Homonuclear Diatomics Research Articles

An excess free energy and chemical potential for hard homonuclear diatomics from integral equation approach

It has been shown that an improved prediction of the thermodynamic quantity for the hard homonuclear diatomics can be performed with an interpolation scheme that relates the thermodynamic property of the hard sphere to that of tangent hard spheres at the same density. Using the analytic expressions based on the solution of an integral equation an excess Helmholtz free energy per particle and chemical potential for hard homonuclear diatomic fluid have been computed. Calculations are carried out for hard homonuclear diatomics with reduced internuclear separations of 0.1 to 1 at reduced densities of 0.2 to 0.9. Our findings for the excess Helmholtz free energy from the Percus–Yevickand Martynov–Sarkisov approximations presents good agreement with available accurate data, having maximum deviations of 15% from it over the separation and density ranges of the calculations. The excess chemical potential from the Martynov–Sarkisov approximation shows better agreement with accurate available data than those from the Percus–Yevick approximation. For the excess chemical potential, a maximum deviation of 9.5% over the range of the calculations has been shown up for the Percus–Yevick approximation.

Discrepant Catalytic Activity of Biochar-Based Fe and Co Homonuclear and Heteronuclear Diatomic Catalysts for Activating Peroxymonosulfate to Degrade Emerging Pollutants

Discrepant Catalytic Activity of Biochar-Based Fe and Co Homonuclear and Heteronuclear Diatomic Catalysts for Activating Peroxymonosulfate to Degrade Emerging Pollutants

High-Precision Trace Hydrogen Sensing by Multipass Raman Scattering.

Despite its growing importance in the energy generation and storage industry, the detection of hydrogen in trace concentrations remains challenging, as established optical absorption methods are ineffective in probing homonuclear diatomics. Besides indirect detection approaches using, e.g., chemically sensitized microdevices, Raman scattering has shown promise as an alternative direct method of unambiguous hydrogen chemical fingerprinting. We investigated the suitability of feedback-assisted multipass spontaneous Raman scattering for this task and examined the precision with which hydrogen can be sensed at concentrations below 2 parts per million. A limit of detection of 60, 30, and 20 parts per billion was obtained at a pressure of 0.2 MPa in a 10-min-long, 120-min-long, and 720-min-long measurement, respectively, with the lowest concentration probed being 75 parts per billion. Various methods of signal extraction were compared, including asymmetric multi-peak fitting, which allowed the resolution of concentration steps of 50 parts per billion, determining the ambient air hydrogen concentration with an uncertainty level of 20 parts per billion.

A simple quantum model for solving two-electron diatomics approximately

Analytical expressions are obtained for the total energy of two-electron heteronuclear diatomics using a minimal basis set consisting of a 1S-Gaussian orbital centered on each atom and a Heitler-London trial wavefunction. The equations are applied to the recently discovered helium hydride cation (2019, Nature 568, 357–9) to understand its stability. Special attention was given to the fulfillment of the virial theorem and the different limiting cases (homonuclear diatomics, short and long internuclear distances). The correctness of equations and numerical results was confirmed via a brute-force Metropolis Monte Carlo integration. Expressions for the moments of the electron density (including the dipole moments) were obtained. The effect of the spin state on the dipole moment is discussed and the model agrees qualitatively with results from more advanced ab initio calculations. I also applied the model to study the metastable helium dimer dication () and the predicted bond length (0.7359 Å) is in good agreement with the experimental value (0.75 ± 0.02 Å). The advantages and limitations of this simple quantum model are discussed.

High-Performance Computational Chemistry in Undergraduate Physical Chemistry: Exercises in Homonuclear Diatomic Molecules

High-Performance Computational Chemistry in Undergraduate Physical Chemistry: Exercises in Homonuclear Diatomic Molecules

Highly Efficient Electrochemical CO2 Reduction on a Precise Homonuclear Diatomic Fe–Fe Catalyst

