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Platonenko A, Gentile F, El-Kelany KE, Dovesi R. The role of the exact Hartree-Fock exchange in the investigation of defects in crystalline systems. Phys Chem Chem Phys 2024. [PMID: 39364576 DOI: 10.1039/d4cp02309a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/05/2024]
Abstract
The role of the exact Hartree-Fock (HF) exchange in determining the band gap and other properties of defects in crystalline solids is investigated. Two defects in diamond, VHd1 and VHq1 (one first neighbour of the vacancy is saturated with hydrogen, and the three unpaired electrons combine to give a quadruplet, 3 spin up, or a doublet, two spin up and one down), are used as test cases. The results obtained with a gradient corrected functional, PBE, one range separate hybrid, HSE06, two full range hybrids, B3LYP and PBE0, and the Hartree-Fock Hamiltonian are compared. The crucial role of the exact HF exchange emerging from this comparison is confirmed by a set of calculations with a variable functional, PBE(X), in which X is the percentage of HF exchange, which is varied from 0 to 100, where PBE(0) coincides with PBE, and PBE(25) with PBE0.
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Affiliation(s)
- Alexander Platonenko
- Institute of Solid State Physics, University of Latvia, 8 Kengaraga street, LV1063, Riga, Latvia.
| | - Francesco Gentile
- Dipartimento di Ingengeria Chimica, dei Materiali e delle Produzioni Industriali DICMAPI, Università degli Studi di Napoli Federico II, Piazzale Vincenzo Tecchio 80, 80125, Napoli, Italy
| | - Khaled E El-Kelany
- Institute of Nanoscience and Nanotechnology, Kafrelsheikh University, Kafr el-shiekh 33516, Egypt
| | - Roberto Dovesi
- Accademia Delle Scienze Di Torino, Via Accademia delle Scienze 6, Torino 10123 (To), Italy
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Quiton SJ, Wu H, Xing X, Lin L, Head-Gordon M. The Staggered Mesh Method: Accurate Exact Exchange Toward the Thermodynamic Limit for Solids. J Chem Theory Comput 2024. [PMID: 39213528 DOI: 10.1021/acs.jctc.4c00771] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/04/2024]
Abstract
In periodic systems, the Hartree-Fock (HF) exchange energy exhibits the slowest convergence of all HF energy components as the system size approaches the thermodynamic limit. We demonstrate that the recently proposed staggered mesh method for Fock exchange energy [Xing, Li, and Lin, Math. Comp., 2024], which is specifically designed to sidestep certain singularities in exchange energy evaluation, can expedite the finite-size convergence rate for the exact exchange energy across a range of insulators and semiconductors when compared to the regular and truncated Coulomb methods. This remains true even for two computationally cheaper versions of this new method, which we call non-SCF and split-SCF staggered mesh. Additionally, a sequence of numerical tests on simple solids showcases the staggered mesh method's ability to improve convergence toward the thermodynamic limit for band gaps, bulk moduli, equilibrium lattice dimensions, energies, and phonon force constants.
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Affiliation(s)
- Stephen Jon Quiton
- College of Chemistry, University of California, Berkeley, California 94720, United States
| | - Hamlin Wu
- College of Chemistry, University of California, Berkeley, California 94720, United States
| | - Xin Xing
- Department of Mathematics, University of California, Berkeley, California 94720, United States
| | - Lin Lin
- Department of Mathematics, University of California, Berkeley, California 94720, United States
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California, 94720, United States
| | - Martin Head-Gordon
- College 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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Pascale F, Gueddida S, Doll K, Dovesi R. Band gap, Jahn-Teller deformation, octahedra rotation in transition metal perovskites LaTiO 3 . J Comput Chem 2024; 45:683-694. [PMID: 38095335 DOI: 10.1002/jcc.27274] [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: 09/08/2023] [Revised: 11/15/2023] [Accepted: 11/17/2023] [Indexed: 03/02/2024]
Abstract
The LaTiO3 perovskite (where Ti is in a d1 state) is investigated by using an all electron Gaussian basis and many functionals, ranging from pure GGA (PBE), to hybrids (full range, B3LYP and PBE0, and range separated, HSE06) to Hartree Fock. Recently, Varignon et al. (Phys. Rev. Res 1, 033131, 2019), showed that, when GGA+U or HSE06 are used, a metallic solution and fractional occupancy of the t2 g subshell are obtained. Here, it is shown that when a full range hybrid functional is used, an integer occupancy is obtained, as suggested by the Jahn-Teller theorem. When the exact exchange percentage varies from 0 to 100, the system is insulating when it exceeds 20. By reducing progressively the symmetry from cubic down to orthorhombic, the relative importance of the Jahn-Teller deformation and of the rotation of the octahedra is explored.
