1
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Dhawan D, Zgid D, Motta M. Quantum Algorithm for Imaginary-Time Green's Functions. J Chem Theory Comput 2024; 20:4629-4638. [PMID: 38761142 DOI: 10.1021/acs.jctc.4c00241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/20/2024]
Abstract
Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function. The calculation of the exact one-particle Green's function remains a significant challenge for classical computers and was attempted only on very small systems. Here, we present a hybrid quantum-classical algorithm to calculate the imaginary-time one-particle Green's function. The proposed algorithm combines the variational quantum eigensolver and the quantum subspace expansion methods to calculate Green's function in Lehmann's representation. We demonstrate the validity of this algorithm by simulating H2 and H4 on quantum simulators and on IBM's quantum devices.
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Affiliation(s)
- Diksha Dhawan
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Mario Motta
- IBM Quantum, Almaden Research Center, San Jose, California 95120, United States
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2
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Venturella C, Hillenbrand C, Li J, Zhu T. Machine Learning Many-Body Green's Functions for Molecular Excitation Spectra. J Chem Theory Comput 2024; 20:143-154. [PMID: 38150268 DOI: 10.1021/acs.jctc.3c01146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2023]
Abstract
We present a machine learning (ML) framework for predicting Green's functions of molecular systems, from which photoemission spectra and quasiparticle energies at quantum many-body level can be obtained. Kernel ridge regression is adopted to predict self-energy matrix elements on compact imaginary frequency grids from static and dynamical mean-field electronic features, which gives direct access to real-frequency many-body Green's functions through analytic continuation and Dyson's equation. Feature and self-energy matrices are represented in a symmetry-adapted intrinsic atomic orbital plus projected atomic orbital basis to enforce rotational invariance. We demonstrate good transferability and high data efficiency of the proposed ML method across molecular sizes and chemical species by showing accurate predictions of density of states (DOS) and quasiparticle energies at the level of many-body perturbation theory (GW) or full configuration interaction. For the ML model trained on 48 out of 1995 molecules randomly sampled from the QM7 and QM9 data sets, we report the mean absolute errors of ML-predicted highest occupied and lowest unoccupied molecular orbital energies to be 0.13 and 0.10 eV, respectively, compared to GW@PBE0. We further showcase the capability of this method by applying the same ML model to predict DOS for significantly larger organic molecules with up to 44 heavy atoms.
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Affiliation(s)
- Christian Venturella
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | | | - Jiachen Li
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Tianyu Zhu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
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3
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Di Felice R, Mayes ML, Richard RM, Williams-Young DB, Chan GKL, de Jong WA, Govind N, Head-Gordon M, Hermes MR, Kowalski K, Li X, Lischka H, Mueller KT, Mutlu E, Niklasson AMN, Pederson MR, Peng B, Shepard R, Valeev EF, van Schilfgaarde M, Vlaisavljevich B, Windus TL, Xantheas SS, Zhang X, Zimmerman PM. A Perspective on Sustainable Computational Chemistry Software Development and Integration. J Chem Theory Comput 2023; 19:7056-7076. [PMID: 37769271 PMCID: PMC10601486 DOI: 10.1021/acs.jctc.3c00419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Indexed: 09/30/2023]
Abstract
The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.
