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Gimbal-Zofka Y, González-Espinoza CE, Rumble CA, Wesolowski TA. Assessment of Approximations to the Embedding Potential in Frozen-Density Embedding Theory for the Calculation of Electric Field Gradients. J Chem Theory Comput 2024; 20:348-356. [PMID: 38116618 DOI: 10.1021/acs.jctc.3c00773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2023]
Abstract
The approximations to the embedding potential in frozen-density embedding theory (FDET) have been assessed for the first time for the calculation of the electric field gradient (EFG) at a nucleus. FDET-based methods using a hierarchy of approximations are applied to evaluate the EFG at the nuclei of an HCl molecule in several noncovalently bound clusters chosen to represent potential liquid or molecular crystal systems. A detailed assessment of such approximations is made for the Hartree-Fock treatment of electron-electron correlation (both in FDET and in the reference calculations for the whole cluster). The emerging choice of the optimal set of approximations is reconfirmed in calculations in which electron-electron calculations are treated at the MP2 level. Our optimized protocol produces average errors in the complexation-induced EFG shift on the order of 25% relative to conventional quantum mechanical calculations for the whole cluster. This protocol is shown to be numerically robust and leads to enormous computational savings compared to a complete quantum mechanical treatment of the embedded species and its environment. For a cluster comprising a Na+ cation and up to 24 water molecules, the computation time is reduced by a factor of 30,000 at the expense of introducing an error in the environment-induced EFG shift of 22%.
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Affiliation(s)
- Yann Gimbal-Zofka
- Départment de Chimie Physique, Université de Genève, 30, quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
| | | | - Christopher A Rumble
- Department of Chemistry, Altoona College, The Pennsylvania State University, 3000 Ivyside Park, Altoona, 16601 Pennsylvania, United States
| | - Tomasz A Wesolowski
- Départment de Chimie Physique, Université de Genève, 30, quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
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2
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Chubak I, Alon L, Silletta EV, Madelin G, Jerschow A, Rotenberg B. Quadrupolar 23Na + NMR relaxation as a probe of subpicosecond collective dynamics in aqueous electrolyte solutions. Nat Commun 2023; 14:84. [PMID: 36604414 PMCID: PMC9816157 DOI: 10.1038/s41467-022-35695-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Accepted: 12/14/2022] [Indexed: 01/07/2023] Open
Abstract
Nuclear magnetic resonance relaxometry represents a powerful tool for extracting dynamic information. Yet, obtaining links to molecular motion is challenging for many ions that relax through the quadrupolar mechanism, which is mediated by electric field gradient fluctuations and lacks a detailed microscopic description. For sodium ions in aqueous electrolytes, we combine ab initio calculations to account for electron cloud effects with classical molecular dynamics to sample long-time fluctuations, and obtain relaxation rates in good agreement with experiments over broad concentration and temperature ranges. We demonstrate that quadrupolar nuclear relaxation is sensitive to subpicosecond dynamics not captured by previous models based on water reorientation or cluster rotation. While ions affect the overall water retardation, experimental trends are mainly explained by dynamics in the first two solvation shells of sodium, which contain mostly water. This work thus paves the way to the quantitative understanding of quadrupolar relaxation in electrolyte and bioelectrolyte systems.
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Affiliation(s)
- Iurii Chubak
- Sorbonne Université CNRS, Physico-Chimie des électrolytes et Nanosystèmes Interfaciaux, F-75005, Paris, France
| | - Leeor Alon
- New York University School of Medicine, Department of Radiology, Center for Biomedical Imaging, 660 First Avenue, New York, NY, 10016, USA
- Center for Advanced Imaging Innovation and Research, Department of Radiology, New York University Grossman School of Medicine, New York, NY, 10016, USA
| | - Emilia V Silletta
- Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, Medina Allende s/n, X5000HUA, Córdoba, Argentina
- Instituto de Física Enrique Gaviola, CONICET, Medina Allende s/n, X5000HUA, Córdoba, Argentina
| | - Guillaume Madelin
- New York University School of Medicine, Department of Radiology, Center for Biomedical Imaging, 660 First Avenue, New York, NY, 10016, USA
- Center for Advanced Imaging Innovation and Research, Department of Radiology, New York University Grossman School of Medicine, New York, NY, 10016, USA
| | - Alexej Jerschow
- New York University, Department of Chemistry, 100 Washington Square E, New York, NY, 10003, USA.
| | - Benjamin Rotenberg
- Sorbonne Université CNRS, Physico-Chimie des électrolytes et Nanosystèmes Interfaciaux, F-75005, Paris, France.
