Lue‐Yung Chow Chiu

Lifetimes of fine structure levels of metastable H2 in the c 3Πu state

Lifetimes of fine structure levels of the v=0 level of the metastable c 3Πu state of H2 are calculated by considering both the forbidden predissociation and the forbidden radiative transition to the same dissociative b 3Σu+ state as the competing decay processes. The decay rate Wp due to forbidden predissociation is calculated for the rotational level N=1 of ortho‐H2 and N=2 of para‐H2. The weak spin–orbit and spin–spin interactions are the perturbative interactions to mix the metastable c 3Πu state with the repulsive b 3Σu+ state. For the fine structure levels J=N, the forbidden predissociative decay rate Wp calculated is approximately 14 times larger than the previously calculated radiative decay rate Wr. The resulting lifetimes for these J=N levels (which are 0.12 msec for N=1 and 0.11 msec for N=2) are shorter than the detection limit of Johnson’s time of flight experiment. For the fine structure levels J=N±1, Wp is approximately 1/3 of Wr (except for case J=N−1=0, where Wp=0) and the resulting lifeti...

Multicenter molecular integrals of spherical Gaussian functions by Fourier transform convolution theorem

The two‐electron four‐center integral of the homogeneous solid spherical harmonic Gaussian‐type functions (GTF’s), r2n+lYlm(r)exp(−αr2), has been evaluated analytically by decomposing it into a linear combination of two‐center integrals through coincidence of centers. The two‐electron two‐center integrals are integrated analytically through the Fourier transformation convolution theorem. A compact integration formula is obtained for a general two‐electron irregular solid spherical harmonic operator [4π/(2L+1)]1/2YLM (r12)/r(L+1)12. This formula is applied to evaluate two‐center integrals of the Coulomb repulsion, the spin–other–orbit interaction and the spin–spin interaction by letting L=0, 1, and 2, respectively. The integration results are in terms of the spherical Laguerre GTF’s, Ln′l′+1/2(σR2)Rl′Yl′m′ ()exp(−σR2), of the relative nuclear coordinate plus one error‐type F‐function term. One‐electron multicenter integrals have also been evaluated through Fourier transformation convolution theorem. The...

A rotational‐dependent analytical solution to the dissociative state: Application to b 3Σ+u state of H2

The rotational‐dependent potential for a dissociative state is represented by U(r)=U0+B1/r +B2/r2+[N(N+1)−Λ2]/2Mr2. An analytical solution ψE(r) of the Schrodinger radial equation, valid for all regions of internuclear distance r and energy E, is obtained in terms of confluent hypergeometric function of the complex arguments. The solution is evaluated by expanding the confluent hypergeometric function onto a basis set of shifted Chebyshev polynomials. The expansion coefficients are recovered by a backward recursion technique. The summation process of Chebyshev polynomials converts a slowly convergent series or a divergent asymptotic series into a rapidly convergent one. The solution thus obtained is applied to calculate the vibrational wave function of the dissociative b 3Σ+u state of H2 to compare with the previous semiclassical WKB wave function. The solution of the rotational‐corrected Morse potential is used for the upper bound c 3Πu state. The bound‐continuum Frank–Condon overlap amplitude is compute...

Spin–Spin Interaction and the Energy Splitting of the Rovibronic Levels of a Linear Triatomic Molecule

Spin–spin interaction and spin–orbit interaction are both considered in studying the fine structure energy splitting of a rovibronic level. The molecule under study is linear triatomic and in the 3Π state. The first‐order spin–orbit interaction is found to be zero except for the vibronic level with K = υ2 + 1, and the first‐order fine structure splitting is therefore due to spin–spin interaction only. By nature of the second‐rank tensor, the spin–spin interaction is also shown to split the over‐all inversion symmetry pairs, namely the + and − of certain J levels. Hunds case a, case b and intermediate cases are considered. The energy of a fine structure level is expressed explicitly in terms of all the quantum numbers and coupling constants such that direct experimental comparison can easily be made. Examples of υ2 = 1 and υ2 = 2 are worked out in detail.

Point‐group selection rules for ΔS=2 multiplicity change: Application to catalysis and organo‐transition metal reaction

Electron spin–spin and second‐order spin‐orbit interaction operators are expanded as products of irreducible representations of symmetry point groups (Oh, Td, D5d, D6d, and C4v). From the transformation of the separated orbit and of the spin part, the selection rules for off‐diagonal matrix elements may be deduced by taking direct products of the ‘‘initial’’ and ‘‘final’’ states. The special ΔMl selection rule for the orbital part of spin–spin interaction after expansion is also discussed. Emphasis is given to the ΔS=2 change connected by these operators. Possible examples of ΔS=2 change in d4, d5, and d6 configurations under the above mentioned point groups are given. As illustrations of the selection rules, the matrix elements for ΔS=2 and ΔMs=2 for these configurations are evaluated in the decoupled representation and given in terms of common parameters. The relevance of these multiplicity change to catalysis and reaction of organo‐transition metal complexes is briefly alluded to.

Excitation transfer between fine structure levels: Angular dependence of the sensitized fluorescence

Excitation transfer is studied theoretically as an integral part of sensitized fluorescence, which is a third order time‐dependent process, namely the excitation of the absorber atom, followed by the transfer of excitation from this atom to the receiver atom and finally the emission of sensitized fluorescence from the receiver atom. The phase correlation transmitted through such a third order process gives rise to the angular distribution of sensitized fluorescence which is shown to depend on the fine structure levels of both atoms. Long range electric dipole‐dipole interaction is used as the mechanism for excitation transfer. Plane wave motion is assumed for the relative motion between two interacting atoms. A general formula is derived for the relative intensities (hence relative cross sections) of the sensitized fluorescence, involving different sets of fine structure levels. This cross‐section ratio turns out to be angular dependent but nevertheless is shown to be expressible in a very simple form whi...