[WIP] QDET demo #1327
[WIP] QDET demo #1327
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| The core idea behind embedding methods is to partition the system and treat the strongly correlated | ||
| subsystem accurately, using high-level quantum mechanical methods, while approximating the effects | ||
| of the surrounding environment in a way that retains computational efficiency. In this demo, we show | ||
| how to implement the quantum defect embedding theory (QDET). The method has been successfully |
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Reference HERE
| subsystem accurately, using high-level quantum mechanical methods, while approximating the effects | ||
| of the surrounding environment in a way that retains computational efficiency. In this demo, we show | ||
| how to implement the quantum defect embedding theory (QDET). The method has been successfully | ||
| applied to study defects in CaO and to calculate excitations of the negatively charged NV center in diamond. |
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| # Implementation | ||
| # -------------- | ||
| # We implement QDET to compute the excitation energies of a negatively charged nitrogen-vacancy | ||
| # defect in diamond []. |
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| # ^^^^^^^^^^^^^^^^^^^^^ | ||
| # Once we have obtained the meanfield description, we can identify our impurity by finding | ||
| # the states that are localized in real space. We can identify these localized states using the | ||
| # localization factor defined as []: |
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| { | |||
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| r"""Quantum Defect Embedding Theory (QDET) | ||
| ========================================= | ||
| Efficient simulation of complex quantum systems remains a significant challenge in chemistry and | ||
| physics. These simulations often require computationally intractable methods for a complete |
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Perhaps you can be more direct here.
For example: "Performing more reliable simulations of advanced materials and molecules remain a significant challenge in quantum chemistry due to the prohibitive cost of wave function methods."
| feature a strongly correlated region, which requires accurate quantum treatment, embedded within a | ||
| larger environment that could be properly treated with cheaper approximations. Examples of such | ||
| systems include point defects in materials [#Galli]_, active site of catalysts [#SJRLee]_, surface phenomenon such | ||
| as adsorption [#Gagliardi]_ and many more. Embedding theories serve as powerful tools for effectively |
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Consider removing the last sentence. Perhaps it is the good place to point out that "Embedding methods serve as powerful tools to accurately capture electronic correlations in the active region while accounting for the screening effects of the environment."
| larger environment that could be properly treated with cheaper approximations. Examples of such | ||
| systems include point defects in materials [#Galli]_, active site of catalysts [#SJRLee]_, surface phenomenon such | ||
| as adsorption [#Gagliardi]_ and many more. Embedding theories serve as powerful tools for effectively | ||
| addressing such problems. |
| addressing such problems. | ||
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| The core idea behind embedding methods is to partition the system and treat the strongly correlated | ||
| subsystem accurately, using high-level quantum mechanical methods, while approximating the effects |
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| subsystem accurately, using high-level quantum mechanical methods, while approximating the effects | |
| subsystem accurately, using wavefunction-based methods, while approximating the effects |
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This is not necessarily the case, for example, SEET and DMFT use Green's function based methods and then there are density based embeddings where different functionals of DFT are used. Here, since we are talking about embedding in general, we don't want to specify wavefunction-based method here.
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| The core idea behind embedding methods is to partition the system and treat the strongly correlated | ||
| subsystem accurately, using high-level quantum mechanical methods, while approximating the effects | ||
| of the surrounding environment in a way that retains computational efficiency. In this demo, we show |
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| of the surrounding environment in a way that retains computational efficiency. In this demo, we show | |
| of the surrounding environment using mean field approximations to retain the computational efficiency. In this demo, we show |
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We don't always treat the environment in a mean-field way, some embedding theories use some form of correction on top of mean-field, fox example, QDET uses GW, DMFT can use GW and DFT both, while SEET uses GF2 or GW.
| ############################################# | ||
| # Theory | ||
| # ------ | ||
| # The core idea in QDET is to construct an effective Hamiltonian that describes the impurity |
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| # The core idea in QDET is to construct an effective Hamiltonian that describes the impurity | |
| # The QDET method allows us to construct an effective Hamiltonian that describes the impurity |
| # L_n = \int_{V \in \ohm} d^3 r |\Psi_n^{KS}(r)|^2 | ||
| # | ||
| # where $V$ is the identified volume including the impurity within the supercell volume $\ohm$. | ||
| # We will use the WEST program to compute the localization factor. This requires creating another |
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Please, add WEST references. See here
| # $W_0^R$, results from screening the bare Coulomb potential, $v$, with the reduced polarizability, | ||
| # $P_0^R = P - P_{imp}$, where $P$ is the system's polarizability and $P_{imp}$ is the impurity's | ||
| # polarizability. However, this definition of the effective interaction, $v_{eff}$, introduces | ||
| # double counting of electrostatic and exchange-correlation effects for the impurity: once via |
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Check the wording above Diksha as per our discussion. I think this might flow better if you define the two-body term, then you define the one-body term and explain the motivation to correct it to avoid double counting the contribution of the active electrons to the Hartree and XC energy.
| # exact removal of double counting corrections at GW level of theory, thus removing the | ||
| # approximation present in the initial DFT based formulation. This formulation also helps capture | ||
| # the response properties and provides access to excited state properties. Another major advantage | ||
| # of QDET is the ease with which it can be used with quantum computers in a hybrid framework. |
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You may want to add the reference to our paper on V_B in hBN.
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.032606
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Thank you @ddhawan11, very nice tutorial! I have left some comments and suggestions.
Co-authored-by: agran2018 <[email protected]>
Co-authored-by: agran2018 <[email protected]>
Co-authored-by: agran2018 <[email protected]>
Co-authored-by: agran2018 <[email protected]>
Co-authored-by: agran2018 <[email protected]>
Co-authored-by: agran2018 <[email protected]>
Co-authored-by: agran2018 <[email protected]>
Co-authored-by: agran2018 <[email protected]>
Co-authored-by: agran2018 <[email protected]>
Co-authored-by: agran2018 <[email protected]>
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