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Eeckhoudt J, Alonso M, Geerlings P, De Proft F. Bond Lengths and Dipole Moments of Diatomic Molecules under Isotropic Pressure with the XP-PCM and GOSTSHYP Models. J Chem Theory Comput 2024; 20:7430-7442. [PMID: 39189061 DOI: 10.1021/acs.jctc.4c00665] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/28/2024]
Abstract
While high-pressure chemistry has a well-established history, methods to simulate pressure at the single-molecule level have been somewhat lacking. The current work aims at comparing two static models (XP-PCM and GOSTSHYP) to apply isotropic pressure to single molecules, focusing on the equilibrium bond length and electric dipole moment of diatomic molecules. Numerical challenges arising in the potential energy surface using the XP-PCM method were examined, and a pragmatic approach was followed to mitigate these. The definition of the cavity was scrutinized, and two approaches to retrieve the isotropic character that could potentially be lost when using the standard methodology were suggested. Subsequently, equilibrium bond lengths under pressure were evaluated, showing reasonable agreement between GOSTSHYP and XP-PCM, but some discrepancies persist. A Taylor series analysis introduced elsewhere was then applied to rationalize the observed trends in terms of the bond surface. Finally, the dipole moment was shown to be highly sensitive to the cavity definition, and qualitative agreement necessitates the use of our adapted procedure.
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Affiliation(s)
- Jochen Eeckhoudt
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
| | - Mercedes Alonso
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
| | - Frank De Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
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2
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Chołuj M, Lipkowski P, Bartkowiak W. HeH + under Spatial Confinement. MOLECULES (BASEL, SWITZERLAND) 2022; 27:molecules27248997. [PMID: 36558130 PMCID: PMC9787572 DOI: 10.3390/molecules27248997] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Revised: 12/02/2022] [Accepted: 12/07/2022] [Indexed: 12/24/2022]
Abstract
In the present study, the influence of spatial confinement on the bond length as well as dipole moment, polarizability and (hyper)polarizabilities of HeH+ ion was analyzed. The effect of spatial confinement was modelled by cylindrically symmetric harmonic oscillator potential, that can be used to mimic high pressure conditions. Based on the conducted research it was found that the spatial confinement significantly affects the investigated properties. Increasing the confinement strength leads to a substantial decrease of their values. This work may be of particular interest for astrochemistry as HeH+ is believed to be the first compound to form in the Universe.
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Cammi R, Chen B. Studying and exploring potential energy surfaces of compressed molecules: a fresh theory from the eXtreme Pressure Polarizable Continuum Model. J Chem Phys 2022; 157:114101. [DOI: 10.1063/5.0104269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present a new theory for studying and exploring the potential energy surface of compressed molecular systems as described within the XP-PCM framework. The effective potential energy surface is defined by the sum of the electronic energy of the compressed system and the pressure-volume work that is necessary in order to create the compression cavity at the given condition of pressure. We show that the resulting total energy Gt is related to the electronic energy by a Legendre transform, in which the pressure and volume of the compression cavity are the conjugate variables. We present an analytical expression for the evaluation of the gradient of the total energy ∇Gt to be used for the geometry optimization of equilibrium geometries and transition states of compressed molecular systems. We also show that, as a result of the Legendre transform property, the potential energy surface can be studied explicitly as function of the pressure, leading to an explicit connection with the well-known Hammond postulate. As a proof of concept, we present the application of the theory to studying and determining of the optimized geometry of compressed methane and the transition state of electrocyclic ring-closure of hexatriene and of H-transfer between two methyl radicals.
