D. R. Herschbach

E.S.R. spectra of matrix isolated alkali atom clusters

E.S.R. spectra assigned to Na3 molecules have been obtained by codepositing sodium atoms and diluent argon on a sapphire surface loosely coupled to a liquid helium cryostat and warmed by a heat leak, to allow aggregation before the alkali atoms are frozen into the argon matrix. The trimer spectra under these conditions were much more intense than the residual atom spectra. The trimer spectra indicate the unpaired electron in these molecules has predominantly s rather than p character. Approximately 95 per cent of the 3s spin density is equally distributed between two of the alkali atoms, with only about 7 per cent of the spin density on the third atom. The trimers thus are not merely van der Waals adducts but involve chemical bonding. Both a covalent molecular orbital model for linear or obtuse isosceles geometry and an ionic charge-transfer model giving M2 +M- or M+M2 - appear qualitatively consistent with the spectra.

Dimensional interpolation for two‐electron atoms

The ground‐state electronic energy of helium‐like atoms is calculated by interpolating between exact solutions for the limiting cases of one‐dimensional and infinite‐dimensional systems. In suitably scaled coordinates, the D=1 limit corresponds to replacing the Coulombic potentials by delta functions. With another choice of scaling, the D=∞ limit reduces to a classical electrostatic problem; the electrons take fixed positions that correspond to replacing wave functions with delta functions. The ground‐state energy for arbitrary dimension D and nuclear charge Z can be represented as eD=e∞[1+c1/D+c2/D2+F(D,Z)/D3]. The first three terms are obtained from a perturbation expansion about D=∞; these correspond, respectively, to the limiting rigid electronic structure (envisioned by G. N. Lewis!) and to harmonic and anharmonic vibrations about that structure. The interpolation function F(D,Z) is approximated as a geometric series, determined by fitting the accurately known energies for the D=1 limit and for D=5. ...

Molecular beam kinetics: Angular distributions and chemiluminescence in reactions of alkali dimers with halogen atoms and molecules

Crossed−beam studies are presented for several reactions of diatomic alkali molecules with halogen atoms and molecules. The alkali dimers are generated by association of atoms in a supersonic nozzle expansion, the halogen atoms by thermal dissociation of molecules. For both the X + K2 and X2 + K2 reactions (X = Cl, Br), the angular distributions of reactively scattered KX peak forwards (in the center−of−mass system) with respect to the incoming alkali dimer, the final relative translational energy of products is fairly high, ∼10−20 kcal/mole, and the total reaction cross sections are large, ∼50−150 A2. For the X + A2 reactions (X = Cl, Br, I; A2 = Na2, K2, Rb2), excited alkali atom emission is observed from nearly all energetically accessible transitions which fall within the spectral range of the experiments (2200−8000 A). Some of these lines come from states located above the reaction exoergicity and thus indicate that the initial relative translation of the reactants is converted into electronic excita...

Statistical theory of angular distributions and rotational orientation in chemical reactions

For A+BC→AB+C exchange reactions governed by a statistical collision complex, a large class of directional properties dependent on the rotational orientation of reactant or product molecules are shown to be determined by only two parameters, Λ=〈l/(l+j) 〉 and Λ′=〈l′/(l′+j′) 〉. Here l and l′ are the initial and final orbital angular momenta and j and j′ the rotational momenta of the reactant and product molecules. The angular distribution and the spatial orientation or polarization of the rotational momentum of product molecules are treated in detail. A classical form of statistical theory is used in which the directional properties are determined by Legendre moments involving averages over various unobserved angles between angular momentum vectors. Numerical formulas that give these averages in terms of Λ and Λ′ are derived from phase space calculations for a wide variety of reaction systems. Comparisons with previous treatments of product angular distributions involving other parameters show these can likewise be expressed in terms of Λ and Λ′. Methods are discussed for estimating these parameters and relating them to other reaction properties.

ESR of matrix isolated alkali superoxides

Abstract ESR spectra of NaO2, KO2, RbO2, and CsO2 in rare gas matrices are consistent with an ionic M+O2− model of isosceles symmetry, in accord with recent vibrational spectra. However, the ESR for CsO2 also shows evidence for an inversion of the uppermost occupied molecular orbitals which can be attributed to a slight covalent mixing of the oxygen valence orbitals with the inner-shell p-orbitals of the metal.

