Computational studies of first-born scattering cross sections II. Moment-theory approach

Margoliash, D. J.; Langhoff, P. W.

doi:10.1016/0021-9991(83)90115-8

Cited by 3 publications

(1 citation statement)

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“…It will be recalled in the above connection that Lanczos−Krylov sequences generated from a given test function (eq 14) constitute optimal invariant subspaces for representations of the associated spectral density, regarded as a function of the energy E α , and, accordingly, are also optimal for corresponding representations of spectral integrals over this measure. , Experience has shown that finite sequences of L 2 Lanczos−Krylov functions can span ever-increasing spatial regions with increasing order, avoid the near linear dependence associated with Rydberg series limits, give pointwise convergent Stieltjes approximations to low-lying discrete states, provide packet-like representations of high-lying discrete and continuum states over finite but large spatial intervals, and give rapidly convergent one-electron transition densities of the type required in evaluation of eq 15. , The formalism furthermore provides rigorous upper and lower bounds on the (cumulative) distribution derived from the density of eq 15. Issues related specifically to the k dependence of Lanczos−Krylov sequences of functions have also been discussed earlier in the context of closely related generalized oscillator-strength densities …”

Section: Implementations Of the Formal Developmentmentioning

confidence: 95%

Spectral Theory of Physical and Chemical Binding^,

Langhoff

1996

J. Phys. Chem.

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A spectral method which provides unified quantum mechanical descriptions of both physical and chemical binding phenomena is reported for constructing the adiabatic electronic potential energy surfaces of aggregates of atoms or other interacting fragments. The formal development, based on use of a direct product of complete sets of atomic spectral eigenstates and the pairwise-additive nature of the total Hamiltonian matrix in this basis, is seen to be exact when properly implemented and to provide a separation theorem for N-body interaction energies in terms of response matrices which can be calculated once and for all for atoms and other fragments of interest. Its perturbation theory expansion provides a generalization of familiar (Casimir−Polder) second-order pairwise-additive and (Axilrod−Teller) third-order nonadditive interaction energies, expressions which are recovered explicitly in the long-range-dipole expansion limit. A program of ab initio computational implementation of the formal development is described on the basis of use of optimal (Stieltjes) representations of complete sets of discrete and continuum atomic spectral states, which provide corresponding finite-matrix representations of the Hamiltonian. The widely employed pairwise-additive approximation to nonbonded N-body interaction energies is obtained from these implementations in appropriate limits. Additionally, the development clarifies and extends rigorously diatomics-in-molecules approaches to potential-surface construction for bonding situations, includes the effects of state mixing and charge distortion missing from semiempirical and perturbation approximations commonly employed in theoretical studies of collision broadening and trapped-radical spectroscopy, and encompasses and demonstrates equivalences among these apparently dissimilar approaches in appropriate limits. Large non-pairwise-additive contributions to the lowest-lying potential energy surfaces are found in illustrative studies of the structure and spectra of physically bound Na−Ar N cryogenic clusters.

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