Electrochemical CO2 reduction (ECR) to value-added chemicals offers a promising approach to mitigate net carbon emission but presents challenges for chemistry because of the high energy barrier originating from CO2 activation or product desorption, as well as the limited fundamental understanding of the reaction mechanism. Herein, a diatomic electrocatalyst with nitrogen-doped porous carbon-anchored homonuclear Fe2N6 sites was precisely prepared for efficiently reducing CO2 to CO. The catalyst achieves CO Faradic efficiency up to 96.0% at −0.6 V (RHE) and a Tafel slope of only 60 mV dec–1, much superior to the single-atom Fe catalyst. Density functional theory calculations reveal that neighboring Fe–Fe centers in the Fe2N6 site facilitate the CO2 activation process via concurrently bonding the C and O atoms of the CO2 molecule. Meanwhile, the reaction barrier of CO desorption on the Fe2N6 site is decreased by the synergy of the dual Fe center, as the distinct CO-adsorbed configuration of the Fe2N6 site is inclined to uptake a second CO2 molecule. This work contributes fundamental understanding of ECR mechanisms and provides deep insights into the rational design of efficient ECR catalysts.

Improved Geometries and Frequencies with the PFD-3B DFT Method.

Bond lengths have been calculated for a test set of 120 diatomic species, including all homonuclear diatomics, hydrides, fluorides, and oxides for elements H through Kr for which experimental data is available for comparison. The performance of the PFD-3B functional is significantly better than competitive DFT methods. The rms error in bond lengths is reduced to 0.01 Å using a moderate size 3Za1Pa + f triple-ζ basis set, with the rms error in harmonic vibrational constants, ωe, equal to 38 cm-1. A very small 2ZP0H basis set is sufficient to calculate anharmonic constants, ωeXe, within ±4 cm-1. The rotational constants, Be, agree with experiment to within ±2%, and the vibration-rotation coupling constants, αe, agree within 10%. The calculated vibrational zero-point energy, ZPE, agrees with experiment to within ±0.06 kcal mol-1 for the diatomic test set, and the error increases to just ±0.11 kcal mol-1 for a set of 12 small polyatomic species. Comparison of a detailed anharmonic analysis of the twisted ethylene cation to the PFI-ZEKE experimental data illustrates the reliability of the PFD-3B for atypical structures.

On the Role of Molecular Polarizability in Positron Coupling to Vibrations in Homonuclear Diatomics

In a previous work [Poveda, Varella, and Mohallem (Poveda et al., Atoms, 2021, 9: 64) it was shown that the bell-like shape of the 0 → 1 vibrational excitation cross section of H2 as a function of the incoming positron energy, with its characteristic sharp onset at threshold, can be accounted for by a simple model which couples the positron to the vibrational mode of the molecule, throught the behavior of the target polarizabitity with the internuclear bond distance. The study, carried out via time-dependent wave-packet dynamics propagation, relies on a two-dimensional potential energy surface involving just the scattering (positron-target) and vibrational (target) coordinates. Here the model is extended to the full three-dimensional configuration space of the positron-diatomic complex, with the cross sections computed within a time-independent close-coupling approach. The present results confirm the previous findings, shedding light on the mechanisms through which a low-energy positron couples to the molecular vibrations.

Mechanistic Insights into Electrocatalytic Nitrogen Reduction Reaction on the Pd‐W Heteronuclear Diatom Supported on C2N Monolayer: Role of H Pre‐Adsorption

The electrocatalytic N2 reduction reaction (eNRR) is a potential alternative to the Haber–Bosch process for ammonia (NH3) production. Tremendous efforts have been made in eNRR catalyst research to promote the practical application of eNRR. In this work, by means of density functional theory calculations and the computational hydrogen electrode model, we evaluated the eNRR performance of 30 single metal atoms supported on a C2N monolayer (M@C2N), and we designed a new thermodynamically stable Pd‐W hetero‐metal diatomic catalyst supported on the C2N monolayer (PdW@C2N). We found that PdW@C2N prefers to adsorb H over N2, and then, the pre‐generated hydrogen‐terminated PdW@C2N selectively adsorbing N2 behaves as the actual functioning “catalyst” to catalyze the eNRR process, exhibiting excellent performance with a low overpotential (0.31 V), an ultra‐low NH3 desorption free energy (0.05 eV), and a high selectivity toward eNRR over hydrogen evolution reaction (HER). Moreover, PdW@C2N shows a superior eNRR performance to its monomer (W@C2N) and homonuclear diatom (W2@C2N) counterparts. The revealed mechanism indicates that the preferential H adsorption over N2 on the active site may not always hamper the eNRR process, especially for heteronuclear diatom catalysts. This work encourages deeper exploration on the competition of eNRR and HER on catalyst surfaces.

Seemingly asymmetric atom-localized electronic densities following laser-dissociation of homonuclear diatomics.

