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Becker S. Understanding Cooperativity in Homo- and Heterometallic Complexes: From Basic Concepts to Design. Chempluschem 2024; 89:e202300619. [PMID: 38317458 DOI: 10.1002/cplu.202300619] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2023] [Revised: 12/12/2023] [Accepted: 02/05/2024] [Indexed: 02/07/2024]
Abstract
Cooperative effects have attracted considerable attention in recent years. These effects are ubiquitous in chemistry and biology and can govern interactions of proteins with other biomolecules, mechanisms of supramolecular recognition and polymerization, catalysis, assembly of compounds on surfaces, and physical properties such as magnetic, electronic or optical properties, e. g. Consequently, the understanding of cooperative effects can lead to a structure-property relation that can pave the way to future applications in various research areas; however, with regard to cooperative effects in homo- and heterometallic complexes, we still are at the beginning of understanding. Nevertheless, concepts to describe cooperativity of metal centers as well as methodologies to investigate and model these effects have emerged over the last years. This concept article gives an overview of these existing concepts, approaches, and strategies to understand cooperative effects in homo- and heterometallic complexes. Special emphasis is put on concepts to define cooperative effects, their quantification, as well as methods to investigate cooperative effects.
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Affiliation(s)
- Sabine Becker
- Fachbereich Chemie, RPTU Kaiserslautern-Landau, Erwin-Schroedinger-Str. 54, 67663, Kaiserslautern, Germany
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2
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He N, Huang M, Evangelista FA. CO Inversion on a NaCl(100) Surface: A Multireference Quantum Embedding Study. J Phys Chem A 2023; 127:1975-1987. [PMID: 36799901 PMCID: PMC9986868 DOI: 10.1021/acs.jpca.2c05844] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/18/2023]
Abstract
We develop a multireference quantum embedding model to investigate a recent experimental observation of the isomerization of vibrationally excited CO molecules on a NaCl(100) surface [Science 2020, 367, 175-178]. To explore this mechanism, we built a reduced potential energy surface of CO interacting with NaCl(100) using a second-order multireference perturbation theory, modeling the adsorbate-surface interaction with our previously developed active space embedding theory (ASET). We considered an isolated CO molecule on NaCl(100) and a high-coverage CO monolayer (1/1), and for both we generated potential energy surfaces parametrized by the CO stretching, adsorption, and inversion coordinates. These surfaces are used to determine stationary points and adsorption energies and to perform a vibrational analysis of the states relevant to the inversion mechanism. We found that for near-equilibrium bond lengths, CO adsorbed in the C-down configuration is lower in energy than in the O-down configuration. Stretching of the C-O bond reverses the energetic order of these configurations, supporting the accepted isomerization mechanism. The vibrational constants obtained from these potential energy surfaces show a small (< 10 cm-1) blue- and red-shift for the C-down and O-down configurations, respectively, in agreement with experimental assignments and previous theoretical studies. Our vibrational analysis of the monolayer case suggests that the O-down configuration is energetically more stable than the C-down one beyond the 16th vibrational excited state of CO, a value slightly smaller than the one from quasi-classical trajectory simulations (22nd) and consistent with the experiment. Our analysis suggests that CO-CO interactions in the monolayer play an important role in stabilizing highly vibrationally excited states in the O-down configuration and reducing the barrier between the C-down and O-down geometries, therefore playing a crucial role in the inversion mechanism.
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Affiliation(s)
- Nan He
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Meng Huang
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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3
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Sargent CT, Metcalf DP, Glick ZL, Borca CH, Sherrill CD. Benchmarking two-body contributions to crystal lattice energies and a range-dependent assessment of approximate methods. J Chem Phys 2023; 158:054112. [PMID: 36754814 DOI: 10.1063/5.0141872] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
Using the many-body expansion to predict crystal lattice energies (CLEs), a pleasantly parallel process, allows for flexibility in the choice of theoretical methods. Benchmark-level two-body contributions to CLEs of 23 molecular crystals have been computed using interaction energies of dimers with minimum inter-monomer separations (i.e., closest contact distances) up to 30 Å. In a search for ways to reduce the computational expense of calculating accurate CLEs, we have computed these two-body contributions with 15 different quantum chemical levels of theory and compared these energies to those computed with coupled-cluster in the complete basis set (CBS) limit. Interaction energies of the more distant dimers are easier to compute accurately and several of the methods tested are suitable as replacements for coupled-cluster through perturbative triples for all but the closest dimers. For our dataset, sub-kJ mol-1 accuracy can be obtained when calculating two-body interaction energies of dimers with separations shorter than 4 Å with coupled-cluster with single, double, and perturbative triple excitations/CBS and dimers with separations longer than 4 Å with MP2.5/aug-cc-pVDZ, among other schemes, reducing the number of dimers to be computed with coupled-cluster by as much as 98%.
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Affiliation(s)
- Caroline T Sargent
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
| | - Derek P Metcalf
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
| | - Zachary L Glick
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
| | - Carlos H Borca
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
| | - C David Sherrill
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
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4
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Chen WK, Fang WH, Cui G. Extending multi-layer energy-based fragment method for excited-state calculations of large covalently bonded fragment systems. J Chem Phys 2023; 158:044110. [PMID: 36725521 DOI: 10.1063/5.0129458] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
Recently, we developed a low-scaling Multi-Layer Energy-Based Fragment (MLEBF) method for accurate excited-state calculations and nonadiabatic dynamics simulations of nonbonded fragment systems. In this work, we extend the MLEBF method to treat covalently bonded fragment ones. The main idea is cutting a target system into many fragments according to chemical properties. Fragments with dangling bonds are first saturated by chemical groups; then, saturated fragments, together with the original fragments without dangling bonds, are grouped into different layers. The accurate total energy expression is formulated with the many-body energy expansion theory, in combination with the inclusion-exclusion principle that is used to delete the contribution of chemical groups introduced to saturate dangling bonds. Specifically, in a two-layer MLEBF model, the photochemically active and inert layers are calculated with high-level and efficient electronic structure methods, respectively. Intralayer and interlayer energies can be truncated at the two- or three-body interaction level. Subsequently, through several systems, including neutral and charged covalently bonded fragment systems, we demonstrate that MLEBF can provide accurate ground- and excited-state energies and gradients. Finally, we realize the structure, conical intersection, and path optimizations by combining our MLEBF program with commercial and free packages, e.g., ASE and SciPy. These developments make MLEBF a practical and reliable tool for studying complex photochemical and photophysical processes of large nonbonded and bonded fragment systems.
