Perspective Plots Research Articles

Hydrates in supersaturated binary sulfuric acid-water vapor

Portions of the free energy surface giving the reversible work W required to form a droplet containing n1 molecules of H2O and n2 molecules of H2SO4 from an initially homogeneous vapor have been calculated for a variety of relative humidities and H2SO4 vapor concentrations. These surfaces are displayed as three dimensional perspective plots. The surfaces predict the existence of stable H2SO4 hydrates in the vapor phase, and the number of hydrates, Nh, with h molecules of H2O per hydrate has been calculated for three different values of the relative humidity. The results of these calculations indicate that virtually all the H2SO4 present, especially for relative humidities greater than 100%, exists in hydrate form. As the relative humidity is increased (i.e., greater than 200%), the distribution of hydrate sized agrees well with that found by Giauque et al. for solid H2O–H2SO4 mixtures. Hydrate formation can exert an appreciable effect on the process of vapor phase nucleation in H2O–H2SO4 mixtures, and must be considered in any theory of nucleation rate.

Avoided intersection of potential energy surfaces: The (H+ + H2, H + H2+) system

Nonempirical electronic structure calculations have been carried out on the two lowest 1A1 states of H 3+. When one proton is infinitely separated from the other two, these 1A1 potential surfaces cross each other. The nature of this avoided intersection is examined by means of potential curves, contour diagrams, and perspective plots. Surface hopping is discussed within a Landau-Zener-Stuckelberg (LZS) framework and the LZS assumptions concerning the surfaces are shown to be reasonable near the avoided intersection. Ab initio LZS parameters are compared with those obtained from the semiempirical diatomics-in-molecules surfaces of Preston and Tully. The agreement is good, better than might have been anticipated.

Dynamics of the Collinear H+H2 Reaction. I. Probability Density and Flux

The time evolution of the collinear H+H2 reaction as given by classical mechanics and by time-dependent quantum mechanics has been studied. The calculations employed the Porter–Karplus potential surface. The relevant equations of motion were solved to high accuracy by direct numerical integration. The evolution of the quantal probability density in the interaction region of the potential surface is shown in a series of perspective plots. Classical mechanics gives an amazingly good description of the probability density and flux patterns during most of the reaction; however, the classical and quantal descriptions begin to diverge near the end of the reaction. Essentially, the classical reaction terminates before the quantal reaction. The dynamic behavior of the reaction is hydrodynamically turbulent, as shown by transient whirlpool formation on the inside of the reaction path. All results reported in this paper are for one average system energy, namely, 0.65 eV (initial average translational energy = 0.38 eV).

Numerical Solution of the (1s1s) and (1s2s) Hydrogenic Pair Equations

The pair functions which determine the exact first-order wave function for the ground state of the three-electron atom have been found with the matrix finite-difference method. The second- and third-order energies for the $(1s1s)^{1}S$, $(1s2s)^{3}S$, and $(1s2s)^{1}S$ states of the two-electron atom are presented along with contour and perspective plots of the pair functions.