Single-centre expansion of Gaussian basis functions and the angular decomposition of their overlap integrals

Kaufmann, Karl; Baumeister, Wolfgang

doi:10.1088/0953-4075/22/1/004

Cited by 51 publications

(45 citation statements)

References 11 publications

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“…The orbitals resulting from the FRC calculations are also used for determining transition moments and for the monocentric analysis of their angular momenta with a special program. 31 Recently we have developed a version of FRC especially adapted to treat Rydberg series of linear molecules converging to an ionic limit split by spin-orbit coupling. 22 With this method, where the spin-orbit coupling constant A of the parent ion is used as the only empirical parameter, it is possible to obtain energy levels and transition moments for the various spin-orbit components of excited Rydberg configurations.…”

Section: Ab Initio Calculationsmentioning

confidence: 99%

High resolution absorption spectrum of jet-cooled OCS between 64 000 and 91 000 cm−1

Cossart‐Magos

Jungen

et al. 2003

The Journal of Chemical Physics

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Section: Ab Initio Calculationsmentioning

confidence: 99%

High resolution absorption spectrum of jet-cooled OCS between 64 000 and 91 000 cm−1

Cossart‐Magos

Jungen

et al. 2003

The Journal of Chemical Physics

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“…In this case, the radial factors can be directly obtained by combining the Gaussian product theorem, and the formula for translation of GTO to another center. This procedure was proposed by Kaufmann and Baumeister and yields:

\begin{array}{l} left & {normale}^{- ξ_{A} | r - {boldnormalR}_{A} |^{2}} {normale}^{- ξ_{B} | r - {boldnormalR}_{B} |^{2}} = \sum_{l = 0}^{\infty} \sum_{m = - l}^{l} {scriptN}_{l m}^{Ω} r^{l} z_{l}^{m} (θ, φ) 2 π {normale}^{- ξ_{A} ξ_{B} R_{A B}^{2} / (ξ_{A} + ξ_{B})} \\ left & \times {scriptN}_{l m}^{Ω} z_{l}^{m} (P) {normale}^{- (ξ_{A} + ξ_{B}) (r^{2} + P^{2})} \sqrt{\frac{π}{(ξ_{A} + ξ_{B}) r P}} I_{l + 1 / 2} [2 (ξ_{A} + ξ_{B}) r P] \end{array}

where

R_{A B} = | {boldnormalR}_{B} - {boldnormalR}_{A} |, P = (ξ_{A} {boldnormalR}_{A} + ξ_{B} {boldnormalR}_{B}) / (ξ_{A} + ξ_{B}), P = | P |

and

I_{l + 1 / 2} (z)

a...…”

Section: Methodsmentioning

confidence: 99%

Efficient algorithm for expanding theoretical electron densities in canterakis–zernike functions

2018

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An algorithm for the efficient computation of Canterakis–Zernike moments of theoretically computed molecular electron densities and rotationally invariant Fingerprint indices derived from them is reported. The algorithm is suitable for any density expressed in terms of Gaussian‐ or Slater‐type functions within the Linear Combination of Atomic Orbitals framework at any level of computation. Electron density is expressed as a one‐center expansion of real regular spherical harmonics times radial factors by means of translation techniques, which facilitates the efficient computation of the moments in terms of a single one‐dimension numerical integration. The performance of the algorithm is analyzed showing that the computation of radial factors in the quadrature points is responsible for almost all computational time. The procedure is applicable to any density obtained with standard packages for molecular structure calculations. © 2018 Wiley Periodicals, Inc.

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“…This was already done in details by Kaufmann and Baumeister [4] where a detailed form of the spherical gaussian…”

Section: Ki − →mentioning

confidence: 99%

“…Defining the wave functions around a single center reduces the complexity of this task [4]. These wave functions have been expressed as linear combinations of atomic orbitals written in terms of Slater-type functions in some studies [5], [6] and in terms of Gaussian-type functions in others [3], [7].…”

Section: Introductionmentioning

confidence: 99%

Triply Differential Ionization Cross Sections of atomic and molecular targets by single electron impact

et al. 2018

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Abstract-We present numerically calculated triply differential cross sections for the simple ionization of two targets, atomic hydrogen and ammonia, in the First Born Approximation framework with one Coulomb wave describing the ejected electron. The partial wave series of the wavefunctions centered around the same origin were used and the intial state molecular wavefunction was derived using information provided by Gaussian03 software for ammonia. The theoretical results are calculated in the geometrical settings and kinematical conditions of previous experiments and are compared to published experimental and theoretical data. The results show good agreement with previous studies based on the same model for hydrogen. The general shape of the triply differential cross sections obtained for ammonia are in acceptable agreement with experimental data in the binary region but not in the recoil region where our simple framework fails to reconstruct the recoil peaks.

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Single-centre expansion of Gaussian basis functions and the angular decomposition of their overlap integrals

Cited by 51 publications

References 11 publications

High resolution absorption spectrum of jet-cooled OCS between 64 000 and 91 000 cm−1

High resolution absorption spectrum of jet-cooled OCS between 64 000 and 91 000 cm−1

Efficient algorithm for expanding theoretical electron densities in canterakis–zernike functions

Triply Differential Ionization Cross Sections of atomic and molecular targets by single electron impact

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