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Affiliation(s)
- Rosa Di Felice
- Departments
of Physics and Astronomy and Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, United States
- CNR-NANO
Modena, Modena 41125, Italy
| | - Maricris L. Mayes
- Department
of Chemistry and Biochemistry, University
of Massachusetts Dartmouth, North Dartmouth, Massachusetts 02747, United States
| | | | | | - Garnet Kin-Lic Chan
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Wibe A. de Jong
- Lawrence
Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Niranjan Govind
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Martin Head-Gordon
- Pitzer Center
for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Matthew R. Hermes
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Karol Kowalski
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hans Lischka
- Department
of Chemistry and Biochemistry, Texas Tech
University, Lubbock, Texas 79409, United States
| | - Karl T. Mueller
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Erdal Mutlu
- Advanced
Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Anders M. N. Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Mark R. Pederson
- Department
of Physics, The University of Texas at El
Paso, El Paso, Texas 79968, United States
| | - Bo Peng
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Ron Shepard
- Chemical
Sciences and Engineering Division, Argonne
National Laboratory, Lemont, Illinois 60439, United States
| | - Edward F. Valeev
- Department
of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | | | - Bess Vlaisavljevich
- Department
of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Theresa L. Windus
- Department
of Chemistry, Iowa State University and
Ames Laboratory, Ames, Iowa 50011, United States
| | - Sotiris S. Xantheas
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
- Advanced
Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Xing Zhang
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Paul M. Zimmerman
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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4
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Kolodzeiski E, Stein CJ. Automated, Consistent, and Even-Handed Selection of Active Orbital Spaces for Quantum Embedding. J Chem Theory Comput 2023; 19:6643-6655. [PMID: 37775093 PMCID: PMC10569175 DOI: 10.1021/acs.jctc.3c00653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Indexed: 10/01/2023]
Abstract
A widely used strategy to reduce the computational cost of quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts, and an environment that is treated at a lower computational level. The system partitioning is mostly based on localized molecular orbitals. When reaction paths or energy differences are to be calculated, it is crucial to keep the orbital space consistent for all structures. Inconsistencies in orbital space can lead to unpredictable errors on the potential energy surface. While successful strategies to ensure this consistency have been established for organic and even metal-organic systems, these methods often fail for metal clusters or nanoparticles with a high density of near-degenerate and delocalized molecular orbitals. However, such systems are highly relevant for catalysis. Accurate yet feasible quantum-mechanical ab initio calculations are therefore highly desired. In this work, we present an approach based on the subsystem projected atomic orbital decomposition algorithm that allows us to ensure automated and consistent partitioning even for systems with delocalized and near-degenerate molecular orbitals and demonstrate the validity of this method for the binding energies of small molecules on transition-metal clusters.
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Affiliation(s)
- Elena Kolodzeiski
- Technical University of Munich, TUM
School of Natural Sciences, Department of Chemistry, Lichtenbergstr. 4, Garching D-85748, Germany
| | - Christopher J. Stein
- Technical University of Munich, TUM
School of Natural Sciences, Department of Chemistry, Lichtenbergstr. 4, Garching D-85748, Germany
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5
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Pokhilko P, Zgid D. Natural orbitals and two-particle correlators as tools for the analysis of effective exchange couplings in solids. Phys Chem Chem Phys 2023; 25:21267-21279. [PMID: 37548912 DOI: 10.1039/d3cp01975f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/08/2023]
Abstract
Using generalizations of spin-averaged natural orbitals and two-particle charge correlators for solids, we investigate the electronic structure of antiferromagnetic transition-metal oxides with a fully self-consistent, imaginary-time GW method. Our findings disagree with the Goodenough-Kanamori (GK) rules that are commonly used for the qualitative interpretation of such solids. First, we found a strong dependence of the natural orbital occupancies on momenta, contradicting GK assumptions. Second, along the momentum path, the character of natural orbitals changes. In particular, the contributions of oxygen 2s orbitals are important, which has not been considered in the GK rules. To analyze the influence of the electronic correlation on the values of effective exchange coupling constants, we use both natural orbitals and two-particle correlators and show that electronic screening modulates the degree of superexchange by stabilizing the charge-transfer contributions, which greatly affects these coupling constants. Finally, we give a set of predictions and recommendations regarding the use of density functional, Green's function, and wave-function methods for evaluating effective magnetic couplings in molecules and solids.
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Affiliation(s)
- Pavel Pokhilko
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA.
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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6
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Meitei OR, Van Voorhis T. Periodic Bootstrap Embedding. J Chem Theory Comput 2023. [PMID: 37155327 DOI: 10.1021/acs.jctc.3c00069] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Bootstrap embedding (BE) is a recently developed electronic structure method that has shown great success at treating electron correlation in molecules. Here, we extend BE to treat surfaces and solids where the wave function is represented in periodic boundary conditions using reciprocal space sums (i.e., k-point sampling). The major benefit of this approach is that the resulting fragment Hamiltonians carry no explicit dependence on the reciprocal space sums, allowing one to apply traditional nonperiodic electronic structure codes to the fragments even though the entire system requires careful consideration of periodic boundary conditions. Using coupled cluster singles and doubles (CCSD) as an example method to solve the fragment Hamiltonians, we present minimal basis set CCSD-in-HF results on 1D conducting polymers. We show that periodic BE-CCSD can typically recover ∼99.9% of the electron correlation energy. We further demonstrate that periodic BE-CCSD is feasible even for complex donor-acceptor polymers of interest to organic solar cells─despite the fact that the monomers are sufficiently large that even a Γ-point periodic CCSD calculation is prohibitive. We conclude that BE is a promising new tool for applying molecular electronic structure tools to solids and interfaces.
