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

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>

Excitation energies, singlet–triplet energy gaps, spin–orbit matrix elements and heavy atom effects in BOIMPYs as possible photosensitizers for photodynamic therapy: a computational investigation

2018 ◽  
Vol 20 (4) ◽  
pp. 2656-2661 ◽  
Author(s):  
Bruna Clara De Simone ◽  
Gloria Mazzone ◽  
Nino Russo ◽  
Emilia Sicilia ◽  
Marirosa Toscano
Keyword(s):  
Photodynamic Therapy ◽  
Photophysical Properties ◽  
Heavy Atom ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Computational Investigation ◽  
Triplet Energy ◽  
Excitation Energies ◽  
Halogen Atoms ◽  
Energy Gaps

Introduction of halogen atoms in different amounts and positions into the BOIMPY skeleton significantly affects its photophysical properties.

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.

Spin-orbit matrix elements for internally contracted multireference configuration interaction wavefunctions

2000 ◽  
Vol 98 (21) ◽  
pp. 1823-1833 ◽  
Author(s):  
ANDREAS BERNING ◽  
MARCUS SCHWEIZER ◽  
HANS-JOACHIM WERNER ◽  
PETER J. KNOWLES ◽  
PAOLO PALMIERI
Keyword(s):  
Configuration Interaction ◽  
Spin Orbit ◽  
Matrix Elements

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>

Study of the dependence of spin-orbit matrix elements on AO basis set composition for inner and valence shells: Results for the multiplet splitting of X 3Σ− and C 3Π of SO and X 2Π in SO+

1983 ◽  
Vol 76 (3) ◽  
pp. 367-383 ◽  
Author(s):  
Rainer Klotz ◽  
Christel M. Marian ◽  
Sigrid D. Peyerimhoff ◽  
Bernd A. Hess ◽  
Robert J. Buenker
Keyword(s):  
Basis Set ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Multiplet Splitting

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.

scholarly journals Potential Functions and Thermodynamic Properties of UC, UN, and UH

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Shuang-Ling Tang ◽  
Yu Wang ◽  
Qi-Ying Xia ◽  
Xue-Hai Ju
Keyword(s):  
Configuration Interaction ◽  
Density Functional ◽  
Least Square Method ◽  
Potential Functions ◽  
Least Square ◽  
Basis Set ◽  
Dissociation Energies ◽  
Anharmonicity Constant ◽  
Different Temperatures ◽  
Relationship Of

Potential energy surface scanning for UC, UN, and UH was performed by configuration interaction (CI), coupled cluster singles and doubles (CCSD) excitation, quadratic configuration interaction (QCISD (T)), and density functional theory PBE1 (DFT-PBE1) methods in coupling with the ECP80MWB_AVQZ + 2f basis set for uranium and 6 − 311 + G∗ for carbon, hydrogen, and nitrogen. The dissociation energies of UC, UN, and UH are 5.7960, 4.5077, and 2.6999 eV at the QCISD (T) levels, respectively. The calculated energy was fitted to the potential functions of Morse, Lennard-Jones, and Rydberg by using the least square method. The anharmonicity constant of UC is 0.0047160. The anharmonic frequency of UC is 780.27 cm−1 which was obtained based on the PBE1 results. For UN, the anharmonicity constant is 0.0049827. The anharmonic frequency is 812.65 cm−1 which was obtained through the PBE1 results. For UH, the anharmonicity constant is 0.017300. The anharmonic frequency obtained via the QCISD (T) results is 1449.8 cm−1. The heat capacity and entropy in different temperatures were calculated using anharmonic frequencies. These properties are in good accordance with the direct DFT-UPBE1 results (for UC and UN) and QCISD (T) results (for UH). The relationship of entropy with temperature was established.

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