Potential Hypersurface Research Articles

A generalized model for the ν-dependence of the anisotropic long-range attractive interaction of alkali dimer-atom systems

State-selective measurements of anisotropic integral cross sections for the scattering of highly vibrationally excited alkali molecules (Li 2, Na 2) with various atoms (He, Ne, Ar, Kr, Na) are used to model simple three-dimensional potential hypersurfaces for these systems by comparison with quantum mechanical IOS scattering calculations. The two necessary fitting parameters in the attractive and repulsive part of the potentials are remarkably similar for all investigated systems and give new insight into the variation of potential energy with vibrational excitation. On the basis of this manifold of improved hypersurfaces, it is possible to account for the net increase in total cross section, anisotropy, and rotational inelasticity for vibrationally hot molecules by a single, generalized expression with a scaling parameter that includes collision energy and vibrational ground state potential well depth.

Gas phase flash pyrolysis of 3-azido-1,2,4-triazole: generation and ultraviolet photoelectron spectrum of N-cyanomethanimine

A dimer of HCN, N-cyanomethanimine 6, was prepared by flash pyrolysis (gas phase, 10−2 mbar) from 3-azido-1,2,4-triazole 1a and detected by ultraviolet photoelectron spectroscopy (HeI). Its ionization potentials were measured and the ionic states sequence proposed, with the aid of ab initio – CI (configuration interaction) calculations. The study of the MNDO potential hypersurface enabled us to propose a mechanism of the thermal reorganization of the precursor 1a. It is shown that the reaction path passes through the formation of the protomer 1b before thermal decomposition and the generation of the nitrene 2b.

Statistical Thermodynamic Calculations of Adsorption Data for the Adsorption of Simple Gases at Solid Surface — A Two Phase Approach

Statistical thermodynamic calculations were carried out in the two-phase approach to describe the temperature dependence of adsorption data for simple gases on homogeneous and heterogeneous solid surface at low coverages. It was shown that the high temperature region is much more sensitive to the kind of model potential function representing the potential hypersurface of the absorbed phase than it is in the low temperature region. At low temperatures [Formula: see text] the adsorption data can be calculated from using a harmonic potential function with good realistic background. For the description of a heterogeneous solid surface a potential function Φ(x,y,z) was proposed by Φ(x,y,z) = Φ(z) + Φ(x,y) or Φ(x,y,z) = Φ(z)-φ(x,y). At low temperatures and small heterogenities [Formula: see text] the adsorption data can be approximated by adding one part related to a Φ(z) potential and another one related to Φ(x,y). If an anharmonic potential function Φ(z) is used a maximum in ΔaC (T) appears caused by the anharmonicity of this function. This high temperature maximum is overlayed by the heterogenity maximum in ΔaC and gives additional peaks if Δε is not in the same order of magnitude than ε0.

A theoretical study of SiC 2+

An ab initio study at the Hartree-Fock level has been carried out to determine the structure of linear and cyclic SiC 2 +. Fourth-order Møller-Plesset perturbation theory reveals that the cyclic isomer (C 2v symmetry) is the most stable, with a 2A 1 ground state. Vibrational analysis at the Hartree-Fock level confirms that, unlike cyclic SiC 2, SiC 2 + (C 2v) is a true minimum on the HF potential hypersurface.

On the potential hypersurface of the dication of cyclotetraphospane

The dications of tetraaminocyclotetraphosphanes decompose easily into diaminophosphenium cations and white phosphorus. The electronic hypersurface of this new type of rearrangement is explored by energy optimized MNDO calculations. Accordingly, in the initial step, rearrangements to various structures take place. The latter are more stable than the precursor dication. In the second step fragmentation of the intermediates occur via retro carbene addition reaction to the energetically most stable products, i.e., the diaminophosphenium cation and white phosphorus. A variety of intermediates are feasible in the rearrangement reaction.

