Ground State Potential Research Articles

Models for bond distance dependent alkali dimer–rare gas potentials

Analytic expressions for Li2–Rg and Na2–Rg electronic ground state potentials (Rg=He,Ne,Ar,Kr,Xe) that depend on all three Jacobian coordinates, atom–molecule distance R, bond length r, and orientation angle γ, are presented. The potentials are obtained by expanding the repulsive and attractive parts in a two-term Legendre expansion and connecting them via generalized damping functions as proposed by Tang and Toennies [J. Chem. Phys. 80, 3726 (1984)]. The bond distance dependence (req=5.051 a.u.≤r≤6.838 a.u. for Li2 and req=5.809 a.u.≤r≤7.607 a.u. for Na2) is introduced in the repulsive part via the r-dependent shift of the repulsive barrier and in the attractive part via the r dependence of the multipole polarizabilities and effective excitation energies. These potentials are shown to agree reasonably with ab initio data. The resulting values of potential well depth ε and equilibrium distance Rm are used to check the validity of recently proposed direct combining rules for r-dependent potentials.

On the inner wings of the ground state potentials of CO and F 2

The reduced potential curve (RPC) method is used for the detection of errors in the construction of the potential and in the spectroscopic constants.

Static potentials from pure SU(2) lattice gauge theory

The potentials between static fundamental colour sources corresponding to the ground state and a number of excited states of the gluon field are studied through a Monte Carlo simulation of SU(2) lattice gauge theory with a technique involving “blocked” paths of spatial links. The results are for β-values of 2.4 and 2.5 and for source separations of up to 1.1 fm. We obtain values for the potentials corresponding to the lowest mode for seven irreducible representations of the symmetry group of the gluon field and also to the first excited mode for two of the representations. The lowest excited potential corresponds to the E u symmetry of the gluon field. The ground state potential exhibits non-perturbative scaling at the β-values studied, but the value of the ratio of lattice spacings is in disagreement with the perturbation theory prediction. The excited potentials scale according to the ground state scaling within the errors. String model predictions for the potentials are compared with our results; similarities and discrepancies are discussed.

Stimulated desorption of neutrals: quantum effects in the Antoniewicz model

The quantum theory of stimulated desorption of a neutral van der Waals bound adsorbate via excitation of an ionized intermediate state is studied. The asymmetric decay introduced by quantum motion in a strongly varying imaginary potential leads to a different dependence of coordinate and velocity on time. The position xcrit which has to be reached, so that the adsorbate has enough kinetic energy to be desorbed is shifted. Both these effects have a tendency to cancel each other. On the other hand the broadening of the wave packet leads to a corresponding broadening of the energy distribution and a certain spread of possible xcrit values. The final result is an increase of the intensity of neutrals combined with a shift of the peak of the intensity distribution to higher energies. The agreement with experiment is partly better, partly worse as compared to classical theory. To obtain full agreement one probably has to use a better adjustment of the real part of the excited state potential: A simple superposition of groundstate plus image potential does not seem to be good enough.

Laser spectroscopy on the A0 +-X1Σ + transition of T1I

The first excited electronic state of TII was investigated by laser excitation and laser fluorescence spectroscopy. Almost completely resolved rotational fine structure was observed with the help of a collimated molecular beam and a single-mode cw dye laser. From the derived Dunham parameters Y lk a RKR potential for the excited state is calculated. The unusual shape of the potential energy curve can be understood as originating from an avoided crossing of the ionic ground-state potential and a non-bonding covalent state of the atomic asymptote (6p) 2P 1 2 (TI)+(5p) 5 2P 3 2 (I).

Analytical model for self-energy operators and exchange-correlation potentials in non-metals

We obtain a simple, analytical and yet accurate description of both ground- and excited-state properties from a tight-binding calculation of (i) the self-energy (ii) the density-functional (DF) exchange-correlation potential, and (iii) the band-gap correction to the one-particle DF eigenvalues. The model self-energy results are to within a few percent of recent first-principles numerical data for diamond, Si and LiCl. The new ground-state potential provides insight into the validity of the local-density approximation in non-metals, in general.

Application of the reduced-potential curve method for the detection of errors or inaccuracies in the analysis of spectra and for the construction of internuclear potentials of diatomic molecules: Alkali diatomic molecules.

Errors in the Rydberg-Klein-Rees potentials for the ground and B-excited states of LiNa and LiK and in the ground-state potential of RbCs are detected using the reduced-potential curve (RPC) method and shown to be due to errors or inaccuracies in the analysis of the spectrum. Using the rules of the RPC scheme, estimates for the left limbs of the ground- and B-state potentials of LiNa and LiK are given which are quite accurate for the ground states. With the use of the RPC method, we also give estimates of the ground-state potentials of ${\mathrm{Rb}}_{2}$ and RbCs up to the dissociation limit. The RPC method is further employed for a calculation of accurate internuclear potentials from inaccurate theoretical ab initio potential curves for a series of molecules. These procedures could be useful for a prediction of the spectrum. The examples should illustrate the predictive and constructive power of the RPC method.

