Application of transfer Hamiltonian quantum mechanics to multi‐scale modeling

Mallik, Aditi; Taylor, De Carlos E.; Runge, Keith; Dufty, James W.

doi:10.1002/qua.20296

Cited by 13 publications

(12 citation statements)

References 23 publications

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“…V g was determined by using eq 3 in which F is the flow rate at standard temperature and pressure, t r and t 0 are the retention times of the retained and unretained probes, respectively, m is the mass of stationary phase, and j is the James-Martin correction factor. 12 For the conditions in these experiments, for which the inlet and outlet pressures are almost equivalent, j is a negligible correction (i.e., j ≈ 1).…”

Section: ' Methodsmentioning

confidence: 94%

“…Many truncation schemes are available in the literature; 9À11 here, we choose to use a method previously developed in the context of silica fracture. 12,13 Comparison must be made to experimental results to validate the level of theory and strategy involved in making these calculations.…”

Section: ' Introductionmentioning

confidence: 99%

“…The physical system includes many hundreds of atoms within a few angstroms of the adsorption site; hence, for computational purposes, the system must be truncated. Many truncation schemes are available in the literature; − here, we choose to use a method previously developed in the context of silica fracture. , …”

Section: Introductionmentioning

confidence: 99%

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Binding of Small Molecules to a Silica Surface: Comparing Experimental and Theoretical Results

Taylor

Runge²,

Cory

et al. 2011

J. Phys. Chem. C

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Section: ' Methodsmentioning

confidence: 94%

Section: ' Introductionmentioning

confidence: 99%

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Binding of Small Molecules to a Silica Surface: Comparing Experimental and Theoretical Results

Taylor

Runge²,

Cory

et al. 2011

J. Phys. Chem. C

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“…In such cases, the atomic interactions are often approximated throughout the system by a set of classical interatomic potentials obtained empirically 3 or from firstprinciples calculations. [4][5][6][7][8] For higher level treatment of quantum effects, the plane wave 9 and recent first-principles tight-binding schemes, [10][11][12][13][14][15][16][17][18] find wide application. In a second category of studies, like those on defects and impurities where localized bonding is dominant, the emphasis is on a limited region immediately surrounding the defect where high accuracy is required, but where the interaction with atoms further away can be approximated.…”

Section: Introductionmentioning

confidence: 99%

Convergence properties of the Harris density functional and the self-consistent atom fragment approximation

Averill

Painter

2006

Phys. Rev. B

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Describing materials properties and behavior over increasing scales of dimension and complexity requires an optimal balance of completeness and accuracy in solving the local density equations. In this study, the convergence properties of a set of schemes that aim to achieve increasing accuracy are systematically examined according to the hierarchical approximations upon which they are based. Specifically, the Harris density functional ͑HDF͒ and related schemes that express the total energy in terms of atomic densities and limited self-consistency are compared within a single consistent framework. Convergence of the HDF energy relative to input density is first tested by carrying out calculations within the non-self-consistent atom fragment and self-consistent atom fragment ͑SCAF͒ approximations and then by supplementing the SCAF density by increasing numbers of partial waves about each atomic site using the self-consistent partial wave ͑SCPW͒ method. The construct of the SCPW method, that solves the local density equations with controlled precision according to the number of partial waves in the site density expansions, enables this study. The rapid convergence of structural properties with an increasing number of partial waves on each site, sometimes even with only L = 0 partial waves, provides additional justification for HDF-based tight-binding and molecular dynamics methods where the interatomic potentials are obtained from the superposition of atomiclike densities. The convergence of ground state structural properties is demonstrated by application to the set of molecules: carbon monoxide, water, orthosilicic acid ͑H 4 SiO 4 ͒, formamide ͑HCONH 2 ͒, iron pentacarbonyl ͓Fe͑CO͒ 5 ͔, and dimanganese decacarbonyl ͓Mn 2 ͑CO͒ 10 ͔.

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“…The test system is a silica nanorod [1] with the proper stoichiometric ratio of Si:O observed in real silica. For the multi-scale modeling of this rod ( The details of this embedding method have been described elsewhere [2], and will not be considered further here. Instead the following focuses on the choice of the classical potential energy and the resulting properties of the CM region.…”

Section: Introductionmentioning

confidence: 99%

Constructing a small strain potential for multi-scale modeling

Mallik

Runge

Cheng

et al. 2005

Molecular Simulation

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Simulation of bulk materials with some components locally far from equilibrium usually requires a computationally intensive quantum mechanical description to capture the relevant mechanisms (e.g. effects of chemistry). Multi-scale modeling entails a compromise whereby the most accurate quantum description is used only where needed and the remaining bulk of the material is replaced by a simpler classical system of point particles. The problem of constructing an appropriate potential energy function for this classical system is addressed here. For problems relating to fracture, a consistent embedding of a quantum (QM) domain in its classical (CM) environment requires that the classical system should yield the same structure and elastic properties as the QM domain for states near equilibrium. It is proposed that an appropriate classical potential can be constructed using ab initio data on the equilibrium structure and weakly strained configurations calculated from the quantum description, rather than the more usual approach of fitting to a wide range of empirical data. This scheme is illustrated in detail for a model system, a silica nanorod that has the proper stiochiometric ratio of Si:O as observed in real silica. The potential energy is chosen to be pairwise additive, with the same pair potential functional form as familiar phenomenological TTAM potential. Here, the parameters are determined using a genetic algorithm with force data obtained directly from a quantum calculation. The resulting potential gives excellent agreement with properties of the reference quantum calculations both for structure (bond lengths, bond angles) and elasticity (Young's modulus). The proposed method for constructing the classical potential is carried out for two different choices for the quantum mechanical description: a transfer Hamiltonian method (NDDO with coupled-cluster parameterization) and density functional theory (with plane wave basis set and PBE exchange correlation functional). The quality of the potentials obtained in both cases is quite good, although the two quantum rods have significant differences.

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Application of transfer Hamiltonian quantum mechanics to multi‐scale modeling

Cited by 13 publications

References 23 publications

Binding of Small Molecules to a Silica Surface: Comparing Experimental and Theoretical Results

Binding of Small Molecules to a Silica Surface: Comparing Experimental and Theoretical Results

Convergence properties of the Harris density functional and the self-consistent atom fragment approximation

Constructing a small strain potential for multi-scale modeling

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