Electronic and nuclear flux analysis on nonadiabatic electron transfer reaction: A view from single‐configuration adiabatic born–huang representation
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Abstract:
A detailed flux analysis on nonadiabatically coupled electronic and nuclear dynamics in the intramolecular electron transfer of LiF is presented. Full quantum dynamics both of electrons and nuclei within two‐state model has uncovered interesting features of the individual fluxes (current of probability density) and correlation between them. In particular, a spatiotemporal oscillatory pattern of electronic flux has been revealed, which reflects the coherence coming from spatiotemporal differential overlap between nuclear wavepackets running on covalent and ionic potential curves. In this regard, a theoretical analogy between the nonadiabatic transitions and the Rabi oscillation is surveyed. We also present a flux–flux correlation between the nuclear and electronic motions, which quantifies the extent of deviation of the actual electronic and nuclear coupled dynamics from the Born–Oppenheimer adiabatic limit, which is composed only of a single product of the adiabatic electronic and nuclear wavefunctions. © 2018 Wiley Periodicals, Inc.Keywords:
Electronic correlation
Rabi cycle
Oscillation (cell signaling)
Born–Oppenheimer approximation
A recently developed method (the GF method) which is equivalent to optimizing the orbitals of a Slater determinant after spin projection has been applied to H−, He, Li+, Be++, Li, Be+,B++, Li−, Be, B+ and C++. These wavefunctions, which can be given an independent particle interpretation, yield better energies than those of the Hartree-Fock method. For example, H− and Li− are correctly predicted to be stable in contradistinction with the Hartree-Fock results. The new correlation energies are tabulated and compared to the Hartree-Fock values. In the case of the two-electron systems the new wavefunctions are nearly at the radial limit, accounting for 93% to 97% of the radial correlation error present in the Hartree-Fock description.
Electronic correlation
Slater determinant
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Abstract ‘This chapter sketches how the electron correlation is treated in post-Hartree-Fock (HF) wavefunction methods. The distinction between static and dynamic correlation is explained. A configuration interaction (CI) wavefunction is a linear combination of several or many Slater determinants (SDs). Following a HF calculation, different SDs can be constructed by replacing 1, 2, 3, … occupied orbitals in the HF wavefunction with 1, 2, 3,… unoccupied or virtual orbitals, leading to pseudo-excited electron configurations at the singles, doubles, triples, … (S, D, T, …) level. The virtual orbitals are usually available as a by-product of the HF calculation in a basis set. Full CI (FCI) considers all possible substitutions, up to N-fold for an N-electron system. FCI is impractical for all but the smallest molecules. CI truncated at a lower level, e.g. S and D, suffers from lack of size extensitivity. Truncated coupled-cluster (CC) is size extensive. Open-shell systems generally require a multi-reference treatment. The chapter concludes with a treatment of the static correlation in the bond breaking of H2.
Electronic correlation
Slater determinant
Coupled cluster
Open shell
Electron configuration
Basis (linear algebra)
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Adiabatic theorem
Born–Huang approximation
Diatomic molecule
Born–Oppenheimer approximation
Adiabatic Quantum Computation
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Diabatic
Born–Oppenheimer approximation
Adiabatic theorem
Vibronic coupling
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The excitation transitions considered are 11S to 21P and 11S to 31P. Electron correlation is introduced into the description of the 11S ground state in a systematic way by using the natural expansion of a configuration-interaction (CI) wavefunction developed by Weiss. By truncating this expansion to the first X terms and renormalizing a series of wavefunctions ranging from a Hartree-Fock equivalent (X=1) to the full CI function (X=15) are obtained. Operating within the first Born approximation, three standard formulations for evaluating f(K) are used and their sensitivity with respect to correlation effects is discussed and a comparison of the present results is made with those of other workers. Although the inclusion of the first correlation configuration in the 11S wavefunction did not necessarily guarantee an improvement in f(K), the introduction of the second correlation term in the natural expansion gave rise to a significant improvement in f(K) for all K regardless of the mode of calculation.
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Full configuration interaction
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The implications of the repulsive Coulombic interaction between two electrons are discussed. They lead to a general correlation property of the wavefunction when the two electrons are close to each other. The importance of this property is illustrated by including a simple correlation function in two pedagogically useful model wavefunctions for the ground state and (2p)2 3P state of He and isoelectronic ions. It leads to a significant improvement in the predicted values for the energies and other properties.
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Electronic correlation
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Born–Oppenheimer approximation
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This report presents a new approach for treating the coupling of electrons and nuclei in quantum mechanical calculations for molecules and condensed matter. It includes the standard "Born-Oppenheimer approximation" as a special case but treats both adiabatic and non-adiabatic corrections using perturbation theory. The adiabatic corrections include all terms that do not explicitly involve the nuclear wavefunctions, so that the nuclei move on a single electronic potential surface. The non-adiabatic corrections, which allow the nuclei to move on more than one potential surface, include coupling between the electronic and nuclear wavefunctions. The method is related to an approach first proposed by Born and Huang, but it differs in the methodology and in the definition of the electronic wavefunctions and potential surfaces. A simple example is worked out to illustrate the mechanics of the technique. The report also includes a review of previous work.
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Born–Huang approximation
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The hydride ion is one of the simplest systems possessing electrons with antiparallel spins and, therefore, it is ideal for a study of electron correlation. Five wavefunctions for H− have been analysed and compared. Two functions were based on the single determinant independent-particle model and three were correlated wavefunctions. The present article is devoted, in the main, to a discussion of radial correlation, hence, graphs are presented for the two-particle density ρ(r1, r2) and the radial density D(r) for each treatment. Values are determined for the coherent x-ray scattering contribution f00(X), the three-dimensional Dirac delta functions 〈δ3(r1)〉 and 〈δ3(r12)〉, and also for 〈rn〉 when −2 ≤ n ≤ 4. In this way, the effect of electron correlation on various physical properties could be examined. In particular, by comparing the results with those obtained from a more accurate wavefunction, it was possible to assess the usefulness of a limited configuration-interaction treatment which employed `floating' orbitals. On the whole, this treatment of H− proved to be good. Finally, it was observed that the inclusion of electron correlation effects within a wavefunction for H− causes the electron density to become more diffuse, the inner regions around the nucleus resembling, fairly closely, the density within an isolated hydrogen atom.
Electronic correlation
Slater determinant
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