1
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Urban L, Laqua H, Thompson TH, Ochsenfeld C. Efficient Exploitation of Numerical Quadrature with Distance-Dependent Integral Screening in Explicitly Correlated F12 Theory: Linear Scaling Evaluation of the Most Expensive RI-MP2-F12 Term. J Chem Theory Comput 2024; 20:3706-3718. [PMID: 38626443 PMCID: PMC11099969 DOI: 10.1021/acs.jctc.4c00193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Revised: 03/23/2024] [Accepted: 03/25/2024] [Indexed: 04/18/2024]
Abstract
We present a linear scaling atomic orbital based algorithm for the computation of the most expensive exchange-type RI-MP2-F12 term by employing numerical quadrature in combination with CABS-RI to avoid six-center-three-electron integrals. Furthermore, a robust distance-dependent integral screening scheme, based on integral partition bounds [Thompson, T. H.; Ochsenfeld, C. J. Chem. Phys. 2019, 150, 044101], is used to drastically reduce the number of the required three-center-one-electron integrals substantially. The accuracy of our numerical quadrature/CABS-RI approach and the corresponding integral screening is thoroughly assessed for interaction and isomerization energies across a variety of numerical integration grids. Our method outperforms the standard density fitting/CABS-RI approach with errors below 1 μEh even for small grid sizes and moderate screening thresholds. The choice of the grid size and screening threshold allows us to tailor our ansatz to a desired accuracy and computational efficiency. We showcase the approach's effectiveness for the chemically relevant system valinomycin, employing a triple-ζ F12 basis set combination (C54H90N6O18, 5757 AO basis functions, 10,266 CABS basis functions, 735,783 grid points). In this context, our ansatz achieves higher accuracy combined with a 135× speedup compared to the classical density fitting based variant, requiring notably less computation time than the corresponding RI-MP2 calculation. Additionally, we demonstrate near-linear scaling through calculations on linear alkanes. We achieved an 817-fold acceleration for C80H162 and an extrapolated 28,765-fold acceleration for C200H402, resulting in a substantially reduced computational time for the latter─from 229 days to just 11.5 min. Our ansatz may also be adapted to the remaining MP2-F12 terms, which will be the subject of future work.
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Affiliation(s)
- Lars Urban
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
- Max
Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
| | - Henryk Laqua
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Travis H. Thompson
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
- Max
Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
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2
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Woźniak AP, Adamowicz L, Pedersen TB, Kvaal S. Gaussians for Electronic and Rovibrational Quantum Dynamics. J Phys Chem A 2024; 128:3659-3671. [PMID: 38687971 PMCID: PMC11089519 DOI: 10.1021/acs.jpca.4c00364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2024] [Revised: 03/23/2024] [Accepted: 04/08/2024] [Indexed: 05/02/2024]
Abstract
The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wave packets that generally will have components of electronic and dissociation continua as well as bound-state contributions. The conceptually most straightforward way to overcome this challenge is to treat the electronic and nuclear degrees of freedom on equal quantum-mechanical footing by not invoking the BO approximation at all. Explicitly correlated Gaussian (ECG) basis functions have proved successful for non-BO calculations of stationary molecular states and energies, reproducing rovibrational absorption spectra with very high accuracy. In this Article, we present a proof-of-principle study of the ability of fully flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational dynamics generated by short, high-intensity laser pulses. By fitting linear combinations of FFECGs to accurate wave function histories obtained on a large real-space grid for a regularized 2D model of the hydrogen atom and for the 2D Morse potential, we demonstrate that FFECGs provide a very compact description of laser-driven electronic and rovibrational dynamics.
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Affiliation(s)
| | - Ludwik Adamowicz
- Department
of Chemistry and Biochemistry, University
of Arizona, 1306 E University Blvd, Tucson, Arizona 85721-0041, United States
| | - Thomas Bondo Pedersen
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Simen Kvaal
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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3
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Lang L, Cezar HM, Adamowicz L, Pedersen TB. Quantum Definition of Molecular Structure. J Am Chem Soc 2024; 146:1760-1764. [PMID: 38199236 PMCID: PMC10811664 DOI: 10.1021/jacs.3c11467] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Revised: 11/21/2023] [Accepted: 11/22/2023] [Indexed: 01/12/2024]
Abstract
Molecular structure, a key concept of chemistry, has remained elusive from the perspective of all-particle quantum mechanics, despite many efforts. Viewing molecular structure as a manifestation of strong statistical correlation between nuclear positions, we propose a practical method based on Markov chain Monte Carlo sampling and unsupervised machine learning. Application to the D3+ molecule unambiguously shows that it possesses an equilateral triangular structure. These results provide a major step forward in our understanding of the molecular structure from fundamental quantum principles.
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Affiliation(s)
- Lucas Lang
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo, Norway
- Technische
Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni
135, 10623 Berlin, Germany
| | - Henrique M. Cezar
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo, Norway
| | - Ludwik Adamowicz
- Centre
for Advanced Study at the Norwegian Academy of Science and Letters, Drammensveien 78, 0271 Oslo, Norway
- Department
of Chemistry and Biochemistry, University
of Arizona, Tucson, Arizona 85721, United States
| | - Thomas B. Pedersen
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo, Norway
- Centre
for Advanced Study at the Norwegian Academy of Science and Letters, Drammensveien 78, 0271 Oslo, Norway
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4
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Shomenov T, Bubin S. Explicitly correlated Gaussians for high-precision variational calculations of S^{e}, P^{e}, and D^{e} states of quantum systems: An efficient algorithm. Phys Rev E 2023; 108:065308. [PMID: 38243521 DOI: 10.1103/physreve.108.065308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Accepted: 11/10/2023] [Indexed: 01/21/2024]
Abstract
In this work we consider an efficient algorithm for variational calculations of quantum few-particle systems in S, P, and D states of the even parity using all-particle explicitly correlated Gaussian (ECG) basis sets. We primarily focus on the description of states where the dominant configuration contains either two particles in p states or a single particle in a d state (all other particles are in s states). The basis functions we consider are products of spherically symmetric ECGs and bipolar harmonics. We introduced a scheme for deriving expressions for matrix elements of the overlap, kinetic and potential energy, as well as their derivatives with respect to the nonlinear parameters of the Gaussians. This allowed us to improve the efficiency of numerical calculations of the matrix elements (which is the most critical part of any code that uses ECGs) by one to two orders of magnitude compared to previous implementations. We provide a complete set of formulas for all basic matrix elements using the formalism of matrix differential calculus and discuss some technical details relevant to their efficient implementation. Lastly, we report a few example calculations of the ^{2}D^{e} states of the Li atom, ^{4}P^{e} and ^{2}D^{e} states of the B atom, and ^{3}P^{e} states of the C atom.
