Diatomic Potential Energy Curves Research Articles

Electron transfer mediated decay of alkali dimers attached to He nanodroplets.

Alkali metal dimers attached to the surface of helium nanodroplets are found to be efficiently doubly ionized by electron transfer mediated decay (ETMD) when photoionizing the helium droplets. This process is evidenced by detecting in coincidence two energetic ions created by Coulomb explosion and one low-kinetic energy electron. The kinetic energy spectra of ions and electrons are reproduced by simple model calculations based on diatomic potential energy curves, and are in agreement with ab initio calculations for the He-Na2 and He-KRb systems. This work demonstrates that ETMD is an important decay channel in heterogeneous nanosystems exposed to ionizing radiation.

Up and away in the potential landscape of diatomic molecule potential energy curves

The understanding of the potential curves of a given molecule has expanded in many ways during my last 52years as an experimental and theoretical molecular chemist/physicist in graduate school in Chemistry at Harvard and in both the Chemistry and Physics Departments at University of Iowa and University of Connecticut. This expansion has been up in energy and vibrational and rotational quantum numbers and away from Re to long range as well. It is clear that Prof. Robert Le Roy, who I have known since the late 1960s, has made many important and greatly appreciated contributions to the landscape I describe below from my personal perspective, especially with regard to long range molecules and solution of the radial Schrödinger equations and related calculations.

On the use of quadratic approximants to model diatomic potential energy curves

Quadratic approximants are shown to have an appropriate functional form for modelling the mathematical structure of the full configuration interaction energy as a function of internuclear distance. The problem of spurious singularities is discussed. Quadratic approximants with additional constraints are constructed so as to avoid spurious singularities and to have the correct dissociation limits. It is shown that these approximants are appropriate for interpolating between computed ab initio energies. The method is tested with a set of full configuration interaction energies for the hydrogen fluoride molecule. The approximants are shown to give an accurate interpolation through the region of moderate bond stretching where direct approximate ab initio computations are difficult. A procedure for parameterizing the approximants to empirical data is developed.

Electron correlation methods based on the random phase approximation

In the past decade, the random phase approximation (RPA) has emerged as a promising post-Kohn–Sham method to treat electron correlation in molecules, surfaces, and solids. In this review, we explain how RPA arises naturally as a zero-order approximation from the adiabatic connection and the fluctuation-dissipation theorem in a density functional context. This is contrasted to RPA with exchange (RPAX) in a post-Hartree–Fock context. In both methods, RPA and RPAX, the correlation energy may be expressed as a sum over zero-point energies of harmonic oscillators representing collective electronic excitations, consistent with the physical picture originally proposed by Bohm and Pines. The extra factor 1/2 in the RPAX case is rigorously derived. Approaches beyond RPA are briefly summarized. We also review computational strategies implementing RPA. The combination of auxiliary expansions and imaginary frequency integration methods has lead to recent progress in this field, making RPA calculations affordable for systems with over 100 atoms. Finally, we summarize benchmark applications of RPA to various molecular and solid-state properties, including relative energies of conformers, reaction energies involving weak and covalent interactions, diatomic potential energy curves, ionization potentials and electron affinities, surface adsorption energies, bulk cohesive energies and lattice constants. RPA barrier heights for an extended benchmark set are presented. RPA is an order of magnitude more accurate than semi-local functionals such as B3LYP for non-covalent interactions rivaling the best empirically parametrized methods. Larger but systematic errors are observed for processes that do not conserve the number of electron pairs, such as atomization and ionization.

Comment on “Ab initio molecular dynamics calculation of ion hydration free energies” [J. Chem. Phys. 130, 204507 (2009)

We suggest that the authors compare their theoretical Gibbs free energies −ΔGhyd (kcal/mol) Li+, 128(1), 135; Cl−, 78(1), 70(2); and Ag+, 120(1) to recent absolute experimental values Li+, 128; Cl−, 74; and Ag+, 119 kcal/mol referenced to that for H+, 266(2) kcal/mol. We present bulk Gibbs hydration free energies and ionic radii for other ions from aqueous electron affinities, monohydration free energies, and diatomic halogen anion potential energy curves consistent with the Born dielectric constant, 3.4, for electrons and protons.

Predicting the gas-liquid transition of mercury from interatomic many-body interaction

A new cross-hierarchical equation of state for expanded fluid mercury is developed by combining quantum-chemical analysis of interatomic interactions and soft-sphere fluid variational approach. The theory incorporates ab initio diatomic potential energy curves and an additional many-body potential describing the associative interaction of an atom with its neighbouring atoms forming a local temporary cluster. The experimental gas-liquid coexistence curves are accurately reproduced without introducing empirical adjustable parameters. The gas-liquid transition is dominated by the many-body interaction, which becomes strongly attractive as the average coordination number increases and the local electronic states change from nonmetallic to metallic.

