Matrix elements of explicitly correlated Gaussian basis functions with arbitrary angular momentum

Joyce, Tennesse; Varga, K.

doi:10.1063/1.4948708

Cited by 8 publications

(4 citation statements)

References 67 publications

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“…In what follows, we summarize the main steps of the calculations (further details can be found in Refs. [35,36,46]).…”

Section: Evaluation Of the Matrix Elementsmentioning

confidence: 99%

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Pre-Born–Oppenheimer molecular structure theory

Mátyus

2018

Molecular Physics

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In pre-Born-Oppenheimer (pre-BO) theory a molecule is considered as a quantum system as a whole, including the electrons and the atomic nuclei on the same footing. This approach is fundamentally different from the traditional quantum chemistry treatment, which relies on the separation of the motion of the electrons and the atomic nuclei. A fully quantum mechanical treatment of molecules has a great promise for future developments and applications. Its most accurate versions may contribute to the definition of new schemes for metrology and testing fundamental physical theories; its approximate versions can provide an efficient theoretical description for molecule-positron interactions and, in general, it would circumvent the tedious computation and fitting of potential energy surfaces and non-adiabatic coupling vectors. To achieve these goals, the review points out important technical and fundamental open questions. Most interestingly, the reconciliation of pre-BO theory with the classical chemistry knowledge touches upon fundamental problems related to the measurement problem of quantum mechanics. I. QUANTUM CHEMISTRY VS. QUANTUM MECHANICS AND CHEMISTRY?We start with a historical overview of the chemical theory of molecular structure and the origins of quantum chemistry, which is followed by a review of methodological details and applications of pre-Born-Oppenheimer theory. A. Historical background: Chemical structure, physical structure from organic chemistry experiments [T]he dominating story in chemistry of the 1860s, 1870s, and 1880s was neither the periodic law, nor the search for new elements, nor the early stages of the study of atoms and molecules as physical entities. It was the maturation, and demonstration of extraordinary scientific and technological power, of the "theory of chemical structure" ... Alan J. Rocke Image and Reality: Kekulé, Kopp, and the Scientific Imagination (The University of Chicago Press, Chicago and London, 2010) During the second half of the 19th century, the pioneering organic chemists generation-represented by Williamson, Kekulé, Butlerov, Crum Brown, Frankland, Wurtz, etc.-had explored an increasing number of chemical transformation in their laboratory experiments and worked towards the establishment of a logical framework for their observations. The "first chemist' conference", held in Karlsruhe on 3 September 1860, resulted in an internationally recognized definition of the atomic masses. This agreement ensured that the same molecular formula was then used for the same substance in all laboratories around the world, and thereby opened the route to the successful development of the theory of chemical structure. The development of the chemical theory has been surrounded by heated debatesabout what is reality and what is mere speculation. We note that contemporary physics (gravitation, electromagnetism) was not able to provide any satisfactory description for molecules. To give a taste of this exciting period, we reproduce a few extracts from Alan J. Rocke's chemical history bo...

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“…In what follows, we summarize the main steps of the calculations (further details can be found in Refs. [35,36,46]).…”

Section: Evaluation Of the Matrix Elementsmentioning

confidence: 99%

“…The resulting expressions [35,36,46] are completely general for basis function with any N total angular momentum quantum number and natural parity, (−1) N (similar functions and working formulae with unnatural parity, (−1) N +1 , were introduced in Ref. [47]).…”

Section: [λ]mentioning

confidence: 99%

Pre-Born–Oppenheimer molecular structure theory

Mátyus

2018

Molecular Physics

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“…The quadratic form involving inter-particle distances in ECGs permits the reduction of the Hamiltonian matrix elements to very simple analytic expressions and the algebraic complexity of the matrix elements does not change with the number of particles. Further, the matrix elements can be generalized for an arbitrary angular momentum 59,69,82,90,90,97,98 . These matrix elements depend on the Gaussian parameters of the ECGs which should be carefully optimized 84,[99][100][101][102][103][104][105] to get highly accurate variational upper bounds.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, direct calculation of nonspherical ECG matrix elements for a general case has also been worked out 90 . In this case, the matrix elements are calculated for any desired product of single-particle coordinates.…”

Section: Introductionmentioning

confidence: 99%

Deformed Explicitly Correlated Gaussians

Beutel,

Ahrens,

Huang

et al. 2021

Preprint

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Deformed correlated Gaussian basis functions are introduced and their matrix elements are calculated. These basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole self-interaction term in the Pauli-Fierz Hamiltonian. Examples are presented showing the accuracy and necessity of deformed Gaussian basis functions to accurately solve light-matter coupled systems in cavity QED.

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