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Affiliation(s)
| | - Sergiy Bubin
- Department of Physics, Nazarbayev University, Astana 010000, Kazakhstan
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5
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Feldmann R, Baiardi A, Reiher M. Second-Order Self-Consistent Field Algorithms: From Classical to Quantum Nuclei. J Chem Theory Comput 2023; 19:856-873. [PMID: 36701300 DOI: 10.1021/acs.jctc.2c01035] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
This work presents a general framework for deriving exact and approximate Newton self-consistent field (SCF) orbital optimization algorithms by leveraging concepts borrowed from differential geometry. Within this framework, we extend the augmented Roothaan-Hall (ARH) algorithm to unrestricted electronic and nuclear-electronic calculations. We demonstrate that ARH yields an excellent compromise between stability and computational cost for SCF problems that are hard to converge with conventional first-order optimization strategies. In the electronic case, we show that ARH overcomes the slow convergence of orbitals in strongly correlated molecules with the example of several iron-sulfur clusters. For nuclear-electronic calculations, ARH significantly enhances the convergence already for small molecules, as demonstrated for a series of protonated water clusters.
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Affiliation(s)
- Robin Feldmann
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Alberto Baiardi
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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6
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Miessen A, Ollitrault PJ, Tacchino F, Tavernelli I. Quantum algorithms for quantum dynamics. NATURE COMPUTATIONAL SCIENCE 2023; 3:25-37. [PMID: 38177956 DOI: 10.1038/s43588-022-00374-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2021] [Accepted: 11/12/2022] [Indexed: 01/06/2024]
Abstract
Among the many computational challenges faced across different disciplines, quantum-mechanical systems pose some of the hardest ones and offer a natural playground for the growing field of quantum technologies. In this Perspective, we discuss quantum algorithmic solutions for quantum dynamics, reporting on the latest developments and offering a viewpoint on their potential and current limitations. We present some of the most promising areas of application and identify possible research directions for the coming years.
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Affiliation(s)
| | - Pauline J Ollitrault
- IBM Quantum, IBM Research - Zurich, Rüschlikon, Switzerland
- QC Ware, Palo Alto, CA, USA
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7
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Yang Z, Wan Z, Liu L, Fu J, Fan Q, Xie F, Zhang Y, Ma J. Achieving vibrational energies of diatomic systems with high quality by machine learning improved DFT method. RSC Adv 2022; 12:35950-35958. [PMID: 36545113 PMCID: PMC9753899 DOI: 10.1039/d2ra07613f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Accepted: 12/08/2022] [Indexed: 12/23/2022] Open
Abstract
When using ab initio methods to obtain high-quality quantum behavior of molecules, it often involves a lot of trial-and-error work in algorithm design and parameter selection, which requires enormous time and computational resource costs. In the study of vibrational energies of diatomic molecules, we found that starting from a low-precision DFT model and then correcting the errors using the high-dimensional function modeling capabilities of machine learning, one can considerably reduce the computational burden and improve the prediction accuracy. Data-driven machine learning is able to capture subtle physical information that is missing from DFT approaches. The results of 12C16O, 24MgO and Na35Cl show that, compared with CCSD(T)/cc-pV5Z calculation, this work improves the prediction accuracy by more than one order of magnitude, and reduces the computation cost by more than one order of magnitude.
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Affiliation(s)
- Zhangzhang Yang
- School of science, Key Laboratory of High Performance Scientific Computation, Xihua UniversityChengdu610039China
| | - Zhitao Wan
- School of science, Key Laboratory of High Performance Scientific Computation, Xihua UniversityChengdu610039China
| | - Li Liu
- School of science, Key Laboratory of High Performance Scientific Computation, Xihua UniversityChengdu610039China
| | - Jia Fu
- School of science, Key Laboratory of High Performance Scientific Computation, Xihua UniversityChengdu610039China
| | - Qunchao Fan
- School of science, Key Laboratory of High Performance Scientific Computation, Xihua UniversityChengdu610039China
| | - Feng Xie
- Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua UniversityBeijing100084China
| | - Yi Zhang
- College of Advanced Interdisciplinary Studies, National University of Defense TechnologyChangsha410073China
| | - Jie Ma
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Laser Spectroscopy Laboratory, College of Physics and Electronics Engineering, Shanxi UniversityTaiyuan030006China
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8
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Nasiri S, Shomenov T, Bubin S, Adamowicz L. Dissociation energy and the lowest vibrational transition in LiH without assuming the non-Born–Oppenheimer approximation. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2147105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Saeed Nasiri
- Department of Physics, Nazarbayev University, Nur-Sultan, Kazakhstan
| | | | - Sergiy Bubin
- Department of Physics, Nazarbayev University, Nur-Sultan, Kazakhstan
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
- Department of Physics, University of Arizona, Tucson, AZ, USA
- Centre for Advanced Study (CAS), the Norwegian Academy of Science and Letters, Oslo, Norway
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9
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Nasiri S, Adamowicz L, Bubin S. Electron affinity of LiH -. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2065375] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Saeed Nasiri
- Department of Physics, Nazarbayev University, Nur-Sultan, Kazakhstan
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
- Department of Physics, University of Arizona, Tucson, AZ, USA
- Centre for Advanced Study (CAS), the Norwegian Academy of Science and Letters, Oslo, Norway
| | - Sergiy Bubin
- Department of Physics, Nazarbayev University, Nur-Sultan, Kazakhstan
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10
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Feldmann R, Muolo A, Baiardi A, Reiher M. Quantum Proton Effects from Density Matrix Renormalization Group Calculations. J Chem Theory Comput 2022; 18:234-250. [PMID: 34978441 DOI: 10.1021/acs.jctc.1c00913] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
We recently introduced [J. Chem. Phys. 2020, 152, 204103] the nuclear-electronic all-particle density matrix renormalization group (NEAP-DMRG) method to solve the molecular Schrödinger equation, based on a stochastically optimized orbital basis, without invoking the Born-Oppenheimer approximation. In this work, we combine the DMRG method with the nuclear-electronic Hartree-Fock (NEHF-DMRG) approach, treating nuclei and electrons on the same footing. Inter- and intraspecies correlations are described within the DMRG method without truncating the excitation degree of the full configuration interaction wave function. We extend the concept of orbital entanglement and mutual information to nuclear-electronic wave functions and demonstrate that they are reliable metrics to detect strong correlation effects. We apply the NEHF-DMRG method to the HeHHe+ molecular ion, to obtain accurate proton densities, ground-state total energies, and vibrational transition frequencies by comparison with state-of-the-art data obtained with grid-based approaches and modern configuration interaction methods. For HCN, we improve on the accuracy of the latter approaches with respect to both the ground-state absolute energy and proton density, which is a major challenge for multireference nuclear-electronic state-of-the-art methods.
