization for 25 states in a state-average SA[S0-S10,T1-T12,Q1-Q2]-CAS(10,10)-SCF calculation for the retinal molecule using a def2-TZVP basis. The FDE ansatz leads to orbitals localized by definition on the target system, thus facilitating the orbital selection required for CAS methods in complex environments.

Potential-energy curve for the a3Σu+ state of a lithium dimer with Slater-type orbitals

We report state-of-the-art ab initio calculations of the potential energy curve for the $a^3\Sigma_u^+$ state of the lithium dimer conducted to achieve spectroscopic accuracy ($<$1cm$^{-1}$) without any prior adjustment to fit the corresponding experimental data. The nonrelativistic clamped-nuclei component of the interaction energy is calculated with a composite method involving six-electron coupled cluster and full configuration interaction theories combined with basis sets of Slater-type orbitals ranging in quality from double- to sextuple-zeta. To go beyond the nonrelativistic Born-Oppenheimer picture we include both the leading-order relativistic and adiabatic corrections, and find both of these effects to be non-negligible within the present accuracy standards. The potential energy curve developed by us allowed to calculate molecular parameters ($D_e$, $D_0$, $\omega_e$ etc.) for this system, as well as the corresponding vibrational energy levels, with an error of only a few tenths of a wavenumber ($0.2-0.4\,$cm$^{-1}$). We also report an ab initio value for the scattering length of two $^2S$ lithium atoms which determines the stability of the related Bose-Einstein condensate.

Interatomic Coulombic decay of a Li dimer in a coupled electron and nuclear dynamics approach

Interatomic Coulombic decay (ICD) is a fundamental process between atoms or molecules via a neighbor interaction that produces a relaxation of an electronically excited atom or molecule when embedded in an environment. Due to the physical nature of the process, the electronic and nuclear degrees of freedom are coupled. In this paper, we study the ICD process for a lithium dimer by means of the electron and nuclear dynamics (END) approach. The END approach incorporates a full time-dependent description of the electronic and nuclear degrees of freedom, although its current version does not properly account for continuum states and has limitations in the electronic description by using a single determinantal wave function. Despite this, we confirm that the ICD process takes place via a dipole interaction that induces the nuclear motion of the dimer with a consequent electronic population transfer to higher excited states simulating the ionization process. When the dimer approaches a distance of around 11.5 a.u. (6 \AA{}), this ionization process takes place due to the dipole coupling and occurs at the place of the strongest attractive dipole force. Passing that point, we find that the two lithium atoms repel each other via a Coulomb explosion process followed with a consequent kinetic-energy release (KER). We determine the KER and the timing of the ICD process. We point out the strengths and weaknesses of the END approach and the required enhancements to account for a better description of the ICD process in a coupled electron and nuclear dynamics.

Rotational Energy Transfer in Highly Excited States of Lithium Dimer: Experiment and Modeling.

We report level-resolved rate coefficients for collision-induced rotational energy transfer in the 7Li2*-Ne system, with 7Li2* in the highly electronically excited E(3)1Σg+(vi = 4, ji = 31) and F(4)1Σg+(vi = 10, ji = 31) states. The distributions of rate coefficients are strikingly different from those previously measured for the A(1)1Σu+(vi = 2-24, ji = 30) state of the same molecule, falling off much more rapidly with increasing rotational quantum number change |Δj|. The reason for the difference was explored by means of an inverse Monte Carlo approach employing classical trajectories and a model potential, which was adjusted to give agreement with experiment. The modeling strongly suggests that the E and F state interaction potentials are much more nearly isotropic than that of the A state. The resulting dramatic reduction in rate coefficient, especially for large |Δj|, may be relevant in the relaxation of gases at high temperatures.

Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion.

Simulating chemical systems on quantum computers has been limited to a few electrons in a minimal basis. We demonstrate experimentally that the virtual quantum subspace expansion (Takeshita, T.; Phys. Rev. X 2020, 10, 011004, 10.1103/PhysRevX.10.011004) can achieve full basis accuracy for hydrogen and lithium dimers, comparable to simulations requiring 20 or more qubits. We developed an approach to minimize the impact of experimental noise on the stability of the generalized eigenvalue problem, a crucial component of the quantum algorithm. In addition, we were able to obtain an accurate potential energy curve for the nitrogen dimer in a quantum simulation on a classical computer.

