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Otten M, Hermes MR, Pandharkar R, Alexeev Y, Gray SK, Gagliardi L. Localized Quantum Chemistry on Quantum Computers. J Chem Theory Comput 2022; 18:7205-7217. [PMID: 36346785 DOI: 10.1021/acs.jctc.2c00388] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today's quantum devices. Here, we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground-state energy. Our algorithm, termed "local active space unitary coupled cluster" (LAS-UCC), scales linearly with the system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H2)2 into two H2 molecules and by breaking the two double bonds in trans-butadiene, and resource estimates are provided for linear chains of up to 20 H2 molecules.
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Affiliation(s)
- Matthew Otten
- HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, California90265, United States
| | - Matthew R Hermes
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois60637, United States
| | - Riddhish Pandharkar
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois60637, United States
| | - Yuri Alexeev
- Computational Science Division, Argonne National Laboratory, Lemont, Illinois60439, United States
| | - Stephen K Gray
- Center for Nanoscale Materials, Argonne National Laboratory, Lemont, Illinois60439, United States
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois60637, United States.,Argonne National Laboratory, Lemont, Illinois60439, United States
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2
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Ravera E, Gigli L, Fiorucci L, Luchinat C, Parigi G. The evolution of paramagnetic NMR as a tool in structural biology. Phys Chem Chem Phys 2022; 24:17397-17416. [PMID: 35849063 DOI: 10.1039/d2cp01838a] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Paramagnetic NMR data contain extremely accurate long-range information on metalloprotein structures and, when used in the frame of integrative structural biology approaches, they allow for the retrieval of structural details to a resolution that is not achievable using other techniques. Paramagnetic data thus represent an extremely powerful tool to refine protein models in solution, especially when coupled to X-ray or cryoelectron microscopy data, to monitor the formation of complexes and determine the relative arrangements of their components, and to highlight the presence of conformational heterogeneity. More recently, theoretical and computational advancements in quantum chemical calculations of paramagnetic NMR observables are progressively opening new routes in structural biology, because they allow for the determination of the structure within the coordination sphere of the metal center, thus acting as a loupe on sites that are difficult to observe but very important for protein function.
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Affiliation(s)
- Enrico Ravera
- Magnetic Resonance Center (CERM), University of Florence, via Luigi Sacconi 6, Sesto Fiorentino, 50019, Italy.,Department of Chemistry "Ugo Schiff", University of Florence, via della Lastruccia 3, Sesto Fiorentino, 50019, Italy.,Consorzio Interuniversitario Risonanze Magnetiche Metallo Proteine (CIRMMP), via Luigi Sacconi 6, Sesto Fiorentino, 50019, Italy.
| | - Lucia Gigli
- Magnetic Resonance Center (CERM), University of Florence, via Luigi Sacconi 6, Sesto Fiorentino, 50019, Italy.,Department of Chemistry "Ugo Schiff", University of Florence, via della Lastruccia 3, Sesto Fiorentino, 50019, Italy.,Consorzio Interuniversitario Risonanze Magnetiche Metallo Proteine (CIRMMP), via Luigi Sacconi 6, Sesto Fiorentino, 50019, Italy.
| | - Letizia Fiorucci
- Magnetic Resonance Center (CERM), University of Florence, via Luigi Sacconi 6, Sesto Fiorentino, 50019, Italy.,Department of Chemistry "Ugo Schiff", University of Florence, via della Lastruccia 3, Sesto Fiorentino, 50019, Italy.,Consorzio Interuniversitario Risonanze Magnetiche Metallo Proteine (CIRMMP), via Luigi Sacconi 6, Sesto Fiorentino, 50019, Italy.
| | - Claudio Luchinat
- Magnetic Resonance Center (CERM), University of Florence, via Luigi Sacconi 6, Sesto Fiorentino, 50019, Italy.,Department of Chemistry "Ugo Schiff", University of Florence, via della Lastruccia 3, Sesto Fiorentino, 50019, Italy.,Consorzio Interuniversitario Risonanze Magnetiche Metallo Proteine (CIRMMP), via Luigi Sacconi 6, Sesto Fiorentino, 50019, Italy.
| | - Giacomo Parigi
- Magnetic Resonance Center (CERM), University of Florence, via Luigi Sacconi 6, Sesto Fiorentino, 50019, Italy.,Department of Chemistry "Ugo Schiff", University of Florence, via della Lastruccia 3, Sesto Fiorentino, 50019, Italy.,Consorzio Interuniversitario Risonanze Magnetiche Metallo Proteine (CIRMMP), via Luigi Sacconi 6, Sesto Fiorentino, 50019, Italy.
