Application of the group function theory to infinite systems

Kantorovich, Lev

doi:10.1002/(sici)1097-461x(2000)76:4<511::aid-qua3>3.0.co;2-2

Cited by 10 publications

(16 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In section 3, we analyse in detail the toy model and obtain an exact expression for RDM-1 in the limit of an infinite ring size. This result will enable us to conclude that the conjecture [17] that the pre-factors are equal to unity is only approximate. In section 4, we develop a general method for calculating the pre-factors in a form of a power series expansion with respect to overlap.…”

Section: Introductionmentioning

confidence: 81%

“…If each of the group functions I is given as a sum of Slater determinants with molecular orbitals expanded via some atomic orbitals (AOs) basis set, then the matrix elements P qT are eventually expressed as a sum of products of simple overlap integrals between the AOs of different electron groups (see, e.g. [17]). It is important to note here that a total contribution of a non-linked AD is exactly equal to the product of contributions associated with each of its linked parts [14].…”

Section: The Arrow Diagram Theorymentioning

confidence: 99%

“…It was suggested in [17] that the mean value of a symmetrical operator (3) may be cast in a form of a linear combination of all linked ADs with the pre-factors equal to unity. However, a more critical look at the theory made in this paper demonstrates that this result is approximate and only works if the overlap between different group functions is relatively small.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Arrow diagram approach to nonorthogonal electron group functions in extended systems

Wang¹,

Kantorovich²

2005

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

For nonorthogonal electron group functions, the arrow diagram (AD) method (Kantorovich and Zapol 1992 J. Chem. Phys. 96 8420; 1992 J. Chem. Phys. 96 8427) provides a convenient procedure for calculating matrix elements| O | of arbitrary symmetrical operators O. The total wavefunction of the system = A I I is represented as an antisymmetrized product of nonorthogonal many-electron group functions I of each group I in the system. For extended (e.g. infinite) systems the calculation of the mean value of an operator is ill defined, however, as it requires that each term of the diagram expansion be divided by the normalization integral S = | which is given by an AD expansion as well. In this work, we cast the mean value of a symmetrical operator in a form of an AD expansion which is a linear combination of linked ADs. By analysing an exactly solvable one-dimensional Hartree-Fock problem, we find that pre-factors, attached to every linked AD in the linear combination, can be expanded in a power series with respect to overlap. A general method of calculating these pre-factors in a form of a power series expansion with respect to overlap is suggested. This advance makes the AD theory applicable to extended systems, and allows one to calculate the mean value of an arbitrary symmetrical operator correct up to the desired order of overlap within the group function theory. In particular, we derive the effective Hamiltonian of a quantum cluster surrounded by overlapping group functions (e.g. bonds) in the environment region which is correct up to the second order with respect to overlap (an embedding problem).

show abstract

Section: Introductionmentioning

confidence: 81%

Section: The Arrow Diagram Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Arrow diagram approach to nonorthogonal electron group functions in extended systems

Wang¹,

Kantorovich²

2005

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…Following (Kantorovich, 1983(Kantorovich, , 1988(Kantorovich, , 2000a, in a construction of a quantum mechanical / molecular mechanical model it is useful to consider the whole extended system as a set of structural elements, each of which is associated with an electronic group, which, as mentioned, can be realised as an ion or a chemical bond. Such structural elements may be polarised or locally excited (transferred into an excited state) by external fields but remain intact, if the fields are sufficiently weak.…”

Section: Many Electron Problem Electron Groups Localisation and Strmentioning

confidence: 99%

Quantum Mechanical/Molecular Mechanical (QM/MM) Approaches

Catlow

Buckeridge

Farrow

et al. 2017

Handbook of Solid State Chemistry

View full text Add to dashboard Cite

Computational modeling techniques are now standard tools in solid‐state science. They are used routinely to model and predict structures, to investigate defect, transport, and spectroscopic properties of solids, to simulate sorption and diffusion, to develop models for nucleation and growth of solids, and increasingly to model and predict reaction mechanisms. They are applied to bulk solids, surfaces, and nanostructures, and successful applications are reported for all major classes of solid: metals, semiconductors, inorganic and ceramic materials, and molecular crystals. Modeling methods are now indeed tools that are used to guide, interpret, and predict experiment.

show abstract

“…[37][38][39][40][41][42][43] Our focus in the present work is on the implementation of this approach in the ChemShell package, 44,45 where the defect and immediately surrounding region (typically ∼100 atoms) are treated at a QM level of theory, using a Gaussian basis set and a hybrid functional for exchange and correlation to determine the electronic structure accurately. This cluster is embedded in a larger region (typically ∼10 000 atoms), which is treated at an MM level of theory using a polarizable shell model, to provide an accurate elastic and dielectric response of the infinite system to defect formation.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional embedded cluster approach to modeling CdS nanowires

Buckeridge

Bromley

Walsh

et al. 2013

The Journal of Chemical Physics

View full text Add to dashboard Cite

The Perdew-Burke-Ernzerhof exchange-correlation functional applied to the G2-1 test set using a plane-wave basis set The Journal of Chemical Physics 122, 234102 (2005) We present an embedded cluster model to treat one-dimensional nanostructures, using a hybrid quantum mechanical/molecular mechanical (QM/MM) approach. A segment of the nanowire (circa 50 atoms) is treated at a QM level of theory, using density functional theory (DFT) with a hybrid exchange-correlation functional. This segment is then embedded in a further length of wire, treated at an MM level of theory. The interaction between the QM and MM regions is provided by an embedding potential located at the interface. Point charges are placed beyond the ends of the wire segment in order to reproduce the Madelung potential of the infinite system. We test our model on the ideal system of a CdS linear chain, benchmarking our results against calculations performed on a periodic system using a plane-wave DFT approach, with electron exchange and correlation treated at the same level of approximation in both methods. We perform our tests on pure CdS and, importantly, the system containing a single In or Cu impurity. We find excellent agreement in the determined electronic structure using the two approaches, validating our embedded cluster model. As the hybrid QM/MM model avoids spurious interactions between charged defects, it will be of benefit to the analysis of the role of defects in nanowire materials, which is currently a major challenge using a plane-wave DFT approach. Other advantages of the hybrid QM/MM approach over plane-wave DFT include the ability to calculate ionization energies with an absolute reference and access to high levels of theory for the QM region which are not incorporated in most plane-wave codes. Our results concur with available experimental data.

show abstract

Application of the group function theory to infinite systems

Cited by 10 publications

References 35 publications

Arrow diagram approach to nonorthogonal electron group functions in extended systems

Arrow diagram approach to nonorthogonal electron group functions in extended systems

Quantum Mechanical/Molecular Mechanical (QM/MM) Approaches

One-dimensional embedded cluster approach to modeling CdS nanowires

Contact Info

Product

Resources

About