R. N. Porter

H3 +: Abinitio calculation of the vibration spectrum

The vibration spectrum of H3 + is calculated from the representation of a previously reported [J. Chem Phys. 60, 4251 (1974)] ab initio potential‐energy surface in a fifth degree Simons–Parr–Finlan (SPF) expansion. Morse‐ and harmonic‐oscillator basis functions are used to describe the motions of the three oscillators and the Harris–Engerholm–Gwinn quadrature technique is used to obtain matrix elements of the Hamiltonian in the basis of vibrational configurations. Our variational method is thus analogous to configuration– interaction calculations for electronic states. The ground state is found to have a zero‐point energy of 4345 cm−1 and a vibrationally averaged geometry of R1=R2=0.91396 A, ϑ=60.0012°, where ϑ is the angle between the two equivalent bonds. The transition frequencies for the E and A1 fundamentals are ?E=2516 cm−1 and ?A=3185 cm−1 and those for the corresponding first overtones of the bending mode are 2?E=5004±4 cm−1 and 2?A=4799 cm−1. The first overtone of the breathing mode is 6264 cm−1....

Quasiclassical selection of initial coordinates and momenta for a rotating Morse oscillator

The classical orbits of a rotating Morse oscillator are calculated by means of Hamilton–Jacoby theory after truncating the Hamiltonian to permit analytical solution. Except at very high J, the approximate analytic orbit for the radial coordinate is in good agreement with that obtained by numerical integration of the exact equations of motion. Bohr quantization gives an expression for the rotation–vibration energy correct through quadratic terms in (v+1/2) and J (J+1), where v and J are the vibrational and rotational quantum numbers, respectively. The principal result is an analytic prescription for obtaining values of the coordinates and momenta, given v, J, and a set of random numbers, that facilitates properly weighted quasiclassical selection of initial states of diatomic molecules in trajectory calculations.

H3+: Geometry dependence of electronic properties

As the first step to the ab initio calculation of the vibration‐rotation spectrum of the H3+ ion, we present results of configuration‐interaction calculations of the potential‐energy surface and the geometry‐dependent electric dipole and quadrupole moments for the ground electronic state. Interpolation on the potential‐energy surface, required for setting up the Hamiltonian matrix for nuclear motion, is facilitated by use of generalized Morse functions and Fourier analysis. An analysis of the equilibrium geometry and harmonic force constants is based upon the present and previous calculations. We conclude that H3+ has its potential minimum in an equilateral geometry with bond distances of 1.65 a.u. and harmonic frequencies ωA=3471 cm−1 and ωE=2814 cm−1.

Classical dynamical investigations of reaction mechanism in three‐body hydrogen‐halogen systems

A theoretical investigation of the reaction mechanisms in eight different three‐body hydrogen‐halogen reactions has been accomplished by means of Monte Carlo averages over classical trajectories computed on reasonable semiempirical potential‐energy surfaces. Two of the surfaces employed contain a single adjustable parameter characteristic of a halogen core charge while six others result from unadjusted computations. The analysis shows that dynamic effects resulting from momentum transfer require the reactions M2+X=MX+M (M=H,D, or T; X=Br or I) to proceed through excited vibrational states of M2. Reaction of the ground vibrational state is dynamically forbidden in each case. Reaction rate coefficients, associated activation energies, pre‐exponential factors, and kinetic isotope effects calculated from rotationally averaged reaction cross sections are in reasonable agreement with experiment. The computations further suggest an origin for the isotope effect that is significantly different from that derived f...

Dynamics of the Molecular and Atomic Mechanisms for the Hydrogen‐Iodine Exchange Reaction

Theoretical treatment of both the molecular and atomic mechanisms for the hydrogen‐iodine exchange reaction (H2+I2→ 2HI) is accomplished by means of extensive classical trajectories calculated on a reasonable potential‐energy surface in which the single adjustable parameter is the iodine‐core effective charge. The analysis shows the molecular mechanism to be dynamically forbidden, but gives an over‐all rate constant for the atomic mechanism in substantial agreement with the experimental values. The formation of a weak H2I complex is predicted to play an important dynamical role if the atomic mechanism is limited to reactions with collision complexes involving no more than two hydrogen atoms and two iodine atoms. Excellent agreement with experiment is obtained for the rate constant for the recombination I+I+H2→ I2+H2 and its negative temperature coefficient. Trajectories for the latter reaction are rich in multiple exchange of internal energy between the molecular species, but the formation of H2I is predi...

