# Oppenheimer

That is, a molecule for which the minimum of the Born-Oppenheimer potential energy function corresponds to a [c.182]

Born M and Oppenheimer R 1927 Concerning the quantum theory of molecules Ann. Phys., Lpz 84 457-84 [c.1148]

B3.1.1.1 THE UNDERLYING THEORETICAL BASIS—THE BORN-OPPENHEIMER MODEL [c.2154]

B3.1.1.2 NON-BORN-OPPENHEIMER CORRECTIONS—RADIATIONLESS TRANSITIONS [c.2155]

Born M and Oppenheimer J R 1927 Ann. Phys., Lpz 84 457 [c.2192]

Pack R T and Hirschfelder J O 1970 Energy corrections to the Born-Oppenheimer approximation. The best adiabatic approximation J. Chem. Phys. 52 521-34 [c.2192]

Early treatments of molecules in which non-Born-Oppenheimer terms were included were made in [c.2192]

Mead C A and Truhlar D G 1979 On the determination of Born-Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei J. Chem. Phys. 70 2284 [c.2330]

NON-ADIABATIC EFFECTS IN CHEMICAL REACTIONS EXTENDED BORN-OPPENHEIMER EQUATIONS AND ITS APPLICATIONS [c.39]

Appendix A The Jahn-Teller Model and the Herzberg-Longuet-Higgins Phase Appendix B The Bom-Oppenheimer Treatment Appendix C Formulation of the Vector Potential References [c.40]

APPENDIX B THE BORN-OPPENHEIMER TREATMENT [c.82]

The approximation involved in Eq. (B.17) is known as the Bom-Oppenheimer approximation and this equation is called the Bom-Oppenheimer equation. [c.85]

M. Born and J. R, Oppenheimer, Ann. Phy. Leipzig 84, 457 (1927), [c.90]

The theory of Bom-Oppenheimer (BO) [62,63] has been hailed (in an authoritative but unfortunately unidentified source) as one of the greatest [c.98]

Yang-Mills field is conditioned by the finiteness of the basic Bom-Oppenheimer set. Detailed topics are noted in the introductory Section I. [c.169]

M. Born and R. J, Oppenheimer, Ann. Physik (Leipzig) 89, 457 (1927). [c.170]

M. Bom and J. R. Oppenheimer, Ann. Phys. (Leipzig) 84, 457 (1927), [c.215]

Many molecular beam experiments are performed at collision energies from a fraction of an electron volt to tens of electron volts. In such cases two or more stationary molecular electronic states and their potential energy surfaces can provide an adequate description provided also the effects of the nonadiabatic coupling terms are taken into account. Even in cases where a single PES is sufficient to describe the relevant forces on the participating nuclei one should augment the Bom-Oppenheimer PES with the diagonal kinetic energy correction to produce the so-called adiabatic approximation, something that is only rarely done in practice. [c.221]

B. Born-Oppenheimer Molecular Dynamics [c.250]

Knowledge of the underlying nuclear dynamics is essential for the classification and description of photochemical processes. For the study of complicated systems, molecular dynamics (MD) simulations are an essential tool, providing information on the channels open for decay or relaxation, the relative populations of these channels, and the timescales of system evolution. Simulations are particularly important in cases where the Bom-Oppenheimer (BO) approximation breaks down, and a system is able to evolve non-adiabatically, that is, in more than one electronic state. [c.251]

B. Born-Oppenheimer Molecular Dynamics [c.264]

Within the Bom-Oppenheimer (BO) approximation, A) and B) may be written as the product of an electronic wave function, M)gj and a nuclear wave function M) . [c.330]

Within the Bom-Oppenheimer approximation, the electronic wave function R)ei, is well defined, throughout the reaction and may be written analogously [cf. Eq. (6)] [c.344]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION OF MOLECULAR POTENTIAL ENERGIES [c.399]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION [c.401]

II. CRUDE BORN-OPPENHEIMER APPROXIMATION [c.401]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION [c.403]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION 511 [c.405]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION 513 [c.407]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION [c.409]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION [c.411]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION [c.413]

THE CRUDE BORN—OPPENHEIMER ADIABATIC APPROXIMATION 521 Consider the integral [c.415]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION 523 According to Eq. (A. 16), [c.417]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION 525 [c.419]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION [c.421]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION 529 1. First-Order Derivatives [c.423]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION 531 Thus, we obtain [c.425]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION 533 [c.427]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION 535 [c.429]

