Grigory A. Natanson

Melting and surface tension in microclusters

Approximate partition functions are constructed from approximate quantum mechanical models of near‐rigid, solidlike and nonrigid, liquidlike clusters. The Helmholtz free energies are evaluated for these clusters as functions of temperature T and cluster size N. The thermodynamic temperatures of melting, at which the free energies of the two forms are equal, match well with the melting temperatures determined from classical simulations of Ar clusters. Moreover, the effective coexistence ranges of temperature for solid‐ and liquidlike forms are approximately the same as the range of ‘‘supercooling’’ and ‘‘superheating’’ found in molecular dynamics computations of Ar. The surface tension is determined from an expansion of the free energy in powers of N−1/3. The concept of melting in small clusters, as a transition from a near‐rigid, small‐amplitude vibrator to a nonrigid molecule capable of frequent passage from one local equilibrium geometry to another, is related to the recent proposal by Stillinger and We...

Unequal freezing and melting temperatures for clusters

Abstract Using a previously introduced quantum statistical model, analyze necessary and sufficient conditions on the density of states for coexistence of liquid and solid clusters. We conclude that clusters of N particles have sharp freezing and melting temperatures limiting the ranges of phase stability and that these temperatures are unequal.

Internal motion of a non-rigid molecule and its relation to the reaction path

The Eckart-Sayvetz and Hofacker-Marcus conditions for separation of large- and small-amplitude motions are discussed. Some advantages of rectilinear vibrational coordinates are outlined and a local equivalence between them and geodesic coordinates is proved. It is shown that the extremum condition for the adiabatic potential and the local Hofacker-Marcus conditions determine a unique geometrical structure of any one-parameter semirigid bound-state model and a unique reaction path in the space of internal variables. These conditions lead to the so-called intrinsic path. Some properties of this path as a particular case of steepest descent (ascent) paths in a Riemann space are analysed. The accurate hamiltonian based on a linear semirigid model and the global Eckart-Sayvetz conditions is projected into the subspace of internal variables describing linear configurations and the resulting extra potential term is discussed.

Calculation of rovibrational spectra of water by means of particles‐on‐concentric‐spheres models. I. Ground stretching vibrational state

A new method is presented to compute bending frequencies and rotational structure in the ground and excited bending states of water‐like molecules. As a zeroth‐order approximation the water molecule is simulated by the two hydrogens confined to move on a sphere around the oxygen. Even the simplest approximation, choosing the radius of the sphere equal to the equilibrium bond length, gives better results for rotational levels than the rigid bender model does. A further improvement for both bending frequencies and rotational energy levels, especially in excited bending states, has been achieved by introducing an effective radius and an effective mass. These are calculated by averaging over stretching motions to reduce the Schrodinger equation to only the rotational and bending degrees of freedom.

Calculation of rovibrational spectra of water by means of particles‐on‐concentric‐spheres models. II. Excited states of stretching vibrations

It is shown that adiabatic separation of high‐frequency stretching modes from bending and overall rotational motions in triatomic molecules XY2 leads naturally to the particles‐on‐a‐sphere (POS) model treated previously [J. Chem. Phys. 81, 3400 (1984)]. Solution of the rovibrational problem using a further approximation in which stretching motions are treated as uncoupled modes is then investigated in detail. It is shown that, for states with a significantly larger number of quanta in one bond than the other, the POS model in this approximation yields energy levels that are essentially identical with those for the particles‐on‐concentric‐spheres (POCS) model, where the latter is obtained using a different decoupling of the basic set of differential equations.

Theoretical intensities for rotation-vibration lines of water using particles-on-a-sphere wavefunctions

Using variational wavefunctions calculated from the particles+m-a-sphere model, and an ab initio electric dipole moment function, we have calculated intensities for the allowed rotation-vibration transitions involving states with J=O, 1, 2 in the pure rotational, v2, and 2v2 bands of water. A comparison of our results with experimental and rigid-rotor intensities suggests that our wavefunctions correctly take into account substantial rotation-bending interactions, but run into difficulties for the 2~5 band, where the neglected stretch-bend interactions are important.

Collective and Independent-Particle Motion in Simple Atoms and Molecules: a Unification?

The evidence is reviewed that implies electrons in doubly-excited states of helium behave like the atoms of a linear triatomic molecule. The relation between molecule-like collective motion and independent- particle, solar-system-like motion is explored via the model problem of two interacting particles on concentric spheres. The state of understanding of independent-particle motion for atoms in small polyatomic molecules is surveyed briefly and the proposal is explored that some small molecules, such as dihydrides, might exhibit independent-particle rotational motion in sufficiently highly excited local mode states.

Particles-on-a-sphere method for computing the rotational-vibrational spectrum of H2O

Abstract An adiabatic separation of fast stretching from slow bending and rotational motion has been made for the water molecule. Two programs are presented; one solves the Schrodinger equation over the radial coordinates to obtain the stretching eigenvalues and eigenfunctions, as well as an effective bending potential and moment of inertia. The second program uses the results of the first as part of the Hamiltonian to solve the Schrodinger equation over the angular variables in order to obtain the rotational-bending levels. The radial program can construct the effective bending potential in either of two ways. The first is to solve the radial equation at only the equilibrium bending angle, and use the resulting wavefunctions to average over the radial coordinates at selected bending angles. The second method is to solve the radial equation at several values of the bending angle, and use the eigenvalues as points on the effective bending potential. The angular program presented here is suitable for using the results from the first method, and may be used with the results of the second method provided that only one value for the moment of inertial is used as input.

Splitting the degeneracy of harmonically-bound identical spinless bosons: Pairwise delta-function potentials

Abstract The formalism developed in Part I is applied to the pairwise δ-function potential. For this purpose the first-order perturbation caused by the δ-potential is expressed in terms of creation and annihilation operators. Splittings of energy levels are calculated for low excited states of three-, four-, and five-particle systems. The correlation diagrams are constructed to connect the energy levels of clusters corresponding to this nearly-nonrigid limit and those of the nearly-rigid molecules calculated in the harmonic approximation. The construction is carried out for an arbitrary pairwise interaction between three or four particles and for the Lennard-Jones potential in the case of the five-particle system.

A choice of the semirigid bender model of the water molecule

Abstract In order to minimize momentum coupling between small- and large-amplitude internal motions special intrinsic semirigid models should be used. The intrinsic model for the water molecule is constructed as a Taylor series in the bending angle. Using sets of ab initio force constants up to quartic, expansions can be found up to and including cubic terms. A polynomial fit to the ab initio value of the bond length of the linear saddle configuration is used to find the quartic term in the expansion.