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Relevant bibliographies by topics / Coulomb operator, Quantum chemistry

Academic literature on the topic 'Coulomb operator, Quantum chemistry'

Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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Journal articles on the topic "Coulomb operator, Quantum chemistry"

1

Berry, Dominic W., Craig Gidney, Mario Motta, Jarrod R. McClean, and Ryan Babbush. "Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization." Quantum 3 (December 2, 2019): 208. http://dx.doi.org/10.22331/q-2019-12-02-208.

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Recent work has dramatically reduced the gate complexity required to quantum simulate chemistry by using linear combinations of unitaries based methods to exploit structure in the plane wave basis Coulomb operator. Here, we show that one can achieve similar scaling even for arbitrary basis sets (which can be hundreds of times more compact than plane waves) by using qubitized quantum walks in a fashion that takes advantage of structure in the Coulomb operator, either by directly exploiting sparseness, or via a low rank tensor factorization. We provide circuits for several variants of our algorithm (which all improve over the scaling of prior methods) including one with O~(N3/2λ) T complexity, where N is number of orbitals and λ is the 1-norm of the chemistry Hamiltonian. We deploy our algorithms to simulate the FeMoco molecule (relevant to Nitrogen fixation) and obtain circuits requiring about seven hundred times less surface code spacetime volume than prior quantum algorithms for this system, despite us using a larger and more accurate active space.

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2

Oleynichenko, Alexander V., Andréi Zaitsevskii, Nikolai S. Mosyagin, Alexander N. Petrov, Ephraim Eliav, and Anatoly V. Titov. "LIBGRPP: A Library for the Evaluation of Molecular Integrals of the Generalized Relativistic Pseudopotential Operator over Gaussian Functions." Symmetry 15, no. 1 (January 9, 2023): 197. http://dx.doi.org/10.3390/sym15010197.

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Generalized relativistic pseudopotentials (GRPP) of atomic cores implying the use of different potentials for atomic electronic shells with different principal quantum numbers give rise to accurate and reliable relativistic electronic structure models of atoms, molecules, clusters, and solids. These models readily incorporate the effects of Breit electron–electron interactions and one-loop quantum electrodynamics effects. Here, we report the computational procedure for evaluating one-electron integrals of GRPP over contracted Gaussian functions. This procedure was implemented in a library of routines named LIBGRPP, which can be integrated into existing quantum chemistry software, thus enabling the application of various methods to solve the many-electron problem with GRPPs. Pilot applications to electronic transitions in the ThO and UO2 molecules using the new library and intermediate-Hamiltonian Fock space relativistic coupled cluster method are presented. Deviations of excitation energies obtained within the GRPP approach from their all-electron Dirac–Coulomb–Gaunt counterparts do not exceed 50 cm−1 for the 31 lowest-energy states of ThO and 110 cm−1 for the 79 states of UO2. The results clearly demonstrate that rather economical tiny-core GRPP models can exceed in accuracy relativistic all-electron models defined by Dirac–Coulomb and Dirac–Coulomb–Gaunt Hamiltonians.

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3

Nag, Nivedita, and Rajkumar Roychoudhury. "Algebraic Approach to the Fixed Point Structure of the Quantum Mechanical Dirac -Coulomb System." Zeitschrift für Naturforschung A 50, no. 11 (November 1, 1995): 995–97. http://dx.doi.org/10.1515/zna-1995-1104.

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Abstract It is shown that a non-perturbative ß like function can be obtained for a Dirac-Coulomb system with both vector and scalar couplings using the properties of 0(2,1) algebra and the tilting operator mechanism.

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4

Chi, Xuguang, Angbo Fang, Wuyi Hsiang, and Ping Sheng. "Kinetic energy operator approach to the quantum three-body problem with Coulomb interactions." Solid State Communications 141, no. 4 (January 2007): 173–77. http://dx.doi.org/10.1016/j.ssc.2006.10.031.

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5

Kay, Bernard S. "A product picture for quantum electrodynamics." AVS Quantum Science 4, no. 3 (September 2022): 031401. http://dx.doi.org/10.1116/5.0085813.