Laser spectroscopy of matrix-isolated metal diatomics

Resonance Raman and optical absorption spectra of matrix-isolated transition-metal diatomics have provided valuable vibrational data for these molecules. We have performed LeRoy–Bernstein analysis on four such diatomics, Sc2, Ti2, Mn2 and Fe2, to determine their bond dissociation energies. The value obtained for Mn2 confirms it to be a very weakly bound molecule. Moreover we propose that Fe2 does not possess a large number of states close to the ground state, since the value obtained for it, 1.3+0.4–0.1eV, is close to the quantity calculated from mass-spectral data by assuming a small density of states close to the ground state. The spectrum of Mn2, which is known to be an antiferromagnetically coupled pair of Mn atoms, is very sensitive to temperature as a result of the presence of low-lying spin states resulting from the antiferromagnetic coupling. The temperature variation of the resonance Raman spectrum of this molecule suggests that there is rapid equilibration, not only among ground spin states but also among excited spin states, implying that Mn2 is an antiferromagnetic dimer in at least one of its excited states. The trend in the force constants of the first-row transitionmetal diatomics is discussed in terms of the interplay between s and d bonding. A suggestion is made that near the centre of the first row one might encounter a diatomic with a double-minimum ground-state potential; Cr2 is identified as a likely candidate.

Reducedab initio theoretical internuclear potentials of diatomic molecules

Ab initio theoretical ground state potentials of diatomic molecules calculated with the use of the variational CI-MO (configuration interaction method based on molecular orbitals) are analyzed with the use of the RPC (reduced potential curve) method. It is shown on a series of examples that the following statement is true even for inaccurateab initio calculations: in reduced form, the theoretical potential coincides to a high degree of accuracy with the reduced RKR (Rydberg-Klein-Rees) potential calculated from the spectroscopic data. Thus, with the use of the RPC method, even inaccurateab initio calculations (in particular for heavier molecules) may be used for the construction of rather accurate internuclear potentials and hence obtain a practical significance. The statement also holds for excited states if strong perturbations are not present.

Potential characteristics of the mercury-methane van der Waals complex

The Hg-CH 4 van der Waals complex has been studied in a supersonic jet expansion, in transitions correlated with the 6 1S 0→6 3P 1 mercury transitions. Fuorescence excitation spectra and action spectra have been recorded to analyse the corresponding transitions X→A and X→B. Through isotopic substitution of methane with deuterated methane, the origin band is assigned, and the vibrations of the complex characterised in a simple quasi-diatomic fashion as stretching and bending motions of methane with respect to mercury. These motions correspond to the radial and angular potentials of the complex. Emission spectra from selected stretch levels in the A and B states have confirmed the vibrational quantum assignment and provided a full determination of the radial ground-state potential.

ChemInform Abstract: Structure and Redox and Photophysical Properties of a Series of Ruthenium Heterocycles Based on the Ligand 2,3‐Bis(2‐pyridyl)quinoxaline.

AbstractThe preparation of the complexes (I) is carried out following known methods (no yields given).

Spectroscopic studies of cryogenic fluids: Benzene in propane

Energy shifts and bandwidths for the 1B2u↔1A1g optical absorption and emission transitions of benzene dissolved in propane are presented as a function of pressure, temperature, and density. Both absorption and emission spectra exhibit shifts to lower energy as a function of density, whereas no shifts are observed if density is kept constant and temperature and pressure are varied simultaneously. Density is thus the fundamental microscopic parameter for energy shifts of optical transitions. The emission half-width is a linear function of both temperature and pressure but the absorption half-width is dependent only upon pressure. These results are interpreted qualitatively in terms of changes occurring in the intermolecular potentials of the ground and excited states. Both changes in shape of and separation between the ground and excited state potentials are considered as a function of density. Classical dielectric (Onsager–Böttcher), microscopic dielectric (Wertheim) and microscopic quantum statistical mechanical (Schweizer–Chandler) theories of solvent effects on solute electronic spectra are compared with the experimental results. Calculations suggest limited applicability of dielectric theories but good agreement between experiment and microscopic theory. The results demonstrate the usefulness of cryogenic solutions for high pressure, low temperature spectroscopic studies of liquids.

Xenon oxide and xenon sulfide emission systems at 234 and 227 nm

The two-body quenching reactions of Xe(6p) ★ excited-state atoms with N 2O and OCS provide moderately efficient sources for generating the electronically excited (ionic) states of XeO ★ and XeS ★. These ionic states decay radiatively via bound-free transitions to the ground-state potentials with intensity maxima at 234 and 227 nm for XeO ★ and XeS ★, respectively. The quenching kinetics of Xe(6p[1/2] 0 and 6p[3/2] 2) with N 2O, OCS, NO 2, SO 2, O 2 and CO, and the formation kinetics of XeO ★ and XeS ★ are discussed.

