Diatomic Potential Research Articles

An Accurate and Transferable Intermolecular Diatomic Hydrogen Potential for Condensed Phase Simulation.

An anisotropic many-body H2 potential energy function has been developed for use in heterogeneous systems. The intermolecular potential has been derived from first principles and expressed in a form that is readily transferred to exogenous systems, e.g. in modeling H2 sorption in solid-state materials. Explicit many-body polarization effects, known to be important in simulating hydrogen at high density, are incorporated. The analytic form of the potential energy function is suitable for methods of statistical physics, such as Monte Carlo or Molecular Dynamics simulation. The model has been validated on dense supercritical hydrogen and demonstrated to reproduce the experimental data with high accuracy.

A new genetic algorithm to be used in the direct fit of potential energy curves to ab initio and spectroscopic data

We propose a two-step genetic algorithm (GA) to fit potential energy curves to both ab initio and spectroscopic data. In the first step, the GA is applied to fit only the ab initio points; the parameters of the potential so obtained are then used in the second-step GA optimization, where both ab initio and spectroscopic data are included in the fitting procedure. We have tested this methodology for the extended-Rydberg function, but it can be applied to other functions providing they are sufficiently flexible to fit the data. The results for NaLi and Ar2 diatomic molecules show that the present method provides an efficient way to obtain diatomic potentials with spectroscopic accuracy.

Quantum dynamics of an excited alkali atom in a noble gas cluster: Lithium attached to a helium cluster

An alkali atom-noble gas cluster system is considered as a model for solvation effects in optical spectra, within a quantum-classical description based on the density operator of a many-atom system and its partial Wigner transform. This leads to an eikonal-time-dependent molecular orbital treatment suitable for a time-dependent description of the coupling of light emission and atom dynamics in terms of the time-dependent electric dipole of the whole system. As an application, we consider an optically excited lithium atom as the dopant in a helium cluster at 0.5 K. We describe the motions of the excited Li atom interacting with a cluster of He atoms and calculate the time-dependent electric dipole of the Li-He(99) system during the dynamics. The electronic Hamiltonian is taken as a sum of three-body Li-He diatomic potentials including electronic polarization and repulsion, with l-dependent atomic pseudopotentials for Li and He, while we use a modified pair potential for He-He. The calculations involve the coupling of 12 quantum states with 300 classical degrees of freedom. We present results for the dynamics and spectra of a Li atom interacting with a model cluster surface of He atoms and also interacting with a droplet of He. We have found that the Li atom is attracted or repulsed from the He surface, depending on the orientation of its 2p orbitals. The spectra and dynamics of Li inside and at the surface of a cluster are found to be strongly dependent on its electronic states, its velocity direction, and whether light is present during emission or not.

Equation of state for expanded fluid mercury: Variational theory with many-body interaction

A variational associating fluid theory is proposed to describe equations of state for expanded fluid mercury. The theory is based on the soft-sphere variational theory, incorporating an ab initio diatomic potential and an attractive many-body potential; the latter is evaluated with quantum chemical methods and expressed as a function of the local atomic coordination number and the nearest-neighbor distance. The resultant equation of state can reproduce the observed gas-liquid coexistence curve with good accuracy, without introducing phenomenological effective pair potentials. Various thermodynamic quantities such as pressure, isocloric thermal pressure coefficient, adiabatic sound velocity, and specific heat are calculated over a wide density-temperature range and compared with available experimental data.

Exact path integral treatment of a diatomic molecule potential

A rigorous evaluation of the path integral for Green’s function associated with a four-parameter potential for a diatomic molecule is presented. A closed form of Green’s function is obtained for different shapes of this potential. When the deformation parameter λ is λ<0 or 0<λ<1, it is found that the quantization conditions are transcendental equations that require a numerical solution. For λ⩾1 and r∊](1∕η)lnλ,∞[, the energy spectrum and the normalized wave functions of the bound states are derived. Particular cases of this potential which appear in the literature are also briefly discussed.

Unified path integral treatment for generalized Hulthén and Woods–Saxon potentials

A rigorous path integral discussion of the s states for a diatomic molecule potential with varying shape, which generalizes the Hulthén and the Woods–Saxon potentials, is presented. A closed form of the Green’s function is obtained for different shapes of this potential. For λ ⩾ 1 and ( 1 / η ) ln λ < r < ∞ , the energy spectrum and the normalized wave functions of the bound states are derived. When the deformation parameter λ is 0 < λ < 1 or λ < 0, it is found that the quantization conditions are transcendental equations that require numerical solutions. The special cases corresponding to a screened potential ( λ = 1), the deformed Woods–Saxon potential ( λ = q e ηR ), and the Morse potential ( λ = 0) are likewise treated.