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Affiliation(s)
- Robin Feldmann
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Andrea Muolo
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
| | - Alberto Baiardi
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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11
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Affiliation(s)
- Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie Vladimir-Prelog-Weg 2 8093 Zürich Switzerland
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12
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Beutel M, Ahrens A, Huang C, Suzuki Y, Varga K. Deformed explicitly correlated Gaussians. J Chem Phys 2021; 155:214103. [PMID: 34879658 DOI: 10.1063/5.0066427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Deformed explicitly correlated Gaussian (DECG) basis functions are introduced, and their matrix elements are calculated. All matrix elements can be calculated analytically in a closed form, except the Coulomb one, which has to be approximated by a Gaussian expansion. The DECG basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole self-interaction term in the Pauli-Fierz Hamiltonian. Examples are presented showing the accuracy and necessity of deformed Gaussian basis functions to accurately solve light-matter coupled systems in cavity QED.
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Affiliation(s)
- Matthew Beutel
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - Alexander Ahrens
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - Chenhang Huang
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | | | - Kálmán Varga
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
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13
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Aebersold LE, Ulusoy IS, Wilson AK. Electron-nuclear quantum dynamics of diatomic molecules: nonadiabatic signatures in molecular spectra. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1988743] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Lucas E. Aebersold
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
| | - Inga S. Ulusoy
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
- Scientific Software Center, Interdisciplinary Center for Scientific Computing, Heidelberg University, Heidelberg, Germany
| | - Angela K. Wilson
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
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14
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15
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Schneider PE, Tao Z, Pavošević F, Epifanovsky E, Feng X, Hammes-Schiffer S. Transition states, reaction paths, and thermochemistry using the nuclear–electronic orbital analytic Hessian. J Chem Phys 2021; 154:054108. [DOI: 10.1063/5.0033540] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
| | - Zhen Tao
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, USA
| | - Fabijan Pavošević
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, USA
| | - Evgeny Epifanovsky
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
| | - Xintian Feng
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
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16
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Mátyus E, Cassam-Chenaï P. Orientational decoherence within molecules and emergence of the molecular shape. J Chem Phys 2021; 154:024114. [PMID: 33445882 DOI: 10.1063/5.0036568] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The question of classicality is addressed in relation with the shape of the nuclear skeleton of molecular systems. As the most natural environment, the electrons of the molecule are considered as continuously monitoring agents for the nuclei. For this picture, an elementary formalism of decoherence theory is developed and numerical results are presented for few-particle systems. The numerical examples suggest that the electron-nucleus Coulomb interaction is sufficient for inducing a blurred shape with strong quantum coherences in compounds of the lightest elements, H2, D2, T2, and HeH+.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
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17
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Ferenc D, Korobov VI, Mátyus E. Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of ^{4}He_{2}^{+} (X ^{2}Σ_{u}^{+}). PHYSICAL REVIEW LETTERS 2020; 125:213001. [PMID: 33274993 DOI: 10.1103/physrevlett.125.213001] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2020] [Accepted: 09/23/2020] [Indexed: 06/12/2023]
Abstract
The rovibrational intervals of the ^{4}He_{2}^{+} molecular ion in its X ^{2}Σ_{u}^{+} ground electronic state are computed by including the nonadiabatic, relativistic, and leading-order quantum-electrodynamics corrections. Good agreement of theory and experiment is observed for the rotational excitation series of the vibrational ground state and the fundamental vibration. The lowest-energy rotational interval is computed to be 70.937 69(10) cm^{-1} in agreement with the most recently reported experimental value, 70.937 589(23)(60)_{sys} cm^{-1} [L. Semeria et al., Phys. Rev. Lett. 124, 213001 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.213001].
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Affiliation(s)
- Dávid Ferenc
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Vladimir I Korobov
- Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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18
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Sibaev M, Polyak I, Manby FR, Knowles PJ. Molecular second-quantized Hamiltonian: Electron correlation and non-adiabatic coupling treated on an equal footing. J Chem Phys 2020; 153:124102. [DOI: 10.1063/5.0018930] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Marat Sibaev
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Iakov Polyak
- 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
| | - Peter J. Knowles
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
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19
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Ollitrault PJ, Baiardi A, Reiher M, Tavernelli I. Hardware efficient quantum algorithms for vibrational structure calculations. Chem Sci 2020; 11:6842-6855. [PMID: 32874524 PMCID: PMC7448527 DOI: 10.1039/d0sc01908a] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2020] [Accepted: 06/02/2020] [Indexed: 11/21/2022] Open
Abstract
We introduce a framework for the calculation of ground and excited state energies of bosonic systems suitable for near-term quantum devices and apply it to molecular vibrational anharmonic Hamiltonians. Our method supports generic reference modal bases and Hamiltonian representations, including the ones that are routinely used in classical vibrational structure calculations. We test different parametrizations of the vibrational wavefunction, which can be encoded in quantum hardware, based either on heuristic circuits or on the bosonic Unitary Coupled Cluster Ansatz. In particular, we define a novel compact heuristic circuit and demonstrate that it provides a good compromise in terms of circuit depth, optimization costs, and accuracy. We evaluate the requirements, number of qubits and circuit depth, for the calculation of vibrational energies on quantum hardware and compare them with state-of-the-art classical vibrational structure algorithms for molecules with up to seven atoms.
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Affiliation(s)
- Pauline J Ollitrault
- IBM Quantum , IBM Research - Zurich , Säumerstrasse 4 , 8803 Rüschlikon , Switzerland .
- Laboratory of Physical Chemistry , ETH Zürich , Vladimir-Prelog-Weg 2 , 8093 Zürich , Switzerland .
| | - Alberto Baiardi
- Laboratory of Physical Chemistry , ETH Zürich , Vladimir-Prelog-Weg 2 , 8093 Zürich , Switzerland .
| | - Markus Reiher
- Laboratory of Physical Chemistry , ETH Zürich , Vladimir-Prelog-Weg 2 , 8093 Zürich , Switzerland .
| | - Ivano Tavernelli
- IBM Quantum , IBM Research - Zurich , Säumerstrasse 4 , 8803 Rüschlikon , Switzerland .