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Affiliation(s)
- Wen-Kai Chen
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Ganglong Cui
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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5
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Speake BT, Irons TJP, Wibowo M, Johnson AG, David G, Teale AM. An Embedded Fragment Method for Molecules in Strong Magnetic Fields. J Chem Theory Comput 2022; 18:7412-7427. [PMID: 36414537 DOI: 10.1021/acs.jctc.2c00865] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
An extension of the embedded fragment method for calculations on molecular clusters is presented, which includes strong external magnetic fields. The approach is flexible, allowing for calculations at the Hartree-Fock, current-density-functional theory, Møller-Plesset perturbation theory, and coupled-cluster levels using London atomic orbitals. For systems consisting of discrete molecular subunits, calculations using London atomic orbitals can be performed in a computationally tractable manner for systems beyond the reach of conventional calculations, even those accelerated by resolution-of-the-identity or Cholesky decomposition methods. To assess the applicability of the approach, applications to water clusters are presented, showing how strong magnetic fields enhance binding within the clusters. However, our calculations suggest that, contrary to previous suggestions in the literature, this enhanced binding may not be directly attributable to strengthening of hydrogen bonding. Instead, these results suggest that this arises for larger field strengths as a response of the system to the presence of the external field, which induces a charge density build up between the monomer units. The approach is embarrassingly parallel and its computational tractability is demonstrated for clusters of up to 103 water molecules in triple-ζ basis sets, which would correspond to conventional calculations with more than 12 000 basis functions.
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Affiliation(s)
- Benjamin T Speake
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom
| | - Tom J P Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom
| | - Meilani Wibowo
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom
| | - Andrew G Johnson
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom
| | - Grégoire David
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom.,Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes)-UMR 6226, F-35000 Rennes, France
| | - Andrew M Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, United KIngdom.,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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6
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Liu J, He X. Recent advances in quantum fragmentation approaches to complex molecular and condensed‐phase systems. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1650] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Jinfeng Liu
- Department of Basic Medicine and Clinical Pharmacy China Pharmaceutical University Nanjing China
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, School of Chemistry and Molecular Engineering East China Normal University Shanghai China
| | - Xiao He
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, School of Chemistry and Molecular Engineering East China Normal University Shanghai China
- New York University‐East China Normal University Center for Computational Chemistry New York University Shanghai Shanghai China
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7
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Abstract
Quantum embedding schemes are a promising way to extend multireference computations to large molecules with strong correlation effects localized on a small number of atoms. This work introduces a second-order active-space embedding theory [ASET(2)] which improves upon mean-field frozen embedding by treating fragment-environment interactions via an approximate canonical transformation. The canonical transformation employed in ASET(2) is formulated using the driven similarity renormalization group. The ASET(2) scheme is benchmarked on the N═N bond dissociation in pentyldiazene, the S0 to S1 excitation in 1-octene, and the interaction energy of the O2-benzene complex. The ASET(2) explicit treatment of fragment-environment interactions beyond the mean-field level generally improves the accuracy of embedded computations, and it becomes necessary to achieve an accurate description of excitation energies of 1-octene and the singlet-triplet gap of the O2-benzene complex.
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Affiliation(s)
- Nan He
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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8
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Hellmers J, König C. A unified and flexible formulation of molecular fragmentation schemes. J Chem Phys 2021; 155:164105. [PMID: 34717347 DOI: 10.1063/5.0059598] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
We present a flexible formulation for energy-based molecular fragmentation schemes. This framework does not only incorporate the majority of existing fragmentation expansions but also allows for flexible formulation of novel schemes. We further illustrate its application in multi-level approaches and for electronic interaction energies. For the examples of small water clusters, a small protein, and protein-protein interaction energies, we show how this flexible setup can be exploited to generate a well-suited multi-level fragmentation expansion for the given case. With such a setup, we reproduce the electronic protein-protein interaction energy of ten different structures of a neurotensin and an extracellular loop of its receptor with a mean absolute deviation to the respective super-system calculations below 1 kJ/mol.
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Affiliation(s)
- Janine Hellmers
- Institute of Physical Chemistry and Electrochemistry, Leibniz University Hannover, Hannover, Germany
| | - Carolin König
- Institute of Physical Chemistry and Electrochemistry, Leibniz University Hannover, Hannover, Germany
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9
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Nguyen ALP, Mason TG, Freeman BD, Izgorodina EI. Prediction of lattice energy of benzene crystals: A robust theoretical approach. J Comput Chem 2021; 42:248-260. [PMID: 33231872 DOI: 10.1002/jcc.26452] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2020] [Revised: 10/29/2020] [Accepted: 10/30/2020] [Indexed: 01/09/2023]
Abstract
We present an inexpensive and robust theoretical approach based on the fragment molecular orbital methodology and the spin-ratio scaled second-order Møller-Plesset perturbation theory to predict the lattice energy of benzene crystals within 2 kJ⋅mol-1 . Inspired by the Harrison method to estimate the Madelung constant, the proposed approach calculates the lattice energy as a sum of two- and three-body interaction energies between a reference molecule and the surrounding molecules arranged in a sphere. The lattice energy converges rapidly at a radius of 13 Å. Adding the corrections to account for a higher correlated level of theory and basis set superposition for the Hartree Fock (HF) level produced a lattice energy of -57.5 kJ⋅mol-1 for the benzene crystal structure at 138 K. This estimate is within 1.6 kJ⋅mol-1 off the best theoretical prediction of -55.9 kJ⋅mol-1 . We applied this approach to calculate lattice energies of the crystal structures of phase I and phase II-polymorphs of benzene-observed at a higher temperature of 295 K. The stability of these polymorphs was correctly predicted, with phase II being energetically preferred by 3.7 kJ⋅mol-1 over phase I. The proposed approach gives a tremendous potential to predict stability of other molecular crystal polymorphs.
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Affiliation(s)
- Anh L P Nguyen
- School of Chemistry, Monash University, Clayton, Victoria, Australia
| | - Thomas G Mason
- School of Chemistry, Monash University, Clayton, Victoria, Australia
| | - Benny D Freeman
- Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas, USA
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10
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Aslamazova TR, Kotenev VA, Lomovskaya NY, Lomovskoi VA, Shatokhina SA, Tsivadze AY. Analyzing Dissipative Processes in a Filled Polymer Using Data from Mechanical Relaxation Spectroscopy. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2020. [DOI: 10.1134/s0036024420070067] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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11
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Sylvetsky N. Toward Simple, Predictive Understanding of Protein-Ligand Interactions: Electronic Structure Calculations on Torpedo Californica Acetylcholinesterase Join Forces with the Chemist's Intuition. Sci Rep 2020; 10:9218. [PMID: 32513975 PMCID: PMC7280257 DOI: 10.1038/s41598-020-65984-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Accepted: 05/13/2020] [Indexed: 11/09/2022] Open
Abstract
Contemporary efforts for empirically-unbiased modeling of protein-ligand interactions entail a painful tradeoff - as reliable information on both noncovalent binding factors and the dynamic behavior of a protein-ligand complex is often beyond practical limits. We demonstrate that information drawn exclusively from static molecular structures can be used for reproducing and predicting experimentally-measured binding affinities for protein-ligand complexes. In particular, inhibition constants (Ki) were calculated for seven different competitive inhibitors of Torpedo californica acetylcholinesterase using a multiple-linear-regression-based model. The latter, incorporating five independent variables - drawn from QM cluster, DLPNO-CCSD(T) calculations and LED analyses on the seven complexes, each containing active amino-acid residues found within interacting distance (3.5 Å) from the corresponding ligand - is shown to recover 99.9% of the sum of squares for measured Ki values, while having no statistically-significant residual errors. Despite being fitted to a small number of data points, leave-one-out cross-validation statistics suggest that it possesses surprising predictive value (Q2LOO=0.78, or 0.91 upon removal of a single outlier). This thus challenges ligand-invariant definitions of active sites, such as implied in the lock-key binding theory, as well as in alternatives highlighting shape-complementarity without taking electronic effects into account. Broader implications of the current work are discussed in dedicated appendices.
