Variational treatment of electron-polyatomic molecule scattering calculations using adaptive overset grids

The Complex Kohn variational method for electron-polyatomic molecule scattering is formulated using an overset grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense, atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free particle Green's function and potential, $\hat{G}^+_0\hat{V}$ on the overset grid in a "Born-Arnoldi" solution of the working equations. The theory is shown to be equivalent to a specific Pad\'e approximant to the $T$-matrix, and has rapid convergence properties, both in the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF$_4$ in the static-exchange approximation, and compared in detail with calculations performed with the numerical Schwinger variational approach based on single center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described

Probing autoionizing states of molecular oxygen with XUV transient absorption: Electronic symmetry dependent lineshapes and laser induced modification

The dynamics of autoionizing Rydberg states of oxygen are studied using attosecond transient absorption technique, where extreme ultraviolet (XUV) initiates molecular polarization and near infrared (NIR) pulse perturbs its evolution. Transient absorption spectra show positive optical density (OD) change in the case of $ns\sigma_g$ and $nd\pi_g$ autoionizing states of oxygen and negative OD change for $nd\sigma_g$ states. Multiconfiguration time-dependent Hartree-Fock (MCTDHF) calculation are used to simulate the transient absorption spectra and their results agree with experimental observations. The time evolution of superexcited states is probed in electronically and vibrationally resolved fashion and we observe the dependence of decay lifetimes on effective quantum number of the Rydberg series. We model the effect of near-infrared (NIR) perturbation on molecular polarization and find that the laser induced phase shift model agrees with the experimental and MCTDHF results, while the laser induced attenuation model does not. We relate the electron state symmetry dependent sign of the OD change to the Fano parameters of the static absorption lineshapes.Comment: 15 pages, 8 figure

Ultrafast Rydberg-state dissociation in oxygen: Identifying the role of multielectron excitations

We investigated the fragmentation dynamics of highly excited states of molecular oxygen using femtosecond transient photoelectron spectroscopy. An extreme ultraviolet (XUV) pulse populates the autoionizing Rydberg series converging to O-2(+) c(4)Sigma(-)(u), and a femtosecond near-infrared (IR) pulse was used to photoionize these states as they dissociate. Monitoring the differential photoelectron spectra as a function of time delay allowed us to obtain the relaxation lifetimes of these Rydberg states. We observed a photoelectron signal corresponding to the formation of a 4p excited atomic oxygen fragment, which is not an expected dissociation product of the (O-2(+) c(4)Sigma(-)(u))nl sigma(g) Rydberg series. Analysis of the time-dependent photoelectron spectra and photoionization calculations indicate that this fragment results from a previously unexplored (O-2(+) (4)Pi(g))4p repulsive state and that, contrary to expectations, this multielectron excitation pathway presents a substantial cross section. Our study demonstrates that two-color time-resolved differential photoelectron spectroscopy is an excellent tool to study the fragmentation dynamics of such multielectron excited states, which are not easily probed by other means.US Army Research Laboratory; U.S. Army Research Office [W911NF-14-1-0383]; National Science Foundation (NSF) [PHY-1505556]; U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) [DE-SC0018251]; US Department of Energy Chemical Sciences, Geosciences, and Biosciences Division [DE-AC02-05CH11231]This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Exploring Spin Symmetry-Breaking Effects for Static Field Ionization of Atoms: Is There an Analog to the Coulson-Fischer Point in Bond Dissociation?

L\"owdin's symmetry dilemma is an ubiquitous issue in approximate quantum chemistry. In the context of Hartree-Fock (HF) theory, the use of Slater determinants with some imposed constraints to preserve symmetries of the exact problem may lead to physically unreasonable potential energy surfaces. On the other hand, lifting these constraints leads to the so-called broken symmetry solutions that usually provide better energetics, at the cost of losing information about good quantum numbers that describe the state of the system. This behavior has been previously extensively studied in the context of bond dissociation. This paper studies the behavior of different classes of Hartree-Fock spin polarized solutions (restricted, unrestricted, generalized) in the context of ionization by strong static electric fields. We find that, for simple two-electron systems, UHF is able to provide a qualitatively good description of states involved during the ionization process (neutral, singly-ionized and doubly ionized states), whereas RHF fails to describe the singly ionized state. For more complex systems, even though UHF is able to capture some of the expected characteristics of the ionized states, it is constrained to a single $M_s$ (diabatic) manifold in the energy surface as a function of field intensity. In this case a better qualitative picture can be painted by GHF as it is able to explore different spin manifolds and follow the lowest solution due to lack of collinearity constraints on the spin quantization axis