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Affiliation(s)
- Roberto Cammi
- Dipartimento di Scienze Chimica della Vita e della Sostenibilità Ambientale, Università degli Studi di Parma, Italy
| | - Bo Chen
- Donostia international physics center, Spain
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Eeckhoudt J, Bettens T, Geerlings P, Cammi R, Chen B, Alonso M, De Proft F. Conceptual density functional theory under pressure: Part I. XP-PCM method applied to atoms. Chem Sci 2022; 13:9329-9350. [PMID: 36093025 PMCID: PMC9384819 DOI: 10.1039/d2sc00641c] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Accepted: 07/14/2022] [Indexed: 11/21/2022] Open
Abstract
High pressure chemistry offers the chemical community a range of possibilities to control chemical reactivity, develop new materials and fine-tune chemical properties. Despite the large changes that extreme pressure brings to the table, the field has mainly been restricted to the effects of volume changes and thermodynamics with less attention devoted to electronic effects at the molecular scale. This paper combines the conceptual DFT framework for analyzing chemical reactivity with the XP-PCM method for simulating pressures in the GPa range. Starting from the new derivatives of the energy with respect to external pressure, an electronic atomic volume and an atomic compressibility are found, comparable to their enthalpy analogues, respectively. The corresponding radii correlate well with major known sets of this quantity. The ionization potential and electron affinity are both found to decrease with pressure using two different methods. For the electronegativity and chemical hardness, a decreasing and increasing trend is obtained, respectively, and an electronic volume-based argument is proposed to rationalize the observed periodic trends. The cube of the softness is found to correlate well with the polarizability, both decreasing under pressure, while the interpretation of the electrophilicity becomes ambiguous at extreme pressures. Regarding the electron density, the radial distribution function shows a clear concentration of the electron density towards the inner region of the atom and periodic trends can be found in the density using the Carbó quantum similarity index and the Kullback-Leibler information deficiency. Overall, the extension of the CDFT framework with pressure yields clear periodic patterns.
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Affiliation(s)
- J Eeckhoudt
- General Chemistry Department (ALGC), Vrije Universiteit Brussel (VUB) Brussels Belgium
| | - T Bettens
- General Chemistry Department (ALGC), Vrije Universiteit Brussel (VUB) Brussels Belgium
| | - P Geerlings
- General Chemistry Department (ALGC), Vrije Universiteit Brussel (VUB) Brussels Belgium
| | - R Cammi
- Department of Chemical Science, Life Science and Environmental Sustainability, University of Parma Parma Italy
| | - B Chen
- Donostia International Physics Center Donostia-San Sebastian Spain
- IKERBASQUE, Basque Foundation for Science Plaza Euskadi 5 48009 Bilbao Spain
| | - M Alonso
- General Chemistry Department (ALGC), Vrije Universiteit Brussel (VUB) Brussels Belgium
| | - F De Proft
- General Chemistry Department (ALGC), Vrije Universiteit Brussel (VUB) Brussels Belgium
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An Observation Related to the Pressure Dependence of Ionic Radii. GEOSCIENCES 2022. [DOI: 10.3390/geosciences12060246] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
Here it is shown that the crystal radii of ions are represented by a simple relation rcryst = rB3√(10 m)/N, where m and N are small integer numbers determined by the principal and orbital quantum numbers and valence, and rB is the Bohr radius. The relation holds to within 5%. This finding elucidates that despite their original definition crystal- and ionic radii are not classical but represent the limiting case of spherically symmetric spatial averages of the valence electron states and, therefore, are able to reflect changes in the valence electron configuration with pressure and temperature. The relation is used to show general pressure-effects on the radii, in particular the increase of bond coordination with pressure and metallization as limiting state. The pressure-effect is exemplified for the elements Mg and Si as major constituent cations in the Earth’s mantle, and for Ba as a large ionic lithophile element. It is found that at least to about 140 GPa the radii depend linearly on pressure. Further, if a generalization is permitted for just three elements, the pressure-dependence is lesser the higher the charge of the ion. The three elements exhibit a much weaker pressure-dependence than previously calculated non-bonding radii. For mantle geochemistry this finding implies that elements incompatible in the upper mantle remain so for the main lower mantle minerals bridgmanite and periclase and are hosted by davemaoite.
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Cammi R, Chen B. The second derivative of the electronic energy with respect to the compression scaling factor in the XP-PCM model: Theory and applications to compression response functions of atoms. J Comput Chem 2022; 43:1176-1185. [PMID: 35506517 DOI: 10.1002/jcc.26883] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Revised: 04/08/2022] [Accepted: 04/15/2022] [Indexed: 11/09/2022]
Abstract
We present the analytical theory for the second derivative of the electronic energy with respect to the scaling factor of the compression cavity within the eXtreme pressure polarizable continuum model (XP-PCM) for the study of compressed atomic and molecular systems. The theory has been exploited to study compression response functions describing how the atomic/molecular properties are effected by an external pressure. The response functions considered include the atomic compressibility and the pressure coefficients of the ionization energy (IE) and electron affinity (EA). The theory has been validated by numerical application to compressed neon, argon, and krypton atoms.