Recent experiments on laser-dissociation of aligned homonuclear diatomic molecules show an asymmetric forward-backward (spatial) electron-localization along the laser polarization axis. Most theoretical models attribute this asymmetry to interference effects between gerade and ungerade vibronic states. Presumably due to alignment, these models neglect molecular rotations and hence infer an asymmetric (post-dissociation) charge distribution over the two identical nuclei. In this paper, we question the equivalence that is made between spatial electron-localization, observed in experiments, and atomic electron-localization, alluded by these theoretical models. We show that (seeming) agreement between these models and experiments is due to an unfortunate omission of nuclear permutation symmetry, i.e., quantum statistics. Enforcement of the latter requires mandatory inclusion of the molecular rotational degree of freedom, even for perfectly aligned molecules. Unlike previous interpretations, we ascribe spatial electron-localization to the laser creation of a rovibronic wavepacket that involves field-free molecular eigenstates with opposite space-inversion symmetry i.e., even and odd parity. Space-inversion symmetry breaking would then lead to an asymmetric distribution of the (space-fixed) electronic density over the forward and backward hemisphere. However, owing to the simultaneous coexistence of two indistinguishable molecular orientational isomers, our analytical and computational results show that the post-dissociation electronic density along a specified space-fixed axis is equally shared between the two identical nuclei-a result that is in perfect accordance with the principle of the indistinguishability of identical particles.

Ellipticity of High-Order Harmonics Generated by Aligned Homonuclear Diatomic Molecules Exposed to an Orthogonal Two-Color Laser Field

We investigate emission rate and ellipticity of high-order harmonics generated exposing a homonuclear diatomic molecule, aligned in the laser-field polarization plane, to a strong orthogonally polarized two-color (OTC) laser field. The linearly polarized OTC-field components have frequencies rω and sω, where r and s are integers. Using the molecular strong-field approximation with dressed initial state and undressed final state, we calculate the harmonic emission rate and harmonic ellipticity for frequency ratios 1:2 and 1:3. The obtained quantities depend strongly on the relative phase between the laser-field components. We show that with the OTC field it is possible to generate elliptically polarized high-energy harmonics with high emission rate. To estimate the relative phase for which the emission rate is maximal we use the simple man’s model. In the harmonic spectra as a function of the molecular orientation there are two types of minima, one connected with the symmetry of the molecular orbital and the other one due to destructive interference between different contributions to the recombination matrix element, where we take into account that the electron can be ionized and recombine at the same or different atomic centers. We derive a condition for the interference minima. These minima are blurred in the OTC field except in the cases where the highest occupied molecular orbital is modeled using only s or only p orbitals in the linear combination of the atomic orbitals. This allows us to use the interference minima to assess which atomic orbitals are dominant in a particular molecular orbital. Finally, we show that the harmonic ellipticity, presented in false colors in the molecular-orientation angle vs. harmonic-order plane, can be large in particular regions of this plane. These regions are bounded by the curves determined by the condition that the harmonic ellipticity is approximately zero, which is determined by the minima of the T-matrix contributions parallel and perpendicular to the fundamental component of the OTC field.

Does nuclear permutation symmetry allow dynamical localization in symmetric double-well achiral molecules?

We discuss the effect of molecular symmetry on coherent tunneling in symmetric double-well potentials whose two molecular equilibrium configurations are interconverted by nuclear permutations. This is illustrated with vibrational tunneling in ammonia molecules, electronic tunneling in the dihydrogen cation, and laser-induced rotational tunneling of homonuclear diatomics. In this contribution, we reexamine the textbook picture of coherent tunneling in such potentials, which is depicted with a wavepacket shuttling back and forth between the two potential-wells. We show that the common application of this picture to the aforementioned molecules contravenes the principle of the indistinguishability of identical particles. This conflict originates from the sole consideration of the dynamics of the tunneling-mode, connecting the double-well energy minima, and complete omission of all the remaining molecular degrees of freedom. This gives rise to double-well wavepackets that are nonsymmetric under nuclear permutations. To obey quantum statistics, we show that the double-well eigenstates composing these wavepackets must be entangled with the wavefunctions that describe all the omitted molecular modes. These wavefunctions have compensating and opposite nuclear permutation symmetry. This in turn leads to complete quenching of interference effects behind localization in one potential-well or another. Indeed, we demonstrate that the reduced density of probability of the symmetrized molecular wavefunction, where all the molecular coordinates but the tunneling-mode are integrated out, is symmetrically distributed over the two potential-wells, at all times. This applies to any multilevel wavepacket of isotropic or fully aligned symmetric double-well achiral molecules. However, in the case of coherent electronic or vibrational tunneling, fully aligned molecules may exhibit dynamical localization in the space-fixed frame, where the tunneling-mode density shuttles between the opposite directions of the alignment axis. This dynamical spatial-localization results from linear combinations of molecular states that have opposite parity. In summary, this study shows that dynamical localization of the tunneling-mode density on either of the two indistinguishable molecular equilibrium configurations of symmetric double-well achiral molecules is forbidden by quantum statistics, whereas its dynamical localization in the space-fixed frame is allowed by parity. The subtle distinction between these two types of localization has far-reaching implications in the interpretation of many ultrafast molecular dynamics experiments.

