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Shee A, Yeh CN, Peng B, Kowalski K, Zgid D. Triple Excitations in Green's Function Coupled Cluster Solver for Studies of Strongly Correlated Systems in the Framework of Self-Energy Embedding Theory. J Phys Chem Lett 2023; 14:2416-2424. [PMID: 36856741 DOI: 10.1021/acs.jpclett.2c03616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Embedding theories became important approaches used for accurate calculations of both molecules and solids. In these theories, a small chosen subset of orbitals is treated with an accurate method, called an impurity solver, capable of describing higher correlation effects. Ideally, such a chosen fragment should contain multiple orbitals responsible for the chemical and physical behavior of the compound. Handling a large number of chosen orbitals presents a very significant challenge for the current generation of solvers used in the physics and chemistry community. Here, we develop a Green's function coupled cluster singles doubles and triples (GFCCSDT) solver that can be used for a quantitative description in both molecules and solids. This solver allows us to treat orbital spaces that are inaccessible to other accurate solvers. At the same time, GFCCSDT maintains high accuracy of the resulting self-energy. Moreover, in conjunction with the GFCCSD solver, it allows us to test the systematic convergence of computational studies. Developing the CC family of solvers paves the road to fully systematic Green's function embedding calculations in solids. In this paper, we focus on the investigation of GFCCSDT self-energies for a strongly correlated problem of SrMnO3 solid. Subsequently, we apply this solver to solid MnO showing that an approximate variant of GFCCSDT is capable of yielding a high accuracy orbital resolved spectral function.
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Affiliation(s)
- Avijit Shee
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Chia-Nan Yeh
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Bo Peng
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Karol Kowalski
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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Vila FD, Rehr JJ, Pathak H, Peng B, Panyala A, Mutlu E, Bauman NP, Kowalski K. Real-time equation-of-motion CC cumulant and CC Green's function simulations of photoemission spectra of water and water dimer. J Chem Phys 2022; 157:044101. [DOI: 10.1063/5.0099192] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Newly developed coupled-cluster (CC) methods enable simulations of ionization potentials and spectral functions of molecular systems in a wide range of energy scales ranging from core-binding to valence. This paper discusses results obtained with the real-time equation-of-motion CC cumulant approach (RT-EOM-CC), and CC Green's function (CCGF) approaches in applications to the water and water dimer molecules. We compare the ionization potentials obtained with these methods for the valence region with the results obtained with the CCSD(T) formulation as a difference of energies for N and N-1 electron systems. All methods show good agreement with each other. They also agree well with experiment, with errors usually below 0.1 eV for the ionization potentials.We also analyze unique features of the spectral functions, associated with the position of satellite peaks, obtained with the RT-EOM-CC and CCGF methods employing single and double excitations, as a function of the monomer OH bond length and the proton transfer coordinate in the dimer. Finally, we analyze the impact of the basis set effects on the quality of calculated ionization potentials and find that the basis set effects are less pronounced for the augmented-type sets.