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Affiliation(s)
- Nitai Sylvetsky
- Department of Organic Chemistry, Weizmann Institute of Science, 7610001, Rehovot, Israel.
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12
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He N, Evangelista FA. A zeroth-order active-space frozen-orbital embedding scheme for multireference calculations. J Chem Phys 2020; 152:094107. [PMID: 33480706 DOI: 10.1063/1.5142481] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Multireference computations of large-scale chemical systems are typically limited by the computational cost of quantum chemistry methods. In this work, we develop a zeroth-order active space embedding theory [ASET(0)], a simple and automatic approach for embedding any multireference dynamical correlation method based on a frozen-orbital treatment of the environment. ASET(0) is combined with the second-order multireference driven similarity renormalization group and tested on several benchmark problems, including the excitation energy of 1-octene and bond-breaking in ethane and pentyldiazene. Finally, we apply ASET(0) to study the singlet-triplet gap of p-benzyne and 9,10-anthracyne diradicals adsorbed on a NaCl surface. Our results show that despite its simplicity, ASET(0) is a powerful and sufficiently accurate embedding scheme applicable when the coupling between the fragment and the environment is in the weak to medium regime.
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Affiliation(s)
- Nan He
- Department of Chemistry, Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Francesco A Evangelista
- Department of Chemistry, Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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13
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Sakti AW, Nishimura Y, Nakai H. Recent advances in quantum‐mechanical molecular dynamics simulations of proton transfer mechanism in various water‐based environments. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1419] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Aditya W. Sakti
- Element Strategy Initiative for Catalysts and Batteries (ESICB) Kyoto University Kyoto Japan
| | - Yoshifumi Nishimura
- Waseda Research Institute for Science and Engineering (WISE) Waseda University Tokyo Japan
| | - Hiromi Nakai
- Element Strategy Initiative for Catalysts and Batteries (ESICB) Kyoto University Kyoto Japan
- Waseda Research Institute for Science and Engineering (WISE) Waseda University Tokyo Japan
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering Waseda University Tokyo Japan
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14
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Mi W, Ramos P, Maranhao J, Pavanello M. Ab Initio Structure and Dynamics of CO 2 at Supercritical Conditions. J Phys Chem Lett 2019; 10:7554-7559. [PMID: 31738567 DOI: 10.1021/acs.jpclett.9b03054] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Green technologies rely on green solvents and fluids. Among them, supercritical CO2 already finds many important applications. The molecular-level understanding of the dynamics and structure of this supercritical fluid is a prerequisite for rational design of future green technologies. Unfortunately, the commonly employed Kohn-Sham density functional theory (DFT) is too computationally demanding to produce meaningfully converged dynamics within a reasonable time and with a reasonable computational effort. Thanks to subsystem DFT, we analyze finite-size effects by considering simulation cells of varying sizes (up to 256 independent molecules in the cell) and finite-time effects by running 100 ps trajectories. We find that the simulations are in reasonable and semiquantitative agreement with the available neutron diffraction experiments and that, as opposed to the gas phase, the CO2 molecules in the fluid are bent with an average OCO angle of 175.8°. Our simulations also confirm that the dimer T-shape is the most prevalent configuration. Our results further strengthen the experiment-simulation agreement for this fluid when comparing radial distribution functions and diffusion coefficient, confirming subsystem DFT as a viable tool for modeling structure and dynamics of condensed-phase systems.
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Affiliation(s)
- Wenhui Mi
- Department of Chemistry , Rutgers University , Newark , New Jersey 07102 , United States
| | - Pablo Ramos
- Department of Chemistry , Rutgers University , Newark , New Jersey 07102 , United States
| | - Jack Maranhao
- Department of Chemistry , Rutgers University , Newark , New Jersey 07102 , United States
| | - Michele Pavanello
- Department of Chemistry , Rutgers University , Newark , New Jersey 07102 , United States
- Department of Physics , Rutgers University , Newark , New Jersey 07102 , United States
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15
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Liu KY, Herbert JM. Energy-Screened Many-Body Expansion: A Practical Yet Accurate Fragmentation Method for Quantum Chemistry. J Chem Theory Comput 2019; 16:475-487. [PMID: 31765559 DOI: 10.1021/acs.jctc.9b01095] [Citation(s) in RCA: 41] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
We introduce an implementation of the truncated many-body expansion, MBE(n), in which the n-body corrections are screened using the effective fragment potential force field, and only those that exceed a specified energy threshold are computed at a quantum-mechanical level of theory. This energy-screened MBE(n) approach is tested at the n = 3 level for a sequence of water clusters, (H2O)N=6-34. A threshold of 0.25 kJ/mol eliminates more than 80% of the subsystem electronic structure calculations and is even more efficacious in that respect than is distance-based screening. Even so, the energy-screened MBE(3) method is faithful to a full-system quantum chemistry calculation to within 1-2 kJ/mol/monomer, even in good quality basis sets such as aug-cc-pVTZ. These errors can be reduced by means of a two-layer approach that involves a Hartree-Fock calculation for the entire cluster. Such a correction proves to be necessary in order to obtain accurate relative energies for conformational isomers of (H2O)20, but the cost of a full-system Hartree-Fock calculation remains smaller than the cost of three-body subsystem calculations at correlated levels of theory. At the level of second-order Møller-Plesset perturbation theory (MP2), a screened MBE(3) calculation plus a full-system Hartree-Fock calculation is less expensive than a full-system MP2 calculation starting at N = 12 water molecules. This is true even if all MBE(3) subsystem calculations are performed on a single 40-core compute node, i.e., without significant parallelization. Energy-screened MBE(n) thus provides a fragment-based method that is accurate, stable in large basis sets, and low in cost, even when the latter is measured in aggregate computer time.
