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Ye HZ, Tran HK, Van Voorhis T. Accurate Electronic Excitation Energies in Full-Valence Active Space via Bootstrap Embedding. J Chem Theory Comput 2021; 17:3335-3347. [PMID: 33957050 DOI: 10.1021/acs.jctc.0c01221] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Fragment embedding has been widely used to circumvent the high computational scaling of using accurate electron correlation methods to describe the electronic ground states of molecules and materials. However, similar applications that utilize fragment embedding to treat electronic excited states are comparably less reported in the literature. The challenge here is twofold. First, most fragment embedding methods are most effective when the property of interest is local, but the change of the wave function upon excitation is nonlocal in general. Second, even for local excitations, an accurate estimate of, for example, the excitation energy can still be challenging owing to the need for a balanced treatment of both the ground and the excited states. In this work, we show that bootstrap embedding (BE), a fragment embedding method developed recently by our group, is promising toward describing general electronic excitations. Numerical simulations show that the excitation energies in full-valence active space (FVAS) can be well-estimated by BE to an error of ∼0.05 eV using relatively small fragments, for both local excitations and the excitations of some large dye molecules that exhibit strong charge-transfer characters. We hence anticipate BE to be a promising solution to accurately describing the excited states of large chemical systems.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Henry K Tran
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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Chi YC, Shaban Tameh M, Huang C. Efficient Embedded Cluster Density Approximation Calculations with an Orbital-Free Treatment of Environments. J Chem Theory Comput 2021; 17:2737-2751. [PMID: 33856795 DOI: 10.1021/acs.jctc.0c01133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The computational cost of the Kohn-Sham density functional theory (KS-DFT), employing advanced orbital-based exchange-correlation (XC) functionals, increases quickly for large systems. To tackle this problem, we recently developed a local correlation method in the framework of KS-DFT: the embedded cluster density approximation (ECDA). The aim of ECDA is to obtain accurate electronic structures in an entire system. With ECDA, for each atom in a system, we define a cluster to enclose that atom, with the rest atoms treated as the environment. The system's electron density is then partitioned among the cluster and the environment. The cluster's XC energy density is then calculated based on its electron density using an advanced orbital-based XC functional. The system's XC energy is obtained by patching all clusters' XC energy densities in an atom-by-atom manner. In our previous formulation of ECDA, environments were treated by KS-DFT, which makes the following two tasks computationally expensive for large systems. The first task is to partition the system's electron density among a cluster and its environment. The second task is to solve the environments' Sternheimer equations for calculating the system's XC potential. In this work, we remove these two computational bottlenecks by treating the environments with the orbital-free (OF) DFT. The new method is called ECDA-envOF. The performance of ECDA-envOF is examined in two systems: ester and Cl-tetracene, for which the exact exchange (EXX) is used as the advanced XC functional. We show that ECDA-envOF gives results that are very close to the previous formulation in which the environments were treated by KS-DFT. Therefore, ECDA-envOF can be used for future large-scale simulations. Another focus of this work is to examine ECDA-envOF's performance on systems having different bond types. With ECDA-envOF, we calculate the energy curves for stretching/compressing some covalent, metallic, and ionic systems. ECDA-envOF's predictions agree well with the benchmarks by using reasonably large clusters. These examples demonstrate that ECDA-envOF is nearly a black-box local correlation method for investigating heterogeneous materials in which different bond types exist.
