Molecular systems finite element

Coupling Atomistic and Continuum Length Scales in Heteroepitaxial Systems Multiscale Molecular-Dynamics/Finite-Element Simulations of Strain Relaxation in Si/Si3N4 Nanopixels. 

Molecular calculations provide approaches to supramolecular structure and to the dynamics of self-assembly by extending atomic-molecular physics. Alternatively, the tools of finite element analysis can be used to approach the simulation of self-assembled film properties. The voxel4 size in finite element analysis needs be small compared to significant variation in structure-property relationships for self-assembled structures, this implies use of voxels of nanometer dimensions. However, the continuum constitutive relationships utilized for macroscopic-system calculations will be difficult to extend at this scale because nanostructure properties are expected to differ from microstructural properties. In addition, in structures with a high density of boundaries (such as thin multilayer films), poorly understood boundary conditions may contribute to inaccuracies. 

Until recently, only estimates of the Hartree-Fock limit were available for molecular systems. Now, finite difference [16-24] and finite element [25-28] calculations can yield Hartree-Fock energies for diatomic molecules to at least the 1 ghartree level of accuracy and, furthermore, the ubiquitous finite basis set approach can be developed so as to approach this level of accuracy [29,30] whilst also supporting a representation of the whole one-electron spectrum which is an essential ingredient of subsequent correlation treatments. 

G. Scalmani, N. Rega, M. Cossi and V. Barone, Finite elements molecular surface in continuum solvent models for large chemical systems, J. Comput. Meth. Science Eng., 2 (2001) 159-164. 

An application of the molecular cubic lattice of systematically constructed distributed basis sets to the linear H%+ system, for which finite element results are available(68), has also been described(69). 

The development of a full angular momentum, three dimensional, smooth exterior complex dilated, finite element method for computing bound and resonant states in a wide class of quantum systems is described. Applications to the antiprotonic helium system, doubly excited states in the helium atom and to a model of a molecular van der Waals complex are discussed. 2001 by Academic Press. 

Our current direction is to study dynamical processes in atomic and molecular two- and three-body systems. We use a technique which formally is based on the mathematical theory of dilation analytic functions. Numerically these results axe realized though a fully three-dimensional finite element method applied to a total angular-momentum representation. We here show how generalizations of our previously published two-body methods to three-body systems are possible without formal approximations. 

The dynamic response functions of finite interacting systems have most commonly been obtained from an explicit computation of the eigenstates of the Hamiltonian and the matrix elements of the appropriate operators in the basis of these eigenstates [115]. This has been a widely used method particularly in the computation of the dynamic NLO coefficients of molecular systems and is known as the sum-over-states (SOS) method. In the case of model Hamiltonians, the technique that has been widely exploited to study dynamics is the Lanczos method [116]. The spectral intensity corresponding to an operator O is given by ... 

A number of approaches to connect multiple-scale simulation in finite-element techniques have been published [31-34], They are able to describe macroscopically inhomogeneous strain (e.g., cracks)—even dynamic simulations have been performed [35]—but invariably require artificial constraints on the atomistic scale [36], Recently, an approach has been introduced that considers a system comprising an inclusion of arbitrary shape embedded in a continuous medium [20], The inclusion behavior is described in an atomistically detailed manner [37], whereas the continuum is modeled by a displacement-based Finite-Element method [38,39], The atomistic model provides state- and configuration-dependent material properties, inaccessible to continuum models, and the inclusion in the atomistic-continuum model acts as a magnifying glass into the molecular level of the material. 

However, the length and time scales that molecular-based simulations can probe are still very limited (tens of nanosecond and a few nanometers), due to computer memory and CPU power limitations. On the other hand, nanoscale flows are often a part of larger scale devices that could contain both nanochannels and microfluidic domains. The dynamics of these systems depends on the intimate connection of different scales from nanoscale to microscale and beyond. MD simulation cannot simulate the whole systems due to its prohibitive computational cost, whereas continuum Navier-Stokes simulation cannot elucidate the details in the small scales. These limitations and the practical needs arising from the study of multiscale problems have motivated research on multiscale (or hybrid) simulation techniques that bridge a wider range of time and length scales with the minimum loss of information. A hybrid molecular-continuum scheme can make such multiscale computation feasible. A molecular-based method, such as MD for liquid or DSMC for gas, is used to describe the molecular details within the desired, localized subdomain of the large system. A continuum method, such as finite element or finite volume based Navier-Stokes/Stokes simulation, is used to describe the continuum flow in the remainder of the system Such hybrid method can be applied to solve the multiscale phenomena in gas, liquid, or solid. 

In this section, we discuss hybrid methodologies that explore the dynamical evolution of systems composed of a continuum region (usually described using finite-element methods) coupled to a discrete one [modeled using molecular dynamics (MD) algorithms and semiempirical classical potentials]. 

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