First UHF Implementation of the Incremental Scheme for Open-Shell Systems

Anacker, Tony; Tew, David P.; Friedrich, Joachim

doi:10.1021/acs.jctc.5b00933

Cited by 15 publications

(17 citation statements)

References 184 publications

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“…The present open-shell local MP2 Ansatz is constructed analogously to our highly efficient closed-shell local MP2 (LMP2) implementation. 38 , 88 , 89 The LMP2 approach employs ideas from fragmentation approaches, such as the incremental expansion 78 , 86 , 87 up to orbital pairs, which can also be interpreted as pair approximations for distant orbital pairs as employed frequently in direct local correlation approaches. 36 , 60 − 62 , 64 , 67 The main correlation energy contribution is obtained using orbital-specific basis sets reminiscent of the cluster-in-molecule, 76 , 80 , 82 as well as the divide-expand-consolidate 84 , 85 models.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Linear-Scaling Open-Shell MP2 Approach: Algorithm, Benchmarks, and Large-Scale Applications

Szabó

Csóka

Kállay

et al. 2021

J. Chem. Theory Comput.

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A linear-scaling local second-order Møller–Plesset (MP2) method is presented for high-spin open-shell molecules based on restricted open-shell (RO) reference functions. The open-shell local MP2 (LMP2) approach inherits the iteration- and redundancy-free formulation and the completely integral-direct, OpenMP-parallel, and memory and disk use economic algorithms of our closed-shell LMP2 implementation. By utilizing restricted local molecular orbitals for the demanding integral transformation step and by introducing a novel long-range spin-polarization approximation, the computational cost of RO-LMP2 approaches that of closed-shell LMP2. Extensive benchmarks were performed for reactions of radicals, ionization potentials, as well as spin-state splittings of carbenes and transition-metal complexes. Compared to the conventional MP2 reference for systems of up to 175 atoms, local errors of at most 0.1 kcal/mol were found, which are well below the intrinsic accuracy of MP2. RO-LMP2 computations are presented for challenging protein models of up to 601 atoms and 11 000 basis functions, which involve either spin states of a complexed iron ion or a highly delocalized singly occupied orbital. The corresponding runtimes of 9–15 h obtained with a single, many-core CPU demonstrate that MP2, as well as spin-scaled MP2 and double-hybrid density functional methods, become widely accessible for open-shell systems of unprecedented size and complexity.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Linear-Scaling Open-Shell MP2 Approach: Algorithm, Benchmarks, and Large-Scale Applications

Szabó

Csóka

Kállay

et al. 2021

J. Chem. Theory Comput.

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“…appearing in the expansion of Eq. 1 can be orbitals, atoms, molecules, or fragments 54,[67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84] . In addition, depending on the nature of the correlation problem or the available computational resources, any suitable algorithm can be chosen to predict the correlation energies, whether geared towards classical or quantum computing architectures.…”

Section: A Methods Of Incrementsmentioning

confidence: 99%

“…In addition, depending on the nature of the correlation problem or the available computational resources, any suitable algorithm can be chosen to predict the correlation energies, whether geared towards classical or quantum computing architectures. Some classical algorithms studied within the framework of the method of increments include the CC 71,76,79 and FCI approaches [54][55][56] . As for quantum algorithms, the phase estimation algorithm (PEA) 85,86 or the VQE 20 can be used.…”

Section: A Methods Of Incrementsmentioning

confidence: 99%

Scaling Up Electronic Structure Calculations on Quantum Computers: The Frozen Natural Orbital Based Method of Increments

Verma,

Huntington,

Coons

et al. 2020

Preprint

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Quantum computing is a new computing paradigm that holds great promise for the efficient simulation of quantum mechanical systems. However, the hardware envelope provided by noisy, intermediate-scale quantum (NISQ) devices is still small compared to the size of molecules that are relevant to industry. In the present paper, the method of increments (MI) is introduced to help expedite the application of NISQ devices for quantum chemistry simulations. The MI approach expresses the electron correlation energy of a molecular system as a truncated many-body expansion in terms of orbitals, atoms, molecules, or fragments. Here, the electron correlation of the system is expanded in terms of occupied orbitals, and the MI approach is employed to systematically reduce the occupied orbital space. At the same time, the virtual orbital space is reduced based on the frozen natural orbitals (FNO), which are obtained using a one-particle density matrix from second-order, many-body perturbation theory. In this way, a method referred to as the MI-FNO approach is constructed for the systematic reduction of both the occupied space and the virtual space in quantum chemistry simulations. The subproblems resulting from the MI-FNO reduction can then be solved by any algorithm, including quantum algorithms such as the phase estimation algorithm and the variational quantum eigensolver, to predict the correlation energies of a molecular system. The accuracy and feasibility of the MI-FNO approach are investigated for the case of small molecules-i.e., BeH 2 , CH 4 , NH 3 , H 2 O, and HF-within a cc-pVDZ basis set. Then, the efficacy of the proposed framework is investigated for larger molecules used in realistic industrial applications using a qubit-count estimation on an industrially relevant, mediumsized catalyst molecule, the "constrained geometry" olefin polymerization catalyst. We show that, even by employing a modest truncation of the virtual space, the MI-FNO approach reduces the qubit requirement by almost a factor of one half. In doing so, our approach can facilitate hardware experiments based on smaller, yet more realistic, chemistry problems, assisting in the characterization of NISQ devices. Moreover, reducing the qubit requirement can help scale up the size of molecular systems that can be simulated in quantum chemistry applications, which can greatly enhance computational chemistry studies for large-scale industrial applications.

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“…Three main schemes have been developed in this category. In the incremental scheme, [88][89][90][91][92][93] the correlation energy is expressed as a many-body expansion. The MOs are thus divided into single fragments (one-body) and the accuracy is controlled by the size of the fragments as well as the order of the expansion (usually using a two-body or three-body expansion).…”

Section: Fragment-based Correlation Approachesmentioning

confidence: 99%

The divide–expand–consolidate coupled cluster scheme

Kjærgaard

Baudin

Bykov

et al. 2017

WIREs Comput Mol Sci

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The Divide‐Expand‐Consolidate (DEC) scheme is a linear‐scaling and massively parallel framework for high accuracy coupled cluster (CC) calculations on large molecular systems. It is designed as a black‐box method, which ensures error control in the correlation energy and molecular properties. DEC is combined with a massively parallel implementation to fully utilize modern manycore architectures providing a fast time to solution. The implementation ensures performance portability and will straightforwardly benefit from new hardware developments. The DEC scheme has been applied to several levels of CC theory and extended the range of application of those methods. WIREs Comput Mol Sci 2017, 7:e1319. doi: 10.1002/wcms.1319 This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry

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First UHF Implementation of the Incremental Scheme for Open-Shell Systems

Cited by 15 publications

References 184 publications

Linear-Scaling Open-Shell MP2 Approach: Algorithm, Benchmarks, and Large-Scale Applications

Linear-Scaling Open-Shell MP2 Approach: Algorithm, Benchmarks, and Large-Scale Applications

Scaling Up Electronic Structure Calculations on Quantum Computers: The Frozen Natural Orbital Based Method of Increments

The divide–expand–consolidate coupled cluster scheme

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