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Affiliation(s)
- Yu-Chieh Chi
- Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306, United States
| | - Maliheh Shaban Tameh
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Chen Huang
- Department of Scientific Computing, Materials Science and Engineering Program, National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, United States
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Ye HZ, Tran HK, Van Voorhis T. Bootstrap Embedding For Large Molecular Systems. J Chem Theory Comput 2020; 16:5035-5046. [PMID: 32589842 DOI: 10.1021/acs.jctc.0c00438] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Recent developments in quantum embedding theories have provided attractive approaches to correlated calculations for large systems. In this work, we extend our previous work [J. Chem. Theory Comput. 2019, 15, 4497-4506; J. Phys. Chem. Lett. 2019, 10, 6368-6374] on bootstrap embedding (BE) to enable correlated ab initio calculations at the coupled cluster with singles and doubles (CCSD) level for large molecules. We introduce several new algorithmic developments that significantly reduce the computational cost of BE, while maintaining its accuracy. The resulting implementation scales as O(N3) for the integral transform and O(N) for the CCSD calculation. Numerical results on a series of conjugated molecules suggest that BE with reasonably sized fragments can recover more than 99.5% of the total correlation energy of a full CCSD calculation, while the required computational resources (time and storage) compare favorably to one popular local correlation scheme: domain localized pair natural orbital (DLPNO). The largest BE calculation in this work involves ∼2900 basis functions and can be performed on a single node with 16 CPU cores and 64 GB of memory in a few days. We anticipate that these developments represent an important step toward the application of BE to solve practical problems.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Henry K Tran
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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Wen X, Graham DS, Chulhai DV, Goodpaster JD. Absolutely Localized Projection-Based Embedding for Excited States. J Chem Theory Comput 2019; 16:385-398. [DOI: 10.1021/acs.jctc.9b00959] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Xuelan Wen
- Department of Chemistry, University of Minnesota, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455, United States
| | - Daniel S. Graham
- Department of Chemistry, University of Minnesota, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455, United States
| | - Dhabih V. Chulhai
- Department of Chemistry, University of Minnesota, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455, United States
| | - Jason D. Goodpaster
- Department of Chemistry, University of Minnesota, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455, United States
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Huang C. Correction to “Embedded Cluster Density Approximation for Exchange–Correlation Energy: A Natural Extension of the Local Density Approximation”. J Chem Theory Comput 2019; 15:6550. [DOI: 10.1021/acs.jctc.9b01007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Abstract
Recent developments in quantum embedding have offered an attractive approach to describing electron correlation in molecules. However, previous methods such as density matrix embedding theory (DMET) require rigid partitioning of the system into fragments, which creates significant ambiguity for molecules. Bootstrap embedding (BE) is more flexible because it allows overlapping fragments, but when done on an orbital-by-orbital basis, BE introduces ambiguity in defining the connectivity of the orbitals. In this Letter, we present an atom-based fragment definition that significantly augments BE's performance in molecules. The resulting method, which we term atom-based BE, is very effective at recovering valence electron correlation in moderate-sized bases and delivers near-chemical-accuracy results using extrapolation. We anticipate atom-based BE may lead to a low-scaling and highly accurate approach to electron correlation in large molecules.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Troy Van Voorhis
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
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Huang C. Analytical energy gradient for the embedded cluster density approximation. J Chem Phys 2019; 151:134101. [DOI: 10.1063/1.5112789] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chen Huang
- Department of Scientific Computing, Materials Science and Engineering Program, and National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, USA
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Abstract
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Fragment
embedding is one way to circumvent the high computational
scaling of accurate electron correlation methods. The challenge of
applying fragment embedding to molecular systems primarily lies in
the strong entanglement and correlation that prevent accurate fragmentation
across chemical bonds. Recently, Schmidt decomposition has been shown
effective for embedding fragments that are strongly coupled to a bath
in several model systems. In this work, we extend a recently developed
quantum embedding scheme, bootstrap embedding (BE), to molecular systems.
The resulting method utilizes the matching conditions naturally arising
from using overlapping fragments to optimize the embedding. Numerical
simulation suggests that the accuracy of the embedding improves rapidly
with fragment size for small molecules, whereas larger fragments that
include orbitals from different atoms may be needed for larger molecules.
BE scales linearly with system size (apart from an integral transform)
and hence can potentially be useful for large-scale calculations.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Nathan D Ricke
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Henry K Tran
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Troy Van Voorhis
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
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