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Affiliation(s)
- Kuan-Yu Liu
- Department of Chemistry and Biochemistry , The Ohio State University , Columbus , Ohio 43210 , United States
| | - John M Herbert
- Department of Chemistry and Biochemistry , The Ohio State University , Columbus , Ohio 43210 , United States
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16
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Modrzejewski M, Yourdkhani S, Klimeš J. Random Phase Approximation Applied to Many-Body Noncovalent Systems. J Chem Theory Comput 2019; 16:427-442. [DOI: 10.1021/acs.jctc.9b00979] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Marcin Modrzejewski
- Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Sirous Yourdkhani
- Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
| | - Jiří Klimeš
- Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
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17
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Abstract
Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.
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Affiliation(s)
- John M Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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18
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Borca CH, Bakr BW, Burns LA, Sherrill CD. CrystaLattE: Automated computation of lattice energies of organic crystals exploiting the many-body expansion to achieve dual-level parallelism. J Chem Phys 2019; 151:144103. [PMID: 31615262 DOI: 10.1063/1.5120520] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
We present an algorithm to compute the lattice energies of molecular crystals based on the many-body cluster expansion. The required computations on dimers, trimers, etc., within the crystal are independent of each other, leading to a naturally parallel approach. The algorithm exploits the long-range three-dimensional periodic order of crystals to automatically detect and avoid redundant or unnecessary computations. For this purpose, Coulomb-matrix descriptors from machine learning applications are found to be efficient in determining whether two N-mers are identical. The algorithm is implemented as an open-source Python program, CrystaLattE, that uses some of the features of the Quantum Chemistry Common Driver and Databases library. CrystaLattE is initially interfaced with the quantum chemistry package Psi4. With CrystaLattE, we have applied the fast, dispersion-corrected Hartree-Fock method HF-3c to the lattice energy of crystalline benzene. Including all 73 symmetry-unique dimers and 7130 symmetry-unique trimers that can be formed from molecules within a 15 Å cutoff from a central reference monomer, HF-3c plus an Axilrod-Teller-Muto estimate of three-body dispersion exhibits an error of only -1.0 kJ mol-1 vs the estimated 0 K experimental lattice energy of -55.3 ± 2.2 kJ mol-1. The convergence of the HF-3c two- and three-body contributions to the lattice energy as a function of intermonomer distance is examined.
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Affiliation(s)
- Carlos H Borca
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Brandon W Bakr
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Lori A Burns
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - C David Sherrill
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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19
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Bakó I, Mayer I, Hamza A, Pusztai L. Two- and three-body, and relaxation energy terms in water clusters: Application of the hierarchical BSSE corrected decomposition scheme. J Mol Liq 2019. [DOI: 10.1016/j.molliq.2019.04.088] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
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20
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Khire SS, Gadre SR. Pragmatic Many-Body Approach for Economic MP2 Energy Estimation of Molecular Clusters. J Phys Chem A 2019; 123:5005-5011. [PMID: 31117601 DOI: 10.1021/acs.jpca.9b03481] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We propose a procedure, within the many-body analysis (MBA) framework, for an economic yet accurate estimation of the correlated method-based energies of large molecular clusters employing Dunning's augmented basis sets. The basis of the procedure is to segregate the Hartree-Fock ( EHF) and correlation energy ( EC) estimations. EHF is found to differ by tens of millihartrees (mH) from its full-calculation (FC) counterpart on truncating the MBA expansion at the two-body (MBA-2) level. On the contrary, EC is estimated with smaller error on modest hardware with limited computation time at the (MBA-2) level. In view of this, we adopt a pragmatic method wherein the EHF (accurate to five decimal places) is taken from the FC, whereas EC is estimated at the MBA-2 level. This method is applied to a variety of medium to large molecular clusters at the MP2 level. Preliminary results at the CCSD(T) level for (H2O)16 and (H2O)17 are also reported with tremendous savings in wall-clock time and resources. The typical errors in MP2 and CCSD(T) energies per monomer are up to 0.1 and 0.2 mH, respectively. Thus the present method, balancing accuracy and computational economy, opens a way for estimating energies of large molecular clusters using correlated theories with large basis sets.
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Affiliation(s)
- Subodh S Khire
- Interdisciplinary School of Scientific Computing , Savitribai Phule Pune University , Pune 411007 , India
| | - Shridhar R Gadre
- Interdisciplinary School of Scientific Computing , Savitribai Phule Pune University , Pune 411007 , India
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21
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Al-Hamdani YS, Tkatchenko A. Understanding non-covalent interactions in larger molecular complexes from first principles. J Chem Phys 2019; 150:010901. [PMID: 30621423 PMCID: PMC6910608 DOI: 10.1063/1.5075487] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2018] [Accepted: 12/05/2018] [Indexed: 01/02/2023] Open
Abstract
Non-covalent interactions pervade all matter and play a fundamental role in layered materials, biological systems, and large molecular complexes. Despite this, our accumulated understanding of non-covalent interactions to date has been mainly developed in the tens-of-atoms molecular regime. This falls considerably short of the scales at which we would like to understand energy trends, structural properties, and temperature dependencies in materials where non-covalent interactions have an appreciable role. However, as more reference information is obtained beyond moderately sized molecular systems, our understanding is improving and we stand to gain pertinent insights by tackling more complex systems, such as supramolecular complexes, molecular crystals, and other soft materials. In addition, accurate reference information is needed to provide the drive for extending the predictive power of more efficient workhorse methods, such as density functional approximations that also approximate van der Waals dispersion interactions. In this perspective, we discuss the first-principles approaches that have been used to obtain reference interaction energies for beyond modestly sized molecular complexes. The methods include quantum Monte Carlo, symmetry-adapted perturbation theory, non-canonical coupled cluster theory, and approaches based on the random-phase approximation. By considering the approximations that underpin each method, the most accurate theoretical references for supramolecular complexes and molecular crystals to date are ascertained. With these, we also assess a handful of widely used exchange-correlation functionals in density functional theory. The discussion culminates in a framework for putting into perspective the accuracy of high-level wavefunction-based methods and identifying future challenges.