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Affiliation(s)
- Oinam Romesh Meitei
- 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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7
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Nusspickel M, Ibrahim B, Booth GH. Effective Reconstruction of Expectation Values from Ab Initio Quantum Embedding. J Chem Theory Comput 2023; 19:2769-2791. [PMID: 37155201 DOI: 10.1021/acs.jctc.2c01063] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary "cluster" problems to exploit the locality of the correlated physics. In this work, we critically review approaches to recombine these fragmented solutions in order to compute nonlocal expectation values, including the total energy. Starting from the democratic partitioning of expectation values used in density matrix embedding theory, we motivate and develop a number of alternative approaches, numerically demonstrating their efficiency and improved accuracy as a function of increasing cluster size for both energetics and nonlocal two-body observables in molecular and solid state systems. These approaches consider the N-representability of the resulting expectation values via an implicit global wave function across the clusters, as well as the importance of including contributions to expectation values spanning multiple fragments simultaneously, thereby alleviating the fundamental locality approximation of the embedding. We clearly demonstrate the value of these introduced functionals for reliable extraction of observables and robust and systematic convergence as the cluster size increases, allowing for significantly smaller clusters to be used for a desired accuracy compared to traditional approaches in ab initio wave function quantum embedding.
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Affiliation(s)
- Max Nusspickel
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - Basil Ibrahim
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - George H Booth
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
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8
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Liu Y, Meitei OR, Chin ZE, Dutt A, Tao M, Chuang IL, Van Voorhis T. Bootstrap Embedding on a Quantum Computer. J Chem Theory Comput 2023; 19:2230-2247. [PMID: 37001026 DOI: 10.1021/acs.jctc.3c00012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
Abstract
We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match─at little additional computational cost─full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.
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Affiliation(s)
- Yuan Liu
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Oinam R. Meitei
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Zachary E. Chin
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Arkopal Dutt
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Max Tao
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Isaac L. Chuang
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Electrical Engineering and Computer Science, 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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9
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Laughon K, Yu JM, Zhu T. Periodic Coupled-Cluster Green's Function for Photoemission Spectra of Realistic Solids. J Phys Chem Lett 2022; 13:9122-9128. [PMID: 36162126 DOI: 10.1021/acs.jpclett.2c02534] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
We present an efficient implementation of the coupled-cluster Green's function (CCGF) method for simulating photoemission spectra of periodic systems. We formulate the periodic CCGF approach with Brillouin zone sampling in the Gaussian basis at the coupled-cluster singles and doubles (CCSD) level. To enable CCGF calculations of realistic solids, we propose an active-space self-energy correction scheme by combining CCGF with the cheaper many-body perturbation theory (GW) and implement the model order reduction (MOR) frequency interpolation technique. We find that the active-space self-energy correction and MOR techniques significantly reduce the computational cost of CCGF while maintaining the high accuracy. We apply the developed CCGF approaches to compute spectral properties and band structure of silicon (Si) and zinc oxide (ZnO) crystals using triple-ζ Gaussian basis sets and medium-size k-point sampling and find good agreement with experimental measurements.
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Affiliation(s)
- Katelyn Laughon
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Jason M Yu
- Department of Chemistry, University of California, Irvine, Irvine, California 92697, United States
| | - Tianyu Zhu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
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10
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Vorwerk C, Sheng N, Govoni M, Huang B, Galli G. Quantum embedding theories to simulate condensed systems on quantum computers. NATURE COMPUTATIONAL SCIENCE 2022; 2:424-432. [PMID: 38177872 DOI: 10.1038/s43588-022-00279-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Accepted: 06/14/2022] [Indexed: 01/06/2024]
Abstract
Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties that are more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate-scale quantum computers using embedding theories, and we give examples for a specific class of materials, that is, solid materials hosting spin defects. These are promising systems to build future quantum technologies, such as quantum computers, quantum sensors and quantum communication devices. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.
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Affiliation(s)
- Christian Vorwerk
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | - Nan Sheng
- Department of Chemistry, University of Chicago, Chicago, IL, USA
| | - Marco Govoni
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, IL, USA.
| | - Benchen Huang
- Department of Chemistry, University of Chicago, Chicago, IL, USA
| | - Giulia Galli
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA.