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Affiliation(s)
- Roberto Cammi
- Dipartimento di Scienze Chimiche della Vita e della Sostenibilitá Ambientale, Università degli Studi di Parma, Parma, Italy
| | - Bo Chen
- Donostia International Physics Center, Paseo Manuel de Lardizabal 4, Donostia-San Sebastian, Spain.,IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
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Boccalini M, Cammi R, Pagliai M, Cardini G, Schettino V. Toward an Understanding of the Pressure Effect on the Intramolecular Vibrational Frequencies of Sulfur Hexafluoride. J Phys Chem A 2021; 125:6362-6373. [PMID: 34263605 PMCID: PMC8389992 DOI: 10.1021/acs.jpca.1c02595] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The structural and vibrational properties of the molecular units of sulfur hexafluoride crystal as a function of pressure have been studied by the Extreme Pressure Polarizable Continuum Model (XP-PCM) method. Within the XP-PCM model, single molecule calculations allow a consistent interpretation of the experimental measurements when considering the effect of pressure on both the molecular structure and the vibrational normal modes. This peculiar aspect of XP-PCM provides a detailed description of the electronic origin of normal modes variations with pressure, via the curvature of the potential energy surface and via the anharmonicity of the normal modes. When applied to the vibrational properties of the sulfur hexafluoride crystal, the XP-PCM method reveals a hitherto unknown interpretation of the effects of the pressure on the vibrational normal modes of the molecular units of this crystal.
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Affiliation(s)
- Matteo Boccalini
- Dipartimento di Chimica "Ugo Schiff", Università degli Studi di Firenze, Via della Lastruccia 3, 50019 Sesto Fiorentino, Italy
| | - Roberto Cammi
- Dipartimento di Scienze Chimiche, della Vita e della Sostenibilità Ambientale, Universitá degli Studi di Parma, Parco Area delle Scienze 11/a, 43124 Parma, Italy
| | - Marco Pagliai
- Dipartimento di Chimica "Ugo Schiff", Università degli Studi di Firenze, Via della Lastruccia 3, 50019 Sesto Fiorentino, Italy
| | - Gianni Cardini
- Dipartimento di Chimica "Ugo Schiff", Università degli Studi di Firenze, Via della Lastruccia 3, 50019 Sesto Fiorentino, Italy
| | - Vincenzo Schettino
- Dipartimento di Chimica "Ugo Schiff", Università degli Studi di Firenze, Via della Lastruccia 3, 50019 Sesto Fiorentino, Italy
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Rahm M, Erhart P, Cammi R. Relating atomic energy, radius and electronegativity through compression. Chem Sci 2021; 12:2397-2403. [PMID: 34164004 PMCID: PMC8179346 DOI: 10.1039/d0sc06675c] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Trends in atomic properties are well-established tools for guiding the analysis and discovery of materials. Here, we show how compression can reveal a long sought-after connection between two central chemical concepts - van-der-Waals (vdW) radii and electronegativity - and how these relate to the driving forces behind chemical and physical transformations.
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Affiliation(s)
- Martin Rahm
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology SE-412 96 Gothenburg Sweden
| | - Paul Erhart
- Department of Physics, Chalmers University of Technology SE-412 96 Gothenburg Sweden
| | - Roberto Cammi
- Department of Chemical Science, Life Science and Environmental Sustainability, University of Parma Parma Italy
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Rahm M, Ångqvist M, Rahm JM, Erhart P, Cammi R. Non-Bonded Radii of the Atoms Under Compression. Chemphyschem 2020; 21:2441-2453. [PMID: 32896974 DOI: 10.1002/cphc.202000624] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Revised: 09/07/2020] [Indexed: 12/19/2022]
Abstract
We present quantum mechanical estimates for non-bonded, van der Waals-like, radii of 93 atoms in a pressure range from 0 to 300 gigapascal. Trends in radii are largely maintained under pressure, but atoms also change place in their relative size ordering. Multiple isobaric contractions of radii are predicted and are explained by pressure-induced changes to the electronic ground state configurations of the atoms. The presented radii are predictive of drastically different chemistry under high pressure and permit an extension of chemical thinking to different thermodynamic regimes. For example, they can aid in assignment of bonded and non-bonded contacts, for distinguishing molecular entities, and for estimating available space inside compressed materials. All data has been made available in an interactive web application.
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Affiliation(s)
- Martin Rahm
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Mattias Ångqvist
- Department of Physics, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - J Magnus Rahm
- Department of Physics, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Paul Erhart
- Department of Physics, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Roberto Cammi
- Department of Chemical Science, Life Science and Environmental Sustainability, University of Parma, Parma, Italy
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