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20
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Yu Q, Pavošević F, Hammes-Schiffer S. Development of nuclear basis sets for multicomponent quantum chemistry methods. J Chem Phys 2020; 152:244123. [PMID: 32610964 DOI: 10.1063/5.0009233] [Citation(s) in RCA: 43] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The nuclear-electronic orbital (NEO) framework provides a practical approach for directly incorporating nuclear quantum effects and non-Born-Oppenheimer effects of specified nuclei, typically protons, into quantum chemistry calculations. Multicomponent wave function based methods, such as NEO coupled cluster singles and doubles, and multicomponent density functional theory (DFT), such as NEO-DFT, require the appropriate selection of electronic and nuclear basis sets. Although a wide array of electronic basis sets are available, systematically developed nuclear basis sets that balance accuracy and efficiency have been lacking. Herein, a series of nuclear basis sets are developed and shown to be accurate and efficient for describing both ground and excited state properties of multicomponent systems in which electrons and specified protons are treated quantum mechanically. Three series of Gaussian-type nuclear basis sets, denoted PB4, PB5, and PB6, are developed with varying levels of angular momentum. A machine-learning optimization procedure relying on the Gaussian process regression method is utilized to accelerate the optimization process. The basis sets are validated in terms of predictions of ground state energies, proton densities, proton affinities, and proton vibrational excitation energies, allowing the user to select the desired balance between accuracy and efficiency for the properties of interest. These nuclear basis sets will enhance the tractability of NEO methods for applications to a wide range of chemical systems.
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Affiliation(s)
- Qi Yu
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Fabijan Pavošević
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
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21
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Bubin S, Adamowicz L. Computer program ATOM-MOL-nonBO for performing calculations of ground and excited states of atoms and molecules without assuming the Born-Oppenheimer approximation using all-particle complex explicitly correlated Gaussian functions. J Chem Phys 2020; 152:204102. [PMID: 32486658 DOI: 10.1063/1.5144268] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we describe a computer program called ATOM-MOL-nonBO for performing bound state calculations of small atoms and molecules without assuming the Born-Oppenheimer approximation. All particles forming the systems, electrons and nuclei, are treated on equal footing. The wave functions of the bound states are expanded in terms of all-particle one-center complex explicitly correlated Gaussian functions multiplied by Cartesian angular factors. As these Gaussian functions are eigenfunctions of the operator representing the square of the total angular momentum of the system, the problem separates and calculations of states corresponding to different values of the total rotational quantum number can be solved independently from each other. Due to thorough variational optimization of the Gaussian exponential parameters, the method allows us to generate very accurate wave functions. The optimization is aided by analytically calculated energy gradient determined with respect to the parameters. Three examples of calculations performed for diatomic and triatomic molecules are shown as an illustration of calculations that can be performed with this program. Finally, we discuss the limitations, applicability range, and bottlenecks of the program.
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Affiliation(s)
- Sergiy Bubin
- Department of Physics, School of Sciences and Humanities, Nazarbayev University, Nur-Sultan 010000, Kazakhstan
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry and Department of Physics, University of Arizona, Tucson, Arizona 85721, USA and Interdisciplinary Center for Modern Technologies, Nicolaus Copernicus University, Toruń PL 87-100, Poland
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22
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Muolo A, Baiardi A, Feldmann R, Reiher M. Nuclear-electronic all-particle density matrix renormalization group. J Chem Phys 2020; 152:204103. [PMID: 32486651 DOI: 10.1063/5.0007166] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
We introduce the Nuclear-Electronic All-Particle Density Matrix Renormalization Group (NEAP-DMRG) method for solving the time-independent Schrödinger equation simultaneously for electrons and other quantum species. In contrast to the already existing multicomponent approaches, in this work, we construct from the outset a multi-reference trial wave function with stochastically optimized non-orthogonal Gaussian orbitals. By iterative refining of the Gaussians' positions and widths, we obtain a compact multi-reference expansion for the multicomponent wave function. We extend the DMRG algorithm to multicomponent wave functions to take into account inter- and intra-species correlation effects. The efficient parameterization of the total wave function as a matrix product state allows NEAP-DMRG to accurately approximate the full configuration interaction energies of molecular systems with more than three nuclei and 12 particles in total, which is currently a major challenge for other multicomponent approaches. We present the NEAP-DMRG results for two few-body systems, i.e., H2 and H3 +, and one larger system, namely, BH3.
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Affiliation(s)
- Andrea Muolo
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Alberto Baiardi
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Robin Feldmann
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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23
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Pavošević F, Culpitt T, Hammes-Schiffer S. Multicomponent Quantum Chemistry: Integrating Electronic and Nuclear Quantum Effects via the Nuclear–Electronic Orbital Method. Chem Rev 2020; 120:4222-4253. [DOI: 10.1021/acs.chemrev.9b00798] [Citation(s) in RCA: 53] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Tanner Culpitt
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
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24
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Rowan K, Schatzki L, Zaklama T, Suzuki Y, Watanabe K, Varga K. Simulation of a hydrogen atom in a laser field using the time-dependent variational principle. Phys Rev E 2020; 101:023313. [PMID: 32168589 DOI: 10.1103/physreve.101.023313] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2019] [Accepted: 02/11/2020] [Indexed: 06/10/2023]
Abstract
The time-dependent variational principle is used to optimize the linear and nonlinear parameters of Gaussian basis functions to solve the time-dependent Schrödinger equation in one and three dimensions for a one-body soft Coulomb potential in a laser field. The accuracy is tested comparing the solution to finite difference grid calculations using several examples. The approach is not limited to one particle systems and the example presented for two electrons demonstrates the potential to tackle larger systems using correlated basis functions.