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We present a short account of our work to provide quantum electrodynamics (QED) with a product picture. We aim to complement the longer exposition in a recent paper in Foundations of Physics and to help to make that work more accessible. The product picture is a formulation of QED, equivalent to standard Coulomb gauge QED, in which the Hilbert space arises as (a certain physical subspace of) a product of a Hilbert space for the electromagnetic field and a Hilbert space for charged matter (i.e., the Dirac field) and the Hamiltonian arises as the sum of an electromagnetic Hamiltonian, a charged matter Hamiltonian, and an interaction term. (The Coulomb gauge formulation of QED is not a product picture because, in it, the longitudinal part of the electromagnetic field is made out of charged matter operators.) We also recall a “Contradictory Commutator Theorem” for QED, which exposes flaws in previous attempts at temporal gauge quantization of QED, and we explain how our product picture appears to offer a way to overcome those flaws. Additionally, we discuss the extent to which that theorem may be generalized to Yang–Mills fields. We also develop a product picture for nonrelativistic charged particles in interaction with the electromagnetic field and point out how this leads to a novel way of thinking about the theory of many nonrelativistic electrically charged particles with Coulomb interactions. In an afterword, we explain how the provision of a product picture for QED gives hope that one will be able likewise to have a product picture for (Yang Mills and for) quantum gravity—the latter being needed to make sense of the author's matter-gravity entanglement hypothesis. Also, we briefly discuss some similarities and differences between that hypothesis and its predictions and ideas of Roger Penrose related to a possible role of gravity in quantum state reduction and related to cosmological entropy.

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6

Zhang, Xin, Wei Zhang, Xin-Jun Ma, Pei-Fang Li, Yong Sun, and Jing-Lin Xiao. "The Impurity and Decay-Magnetic Polaron Effects in III–V Compound Gaussian Quantum Wells." Coatings 12, no. 8 (July 29, 2022): 1072. http://dx.doi.org/10.3390/coatings12081072.

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The effects of a decay magnetic field and hydrogen-like impurities on the ground-state binding energy (GSBE) and ground-state energy (GSE) of weak-coupling bound polarons in asymmetrical Gaussian potential (AGP) III–V compound quantum wells (QWs) were studied based on unitary transformation methods and linear combination operators. By numerical calculation, we found that the polarons were affected by the AGP, the decay magnetic field, Coulomb impurities, and the type of crystal, which led to a series of interesting phenomena, such as changes in the ground-state energy and the ground-state binding energy. The results obtained provide good theoretical guidance for optoelectronic devices and quantum information.

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7

Mathieu, J., L. Marchildon, and D. Rochon. "The bicomplex quantum Coulomb potential problem." Canadian Journal of Physics 91, no. 12 (December 2013): 1093–100. http://dx.doi.org/10.1139/cjp-2013-0261.

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Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper provides an analytical solution of the quantum Coulomb potential problem formulated in terms of bicomplex numbers. We define the problem by introducing a bicomplex hamiltonian operator and extending the canonical commutation relations to the form [Formula: see text], where ξ is a bicomplex number. Following Pauli’s algebraic method, we find the eigenvalues of the bicomplex hamiltonian. These eigenvalues are also obtained, along with appropriate eigenfunctions, by solving the extension of Schrödinger’s time-independent differential equation. Examples of solutions are displayed. There is an orthonormal system of solutions that belongs to a bicomplex Hilbert space.

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8

SHIROKOV, M. I. "REGULARIZATION OF THE MULTIPOLAR FORM OF QUANTUM ELECTRODYNAMICS." International Journal of Modern Physics A 07, no. 28 (November 10, 1992): 7065–77. http://dx.doi.org/10.1142/s0217751x92003240.

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The multipolar form of quantum electrodynamics has been proposed by Power, Zienau et al. It is widely used in nonrelativistic calculations but has the deficiency: its Hamiltonian has a divergent operator term. It is shown that the divergency can be removed by a regularization of the unitary transformation which converts the Coulomb gauge into the multipolar form. The regularized multipolar form is proven to have the same ultraviolet radiative divergencies as the Coulomb gauge electrodynamics. It is also demonstrated that the interaction with soft photons is represented by the usual electric dipole term e qE and interatomic Coulomb interactions persist to be absent.

