Paul M. Holland

The thermochemical properties of gas‐phase transition metal ion complexes

Gas phase ion clustering reactions of the form A+(L)n+L⇄A +(L)n+1 were studied using high pressure mass spectrometry. Equilibrium constants together with enthalpy, entropy, and free energy changes were determined for stepwise clustering reactions of water about the Ag+ ion with n=0 to5 and the Cu+ ion with n=2 to4, ammonia about the Ag+ and Cu+ ions from n=1 and n=2 to4, respectively, and pyridine about the Ag+ and H+ ion from n=2 and n=1 to  3, respectively. These results, together with those of other studies, show evidence for the existence of structure in some cluster ions. Considerations of bonding and entropy, together with comparisons with the results of ion chemistry in the liquid phase, suggest that such structures can be attributed to several types of cluster ion systems, including gas phase analogs of traditional ’’coordination complexes’’ known in the aqueous phase.

The properties of ion clusters and their relationship to heteromolecular nucleation

Ion induced heteromolecular nucleation may be formulated in terms of either a kinetic or a steady‐state thermodynamic model. In the case of the former, nucleation is expressed in terms of the rate constants of the individual association reactions leading to the formation of the ion cluster prenucleation embryos. The thermodynamic approach, on the other hand, leads implicitly to the concept of an energy barrier to nucleation. The two formulations are examined in detail and shown to be complementary. An assessment of the validity of the classical charged liquid drop expression, referred to as the Thomson equation, is made by comparing predicted and experimental values. Although the equation is shown to be useful for calculating the enthalpies of ligand attachment to ions at moderate and larger cluster sizes, in the case of entropies it is only moderately successful for hydration reactions and totally fails for ammonia clustering about ions. It is concluded that the Thomson equation is inadequate for treating the general heteromolecular phenomenon and that methods which are able to effectively take large numbers of configurations into account offer the most promise in describing the molecular properties of clusters. Experimental entropy data indicate that the structures of certain ion clusters are more ordered than accounted for by the classical charged liquid drop formulations. Further examination of these data in light of the Sakur–Tetrode equation indicates the existence of low lying excited internal vibrational modes in ion clusters. These considerations suggest that vibrational frequencies on the order of 1.7×1012 sec−1 are present in clusters of two or more ligands.

A model for the formation and stabilization of charged water clathrates

A model for the formation and stabilization of charged water clathrates is presented which accounts for observed anomalies in H+(H2O)n ion distributions. These anomalies are observed in both ion cluster and neutral expansions and are consistent with the sizes expected for clathrate ions. That the same sizes are observed in both ion cluster and neutral expansions strongly suggests that a rapid ionic process is responsible for their formation. The proposed model is based on the high mobility and bonding effects of the ’’excess’’ proton in water. Computer simulations suggest that ’’excess’’ proton movement in a water clathrate would be suitable for stabilizing the clathrate structure as well as giving it access to a large number of nearly degenerate proton configurations. The formation of clathrates in charged water clusters of proper size can be ascribed to the following: rapid ’’excess’’ proton movement, a strong preference of the H3O+ for a 3‐coordinate bonding structure (which is compatible with hydrogen...

Binary collision dynamics and numerical evaluation of dilute gas transport properties for potentials with multiple extrema

Prediction of gaseous transport properties requires calculation of Chapman–Enskog collision integrals which depend on all possible binary collision trajectories. The interparticle potential is required as input, and for a variety of applications involving monatomic gases the Hulburt–Hirschfelder potential is useful since it is determined entirely from spectroscopic information and can accomodate the long‐range maxima and minima found in many systems. Hulburt–Hirschfelder potentials are classified into five distinct types according to their qualitative binary collision dynamics, which in general can be quite complex and can exhibit ’’double orbiting’’, i.e., a pair of orbiting impact parameters for a single energy of collision. The collision integral program of O’Hara and Smith has been revised extensively to accomodate all physical cases of the Hulburt—Hirschfelder potential, and the required numerical methods are described and justified. The revised program substantially extends the range of potentials f...