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Affiliation(s)
- Keefer Rowan
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - Louis Schatzki
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - Timothy Zaklama
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - Yasumitsu Suzuki
- Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan
| | - Kazuyuki Watanabe
- Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan
| | - Kálmán Varga
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
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25
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Baiardi A, Reiher M. The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges. J Chem Phys 2020; 152:040903. [DOI: 10.1063/1.5129672] [Citation(s) in RCA: 85] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Affiliation(s)
- Alberto Baiardi
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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26
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Treating the motion of nuclei and electrons in atomic and molecular quantum mechanical calculations on an equal footing: Non-Born–Oppenheimer quantum chemistry. ADVANCES IN QUANTUM CHEMISTRY 2020. [DOI: 10.1016/bs.aiq.2020.05.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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27
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Culpitt T, Yang Y, Schneider PE, Pavošević F, Hammes-Schiffer S. Molecular Vibrational Frequencies with Multiple Quantum Protons within the Nuclear-Electronic Orbital Framework. J Chem Theory Comput 2019; 15:6840-6849. [PMID: 31618582 DOI: 10.1021/acs.jctc.9b00665] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The nuclear-electronic orbital (NEO) approach treats all electrons and specified nuclei, typically protons, on the same quantum mechanical level. Proton vibrational excitations can be calculated using multicomponent time-dependent density functional theory (NEO-TDDFT) for fixed classical nuclei. Recently the NEO-DFT(V) approach was developed to enable the calculation of molecular vibrational frequencies for modes composed of both classical and quantum nuclei. This approach uses input from NEO-TDDFT to construct an extended NEO Hessian that depends on the expectation values of the quantum protons as well as the classical nuclear coordinates. Herein strategies are devised for extending these approaches to molecules with multiple quantum protons in a self-contained, effective, and computationally practical manner. The NEO-TDDFT method is shown to describe vibrational excitations corresponding to collective nuclear motions, such as linear combinations of proton vibrational excitations. The NEO-DFT(V) approach is shown to incorporate the most significant anharmonic effects in the molecular vibrations, particularly for the hydrogen stretching modes. These theoretical strategies pave the way for a wide range of multicomponent quantum chemistry applications.
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Affiliation(s)
- Tanner Culpitt
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Yang Yang
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Patrick E Schneider
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Fabijan Pavošević
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
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28
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Muolo A, Mátyus E, Reiher M. H 3 + as a five-body problem described with explicitly correlated Gaussian basis sets. J Chem Phys 2019; 151:154110. [PMID: 31640358 DOI: 10.1063/1.5121318] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Various explicitly correlated Gaussian (ECG) basis sets are considered for the solution of the molecular Schrödinger equation with particular attention to the simplest polyatomic system, H3 +. Shortcomings and advantages are discussed for plain ECGs, ECGs with the global vector representation, floating ECGs and their numerical projection, and ECGs with complex parameters. The discussion is accompanied with particle density plots to visualize the observations. In order to be able to use large complex ECG basis sets in molecular calculations, a numerically stable algorithm is developed, the efficiency of which is demonstrated for the lowest rotationally and vibrationally excited states of H2 and H3 +.
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Affiliation(s)
- Andrea Muolo
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Markus Reiher
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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29
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The any particle molecular orbital/molecular mechanics approach. J Mol Model 2019; 25:316. [PMID: 31529219 DOI: 10.1007/s00894-019-4153-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2019] [Accepted: 08/14/2019] [Indexed: 10/26/2022]
Abstract
A computational scheme is proposed to broaden the range of applications of multicomponent methodologies for the study of local properties of big molecular systems existing in the gas phase and in solvated environments. This scheme extends the any particle molecular orbital (APMO) approach in the quantum mechanics/molecular mechanics (QM/MM) framework. As a first assessment of the performance of the proposed approach, we estimate the proton affinities (PAs) of seventy amines in the gas phase and the proton binding energies (PBEs) in the gas phase and in an explicitly solvated environment of the sixty-one protons present in the chignolin protein. These calculations are performed with the QM/MM versions of the APMO second-order proton propagator (APMO-PP2) and the APMO extended Koopmans' theorem (APMO-KT) approaches. Calculated PAs and PBEs show significant reductions in the computational effort with a reduced loss in accuracy. These results suggest that the APMO/MM scheme might be used as a low-cost multi-component alternative for studies of local properties in big molecular systems. Graphical Abstract QMMM regions and CPU times for the APMO/MM approach.
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30
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The 2S Rydberg series of the lithium atom. Calculations with all-electron explicitly correlated Gaussian functions. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2019.06.051] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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31
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Cao Y, Romero J, Olson JP, Degroote M, Johnson PD, Kieferová M, Kivlichan ID, Menke T, Peropadre B, Sawaya NPD, Sim S, Veis L, Aspuru-Guzik A. Quantum Chemistry in the Age of Quantum Computing. Chem Rev 2019; 119:10856-10915. [PMID: 31469277 DOI: 10.1021/acs.chemrev.8b00803] [Citation(s) in RCA: 265] [Impact Index Per Article: 53.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.
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Affiliation(s)
- Yudong Cao
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan Romero
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan P Olson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Matthias Degroote
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada
| | - Peter D Johnson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Mária Kieferová
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Physics and Astronomy , Macquarie University , Sydney , NSW 2109 , Australia.,Institute for Quantum Computing and Department of Physics and Astronomy , University of Waterloo , Waterloo , Ontario N2L 3G1 , Canada
| | - Ian D Kivlichan
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States
| | - Tim Menke
- Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States.,Research Laboratory of Electronics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States.,Department of Physics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Borja Peropadre
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Nicolas P D Sawaya
- Intel Laboratories , Intel Corporation , Santa Clara , California 95054 United States
| | - Sukin Sim
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic v.v.i. , Doleǰskova 3 , 18223 Prague 8, Czech Republic
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Canadian Institute for Advanced Research , Toronto , Ontario M5G 1Z8 , Canada.,Vector Institute for Artificial Intelligence , Toronto , Ontario M5S 1M1 , Canada
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32
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Pavošević F, Hammes-Schiffer S. Multicomponent coupled cluster singles and doubles and Brueckner doubles methods: Proton densities and energies. J Chem Phys 2019; 151:074104. [PMID: 31438716 DOI: 10.1063/1.5116113] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The nuclear-electronic orbital (NEO) framework enables computationally practical coupled cluster calculations of multicomponent molecular systems, in which all electrons and specified nuclei, typically protons, are treated quantum mechanically. In addition to energies, computing accurate proton densities is essential for the calculation of reliable molecular properties, including vibrationally averaged geometries and vibrational frequencies. Herein, the Lagrangian formalism for the multicomponent coupled cluster with single and double excitations (NEO-CCSD) method is derived and implemented. The multicomponent coupled cluster with double excitations method using optimized Brueckner orbitals, denoted as NEO-BCCD, is also developed. Both of these methods are used to compute the proton densities for two molecular systems. The results illustrate that orbital relaxation effects, which can be included either indirectly with the NEO-CCSD method or directly with the NEO-BCCD method, are critical for computing even qualitatively accurate proton densities. Both methods are also able to provide accurate proton affinities and vibrationally averaged optimized geometries. This Lagrangian formalism will enable the calculation of other properties such as analytical nuclear gradients and Hessians with NEO coupled cluster methods. Moreover, the accuracy of these methods may be improved systematically by the inclusion of higher-order excitations. Thus, this work provides the foundation for a wide range of future methodological developments and applications within the NEO framework.