Probing the nonlocal approximation to resonant collisions ofelectrons with diatomic molecules

A numerically solvable two-dimensional model introduced bythe authors [Phys. Rev. A 73, 032721 (2006)]is used to investigate thevalidity of the nonlocal approximation to the dynamics of resonantcollisions of electrons with diatomic molecules. The nonlocalapproximation to this model is derived in detail, all underlyingassumptions are specified and explicit expressions for the resonant andnon-resonant (background) T matrix for the studied processes are given.Different choices of the so-called discrete state, which fully determinesthe nonlocal approximation, are discussedand it is shown that a physicalchoice of this state can in general give poorer results than otherchoices that minimize the non-adiabatic effects and/or the backgroundterms of the T matrix. The background contributions to the crosssections, which are usually not considered in the resonant theory ofelectron-molecule collisions, can be significant not only for elasticscattering but also for the inelastic process of vibrationalexcitation

Triple Differential Cross sections and Nuclear Recoil in Two-Photon Double Ionization of Helium

Triple differential cross sections (TDCS) for two-photon double ionization of helium are calculated using the method of exterior complex scaling both above and below the threshold for sequential ionization (54.4 eV). It is found that sequential ionization produces characteristic behavior in the TDCS that identifies that process when it is in competition with nonsequential ionization. Moreover we see the signature in the TDCS and nuclear recoil cross sections of"virtual sequential ionization" below the threshold for the sequential process

Three-body breakup in dissociative electron attachment to the water molecule

We report the results of {\em ab initio} calculations on dissociative electron attachment (DEA) to water that demonstrate the importance of including three-body breakup in the dissociation dynamics. While three-body breakup is ubiquitous in the analogous process of dissociative recombination, its importance in low-energy dissociative electron attachment to a polyatomic target has not previously been quantified. Our calculations, along with our earlier studies of DEA into two-body channels, indicate that three-body breakup is a major component of the observed O- cross section. The local complex potential model provides a generally accurate picture of the experimentallyobserved features in this system, reproducing some quantitatively, others qualitatively, and one not at all

Progress in the application of classical S

Methods are described which effectively solve two of the technical difficulties associated with applying classical S‐matrix theory to inelastic/reactive scattering. Specifically, it is shown that rather standard numerical methods can be used to solve the ’’root search’’ problem (i.e., the nonlinear boundary value problem necessary to impose semiclassical quantum conditions at the beginning and the end of the classical trajectories) and also how complex classical trajectories, which are necessary to describe classically forbidden (i.e., tunneling) processes, can be computed in a numerically stable way. Application is made to vibrational relaxation of H{sub 2} by collision with He (within the helicity conserving approximation). The only remaining problem with regard to applying classical S‐matrix theory to complex collision processes has to do with the availability of multidimensional uniform asymptotic formulas for interpolating the ’’primitive’’ semiclassical expressions between their various regions of validity

Hake age estimation: state of the art and progress towards a solution

Since 1992, northern and southern hake (Merluccius merluccius) stock assessments have used age data based on otolith analysis. Age data for stock assessment is provided by different institutions, which implies a quantification of age‐reading precision to estimate assessment quality indicators. During this period, considerable effort has been made to improve the precision of age data by means of successive agereading calibration exercises, exchanges, and workshops in 1997, 1999, 2001, and 2004. This goal was partly achieved, and experts recently agreed on standard criteria (Piñeiro and Saínza, 2003) that allowed an acceptable precision to be reached for ages up to 3 years (Piñeiro et al., 2004). However, these criteria have never been validated, and recent mark ‒ recapture experiments are not in line with ageing results based on the standard criteria. Given the impact of bias in age estimation on stock assessment results, consequent management advice, and concern about the state of the hake stocks (ICES, 2007a, 2007b), a report on the current state of the art is needed. The main goal of this report is to present a synthesis of the work carried out over the years by researchers involved in providing age data for stock assessment, mainly on age‐reading calibration exercises, and current knowledge regarding the growth and ageing of this species. This report also includes recommendations for future work aimed at achieving validated age‐reading criteria

An efficient basis set representation for calculating electrons in molecules

The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron matrix elements among orbitals requires only O(N log(N)) multiplication operations, not O(N^4), where N is the number of basis functions; N = n^3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionization potentials are reported for one- (He^+, H_2^+ ), two- (H_2, He), ten- (CH_4) and 56-electron (C_8H_8) systems.Comment: Submitted to JC