Application and development of the Schwinger multichannel scattering theory and the partial differential equation theory of electron-molecule scattering

One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation

A systematic study of neutral and charged 3d-metal trioxides and tetraoxides

Using density functional theory with generalized gradient approximation, we have performed a systematic study of the structure and properties of neutral and charged trioxides (MO3) and tetraoxides (MO4) of the 3d-metal atoms. The results of our calculations revealed a number of interesting features when moving along the 3d-metal series. (1) Geometrical configurations of the lowest total energy states of neutral and charged trioxides and tetraoxides are composed of oxo and/or peroxo groups, except for CuO3 − and ZnO3 − which possess a superoxo group, CuO4 + and ZnO4 + which possess two superoxo groups, and CuO3 +, ZnO3 +, and ZnO4 −which possess an ozonide group. While peroxo groups are found in the early and late transition metals, all oxygen atoms bind chemically to the metal atom in the middle of the series. (2) Attachment or detachment of an electron to/from an oxide often leads to a change in the geometry. In some cases, two dissociatively attached oxygen atoms combine and form a peroxo group or a peroxo group transforms into a superoxo group and vice versa. (3) The adiabatic electron affinity of as many as two trioxides (VO3 and CoO3) and four tetraoxides (TiO4, CrO4, MnO4, and FeO4) are larger than the electron affinity of halogen atoms. All these oxides are hence superhalogens although only VO3 and MnO4 satisfy the general superhalogen formula

Interactions of a Mn atom with halogen atoms and stability of its half-filled 3d-shell

Using density functional theory with hybrid exchange-correlation potential, we have calculated the geometrical and electronic structure, relative stability, and electron affinities of MnX ncompounds (n = 1–6) formed by a Mn atom and halogen atoms X = F, Cl, and Br. Our objective is to examine the extent to which the Mn–X interactions are similar and to elucidate if/how the half-filled 3d-shell of a Mn atom participates in chemical bonding as the number of halogen atoms increases. While the highest oxidation number of the Mn atom in fluorides is considered to be +4, the maximum number of halogen atoms that can be chemically attached in the MnX n −anions is 6 for X = F, 5 for X = Cl, and 4 for X = Br. The MnCl n and MnBr n neutrals are superhalogens for n ≥ 3, while the superhalogen behavior of MnF n begins with n = 4. These results are explained to be due to the way different halogen atoms interact with the 3d electrons of Mn atom

Does N-2(-) exist? A coupled-cluster study

Potential energy curves of the ground-state N2 molecule and its doublet N−2 anion are calculated at the coupled-cluster level with single and double excitations and with noniterative triples [CCSD(T)] as well as with the multireference averaged-quadratic coupled-cluster (MR-AQCC) method. The N−2 anion is shown to be temporary and decays to its neutral parent plus a free electron at bond lengths shorter than ≈1.4 and larger than ≈2.5 Å. Thus, the N−2 anion exists within the 1.4⩽R(N–N)⩽2.5 Å range at the Born–Oppenheimer approximation

ROCs in Eyewitness Identification:Instructions versus Confidence Ratings

From the perspective of signal-detection theory, different lineup instructions may induce different levels of response bias (Clark, 2005). If so, then collecting correct and false identification rates across different instructional conditions will trace out the ROC – the same ROC that, theoretically, could also be traced out from a single instruction condition in which each eyewitness decision is accompanied by a confidence rating. We tested whether the two approaches do in fact yield the same ROC. Participants were assigned to a confidence rating condition or to an instructional biasing condition (liberal, neutral, unbiased, or conservative). After watching a video of a mock crime, participants were presented with instructions followed by a 6-person simultaneous photo lineup. The ROCs from both methods were similar, but they were not exactly the same. These findings have potentially important policy implications for how the legal system should go about controlling eyewitness response bias