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Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
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33
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Mátyus E, Teufel S. Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states. J Chem Phys 2019; 151:014113. [PMID: 31272174 DOI: 10.1063/1.5097899] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The quantum mechanical motion of the atomic nuclei is considered over a single- or a multidimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear configurations. The electron-nucleus Hamiltonian is block-diagonalized up to O(εn+1) through a unitary transformation of the electronic subspace, and the corresponding nth-order effective Hamiltonian is derived for the quantum nuclear motion. Explicit but general formulas are given for the second- and the third-order corrections. As a special case, the second-order Hamiltonian corresponding to an isolated electronic state is recovered which contains the coordinate-dependent mass-correction terms in the nuclear kinetic energy operator. For a multidimensional, explicitly coupled electronic band, the second-order Hamiltonian contains the usual Born-Oppenheimer terms and nonadiabatic corrections, but generalized mass-correction terms appear as well. These, earlier neglected terms, perturbatively account for the outlying (discrete and continuous) electronic states not included in the explicitly coupled electronic subspace.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
| | - Stefan Teufel
- Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
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34
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Pavošević F, Hammes-Schiffer S. Multicomponent equation-of-motion coupled cluster singles and doubles: Theory and calculation of excitation energies for positronium hydride. J Chem Phys 2019; 150:161102. [DOI: 10.1063/1.5094035] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
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35
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Yang Y, Schneider PE, Culpitt T, Pavošević F, Hammes-Schiffer S. Molecular Vibrational Frequencies within the Nuclear-Electronic Orbital Framework. J Phys Chem Lett 2019; 10:1167-1172. [PMID: 30776246 DOI: 10.1021/acs.jpclett.9b00299] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
A significant challenge for multicomponent quantum chemistry methods is the calculation of vibrational frequencies for comparison to experiment. The nuclear-electronic orbital (NEO) approach treats specified nuclei, typically key protons, quantum mechanically. The Born-Oppenheimer separation between the quantum and classical nuclei prevents the direct calculation of vibrational frequencies corresponding to modes composed of both types of nuclei. Herein an effective strategy for calculating the vibrational frequencies of the entire molecule within the NEO framework is devised and implemented. This strategy requires diagonalization of an extended NEO Hessian that depends on the expectation values of the quantum nuclei as well as the coordinates of the classical nuclei and is constructed with input from multicomponent time-dependent density functional theory (NEO-TDDFT). Application of this NEO-DFT(V) approach to molecular systems illustrates that it accurately incorporates the most significant anharmonic effects. This general theoretical formulation opens up a broad spectrum of new directions for multicomponent quantum chemistry.
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Affiliation(s)
- Yang Yang
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Patrick E Schneider
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Tanner Culpitt
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Fabijan Pavošević
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
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36
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Chavez EM, Bubin S, Adamowicz L. Implementation of explicitly correlated complex Gaussian functions in calculations of molecular rovibrational J=1 states without Born-Oppenheimer approximation. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2019.01.013] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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37
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Raghavan SS, Niraikulam A, Gunasekaran K. Side chain torsion dictates planarity and ionizability of green fluorescent protein's chromophore leading to spectral perturbations. J Biomol Struct Dyn 2019; 37:4450-4459. [PMID: 30488782 DOI: 10.1080/07391102.2018.1552196] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Abstract
Spectral characteristics of fluorescent proteins (FPs) are well studied, and through protein engineering, several FP variants constituting entire visible spectrum have been created. One of the most common mechanisms attributed to spectral shifts in FP is excited state proton transfer (ESPT), hydroxyl moiety protonation and deprotonation, along with chromophore cis-trans isomerism. The most widely studied FPs are those derived from avGFP (Aequorea victoria GFP) and Dsred (Discosoma coral). Apart from the above mechanism, certain interacting residues are said to play a vital role in altering the proton transfer pathway leading to numerous spectral variants. Similarly, the hydrogen-bonded networks solely cannot dictate the energy landscape of FPs. Non-bonded interactions also can create secondary harmonic shifts by dipole-dipole inductions. Side chain contacts tend to alter the topological and torsional geometry, thereby disturbing the chromophore's planarity. Side chain torsional variations have almost been unaccounted for their distortions in FPs. We hypothesize the torsional landscape and altered residual interactions as prominent factors for the spectral shifts. Through our 200 ns molecular dynamics investigation, we prospect that van der Waals packing in Dsred is more compact than that of avGFP, thus creating a low solvent occupiable environment and reduced solvent interactions having higher red spectral shift. The torsional changes of wild avGFP, S65T avGFP and Dsred have been studied to comprehend the inter-residual contact distance and the geometrical descriptors. Communicated by Ramaswamy H. Sarma.
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Affiliation(s)
- S Sriram Raghavan
- Department of Crystallography and Biophysics, University of Madras , Chennai , Tamil Nadu , India
| | - Ayyadurai Niraikulam
- Division of Biotechnology, Council of Scientific and Industrial Research-Central Leather Research Institute (CSIR-CLRI) , Chennai , Tamil Nadu , India
| | - Krishnasamy Gunasekaran
- Department of Crystallography and Biophysics, University of Madras , Chennai , Tamil Nadu , India
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38
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Pavošević F, Culpitt T, Hammes-Schiffer S. Multicomponent Coupled Cluster Singles and Doubles Theory within the Nuclear-Electronic Orbital Framework. J Chem Theory Comput 2018; 15:338-347. [DOI: 10.1021/acs.jctc.8b01120] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Tanner Culpitt
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
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39
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Muolo A, Mátyus E, Reiher M. Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations. J Chem Phys 2018; 149:184105. [PMID: 30441913 DOI: 10.1063/1.5050462] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Numerical projection methods are elaborated for the calculation of eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with selected rotational and parity quantum numbers employing shifted explicitly correlated Gaussian functions, which are, in general, not eigenfunctions of the total angular momentum and parity operators. The increased computational cost of numerically projecting the basis functions onto the irreducible representations of the three dimensional rotation-inversion group is the price to pay for the increased flexibility of the basis functions. This increased flexibility allowed us to achieve a substantial improvement for the variational upper bound to the Pauli-allowed ground-state energy of the H 3 + = { p + , p + , p + , e - , e - } molecular ion treated as an explicit five-particle system. We compare our pre-Born-Oppenheimer result obtained for this molecular ion with rotational-vibrational calculations carried out on a potential energy surface.