Classical Trajectory Methods in Molecular Collisions

The dynamics of a molecular scattering process is described in exact terms by the solutions to the Schrodinger equation in which the kinetic energy and the electrodynamical interactions of all the nuclei and electrons of the colliding partners are used. If the process to be studied can be assumed to be adiabatic, the Born-Oppenheimer separation can be invoked, and the Schrodinger equation for the scattering is reduced to the problem of nuclear motion on a potential energy surface known as a function of all the internuclear distances. The accuracy of quantum mechanical calculations of the measurable attributes of molecular collisions is limited only by the accuracy of the potential energy surface and by the number of basis functions that can be afforded in terms of computer core storage size and processing time. The technical and economic questions are therefore 1 How accurate must a calculation be in order to test predictions of a given theory against a given experimental result, and how is this accuracy most efficiently achieved? 2 What calculational expense is commensurate with the scientific value of the result?

Correlated wavefunctions, energies, and one‐electron radial densities for S states of the He atom

A priori approximation of integral‐transform wavefunctions by Gauss quadrature provides an efficient and simple method for obtaining a finite approximation to the complete set of eigenfunctions of the Hamiltonian of a two‐electron atom. These functions are described, and the energies and one‐electron radial densities of the lower‐lying S states of the He atom and the. ground state of H− are given. The energies are close to the exact values obtained from conventional variational results with Hylleraas‐type functions extrapolated to the limit of an infinity of terms. The one‐electron radial densities of the S states of He are found to have n −2 pseudonodes, where n is the principal quantum number, the triplet‐state pseudonodes lying slightly closer to the origin than those of the corresponding singlet states.

Comparison of the combined phase‐space/trajectory and quasiclassical trajectory methods in the study of reaction dynamics: H + I2 and H + Br2

Results for the combined phase−space/classical trajectory (CPST) and standard quasiclassical trajectory (SQCT) procedures for investigating the dynamics of homogeneous gas−phase reactions are compared in the case of H + X2 → HX + X (X = Br or I). The relative absence of dynamical effects for these systems permits SQCT calculations with low statistical error and would seem to enhance the validity of the basic assumptions of CPST. The high reduced mass of X2 also reduces differences between CPST and SQCT that arise from quantization of internal X2 states in the latter method. When the critical phase−space surface is chosen so that its configuration−space projection traverses only regions of low three−body interaction (< 2 kcal/mole), the CPST computed rate coefficients and angular distributions are in qualitative accord with SQCT results. When phase−space points on the critical surface are integrated back into the reactant phase space, nonequilibrium distributions are obtained for the distribution of relati...

Classical dynamics of triatomic systems: Energized harmonic molecules

The dynamical assumptions underlying the Slater and RRK classical‐mechanical theories of unimolecular reaction rates are investigated. The predictions of these theories for several nonlinear, triatomic, harmonically bonded molecular models are compared with the results obtained from the integration of the classical equations of motion. The accuracy of the small‐vibration and weak‐coupling assumptions are found to break down at energies above about one‐quarter of a bond dissociation energy. Nonetheless, the small‐vibration approximation predicts reaction frequencies in good agreement with the exact results for the models. The effects of rotation on intramolecular energy exchange are examined and found to be significant.

Reduced Green’s functions and perturbed Hartree–Fock calculations. I. Formulation of the theory

A diagrammatic analysis is developed to implement the derivation of a set of integral equations for first‐order coupled perturbed Hartree–Fock orbitals in the presence of a one‐particle perturbation. A general formulation is given in terms of an arbitrary, but well characterized, reduced one‐particle Green’s function so that the difficulties of either obtaining a sufficiently complete set of virtual orbitals or of using an explicit form of the reduced Green’s function corresponding to the Fock operator are obviated.