Born-Oppenheimer Treatment Research Articles

Erratum to “A two-dimensional Born–Oppenheimer treatment of intramolecular electron transfer reactions”

On p. 71, the expression for p in Eq. (8) should read p=2[C2]. On p. 72, Eq. (18) should read s=2 V0 /Es. On p. 73, Eqs. (30) and (31), the symbol d should be replaced by b. On p. 74, Eq. (38) should read la(a−2m)−2mnl sign V+ (a−m)−n=0. On p. 76, right-hand column, line 2 from bottom, the phrase ‘functions Qn ’ should read ‘functions Q9n ’. On p. 80, the third column of numbers in Table 4 (DU) should be replaced by the following entries: 0.0092, 0.013, 0.014, 0.024, 0.031, 0.035.

A two-dimensional Born–Oppenheimer treatment of intramolecular electron transfer reactions

The Born–Oppenheimer (BO) formulation of polar solvation is developed and implemented at the semiemperical (PM3) configuration interaction (CI) level, yielding estimates of electron transfer (ET) coupling elements (V0) for intramolecular ET in several families of radical ion systems. In contrast to the traditional treatment based on a single solvent coordinate and a fixed gas-phase coupling element, the present treatment yields a self-consistent characterization of kinetic parameters in a 2-dimensional solvent framework which includes an exchange coordinate. The dependence of V0 on inertial solvent contributions and on donor/acceptor separation (rDA) is discussed.

Non-resonant energy transfer between Tb3+ and Eu3+ in the cubic hexachloroelpasolite crystals Cs2NaTb1-xEuxCl6 (x=0.01-0.15)

Luminescence decay curves have been measured for the Eu3+ emission and Tb3+ emission in the cubic crystals Cs2NaTb1-xEuxCl6 at 80 and 293 K using pulsed dye laser excitation into the 5D4 state of Tb3+ and the 5D1 state of Eu3+. For excitation of Tb3+, efficient energy transfer occurs to the 5D0 state (but not the 5D1 state) of Eu3+ and there is fast energy migration within the 5D4 state. When excitation is into the 5D1 state of Eu3+, phonon-assisted coupling to the Tb3+ ions results in enhanced relaxation to the 5D0 state but the lifetime of 5D0 is not affected by the presence of Tb3+. In all cases the non-resonant energy transfer involves creation or annihilation of phonons which have odd parity with respect to the metal centers and cannot be explained within the usual Born-Oppenheimer treatment of phonon-assisted energy transfer. The mechanism of the energy transfer processes is considered in detail.

Corrections to the Born-Oppenheimer treatment of the tunneling splitting in the hydrogen fluoride dimer

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTCorrections to the Born-Oppenheimer treatment of the tunneling splitting in the hydrogen fluoride dimerEdwin L. Sibert IIICite this: J. Phys. Chem. 1989, 93, 13, 5022–5024Publication Date (Print):June 1, 1989Publication History Published online1 May 2002Published inissue 1 June 1989https://doi.org/10.1021/j100350a005RIGHTS & PERMISSIONSArticle Views53Altmetric-Citations32LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (383 KB) Get e-Alerts

A geometric interpretation for the interacting-boson-fermion model

A geometric oriented approach for studying the interacting-boson-fermion model for odd- A nuclei is presented. A deformed single-particle hamiltonian is derived by means of an algebraic Born-Oppenheimer treatment. Observables concerning spectrum and transitions are calculated for the case of a single- j fermion coupled to a prolate core boson number and arbitrary deformation.

Energies and dynamical couplings of 1,3σ and 1,3Π states of NaHe +, modified with a common translation factor

In a recent publication the energies and radial couplings for the 1σ and 3σ states of the NaHe + quasimolecule were presented and their main characteristics studied. A conclusion of this study was that the strong dependence of the radial couplings on the choice of origin of electronic coordinates precluded a molecular treatment of He + + Na collisions, unless translation factors were introduced. The present work improves the previous Born—Oppenheimer treatment, and shows how the dynamical couplings, modified by the introduction of a common translation factor, have a behaviour that is not only more correct, but in fact simpler than that of the original Born—Oppenheimer states. In addition, energies and couplings for the 1Π and 3Π states of lowest energy, which are populated during the collision, are evaluated.

Numerical coupled Hartree–Fock study of the total (electronic and nuclear) parallel polarizability and hyperpolarizability for the FH, H+2, HD+, and D+2 molecules

Polarizabilities and hyperpolarizabilities of molecules have both electronic and vibrational contributions. The latter can be important in experimental determinations involving static electric fields, as in the Kerr effect. This paper reports purely numerical coupled Hartree–Fock calculations for the electronic states of FH. Electronic energy surfaces obtained for different electric field strengths are then used to solve, numerically, the nuclear equation for several vibrational states. The vibrational contributions to βzzz exceed the electronic component and change the sign of the total hyperpolarizability. γzzzz is similarly increased by an order of magnitude. It is also shown that a Born–Oppenheimer treatment of H+2 for γzzzz is in perfect agreement with a recent fully nonadiabatic three particle solution.

Adiabatic wave functions beyond the Born–Oppenheimer approximation: Phase linking between electrons and nuclei

In order to improve the Born–Oppenheimer treatment of adiabaticity we impose to the electronic and nuclear wave functions to have a well defined phase difference. It enables us to correctly evaluate matrix elements of such quantities as momenta which are poorly evaluated in the Born–Oppenheimer description. The phase factor obeys an equation which we solve by successive approximations and leads to simple expressions for this phase factor. Taking the coupling of two harmonic oscillators as an exactly soluble example which may also be treated within this adiabatic approximation we show that the proposed formalism is rather easy to use and leads to significant improvements with respect to Born–Oppenheimer treatments. We suggest that this framework might be useful when treating systems which are weakly coupled but are not so different in their time evolutions as are electrons and nuclei.

Resonant Vibrational Excitation ofN2by Low-Energy Electrons: AnAb Initio R-Matrix Calculation

The resonant vibrational excitation of ${\mathrm{N}}_{2}$ by low-energy electrons is used to illustrate the newly developed $R$-matrix theory of vibrational excitation and dissociative attachment of Schneider, Le Dourneuf, and Burke. The ab initio calculations are performed which clearly illustrate the role of the internal states in describing these excitation processes and support the authors' contention that the essential physics is completely contained within a Born-Oppenheimer treatment of the total molecular Hamiltonian.