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Hasecke L, Mata RA. Optimization of Quantum Nuclei Positions with the Adaptive Nuclear-Electronic Orbital Approach. J Phys Chem A 2024; 128:3205-3211. [PMID: 38619054 PMCID: PMC11056972 DOI: 10.1021/acs.jpca.4c00096] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2024] [Revised: 03/08/2024] [Accepted: 03/08/2024] [Indexed: 04/16/2024]
Abstract
The use of multicomponent methods has become increasingly popular over the last years. Under this framework, nuclei (commonly protons) are treated quantum mechanically on the same footing as the electronic structure problem. Under the use of atomic-centered orbitals, this can lead to some complications as the ideal location of the nuclear basis centers must be optimized. In this contribution, we propose a straightforward approach to determine the position of such centers within the self-consistent cycle of a multicomponent calculation, making use of individual proton charge centroids. We test the method on model systems including the water dimer, a protonated water tetramer, and a porphine system. Comparing to numerical gradient calculations, the adaptive nuclear-electronic orbital (NEO) procedure is able to converge the basis centers to within a few cents of an Ångström and with less than 0.1 kcal/mol differences in absolute energies. This is achieved in one single calculation and with a small added computational effort of up to 80% compared to a regular NEO- self-consistent field run. An example application for the human transketolase proton wire is also provided.
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Affiliation(s)
- Lukas Hasecke
- Institute of Physical Chemistry, University
of Göttingen, Tammannstrasse 6, 37077 Göttingen, Germany
| | - Ricardo A. Mata
- Institute of Physical Chemistry, University
of Göttingen, Tammannstrasse 6, 37077 Göttingen, Germany
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2
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Nykänen A, Miller A, Talarico W, Knecht S, Kovyrshin A, Skogh M, Tornberg L, Broo A, Mensa S, Symons BCB, Sahin E, Crain J, Tavernelli I, Pavošević F. Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals. J Chem Theory Comput 2023; 19:9269-9277. [PMID: 38081802 DOI: 10.1021/acs.jctc.3c01091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2023]
Abstract
Nuclear quantum effects such as zero-point energy and hydrogen tunneling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets, whereas realistic simulations beyond the Born-Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H2 and D2 molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method─an important step toward accurate simulations involving nonclassical nuclei and non-Born-Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects, and we demonstrate that inclusion of correlation energy systematically improves the prediction of difference in the zero-point energy (ΔZPE) between isotopes.
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Affiliation(s)
- Anton Nykänen
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
| | - Aaron Miller
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
- School of Physics, Trinity College Dublin, College Green Dublin 2, Ireland
| | - Walter Talarico
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
- Department of Applied Physics, QTF Centre of Excellence, Center for Quantum Engineering, Aalto University School of Science, Aalto FIN-00076, Finland
| | - Stefan Knecht
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
- ETH Zürich, Department of Chemistry and Applied Life Sciences Vladimir-Prelog-Weg 1-5/10, Zürich 8093, Switzerland
| | - Arseny Kovyrshin
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Mårten Skogh
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Gothenburg 412 96, Sweden
| | - Lars Tornberg
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Anders Broo
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Stefano Mensa
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, U.K
| | | | - Emre Sahin
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, U.K
| | - Jason Crain
- IBM Research Europe, Hartree Centre STFC Laboratory, Sci-Tech Daresbury, Warrington WA4 4AD, U.K
- Department of Biochemistry, University of Oxford, Oxford OX1 3QU, U.K
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Feldmann R, Baiardi A, Reiher M. Symmetry-Projected Nuclear-Electronic Hartree-Fock: Eliminating Rotational Energy Contamination. J Phys Chem A 2023; 127:8943-8954. [PMID: 37831620 PMCID: PMC10614303 DOI: 10.1021/acs.jpca.3c04822] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Revised: 08/31/2023] [Indexed: 10/15/2023]
Abstract
We present a symmetry projection technique for enforcing rotational and parity symmetries in nuclear-electronic Hartree-Fock wave functions, which treat electrons and nuclei on equal footing. The molecular Hamiltonian obeys rotational and parity inversion symmetries, which are, however, broken by expanding in Gaussian basis sets that are fixed in space. We generate a trial wave function with the correct symmetry properties by projecting the wave function onto representations of the three-dimensional rotation group, i.e., the special orthogonal group in three dimensions SO(3). As a consequence, the wave function becomes an eigenfunction of the angular momentum operator which (i) eliminates the contamination of the ground-state wave function by highly excited rotational states arising from the broken rotational symmetry and (ii) enables the targeting of specific rotational states of the molecule. We demonstrate the efficiency of the symmetry projection technique by calculating the energies of the low-lying rotational states of the H2 and H3+ molecules.
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Affiliation(s)
- Robin Feldmann
- ETH Zürich, Department of Chemistry
and Applied Biosciences, Vladimir-Prelog-Weg 2, Zürich 8093, Switzerland
| | - Alberto Baiardi
- ETH Zürich, Department of Chemistry
and Applied Biosciences, Vladimir-Prelog-Weg 2, Zürich 8093, Switzerland
| | - Markus Reiher
- ETH Zürich, Department of Chemistry
and Applied Biosciences, Vladimir-Prelog-Weg 2, Zürich 8093, Switzerland
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Samsonova I, Tucker GB, Alaal N, Brorsen KR. Hydrogen-Atom Electronic Basis Sets for Multicomponent Quantum Chemistry. ACS OMEGA 2023; 8:5033-5041. [PMID: 36777583 PMCID: PMC9910068 DOI: 10.1021/acsomega.2c07782] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 01/13/2023] [Indexed: 06/18/2023]
Abstract
Multicomponent methods are a conceptually simple way to include nuclear quantum effects into quantum chemistry calculations. In multicomponent methods, the electronic molecular orbitals are described using the linear combination of atomic orbitals approximation. This requires the selection of a one-particle electronic basis set which, in practice, is commonly a correlation-consistent basis set. In multicomponent method studies, it has been demonstrated that large electronic basis sets are required for quantum hydrogen nuclei to accurately describe electron-nuclear correlation. However, as we show in this study, much of the need for large electronic basis sets is due to the correlation-consistent electronic basis sets not being optimized to describe nuclear properties and electron-nuclear correlation. Herein, we introduce a series of correlation-consistent electronic basis sets for hydrogen atoms called cc-pVnZ-mc with additional basis functions optimized to reproduce multicomponent density functional theory protonic densities. These new electronic basis sets are shown to yield better protonic densities with fewer electronic basis functions than the standard correlation-consistent basis sets and reproduce other protonic properties such as proton affinities and protonic excitation energies, even though they were not optimized for these purposes. The cc-pVnZ-mc basis sets should enable multicomponent many-body calculations on larger systems due to the improved computational efficiency they provide for a given level of accuracy.
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