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.

Modeling diatomic potential energy curves through the generalized exponential function

In the present work, an alternative family of analytical potential energy curves (PECs) has been developed for diatomic systems. These kinds of functions, that are based on q-exponential, are used here to generalize the usual Bond Order (BO) and Rydberg analytical PECs of diatomic molecular systems. The diatomic systems H 2 + and Li 2 have been examined by means of this alternative approach. In particular, the computed vibrational spectra and spectroscopic constants were found to be in good agreement with the available experimental data.

Analysis of excited mercury clusters with diatomic potential energy curves

Abstract Cohesive properties of small mercury clusters are analyzed for electronic ground and excited states on the basis of the diatomics-in-molecules method. The theory takes into account ab initio diatomic potential energy curves and configuration mixing of the ground and excited 1Σg states. Increment of binding energies due to s–p mixing is thus predicted in the ground state. Optimized structures of the clusters in the lowest excited state exhibit peculiar D4h and C4v symmetries with significantly small nearest-neighbor distance. As the cluster size increases, the bottom of the excited energy level is lowered rapidly. The calculated potential energy surfaces exhibit strong dependence of excitation energy gap on interatomic separation.

Theoretical potential energy surfaces for excited mercury trimers

Potential energy surfaces are calculated for electronic excited states of mercury trimers (Hg 3) correlating to Hg(6 1P,6 3P) + Hg(6 1S) + Hg(6 1S) asymptotes. The theory is based on the diatomics-in-molecules (DIM) method with the aid of the existing ab initio diatomic potential energy curves and the atomic spin–orbit interaction parameters. Stability of the trimers with C 2v symmetry is investigated in detail. It is thus shown that the lowest excited level corresponds to the metastable A 1 ′ state in the equilateral triangle (D 3h) configuration, which is located at 3.04 eV above the energy of infinitely separated ground-state atoms. The energy of dipole allowed transition from the bottom of the A 0 u + state to the ground X 0 g + state in the symmetric linear (D ∞h) configuration is predicted to be 2.55 eV (4870 Å), which accounts for the well known 4850 Å continuum emission observed through many previous experiments. The origin of the 2170 Å fluorescence band is discussed in connection with higher excited states of Hg 3.

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.

Spin-orbit branching in the collision-induced dissociation reaction of He(1S)+HF(X 1Σ+)→He(1S)+H(2S1/2)+F(2P3/2,1/2)

The collision-induced dissociation process, He(1S0)+HF(X 1Σ0+)→He(1S0)+H(2S1/2)+F(2P3/2,1/2), has been studied using a three-dimensional semiclassical coupled wave packet method with a focus on electronically nonadiabatic transitions induced by spin-orbit interaction. The radial motion is described by classical mechanics and the other degrees of freedom are treated quantum mechanically. The diabatic potential energy surfaces have been constructed with the diatomics-in-molecule approach. The diatomic potential energy curves for the ground and excited states are obtained from the ab initio electronic structure calculations at the multireference configuration interaction level. The calculated spin-orbit branching fraction depends only weakly on the initial vibrational quantum number of HF and on the total angular momentum. This implies that the branching fraction is determined mainly in the large-rHF regions where the spin-orbit interaction of the F atom is dominant. We also found that the electronic anisotropy interaction between the He atom and the F atom in HF plays a less important role in collision-induced dissociation processes.

Experimental and theoretical study of the electronic spectrum of the BAr2 complex: Transition to the excited valence B(2s2p2 2D) state

The 2s2p2 2D←2s22p 2P valence transition in the BAr2 cluster is investigated in a collaborative experimental and theoretical study. Laser fluorescence excitation spectra of a supersonic expansion of B atoms entrained in Ar at high source backing pressures display several features not assignable to the BAr complex. Resonance fluorescence is not observed, but instead emission from the lower 3s state. Size-selected fluorescence depletion spectra show that these features in the excitation spectrum are primarily due to the BAr2 complex. This electronic transition within BAr2 is modeled theoretically, similarly to our earlier study of the 3s←2p transition [M. H. Alexander et al., J. Chem. Phys. 106, 6320 (1997)]. The excited potential energy surfaces of the fivefold degenerate B(2s2p2 2D) state within the ternary complex are computed in a pairwise–additive model employing diatomic BAr potential energy curves which reproduce our previous experimental observations on the electronic states emanating from the B(2D)+Ar asymptote. The simulated absorption spectrum reproduces reasonably well the observed fluorescence depletion spectrum. The theoretical model lends insight into the energetics of the approach of B to multiple Ar atoms, and how the orientation of B p-orbitals governs the stability of the complex.