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Affiliation(s)
| | - John J. Rehr
- Department of Physics, University of Washington College of Arts and Sciences, United States of America
| | - Himadri Pathak
- Pacific Northwest National Laboratory, Pacific Northwest National Laboratory, United States of America
| | - Bo Peng
- Pacific Northwest National Laboratory, United States of America
| | - Ajay Panyala
- Pacific Northwest National Laboratory, United States of America
| | - Erdal Mutlu
- Pacific Northwest National Laboratory, United States of America
| | | | - Karol Kowalski
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, United States of America
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Vila FD, Kowalski K, Peng B, Kas JJ, Rehr JJ. Real-Time Equation-of-Motion CCSD Cumulant Green's Function. J Chem Theory Comput 2022; 18:1799-1807. [PMID: 35157796 DOI: 10.1021/acs.jctc.1c01179] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Many-body excitations in X-ray photoemission spectra have been difficult to simulate from first principles. We have recently developed a cumulant-based one-electron Green's function method using the real-time coupled-cluster-singles equation-of-motion approach (RT-EOM-CCS) that provides a general framework for treating these problems. Here we extend this approach to include double excitations in the ground-state energy and in the coupled cluster amplitudes, which have been implemented using subroutines generated by the Tensor Contraction Engine (TCE). As in the case of the singles approximation, RT-EOM-CCSD yields a nonperturbative cumulant form of the Green's function in terms of the time-dependent cluster amplitudes, adding nonlinear corrections to the traditional cumulant forms. The extended approach is applied to the core-hole spectral function for small molecular systems. We find that, when core-optimized basis sets are used, the doubles contributions reduce the mean absolute errors in the core binding energies of the 10e systems from 0.8 to 0.3 eV. They also significantly improve the quasiparticle-satellite gap by reducing its overestimation from about 3-5 to about 0-1 eV in CH4, NH3, and H2O, and also improving the overall shape of the satellite features. Finally, we demonstrate the application of the new implementation to the larger, classical XPS ESCA series of molecules and show that the singles approximation can be paired with a modest basis set to study carbon speciation.
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Affiliation(s)
- F D Vila
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - K Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - B Peng
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - J J Kas
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - J J Rehr
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
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Vila FD, Kas JJ, Rehr JJ, Kowalski K, Peng B. Equation-of-Motion Coupled-Cluster Cumulant Green's Function for Excited States and X-Ray Spectra. Front Chem 2021; 9:734945. [PMID: 34631660 PMCID: PMC8493088 DOI: 10.3389/fchem.2021.734945] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 09/06/2021] [Indexed: 11/13/2022] Open
Abstract
Green’s function methods provide a robust, general framework within many-body theory for treating electron correlation in both excited states and x-ray spectra. Conventional methods using the Dyson equation or the cumulant expansion are typically based on the GW self-energy approximation. In order to extend this approximation in molecular systems, a non-perturbative real-time coupled-cluster cumulant Green’s function approach has been introduced, where the cumulant is obtained as the solution to a system of coupled first order, non-linear differential equations. This approach naturally includes non-linear corrections to conventional cumulant Green’s function techniques where the cumulant is linear in the GW self-energy. The method yields the spectral function for the core Green’s function, which is directly related to the x-ray photoemission spectra (XPS) of molecular systems. The approach also yields very good results for binding energies and satellite excitations. The x-ray absorption spectrum (XAS) is then calculated using a convolution of the core spectral function and an effective, one-body XAS. Here this approach is extended to include the full coupled-cluster-singles (CCS) core Green’s function by including the complete form of the non-linear contributions to the cumulant as well as all single, double, and triple cluster excitations in the CC amplitude equations. This approach naturally builds in orthogonality and shake-up effects analogous to those in the Mahan-Noizeres-de Dominicis edge singularity corrections that enhance the XAS near the edge. The method is illustrated for the XPS and XAS of NH3.
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Affiliation(s)
- F D Vila
- Department of Physics, University of Washington, Seattle, WA, United States
| | - J J Kas
- Department of Physics, University of Washington, Seattle, WA, United States
| | - J J Rehr
- Department of Physics, University of Washington, Seattle, WA, United States
| | - K Kowalski
- Physical and Computational Science Directorate, Pacific Northwest National Laboratory, Richland, WA, United States
| | - B Peng
- Physical and Computational Science Directorate, Pacific Northwest National Laboratory, Richland, WA, United States
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Vila FD, Rehr JJ, Kas JJ, Kowalski K, Peng B. Real-Time Coupled-Cluster Approach for the Cumulant Green's Function. J Chem Theory Comput 2020; 16:6983-6992. [PMID: 33108872 DOI: 10.1021/acs.jctc.0c00639] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Green's function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states and spectra. Here, we develop the cumulant form of the one-electron Green's function using a real-time coupled-cluster equation-of-motion approach, in an extension of our previous study (Rehr J.; et al. J. Chem. Phys. 2020, 152, 174113). The approach yields a nonperturbative expression for the cumulant in terms of the solution to a set of coupled first-order, nonlinear differential equations. The method thereby adds nonlinear corrections to traditional cumulant methods, which are linear in the self-energy. The approach is applied to the core-hole Green's function and is illustrated for a number of small molecular systems. For these systems, we find that the nonlinear contributions yield significant improvements, both for quasiparticle properties such as core-level binding energies and for inelastic losses that correspond to satellites observed in photoemission spectra.