Vibrational frequency shifts induced by molecular compression of pyridine in solution

Pressure‐induced vibrational frequency shifts are calculated for a diatomic oscillator immersed in a benign solvent, employing a simplified version of the Schweizer–Chandler model for solute–solvent interaction. The repulsive contribution is determined from the pair distribution function for hard‐sphere cavities. Interpolative evaluation of the pair distribution function is facilitated by noting that to an excellent approximation the pertinent expansion coefficients are merely linear functions of the reduced density. The treatment is applied to the quasidiatomic ring breathing vibrations of neat liquid pyridine, benzene, and toluene and to solutions of pyridine in several solvents including H2O, D2O, CH3OH, CHCl3, dimethylformamide, and toluene. The predicted pressure dependence of the ring breathing frequency is in the range ∂ν/∂P≈0.3–0.8 cm−1/kbar for all these systems. The corresponding compression of the mean ring radius is in the range 0.9 to 2.0×10−4 A/kbar. Especially for the associated solvents, t...

Molecular beam kinetics: Exchange reactions of deuterium atoms with hydrogen halides

A crossed‐beam study finds the reactions of D atoms with HCl, HBr, and HI give large yields of DCl, DBr, and DI, corresponding to reaction cross sections of the order 1–10 A2. This demonstrates that the exceptionally small steric factors or transmission coefficients previously inferred from analysis of chain reaction mechanisms are low by several orders of magnitude. The reactively scattered deuterium halides recoil predominantly into the backward hemisphere with respect to the incident D atoms. In each case, the reaction exoergicity is ∼1 kcal/mole and the mean initial collision energy is 9 kcal/mole (with the D beam at 2800 °K, the hydrogen halide at 250 °K). The most probable final relative translational energy of the products is ≳4 kcal/mole for the HCl and HBr reactions and 7 kcal/mole for the HI reaction. The magnitude of the reaction cross sections and the predominant backward recoil and translational energy of the products are consistent with recent classical trajectory calculations based on semie...

Inversion of orbiting scattering from elastic collisions of reactive molecules

For elastic scattering produced by an attractive, spherically symmetric potential, the classical deflection angle is a single‐valued function for impact parameters equal to or greater than that which gives orbiting at the centrifugal barrier. If reaction removes contributions from smaller impact parameters, the potential in this outer region can be derived from the elastic scattering by a simple inversion procedure. This is obtained by slightly modifying the Firsov method, so as to integrate from small angles inwards. Close to the centrifugal barrier, the scattering is determined primarily by the first and second derivatives of the potential, and an approximate inversion method for obtaining the derivatives is also given. These procedures are applied to data for nonreactive scattering of K atoms from Cl2, Br2, I2, and ICl. The results indicate the orbiting model is a useful approximation for such reactions in the thermal range, although a less simple treatment is necessary at higher energies. The potentia...

Electron correlation calibrated at the large dimension limit

Correlation energies (CEs) for two‐electron atom ground states have recently been obtained to good approximation from a simple perturbation treatment using 1/D as the expansion parameter, with D the dimensionality of space. In hydrogenic units, the CE varies almost linearly with 1/D between limits at D→1 and D→∞ which are exactly calculable. However, for D→∞ the CE is only about 35% smaller than the ‘‘true‐world’’ value at D=3. This is in striking contrast to the analogous error in the mean field approximation of statistical mechanics, which vanishes for sufficiently large D. Here we show that the CE for D→∞ can be made to vanish by modifying the Hartree–Fock (HF) variational wave function. A separable form is retained but a factor Θ(θ) is included, with θ the angle between the electron–nucleus radii r1 and r2. Likewise, the error in the HF value for the first derivative of the energy with respect to 1/D can be made to vanish by employing a suitable choice of coordinates in separate factors of the wave fu...

Asymptotic approximation for ionic-covalent configuration mixing in hydrogen and alkali hydrides

A pseudo-potential treatment of ionic-covalent configuration interaction or curve-crossing is given which employs simple but asymptotically exact wavefunctions and avoids introducing orbital approximations. The asymptotic wavefunctions are determined solely from known atomic parameters: the ionization potential of the donor species and the electron affinnity and Slater atomic radius of the acceptor. The splitting ΔV(R c) between the adiabatic potential curves at the diabatic ionic-covalent crossing radius R c and the potential curves for R⪸R c are derived from two and three-state secular equations. Results are given for excited electronic states of H2, particularly the B 1Σ u + state which involves interaction of H(1s)+H(2s, 2p) and H++H-(1s2) configurations, and for the ground and several excited 1Σ+ states of LiH and other alkali hydrides. Comparisons with spectroscopic data and various theoretical calculations show that for large R c the simple asymptotic approximation gives good accuracy, within 10–20...