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Affiliation(s)
- Andrea Muolo
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Edit Mátyus
- Institute of Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Markus Reiher
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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40
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Stanke M, Adamowicz L. Magnetic orbit-orbit interaction involving electrons and the nucleus orbiting around the center of mass in 1S and 1P Rydberg states of helium. Finite-nuclear-mass calculations with explicitly correlated Gaussian functions. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.09.060] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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41
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
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Nakatsuji H, Nakashima H, Kurokawa YI. Solving the Schrödinger equation of atoms and molecules: Chemical-formula theory, free-complement chemical-formula theory, and intermediate variational theory. J Chem Phys 2018; 149:114105. [PMID: 30243277 DOI: 10.1063/1.5040376] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Chemistry is governed by the principle of quantum mechanics as expressed by the Schrödinger equation (SE) and Dirac equation (DE). The exact general theory for solving these fundamental equations is therefore a key for formulating accurately predictive theory in chemical science. The free-complement (FC) theory for solving the SE of atoms and molecules proposed by one of the authors is such a general theory. On the other hand, the working theory most widely used in chemistry is the chemical formula that refers to the molecular structural formula and chemical reaction formula, collectively. There, the central concepts are the local atomic concept, transferability, and from-atoms-to-molecule concept. Since the chemical formula is the most successful working theory in chemistry ever existed, we formulate our FC theory to have the structure reflecting the chemical formula. Our basic postulate is that as far as the SE is the principle of chemistry, its solutions for chemistry should have the structure that can be related to the chemical formulas. So, in this paper, we first formulate a theory that designs the wave function to reflect the structure of the chemical formula. We call this theory chemical formula theory (CFT). In the CFT, we place the valence ground and excited states of each atom at each position of the chemical formula of the molecule and let them interact using their free valences to form the ground and excited states of the molecule. The principle there is the variational principle so that the ground and excited states obtained satisfy the orthogonality and Hamiltonian-orthogonality relations. Then, we formulate the exact FC theory starting from the initial functions produced by the CFT. This FC theory is referred to as free-complement chemical-formula theory (FC-CFT), which is expected to describe efficiently the solution of the SE by the above reason. The FC-CFT wave function is modified from that of CFT. Since this modification is done by the exact SE, its analysis may give some insights to chemists that assist their chemistry. Thus, this theory would be not only exact but also conceptually useful. Furthermore, the intermediate theory between CFT and FC-CFT would also be useful. There, we use only integratable functions and apply the variational principle so that we refer to this theory as FC-CFT-variational (FC-CFT-V). It is an advanced theory of CFT. Since the variational method is straightforward and powerful, we can do extensive chemical studies in a reasonable accuracy. After finishing such studies, if we still need an exact level of solutions, we add the remaining functions of the FC-CFT and perform the exact calculations. Furthermore, when we deal with large and even giant molecules, the inter-exchange (iExg) theory for the antisymmetry rule introduced previously leads to a large simplification. There, the inter-exchanges between distant electron pairs fade away so that only Coulombic interactions survive. Further in giant systems, even an electrostatic description becomes possible. Then, the FC-CFT for exactly solving the SE would behave essentially to order N for large and giant molecular systems, though the pre-factor should be very large and must be minimized.
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Affiliation(s)
- Hiroshi Nakatsuji
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
| | - Hiroyuki Nakashima
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
| | - Yusaku I Kurokawa
- Quantum Chemistry Research Institute, Kyoto Technoscience Center 16, 14 Yoshida Kawaramachi, Sakyo-ku, Kyoto 606-8305, Japan
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43
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Yang Y, Culpitt T, Tao Z, Hammes-Schiffer S. Stability conditions and local minima in multicomponent Hartree-Fock and density functional theory. J Chem Phys 2018; 149:084105. [DOI: 10.1063/1.5040353] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yang Yang
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Tanner Culpitt
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Zhen Tao
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
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Fabi A, Alesini D, Valle E, Moscetti L, Caputo R, Caruso M, Carbognin L, Ciccarese M, La Verde N, Arpino G, Cannita K, Paris I, Santini D, Montemurro F, Russillo M, Ferretti G, Filippelli G, Rossello R, Fabbri A, Zambelli A, Leonardi V, D'Ottavio AM, Nisticò C, Stani S, Giampaglia M, Scandurra G, Catania G, Malaguti P, Giannarelli D, Cognetti F. T-DM1 and brain metastases: Clinical outcome in HER2-positive metastatic breast cancer. Breast 2018; 41:137-143. [PMID: 30092500 DOI: 10.1016/j.breast.2018.07.004] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Revised: 07/11/2018] [Accepted: 07/11/2018] [Indexed: 11/26/2022] Open
Abstract
BACKGROUND We reported the results of an Italian large retrospective analysis that evaluated the effectiveness and safety of T-DM1 in 'field-practice' breast cancer patients. We performed a sub-analysis to investigate the clinical activity of T-DM1 in patients with brain metastases (BMs). METHODS The records of 87 adult women with HER2-positive breast cancer and BMs treated with T-DM1 were reviewed. Their clinical outcomes were compared with those of 216 patients without central nervous system (CNS) involvement. RESULTS Response to T-DM1 treatment in BMs was available for 53 patients in the BM group (60.9%): two patients reported a complete response (3.8%), 11 patients obtained partial response (20.7%; overall response rate: 24.5%), 16 patients had a stable disease (30.1%). Regarding extracranial disease, a total of 77 and 191 patients were evaluable for response in BM group and non-BM group, respectively. The overall response rate was 35.1% in the BM group and 38.3% in the non-BM group; disease control rate was 53.3% and 66.6%, respectively. At a median follow-up of 16 months (range: 1-55), median cumulative progression-free survival (PFS) was 7 months (95% CI: 5.4-8.6) in the BM group and 8 months (95% CI: 5.7-10.3) in the non-BM group. In the second-line setting, PFS was 5 (95% CI: 3.1-6.9) versus 11 (95% CI: 7.1-14.9) months (p = 0.01). Overall survival was 14 months (95% CI: 12.2-15.8) in the BM group and 32 months (95% CI: 24.4-39.6) in the non-BM group (p < 0.0001). CONCLUSIONS T-DM1 is active in breast cancer patients with BMs.
