Calculation of Siegert eigenvalues for molecular systems: results for He(21,3S)+ H

Abstract

The variational calculation of Siegert eigenvalues has previously been shown to provide reliable positions and widths for atomic resonances. This approach is herein extended to molecular problems, and the first such calculations for a molecular autoionizing system, He(2 1 ,3S) + H ~ He + H+ + are reported.

An ab initio study on Penning ionization of a polyatomic target: H2O–He* (2 3S)

“…The atomic systems studied are H-He*͑2 3 S͒, 4 -9 -He*͑2 1 S͒, 4,7,8 He-He*(2 3 S,2 1 S), 10 He*͑2 3 S͒ -He*͑2 3 S͒, [11][12][13] -He*͑2 1 S͒, 12,13 Li-He*͑2 3 S͒, 9,14,15 -He*͑2 1 S͒, 14,15 Na-He*(2 3 S,2 1 S), 9,16 K-He*͑2 3 S͒, 17,18 and -He*͑2 1 S͒. 17 However, a few molecular systems are studied.…”

“…6,8,[19][20][21][22] This reason may be that calculations of resonance potentials ͑V*͒ and widths ͑⌫͒ are difficult. Hickman et al and Cohen et al obtained resonance potentials and widths for the H 2 -He*͑2 3 S͒, 6,19 -He*͑2 1 S͒ 8,19 systems, and performed dynamical calculations based on the potentials and widths obtained. 19, 23 Bentley 20 calculated the H 2 O-Ne* ͑2 3 P͒ potential, and explained the preference of the A 1 ionization.…”

The Siegert methods in resonance scattering: Relation to L2 methods

“…These authors thus demonstrated that the SM could be employed in a more straightforward manner [with Im(k) < 0, throughout]. The purpose of this letter is to shed further light upon this situation by showing that the "tricks" [replacing Im(k) by -Im(k) or bya small positive number] used by Miller et al [2,3] are, in fact, valid because they can be viewed as nothing more than special coordinate rotation (CR) calculations involving L2 basis functions.…”

“…6 is that one can scale a single orbital in any multi-electron Slater determinant; the antisymmetric nature of such determinants assures that indistinguishability is not violated. The physical motivation for considering this proposition is that only a single electron is unbound in the kind of electron-molecule scattering processes m a t commonly studied [2,3,4,6]; the remaining electrons are bound and should have their energy unchanged by coordinate rotation [ U I . …”

“…The approaches taken in Refs. 2 and 3 to avoid this problem were to evaluate the requisite integrals over the Hamiltonian either with Im(k) replaced by -Im(k) [2] or with Im(k) slightly positive so that exp(ikr)/r is L2 [3]. That is, although the resonance energy and the true Siegert wavefunction have Im k < 0, the necessary integrals are evaluated for Im k > 0 and it is assumed that the resulting eigenvalues are independent of this fact (i.e., that E ( k ) = h2k2/2m is analytic in k).…”