First-principles dynamics treatment of light emission in collisions between alkali-metal atoms and noble-gas atoms at10keV

Collision-induced light emission during the interaction of an alkali-metal atom and a noble-gas atom is treated within a first-principles, or direct, dynamics approach that calculates a time-dependent electric dipole for the whole system, and spectral emission cross sections from its Fourier transform. These cross sections are very sensitive to excited diatomic potentials and a source of information on their shape. The coupling between electronic transitions and nuclear motions is treated with atomic pseudopotentials and an electronic density matrix coupled to trajectories for the nuclei. A recently implemented pseudopotential parametrization scheme is used here for the ground and excited states of the LiHe system, and to calculate state-to-state dipole moments. To verify the accuracy of our new parameters, we recalculate the integral cross sections for the LiHe system in the keV energy regime and obtain agreement with other results from theory and experiment. We further present results for the emission spectrum from $10\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ $\mathrm{Li}(2s)+\mathrm{He}$ collisions, and compare them to experimental values available in the region of light emitted at $300--900\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$.

Diatoms and ostracods as mid-Holocene palaeoenvironmental indicators, North Stromatolite Lake, Coorong National Park, South Australia*

The Holocene carbonate sequence of perennial North Stromatolite Lake, located adjacent to the Coorong Lagoon near Salt Creek, South Australia, includes a prominent sapropelic unit (7 – 12% total organic carbon), in places more than 2 m thick, that was sampled for the purpose of radiocarbon dating and documenting its diatom and ostracod biostratigraphy. The recovered ostracods were also subjected to carbon and oxygen isotopic analysis. The bulk organic matter at the base of the sapropel yielded an uncalibrated 14C age of 6080 ± 60 y BP. Diatoms, where preserved, are almost exclusively benthic. Stratigraphic variation of the proportions of key indicator species in diatom assemblages records a marked oscillation between oligosaline and eusaline conditions in the hypolimnion during deposition of the sapropel. Ostracod carbon isotope data indicate that the lake at this time was eutrophic, thereby enriching the dissolved inorganic carbon of the hypolimnion in 13C. However, the observed secular variation in δ13C implies a mid-sapropel drop in productivity, caused by a freshening of the lake. Ostracod δ18O values display an overall increase through the sapropel consistent with the rising salinity of the hypolimnion. The existence of a flourishing benthic ostracod community, together with the valve ornamentation of Osticythere baragwanathi, indicates that the bottom waters were well oxygenated. Thus, anoxia was not a prerequisite for sapropel accumulation. The biostratigraphy and chemostratigraphy of the sapropel concur in suggesting a lack of climatic uniformity during its deposition, a period of ∼1200 years. This study therefore highlights the potential of diatoms and ostracods in shallow perennial alkaline lakes along the Coorong coastal plain as proxies for short-term (102 – 103 years) Holocene palaeoenvironmental change in southeastern Australia.

A genetic algorithm to build diatomic potentials

Through the last years, several types of numerical and combinatorial optimization algorithms have been used as useful tools to minimize functional forms. Generally, when those forms are non-linear or occur in problems without a specific optimization method, stochastic methods based on search algorithms have shown good results due to its smaller susceptibility to be trapped in a local minimum. Besides that, they can easily be implemented to work with other techniques, in this class of algorithms, the genetic ones have received special attention because they are a robust optimization tool. An algorithm can be named genetic when it uses some kind of codification to transform a set of possible solutions of a given problem in a population that will evolve subject to operators inspired, or not, by mechanisms of natural selection. In other words, they work with a population of solutions to obtain better solutions in the next generation. To do this, they use only information of cost and prize. In this work, we propose a genetic algorithm optimization technique (GAOT) to fit diatomic potential energy curves. In order to show this method, we obtain the analytical functions of the H 2 + and Li 2 systems using ab initio energy calculations with Rydberg trial functions. The diatomic vibrational energy spectra is determined from these potentials and the results are compared with other methods. This study shows that the quality of the GAOT fitting is as good as the best optimization techniques recommended to fit diatomic systems. This technique is very important because it arises as a new option to fit potential energy curves for diatomic reactions.

