Acceleration of Ab Initio QM/MM Calculations under Periodic Boundary Conditions by Multiscale and Multiple Time Step Approaches

2014 ◽  
Vol 10 (10) ◽  
pp. 4175-4183 ◽  
Author(s):  
Kwangho Nam
Keyword(s):  
Boundary Conditions ◽  
Ab Initio ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Multiple Time ◽  
Time Step ◽  
Multiple Time Step

Band engineering and charge separation in the Mo1−xWxS2/TiO2heterostructure by alloying: first principle prediction

RSC Advances ◽  
2015 ◽  
Vol 5 (36) ◽  
pp. 28460-28466 ◽  
Author(s):  
M. Faraji ◽  
M. Sabzali ◽  
S. Yousefzadeh ◽  
N. Sarikhani ◽  
A. Ziashahabi ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Ab Initio ◽  
Electronic Properties ◽  
Charge Separation ◽  
Density Functional Calculations ◽  
Density Functional ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
First Principle ◽  
Band Engineering

The composition dependent electronic properties of the Mo1−xWxS2monolayer deposited over a TiO2(110) substrate were investigated based onab initiodensity functional calculations by applying periodic boundary conditions.

scholarly journals Multiple time step integrators in ab initio molecular dynamics

2014 ◽  
Vol 140 (8) ◽  
pp. 084116 ◽  
Author(s):  
Nathan Luehr ◽  
Thomas E. Markland ◽  
Todd J. Martínez
Keyword(s):  
Molecular Dynamics ◽  
Ab Initio ◽  
Ab Initio Molecular Dynamics ◽  
Multiple Time ◽  
Time Step ◽  
Multiple Time Step

Molecular Dynamics Using Non-Variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

2019 ◽  
Author(s):  
Pier Paolo Poier ◽  
Louis Lagardere ◽  
Jean-Philip Piquemal ◽  
Frank Jensen
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Force Fields ◽  
Periodic Boundary Conditions ◽  
Computational Effort ◽  
Polarizable Force Fields ◽  
Energy Models ◽  
Capacity Model ◽  
Energy Gradient ◽  
Polarization Models

<div> <div> <div> <p>We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. </p><div> <div> <div> <p>By making use of a Lagrange formalism, however, this computational demanding task can be re- placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p><div><div><div> </div> </div> </div> <p> </p><div> <div> <div> <p>variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p> </div> </div> </div> </div> </div> </div> </div> </div> </div>

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

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