MNDOC Calculations of the Potential Surfaces for Photochemical α‐Cleavage

A combination of a semiempirical MO calculation and a limited configuration interaction calculation has been used successfully for the prediction of photoproducts as a function of the excited state of the reactant. As example, the α‐cleavage of formaldehyde was investigated. The potential hypersurfaces of the S0 Sa and Ta states for planar formaldehyde were calculated as functions of the CH1 distance and of the H2CO angle.

Comparison of Various Potential Models for the Simulation of the Pressure of Liquid and Fluid N2

Abstract We have performed molecular dynamics (MD) calcuations with 256 particles to simulate the pressure of liquid and fluid nitrogen in the low and the high pressure regions. The pressure in MD calculations is extremely sensitive for the form of the potential employed and therefore this quantity is best suited to test intermolecular potentials. We have studied eight different potential models including a three-body potential. Of the potential functions considered, the existing purely effective Lennard-Jones (LJ) potentials- 1-centre and 2-centres-do not suffice to give the experimental pressure for the whole pressure range. The 2-LJ-centres models derived from potential hypersurfaces calculated by “ab initio” methods produce slightly better results and led to an optimal model potential which reflects the experimental data within the statistical error of the MD. The 2-LJ centres model potential function we used for the fit cannot model the fine structure of the “ab initio” calculated hypersurface, but describes it in a balanced way when the higher energies are excluded systematically. We have achieved this by a certain weighting procedure.

Equilibrium isomeric mixtures: potential energy hypersurfaces as the origin of the overall thermodynamics and kinetics

Abstract Potential energy hypersurfaces are now most frequently represented by the location and characterization of their stationary (critical) points. Model studies have demonstrated that hundreds of stationary points can be present on some potential hypersurfaces of chemical interest. Any structure-dependent observed quantity can thus have a convolutional nature, being composed of contributions of relevant stationary points. This article focuses on equilibrium and rate processes; it deals with situations in which component of an equilibrium is represented by a group of several different local energy minima and/or when several different saddle points serve as activated complexes in a single rate process. Particular attention is paid to the case where two or more isomeric structures of comparable stability coexist, the isomers being indistinguishable under observational conditions. Evaluations of overall, convolutional standard and/or activation reaction terms based on the stationary-point hypersurface re...

Scattering of highly vibrationally excited Li2 from He and Kr

Total integral scattering cross sections have been measured for Li2 molecules in selected rotational and vibrational states up to v=21. The vibrationally highly excited states with energies up to 80% of the dissociation energy were prepared by Franck–Condon laser pumping. With increasing vibrational quantum number the observed cross sections show first a 10% decrease followed by a 20%–25% rise. A model potential has been developed based on an ab initio potential for the vibrational ground state to account for the effect of vibrational stretching. The results provide for the first time direct information on the bond-distance dependence r of the complete potential hypersurface V(R,r,γ) (R distance between centers of mass and γ angle between r and R) of an atom–molecule system.

Molecular beam scattering measurements of differential cross sections for D+H2(v=0)→HD+H at Ec.m.=1.5 eV

The reaction D+H2→HD+H has been studied in a crossed molecular beam scattering experiment at a most probable collision energy of Ec.m.=1.5 eV. Angular and time-of-flight distributions of the HD product have been measured over a wide range of angles. The experimental data are compared with quasiclassical trajectory (QCT) calculations on the LSTH potential hypersurface. The QCT calculations fit the experimental data quite satisfactorily. The sensitivity of the experiment to the different properties of the cross section has been investigated.

Mass spectroscopic study of some novel water clusters: (H2O) n + ;n>3

A near atmospheric pressure ion source with a β-emitter as electron source is used to inject ions into a supersonic water expansion. Cluster ions of the structure (H2O)+n have been observed forn up to 8. Forn>3 these cluster ions cannot be obtained by ionization of water clusters in vacuum, but they can be grown in the cold environment of a supersonic beam. Extremely clean conditions are necessary for the observation of these cluster ions. The data can be explained by assuming that the local potential minimum calculated for the (H2O)n+,n=2, potential hypersurface exists also forn>2. The model developed to explain these data is similar to that proposed for ionized rare gas clusters.

