Investigation of electron–hole correlation using explicitly correlated configuration interaction method

Elward, Jennifer M.; Hoffman, Jacob B.; Chakraborty, Arindam

doi:10.1016/j.cplett.2012.03.050

Cited by 21 publications

(41 citation statements)

References 41 publications

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“…A parabolic potential was chosen because they have been used extensively 23,25,26,[100][101][102][103][104][105][106][107][108][109] to represent the confinement potential experienced by excitons in nanoparticles. The values of the force constant parameter, k, were selected such that the confining potential spanned from weakly confining region (k = 1.0 × 10 −4 a.u.)…”

Section: Physical System and Computational Detailsmentioning

confidence: 99%

Development of the Multicomponent Coupled-Cluster Theory for Investigation of Multiexcitonic Interactions

Ellis

Aggarwal²,

Chakraborty

2015

J. Chem. Theory Comput.

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Multicomponent systems are defined as chemical systems that require a quantum mechanical description of two or more different types of particles. Non-Born-Oppenheimer electron-nuclear interactions in molecules, electron-hole interactions in electronically excited nanoparticles, and electron-positron interactions are examples of physical systems that require a multicomponent quantum mechanical formalism. The central challenge in the theoretical treatment of multicomponent systems is capturing the many-body correlation effects that exist not only between particles of identical types (electron-electron) but also between particles of different types (electron-nuclear and electron-hole). In this work, the development and implementation of multicomponent coupled-cluster (mcCC) theory for treating particle-particle correlation in multicomponent systems are presented. This method provides a balanced treatment of many-particle correlation effects in a general multicomponent system while maintaining a size-consistent and size-extensive formalism. The coupled-cluster ansatz presented here is an extension of the electronic structure CCSD formulation for multicomponent systems and is defined as |ΨmcCC⟩ = eT1I+T2I+T1II+T2II+T11I,II+T12I,II+T21I,II+T22I,II|0I0II⟩. The cluster amplitudes in the mcCC wave function were obtained by projecting the mcCC Schrödinger equation onto a direct product space of singly and doubly excited states of type I and II particles and then solving the resulting mcCC equations iteratively. These equations were derived using an automated application of the generalized Wick’s theorem and were implemented using a computer-assisted source code generation approach. The applicability of the mcCC method was demonstrated by calculating ground state energies of multicomponent Hooke's atom and positronium hydride systems as well as by calculating exciton and biexciton binding energies in multiexcitonic systems. For each case, the mcCC results were benchmarked against full configuration interaction (FCI) calculations and were found to be in excellent agreement with the FCI results. The effect of neglecting certain classes of multicomponent connected excitation terms from the mcCC wave function was also investigated. The results from this study demonstrate that connected cluster operators that generate simultaneous excitation in type I and type II space are critical for capturing electron-hole correlation in multiexcitonic systems.

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Section: Physical System and Computational Detailsmentioning

confidence: 99%

Development of the Multicomponent Coupled-Cluster Theory for Investigation of Multiexcitonic Interactions

Ellis

Aggarwal²,

Chakraborty

2015

J. Chem. Theory Comput.

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“…The functional form of the congruent transformed operators and the Fock operators have been derived earlier and can be found in Ref. 80. The single-particle basis for electrons and holes are constructed from the eigenfunctions of zeroth order single-particle Hamiltonian…”

Section: Theorymentioning

confidence: 99%

Effect of Dot Size on Exciton Binding Energy and Electron–Hole Recombination Probability in CdSe Quantum Dots

Elward

Chakraborty

2013

J. Chem. Theory Comput.

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Large exciton binding energy Small exciton binding energy Cd 74608 Se 74837 Cd 199 Se 195 Cd 1012 Se 1063 ΔE ΔE ΔE valence valence conduction conduction conduction valence 0 0.5 1 EBE 0 0.5 1 EBE 0 0.5 1 EBE Peh Peh Peh Radius of quantum dotExciton binding energy and electron-hole recombination probability are presented as the two important metrics for investigating effect of dot size on electronhole interaction in CdSe quantum dots. Direct computation of electron-hole recombination probability is challenging because it requires an accurate mathematical description of electron-hole wavefunction in the neighborhood of the electron-hole coalescence point. In this work, we address this challenge by solving the electron-hole Schrodinger equation using the electron-hole explicitly correlated Hartree-Fock (eh-XCHF) method. The calculations were performed for a series of CdSe clusters ranging from Cd 20 Se 19 to Cd 74608 Se 74837 that correspond to dot diameter range of 1 − 20 nm. The calculated exciton binding energies and electron-hole recombination probabilities were found to decrease with increasing dot size. Both of these quantities were found to scale as D −n dot with respect to the dot diameter D. One of the key insights from this study is that the electron-hole recombination probability decreases at a much faster rate than the exciton binding energy as a function of dot size. It was found that an increase in the dot size by a factor of 16.1, resulted in a decrease in the exciton binding energy and electron-hole recombination probability by a factor of 14.4 and 5.5 × 10 6 , respectively.

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“…), the continuous tunability of electron correlation effects makes the two-electron harmonium atom a convenient benchmark that has been already applied to a multitude of electronic structure methods, including those based on DFT [5][6][7][8][9][10][11][12][13][14][15] and other formalisms. [16][17][18] Unfortunately, its general usefulness is severely limited by its failure to provide any new information for those approximate electron correlation methods that are already exact for two-electron systems.…”

Section: Introductionmentioning

confidence: 99%

Benchmark calculations on the lowest-energy singlet, triplet, and quintet states of the four-electron harmonium atom

Ciosłowski

Strasburger

Matito³

2014

The Journal of Chemical Physics

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Benchmark calculations on the lowest-energy singlet, triplet, and quintet states of the four-electron harmonium atom For a wide range of confinement strengths ω, explicitly-correlated calculations afford approximate energies E(ω) of the ground and low-lying excited states of the four-electron harmonium atom that are within few μhartree of the exact values, the errors in the respective energy components being only slightly higher. This level of accuracy constitutes an improvement of several orders of magnitude over the previously published data, establishing a set of benchmarks for stringent calibration and testing of approximate electronic structure methods. Its usefulness is further enhanced by the construction of differentiable approximants that allow for accurate computation of E(ω) and its components for arbitrary values of ω. The diversity of the electronic states in question, which involve both single-and multideterminantal first-order wavefunctions, and the availability of the relevant natural spinorbitals and their occupation numbers make the present results particularly useful in research on approximate density-matrix functionals. The four-electron harmonium atom is found to possess the 3 P + triplet ground state at strong confinements and the 5 S − quintet ground state at the weak ones, the energy crossing occurring at ω ≈ 0.0240919. © 2014 AIP Publishing LLC.

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Investigation of electron–hole correlation using explicitly correlated configuration interaction method

Cited by 21 publications

References 41 publications

Development of the Multicomponent Coupled-Cluster Theory for Investigation of Multiexcitonic Interactions

Development of the Multicomponent Coupled-Cluster Theory for Investigation of Multiexcitonic Interactions

Effect of Dot Size on Exciton Binding Energy and Electron–Hole Recombination Probability in CdSe Quantum Dots

Benchmark calculations on the lowest-energy singlet, triplet, and quintet states of the four-electron harmonium atom

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