Comparison of empirical closed-form functions for fitting diatomic interaction potentials of ground state first- and second-row diatomics

Twenty-one empirical potentials, having simple functional forms and varying numbers of adjustable parameters, were fitted to experimental RKR data for the ground states of 14 first- and second-row diatomics. The goodness-of-fit was evaluated in each case using the statistical least-squares Z-test of Murrell and Sorbie, and functions with more parameters generally produced better fits (lower Z values), as expected. The dependence of the goodness-of-fit varied in a complicated way with the number of adjustable parameters; for a given number of parameters, some functions outperformed others, indicating that certain functional forms give rise to inherently better empirical potentials, at least for the limited set of diatomics selected here.

Survey of the Chemical Defence Potential of Diatoms: Screening of Fifty Species for α,β,γ,δ-unsaturated aldehydes

In recent years a negative influence of diatom-derived alpha,beta,gamma,delta-unsaturated aldehydes (PUA) on the reproductive success of copepods and invertebrates has been suggested. Since adverse chemical properties of diatoms would question the traditional view of the marine food web, this defense mechanism has been investigated in detail, but the PUA-release by test organisms has only been determined in a few cases. The observed effects were nevertheless frequently discussed from a general point of view often leading to contradictory conclusions. We have examined the PUA-production of 51 diatom species (71 isolates) in order to provide a basis for the interpretation of laboratory and field results on the influence of diatom food on the reproductive success of their consumers. PUA-production is species and strain dependent. Thirty-six percent of the investigated species (38% of the cultivated isolates) release alpha,beta,gamma,delta-unsaturated aldehydes upon cell disruption in concentrations from 0.01 to 9.8 fmol per cell. Thalassiosira rotula and Thalassiosira pacifica, major spring-bloom forming diatoms isolated from Roscoff (Bretagne, English Channel, France) and Puget Sound (Washington, USA) were among the PUA-producing strains.

Solutions of the Dirac equation with the four-parameter diatomic potential

In this Letter, treating four-parameter diatomic potential as the even component of the Dirac equation, we use the supersymmetric quantum mechanics to obtain the relativistic bound state energy spectrum and the corresponding spinor wave-functions. Some interesting results including the standard Hulthén and Morse potentials are also discussed.

Can resonances occur in the photodissociation continuum of a diatomic molecule? The role of potential discontinuities

Continuum resonances are standard fare in the instructional literature for quantum mechanics, where they arise from the continuity conditions imposed on one-dimensional wavefunctions for piecewise-constant potential energy functions. Such resonance structure weakens progressively as the discontinuity in the potential is smoothed, showing that the structure is specifically attributable to the discontinuity. Since diatomic molecular potential energy curves seldom vary rapidly on the distance scale of the period of the wavefunction, such continuum resonances are not expected in absorption continua. A historically interesting prediction of such structure in the Schumann–Runge continuum (B ← X) of O2 is attributed to the inadvertent incorporation of discontinuity in the B-state potential curve employed in the computations.Key words: quantum mechanics, continuum resonance, diatomic absorption, photodissociation continuum, numerical methods.

Dynamics of silicon metabolism and silicon isotopic discrimination in a marine diatomas a function of pCO2

Opal accumulation rates in sediments have been used as a proxy for carbon flux, but there is poor understanding of the factors that regulate the Si quota of diatoms. Natural variation in silicon isotopes (δ30Si) in diatom frustules recovered from sediment cores are an alternative to opal mass for reconstructing diatom Si use and potential C export over geological timescales. Understanding the physiological factors that may influence the Si quota and the δ30Si isotopic signal is vital for interpreting biogenic silica as a paleoproxy. We investigated the influence of pCO2 on the Si quota, fluxes across the cell membrane, and frustule dissolution in the marine diatom Thalassiosira weissflogii and determined the effect that pCO2 has on the isotopic fractionation of Si. We found that our Si flux estimates mass balance and, for the first time, describe the Si budget of a diatom. The Si quota rose in cells grown with low pCO2 (100 ppm) compared with controls (370 ppm), and the increased quota was the result of greater retention of Si (i.e., lower losses of Si through efflux and dissolution). The ratio of efflux : influx decreased twofold as pCO2 decreased from 750 to 100 ppm. The efflux of silicon is shown to significantly bias measurements of silica dissolution rates determined by isotope dilution, but no effect on the Si isotopic enrichment factor (ε) was observed. The latter effect suggests that silicon isotopic discrimination in diatoms is set by the Si transport step rather than by the polymerization step. This observation supports the use of the v signal of biogenic silica as an indicator of the percentage utilization of silicic acid.