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Affiliation(s)
- Alessandra Fabi
- Oncologia Medica 1, Istituto Nazionale Tumori "Regina Elena", Roma, Italy.
| | - Daniele Alesini
- Oncologia Medica 1, Istituto Nazionale Tumori "Regina Elena", Roma, Italy
| | | | | | | | | | | | | | - Nicla La Verde
- Oncologia Medica, PO Fatebenefratelli e Oftalmico, Milano, Italy
| | - Grazia Arpino
- Oncologia Medica, Università Federico II, Napoli, Italy
| | - Katia Cannita
- Oncologia Medica, Ospedale S. Salvatore, Università dell'Aquila, Italy
| | - Ida Paris
- Oncologia e Ginecologica Polo Donna, Policlinico A.Gemelli, Roma, Italy
| | - Daniele Santini
- Oncologia Medica, Campus Bio-medico Universitario, Roma, Italy
| | - Filippo Montemurro
- Investigative Clinical Oncology, Cancer Institute-FPO, IRCCS, Candiolo, Torino, Italy
| | | | - Gianluigi Ferretti
- Oncologia Medica 1, Istituto Nazionale Tumori "Regina Elena", Roma, Italy
| | | | - Rosalba Rossello
- Oncologia Medica, Ospedale S. Vincenzo, Taormina, Messina, Italy
| | | | | | | | | | - Cecilia Nisticò
- Oncologia Medica 1, Istituto Nazionale Tumori "Regina Elena", Roma, Italy
| | | | | | - Giusy Scandurra
- Oncologia Medica, Ospedale per le Emergenze Cannizzaro, Catania, Italy
| | - Giovanna Catania
- Oncologia Medica 1, Istituto Nazionale Tumori "Regina Elena", Roma, Italy
| | - Paola Malaguti
- Oncologia Medica 1, Istituto Nazionale Tumori "Regina Elena", Roma, Italy
| | - Diana Giannarelli
- Unità di Biostatistica, Istituto Nazionale Tumori "Regina Elena", Roma, Italy
| | - Francesco Cognetti
- Oncologia Medica 1, Istituto Nazionale Tumori "Regina Elena", Roma, Italy
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Bayne MG, Scher JA, Ellis BH, Chakraborty A. Linked-Cluster Formulation of Electron–Hole Interaction Kernel in Real-Space Representation without Using Unoccupied States. J Chem Theory Comput 2018; 14:3656-3666. [DOI: 10.1021/acs.jctc.8b00123] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Michael G. Bayne
- Department of Chemistry, Syracuse University, Syracuse, New York 13244 United States
| | - Jeremy A. Scher
- Department of Chemistry, Syracuse University, Syracuse, New York 13244 United States
| | - Benjamin H. Ellis
- Department of Chemistry, Syracuse University, Syracuse, New York 13244 United States
| | - Arindam Chakraborty
- Department of Chemistry, Syracuse University, Syracuse, New York 13244 United States
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Muolo A, Mátyus E, Reiher M. Generalized elimination of the global translation from explicitly correlated Gaussian functions. J Chem Phys 2018; 148:084112. [PMID: 29495776 DOI: 10.1063/1.5009465] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper presents the multi-channel generalization of the center-of-mass kinetic energy elimination approach [B. Simmen et al., Mol. Phys. 111, 2086 (2013)] when the Schrödinger equation is solved variationally with explicitly correlated Gaussian functions. The approach has immediate relevance in many-particle systems which are handled without the Born-Oppenheimer approximation and can be employed also for Dirac-type Hamiltonians. The practical realization and numerical properties of solving the Schrödinger equation in laboratory-frame Cartesian coordinates are demonstrated for the ground rovibronic state of the H2+={p+,p+,e-} ion and the H2 = {p+, p+, e-, e-} molecule.
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Affiliation(s)
- Andrea Muolo
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Edit Mátyus
- Institute of Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Markus Reiher
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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Posada E, Moncada F, Reyes A. The any particle molecular orbital grid-based Hartree-Fock (APMO-GBHF) approach. J Chem Phys 2018; 148:084113. [PMID: 29495795 DOI: 10.1063/1.5012521] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Edwin Posada
- Departament of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30, #45-03 Bogotá, Colombia
| | - Félix Moncada
- Departament of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30, #45-03 Bogotá, Colombia
| | - Andrés Reyes
- Departament of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30, #45-03 Bogotá, Colombia
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48
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Rayka M, Goli M, Shahbazian S. Toward a muon-specific electronic structure theory: effective electronic Hartree-Fock equations for muonic molecules. Phys Chem Chem Phys 2018; 20:4466-4477. [PMID: 29372727 DOI: 10.1039/c7cp07599e] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.
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Affiliation(s)
- Milad Rayka
- Department of Physics and Department of Physical and Computational Chemistry, Shahid Beheshti University, G. C., Evin, P.O. Box 19395-4716, Tehran, 19839, Iran.
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49
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Explicitly-correlated non-born-oppenheimer calculations of the HD molecule in a strong magnetic field. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.06.016] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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50
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Charry J, Pedraza-González L, Reyes A. On the physical interpretation of the nuclear molecular orbital energy. J Chem Phys 2017; 146:214103. [PMID: 28576090 PMCID: PMC5453789 DOI: 10.1063/1.4984098] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2017] [Accepted: 05/11/2017] [Indexed: 11/14/2022] Open
Abstract
Recently, several groups have extended and implemented molecular orbital (MO) schemes to simultaneously obtain wave functions for electrons and selected nuclei. Many of these schemes employ an extended Hartree-Fock approach as a first step to find approximate electron-nuclear wave functions and energies. Numerous studies conducted with these extended MO methodologies have explored various effects of quantum nuclei on physical and chemical properties. However, to the best of our knowledge no physical interpretation has been assigned to the nuclear molecular orbital energy (NMOE) resulting after solving extended Hartree-Fock equations. This study confirms that the NMOE is directly related to the molecular electrostatic potential at the position of the nucleus.
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Affiliation(s)
- Jorge Charry
- Department of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30 #45-03, Bogotá, Colombia
| | - Laura Pedraza-González
- Department of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30 #45-03, Bogotá, Colombia
| | - Andrés Reyes
- Department of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30 #45-03, Bogotá, Colombia
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