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9

Varganov, Sergey A., Andrew T. B. Gilbert, Evelyne Deplazes, and Peter M. W. Gill. "Resolutions of the Coulomb operator." Journal of Chemical Physics 128, no. 20 (May 28, 2008): 201104. http://dx.doi.org/10.1063/1.2939239.

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Bai, Shuming, Peng Zhang, Panayiotis Antoniou, Spiros S. Skourtis, and David N. Beratan. "Quantum interferences among Dexter energy transfer pathways." Faraday Discussions 216 (2019): 301–18. http://dx.doi.org/10.1039/c9fd00007k.

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We explore Dexter coupling pathway interferences in non-covalent assemblies, employing a method that enables the assessment of Dexter coupling pathway strengths, interferences, and their physical origins in the context of one-particle and two-particle (i.e., coulombic) operators.

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Dissertations / Theses on the topic "Coulomb operator, Quantum chemistry"

1

Hyder, Asif M. "Green's operator for Hamiltonians with Coulomb plus polynomial potentials." California State University, Long Beach, 2013.

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2

Clark, B. James. "Topics in quantum chemistry, coulomb integral damping and the bond directionality principle." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq22292.pdf.

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Rolon, Soto Juan Enrique. "Coherent Exciton Phenomena in Quantum Dot Molecules." Ohio University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1314742055.

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4

Levitt, Antoine. "Etude théorique et numérique de modèles non linéaires en mécanique quantique." Phd thesis, Université Paris Dauphine - Paris IX, 2013. http://tel.archives-ouvertes.fr/tel-00881031.

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Dans cette thèse, on étudie plusieurs modèles et problèmes issus de la mécanique quantique. Ces modèles interviennent naturellement en chimie quantique pour le calcul de la structure électronique de la matière. Ils présentent des difficultés théoriques liées aux problèmes d'existence de solutions et à leur calcul numérique. Cette thèse est une contribution à l'étude de ces problèmes.

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5

Limpanuparb, Taweetham. "Applications of Resolutions of the Coulomb Operator in Quantum Chemistry." Phd thesis, 2011. http://hdl.handle.net/1885/8879.

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This dissertation shows that the Coulomb operator and the long-range Coulomb operators can be resolved as a sum of products of one-particle functions. These resolutions provide a potent new route to tackle quantum chemical problems. Replacing electron repulsion terms in Schrodinger equations by the truncated resolutions yields the reduced-rank Schrodinger equations (RRSE). RRSEs are simpler than the original equations but yield energies with chemical accuracy even for low-rank approximations. Resolutions of the Coulomb operator factorize Coulomb matrix elements to Cholesky-like sums of products of auxiliary integrals. This factorization is the key to the reduction of computational cost of quantum chemical methods.

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6

Veis, Libor. "Nerelativistické a relativistické výpočty energií molekul na kvantových počítačích." Doctoral thesis, 2012. http://www.nusl.cz/ntk/nusl-330398.

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Quantum computers are appealing for their ability to solve some tasks much faster than their classical counterparts. In fact, they have a potential to perform the full configuration interaction (FCI) energy calculations with a polynomial scaling only. This is in contrast to con- ventional computers where FCI scales exponentially. We provide a detailed description of the quantum version of the FCI method and the results of numerical simulations of the ground and excited state energy calculations of the methylene molecule. We further generalize this method to the relativistic four component regime and show how to efficiently solve the eigenproblem of the Dirac-Coulomb(-Breit) Hamiltonian on a quantum computer. We demonstrate the func- tionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with 3 qubits and 9 or 10 CNOTs, which implement a proof-of-principle relativistic quantum chemical calculation for this molecule and might be suitable for an experimental realization. 1

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Books on the topic "Coulomb operator, Quantum chemistry"

1

Introduction to Quantum Graphs (Mathematical Surveys and Monographs). American Mathematical Society, 2012.