- Department of Chemistry, University of Chicago, Chicago, IL, USA.
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, IL, USA.
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11
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Sheng N, Vorwerk C, Govoni M, Galli G. Green's Function Formulation of Quantum Defect Embedding Theory. J Chem Theory Comput 2022; 18:3512-3522. [PMID: 35648660 DOI: 10.1021/acs.jctc.2c00240] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
We present a Green's function formulation of the quantum defect embedding theory (QDET) where a double counting scheme is rigorously derived within the G0W0 approximation. We then show the robustness of our methodology by applying the theory with the newly derived scheme to several defects in diamond. Additionally, we discuss a strategy to obtain converged results as a function of the size and composition of the active space. Our results show that QDET is a promising approach to investigate strongly correlated states of defects in solids.
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Affiliation(s)
- Nan Sheng
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Christian Vorwerk
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Marco Govoni
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States.,Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Giulia Galli
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States.,Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States.,Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
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12
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Van Benschoten WZ, Shepherd JJ. Piecewise Interaction Picture Density Matrix Quantum Monte Carlo. J Chem Phys 2022; 156:184107. [DOI: 10.1063/5.0094290] [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
The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact $N$-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC method (IP-DMQMC) which overcomes the limitation of only sampling one inverse temperature point at a time, instead allowing for the sampling of a temperature range within a single calculation thereby reducing the computational cost. At the target inverse temperature, instead of ending the simulation, we incorporate a change of picture away from the interaction picture. The resulting equations of motion have piecewise functions and use the interaction picture in the first phase of a simulation, followed by the application of the Bloch equation once the target inverse temperature is reached. We find that the performance of this method is similar to or better than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.
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13
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Ye HZ, Berkelbach TC. Correlation-Consistent Gaussian Basis Sets for Solids Made Simple. J Chem Theory Comput 2022; 18:1595-1606. [PMID: 35192359 DOI: 10.1021/acs.jctc.1c01245] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The rapidly growing interest in simulating condensed-phase materials using quantum chemistry methods calls for a library of high-quality Gaussian basis sets suitable for periodic calculations. Unfortunately, most standard Gaussian basis sets commonly used in molecular simulation show significant linear dependencies when used in close-packed solids, leading to severe numerical issues that hamper the convergence to the complete basis set (CBS) limit, especially in correlated calculations. In this work, we revisit Dunning's strategy for construction of correlation-consistent basis sets and examine the relationship between accuracy and numerical stability in periodic settings. We find that limiting the number of primitive functions avoids the appearance of problematic small exponents while still providing smooth convergence to the CBS limit. As an example, we generate double-, triple-, and quadruple-ζ correlation-consistent Gaussian basis sets for periodic calculations with Goedecker-Teter-Hutter (GTH) pseudopotentials. Our basis sets cover the main-group elements from the first three rows of the periodic table. Especially for atoms on the left side of the periodic table, our basis sets are less diffuse than those used in molecular calculations. We verify the fast and reliable convergence to the CBS limit in both Hartree-Fock and post-Hartree-Fock (MP2) calculations, using a diverse test set of 19 semiconductors and insulators.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States.,Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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14
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Abstract
Quantum embedding schemes are a promising way to extend multireference computations to large molecules with strong correlation effects localized on a small number of atoms. This work introduces a second-order active-space embedding theory [ASET(2)] which improves upon mean-field frozen embedding by treating fragment-environment interactions via an approximate canonical transformation. The canonical transformation employed in ASET(2) is formulated using the driven similarity renormalization group. The ASET(2) scheme is benchmarked on the N═N bond dissociation in pentyldiazene, the S0 to S1 excitation in 1-octene, and the interaction energy of the O2-benzene complex. The ASET(2) explicit treatment of fragment-environment interactions beyond the mean-field level generally improves the accuracy of embedded computations, and it becomes necessary to achieve an accurate description of excitation energies of 1-octene and the singlet-triplet gap of the O2-benzene complex.