Covalent organic framework with high capacity for the lithium ion battery anode: insight into intercalation of Li from first-principles calculations

Covalent organic frameworks (COFs) generally have high stability, large charge capacity and wide ion diffusion paths, and they may serve as the potential electrode materials for lithium ion batteries. Here we explored the structural, electronic, and lithium-storage properties of the newly synthesized NUS-2 COF material by first-principles calculations. The present results indicate that the micropore environment and the presence of the carbonyl oxygens in the NUS-2 COF can prevent the formation of lithium dimer and the aggregation of lithium bulk, which can improve lithiation efficiency. The predicted maximum theoretical capacity is as high as 742.8 mAh g−1 and the average cell voltage varies from 3.35 V for Li@NUS-2 to 2.04 V for 14Li@NUS-2, suggesting that the NUS-2 COF material should be a quite suitable lithium-storage anode material.

Electronic transition dipole moment and radiative lifetime calculations of lithium dimer ion-pair states

We present here a computational study of the lifetimes of the ion-pair n1Σg+, n = 3–6, states of lithium dimer. The lifetimes are calculated using ab initio electronic transition dipole moment functions and combination of experimental and ab initio potential curves. The ab initio calculations are carried out using the full configuration-interaction method. The lifetime calculations include the radiative contributions of all the allowed bound–bound and bound-free transitions to lower electronic states. In addition, to test the computational methods used in this work, we have calculated the lifetimes of levels of the lowest excited singlet, A1Σu+, state of lithium dimer.

Non-nuclear attractors in small charged lithium clusters, Limq (m = 2-5, q = ±1), with QTAIM and the Ehrenfest force partitioning.

In this investigation we explore the function and existence of the non-nuclear attractor (NNA) for a series of small charged lithium clusters Limq (m = 2-5, q = ±1) using QTAIM and the Ehrenfest force F(r) partitioning schemes. The NNAs were found to be present in all of the Limq (m = 2-5, q = ±1) clusters for QTAIM, in contrast none were found for F(r). We discovered that the anionic and cationic lithium dimers are limiting cases for minimal and maximal impact of the NNA related to the relative sparseness of total charge density ρ(r) distributions respectively. Evidence is found that the NNA in the anionic dimer is in the process of being annihilated by two neighboring BCPs. We provide a measure of the size of the NNA and find for Limq (m = 2-5, q = ±1) that larger NNAs correlate with increased Li-Li separations. The NNA was determined to be a persistent feature by varying the Li separations for the cationic and anionic dimers. Very large Li separations failed to induce an NNA in the F(r) anionic dimer and therefore we conclude that F(r) is unable to detect NNAs. The metallicity ξ(rb) was also used to measure the sparseness of the distribution of ρ(r) and significant metallic character, on the basis of ξ(rb) > 1, was present for QTAIM but not for F(r), providing further evidence that F(r) cannot detect NNAs. Advantages of the use of Ehrenfest force F(r) partitioning scheme are discussed that include the design of nano-devices through tuning of the Ehrenfest potential VF(b) by the application of external forces such as a constant electric or strain field.

A Redox-Active Bis(ferrocenyl)germylene and Its Reactivity.

Bis(ferrocenyl)germylene Fc*2 Ge: [2; Fc*=2,5-bis(3,5-di-tert-butylphenyl)-1-ferrocenyl] was isolated in the form of red crystals from the reaction of the sterically demanding ferrocenyl lithium dimer (Fc*Li)2 and GeI2 . Bis(ferrocenyl)germylene 2 exhibits extraordinary thermal stability in hydrocarbon solution and the solid state, as well as stable redox behavior. Moreover, it undergoes a ligand-redistribution reaction with GeCl2 ⋅(dioxane) to afford the corresponding chlorogermylene, which was isolated upon coordination with PBu3 .

Fock space coupled cluster study of the 11Πg state of the Li2 molecule

ABSTRACTRecently reported (M. Musiał, J. Chem. Phys., 136, 134111 (2012)) multireference coupled cluster method formulated in the (2,0) sector of the Fock space proved to be an efficient scheme in the treatment of potential energy curves (PECs) for alkali metal diatomics Me2. The (2,0) sector provides description of states obtained by an attachment of two electrons to the reference which for the Me2 is a doubly ionised Me+ 22 system. The latter has a very concrete advantage in the calculations of the PECs since it dissociates into closed shell fragments (Me+ 22 → Me++Me+); hence, the restricted Hartree–Fock reference can be used in the whole range of interatomic distances. In this work, an accurate PEC and vibrational energy levels are obtained for the state of the lithium dimer. The average deviation of the vibrational term values from experiment is 0.79 wavenumber and is significantly lower than that provided by other theoretical works.