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3
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Kreplin DA, Werner HJ. A combined first- and second-order optimization method for improving convergence of Hartree–Fock and Kohn–Sham calculations. J Chem Phys 2022; 156:214111. [DOI: 10.1063/5.0094292] [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
In this work, we investigate the optimization of Hartree–Fock (HF) orbitals with our recently proposed combined first- and second-order (SO-SCI) method, which was originally developed for multi-configuration self-consistent field (MCSCF) and complete active space SCF (CASSCF) calculations. In MCSCF/CASSCF, it unites a second-order optimization of the active orbitals with a Fock-based first-order treatment of the remaining closed-virtual orbital rotations. In the case of the single-determinant wavefunctions, the active space is replaced by a preselected “second-order domain,” and all rotations involving orbitals in this subspace are treated at second-order. The method has been implemented for spin-restricted and spin-unrestricted Hartree–Fock (RHF, UHF), configuration-averaged Hartree–Fock (CAHF), as well as Kohn–Sham (KS) density functional theory (RKS, UKS). For each of these cases, various choices of the second-order domain have been tested, and appropriate defaults are proposed. The performance of the method is demonstrated for several transition metal complexes. It is shown that the SO-SCI optimization provides faster and more robust convergence than the standard SCF procedure but requires, in many cases, even less computation time. In difficult cases, the SO-SCI method not only speeds up convergence but also avoids convergence to saddle-points. Furthermore, it helps to find spin-symmetry broken solutions in the cases of UHF or UKS. In the case of CAHF, convergence can also be significantly improved as compared to a previous SCF implementation. This is particularly important for multi-center cases with two or more equal heavy atoms. The performance is demonstrated for various two-center complexes with different lanthanide atoms.
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Affiliation(s)
- David A. Kreplin
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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Swain A, Sen A, Rajaraman G. Are lanthanide-transition metal direct bonds a route to achieving new generation {3d-4f} SMMs? Dalton Trans 2021; 50:16099-16109. [PMID: 34647556 DOI: 10.1039/d1dt02256c] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Lanthanide based single-molecule magnets are gaining wide attention due to their potential applications in emerging technologies. One of the main challenges in this area is quenching quantum tunnelling of magnetisation (QTM), which often undercuts the magnetisation reversal barrier. Among the several strategies employed, enhancing exchange coupling has been studied in detail, with large exchanges resulting in stronger quenching of QTM effects. Lanthanides, however, suffer from weak exchanges offered by the deeply buried 4f orbitals and the numerous attempts to enhance the exchange coupling in the {3d-4f} pairs have not exceeded values larger than 30 cm-1. In this work, using a combination of DFT and the ab initio CASSCF/RASSI-SO method, we have explored lanthanide-transition metal direct bonds as a tool to quench QTM effects. In this direction, we have modelled [PyCp2LnMCp(CO)2] (Ln = Gd(III), Dy(III), and Er(III) and M = V(0), Mn(0), Co(0) and Fe(I) and here PyCp2 = [2,6-(CH2C5H3)2C5H3N]2- using [PyCp2DyFeCp(CO)2] as an example as reported by Nippe et al. (C. P. Burns, X. Yang, J. D. Wofford, N. S. Bhuvanesh, M. B. Hall and M. Nippe, Angew. Chem., Int. Ed. 2018, 57, 8144). Bonding analysis reveals a dative Ln-TM bond with a donation of π(V/Mndxy-π*CO) to 5dz2 (Gd) in the case of Gd-V and Gd-Mn and 4s(Co) to 5dxy/5dyz (Gd) for Gd-Co with the transition metal ion being found in the low-spin S = ½ configurations in all the cases. B3LYP/TZV (Gd;CSDZ) calculations on [PyCp2GdMCp(CO)2] yield JGd-V = -46.1 cm-1, JGd-Mn = -57.1 cm-1, JGd-Co = +55.3 cm-1, JGd-Fe+ = +13.9 cm-1, JGd-Vhs = -162.1 cm-1 and JGd-Mnhs = -343.9 cm-1 and unveiling record-high J values for {3d-4f} complexes. The mechanism of magnetic coupling is developed, which discloses the dominating presence of strong 3d-4f orbital overlaps in most of the cases studied, leading to antiferromagnetic exchange. When these overlaps are weaker and 3d to Gd(5dz2), charge transfer dominates, yielding a ferromagnetic coupling for the Gd-Co/Gd-Fe+ complexes. Calculations performed on the anisotropic Dy(III) and Er(III) complexes reveal that the ground state gzz axis lies along the Cp-Ln-Cp axis and the Ln-TM bonds, respectively. Thus the Ln-TM bond hinders the single-ion anisotropy of Dy(III) by offering equatorial ligation and lowering the mJ = ±½ state energy, and at the same time, helping in enhancing the axiality of Er(III). When strong {3d-4f} exchange couplings are introduced, record-high barrier heights as high as 229 cm-1 were accomplished. Furthermore, the exchange coupling annihilates the QTM effects and suggests the lanthanide-transition metal direct bond as a viable alternative to enhance exchange coupling to bring {3d-4f} complexes back in the race for high-blocking SMMs.