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Affiliation(s)
- Nan He
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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15
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Graham DS, Wen X, Chulhai DV, Goodpaster J. Huzinaga Projection Embedding for Efficient and Accurate Energies of Systems with Localized Spin-densities. J Chem Phys 2022; 156:054112. [DOI: 10.1063/5.0076493] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Xuelan Wen
- Department of Chemistry, University of Minnesota Twin Cities, United States of America
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16
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Shee A, Yeh CN, Zgid D. Exploring Coupled Cluster Green's Function as a Method for Treating System and Environment in Green's Function Embedding Methods. J Chem Theory Comput 2022; 18:664-676. [PMID: 34989565 DOI: 10.1021/acs.jctc.1c00712] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Within the self-energy embedding theory (SEET) framework, we study the coupled cluster Green's function (GFCC) method in two different contexts: as a method to treat either the system or the environment present in the embedding construction. Our study reveals that when GFCC is used to treat the environment we do not see improvement in total energies in comparison to the coupled cluster method itself. To rationalize this puzzling result, we analyze the performance of GFCC as an impurity solver with a series of transition metal oxides. These studies shed light on the strength and weaknesses of such a solver and demonstrate that such a solver gives very accurate results when the size of the impurity is small. We investigate if it is possible to achieve a systematic accuracy of the embedding solution when we increase the size of the impurity problem. We found that in such a case, the performance of the solver worsens, both in terms of finding the ground state solution of the impurity problem and the self-energies produced. We concluded that increasing the rank of GFCC solver is necessary to be able to enlarge impurity problems and achieve a reliable accuracy. We also have shown that natural orbitals from weakly correlated perturbative methods are better suited than symmetrized atomic orbitals (SAO) when the total energy of the system is the target quantity.
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Affiliation(s)
- Avijit Shee
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Chia-Nan Yeh
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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17
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Dhawan D, Metcalf M, Zgid D. Dynamical Self-energy Mapping (DSEM) for Creation of Sparse Hamiltonians Suitable for Quantum Computing. J Chem Theory Comput 2021; 17:7622-7631. [PMID: 34739754 DOI: 10.1021/acs.jctc.1c00931] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
We present a two-step procedure called the dynamical self-energy mapping (DSEM) that allows us to find a sparse Hamiltonian representation for molecular problems. In the first part of this procedure, the approximate self-energy of a molecular system is evaluated using a low-level method and subsequently a sparse Hamiltonian is found that best recovers this low-level dynamic self-energy. In the second step, such a sparse Hamiltonian is used by a high-level method that delivers a highly accurate dynamical part of the self-energy that is employed in later calculations. The tests conducted on small molecular problems show that the sparse Hamiltonian parameterizations lead to very good total energies. DSEM has the potential to be used as a classical-quantum hybrid algorithm for quantum computing where the sparse Hamiltonian containing only O(n2) terms on a Gaussian orbital basis, where n is the number of orbitals in the system, could reduce the depth of the quantum circuit by at least an order of magnitude when compared with simulations involving a full Hamiltonian.
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Affiliation(s)
- Diksha Dhawan
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Mekena Metcalf
- Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States.,Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
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18
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Ahn C, Cavalleri A, Georges A, Ismail-Beigi S, Millis AJ, Triscone JM. Designing and controlling the properties of transition metal oxide quantum materials. NATURE MATERIALS 2021; 20:1462-1468. [PMID: 33941911 DOI: 10.1038/s41563-021-00989-2] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Accepted: 03/17/2021] [Indexed: 06/12/2023]
Abstract
This Perspective addresses the design, creation, characterization and control of synthetic quantum materials with strong electronic correlations. We show how emerging synergies between theoretical/computational approaches and materials design/experimental probes are driving recent advances in the discovery, understanding and control of new electronic behaviour in materials systems with interesting and potentially technologically important properties. The focus here is on transition metal oxides, where electronic correlations lead to a myriad of functional properties including superconductivity, magnetism, Mott transitions, multiferroicity and emergent behaviour at picoscale-designed interfaces. Current opportunities and challenges are also addressed, including possible new discoveries of non-equilibrium phenomena and optical control of correlated quantum phases of transition metal oxides.
