On the connection between probability density analysis, QTAIM, and VB theory

2020 ◽  
Vol 22 (44) ◽  
pp. 25892-25903
Author(s):  
Leonard Reuter ◽  
Arne Lüchow
Keyword(s):  
Probability Density ◽  
Density Analysis ◽  
Electron Probability Density ◽  
Lewis Structures

The Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|2.

scholarly journals Decoding the Chemical Bond—On the Connection between Probability Density Analysis, QTAIM, and VB Theory

2020 ◽  
Author(s):  
Leonard Reuter ◽  
Arne Lüchow
Keyword(s):  
Probability Density ◽  
First Principles ◽  
Valence Bond ◽  
Chemical Compounds ◽  
Wave Functions ◽  
Basis Set ◽  
Density Analysis ◽  
Bond Theory ◽  
Lewis Structures

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|². Doing so, we introduce valence bond weight definitions that do not collapse in the basis set limit.

Decoding the Chemical Bond—On the Connection between Probability Density Analysis, QTAIM, and VB Theory

2020 ◽  
Author(s):  
Leonard Reuter ◽  
Arne Lüchow
Keyword(s):  
Probability Density ◽  
First Principles ◽  
Valence Bond ◽  
Chemical Compounds ◽  
Wave Functions ◽  
Basis Set ◽  
Density Analysis ◽  
Bond Theory ◽  
Lewis Structures

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|². Doing so, we introduce a valence bond weight definition that does not collapse in the basis set limit.

scholarly journals Decoding the Chemical Bond—On the Connection between Probability Density Analysis, QTAIM, and VB Theory

2020 ◽  
Author(s):  
Leonard Reuter ◽  
Arne Lüchow
Keyword(s):  
Probability Density ◽  
First Principles ◽  
Valence Bond ◽  
Chemical Compounds ◽  
Wave Functions ◽  
Basis Set ◽  
Density Analysis ◽  
Bond Theory ◽  
Lewis Structures

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|². Doing so, we introduce a valence bond weight definition that does not collapse in the basis set limit.

Time-dependent electric field effect on the photodetachment dynamics of negative ions

2017 ◽  
Vol 95 (5) ◽  
pp. 507-513 ◽  
Author(s):  
De-hua Wang
Keyword(s):  
Electric Field ◽  
Probability Density ◽  
External Electric Field ◽  
Negative Ions ◽  
Time Dependent ◽  
Negative Ion ◽  
Electric Field Effect ◽  
Electron Trajectories ◽  
Oscillatory Pattern ◽  
Electron Probability Density

This paper addresses the photodetachment dynamics of a negative ion in a time-dependent electric field based on the semiclassical open-orbit theory. The photodetached electron probability density in a real time domain is studied in a gradient electric field for the first time. It is found that because of the influence of the gradient electric field, two or more electron trajectories can arrive at a given point on the detector, and the interference effect between these electron trajectories causes oscillatory structures in the electron probability density. Our calculation results suggest that when the external electric field changes very slowly with time, only two electron trajectories can arrive at a given point on the detector and the electron probability density exhibits a regular two-term oscillatory pattern. However, when the electric field changes quickly with time, four electron trajectories can reach the detector, which makes the oscillatory structures in the electron probability density become much more complicated. In addition, the electric field strength, photon energy, and the position of the detector can affect the electron probability density of this system sensitively. Our study provides a clear and intuitive picture for the photodetachment dynamics of the negative ion in the external electric field from a time-dependent viewpoint and may guide the future experimental researches on the photodetachment microscopy of negative ions in the time-dependent electric field.

Joint probability density analysis of the structure and dynamics of the vorticity field of a turbulent boundary layer

1998 ◽  
Vol 367 ◽  
pp. 291-328 ◽  
Author(s):  
LAWRENCE ONG ◽  
JAMES M. WALLACE
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Probability Density ◽  
Velocity Gradient ◽  
Joint Probability ◽  
Simulated Data ◽  
Wall Region ◽  
Rate Of Increase ◽  
Density Analysis ◽  
Joint Probability Density

An experimental study of a turbulent boundary layer at Rθ≈1070 and Rτ≈543 was conducted. Detailed measurements of the velocity vector and the velocity gradient tensor within the near-wall region were performed at various distances from the wall, ranging from approximately y+=14 to y+=89. The measured mean statistical properties of the fluctuating velocity and vorticity components agree well with previous experimental and numerically simulated data. These boundary layer measurements were used in a joint probability density analysis of the various component vorticity and vorticity–velocity gradient products that appear in the instantaneous vorticity and enstrophy transport equations. The vorticity filaments that contribute most to the vorticity covariance Ω[bar]xΩ [bar]y in this region were found to be oriented downstream with angles of inclination to the wall, when projected on the streamwise (x, y)-plane, that decrease with distance moving from the buffer to the logarithmic layer. When projected on the planview (x, z)- and cross-stream (y, z)-planes, the vorticity filaments that most contribute to the vorticity covariances Ω [bar]xΩ [bar]z and Ω [bar]yΩ [bar]z have angles of inclination to the z-ordinate axis that increase with distance from it. All the elements of the ΩiΩj ∂Ui/∂xj term in the enstrophy transport equation, i.e. the term that describes the rate of increase or decrease of the enstrophy by vorticity filament stretching or compression by the strain-rate field, have been examined. On balance, the average stretching of the vorticity filaments is greater than compression at all y+ locations examined here. However, some individual velocity gradient components compress the vorticity filaments, on average, more than they stretch them.

Probing electron probability-density in parabolic quantum wells

1997 ◽  
Vol 1 (1-4) ◽  
pp. 254-258 ◽  
Author(s):  
G. Salis ◽  
K. Ensslin ◽  
K.B. Campman ◽  
K. Maranowski ◽  
A.C. Gossard
Keyword(s):  
Quantum Wells ◽  
Probability Density ◽  
Electron Probability Density ◽  
Parabolic Quantum Wells
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