Side-impact collisions of Ar with NO.

In the realm of molecular collision dynamics, stereochemistry refers to the dependence of the collision outcome on the mutual orientation of the colliding partners. This may involve directed end-on collisions along a molecular bond axis or encounters in which the partner approaches the bond of an oriented molecule from the side. Using both experiment and theory, we show here that in the simplest case of an inelastic collision between an atom and a nearly homonuclear diatom, in which the two atoms have almost the same mass, the scattering dynamics are very distinct for impacts on either side of the molecule. By recording the direction of the scattered particles after the collision, we demonstrate that the intensity of products scattered in the forward direction, near parallel to the initial motion, can be substantially controlled and even maximized by altering the side-on orientation of the quantum state selected NO molecules that collide with Ar atoms. In addition, our findings provide valuable information about the preferred collision mechanism and reveal interesting quantum interference effects.

Analytical Insight into the Effect of Electric Field on Molecular Properties of Homonuclear Diatomic Molecules

Background: The diatomic molecules represent one of the most active classes of materials, and they have been widely used as active materials for important applications. Objective: In this study, the effect of external electric field on molecular properties of four homonuclear diatomic molecules H2, C2, Cl2, and Br2 has been analyzed. Methods: All the calculations are based on the density functional theory (DFT) at the B3LYP/6- 311++G(3df,3pd) level through the Gaussian 09W program package. Results: The studied molecular properties include total energy, density of state (DOS) analysis, frontier molecular orbital energies HOMO and LUMO, energy gap, absorption threshold, internuclear separation, harmonic vibrational frequency, bond force constant, molecular dipole moment, polarizability, chemical potential, chemical hardness and electrophilicity. Conclusion: It has been observed that the interaction of molecules with external electric fields can be used to control and improve the basic properties of homonuclear diatomic molecules for their exploitation in some significant applications in spintronics. Keywords: B3LYP, DFT, diatomic molecules, energy gap, external field.

On the metastability of doubly charged homonuclear diatomics.

Generalized valence bond (GVB) and spin-coupled (SC) calculations were used in conjunction with the generalized product function energy partitioning (GPF-EP) method to describe the origin of metastability in doubly charged homonuclear dications. A model to describe the formation of metastable potential wells based on interference and quasi-classical effects is presented. The GPF-EP picture of dications is the result of polarization-aided strong covalent bonding surpassing Coulomb electrostatic repulsion. Important differences in the quasi-classical density profiles of He22+ and Ne22+ reveal the underlying mechanism that could lead to bound or unbound states. Finally, the nature of the chemical bond of N22+, O22+, and F22+ is described. The results suggest that the ground states of the mentioned dications are bounded and that the depth of the potential wells of these exotic species is related to the interference effect, in the same way as in previously studied neutral molecules.

The intermolecular interaction in D2 - CX4 and O2 - CX4 (X = F, Cl) systems: Molecular beam scattering experiments as a sensitive probe of the selectivity of charge transfer component.