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Affiliation(s)
| | - Andrea Cavalleri
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
| | - Antoine Georges
- Collège de France, Paris, France
- CCQ-Flatiron Institute, New York, NY, USA
| | | | - Andrew J Millis
- CCQ-Flatiron Institute, New York, NY, USA
- Columbia University, New York, NY, USA
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19
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Zhou Y, Gull E, Zgid D. Material-Specific Optimization of Gaussian Basis Sets against Plane Wave Data. J Chem Theory Comput 2021; 17:5611-5622. [PMID: 34448587 DOI: 10.1021/acs.jctc.1c00491] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Since in periodic systems, a given element may be present in different spatial arrangements displaying vastly different physical and chemical properties, an elemental basis set that is independent of physical properties of materials may lead to significant simulation inaccuracies. To avoid such a lack of material specificity within a given basis set, we present a material-specific Gaussian basis optimization scheme for solids, which simultaneously minimizes the total energy of the system and optimizes the band energies when compared to the reference plane wave calculation while taking care of the overlap matrix condition number. To assess this basis set optimization scheme, we compare the quality of the Gaussian basis sets generated for diamond, graphite, and silicon via our method against the existing basis sets. The optimization scheme of this work has also been tested on the existing Gaussian basis sets for periodic systems such as MoS2 and NiO, yielding improved results.
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Affiliation(s)
- Yanbing Zhou
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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20
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Requist R, Gross EKU. Fock-Space Embedding Theory: Application to Strongly Correlated Topological Phases. PHYSICAL REVIEW LETTERS 2021; 127:116401. [PMID: 34558918 DOI: 10.1103/physrevlett.127.116401] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Accepted: 07/15/2021] [Indexed: 06/13/2023]
Abstract
A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the solution of a Schrödinger equation with an effective Hamiltonian that can be viewed as embedding the marginal wave function in the environment of weakly correlated electrons. Here, the complementary equation for the conditional amplitude is replaced by a generalized Kohn-Sham equation, for which an orbital-dependent functional approximation is shown to reproduce the topological phase diagram of a multiband Hubbard model as a function of crystal field and Hubbard parameters. The roles of band filling and interband fluctuations are elucidated.
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Affiliation(s)
- Ryan Requist
- Max Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany and Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - E K U Gross
- Max Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany and Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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21
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Weng G, Vlček V. Efficient treatment of molecular excitations in the liquid phase environment via stochastic many-body theory. J Chem Phys 2021; 155:054104. [PMID: 34364336 DOI: 10.1063/5.0058410] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Accurate predictions of charge excitation energies of molecules in the disordered condensed phase are central to the chemical reactivity, stability, and optoelectronic properties of molecules and critically depend on the specific environment. Herein, we develop a stochastic GW method for calculating these charge excitation energies. The approach employs maximally localized electronic states to define the electronic subspace of a molecule and the rest of the system, both of which are randomly sampled. We test the method on three solute-solvent systems: phenol, thymine, and phenylalanine in water. The results are in excellent agreement with the previous high-level calculations and available experimental data. The stochastic calculations for supercells containing up to 1000 electrons representing the solvated systems are inexpensive and require ≤1000 central processing unit hrs. We find that the coupling with the environment accounts for ∼40% of the total correlation energy. The solvent-to-solute feedback mechanism incorporated in the molecular correlation term causes up to 0.6 eV destabilization of the quasiparticle energy. Simulated photo-emission spectra exhibit red shifts, state-degeneracy lifting, and lifetime shortening. Our method provides an efficient approach for an accurate study of excitations of large molecules in realistic condensed phase environments.
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Affiliation(s)
- Guorong Weng
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, USA
| | - VojtĚch Vlček
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, USA
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22
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Waldrop JM, Windus TL, Govind N. Projector-Based Quantum Embedding for Molecular Systems: An Investigation of Three Partitioning Approaches. J Phys Chem A 2021; 125:6384-6393. [PMID: 34260852 DOI: 10.1021/acs.jpca.1c03821] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Projector-based embedding is a relatively recent addition to the collection of methods that seek to utilize chemical locality to provide improved computational efficiency. This work considers the interactions between the different proposed procedures for this method and their effects on the accuracy of the results. The interplay between the embedded background, projector type, partitioning scheme, and level of atomic orbital (AO) truncation are investigated on a selection of reactions from the literature. The Huzinaga projection approach proves to be more reliable than the level-shift projection when paired with other procedural options. Active subsystem partitioning from the subsystem projected AO decomposition (SPADE) procedure proves slightly better than the combination of Pipek-Mezey localization and Mulliken population screening (PMM). Along with these two options, a new partitioning criteria is proposed based on subsystem von Neumann entropy and the related subsystem orbital occupancy. This new method overlaps with the previous PMM method, but the screening process is computationally simpler. Finally, AO truncation proves to be a robust option for the tested systems when paired with the Huzinaga projection, with satisfactory results being acquired at even the most severe truncation level.