Model study on the photoassociation of a pair of trapped atoms into an ultralong-range molecule

Using the method of quantum-defect theory, we calculate the ultralong-range molecular vibrational states near the dissociation threshold of a diatomic molecular potential which asymptotically varies as $-1/R^3$. The properties of these states are of considerable interest as they can be formed by photoassociation (PA) of two ground state atoms. The Franck-Condon overlap integrals between the harmonically trapped atom-pair states and the ultralong-range molecular vibrational states are estimated and compared with their values for a pair of untrapped free atoms in the low-energy scattering state. We find that the binding between a pair of ground-state atoms by a harmonic trap has significant effect on the Franck-Condon integrals and thus can be used to influence PA. Trap-induced binding between two ground-state atoms may facilitate coherent PA dynamics between the two atoms and the photoassociated diatomic molecule.

Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach

An alternative method for finding exactly solvable quantum mechanical potentials is presented and discussed. As examples of this approach, the hydrogenic (Coulomb) radial potential and the anharmonic Pöschl—Teller diatomic potential are derived. The utility of the latter potential is checked by fitting it to published data for the B electronic state of diatomic iodine. This alternative means of finding exactly solvable quantum mechanical potentials should be of interest and use to physical and theoretical chemists.

Molecular dynamics calculations of melting rates with a novel order parameter: The diatomic Pa3 crystal

A method is presented to design order parameters that can be used as discriminator in two-phase crystal-liquid molecular dynamics simulations. The proposed methodology is an extension to molecular crystal structures of a previously introduced discriminator for the atomic fcc environment [Phys. Rev. Lett. 79, 5074 (1997)] and can be readily applied to any crystal structure with both translational and orientational order. As an example, the discriminator is applied to the molecular Pa3 environment and subsequently used to study crystal melting rates with a diatomic carbon dioxide potential. The system’s melting temperature proves to be below the roughening transition which is exemplified by faceted growth. The dynamically corrected melting rates are easily fitted to a rate law for two-dimensional nucleation and growth from which the melting temperature is deduced. The feasibility of the method for the example system holds promise for more extensive microscopic investigations of molecular crystal growth and melting.

The He–CaH (2Σ+) interaction. I. Three-dimensional ab initio potential energy surface

The interaction potential of the He–CaH(2Σ+) van der Waals complex is computed with the partially spin-restricted open-shell single and double excitation coupled cluster method with perturbative triples [RCCSD(T)] for more than 3700 geometries. An accurate fit of the three-dimensional potential is made available for the RCCSD as well as the RCCSD(T) results. Also the CaH diatomic potential is calculated at the RCCSD(T) level and shown to be very accurate by comparison of computed vibrational levels and rotational constants to spectroscopic data. In the accompanying paper the potentials are employed in a study of collisions of He with CaH at cold and ultracold temperatures.

The triplet He2* Rydberg states and their interaction potentials with ground state He atoms

We report ab initio potential energy curves for the interaction of ground state He atoms with the triplet He2* excimers. Fully converged, unrestricted, open-shell, coupled-cluster method including singles, doubles, and perturbative treatment of triples substitutions (UCCSD(T)) is used to compute the He2*–He potential energy curves for the a(3Σu) and c(3Σg) states. The internally contracted multireference configuration interaction method (ICMRCI) is used to compute the potential energy curves for a(3Σu), b(3Πg), d(3Σu), e(3Πg), f(3Σu), and f(3Πu) states. Where they can be compared, at the potential minima, the ICMRCI and UCCSD(T) methods agree to within 1 cm−1. The method reproduces the diatomic He2 potential with an accuracy of 0.8 cm−1. An accuracy of ∼2 cm−1 is estimated for all reported He2*–He potentials. Calibrations based on Li–He and H2–He interactions are consistent with this expectation. Calculations on tetratomics, He–He2*–He, are carried out to assess the nonadditivity of potentials in various states. At short range, nonadditivity arises from polarization effects, while at long-range its nonadditivity is due to the distortion of the Rydberg electron density by the ground state He atoms. Besides potential energy points, electron density plots are provided.

Shape invariance and the supersymmetry WKB approximation for a diatomic molecule potential

It has been shown that a four-parameter potential for a diatomic molecule is a shape-invariant potential with a translation of parameters. The exact energy spectrum of this potential is obtained by using the shape-invariance approach and the supersymmetry WKB approximation.