Born-Oppenheimer method

Born-Oppenheimer approximation (physchem) The approximation, used in the Born-Oppenheimer method, that the electronic wave functions and energy levels at any instant depend only on the positions of the nuclei at that instant and not on the motions of the nuclei. Also known as adiabatic approximation. born ap an.hT-mar 3,prak s3,ma shan J... 

Born-Oppenheimer method Ipi-tyschemI A method for calculating the force constants between atoms by assuming that the electron motion is so fast compared with the nuclear motions that the electrons follow the motions of the nuclei adiabatically. born ap-an.hTm ar. meth ad ... 

Before we can discuss the recent developments further, we must discuss terminology. This will also provide a guide to earlier literature as well as to the classification we use in our review of recent papers (Section lOd). As mentioned, the total wave function in the Born-Oppenheimer method. is expressed as a product of electronic and vibrational wave functions. What has resulted is that different types of electronic wave functions have been used (which is not necessarily confusing), and that in many cases a particular selection has been called the Born-Oppenheimer approximation (which has led to confusion). We discuss here only the two predominant choices of... 

The process (19.47) has been subject to many theoretical studies [72-74]. The cross-section for v —> v transition is dominant for v v 1, and rapidly decreases when Av = e — v increases. The Born-Oppenheimer method used in [72, 73] for cross-section calculations of process (19.47) can also be applied to calculate the cross-sections for the process (19.48). Cross-section calculations have recently been performed for the process (19.49) with the IOSA method in the energy region up to 9eV [75], The processes (19.50) and (19.51) have been studied in [76] and [77], respectively, where their cross-sections can be found. 

We have derived time-reversible, symplectic, and second-order multiple-time-stepping methods for the finite-dimensional QCMD model. Theoretical results for general symplectic methods imply that the methods conserve energy over exponentially long periods of time up to small fluctuations. Furthermore, in the limit m —> 0, the adiabatic invariants corresponding to the underlying Born-Oppenheimer approximation will be preserved as well. Finally, the phase shift observed for symmetric methods with a single update of the classical momenta p per macro-time-step At should be avoided by... 

In the Car-Parrinello method [6] (and see, e.g., [24, 25, 16, 4]), the adiabatic time-dependent Born-Oppenheimer model is approximated by a fictitious Newtonian dynamics in which the electrons, represented by a set of... 

Both molecular and quantum mechanics methods rely on the Born-Oppenheimer approximation. In quantum mechanics, the Schrodinger equation (1) gives the wave functions and energies of a molecule. 

The applicability of the Born-Oppenheimer approximation for complex molecular systems is basic to all classical simulation methods. It enables the formulation of an effective potential field for nuclei on the basis of the SchrdJdinger equation. In practice this is not simple, since the number of electrons is usually large and the extent of configuration space is too vast to allow accurate initio determination of the effective fields. One has to resort to simplifications and semi-empirical or empirical adjustments of potential fields, thus introducing interdependence of parameters that tend to obscure the pure significance of each term. This applies in... 

The hrst step in theoretical predictions of pathway branching are electronic structure ab initio) calculations to define at least the lowest Born-Oppenheimer electronic potential energy surface for a system. For a system of N atoms, the PES has (iN — 6) dimensions, and is denoted V Ri,R2, - , RiN-6)- At a minimum, the energy, geometry, and vibrational frequencies of stationary points (i.e., asymptotes, wells, and saddle points where dV/dRi = 0) of the potential surface must be calculated. For the statistical methods described in Section IV.B, information on other areas of the potential are generally not needed. However, it must be stressed that failure to locate relevant stationary points may lead to omission of valid pathways. For this reason, as wide a search as practicable must be made through configuration space to ensure that the PES is sufficiently complete. Furthermore, a search only of stationary points will not treat pathways that avoid transition states. 

When the Drude particles are treated adiabatically, a SCF method must be used to solve for the displacements of the Drude particle, d, similarly to the dipoles Jtj in the induced dipole model. The implementation of the SCF condition corresponding to the Born-Oppenheimer approximation is straightforward and the real forces acting on the nuclei must be determined after the Drude particles have attained the energy minimum for a particular nuclear configuration. In the case of N polarizable atoms with positions r, the relaxed Drude particle positions r + d5CF are found by solving... 

With the characterized mechanism, the next key question is the origin of its catalytic power. A prerequisite for this investigation is to reliably compute free energy barriers for both enzyme and solution reactions. By employing on-the-fly Born-Oppenheimer molecular dynamics simulations with the ab initio QM/MM approach and the umbrella sampling method, we have determined free energy profiles for the methyl-transfer reaction catalyzed by the histone lysine methyltransferase SET7/9... 

Experimental probes of Born-Oppenheimer breakdown under conditions where large amplitude vibrational motion can occur are now becoming available. One approach to this problem is to compare theoretical predictions and experimental observations for reactive properties that are sensitive to the Born-Oppenheimer potential energy surface. Particularly useful for this endeavor are recombinative desorption and Eley-Rideal reactions. In both cases, gas-phase reaction products may be probed by modern state-specific detection methods, providing detailed characterization of the product reaction dynamics. Theoretical predictions based on Born-Oppenheimer potential energy surfaces should be capable of reproducing experiment. Observed deviations between experiment and theory may be attributed to Born-Oppenheimer breakdown. 

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