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Affiliation(s)
| | - Theresa L Windus
- Ames Laboratory, Ames, Iowa 50011, United States.,Department of Chemistry, Iowa State University, Ames, Iowa 50011, United States
| | - Niranjan Govind
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
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23
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Liu Y, Shen T, Zhang H, Rubenstein B. Unveiling the Finite Temperature Physics of Hydrogen Chains via Auxiliary Field Quantum Monte Carlo. J Chem Theory Comput 2020; 16:4298-4314. [DOI: 10.1021/acs.jctc.0c00288] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yuan Liu
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, United States
| | - Tong Shen
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, United States
| | - Hang Zhang
- Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, United States
| | - Brenda Rubenstein
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, United States
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Dong X, Zgid D, Gull E, Strand HUR. Legendre-spectral Dyson equation solver with super-exponential convergence. J Chem Phys 2020; 152:134107. [DOI: 10.1063/5.0003145] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Xinyang Dong
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Dominika Zgid
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Hugo U. R. Strand
- Department of Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
- Center for Computational Quantum Physics, The Flatiron Institute, New York, New York 10010, USA
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25
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Banerjee S, Sokolov AY. Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green’s function implementation. J Chem Phys 2019; 151:224112. [DOI: 10.1063/1.5131771] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Samragni Banerjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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26
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Cui ZH, Zhu T, Chan GKL. Efficient Implementation of Ab Initio Quantum Embedding in Periodic Systems: Density Matrix Embedding Theory. J Chem Theory Comput 2019; 16:119-129. [DOI: 10.1021/acs.jctc.9b00933] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
- Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Tianyu Zhu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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27
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Zhu T, Cui ZH, Chan GKL. Efficient Formulation of Ab Initio Quantum Embedding in Periodic Systems: Dynamical Mean-Field Theory. J Chem Theory Comput 2019; 16:141-153. [DOI: 10.1021/acs.jctc.9b00934] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Affiliation(s)
- Tianyu Zhu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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28
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Ramberger B, Sukurma Z, Schäfer T, Kresse G. RPA natural orbitals and their application to post-Hartree-Fock electronic structure methods. J Chem Phys 2019; 151:214106. [DOI: 10.1063/1.5128415] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Benjamin Ramberger
- Faculty of Physics and Center for Computational Materials Sciences, University of Vienna, Sensengasse 8/12, 1090 Vienna, Austria
| | - Zoran Sukurma
- Faculty of Physics and Center for Computational Materials Sciences, University of Vienna, Sensengasse 8/12, 1090 Vienna, Austria
| | - Tobias Schäfer
- Institute for Theoretical Physics, Technical University of Vienna, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Georg Kresse
- Faculty of Physics and Center for Computational Materials Sciences, University of Vienna, Sensengasse 8/12, 1090 Vienna, Austria
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29
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Shee A, Zgid D. Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods. J Chem Theory Comput 2019; 15:6010-6024. [DOI: 10.1021/acs.jctc.9b00603] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Avijit Shee
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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30
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Chatterjee K, Sokolov AY. Second-Order Multireference Algebraic Diagrammatic Construction Theory for Photoelectron Spectra of Strongly Correlated Systems. J Chem Theory Comput 2019; 15:5908-5924. [DOI: 10.1021/acs.jctc.9b00528] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Koushik Chatterjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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31
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Mihm TN, McIsaac AR, Shepherd JJ. An optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas. J Chem Phys 2019; 150:191101. [PMID: 31117769 DOI: 10.1063/1.5091445] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
We explore an alternative to twist averaging in order to obtain more cost-effective and accurate extrapolations to the thermodynamic limit (TDL) for coupled cluster doubles (CCD) calculations. We seek a single twist angle to perform calculations at, instead of integrating over many random points or a grid. We introduce the concept of connectivity, a quantity derived from the nonzero four-index integrals in an MP2 calculation. This allows us to find a special twist angle that provides appropriate connectivity in the energy equation, which yields results comparable to full twist averaging. This special twist angle effectively makes the finite electron number CCD calculation represent the TDL more accurately, reducing the cost of twist-averaged CCD over Ns twist angles from Ns CCD calculations to Ns MP2 calculations plus one CCD calculation.
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Affiliation(s)
- Tina N Mihm
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1002, USA
| | - Alexandra R McIsaac
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - James J Shepherd
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1002, USA
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