Theoretical photoabsorption spectrum of Ar3+

We have calculated the photoabsorption spectrum at 0 K of Ar3+ within the framework of the diatomics-in-molecules (DIM) method using highly accurate diatomic potential energy curves. Both the wavelength of the visible absorption maximum and its corresponding absolute cross-section are predicted in agreement with the experimental data. Finite temperature Monte Carlo simulations have been carried out in order to reproduce the experimental UV absorption band.

Global expression for representing diatomic potential-energy curves.

A three-parameter expression that gives an accurate fit to diatomic potential curves over the entire range of separation for charge transfers between 0 and 1. It is based on a generalization of the universal binding-energy relation of Smith et al. (1989) with a modification that describes the crossover from a partially ionic state to the neutral state at large separations. The expression is tested by comparison with first-principles calculations of the potential curves ranging from covalently bonded to ionically bonded. The expression is also used to calculate spectroscopic constants form a curve fit to the first-principles curves. A comparison is made with experimental values of the spectroscopic constants.

DIM model calculations for (O 2H) + interaction potentials

Several low-lying potential energy surfaces for the (O 2H) + system have been estimated using the diatomics-in-molecules (DIM) approach in a model calculation calibrated with known ab initio information. Main features of ground and lower excited states are qualitatively well reproduced in spite of the fact that the DIM basis was kept rather small. The error from the truncation of the basis set had to be compensated for by empirical adjustments of some of the input diatomic potential energy curves of the excited states. From the topography and crossing behaviour of the resulting potential energy surfaces some predictions concerning the mechanism of inelastic and charge transfer collisions are made.

The rational fraction representation of diatomic potentials

The representation of diatomic potential energy curves by rational fractions using low order polynomials in numerator and denominator is investigated. The rational fraction method, which is illustrated by examples, is shown to fail in providing a robust representation of diatomic potentials for wide application.

Generalization of atoms-in-molecules theory to include independent scaling of inner and outer shells

Scaled atoms-in-molecules (SAIM) theory is required for obtaining diatomic fragment eigenvectors, and often useful for providing diatomic fragment potential energy curves, needed as input in the scaled diatomic-in-molecules (SDIM) method. Independent scaling of inner shells and valence shells is not admitted in the current formulation of SAIM. A new extension is developed here in which atomic eigenfunctions are partitioned into inner-shell and outer-shell components. These component functions are rigorously defined as solutions of two simultaneous eigenvalue equations; the Hamiltonians in these equations add to yield the original total atomic Hamiltonian. The component Hamiltonians so defined are shown to contain potential energy functions which are approximately homogeneous functions of degree minus one; hence, Coulomb-like. Thus, the inner-shell and outer-shell eigenfunctions may be scaled independently using methods generalized from standard scaled atoms-in-molecules (SAIM) theory. Preliminary applications to LiH, BeH, and Li2, and their positive ions, yield dissociation energies accurate to 7 kcal/mol or better.

Atoms-in-molecules calculations on diatomic fragments of polyatomic systems. FH and FH +

Two versions of the atoms-in-molecules method (the original Moffitt scheme and the orthogonalized Moffitt method) are applied to various states of the FH and FH − species to obtain information on diatomic state mixing and potential energy curves needed for a diatomic-in-molecules calculation on (FH 2) +.

Improved a b i n i t i o effective potentials for Ar, Kr, and Xe with applications to their homonuclear dimers

Effective core potentials for the Ar, Kr, and Xe atoms derived from numerical Hartree–Fock and Dirac–Hartree–Fock wave functions are applied in SCF and CI calculations of homonuclear diatomic potential energy curves. Detailed comparisons are made with the all-electron calculations of Wadt for the ground and lowest positive states. Relativistic effects, excluding spin–orbit coupling, are seen to be relatively unimportant. Plots of the potential energy curves and computed spectroscopic constants show excellent agreement with the all-electron results. On the other hand, comparisons with results obtained using effective potentials derived using varients of Phillips–Kleinman procedures show dramatic differences for Xe2 and Xe2+. From SCF calculations on Xe2 and Xe2+ it was found that the explicit inclusion of the spin–orbit operator in the SCF procedure (using ω–ω coupling) results in essentially the same potential curves obtained by adding the spin–orbit correction as a final semiempirical perturbation.