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Affiliation(s)
- Yasmine S Al-Hamdani
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Alexandre Tkatchenko
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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22
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Brandenburg JG, Bannwarth C, Hansen A, Grimme S. B97-3c: A revised low-cost variant of the B97-D density functional method. J Chem Phys 2018; 148:064104. [DOI: 10.1063/1.5012601] [Citation(s) in RCA: 255] [Impact Index Per Article: 42.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Affiliation(s)
- Jan Gerit Brandenburg
- Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AH, United Kingdom
- Thomas Young Centre, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Christoph Bannwarth
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms Universität Bonn, Beringstraße 4, 53115 Bonn, Germany
| | - Andreas Hansen
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms Universität Bonn, Beringstraße 4, 53115 Bonn, Germany
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms Universität Bonn, Beringstraße 4, 53115 Bonn, Germany
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23
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Abstract
Computational approaches based on the fundamental laws of quantum mechanics are now integral to almost all materials design initiatives in academia and industry. If computational materials science is genuinely going to deliver on its promises, then an electronic structure method with consistently high accuracy is urgently needed. We show that, thanks to recent algorithmic advances and the strategy developed in our manuscript, quantum Monte Carlo yields extremely accurate predictions for the lattice energies of materials at a surprisingly modest computational cost. It is thus no longer a technique that requires a world-leading computational facility to obtain meaningful results. While we focus on molecular crystals, the significance of our findings extends to all classes of materials. Computer simulation plays a central role in modern-day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of materials of great technological importance which are challenging for even the most sophisticated ab initio electronic structure theories to accurately describe. This is partly because they are held together by a balance of weak intermolecular forces but also because the primitive cells of molecular crystals are often substantially larger than those of atomic solids. Here, we demonstrate that diffusion quantum Monte Carlo (DMC) delivers subchemical accuracy for a diverse set of molecular crystals at a surprisingly moderate computational cost. As such, we anticipate that DMC can play an important role in understanding and predicting the properties of a large number of molecular crystals, including those built from relatively large molecules which are far beyond reach of other high-accuracy methods.
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24
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Kesharwani MK, Karton A, Sylvetsky N, Martin JML. The S66 Non-Covalent Interactions Benchmark Reconsidered Using Explicitly Correlated Methods Near the Basis Set Limit. Aust J Chem 2018. [DOI: 10.1071/ch17588] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
The S66 benchmark for non-covalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 ‘high-level corrections’ are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the other hand. Implications for earlier benchmarks on the larger S66×8 problem set in particular, and for accurate calculations on non-covalent interactions in general, are discussed. At a slight cost in accuracy, (T) can be considerably accelerated by using sano-V{D,T}Z+ basis sets, whereas half-counterpoise CCSD(F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost.
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25
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Manna D, Kesharwani MK, Sylvetsky N, Martin JML. Conventional and Explicitly Correlated ab Initio Benchmark Study on Water Clusters: Revision of the BEGDB and WATER27 Data Sets. J Chem Theory Comput 2017; 13:3136-3152. [DOI: 10.1021/acs.jctc.6b01046] [Citation(s) in RCA: 69] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Debashree Manna
- Department of Organic Chemistry, Weizmann Institute of Science, 76100 Rechovot, Israel
| | - Manoj K. Kesharwani
- Department of Organic Chemistry, Weizmann Institute of Science, 76100 Rechovot, Israel
| | - Nitai Sylvetsky
- Department of Organic Chemistry, Weizmann Institute of Science, 76100 Rechovot, Israel
| | - Jan M. L. Martin
- Department of Organic Chemistry, Weizmann Institute of Science, 76100 Rechovot, Israel
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26
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Pham CH, Reddy SK, Chen K, Knight C, Paesani F. Many-Body Interactions in Ice. J Chem Theory Comput 2017; 13:1778-1784. [DOI: 10.1021/acs.jctc.6b01248] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- C. Huy Pham
- Department
of Chemistry and Biochemistry, University of California−San Diego, La Jolla, California 92093, United States
| | - Sandeep K. Reddy
- Department
of Chemistry and Biochemistry, University of California−San Diego, La Jolla, California 92093, United States
| | - Karl Chen
- Department
of Chemistry and Biochemistry, University of California−San Diego, La Jolla, California 92093, United States
| | - Chris Knight
- Leadership
Computing Facility, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, United States
| | - Francesco Paesani
- Department
of Chemistry and Biochemistry, University of California−San Diego, La Jolla, California 92093, United States
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27
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Competition of van der Waals and chemical forces on gold–sulfur surfaces and nanoparticles. Nat Rev Chem 2017. [DOI: 10.1038/s41570-017-0017] [Citation(s) in RCA: 74] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
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28
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Liu Y, Ojamäe L. Raman and IR Spectra of Ice Ih and Ice XI with an Assessment of DFT Methods. J Phys Chem B 2016; 120:11043-11051. [PMID: 27690444 DOI: 10.1021/acs.jpcb.6b07001] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
IR and Raman spectroscopic technology can be directly used to identify the occurrence of ferroelectric ice XI in laboratory or extraterrestrial settings. The performance of 16 different DFT methods applied on the ice Ih, VIII, IX, and XI crystal phases is evaluated. Based on a selected DFT computational scheme, the IR and Raman spectra of ice Ih and XI are derived and compared. When the spectra, both IR and Raman, of ice Ih and ice XI are compared, the librational vibrations are found to be the most affected by the proton ordering. The spectroscopic fingerprint of ice XI can be used to distinguish ferroelectric ice XI from ice Ih in the universe. Furthermore, the existence of only one kind of H-bond in ice Ih is demonstrated from the overlapping subspectra for different types of H-bonded pair configurations in 16 isomers of ice Ih, which provides an illustration to the historic debate on whether one or two kinds of H-bonds existed in ice.
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Affiliation(s)
- Yuan Liu
- Department of Chemistry, IFM, Linköping University , SE-581 83 Linköping, Sweden
| | - Lars Ojamäe
- Department of Chemistry, IFM, Linköping University , SE-581 83 Linköping, Sweden
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29
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Klimeš J. Lattice energies of molecular solids from the random phase approximation with singles corrections. J Chem Phys 2016; 145:094506. [DOI: 10.1063/1.4962188] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jiří Klimeš
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejškova 3, CZ-18223 Prague 8, Czech Republic and Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
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30
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Wagner LK, Ceperley DM. Discovering correlated fermions using quantum Monte Carlo. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:094501. [PMID: 27518859 DOI: 10.1088/0034-4885/79/9/094501] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior.
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Affiliation(s)
- Lucas K Wagner
- Department of Physics, University of Illinois at Urbana-Champaign, Champaign, IL, USA
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31
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Singh G, Nandi A, Gadre SR. Breaking the bottleneck: Use of molecular tailoring approach for the estimation of binding energies at MP2/CBS limit for large water clusters. J Chem Phys 2016; 144:104102. [PMID: 26979676 DOI: 10.1063/1.4943115] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
A pragmatic method based on the molecular tailoring approach (MTA) for estimating the complete basis set (CBS) limit at Møller-Plesset second order perturbation (MP2) theory accurately for large molecular clusters with limited computational resources is developed. It is applied to water clusters, (H2O)n (n = 7, 8, 10, 16, 17, and 25) optimized employing aug-cc-pVDZ (aVDZ) basis-set. Binding energies (BEs) of these clusters are estimated at the MP2/aug-cc-pVNZ (aVNZ) [N = T, Q, and 5 (whenever possible)] levels of theory employing grafted MTA (GMTA) methodology and are found to lie within 0.2 kcal/mol of the corresponding full calculation MP2 BE, wherever available. The results are extrapolated to CBS limit using a three point formula. The GMTA-MP2 calculations are feasible on off-the-shelf hardware and show around 50%-65% saving of computational time. The methodology has a potential for application to molecular clusters containing ∼100 atoms.