Van der Waals rovibrational states of atom–molecule complexes: Ar–benzene and Ar–tetrazine

Using an empirical intermolecular potential, we have calculated the van der Waals modes of the atom–molecule complexes Ar–benzene and Ar–tetrazine. In the lower states the atom appears as being localized on one side of the molecular plane. This spectrum can be interpreted qualitatively in terms of one- or two-dimensional oscillators. However, these a very anharmonic and especially the motions along the molecular plane have large amplitudes. At higher energies the increased density of states will lead to an increased coupling between the modes. Furthermore, we have calculated the rotational constants of the complex, which are found to be a good measure for the quality of the ground state potential.

Determination of the secondary well in the 6 2P [formula omitted] CsXe potential

Experimental data existing in the literature on broadening and shift at low densities and on position of the red satellite band of the D 1 line of Cs perturbed by Xe are used to obtain information on the range 6Å-∞ of the difference potential. Assuming a Lennard-Jones (n-6) model, best agreement is obtained for n=8 and n=7, in accordance with the low curvature expected for a secondary well. Potential for the first excited state is obtained by addition of the difference potential to the ground state potential, and the parameters of the resulting secondary well are given.

Ground-state properties and pair potentials for paramagnetic iron and nickel

Within a framework of the local density functional formalism the static properties and radial pair potentials for paramagnetic iron and nickel are computed. The construction of pair potential is based on the assumption that the cohesive energy can be expressed as a sum of pair interaction energies. The pair potentials for both metals are expressed by Morse functions.

Investigation of the K(2S, 2P)–Hg interaction at collision energies between 0.5 and 6 eV

Measurements of total differential cross sections for the scattering of laser-excited K(4 2P3/2) atoms by ground state mercury atoms have been performed in a crossed beam experiment at center-of-mass energies between 0.5 and 6 eV. Characteristic features of the cross section are two well resolved rainbow structures which we can assign to the ∑ and the Π branch of the excited state potential in the scope of the elastic approximation. At energies above 2.1 eV we observe an additional structure in the cross section at large angles which shows the same dependence on the polarization as the amplitude of the ∑ rainbow. This is attributed to a shoulder in the repulsive part of the B ∑ potential. The simultaneously measured differential cross sections for the scattering of K(2S) atoms by mercury have been used to determine the repulsive portion of the ground state potential by inversion, making use of the precisely known well of the potential for this system.

Liquid helium on a surface: Ground state, excitations, condensate fraction, and impurity potential.

We study the structure of films of $^{4}\mathrm{He}$ atoms adsorbed to a plane substrate. The ground state is described within a variational model developed earlier [E. Krotscheck, G.-X. Qian, and W. Kohn, Phys Rev. B 31, 4245 (1985)]. Euler-Lagrange equations are solved for the one-body and two-body correlations for three different models of the $^{4}\mathrm{substrate}$ interaction. The one-body density shows structure indicating the formation of layers of one, two, three, . . . atoms above the substrate. The solution of the Euler-Lagrange equation also provides the dispersion relation and spatial shape of collective excitations in the system. The results of the ground-state optimization are used to calculate the condensate fraction (i.e., the number of particles with zero momentum parallel to the surface) and the binding energy of a $^{3}\mathrm{He}$ impurity.

Modelling of potential energy curves for diatomics: Reference molecular potential method

A method is suggested for modelling the potential energy curves of diatomics. It involves a search for the mapping which transfers the structural details from an analytically prescribed reference potential. For the ground-state potentials of seven covalent molecules, the accuracy in describing the spectroscopic region is comparable with the best empirical potentials, and the correct asymptotic behaviour at R → 0 and R → ∞ are also obtained.

Interatomic potentials for Zn2from the absorption spectra of the 213.8 nm line

Absorption measurements have been made in the near blue wing and over a 75 nm range in the red wing of the 213.8 nm Zn line for nine temperatures between 685 and 1030 degrees C and for Zn pressures between 2.5*10-3 and 1.3 atm. The data are analysed wit the statistical theory of broadening. At the lowest pressures and near the line centre the line is symmetrical and an oscillator strength of 1.502+or-0.044 is obtained. The red wing is assumed to arise from transitions to a single, non-degenerate excited state with a constant oscillator strength that is one-third the value for the isolated atom. The ground-state and excited-state potentials are then obtained as a function of R3-Rref3 where R is the interatomic separation and Rref is not fixed by the authors' experiment. The depth of the minimum in the ground state is 46 meV with a standard deviation of 10 meV. No minimum in the excited-state potential is seen but a lower limit of 1.2 eV for its depth is fixed. Taking one value of R from the calculation of Hay et al. (1976), the authors have constructed the potentials in terms of R between 0.27 and 1.38 nm. The authors' excited state falls below the calculated result at the smallest values of R.