Dudley R. Herschbach

Anharmonic Potential Constants and Their Dependence upon Bond Length

Empirical study of cubic and quartic vibrational force constants for diatomic molecules shows them to be approximately exponential functions of internuclear distance. A family of curves is obtained, determined by the location of the bonded atoms in rows of the periodic table. Displacements between successive curves correspond closely to those in Badgers rule for quadratic force constants (for which the parameters are redetermined to accord with all data now available). Constants for excited electronic and ionic states appear on practically the same curves as those for the ground states. Predictions based on the diatomic correlations agree with the available cubic constants for bond stretching in polyatomic molecules, regardless of the type of bonding involved. Some implications of these regularities are discussed.

Influence of Vibrations on Molecular Structure Determinations. II. Average Structures Derived from Spectroscopic Data

Formulas are given which enable structural parameters for the average molecular configuration in the ground vibrational state to be calculated for some simple types of molecules. The data required are the observed effective moments of inertia and harmonic force constants. No knowledge of anharmonic constants is necessary. The average structural parameters have a well‐defined physical meaning and are directly comparable with diffraction results. Polyatomic molecules for which explicit calculations are given are CO2, CS2, H2O, SO2, O3, NO2, CH4, HCN, and C2H2. It is found that the average bond lengths involving H are usually 0.003–0.005 A longer than the corresponding D bond. For bonds involving heavier elements isotopic differences are smaller but nonetheless significant. Implications of the results for the general problem of structural determination are discussed.

Influence of Vibrations on Molecular Structure Determinations. III. Inertial Defects

The relationships between various types of moments of inertia and vibration—rotation corrections are developed from general theory, with emphasis on the qualitative physical features and the quantities which may be calculated without knowledge of anharmonic force constants. The inertial defects of planar triatomic and tetratomic molecules and nonplanar molecules with a plane of symmetry are considered, and it is found that simple approximations, which depend mainly on the one or two modes of lowest frequency, give results within 10%—20% of the experimental values. The application of inertial defect corrections in structure analysis is illustrated for the calculation of HH distances in CH2Cl2, SiH2F2, and CH3CXO molecules (X = H, F, Cl, Br).

Molecular Beam Kinetics: Reactions of Alkali Atoms with NO2 and CH3NO2

Magnetic and electric deflection analysis of the scattering of Cs + NO2 shows that the principal product is a paramagnetic, polar molecule. Magnetic analysis of the K + NO2 system indicates that the scattered signal is paramagnetic; a similar study of Na + NO2 shows a small yield of diamagnetic product. For the analogous reactions with CH3NO2, the product is diamagnetic and has a pseudo‐first‐order Stark effect. From these data and thermochemical arguments the principal alkali‐containing products are identified as: for Cs + NO2, a 2Σ electronic state of CsO; for Na + NO2, probably a 2Π state of NaO; for M + CH3NO2, almost certainly MNO2 in a singlet state. The NO2 results indicate that the ground state of the MO molecule changes from 2Π for LiO (the only species which had been previously observed) to 2Σ for CsO. The usual differential surface ionization detection fails for Cs + NO2 and consequently only a very rough estimate of the scattering is obtained; this indicates that the total reaction cross secti...

Reactive Scattering in Crossed Molecular Beams. K Atoms with CH3I and C2H5I

Beams of K atoms are caused to cross beams of CH/sub 3/I or C/sub 2/H/ sub 5/I at an angle of 90 deg , and the angular distributions of reactively scattered KI are measured. The distributions are explained in terms of beam temperatures, cross sections, and reaction energies. Wand Pt-W detectors are used. (T.F.H.)

Empirical Evaluation of the London Potential Energy Surface for the H + H2 Reaction

An empirical potential surface for the hydrogen exchange reaction is derived from the simplest form of the London approximation (neglecting overlap), by evaluating the Coulomb and exchange integrals from the potential curves for the 1Σg+ and 3Σu+ states of H2. This procedure gives an activation energy of 8.9±1.2 kcal/mole, in good agreement with the experimental value of 8.0±0.5 kcal/mole. The potential surface has a single saddle point, and the H: complex is linear and symmetrical, with a bond length of 0.96 A. Simple, explicit formulas for the activation energy and the vibrational force constants are also obtained. The results emphasize the important contribution from the triplet repulsion between the end atoms with parallel spins in the complex.

Molecular Beam Kinetics: Reactions of K Atoms with Alkyl Iodides

Angular distributions of reactively scattered KI have been measured for several K+RI reactions, with R=CH3, C2H5, n‐ and i‐C3H7, n‐, i‐, s‐, and t‐C4H9, n‐C5H11, and n‐C7H15. The reaction cross sections are roughly ∼30 A2 and the activation energies are undetectably small, <0.5 kcal/mole, for the whole series of reactions. The laboratory angular distributions are strongly anisotropic. A qualitative analysis which requires only the conservation laws for energy and momentum shows that these reactions proceed predominantly via a “rebound” mechanism: An observer stationed at the center of mass would see most of the KI recoil into the backward hemisphere (and the R group forward) with respect to the incoming K beam. The kinematic analysis also indicates that for K + CH3I roughly half (60% ± 20%) of the energy of reaction (∼15 ± 5 out of ∼25 kcal/mole) appears as internal excitation of the products, probably mainly in vibrational excitation. As the size of the R group is increased, the backward peaking of the ...

COLLISION MECHANICS IN CROSSED MAXWELLIAN MOLECULAR BEAMS

A general treatment of the mechanics of collision between two Maxwellian molecular beams is described. Expressions are obtained for the distribution in collision energy, for the elastic and reactive collision rates, and for the angular distribution of the center of mass vectors for beams colliding at any angle. The treatment can accommodate any reaction cross section which can be expressed as a step function multiplied by a linear combination of powers of the relative energy.The recoil momentum which affects the product distribution in the laboratory system is discussed, and the treatment is applied to some experimental data on the reaction of K with HBr.

Molecular beam kinetics: Optical model for reactive scattering of alkali atoms and alkyl iodides

Angular distributions of reactively scattered alkali iodides have been measured for reactions of thermal beams of Rb and Cs atoms with beams of alkyl iodides RI, where R=CH3, C2H5, n‐ and i‐C3H7, n‐C4H9, and n‐C5H11. When shifts expected from kinematic differences are taken into account, the qualitative features are found to confirm the results previously obtained for the analogous K atom reactions. The reaction cross sections increase with the size of the alkali atom, from ∼35 A2 for K+CH3I to ∼45 A2 for Rb and ∼75 A2 for Cs. The fall off in intensity of elastically scattered alkali atoms at wide angles also increases for K→Rb→Cs. The anisotropic angular distribution of products, the magnitude of the reaction cross section, and the fall off of the wide‐angle elastic scattering for the K, Rb, and Cs systems are correlated in terms of an extended optical model which simply assumes hard sphere interactions for both the entrance and exit trajectories. The reaction probability derived from the data by use of ...

Analysis of Reactive Scattering in Crossed Molecular Beams

Several effects that must be taken into account in an intempretation of results obtained in a study of the K + HBr -H + KBr reaction in crossed molecular beams are discussed. If the collision yield is measured at a fixed laboratory angle while the speed of one of the beams is varied, the orientation of the velocity vector and the center-ofmass vector with respect to the direction of observation will change continually. This would cause the dependence on the velocity vector and the dependence on the angle between the velocity vectors to be superposed in the results. Results indicated that thds would causs a modification of the results obtained for relative initial kinetic energy. (M.C.G.)