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Book chapters on the topic "Coulomb operator, Quantum chemistry"

1

Gitman, D. M., I. V. Tyutin, and B. L. Voronov. "Dirac Operator with Coulomb Field." In Self-adjoint Extensions in Quantum Mechanics, 411–48. Boston: Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-4662-2_9.

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2

Gallone, Matteo. "Self-Adjoint Extensions of Dirac Operator with Coulomb Potential." In Advances in Quantum Mechanics, 169–85. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58904-6_10.

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3

Karwowski, Jacek. "Dirac Operator and Its Properties." In Handbook of Relativistic Quantum Chemistry, 1–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-642-41611-8_22-1.

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4

Karwowski, Jacek. "Dirac Operator and Its Properties." In Handbook of Relativistic Quantum Chemistry, 3–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-642-40766-6_22.

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5

Keller, Ole. "The Route to the Maxwell–Lorentz Operator Equations in the Coulomb Gauge." In Quantum Theory of Near-Field Electrodynamics, 435–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17410-0_23.

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6

Karwowski, Jacek. "The Dirac Operator in Quantum Chemistry and Physics." In Quantum Systems in Physics, Chemistry, and Biology, 361–74. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50255-7_22.

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7

Gebremedhin, Daniel H., and Charles A. Weatherford. "Two-Range Addition Theorem for Coulomb Sturmians." In Advances in the Theory of Quantum Systems in Chemistry and Physics, 71–81. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-2076-3_4.

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8

Glushkov, Alexander V. "Operator Perturbation Theory for Atomic Systems in a Strong DC Electric Field." In Advances in Quantum Methods and Applications in Chemistry, Physics, and Biology, 161–77. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01529-3_9.

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9

Dyall, Kenneth G., and Knut Faegri. "Spin Separation and the Modified Dirac Equation." In Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.003.0022.

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In the preceding chapters, the theory for calculations based on the Dirac equation has been laid out in some detail. The discussion of the methods included a comparison with equivalent nonrelativistic methods, from which it is apparent that four-component calculations will be considerably more expensive than the corresponding nonrelativistic calculations—perhaps two orders of magnitude more expensive. For this reason, there have been many methods developed that make approximations to the Dirac equation, and it is to these that we turn in this part of the book. There are two elements of the Dirac equation that contribute to the large amount of work: the presence of the small component of the wave function and the spin dependence of the Hamiltonian. The small component is primarily responsible for the large number of two-electron integrals which, as will be seen later, contain all the lowest-order relativistic corrections to the electron–electron interaction. The spin dependence is incorporated through the kinetic energy operator and the correction to the electronic Coulomb interaction, and also through the coupling of the spin and orbital angular momenta in the atomic 2-spinors, which form a natural basis set for the solution of the Dirac equation. Spin separation has obvious advantages from a computational perspective. As we will show for several spin-free approaches below, a spin-free Hamiltonian is generally real, and therefore real spin–orbitals may be employed for the large and small components. The spin can then be factorized out and spin-restricted Hartree–Fock methods used to generate the one-electron functions. In the post-SCF stage, where the no-pair approximation is invoked, the transformation of the integrals from the atomic to the molecular basis produces a set of real molecular integrals that are indistinguishable from a set of nonrelativistic MO integrals, and therefore all the nonrelativistic correlation methods may be employed without modification to obtain relativistic spin-free correlated wave functions. In most cases, spin–free relativistic effects dominate the relativistic corrections to electronic structure. We will show later that in a perturbation expansion based on the nonrelativistic wave function, the spin-free effects for a closed-shell system enter in first order, whereas the spin-dependent effects make their first contribution in second order.

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10

"Evaluation of the Coulomb Repulsion Integral Over 1s AOs." In Quantum Chemistry, 587–90. Elsevier, 2006. http://dx.doi.org/10.1016/b978-012457551-6/50020-2.

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Conference papers on the topic "Coulomb operator, Quantum chemistry"

1

Porter, Richard N., Dong-Qing Wei, and Xi-Jun Wang. "The Quantum Field Theory of the Ensemble Operator." In THEORY AND APPLICATIONS OF COMPUTATIONAL CHEMISTRY—2008. AIP, 2009. http://dx.doi.org/10.1063/1.3108378.

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