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3
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Chubak I, Scalfi L, Carof A, Rotenberg B. NMR Relaxation Rates of Quadrupolar Aqueous Ions from Classical Molecular Dynamics Using Force-Field Specific Sternheimer Factors. J Chem Theory Comput 2021; 17:6006-6017. [PMID: 34570493 DOI: 10.1021/acs.jctc.1c00690] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The nuclear magnetic resonance (NMR) relaxation of quadrupolar nuclei is governed by the electric field gradient (EFG) fluctuations at their position. In classical molecular dynamics (MD), the electron cloud contribution to the EFG can be included via the Sternheimer approximation, in which the full EFG at the nucleus that can be computed using quantum density functional theory (DFT) is considered to be proportional to that arising from the external, classical charge distribution. In this work, we systematically assess the quality of the Sternheimer approximation as well as the impact of the classical force field (FF) on the NMR relaxation rates of aqueous quadrupolar ions at infinite dilution. In particular, we compare the rates obtained using an ab initio parametrized polarizable FF, a recently developed empirical FF with scaled ionic charges and a simple empirical nonpolarizable FF with formal ionic charges. Surprisingly, all three FFs considered yield good values for the rates of smaller and less polarizable solutes (Li+, Na+, K+, Cl-), provided that a model-specific Sternheimer parametrization is employed. Yet, the polarizable and scaled charge FFs yield better estimates for divalent and more polarizable species (Mg2+, Ca2+, Cs+). We find that a linear relationship between the quantum and classical EFGs holds well in all of the cases considered; however, such an approximation often leads to quite large errors in the resulting EFG variance, which is directly proportional to the computed rate. We attempted to reduce the errors by including first order nonlinear corrections to the EFG, yet no clear improvement for the resulting variance has been found. The latter result indicates that more refined methods for determining the EFG at the ion position, in particular those that take into account the instantaneous atomic environment around an ion, might be necessary to systematically improve the NMR relaxation rate estimates in classical MD.
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Affiliation(s)
- Iurii Chubak
- Sorbonne Université CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Laura Scalfi
- Sorbonne Université CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Antoine Carof
- Universite de Lorraine, CNRS, LPCT, F-54000, Nancy, France
| | - Benjamin Rotenberg
- Sorbonne Université CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
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4
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Carof A, Salanne M, Charpentier T, Rotenberg B. Accurate Quadrupolar NMR Relaxation Rates of Aqueous Cations from Classical Molecular Dynamics. J Phys Chem B 2014; 118:13252-7. [DOI: 10.1021/jp5105054] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Antoine Carof
- Sorbonne
Universités,
UPMC Univ. Paris 06, UMR 8234 PHENIX, 75005 Paris, France
- CNRS, UMR
8234
PHENIX, 75005 Paris, France
| | - Mathieu Salanne
- Sorbonne
Universités,
UPMC Univ. Paris 06, UMR 8234 PHENIX, 75005 Paris, France
- CNRS, UMR
8234
PHENIX, 75005 Paris, France
| | - Thibault Charpentier
- CEA, IRAMIS, NIMBE,
LSDRM, UMR CEA-CNRS 3299, F-91191 Gif-sur-Yvette cedex, France
| | - Benjamin Rotenberg
- Sorbonne
Universités,
UPMC Univ. Paris 06, UMR 8234 PHENIX, 75005 Paris, France
- CNRS, UMR
8234
PHENIX, 75005 Paris, France
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5
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Couch S, Howes AP, Kohn SC, Smith ME. 33S solid state NMR of sulphur speciation in silicate glasses. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2004; 26:203-208. [PMID: 15388185 DOI: 10.1016/j.ssnmr.2004.03.007] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2004] [Revised: 03/09/2004] [Indexed: 05/24/2023]
Abstract
33S solid-state NMR is reported from some model crystalline sulphides, sulphates, sulphites and thiosulphates. This is the first report of (33)S NMR signals of the latter two species from a solid. Good quality spectra, which have distinct, well separated shift ranges can be identified for all these groupings, except for sulphites and hydrogen sulphites whose resonances are very broad. Nonetheless the presence of sulphites and hydrogen sulphites can be confirmed from their characteristic sharp, intense time domain echoes. (33)S MAS NMR is also applied to a range of dry and hydrous silicate glasses with approximately 1wt% 99at% (33)S-enriched sulphur. It is clear that in all these glasses sulphate is present, and in mixed cation systems there is some evidence of preferential association of sulphate with a specific cation. In a dry potassium silicate glass sample two resolved (33)S resonances are observed, a sulphate, and the second from thiosulphate. Hence solid state (33)S NMR is shown to be a feasible probe that can be applied to this problem that can readily distinguish different sulphur species.
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Affiliation(s)
- S Couch
- Department of Earth Sciences, University of Bristol, Wills Memorial Building, Queens Rd., Bristol BS8 1RJ, UK
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6
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Aguado A, Madden PA. Ewald summation of electrostatic multipole interactions up to the quadrupolar level. J Chem Phys 2003. [DOI: 10.1063/1.1605941] [Citation(s) in RCA: 94] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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