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Feyersinger F, Hartmann PE, Hoja J, Reinholdt P, Libisch F, Kongsted J, Puschnig P, Boese AD. Dissociation Energies via Embedding Techniques. J Phys Chem A 2024; 128:9275-9286. [PMID: 39402985 DOI: 10.1021/acs.jpca.4c02851] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2024]
Abstract
Due to the large number of interactions, evaluating interaction energies for large or periodic systems results in time-consuming calculations. Prime examples are liquids, adsorbates, and molecular crystals. Thus, there is a high demand for a cheap but still accurate method to determine interaction energies and gradients. One approach to counteract the computational cost is to fragment a large cluster into smaller subsystems, sometimes called many-body expansion, with the fragments being molecules or parts thereof. These subsystems can then be embedded into larger entities, representing the bigger system. In this work, we test several subsystem approaches and explore their limits and behaviors, determined by calculations of trimer interaction energies. The methods presented here encompass mechanical embedding, point charges, polarizable embedding, polarizable density embedding, and density embedding. We evaluate nonembedded fragmentation, QM/MM (quantum mechanics/molecular mechanics), and QM/QM (quantum mechanics/quantum mechanics) embedding theories. Finally, we make use of symmetry-adapted perturbation theory utilizing density functional theory for the monomers to interpret the results. Depending on the strength of the interaction, different embedding methods and schemes prove favorable to accurately describe a system. The embedding approaches presented here are able to decrease the interaction energy errors with respect to full system calculations by a factor of up to 20 in comparison to simple/unembedded approaches, leading to errors below 0.1 kJ/mol.
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Affiliation(s)
- Florian Feyersinger
- Department of Chemistry, University of Graz, Heinrichstraße 28/IV, 8010 Graz, Austria
- Department of Physics, University of Graz, 8010 Graz, Austria
| | - Peter E Hartmann
- Department of Chemistry, University of Graz, Heinrichstraße 28/IV, 8010 Graz, Austria
| | - Johannes Hoja
- Department of Chemistry, University of Graz, Heinrichstraße 28/IV, 8010 Graz, Austria
| | - Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
| | - Florian Libisch
- Institute for Theoretical Physics, TU Wien, 1040 Vienna, Austria
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
| | - Peter Puschnig
- Department of Physics, University of Graz, 8010 Graz, Austria
| | - A Daniel Boese
- Department of Chemistry, University of Graz, Heinrichstraße 28/IV, 8010 Graz, Austria
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2
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Hoja J, List A, Boese AD. Multimer Embedding Approach for Molecular Crystals up to Harmonic Vibrational Properties. J Chem Theory Comput 2024; 20:357-367. [PMID: 38109226 PMCID: PMC10782452 DOI: 10.1021/acs.jctc.3c01082] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2023] [Revised: 11/16/2023] [Accepted: 11/20/2023] [Indexed: 12/20/2023]
Abstract
Accurate calculations of molecular crystals are crucial for drug design and crystal engineering. However, periodic high-level density functional calculations using hybrid functionals are often prohibitively expensive for the relevant systems. These expensive periodic calculations can be circumvented by the usage of embedding methods in which, for instance, the periodic calculation is only performed at a lower-cost level and then monomer energies and dimer interactions are replaced by those of the higher-level method. Herein, we extend such a multimer embedding approach to enable energy corrections for trimer interactions and the calculation of harmonic vibrational properties up to the dimer level. We evaluate this approach for the X23 benchmark set of molecular crystals by approximating a periodic hybrid density functional (PBE0+MBD) by embedding multimers into less expensive calculations using a generalized-gradient approximation functional (PBE+MBD). We show that trimer interactions are crucial for accurately approximating lattice energies within 1 kJ/mol and might also be needed for further improvement of lattice constants and hence cell volumes. Finally, the vibrational properties are already very well captured at the monomer and dimer level, making it possible to approximate vibrational free energies at room temperature within 1 kJ/mol.
