The PBC-GEBF method is a linear-scaling quantum mechanics (QM) method, in which the ground-state energy per unit of a periodic system is approximately estimated from the ground-state energies of a series of finite subsystems. From: Comprehensive Computational Chemistry (First Edition), 2024 ...
Journal of Computational ChemistryT. Amisaki. Precise and efficient Ewald summation for periodic fast multipole method. J. Comput. Chem., 21, 1075 (2000).Amisaki T. Precise and efficient Ewald summation for periodic fast multipole method. J Comput Chem. 2000; 21 :1075....
O. V. Polyakov, “Inequalities for upper bounds of seminorms of the class W r H ω ” in: Approximation of Functions and Summation of Series [in Russian], Dnepropetrovsk University, Dnepropetrovsk (1991), pp. 51–55. About this Article Title On inequalities for seminorms of certain clas...
5. O. Costin, On Borel summation and Stokes phenomena for rank one nonlinear systems of ODE's, Duke Math. J. 93:289–344 (1998). O. Costin, R. D. Costin, and J. Lebowitz, Transition to the continuum of a particle in time-periodic potentials, in Advances in Differential Equations an...
Thus, all elements of the L ×N matrix M are in the range of [0, 1 + α]. The matrix M is called the LMS of the signal x. The second step of the algorithm comprises a row-wise summation of the LMS matrix M N k mk ,i , for k {1,2, ,L} (3) i 1 The ...
To handle long-range interactions, either the size of the simulation box must be increased (which is obvious, but not always feasible), or the Eward summation should be used. A second limitation of the periodicity is that any attempt to obtain quantities or simulate processes (e.g. phase ...
This sum is inconsistent with the electric field in ferroelectric materials. We introduce summation methods based on the concept of neutral charge groups, a notion common in computational chemistry. If a charge group has moments of order < kappa vanishing, then the sum for partial derivative(alpha...
The Royal Society of ChemistryPhysical Chemistry Chemical PhysicsZhang, P., Truhlar, D. G., and Gao, J. (2012). Fragment-based quantum mechanical methods for periodic systems with Ewald summation and mean image charge convention for long-range electrostatic interactions, Phys. Chem. Chem. Phys....
In this method, the average electrostatic potential 蠁 mean , which is introduced to meet the periodic boundary condition, is taken as a parameter during the least squares fitting of the ESP from first-principles calculations and used in the Ewald summation. A comparison of the two methods, i...
In addition, the summation of certain classes of diagrams up to infinite order in the off-diagonal Fock elements as well as the Epstein-Nesbet partitioning of the full Hamiltonian are discussed. The problem of intruder states, frequently encountered in many-body perturbation theory, is dealt with...