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION [c.431]

Quasiclassical Trajectory Calculations on a H -I- D2 Reaction at 2.20 eV in. The Extended Bom-Oppenheimer Approximation [c.39]

One of the most interesting observations in molecular physics was made by Herzberg and Longuet-Higgins (HLH) [1] when they were investigating the Jahn-Teller (JT) conical intersection (Cl) problem [2-15]. These authors found that in the presence of a Cl located at some point in configuration space (CS), the adiabatic electronic wave functions that are parametrically dependent on the nuclear coordinates became multivalued and proposed to correct the deficiency by multiplying the adiabatic wave functions of the two states with a unique phase factor (see Appendix A). More specifically, in the theory of molecular dynamics the Bom-Oppenheimer (BO) treatment [16] (see Appendix B) is based on the fact that the fast-moving electrons are distinguishable from the slow-moving nuclei in a molecular system. The BO approximation [16,17] (see Appendix B) has been made with this distinction and once the electronic eigenvalue problem is solved, the nuclear Schrddinger equation employing the BO approximation should be properly modified in order to avoid wrong observations. The BO approximation implies that the non-adiabatic coupling terms (see Appendix B) [18-30] are negligibly small, that is, it has been assumed that particularly at low-energy processes, the nuclear wave function on the upper electronic surface affect the corresponding lower wave function very little. As a consequence of this approximation, the product of the nuclear wave function on the upper electronic state and the non-adiabatic coupling terms are considered to be very small and will have little effect on the dynamics. On the other hand, when the non-adiabatic coupling terms are sufficiently large or infinitely large, the use of the ordinary BO approximation becomes invalid even at very low energies. Even though the components of the upper state wave function in the total wave function are small enough, their product with large or infinitely large non-adiabatic coupling terms may not be. The reason for having large non-adiabatic coupling terms is that the fast-moving electron may, in certain situations, create exceptionally large forces, causing the nuclei in some regions of CS to be strongly accelerated so that their velocities are no longer negligibly small. In this situation, when these terms responsible for this accelerated motion are ignored within the ordinary BO approximation, the relevance of the ordinary [c.40]

Electronic transitions fexcitations or deexcitations) can take place during the course of a chemical reaction and have important consequences for its dynamics. The motion of electrons and nuclei were first analyzed in a quantum mechanical framework by Bom and Oppenheimer [1], who separated the [c.179]

For some systems consisting of two-to-four atoms of light elements it is currently feasible to consider enough points for, say, the ground-state electronic energy Eo(R) such that appropriate interpolation techniques can produce the energy for all nuclear geometries below some suitable energy cutoff. The resulting function Eo R) is the Bom-Oppenheimer (BO) potential energy surface (PES) of the system. Traditional molecular reaction dynamics proceeds by considering such a PES to be the potential energy for the nuclear dynamics, which, of course, may be treated classically, semiclassically, or by employing quantum mechanical methods. The other energy eigenvalues E (R) similarly yield potential energy surfaces for electronically excited states. Each PES usually exhibits considerable structure for a polyatomic system and can provide instructive picmres with reactant and product valleys, local minima identifying stable species, and transition states providing gateways for the system to travel from one local minimum to another. Avoided crossings or more generally conical intersections and potential surface crossings are regions of dramatic chemical change in the system. The PES in this way provides attractive pictures of dynamical processes, which since the very beginning of molecular reaction dynamics have dominated our ways of thinking about molecular processes. [c.220]

II. Crude Born-Oppenheimer Approximarion in. Hydrogen Molecule Hamiltonian [c.399]

An alternative approximation scheme, also proposed by Bom and Oppenheimer [5-7], employed the straightforward perturbation method. To tell the difference between these two different BO approximation, we call the latter the crude BOA (CBOA). A main purpose of this chapter is to study the original BO approximation, which is often referred to as the crude BO approximation and to develop this approximation into a practical method for computing potential energy suifaces of molecules. [c.401]

See pages that mention the term

**Oppenheimer**:

**[c.2154] [c.64] [c.180] [c.400]**

Modern spectroscopy (2004) -- [ c.19 ]