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Affiliation(s)
- Johannes Hoja
- Department of Chemistry, University
of Graz, Heinrichstraße 28/IV, Graz 8010, Austria
| | - Alexander List
- Department of Chemistry, University
of Graz, Heinrichstraße 28/IV, Graz 8010, Austria
| | - A. Daniel Boese
- Department of Chemistry, University
of Graz, Heinrichstraße 28/IV, Graz 8010, Austria
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3
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Beran GJO. Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials. Chem Sci 2023; 14:13290-13312. [PMID: 38033897 PMCID: PMC10685338 DOI: 10.1039/d3sc03903j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Accepted: 11/02/2023] [Indexed: 12/02/2023] Open
Abstract
The reliability of organic molecular crystal structure prediction has improved tremendously in recent years. Crystal structure predictions for small, mostly rigid molecules are quickly becoming routine. Structure predictions for larger, highly flexible molecules are more challenging, but their crystal structures can also now be predicted with increasing rates of success. These advances are ushering in a new era where crystal structure prediction drives the experimental discovery of new solid forms. After briefly discussing the computational methods that enable successful crystal structure prediction, this perspective presents case studies from the literature that demonstrate how state-of-the-art crystal structure prediction can transform how scientists approach problems involving the organic solid state. Applications to pharmaceuticals, porous organic materials, photomechanical crystals, organic semi-conductors, and nuclear magnetic resonance crystallography are included. Finally, efforts to improve our understanding of which predicted crystal structures can actually be produced experimentally and other outstanding challenges are discussed.
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Affiliation(s)
- Gregory J O Beran
- Department of Chemistry, University of California Riverside Riverside CA 92521 USA
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Rettig A, Lee J, Head-Gordon M. Even Faster Exact Exchange for Solids via Tensor Hypercontraction. J Chem Theory Comput 2023; 19:5773-5784. [PMID: 37586065 DOI: 10.1021/acs.jctc.3c00407] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/18/2023]
Abstract
Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals using the Gaussian plane wave approach. This is done to lower the computational scaling with respect to the number of basis functions (N) and k-points (Nk) at a fixed system size. Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e., a set of points, NISDF) to further reduce computation time and memory usage. This algorithm has linear scaling cost with k-points, no explicit dependence of NISDF on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized k-point meshes, with additional gains for large k-point meshes. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. We perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.
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Affiliation(s)
- Adam Rettig
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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Loboda O, Strizhak P, Góra RW, Cervinka C. Editorial: Fragment-based electronic structure methods for solids. Front Chem 2023; 11:1165201. [PMID: 36909713 PMCID: PMC9996448 DOI: 10.3389/fchem.2023.1165201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2023] [Accepted: 02/16/2023] [Indexed: 02/25/2023] Open
Affiliation(s)
| | - Peter Strizhak
- L.V. Pysarzhevskii Institute of Physical Chemistry, National Academy of Science of Ukraine, Kyiv, Ukraine
| | - Robert W Góra
- Wrocław University of Science and Technology, Wrocław, Poland
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Holmes ST, Vojvodin CS, Schurko RW. Dispersion-Corrected DFT Methods for Applications in Nuclear Magnetic Resonance Crystallography. J Phys Chem A 2020; 124:10312-10323. [DOI: 10.1021/acs.jpca.0c06372] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sean T. Holmes
- Department of Chemistry & Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, United States
| | - Cameron S. Vojvodin
- Department of Chemistry & Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, United States
| | - Robert W. Schurko
- Department of Chemistry & Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, United States
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Chen B, Xu X. XO-PBC: An Accurate and Efficient Method for Molecular Crystals. J Chem Theory Comput 2020; 16:4271-4285. [PMID: 32456429 DOI: 10.1021/acs.jctc.0c00232] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In this work, we propose the XO-PBC method, which combines the eXtended ONIOM method (XO) with the periodic boundary condition (PBC) for the description of molecular crystals. XO-PBC tries to embed a finite cluster cut out from the solid into the periodic environment, making it feasible to employ advanced molecular quantum chemistry methods, which are usually prohibitively expensive for direct PBC calculations. In particular, XO-PBC utilizes the results from force calculations to design the scheme to fragment the molecule when crystals are made of large molecules and to select cluster model systems automatically consisting of dimer up to tetramer interactions for embedding. By applying an appropriate theory to each model, a satisfactory accuracy for the system under study is ensured, while a high efficiency is achieved with massively parallel computing by distributing model systems onto different processors. A comparison of the XO-PBC calculations with the conventional direct PBC calculations at the B3LYP level demonstrates its accuracy at substantially low cost for the description of molecular crystals. The usefulness of the XO-PBC method is further exemplified, showing that XO-PBC is able to predict the lattice energies of various types of molecular crystals within chemical accuracy (<4 kJ/mol) when the doubly hybrid density functional XYG3 is used as the target high level and the periodic PBE as the basic low level. The XO-PBC method provides a general protocol that brings the great predictive power of advanced electronic structure methods from molecular systems to the extended solids.