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Affiliation(s)
- Gurmeet Singh
- Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Apurba Nandi
- Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Shridhar R Gadre
- Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208016, India
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32
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Demerdash O, Head-Gordon T. Convergence of the Many-Body Expansion for Energy and Forces for Classical Polarizable Models in the Condensed Phase. J Chem Theory Comput 2016; 12:3884-93. [DOI: 10.1021/acs.jctc.6b00335] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Omar Demerdash
- Department of Chemistry, ‡Department of Bioengineering, §Department of Chemical
and Biomolecular
Engineering, ∥Chemical Sciences Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, United States
| | - Teresa Head-Gordon
- Department of Chemistry, ‡Department of Bioengineering, §Department of Chemical
and Biomolecular
Engineering, ∥Chemical Sciences Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, United States
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33
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Otero-de-la-Roza A, DiLabio GA, Johnson ER. Exchange–Correlation Effects for Noncovalent Interactions in Density Functional Theory. J Chem Theory Comput 2016; 12:3160-75. [DOI: 10.1021/acs.jctc.6b00298] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- A. Otero-de-la-Roza
- National Institute for Nanotechnology, National Research Council of Canada, 11421 Saskatchewan Drive, Edmonton, Alberta T6G 2M9, Canada
- Department
of Chemistry, University of British Columbia, Okanagan, 3247 University Way, Kelowna, British Columbia V1V 1V7, Canada
| | - Gino A. DiLabio
- National Institute for Nanotechnology, National Research Council of Canada, 11421 Saskatchewan Drive, Edmonton, Alberta T6G 2M9, Canada
- Department
of Chemistry, University of British Columbia, Okanagan, 3247 University Way, Kelowna, British Columbia V1V 1V7, Canada
| | - Erin R. Johnson
- Department
of Chemistry, Dalhousie University, 6274 Coburg Road, Halifax, Nova Scotia B3H 4R2, Canada
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34
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Salim MA, Willow SY, Hirata S. Ice Ih anomalies: Thermal contraction, anomalous volume isotope effect, and pressure-induced amorphization. J Chem Phys 2016; 144:204503. [DOI: 10.1063/1.4951687] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michael A. Salim
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
| | - Soohaeng Yoo Willow
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
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35
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Grimme S, Hansen A, Brandenburg JG, Bannwarth C. Dispersion-Corrected Mean-Field Electronic Structure Methods. Chem Rev 2016; 116:5105-54. [DOI: 10.1021/acs.chemrev.5b00533] [Citation(s) in RCA: 799] [Impact Index Per Article: 99.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Stefan Grimme
- Mulliken Center for Theoretical
Chemistry, Universität Bonn, 53113 Bonn, Germany
| | - Andreas Hansen
- Mulliken Center for Theoretical
Chemistry, Universität Bonn, 53113 Bonn, Germany
| | | | - Christoph Bannwarth
- Mulliken Center for Theoretical
Chemistry, Universität Bonn, 53113 Bonn, Germany
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36
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Gillan MJ, Alfè D, Michaelides A. Perspective: How good is DFT for water? J Chem Phys 2016; 144:130901. [DOI: 10.1063/1.4944633] [Citation(s) in RCA: 478] [Impact Index Per Article: 59.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Michael J. Gillan
- London Centre for Nanotechnology, Gordon St., London WC1H 0AH, United Kingdom
- Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Dario Alfè
- London Centre for Nanotechnology, Gordon St., London WC1H 0AH, United Kingdom
- Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
- Department of Earth Sciences, University College London, London WC1E 6BT, United Kingdom
| | - Angelos Michaelides
- London Centre for Nanotechnology, Gordon St., London WC1H 0AH, United Kingdom
- Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
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37
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Abstract
Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.
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Affiliation(s)
- Gregory J O Beran
- Department of Chemistry, University of California , Riverside, California 92521, United States
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38
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Brandenburg JG, Maas T, Grimme S. Benchmarking DFT and semiempirical methods on structures and lattice energies for ten ice polymorphs. J Chem Phys 2016; 142:124104. [PMID: 25833562 DOI: 10.1063/1.4916070] [Citation(s) in RCA: 71] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Water in different phases under various external conditions is very important in bio-chemical systems and for material science at surfaces. Density functional theory methods and approximations thereof have to be tested system specifically to benchmark their accuracy regarding computed structures and interaction energies. In this study, we present and test a set of ten ice polymorphs in comparison to experimental data with mass densities ranging from 0.9 to 1.5 g/cm(3) and including explicit corrections for zero-point vibrational and thermal effects. London dispersion inclusive density functionals at the generalized gradient approximation (GGA), meta-GGA, and hybrid level as well as alternative low-cost molecular orbital methods are considered. The widely used functional of Perdew, Burke and Ernzerhof (PBE) systematically overbinds and overall provides inconsistent results. All other tested methods yield reasonable to very good accuracy. BLYP-D3(atm) gives excellent results with mean absolute errors for the lattice energy below 1 kcal/mol (7% relative deviation). The corresponding optimized structures are very accurate with mean absolute relative deviations (MARDs) from the reference unit cell volume below 1%. The impact of Axilrod-Teller-Muto (atm) type three-body dispersion and of non-local Fock exchange is small but on average their inclusion improves the results. While the density functional tight-binding model DFTB3-D3 performs well for low density phases, it does not yield good high density structures. As low-cost alternative for structure related problems, we recommend the recently introduced minimal basis Hartree-Fock method HF-3c with a MARD of about 3%.
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Affiliation(s)
- Jan Gerit Brandenburg
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms Universität Bonn, Beringstraße 4, 53115 Bonn, Germany
| | - Tilo Maas
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms Universität Bonn, Beringstraße 4, 53115 Bonn, Germany
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms Universität Bonn, Beringstraße 4, 53115 Bonn, Germany
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39
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Abstract
David Craig (1919–2015) left us with a lasting legacy concerning basic understanding of chemical spectroscopy and bonding. This is expressed in terms of some of the recent achievements of my own research career, with a focus on integration of Craig’s theories with those of Noel Hush to solve fundamental problems in photosynthesis, molecular electronics (particularly in regard to the molecules synthesized by Maxwell Crossley), and self-assembled monolayer structure and function. Reviewed in particular is the relation of Craig’s legacy to: the 50-year struggle to assign the visible absorption spectrum of arguably the world’s most significant chromophore, chlorophyll; general theories for chemical bonding and structure extending Hush’s adiabatic theory of electron-transfer processes; inelastic electron-tunnelling spectroscopy (IETS); chemical quantum entanglement and the Penrose–Hameroff model for quantum consciousness; synthetic design strategies for NMR quantum computing; Gibbs free-energy measurements and calculations for formation and polymorphism of organic self-assembled monolayers on graphite surfaces from organic solution; and understanding the basic chemical processes involved in the formation of gold surfaces and nanoparticles protected by sulfur-bound ligands, ligands whose form is that of Au0-thiyl rather than its commonly believed AuI-thiolate tautomer.