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Affiliation(s)
- F D Vila
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - J J Rehr
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - J J Kas
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - K Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, United States
| | - B Peng
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
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Sharma A, Chattopadhyay S, Sinha D. Exploring the spectroscopic constants of , (main and a satellite) and states of N ion using the Fock-space coupled-cluster with eigenvalue independent partitioning. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1774673] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Amitava Sharma
- Department of Chemistry, ICFAI School of Science, ICFAI University, Kamalghat, India
| | - Sudip Chattopadhyay
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Howrah, India
| | - Dhiman Sinha
- Department of Chemistry, Tripura University (A Central University), Suryamaninagar, India
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Bauman NP, Peng B, Kowalski K. Coupled Cluster Green's function formulations based on the effective Hamiltonians. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1725669] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Nicholas P. Bauman
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Bo Peng
- Advanced Computing, Mathematics, and Data Division, Battelle, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, WA, USA
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Peng B, Kowalski K, Panyala A, Krishnamoorthy S. Green’s function coupled cluster simulation of the near-valence ionizations of DNA-fragments. J Chem Phys 2020; 152:011101. [DOI: 10.1063/1.5138658] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Affiliation(s)
- Bo Peng
- Advanced Computing, Mathematics, and Data Division, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Ajay Panyala
- High Performance Computing, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Sriram Krishnamoorthy
- High Performance Computing, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
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Peng B, Van Beeumen R, Williams-Young DB, Kowalski K, Yang C. Approximate Green's Function Coupled Cluster Method Employing Effective Dimension Reduction. J Chem Theory Comput 2019; 15:3185-3196. [PMID: 30951302 DOI: 10.1021/acs.jctc.9b00172] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The Green's function coupled cluster (GFCC) method, originally proposed in the early 1990s, is a powerful many-body tool for computing and analyzing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, in order for the GFCC to become a method that may be routinely used in the electronic structure calculations, robust numerical techniques and approximations must be employed to reduce its extremely high computational overhead. In our recent studies, it has been demonstrated that the GFCC equations can be solved directly in the frequency domain using iterative linear solvers, which can be easily distributed in a massively parallel environment. In the present work, we demonstrate a successful application of model-order-reduction (MOR) techniques in the GFCC framework. Briefly speaking, for a frequency regime of interest that requires high-resolution descriptions of spectral function, instead of solving the GFCC linear equation of full dimension for every single frequency point of interest, an efficiently solvable linear system model of a reduced dimension may be built upon projecting the original GFCC linear system onto a subspace. From this reduced order model is obtained a reasonable approximation to the full dimensional GFCC linear equations in both interpolative and extrapolative spectral regions. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some selected frequencies within the spectral region of interest. During the iterations, the quality of the subspace, as well as the linear system model, can be systematically improved. The method is tested in this work in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems such as carbon monoxide, 1,3-butadiene, benzene, and adenine. To reach the same level of accuracy as that of the original GFCC method, the application of MOR in the GFCC method is able to significantly lower the original computational cost for the aforementioned molecules in designated frequency regimes. As a byproduct, the reduced order model obtained by this method is found to provide a high-quality initial guess, which improves the convergence rate for the existing iterative linear solver.
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Affiliation(s)
- Bo Peng
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle , Pacific Northwest National Laboratory , K8-91, P.O. Box 999, Richland , Washington 99352 , United States
| | - Roel Van Beeumen
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | - David B Williams-Young
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle , Pacific Northwest National Laboratory , K8-91, P.O. Box 999, Richland , Washington 99352 , United States
| | - Chao Yang
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
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