scholarly journals A Study of L2 Approximations in Atomic Scattering

1990 ◽  
Vol 43 (5) ◽  
pp. 485 ◽  
Author(s):  
AT Stelbovics ◽  
T Winata
Keyword(s):  
Convergence Rates ◽  
Basis Set ◽  
Matrix Elements ◽  
Close Coupling ◽  
Set Size ◽  
Atomic Scattering ◽  
Impact Ionisation ◽  
Three Body ◽  
Continuum Function ◽  
The Continuum

The approximation of Coulomb continuum functions by an L 2 basis is studied using a Laguerre� function basis which can be extended to completeness. Also studied is the convergence rate of L2 approximations to Born matrix elements for electron impact ionisation as a function of basis�set size. This important class of matrix elements occurs in pseudo�state close-coupling calculations, accounting for scattering to the three�body continuum. Convergence rates in both cases are derived analytically and confirmed numerically. We find that the rate of pointwise convergence of L2 expansions to the continuum function is slow, and of conditional type; however, it is proven that the corresponding ionisation matrix elements converge geometrically, Our result agrees with the behaviour observed in pseudo�state calculations.

Convergence of Breit–Pauli spin–orbit matrix elements with basis set size and configuration interaction space: The halogen atoms F, Cl, and Br

2000 ◽  
Vol 112 (13) ◽  
pp. 5624-5632 ◽  
Author(s):  
Andreas Nicklass ◽  
Kirk A. Peterson ◽  
Andreas Berning ◽  
Hans-Joachim Werner ◽  
Peter J. Knowles
Keyword(s):  
Configuration Interaction ◽  
Interaction Space ◽  
Basis Set ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Set Size ◽  
Halogen Atoms

Rotational de-excitations of C3H+ (1Σ+) by collision with He: new ab initio potential energy surface and scattering calculations

2020 ◽  
Vol 494 (4) ◽  
pp. 5675-5681 ◽  
Author(s):  
Sanchit Chhabra ◽  
T J Dhilip Kumar
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Cross Sections ◽  
Energy Surface ◽  
Molecular Ions ◽  
Basis Set ◽  
Rate Coefficients ◽  
Close Coupling ◽  
Collisional Rate Coefficients

ABSTRACT Molecular ions play an important role in the astrochemistry of interstellar and circumstellar media. C3H+ has been identified in the interstellar medium recently. A new potential energy surface of the C3H+–He van der Waals complex is computed using the ab initio explicitly correlated coupled cluster with the single, double and perturbative triple excitation [CCSD(T)-F12] method and the augmented correlation consistent polarized valence triple zeta (aug-cc-pVTZ) basis set. The potential presents a well of 174.6 cm−1 in linear geometry towards the H end. Calculations of pure rotational excitation cross-sections of C3H+ by He are carried out using the exact quantum mechanical close-coupling approach. Cross-sections for transitions among the rotational levels of C3H+ are computed for energies up to 600 cm−1. The cross-sections are used to obtain the collisional rate coefficients for temperatures T ≤ 100 K. Along with laboratory experiments, the results obtained in this work may be very useful for astrophysical applications to understand hydrocarbon chemistry.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

Three-alpha resonant state and its contribution in continuum spectrum

2006 ◽  
Vol 21 (31n33) ◽  
pp. 2351-2358
Author(s):  
C. Kurokawa ◽  
K. Katō
Keyword(s):  
Boundary Condition ◽  
Resonant State ◽  
Level Density ◽  
Complex Scaling ◽  
Scaling Method ◽  
Complex Scaling Method ◽  
Resonant States ◽  
Complex Eigenvalues ◽  
Three Body ◽  
The Continuum

The 3α resonant states of 12 C are investigated by taking into account the correct boundary condition for three-body resonant states. In order to show how the 3α resonant states having complex eigenvalues contribute to the real energy, we calculated the Continuum Level Density in the Complex Scaling Method.

scholarly journals Strongly compact cardinals and the continuum function

2021 ◽  
pp. 103013
Author(s):  
Arthur W. Apter ◽  
Stamatis Dimopoulos ◽  
Toshimichi Usuba
Keyword(s):  
Continuum Function ◽  
Strongly Compact Cardinals ◽  
The Continuum