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40
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Hartman JD, Beran GJO. Fragment-Based Electronic Structure Approach for Computing Nuclear Magnetic Resonance Chemical Shifts in Molecular Crystals. J Chem Theory Comput 2015; 10:4862-72. [PMID: 26584373 DOI: 10.1021/ct500749h] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
First-principles chemical shielding tensor predictions play a critical role in studying molecular crystal structures using nuclear magnetic resonance. Fragment-based electronic structure methods have dramatically improved the ability to model molecular crystal structures and energetics using high-level electronic structure methods. Here, a many-body expansion fragment approach is applied to the calculation of chemical shielding tensors in molecular crystals. First, the impact of truncating the many-body expansion at different orders and the role of electrostatic embedding are examined on a series of molecular clusters extracted from molecular crystals. Second, the ability of these techniques to assign three polymorphic forms of the drug sulfanilamide to the corresponding experimental (13)C spectra is assessed. This challenging example requires discriminating among spectra whose (13)C chemical shifts differ by only a few parts per million (ppm) across the different polymorphs. Fragment-based PBE0/6-311+G(2d,p) level chemical shielding predictions correctly assign these three polymorphs and reproduce the sulfanilamide experimental (13)C chemical shifts with 1 ppm accuracy. The results demonstrate that fragment approaches are competitive with the widely used gauge-invariant projector augmented wave (GIPAW) periodic density functional theory calculations.
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Affiliation(s)
- Joshua D Hartman
- Department of Chemistry, University of California , Riverside, California 92521, United States
| | - Gregory J O Beran
- Department of Chemistry, University of California , Riverside, California 92521, United States
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41
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Del Ben M, Hutter J, VandeVondele J. Probing the structural and dynamical properties of liquid water with models including non-local electron correlation. J Chem Phys 2015; 143:054506. [PMID: 26254660 DOI: 10.1063/1.4927325] [Citation(s) in RCA: 75] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Water is a ubiquitous liquid that displays a wide range of anomalous properties and has a delicate structure that challenges experiment and simulation alike. The various intermolecular interactions that play an important role, such as repulsion, polarization, hydrogen bonding, and van der Waals interactions, are often difficult to reproduce faithfully in atomistic models. Here, electronic structure theories including all these interactions at equal footing, which requires the inclusion of non-local electron correlation, are used to describe structure and dynamics of bulk liquid water. Isobaric-isothermal (NpT) ensemble simulations based on the Random Phase Approximation (RPA) yield excellent density (0.994 g/ml) and fair radial distribution functions, while various other density functional approximations produce scattered results (0.8-1.2 g/ml). Molecular dynamics simulation in the microcanonical (NVE) ensemble based on Møller-Plesset perturbation theory (MP2) yields dynamical properties in the condensed phase, namely, the infrared spectrum and diffusion constant. At the MP2 and RPA levels of theory, ice is correctly predicted to float on water, resolving one of the anomalies as resulting from a delicate balance between van der Waals and hydrogen bonding interactions. For several properties, obtaining quantitative agreement with experiment requires correction for nuclear quantum effects (NQEs), highlighting their importance, for structure, dynamics, and electronic properties. A computed NQE shift of 0.6 eV for the band gap and absorption spectrum illustrates the latter. Giving access to both structure and dynamics of condensed phase systems, non-local electron correlation will increasingly be used to study systems where weak interactions are of paramount importance.
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Affiliation(s)
- Mauro Del Ben
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Jürg Hutter
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Joost VandeVondele
- Department of Materials, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland
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42
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Gillan MJ, Alfè D, Manby FR. Energy benchmarks for methane-water systems from quantum Monte Carlo and second-order Møller-Plesset calculations. J Chem Phys 2015; 143:102812. [PMID: 26374005 DOI: 10.1063/1.4926444] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The quantum Monte Carlo (QMC) technique is used to generate accurate energy benchmarks for methane-water clusters containing a single methane monomer and up to 20 water monomers. The benchmarks for each type of cluster are computed for a set of geometries drawn from molecular dynamics simulations. The accuracy of QMC is expected to be comparable with that of coupled-cluster calculations, and this is confirmed by comparisons for the CH4-H2O dimer. The benchmarks are used to assess the accuracy of the second-order Møller-Plesset (MP2) approximation close to the complete basis-set limit. A recently developed embedded many-body technique is shown to give an efficient procedure for computing basis-set converged MP2 energies for the large clusters. It is found that MP2 values for the methane binding energies and the cohesive energies of the water clusters without methane are in close agreement with the QMC benchmarks, but the agreement is aided by partial cancelation between 2-body and beyond-2-body errors of MP2. The embedding approach allows MP2 to be applied without loss of accuracy to the methane hydrate crystal, and it is shown that the resulting methane binding energy and the cohesive energy of the water lattice agree almost exactly with recently reported QMC values.