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Affiliation(s)
- Abinash Swain
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai - 400076, India.
| | - Asmita Sen
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai - 400076, India.
| | - Gopalan Rajaraman
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai - 400076, India.
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Abstract
Nuclear Magnetic Resonance is particularly sensitive to the electronic structure of matter and is thus a powerful tool to characterize in-depth the magnetic properties of a system. NMR is indeed increasingly recognized as an ideal tool to add precious structural information for the development of Single Ion Magnets, small complexes that are recently gaining much popularity due to their quantum computing and spintronics applications. In this review, we recall the theoretical principles of paramagnetic NMR, with particular attention to lanthanoids, and we give an overview of the recent advances in this field.
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Aravena D, Ruiz E. Spin dynamics in single-molecule magnets and molecular qubits. Dalton Trans 2020; 49:9916-9928. [PMID: 32589181 DOI: 10.1039/d0dt01414a] [Citation(s) in RCA: 57] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Over recent decades, much effort has been made to lengthen spin relaxation/decoherence times of single-molecule magnets and molecular qubits by following different chemical design rules such as maximizing the total spin value, controlling symmetry, enhancing the ligand field or inhibiting key vibrational modes. Simultaneously, electronic structure calculations have been employed to provide an understanding of the processes involved in the spin dynamics of molecular systems and served to refine or introduce new design rules. This review focuses on contemporary theoretical approaches focused on the calculation of spin relaxation/decoherence times, highlighting their main features and scope. Fundamental aspects of experimental techniques for the determination of key Single Molecule Magnet/Spin Qubit properties are also reviewed.
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Affiliation(s)
- Daniel Aravena
- Departamento de Química de los Materiales, Universidad de Santiago de Chile, Santiago 9170022, Chile
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Hermes MR, Pandharkar R, Gagliardi L. Variational Localized Active Space Self-Consistent Field Method. J Chem Theory Comput 2020; 16:4923-4937. [DOI: 10.1021/acs.jctc.0c00222] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Matthew R. Hermes
- Department of Chemistry, Chemical Theory Center, and The Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Riddhish Pandharkar
- Department of Chemistry, Chemical Theory Center, and The Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and The Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
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Werner HJ, Knowles PJ, Manby FR, Black JA, Doll K, Heßelmann A, Kats D, Köhn A, Korona T, Kreplin DA, Ma Q, Miller TF, Mitrushchenkov A, Peterson KA, Polyak I, Rauhut G, Sibaev M. The Molpro quantum chemistry package. J Chem Phys 2020; 152:144107. [PMID: 32295355 DOI: 10.1063/5.0005081] [Citation(s) in RCA: 431] [Impact Index Per Article: 107.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.
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Affiliation(s)
- Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Peter J Knowles
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Frederick R Manby
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
| | - Joshua A Black
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Klaus Doll
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Andreas Heßelmann
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max-Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Andreas Köhn
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Tatiana Korona
- Faculty of Chemistry, University of Warsaw, L. Pasteura 1 St., 02-093 Warsaw, Poland
| | - David A Kreplin
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Qianli Ma
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Thomas F Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | | | - Kirk A Peterson
- Department of Chemistry, Washington State University, Pullman, Washington 99164-4630, USA
| | - Iakov Polyak
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Guntram Rauhut
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Marat Sibaev
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
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Giansiracusa MJ, Al-Badran S, Kostopoulos AK, Whitehead GFS, McInnes EJL, Collison D, Winpenny REP, Chilton NF. Magnetic exchange interactions in symmetric lanthanide dimetallics. Inorg Chem Front 2020. [DOI: 10.1039/d0qi00854k] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Multi-frequency EPR spectra and CASSCF-SO calculations on two symmetric homo-dimetallic lanthanide complexes are used to determine the magnetic exchange coupling in the low-lying states.
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Affiliation(s)
| | - Susan Al-Badran
- Department of Chemistry
- The University of Manchester
- Manchester
- UK
- Chemistry Department
| | | | | | | | - David Collison
- Department of Chemistry
- The University of Manchester
- Manchester
- UK
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10
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Kats D, Werner HJ. Multi-state local complete active space second-order perturbation theory using pair natural orbitals (PNO-MS-CASPT2). J Chem Phys 2019; 150:214107. [DOI: 10.1063/1.5097644] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Daniel Kats
- Max-Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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