Inelastic scattering of interstellar silyl cyanide (SiH3CN) by helium atoms : cross-sections and rate coefficients for A- and E-SiH3CN

2021 ◽  
Vol 507 (4) ◽  
pp. 5264-5271
Author(s):  
Manel Naouai ◽  
Abdelhak Jrad ◽  
Ayda Badri ◽  
Faouzi Najar
Keyword(s):  
Inelastic Scattering ◽  
Total Energy ◽  
Cross Sections ◽  
Three Dimensional ◽  
Basis Set ◽  
Rate Coefficients ◽  
Close Coupling ◽  
Explicitly Correlated ◽  
Correlation Consistent ◽  
Triple Excitation

ABSTRACT Rotational inelastic scattering of silyl cyanide (SiH3CN) molecule with helium (He) atoms is investigated. Three-dimensional potential energy surface (3D-PES) for the SiH3CN–He interacting system is carried out. The ab initio 3D-PES is computed using explicitly correlated coupled cluster approach with single, double, and perturbative triple excitation CCSD(T)-F12a connected to augmented-correlation consistent-polarized valence triple zeta Gaussian basis set. A global minimum at (R = 6.35 bohr; θ = 90○; ϕ = 60○) with a well depth of 52.99 cm−1 is pointed out. Inelastic rotational cross-sections are emphasized for the 22 first rotational levels for total energy up to 500 cm−1 via close coupling (CC) approach in the case of A-SiH3CN and for the 24 first rotational levels for total energy up to 100 cm−1 via CC and from 100 to 500 cm−1 via coupled states (CS) in the case of E-SiH3CN. Rate coefficients are derived for temperature until 80 K for both A- and E-SiH3CN–He systems. Propensity rules are obtained for |ΔJ| = 2 processes with broken parity for A-SiH3CN and for |ΔJ| = 2 processes with |ΔK| = 0 and unbroken parity for E-SiH3CN.

scholarly journals Spin-Orbit Matrix Elements for a Combined Spin-Flip and IP/EA Approach

2020 ◽  
Author(s):  
Oinam Meitei ◽  
Shannon Houck ◽  
Nicholas Mayhall
Keyword(s):  
Mean Field ◽  
Coupling Constants ◽  
Basis Set ◽  
Reduced Density Matrix ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Dynamical Correlation ◽  
The Core ◽  
Reduced Density

We present a practical approach for computing the Breit-Pauli spin-orbit matrix elements of multiconfigurational systems with both spin and spatial degeneracies based on our recently developed RAS-nSF-IP/EA method (JCTC, 15,<br>2278, 2019). The spin-orbit matrix elements over all the multiplet components are computed using a single one-particle reduced density matrix as a result of the Wigner-Eckart theorem. A mean field spin-orbit approximation was used to account for the two-electron contributions. Basis set dependence as well as the effect of including additional excitations is presented. The effect of correlating the core and semi-core orbitals is also examined. Surprisingly accurate results are obtained for spin-orbit coupling constants, despite the fact that the efficient wavefunction approximations we explore neglect the bulk of dynamical correlation.<br>

Efficient computation of one-electron two-centre exchange integrals in ion–atom collisions

1976 ◽  
Vol 54 (9) ◽  
pp. 944-949 ◽  
Author(s):  
Alfred Msezane
Keyword(s):  
Principal Quantum Number ◽  
Computing Time ◽  
Translational Motion ◽  
Matrix Elements ◽  
Efficient Computation ◽  
Close Coupling ◽  
One Dimensional ◽  
State Approximation ◽  
The Matrix ◽  
Exchange Matrix

A scheme is presented for the reduction to one-dimensional integrals of any one-electron two-centre exchange matrix elements which incorporate the momentum associated with the translational motion of the electron. These elements are of the types occurring in close coupling-based treatments of ion–atom collisions. It is shown in a six state approximation, by coupling both eigenstates and pseudostates for the asymmetric He2+–H collision process, that computing time for the evaluation of the matrix elements is determined mainly by the number of different exponents in the matrix elements. The coupling of additional states with the same principal quantum number as the already coupled ones alters computing time insignificantly.

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