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Affiliation(s)
- M J Gillan
- London Centre for Nanotechnology, University College London, Gordon St., London WC1H 0AH, United Kingdom
| | - D Alfè
- London Centre for Nanotechnology, University College London, Gordon St., London WC1H 0AH, United Kingdom
| | - F R Manby
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
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43
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Chmela J, Harding ME, Matioszek D, Anson CE, Breher F, Klopper W. Differential Many-Body Cooperativity in Electronic Spectra of Oligonuclear Transition-Metal Complexes. Chemphyschem 2015; 17:37-45. [DOI: 10.1002/cphc.201500626] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2015] [Revised: 10/06/2015] [Indexed: 12/18/2022]
Affiliation(s)
- Jiří Chmela
- Institute of Physical Chemistry; Karlsruhe Institute of Technology (KIT); Fritz-Haber-Weg 2 76131 Karlsruhe Germany
| | - Michael E. Harding
- Institute of Nanotechnology; Karlsruhe Institute of Technology (KIT); Hermann-von-Helmholtz-Platz 1 76344 Eggenstein-Leopoldshafen Germany
| | - Dimitri Matioszek
- Institute of Inorganic Chemistry; Karlsruhe Institute of Technology (KIT); Engesserstraße 15 76131 Karlsruhe Germany
| | - Christopher E. Anson
- Institute of Inorganic Chemistry; Karlsruhe Institute of Technology (KIT); Engesserstraße 15 76131 Karlsruhe Germany
| | - Frank Breher
- Institute of Inorganic Chemistry; Karlsruhe Institute of Technology (KIT); Engesserstraße 15 76131 Karlsruhe Germany
| | - Wim Klopper
- Institute of Physical Chemistry; Karlsruhe Institute of Technology (KIT); Fritz-Haber-Weg 2 76131 Karlsruhe Germany
- Institute of Nanotechnology; Karlsruhe Institute of Technology (KIT); Hermann-von-Helmholtz-Platz 1 76344 Eggenstein-Leopoldshafen Germany
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44
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Al-Hamdani YS, Alfè D, von Lilienfeld OA, Michaelides A. Water on BN doped benzene: a hard test for exchange-correlation functionals and the impact of exact exchange on weak binding. J Chem Phys 2015; 141:18C530. [PMID: 25399195 DOI: 10.1063/1.4898356] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
Density functional theory (DFT) studies of weakly interacting complexes have recently focused on the importance of van der Waals dispersion forces, whereas the role of exchange has received far less attention. Here, by exploiting the subtle binding between water and a boron and nitrogen doped benzene derivative (1,2-azaborine) we show how exact exchange can alter the binding conformation within a complex. Benchmark values have been calculated for three orientations of the water monomer on 1,2-azaborine from explicitly correlated quantum chemical methods, and we have also used diffusion quantum Monte Carlo. For a host of popular DFT exchange-correlation functionals we show that the lack of exact exchange leads to the wrong lowest energy orientation of water on 1,2-azaborine. As such, we suggest that a high proportion of exact exchange and the associated improvement in the electronic structure could be needed for the accurate prediction of physisorption sites on doped surfaces and in complex organic molecules. Meanwhile to predict correct absolute interaction energies an accurate description of exchange needs to be augmented by dispersion inclusive functionals, and certain non-local van der Waals functionals (optB88- and optB86b-vdW) perform very well for absolute interaction energies. Through a comparison with water on benzene and borazine (B3N3H6) we show that these results could have implications for the interaction of water with doped graphene surfaces, and suggest a possible way of tuning the interaction energy.
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Affiliation(s)
- Yasmine S Al-Hamdani
- Thomas Young Centre and London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
| | - Dario Alfè
- Thomas Young Centre and London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
| | - O Anatole von Lilienfeld
- Institute of Physical Chemistry, Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Angelos Michaelides
- Thomas Young Centre and London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
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45
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Heit YN, Nanda KD, Beran GJO. Predicting finite-temperature properties of crystalline carbon dioxide from first principles with quantitative accuracy. Chem Sci 2015; 7:246-255. [PMID: 29861980 PMCID: PMC5952317 DOI: 10.1039/c5sc03014e] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Accepted: 09/28/2015] [Indexed: 11/21/2022] Open
Abstract
The temperature-dependence of the crystalline carbon dioxide (phase I) structure, thermodynamics, and mechanical properties are predicted in excellent agreement with experiment over a 200 K temperature range using high-level electronic structure calculations.
Molecular crystal structures, thermodynamics, and mechanical properties can vary substantially with temperature, and predicting these temperature-dependencies correctly is important for many practical applications in the pharmaceutical industry and other fields. However, most electronic structure predictions of molecular crystal properties neglect temperature and/or thermal expansion, leading to potentially erroneous results. Here, we demonstrate that by combining large basis set second-order Møller–Plesset (MP2) or even coupled cluster singles, doubles, and perturbative triples (CCSD(T)) electronic structure calculations with a quasiharmonic treatment of thermal expansion, experimentally observable properties such as the unit cell volume, heat capacity, enthalpy, entropy, sublimation point and bulk modulus of phase I crystalline carbon dioxide can be predicted in excellent agreement with experiment over a broad range of temperatures. These results point toward a promising future for ab initio prediction of molecular crystal properties at real-world temperatures and pressures.
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Affiliation(s)
- Yonaton N Heit
- Department of Chemistry , University of California , Riverside , California 92521 , USA . ; Tel: +1-951-827-7869
| | - Kaushik D Nanda
- Department of Chemistry , University of California , Riverside , California 92521 , USA . ; Tel: +1-951-827-7869
| | - Gregory J O Beran
- Department of Chemistry , University of California , Riverside , California 92521 , USA . ; Tel: +1-951-827-7869
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46
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Michaelides A, Martinez TJ, Alavi A, Kresse G, Manby FR. Preface: Special Topic Section on Advanced Electronic Structure Methods for Solids and Surfaces. J Chem Phys 2015; 143:102601. [DOI: 10.1063/1.4930182] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
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47
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Bennie SJ, Stella M, Miller TF, Manby FR. Accelerating wavefunction in density-functional-theory embedding by truncating the active basis set. J Chem Phys 2015; 143:024105. [DOI: 10.1063/1.4923367] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Simon J. Bennie
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Martina Stella
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Thomas F. Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Frederick R. Manby
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
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48
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Gillan MJ. Many-body exchange-overlap interactions in rare gases and water. J Chem Phys 2014; 141:224106. [DOI: 10.1063/1.4903240] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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49
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Del Ben M, VandeVondele J, Slater B. Periodic MP2, RPA, and Boundary Condition Assessment of Hydrogen Ordering in Ice XV. J Phys Chem Lett 2014; 5:4122-8. [PMID: 26278943 DOI: 10.1021/jz501985w] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Ice XV is the hydrogen-ordered form of the ice VI phase whose structure was predicted to be Cc and ferroelectric using periodic DFT approaches. However, neutron diffraction and Raman spectroscopy data show the structure to have P1̅ symmetry and to be antiferroelectric. Recent work1 using fragment-based MP2 and CCSD(T) approaches predicts the experimental structure as the ground state. We have reconsidered this problem using fully periodic MP2 and RPA approaches and find that the ferroelectric Cc structure is the lowest energy configuration. However, ubiquitously employed tinfoil boundary conditions stabilize polar structures. We suggest that ferroelectric Cc crystals can grow within a paraelectric ice VI matrix but may become unstable once a fraction of the matrix has become hydrogen-ordered. The reduction in dielectric constant causes P1̅ and other structures with small polarization to become favored, providing a possible resolution between observation and theoretical predictions.
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Affiliation(s)
- Mauro Del Ben
- †Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Joost VandeVondele
- ‡Department of Materials, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland
| | - Ben Slater
- §Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom
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50
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Heit Y, Beran GJO. Exploiting space-group symmetry in fragment-based molecular crystal calculations. J Comput Chem 2014; 35:2205-14. [DOI: 10.1002/jcc.23737] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2014] [Revised: 07/23/2014] [Accepted: 08/31/2014] [Indexed: 02/03/2023]
Affiliation(s)
- Yonaton Heit
- Department of Chemistry; University of California; Riverside California 92521
| | - Gregory J. O. Beran
- Department of Chemistry; University of California; Riverside California 92521
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