Chemiluminescent reactions of second-row atomic ions. I. Al++H2→AlH+(A 2Π, B 2Σ+)+H

Light emission from the impact of Al+(1S,3P) ions on H2 molecules at 5.2 to 13.8 eVCM was spectrally analyzed. It was found to consist of two band systems. Of the known A 2Π–X 2Σ+ transition, numerous new bands were observed, allowing a first experimental determination of vibrational constants. In addition, a predicted B 2Σ+–X 2Σ+ system was observed for the first time. Relative emission cross sections for the two systems and for the 1S and 3P reactant species were measured. They parallel closely the trends in the isovalent system B++H2. One important difference is, however, the existence of a large (∼3.5 eV) activation barrier in the dominant Al++H2 reaction channel. This is explained in terms of adiabatic potential hypersurfaces.

4-31G ab initio and MNDO semi-empirical calculations on bicyclic CN7–and N8species, and n.m.r. and i.r. studies on15N-labelled CN7–

Hepta-azapentalene anion and octa-azapentalene are predicted by both 4-31G ab initio and MNDO semi-empirical calculations to be true minima on the CN7– and N8 potential hypersurfaces, respectively; 15N scrambling from labelled 5-azidotetrazole anion is shown to occur by 15N n.m.r. and i.r. spectroscopy, all data pointing to the involvement of the bicyclic CN7– intermediate.

Inherent structure theory of liquids in the hard-sphere limit

Atomic pair correlation functions for liquids provide an image of temperature-dependent short-range order. If the thermal ensemble of atomic configurations is mapped (by steepest descent on the potential hypersurface) onto potential energy minima, the pair correlation function from the resulting transformed configurations exhibits substantial image enhancement, revealing short-range order in a much more vivid fashion. Previous studies of model atomic liquids have demonstrated that at fixed density, mapped short-range order is virtually independent of the initial temperature, and thereby amounts to an ‘‘inherent structure’’ for the liquid. The present paper investigates steepest-descent mapping and inherent structure for hard spheres, construed as the infinite-n limit for pair potentials (a/r)n. Methods used are both analytical and simulational, the latter involving molecular dynamics for n=12 and 24. Results show that inherent structures in the hard-sphere limit are randomly packed configurations, where particle radii have been inflated to the point of jamming.

Role of potential-energy scaling in the low-temperature relaxation behavior of amorphous materials.

Under the assumption that the Kohlrausch-Williams-Watts (KWW) function describes relaxation near the glass transition for amorphous substances, implications are explored for the character of the many-body potential-energy function. The analysis proceeds in several stages: (1) The configuration space is uniquely divided into minimum-containing cells by a steepest-descent construction on the potential hypersurface. (2) Attention is confined to the amorphous region of configuration space by projecting out all cells containing local crystalline patterns. (3) The potential is separated into a hard-core part ${\ensuremath{\Phi}}_{c}$ and a ``soft'' remainder ${\ensuremath{\Phi}}_{s}$. (4) ${\ensuremath{\Phi}}_{s}$ is coarse grained (smoothed) over a variable scale of lengths l. (5) A master equation is used to describe the relaxation spectrum subject to the interaction smoothed over any l. The demand that KWW relaxation emerge from the last constrains the statistical topography of ${\ensuremath{\Phi}}_{s}$. Specifically it requires that on widely separated length scales, multiply branched channels of relatively modest elevation change must exist in ${\ensuremath{\Phi}}_{s}$. Furthermore, the separating barriers between these channels tend to be largest in those portions of configuration space sampled by the system at the lowest temperatures, and to scale as lnl.

