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

1985 ◽  
Vol 83 (1) ◽  
pp. 247-254 ◽  
Author(s):  
Y. Marechal
Keyword(s):  
Wave Functions ◽  
Oppenheimer Approximation

scholarly journals Electronic non-adiabatic states: towards a density functional theory beyond the Born–Oppenheimer approximation

2014 ◽  
Vol 372 (2011) ◽  
pp. 20130059 ◽  
Author(s):  
Nikitas I. Gidopoulos ◽  
E. K. U. Gross
Keyword(s):  
Wave Function ◽  
Density Functional ◽  
Adiabatic Approximation ◽  
Complete System ◽  
Wave Functions ◽  
Nuclear Wave Function ◽  
Functional Theory ◽  
Novel Treatment ◽  
Oppenheimer Approximation ◽  
Adiabatic Case

A novel treatment of non-adiabatic couplings is proposed. The derivation is based on a theorem by Hunter stating that the wave function of the complete system of electrons and nuclei can be written, without approximation, as a Born–Oppenheimer (BO)-type product of a nuclear wave function, X ( R ), and an electronic one, Φ R ( r ), which depends parametrically on the nuclear configuration R . From the variational principle, we deduce formally exact equations for Φ R ( r ) and X ( R ). The algebraic structure of the exact nuclear equation coincides with the corresponding one in the adiabatic approximation. The electronic equation, however, contains terms not appearing in the adiabatic case, which couple the electronic and the nuclear wave functions and account for the electron–nuclear correlation beyond the BO level. It is proposed that these terms can be incorporated using an optimized local effective potential.

Excitation and ionization of atoms by electron impact - The Born and Oppenheimer approximations part I and part II

1950 ◽  
Vol 243 (860) ◽  
pp. 93-143 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Wave Functions ◽  
Exact Bound ◽  
Oppenheimer Approximation ◽  
Collision Processes ◽  
The One ◽  
Detailed Balancing ◽  
Conservation Theorem ◽  
Comparison Data

It is important, for many applications, to have reliable data on the magnitudes of the cross-sections for excitation and ionization of atoms and ions by electrons. In part I the usual approximations (those of Born and of Oppenheimer) which are made to obtain theoretical values are critically examined. It is pointed out that the assumption of separable bound wave functions may often lead to considerable errors. In the case of the Oppenheimer approximation the errors may even be such as to give results violating the principle of detailed balancing. Circumstances in which these errors are likely to be serious are analyzed, and precautions which may be taken to reduce them are proposed. The conditions under which the approximations are likely to fail, even when exact bound wave func­- tions are used, appear to be related to the magnitude of certain coupling terms which are ignored in obtaining the approximations. The usefulness of certain conservation theorems which limit the possible size of collision cross-sections is also pointed out. A summary of those general properties of inelastic cross-sections which are reliably given by the theory is included. In part II the available experimental data are compared with the predictions of the Born and Oppenheimer approximations. The collision processes studied include the following: excitation of H, He, Na, Ne and Hg; ionization of H 2 , He, Ne, Hg, Ni ( K ) and Ag (K and LUI). The investigation shows that the Born approximation is the one that should generally be used in the treatment of transitions which can take place without electron exchange having to be invoked. For these the approximation achieves a considerable degree of success. As far as can be judged from the comparison data available, the main defects are that the maxima of the predicted cross-section energy curves tend to be too pronounced, and to be located too close to the critical potentials. In the case of transitions involving a reversal of electron spin the Oppenheimer approximation must be used. Unfortunately, it proves to be very unsatisfactory. Thus for non-hydrogenic systems it may give very different results according to whether a prior or a post interaction is adopted. It leads to frequent violations of the conservation theorem and cannot be relied upon even to give the detailed shape of cross-section against energy curves. By generalizing from the evidence collected, an attempt is made to specify the conditions under which the Born and Oppenheimer approximations are most reliable; on this basis, proposals for systemization are made. Attention is drawn to the fact that some (but by no means all) of the observed excitation functions possess an extremely sharp peak just beyond the critical potential. The theory seems unable to reproduce this peculiar feature. It does not appear in the observed ionization functions.

Magnetotunneling spectroscopy imaging of electron wave functions in self-assembled InAs quantum dots

2001 ◽  
Vol 171 (12) ◽  
pp. 1365
Author(s):  
E.E. Vdovin ◽  
Yu.N. Khanin ◽  
Yu.V. Dubrovskii ◽  
A. Veretennikov ◽  
A. Levin ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Wave Functions ◽  
Electron Wave ◽  
Inas Quantum Dots ◽  
Self Assembled

Gravity as the curvature of the wave function of the universe.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Main Task ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Relative Wave Function ◽  
New Equation ◽  
The Universe

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.

On the conformational structure of nicotinamide and methyl-1,4-dihydronicotinamide

1979 ◽  
Vol 44 (9) ◽  
pp. 2633-2638 ◽  
Author(s):  
Hans-Jörg Hofmann ◽  
Josef Kuthan
Keyword(s):  
Molecular Structure ◽  
Continuum Model ◽  
Model Analysis ◽  
Wave Functions ◽  
Conformational Structure ◽  
Influence Of Solvent

The conformation of nicotinamide (I) and 1-methyl-1,4-dihydronicotinamide (II) was examined using the NDDO method. The influence of solvent on the molecular structure of the title compounds was estimated by means of a continuum model. Analysis of the NDDO wave functions contributes to the knowledge about the mechanism of the NADH reduction.

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