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Affiliation(s)
- Bozhu Chen
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai, 200433, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai, 200433, China
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Greenwell C, McKinley JL, Zhang P, Zeng Q, Sun G, Li B, Wen S, Beran GJO. Overcoming the difficulties of predicting conformational polymorph energetics in molecular crystals via correlated wavefunction methods. Chem Sci 2020; 11:2200-2214. [PMID: 32190277 PMCID: PMC7059316 DOI: 10.1039/c9sc05689k] [Citation(s) in RCA: 42] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2019] [Accepted: 01/13/2020] [Indexed: 11/21/2022] Open
Abstract
Molecular crystal structure prediction is increasingly being applied to study the solid form landscapes of larger, more flexible pharmaceutical molecules. Despite many successes in crystal structure prediction, van der Waals-inclusive density functional theory (DFT) methods exhibit serious failures predicting the polymorph stabilities for a number of systems exhibiting conformational polymorphism, where changes in intramolecular conformation lead to different intermolecular crystal packings. Here, the stabilities of the conformational polymorphs of o-acetamidobenzamide, ROY, and oxalyl dihydrazide are examined in detail. DFT functionals that have previously been very successful in crystal structure prediction perform poorly in all three systems, due primarily to the poor intramolecular conformational energies, but also due to the intermolecular description in oxalyl dihydrazide. In all three cases, a fragment-based dispersion-corrected second-order Møller-Plesset perturbation theory (MP2D) treatment of the crystals overcomes these difficulties and predicts conformational polymorph stabilities in good agreement with experiment. These results highlight the need for methods which go beyond current-generation DFT functionals to make crystal polymorph stability predictions truly reliable.
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Affiliation(s)
- Chandler Greenwell
- Department of Chemistry , University of California , Riverside , California 92521 , USA . ; Tel: +1-951-827-7869
| | - Jessica L McKinley
- Department of Chemistry , University of California , Riverside , California 92521 , USA . ; Tel: +1-951-827-7869
| | - Peiyu Zhang
- Xtalpi, Inc. , 245 Main St, 12th Floor , Cambridge , MA 02142 , USA
| | - Qun Zeng
- Xtalpi, Inc. , 245 Main St, 12th Floor , Cambridge , MA 02142 , USA
| | - Guangxu Sun
- Xtalpi, Inc. , 245 Main St, 12th Floor , Cambridge , MA 02142 , USA
| | - Bochen Li
- Xtalpi, Inc. , 245 Main St, 12th Floor , Cambridge , MA 02142 , USA
| | - Shuhao Wen
- Xtalpi, Inc. , 245 Main St, 12th Floor , Cambridge , MA 02142 , USA
| | - Gregory J O Beran
- Department of Chemistry , University of California , Riverside , California 92521 , USA . ; Tel: +1-951-827-7869
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9
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Dolgonos GA, Boese AD. Adjusting dispersion parameters for the density-functional tight-binding description of molecular crystals. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2019.01.027] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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10
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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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Dolgonos GA, Hoja J, Boese AD. Revised values for the X23 benchmark set of molecular crystals. Phys Chem Chem Phys 2019; 21:24333-24344. [DOI: 10.1039/c9cp04488d] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A revised reference value set for molecular crystals: X23b; new cell volumes and lattice energies including volumetric expansion due to zero-point energy and thermal effects.
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Affiliation(s)
| | - Johannes Hoja
- Institute of Chemistry
- University of Graz
- 8010 Graz
- Austria
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12
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LeBlanc LM, Johnson ER. Crystal-energy landscapes of active pharmaceutical ingredients using composite approaches. CrystEngComm 2019. [DOI: 10.1039/c9ce00895k] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
Composite methods employing dispersion-corrected DFT consistently identify experimentally isolated polymorphs as the lowest-energy crystal structures of common APIs.
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Affiliation(s)
- Luc M. LeBlanc
- Department of Chemistry
- Dalhousie University
- Halifax
- Canada
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