Cluster isomerism — theoretical treatments and thermodynamic consequences: A case study of C 0p with CO 2 clusters

It often happens that several different structures of comparable stability are recognized under a single summary cluster formula on the potential hypersurfaces used in theoretical studies of clusters. This is true for both clusters in the gas phase and for those formed by gas-solid interactions. Typically, contemporary experimental techniques do not permit differentiation between these individual isomeric structures. Therefore, a thermodynamically consistent treatment is considered for theoretical simulation of the overall thermodynamic terms obtained from ordinary experiments involving clusters. Special attention is paid to the heat capacity term whose observed values may be strongly affected by contributions from isomerism. The isomerism of (CO 2) 2 is considered for illustration, with application of the ab initio cluster parameters.

A model for free-radical reactions

Using an EHT type Hamiltonian the Heitler-London-VB treatment of the three-centre three-electron problem is simplified such that the interesting features of the potential hypersurfaces of arbitrary three-centre three-electron systems can be obtained simply from the knowledge of atomic orbital energies and overlap integrals. The method is applied to the hypersurfaces of the H3 system and extensions of the discussion of general radical reactions are indicated.

NH3 trapped in nitrogen and rare gas matrices. I. Potential surface analysis

Abstract New results obtained from the high-resolution study of the ν2 mode of nitrogen-trapped ammonia have prompted us to investigate both the internal (vibration and inversion) and external (translation and orientation) degrees of freedom of the symmetric top. In a first step, the overall potential is built from the usual internal NH3 term supplemented by an a priori NH3 interaction contribution. This latter contribution appears as a sum over the lattice of a pairwise potential containing molecular and atomic terms. Large eccentricity values (0.36 A) are calculated for the NH3 equilibrium configurations. A high barrier to flip-flap reorientation (= 850 cm−1) and a comparatively moderate one (= 90 cm−1) to proper rotation (spinning) around the C3 axis are predicted. Twelve different sets of equilibrium coordinates involving inversion, orientation, proper rotation and translation (eccentricity) yield equivalent potential wells. A number of sections through the potential hypersurface - those connecting two by two the equivalent wells - is critically described. The adequacy of the potential is guaranteed by comparing the calculated librational frequency (νL = 167 cm−1) to the experimental one (νL = 174 cm−1).

An intermoleeular potential function for the N2−H2O system fromab initioMO calculations

An intermolecular potential function for the N2−H2O system is derived from ab initio MO calculations with a minimal basis set. An angular dependence of the functions is necessary in order to reproduce all the minima of the ab initio surface. The fitting appears satisfactory, especially for bound geometries. Some problems connected with the fitting of potential hypersurfaces are discussed.

A simple theoretical model for the van der Waals potential at intermediate distances. IV. The bond distance dependence of the potential hypersurfaces for He–H2 and Ne–H2 also for the repulsive region

A simple theory for the van der Waals potential in the region of the well minimum, which previously has been successfully applied to the prediction of the isotropic atom–atom [J. Chem. Phys. 66, 1496 (1977)] and the anisotropic atom–diatom potentials [J. Chem. Phys. 68, 5501 (1978); 74, 1148 (1981)], has been extended to calculate the full potential hypersurface including the H2 bond distance dependence for He–H2 and Ne–H2. By taking advantage of the known potential parameters in the united atom limits He–He and Ne–He, respectively, the potential hypersurface is predicted over a wide range of bond distances. The model is modified to also provide a good estimate of the true potential in the repulsive region (V≃1 eV). The results for He–H2 are compared with a recently calculated CI type hypersurface [Meyer, Hariharan, and Kutzelnigg, J. Chem. Phys. 73, 1880 (1980)] and found to be in good agreement in the region of intermediate distances of the center of masses (R≈3.0 Å), and for H2 bond distances r in the range (0.50–1.00 Å). The R dependence of the vibrational coupling matrix elements are presented for both systems and the implications for the vibrational relaxation rates of both systems are discussed.