Gas phase collisions of a D2 projectile by CF4 and by CCl4 targets have been investigated with the molecular beam technique. The integral cross section, Q, has been measured for both collisional systems in the thermal energy range and oscillations due to the quantum "glory" interference have been resolved in the velocity dependence of Q. The analysis of the measured Q(v) data provided novel information on the anisotropic potential energy surfaces of the studied systems at intermediate and large separation distances. The relative role of the most relevant types of contributions to the global interaction has been characterized. Extending the phenomenology of a weak intermolecular halogen bond, the present work demonstrates that while D2 - CF4 is basically bound through the balance between size (Pauli) repulsion and dispersion attraction, an appreciable intermolecular bond stabilization by charge transfer is operative in D2 - CCl4. We also demonstrated that the present analysis is consistent with that carried out for the F(2P)-D2 and Cl(2P)-D2 systems, previously characterized by scattering experiments performed with state-selected halogen atom beams. A detailed comparison of the present and previous results on O2-CF4 and O2-CCl4 systems pinpointed striking differences in the behavior of hydrogen and oxygen molecules when they interact with the same partner, mainly due to the selectivity of the charge transfer component. The present work contributes to cast light on the nature and role of the intermolecular interaction in prototype systems, involving homo-nuclear diatoms and symmetric halogenated molecules.

Development of molecular closures for the reference interaction site model theory with application to square-well and Lennard-Jones homonuclear diatomics

Inspired by significant improvements obtained for the performances of the polymer reference interaction site model (PRISM) theory of the fluid phase when coupled with ‘molecular closures’ (Schweizer and Yethiraj 1993 J. Chem. Phys. 98 9053), we exploit a matrix generalization of this concept, suitable for the more general RISM framework. We report a preliminary test of the formalism, as applied to prototype square-well homonuclear diatomics. As for the structure, comparison with Monte Carlo shows that molecular closures are slightly more predictive than their ‘atomic’ counterparts, and thermodynamic properties are equally accurate. We also devise an application of molecular closures to models interacting via continuous, soft-core potentials, by using well established prescriptions in liquid state perturbation theories. In the case of Lennard-Jones dimers, our scheme definitely improves over the atomic one, providing semi-quantitative structural results, and quite good estimates of internal energy, pressure and phase coexistence. Our finding paves the way to a systematic employment of molecular closures within the RISM framework to be applied to more complex systems, such as molecules constituted by several non-equivalent interaction sites.

Deviations from Born-Oppenheimer mass scaling in spectroscopy and ultracold molecular physics

We investigate Born-Oppenheimer breakdown (BOB) effects (beyond the usual mass scaling) for the electronic ground states of a series of homonuclear and heteronuclear alkali-metal diatoms, together with the Sr2 and Yb2 diatomics. Several widely available electronic structure software packages are used to calculate the leading contributions to the total isotope shift for commonly occurring isotopologs of each species. Computed quantities include diagonal Born-Oppenheimer corrections (mass shifts) and isotopic field shifts. Mass shifts dominate for light nuclei up to and including K, but field shifts contribute significantly for Rb and Sr and are dominant for Yb. We compare the ab initio mass-shift functions for Li2, LiK and LiRb with spectroscopically derived ground-state BOB functions from the literature. We find good agreement in the values of the functions for LiK and LiRb at their equilibrium geometries, but significant disagreement with the shapes of the functions for all 3 systems. The differences may be due to contributions of nonadiabatic terms to the empirical BOB functions. We present a semiclassical model for the effect of BOB corrections on the binding energies of near-threshold states and the positions of zero-energy Feshbach resonances.

Hylleraas hydride binding energy: diatomic electron affinities.

Theoretical adiabatic electron affinities are often considered inaccurate because they are referenced to only a single value. Ground state electron affinities for all the main group elements and homonuclear diatomics were identified recently using the normalized binding energy of the hydrogen atom: [0.75420375(3)/2 = 0.37710187(1) eV]. Here we revisit experimental values and extend the identifications to diatomics in the G2-1 set. We assign new ground state electron affinities: (eV) Cl2, 3.2(2); Br2, 2.87(14); CH, 2.1(2); H2, 0.6 ; NH, 1.1, SiH, 1.90. Anion Morse potentials are calculated for H2 and N2 from positive electron affinities and for hyperfine superoxide states for the first time.

Correlation consistent basis sets for the atoms In-Xe.

In this work, the correlation consistent family of Gaussian basis sets has been expanded to include all-electron basis sets for In-Xe. The methodology for developing these basis sets is described, and several examples of the performance and utility of the new sets have been provided. Dissociation energies and bond lengths for both homonuclear and heteronuclear diatomics demonstrate the systematic convergence behavior with respect to increasing basis set quality expected by the family of correlation consistent basis sets in describing molecular properties. Comparison with recently developed correlation consistent sets designed for use with the Douglas-Kroll Hamiltonian is provided.