Gas phase complexes: considerations of the stability of clusters in the sulfur trioxide—water system

Abstract Calculations of the structure of H2SO4, the SO3·H2O adduct, and the magnitude of the barrier between them, were made with the CNDO/2 method. The results suggest the importance of small cluster formation in the gas phase reaction of SO3 and H2O, and offer an explanation for its observed rapid rate.

Ion association processes and ion clustering: Elucidating transitions from the gaseous to the condensed phase

Abstract Current understanding of the properties, structure, and mechanisms of formation of small clusters formed by the attachment of molecules to ions is reviewed. The work is shown to have a bearing on an understanding of the nature of small complexes which are observed to form in the ionizers of mass spectrometers, in radiolysis, in the widely differing conditions present in combustion processes, the weakly ionizing plasma surrounding the earth, and in interstellar media. Particular emphasis is given to the application of the results to the field of interphase physics which is concerned with elucidating the details of the collective effects responsible for nucleation phenomena, the development of surfaces, and the solvation of ions in the condensed state.

Transport properties of monatomic carbon

Transport properties of monatomic gases depend on the two‐body atom–atom interaction potential. When two ground state carbon atoms interact, they can follow any of 18 potential energy curves corresponding to the C2 molecule. Accurate representations of these curves have been obtained for each of the 18 states and transport collision integrals have been calculated for each state. Those states with an attractive minimum in the potential have been represented by the Hulburt–Hirschfelder potential and the purely repulsive states have been represented by the exponential repulsive potential. The collision integrals are compared with results obtained in previous studies. The effects of the details of the potential on the resulting transport collision integrals are discussed.

Studies of the structure and bonding of inorganic clusters

Abstract Thermodynamic properties are given for the reactions: Na + (SO 2 ) n + SO 2 ⇌ Na + (SO 2 ) n +1, n= 1 to 3 , Ag + (H 2 O) n + H 2 O ⇌ Ag + (H 2 O) n+1 , n = 0 to 5 , Ag + (NH 3 ) n + NH 3 ⇌ Ag + (NH 3 ) n+1 , n = 2 to 4 . Comparisons are made, using these and previous data, between Na+ and Cl− in the clustering of H2O and SO2 and between Ag+, K+ and Na+ in the clustering of H2O and NH3.

Calculation of the thermophysical properties of ground state sodium atoms

Transport properties of dilute monatomic gases depend on the two body interaction potentials between the atoms. When two ground state sodium atoms interact, they can follow either of two potential energy curves corresponding to the Na2 molecule in the X 1Σ+g or the 3Σ+u state. Transport collision integrals and second virial coefficients of monatomic sodium have been calculated by accurately representing quantum mechanical potential energy curves with the Hulburt–Hirschfelder potential. The generally good agreement of calculated viscosities and second virial coefficients with the available experimental viscosities and with previously calculated virial coefficients provides further evidence that this approach can be used for accurate estimates of thermophysical properties under conditions where experimental data are sparse or unavailable.

Thermodynamic properties of nitrogen molecules at high temperatures

Calculations of the second virial coefficients and their derivatives for the Hulburt-Hirschfelder (HH) and other accurate interaction potentials are used to determine the thermodynamic properties of nitrogen at high temperatures. Unlike the usual methods employing partition functions, which are most accurate at low temperatures where the energy levels are precisely known, the virial coefficient method depends on integrating over potential energy functions which provide a useful description of energies even near the top of the potential well, a region where the vibrational-rotational energy levels are not readily accessible. This makes this method particularly useful for predicting high-temperature properties outside the range of laboratory measurements and beyond the useful limits of the partition function approach. In the present work, we use the virial coefficient method to predict the heat capacities and enthalpies of nitrogen up to 25,000 K.