Calculation of Intermolecular Interaction Energies by Direct Numerical Integration over Electron Densities. 2. An Improved Polarization Model and the Evaluation of Dispersion and Repulsion Energies

2003 ◽  
Vol 107 (10) ◽  
pp. 2344-2353 ◽  
Author(s):  
A. Gavezzotti
Keyword(s):  
Numerical Integration ◽  
Intermolecular Interaction ◽  
Interaction Energies ◽  
Electron Densities ◽  
Polarization Model ◽  
Direct Numerical Integration

scholarly journals Intermolecular interaction energies in transition metal coordination compounds

CrystEngComm ◽  
2015 ◽  
Vol 17 (48) ◽  
pp. 9300-9310 ◽  
Author(s):  
Andrew G. P. Maloney ◽  
Peter A. Wood ◽  
Simon Parsons
Keyword(s):  
Transition Metal ◽  
Transition Metals ◽  
Crystal Structures ◽  
Intermolecular Interaction ◽  
Coordination Compounds ◽  
Metal Coordination ◽  
Interaction Energies

The PIXEL method has been parameterised and validated for transition metals, extending its applicability from ~40% to ~85% of all published crystal structures.

A Quasiperiodic Mathieu Equation

1995 ◽  
Author(s):  
Richard Rand ◽  
Rachel Hastings
Keyword(s):  
Numerical Integration ◽  
Mathieu Equation ◽  
Stability Regions ◽  
Regions Of Stability ◽  
Extensive Computation ◽  
The Stability ◽  
Direct Numerical Integration

Abstract In this work we investigate the following quasiperiodic Mathieu equation: x ¨ + ( δ + ϵ cos ⁡ t + ϵ cos ⁡ ω t ) x = 0 We use numerical integration to determine regions of stability in the δ–ω plane for fixed ϵ. Graphs of these stability regions are presented, based on extensive computation. In addition, we use perturbations to obtain approximations for the stability regions near δ=14 for small ω, and we compare the results with those of direct numerical integration.

Fully developed travelling wave solutions and bubble formation in fluidized beds

1997 ◽  
Vol 334 ◽  
pp. 157-188 ◽  
Author(s):  
B. J. GLASSER ◽  
I. G. KEVREKIDIS ◽  
S. SUNDARESAN
Keyword(s):  
Numerical Integration ◽  
Fluidized Beds ◽  
Bubble Formation ◽  
Travelling Wave ◽  
Numerical Continuation ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Averaged Equations ◽  
Wide Range ◽  
Direct Numerical Integration

It is well known that most gas fluidized beds of particles bubble, while most liquid fluidized beds do not. It was shown by Anderson, Sundaresan & Jackson (1995), through direct numerical integration of the volume-averaged equations of motion for the fluid and particles, that this distinction is indeed accounted for by these equations, coupled with simple, physically credible closure relations for the stresses and interphase drag. The aim of the present study is to investigate how the model equations afford this distinction and deduce an approximate criterion for separating bubbling and non-bubbling systems. To this end, we have computed, making use of numerical continuation techniques as well as bifurcation theory, the one- and two-dimensional travelling wave solutions of the volume-averaged equations for a wide range of parameter values, and examined the evolution of these travelling wave solutions through direct numerical integration. It is demonstrated that whether bubbles form or not is dictated by the value of Ω = (ρsv3t/Ag) 1/2, where ρs is the density of particles, vt is the terminal settling velocity of an isolated particle, g is acceleration due to gravity and A is a measure of the particle phase viscosity. When Ω is large (> ∼ 30), bubbles develop easily. It is then suggested that a natural scale for A is ρsvtdp so that Ω2 is simply a Froude number.

Stacked and H-Bonded Cytosine Dimers. Analysis of the Intermolecular Interaction Energies by Parallel Quantum Chemistry and Polarizable Molecular Mechanics.

2015 ◽  
Vol 119 (30) ◽  
pp. 9477-9495 ◽  
Author(s):  
Nohad Gresh ◽  
Judit E. Sponer ◽  
Mike Devereux ◽  
Konstantinos Gkionis ◽  
Benoit de Courcy ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Molecular Mechanics ◽  
Intermolecular Interaction ◽  
Interaction Energies
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