Effect of embedding and cluster size on the ab initio study of potassium adsorption at rutile(110)

Bredow, Thomas

doi:10.1002/(sici)1097-461x(1999)75:2<127::aid-qua6>3.0.co;2-r

Cited by 21 publications

(22 citation statements)

References 26 publications

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“…Since the density is calculated in the same point r =r ′ in Eqs. (10), (11) and ( 14), the regions A and B in these equations are either the same or not far away from each other. Therefore, to calculate (∆ n ) Aa,Bb one can simply choose a sufficiently big finite cluster of atoms (in fact, the cluster radius should be at least of the order of n 2 r * c , where r * c is the decay length of the overlap integral) with regions A and B somewhere in its centre and then calculate the complete ovelrap matrix for it, ∆.…”

Section: Resultsmentioning

confidence: 99%

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Electron density of periodic systems derived from non-orthogonal localized orbitals

Kantorovich¹,

Danyliv

2004

J. Phys.: Condens. Matter

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Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix into a power series can only be used when the orbitals are highly localised (e.g. ionic systems). In other cases including covalent crystals or those with an intermediate type of chemical bonding this method may be either numerically inefficient or fail altogether. Instead, we suggest an exact and numerically efficient method which can be used for orbitals of practically arbitrary localisation. Theory is illustrated by numerical calculations on a model system.

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Section: Resultsmentioning

confidence: 99%

“…We obtain, that the correct n−th order expansion for the image density in the notations of Eqs. ( 10), (11) should have the form:…”

Section: Methods Based On the Expansion Of The Inverse Of The Overlap...mentioning

confidence: 99%

Electron density of periodic systems derived from non-orthogonal localized orbitals

Kantorovich¹,

Danyliv

2004

J. Phys.: Condens. Matter

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“…A quantum cluster embedding is a powerful computational tool in electronic structure theory of extended systems, such as points defects in the bulk of crystalline 1,2 or amorphous 3 systems, adsorption species on crystal surfaces and surface defects, [4][5][6] or large biological molecules. [7][8][9][10] The embedding methods originate from a model in which a single local perturbation in the direct space of the entire system ͑the quantum cluster͒ is considered in great detail using highquality quantum-mechanical ͑QM͒ methods ͑the QM region͒, whereas a more approximate method ͓usually based on molecular mechanics ͑MM͒ force fields͔ is used to account for the rest of the system surrounding the cluster ͑the MM region͒.…”

Section: Introductionmentioning

confidence: 99%

Treating periodic systems using embedding: Adams-Gilbert approach

2007

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A direct-space electronic structure method for electronic structure calculations of periodic systems, based on highly localized ͑noncanonical͒ molecular orbitals ͑MOs͒ and the quantum cluster embedding, is suggested. The method utilizes a modified Adams-Gilbert approach that allows one to find self-consistently ͑for the given geometry͒ the system energy and the corresponding localized MOs which give the correct total electron density. The approach suggested here can also be considered as an exact derivation of embedded quantum cluster models. We illustrate this method on a Hartree-Fock calculation of a model periodic He system and the MgO crystal, and the results are compared with a conventional approach based on canonical Bloch-like orbitals as implemented in the CRYSTAL code. Our method, which scales linearly with the system size, can also be used to solve the Kohn-Sham equations of density-functional theory.

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“…These methods, developed mostly within the quantum chemistry community, and usually referred to as QM/MM have proven to be extremely successful [8,9,10,11,12]. Note that some other embedding schemes [13,14,15,16,17,18,19] developed mostly in the solid state community are very close in spirit to the QM/MM methods.…”

Section: Introductionmentioning

confidence: 99%

Comparison of localization procedures for applications in crystal embedding

Danyliv

Kantorovich

2004

Phys. Rev. B

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With the aim of future applications in quantum mechanical embedding in extended systems such as crystals, we suggest a simple and computationally efficient method which enables construction of a set of nonorthogonal highly localized one-electron orbitals for periodic nonmetallic crystals which reflect their chemical nature. The orbitals are also used to build up the Hartree-Fock (HF) electron density of the entire crystals. The simplicity of the method stems from the fact that it does not require usage and/or modification of periodic electronic structure codes, and is instead based on the HF calculation of a sequence of finite clusters with subsequent application of a localization procedure to transform the HF canonical molecular orbitals. Two extreme cases of chemical bonding, ionic (MgO crystal) and covalent (Si crystal), are considered for which a number of known localization schemes are applied and compared. With some modifications our method can also be applied to nonperiodic nonmetallic systems as well.

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Effect of embedding and cluster size on the ab initio study of potassium adsorption at rutile(110)

Cited by 21 publications

References 26 publications

Electron density of periodic systems derived from non-orthogonal localized orbitals

Electron density of periodic systems derived from non-orthogonal localized orbitals

Treating periodic systems using embedding: Adams-Gilbert approach

Comparison of localization procedures for applications in crystal embedding

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