Infinite-order diagrammatic summation approach to the explicitly correlated congruent transformed Hamiltonian

Bayne, Michael G.; Drogo, John; Chakraborty, Arindam

doi:10.1103/physreva.89.032515

Cited by 6 publications

(8 citation statements)

References 51 publications

(94 reference statements)

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“…The motivation for the above condition is based on the previous observations [39,90,91] that the form of the explicitly correlated wave function in the neighborhood of the electronelectron coalescence point plays a significant role in the accurate treatment of electronelectron correlation. Comparing the left and right side of the above equation, we define geminal parameter as,…”

Section: B Determination Of Correlation Functionmentioning

confidence: 99%

“…[78] The applicability of geminal operator approach for treating electron correlation [79][80][81] has also been demonstrated by Rassolov et al in a series articles for various chemical systems. [82][83][84][85][86][87][88] A congruent-transformed approach using an explicitly-correlated geminal operator has also been developed by Elward et al [89] and Bayne et al [90] The goal of this work is to use an explicitly correlated reference function to project out non-contributing terms in a CI expansion before the start of the CI calculation. Starting with an ansätz for the explicitly correlated wave function and using many-body diagrammatic techniques, we derive effective particle-hole excitation operators that project out low-amplitude excitations.…”

Section: Introductionmentioning

confidence: 99%

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Construction of explicitly correlated geminal-projected particle-hole creation operators for many-electron systems using the diagrammatic factorization approach

et al. 2016

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The computational cost of performing a configuration interaction (CI) calculation for treating electron-electron correlation is directly proportional to the number of terms in the CI expansion. In this work, we present a diagrammatic projection approach for a priori identification of non-contributing terms in a CI expansion. This method known as the geminal-projected configuration interaction (GP-CI) method is based on using a two-body R12 geminal operator for describing electron-electron correlation in a reference many-electron wave function. The diagrammatic projection procedure was performed by first deriving the Hugenholtz diagrams of the energy expression of the R12 reference wave function and then performing diagrammatic factorization of effective particle-hole creation operators. The projection operation, which is a functional of the geminal function, was defined and used for the construction of the geminal-projected particle-hole creation operators. The form of the two-body R12 geminal operator was derived analytically by imposing an approximate Kato cusp condition. A linear combination of the geminal-projected oneparticle one-hole and two-particle two-hole operators were used for the construction of the GP-CI wave function. The applicability and implementation of the diagrammatic projection method was demonstrated by performing proof-of-concept calculations on an isoelectronic series of 10 electron systems: CH 4 , NH 3 , H 2 O, HF, Ne. The results from the calculations show that, as compared to conventional CI calculations, the GP-CI method was able to substantially reduce the size of the CI space (by a factor of 6-9) while maintaining an accuracy of 10 −5 Hartrees for the ground state energies. These results demonstrate the ability of the diagrammatic projection procedure to identify non-contributing states using an analytical form of the R12 geminal correlator operator. The geminal-projection method was also applied to second order Moller-Plesset perturbation theory (GP-MP2) giving similar results to the GP-CI method in terms of reduction of the double excitation space and accuracy to the ground state energy. This work also extends the analytical derivation of the geminal-projected particle-hole creation operators that were used for the construction of the CI wave function to coupled-cluster theory (GP-CCSD). This general derivation can also be applied to other many-electron theories and multi-determinant quantum Monte Carlo calculations.

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Section: B Determination Of Correlation Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Construction of explicitly correlated geminal-projected particle-hole creation operators for many-electron systems using the diagrammatic factorization approach

et al. 2016

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“…Instead of evaluating the above equation directly, it is more efficient to first transform the operators and then perform the integration over the coordinates. The transformed operators are obtained by performing congruent transformation 109,110 which is defined as follows…”

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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“…Slater , and Hylleraas , first used the explicitly correlated wave function calculating the ground state energy in helium atom in 1929. Since then and especially within the past 30 years, the inclusion of explicit correlation has been implemented in various methods such as variational Monte Carlo, , transcorrelated Hamiltonian, ,,− explicitly correlated Hartree–Fock, − geminal augmented MCSCF, the electronic mean field configuration interaction method, and the strongly orthogonal geminal method. , The field of explicitly correlated method has been recently reviewed by various authors. − …”

Section: Introductionmentioning

confidence: 99%

Linked-Cluster Formulation of Electron–Hole Interaction Kernel in Real-Space Representation without Using Unoccupied States

Bayne

Scher

Ellis

et al. 2018

J. Chem. Theory Comput.

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Electron-hole or quasiparticle representation plays a central role in describing electronic excitations in many-electron systems. For charge-neutral excitation, the electron-hole interaction kernel is the quantity of interest for calculating important excitation properties such as optical gap, optical spectra, electron-hole recombination, and electron-hole binding energies. The electron-hole interaction kernel can be formally derived from the density-density correlation function using both Green's function and time-dependent density functional theory (TDDFT) formalism. The accurate determination of the electron-hole interaction kernel remains a significant challenge for precise calculations of optical properties in the GW+BSE formalism. From the TDDFT perspective, the electron-hole interaction kernel has been viewed as a path to systematic development of frequency-dependent exchange-correlation functionals. Traditional approaches, such as many-body perturbation theory formalism, use unoccupied states (which are defined with respect to Fermi vacuum) to construct the electron-hole interaction kernel. However, the inclusion of unoccupied states has long been recognized as the leading computational bottleneck that limits the application of this approach for larger finite systems. In this work, an alternative derivation that avoids using unoccupied states to construct the electron-hole interaction kernel is presented. The central idea of this approach is to use explicitly correlated geminal functions for treating electron-electron correlation for both ground and excited state wave functions. Using this ansatz, it is derived using both diagrammatic and algebraic techniques that the electron-hole interaction kernel can be expressed only in terms of linked closed-loop diagrams. It is proved that the cancellation of unlinked diagrams is a consequence of linked-cluster theorem in real-space representation. The electron-hole interaction kernel derived in this work was used to calculate excitation energies in many-electron systems, and results were found to be in good agreement with the EOM-CCSD and GW+BSE methods. The numerical results highlight the effectiveness of the developed method for overcoming the computational barrier of accurately determining the electron-hole interaction kernel to applications of large finite systems such as quantum dots and nanorods.

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Infinite-order diagrammatic summation approach to the explicitly correlated congruent transformed Hamiltonian

Cited by 6 publications

References 51 publications

Construction of explicitly correlated geminal-projected particle-hole creation operators for many-electron systems using the diagrammatic factorization approach

Construction of explicitly correlated geminal-projected particle-hole creation operators for many-electron systems using the diagrammatic factorization approach

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

Linked-Cluster Formulation of Electron–Hole Interaction Kernel in Real-Space Representation without Using Unoccupied States

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