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Kats D, Christlmaier EMC, Schraivogel T, Alavi A. Orbital optimisation in xTC transcorrelated methods. Faraday Discuss 2024. [PMID: 39072553 DOI: 10.1039/d4fd00036f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/30/2024]
Abstract
We present a combination of the bi-orthogonal orbital optimisation framework with the recently introduced xTC version of transcorrelation. This allows us to implement non-iterative perturbation based methods on top of the transcorrelated Hamiltonian. Additionally, the orbital optimisation influences results of other truncated methods, such as the distinguishable cluster with singles and doubles. The accuracy of these methods in comparison to standard xTC methods is demonstrated, and the advantages and disadvantages of the orbital optimisation are discussed.
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Affiliation(s)
- Daniel Kats
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany.
| | | | - Thomas Schraivogel
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany.
| | - Ali Alavi
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany.
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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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Christlmaier EM, Kats D, Alavi A, Usvyat D. Full Configuration Interaction Quantum Monte Carlo treatment of fragments embedded in a periodic mean field. J Chem Phys 2022; 156:154107. [DOI: 10.1063/5.0084040] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an embedded fragment approach for high-level quantum chemical calculations on local features in periodic systems. The fragment is defined as a set of localized orbitals (occupied and virtual) corresponding to a converged periodic Hartree-Fock solution. These orbitals serve as the basis for the in-fragment post-Hartree Fock treatment. The embedding field for the fragment, consisting of the Coulomb and exchange potential from the rest of the crystal, is included in the fragment's one-electron Hamiltonian. As an application of the embedded fragment approach we investigate the performanceof full configuration interaction quantum Monte Carlo (FCIQMC) with the adaptive shift. As the orbital choice we use the natural orbitals from the distinguishable cluster method with singles and doubles. FCIQMC is a stochastic approximation to the full CI method and can be routinely applied to much larger active spaces than the latter. This makes this method especially attractive in the context of open shell defects in crystals, where fragments of adequate size can be ratherlarge. As a test case we consider dissociation of a fluorine atom from a fluorographane surface. This process poses a challenge for high-level electronic structure models as both the static and dynamic correlations are essential here. Furthermore the active space for an adequate fragment (32 electrons in 173 orbitals) is already quite large even for FCIQMC. Despite this, FCIQMC delivers accurate dissociation and total energies.
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Affiliation(s)
| | - Daniel Kats
- Max-Planck-Institute for Solid State Research, Germany
| | - Ali Alavi
- Max-Planck-Institute for Solid State Research, Germany
| | - Denis Usvyat
- Institute of Chemistry, Humboldt University of Berlin, Germany
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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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Mullan T, Maschio L, Saalfrank P, Usvyat D. Reaction barriers on non-conducting surfaces beyond periodic local MP2: Diffusion of hydrogen on \ce{\alpha-Al2O3}(0001) as a test case. J Chem Phys 2022; 156:074109. [DOI: 10.1063/5.0082805] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Lorenzo Maschio
- Dipartimento di Chimica, Università degli Studi di Torino, Italy
| | - Peter Saalfrank
- Institut für Chemie, Universität Potsdam Institut für Chemie, Germany
| | - Denis Usvyat
- Institute of Chemistry, Humboldt University of Berlin, Germany
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Schäfer T, Gallo A, Irmler A, Hummel F, Grüneis A. Surface science using coupled cluster theory via local Wannier functions and in-RPA-embedding: The case of water on graphitic carbon nitride. J Chem Phys 2021; 155:244103. [PMID: 34972356 DOI: 10.1063/5.0074936] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A first-principles study of the adsorption of a single water molecule on a layer of graphitic carbon nitride is reported employing an embedding approach for many-electron correlation methods. To this end, a plane-wave based implementation to obtain intrinsic atomic orbitals and Wannier functions for arbitrary localization potentials is presented. In our embedding scheme, the localized occupied orbitals allow for a separate treatment of short-range and long-range correlation contributions to the adsorption energy by a fragmentation of the simulation cell. In combination with unoccupied natural orbitals, the coupled cluster ansatz with single, double, and perturbative triple particle-hole excitation operators is used to capture the correlation in local fragments centered around the adsorption process. For the long-range correlation, a seamless embedding into the random phase approximation yields rapidly convergent adsorption energies with respect to the local fragment size. Convergence of computed binding energies with respect to the virtual orbital basis set is achieved employing a number of recently developed techniques. Moreover, we discuss fragment size convergence for a range of approximate many-electron perturbation theories. The obtained benchmark results are compared to a number of density functional calculations.
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Affiliation(s)
- Tobias Schäfer
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
| | - Alejandro Gallo
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
| | - Andreas Irmler
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
| | - Felix Hummel
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
| | - Andreas Grüneis
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
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Schraivogel T, Kats D. Accuracy of the distinguishable cluster approximation for triple excitations for open-shell molecules and excited states. J Chem Phys 2021; 155:064101. [PMID: 34391360 DOI: 10.1063/5.0059181] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The distinguishable cluster approximation for triple excitations has been applied to calculate thermochemical properties and excited states involving closed-shell and open-shell species, such as small molecules, 3d transition metal atoms, ozone, and an iron-porphyrin model. Excitation energies have been computed using the ΔCC approach by directly optimizing the excited states. A fixed-reference technique has been introduced to target selected spin-states for open-shell molecular systems. The distinguishable cluster approximation consistently improves coupled cluster with singles doubles and triples results for absolute and relative energies. For excited states dominated by a single configuration state function, the fixed-reference approach combined with high-level coupled-cluster methods has a comparable accuracy to the corresponding equation-of-motion coupled-cluster methods with a negligible amount of spin contamination.
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Affiliation(s)
- Thomas Schraivogel
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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Callahan JM, Lange MF, Berkelbach TC. Dynamical correlation energy of metals in large basis sets from downfolding and composite approaches. J Chem Phys 2021; 154:211105. [PMID: 34240964 DOI: 10.1063/5.0049890] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Coupled-cluster theory with single and double excitations (CCSD) is a promising ab initio method for the electronic structure of three-dimensional metals, for which second-order perturbation theory (MP2) diverges in the thermodynamic limit. However, due to the high cost and poor convergence of CCSD with respect to basis size, applying CCSD to periodic systems often leads to large basis set errors. In a common "composite" method, MP2 is used to recover the missing dynamical correlation energy through a focal-point correction, but the inadequacy of finite-order perturbation theory for metals raises questions about this approach. Here, we describe how high-energy excitations treated by MP2 can be "downfolded" into a low-energy active space to be treated by CCSD. Comparing how the composite and downfolding approaches perform for the uniform electron gas, we find that the latter converges more quickly with respect to the basis set size. Nonetheless, the composite approach is surprisingly accurate because it removes the problematic MP2 treatment of double excitations near the Fermi surface. Using this method to estimate the CCSD correlation energy in the combined complete basis set and thermodynamic limits, we find that CCSD recovers 85%-90% of the exact correlation energy at rs = 4. We also test the composite approach with the direct random-phase approximation used in place of MP2, yielding a method that is typically (but not always) more cost effective due to the smaller number of orbitals that need to be included in the more expensive CCSD calculation.
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Affiliation(s)
- James M Callahan
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Malte F Lange
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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Hansen AS, Aurbakken E, Pedersen TB. Smooth potential-energy surfaces in fragmentation-based local correlation methods for periodic systems. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1896046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- A. S. Hansen
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
| | - E. Aurbakken
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
| | - T. B. Pedersen
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
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