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Affiliation(s)
- F Pascale
- Université de Lorraine-Nancy, CNRS, LEMTA, Nancy, France
| | - S Gueddida
- Université de Lorraine-Nancy, CNRS, LPCT, UMR, Vandoeuvre-lés-Nancy, France
| | - K Doll
- University of Stuttgart, Molpro Quantum Chemistry Software, Institute of Theoretical Chemistry, Stuttgart, Germany
| | - R Dovesi
- Accademia Delle Science di Torino, Torinoto, Italy
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Chakraborty R, Talbot JJ, Shen H, Yabuuchi Y, Carsch KM, Jiang HZH, Furukawa H, Long JR, Head-Gordon M. Quantum chemical modeling of hydrogen binding in metal-organic frameworks: validation, insight, predictions and challenges. Phys Chem Chem Phys 2024; 26:6490-6511. [PMID: 38324335 DOI: 10.1039/d3cp05540j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2024]
Abstract
A detailed chemical understanding of H2 interactions with binding sites in the nanoporous crystalline structure of metal-organic frameworks (MOFs) can lay a sound basis for the design of new sorbent materials. Computational quantum chemical calculations can aid in this quest. To set the stage, we review general thermodynamic considerations that control the usable storage capacity of a sorbent. We then discuss cluster modeling of H2 ligation at MOF binding sites using state-of-the-art density functional theory (DFT) calculations, and how the binding can be understood using energy decomposition analysis (EDA). Employing these tools, we illustrate the connections between the character of the MOF binding site and the associated adsorption thermodynamics using four experimentally characterized MOFs, highlighting the role of open metal sites (OMSs) in accessing binding strengths relevant to room temperature storage. The sorbents are MOF-5, with no open metal sites, Ni2(m-dobdc), containing Lewis acidic Ni(II) sites, Cu(I)-MFU-4l, containing π basic Cu(I) sites and V2Cl2.8(btdd), also containing π-basic V(II) sites. We next explore the potential for binding multiple H2 molecules at a single metal site, with thermodynamics useful for storage at ambient temperature; a materials design goal which has not yet been experimentally demonstrated. Computations on Ca2+ or Mg2+ bound to catecholate or Ca2+ bound to porphyrin show the potential for binding up to 4 H2; there is precedent for the inclusion of both catecholate and porphyrin motifs in MOFs. Turning to transition metals, we discuss the prediction that two H2 molecules can bind at V(II)-MFU-4l, a material that has been synthesized with solvent coordinated to the V(II) site. Additional calculations demonstrate binding three equivalents of hydrogen per OMS in Sc(I) or Ti(I)-exchanged MFU-4l. Overall, the results suggest promising prospects for experimentally realizing higher capacity hydrogen storage MOFs, if nontrivial synthetic and desolvation challenges can be overcome. Coupled with the unbounded chemical diversity of MOFs, there is ample scope for additional exploration and discovery.
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Affiliation(s)
- Romit Chakraborty
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
- Department of Chemistry, University of California, Berkeley, CA 94720, USA.
| | - Justin J Talbot
- Department of Chemistry, University of California, Berkeley, CA 94720, USA.
| | - Hengyuan Shen
- Department of Chemistry, University of California, Berkeley, CA 94720, USA.
| | - Yuto Yabuuchi
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
- Department of Chemistry, University of California, Berkeley, CA 94720, USA.
| | - Kurtis M Carsch
- Department of Chemistry, University of California, Berkeley, CA 94720, USA.
| | - Henry Z H Jiang
- Department of Chemistry, University of California, Berkeley, CA 94720, USA.
| | - Hiroyasu Furukawa
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
- Department of Chemistry, University of California, Berkeley, CA 94720, USA.
| | - Jeffrey R Long
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
- Department of Chemistry, University of California, Berkeley, CA 94720, USA.
- Department of Chemical and Biomedical Engineering, University of California, Berkeley, CA 94720, USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, CA 94720, USA.
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, 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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Qin X, Shang H, Yang J. Efficient implementation of analytical gradients for periodic hybrid functional calculations within fitted numerical atomic orbitals from NAO2GTO. Front Chem 2023; 11:1232425. [PMID: 37577064 PMCID: PMC10413557 DOI: 10.3389/fchem.2023.1232425] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 07/13/2023] [Indexed: 08/15/2023] Open
Abstract
The NAO2GTO scheme provides an efficient way to evaluate the electron repulsion integrals (ERIs) over numerical atomic orbitals (NAOs) with auxiliary Gaussian-type orbitals (GTOs). However, the NAO2GTO fitting will significantly impact the accuracy and convergence of hybrid functional calculations. To address this issue, here we propose to use the fitted orbitals as a new numerical basis to properly handle the mismatch between NAOs and fitted GTOs. We present an efficient and linear-scaling implementation of analytical gradients of Hartree-Fock exchange (HFX) energy for periodic HSE06 calculations with fitted NAOs in the HONPAS package. In our implementation, the ERIs and their derivatives for HFX matrix and forces are evaluated analytically with the auxiliary GTOs, while other terms are calculated using numerically discretized GTOs. Several integral screening techniques are employed to reduce the number of required ERI derivatives. We benchmark the accuracy and efficiency of our implementation and demonstrate that our results of lattice constants, bulk moduli, and band gaps of several typical semiconductors are in good agreement with the experimental values. We also show that the calculation of HFX forces based on a master-worker dynamic parallel scheme has a very high efficiency and scales linearly with respect to system size. Finally, we study the geometry optimization and polaron formation due to an excess electron in rutile TiO2 by means of HSE06 calculations to further validate the applicability of our implementation.
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Affiliation(s)
- Xinming Qin
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui, China
| | - Honghui Shang
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui, China
| | - Jinlong Yang
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui, China
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, Anhui, China
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Sun Q. Exact exchange with range-separated algorithm for thermodynamic limit of periodic Hartree-Fock theory. J Chem Phys 2023; 159:024108. [PMID: 37428044 DOI: 10.1063/5.0155815] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Accepted: 06/20/2023] [Indexed: 07/11/2023] Open
Abstract
The expensive cost of computing exact exchange in periodic systems limits the application range of density functional theory with hybrid functionals. To reduce the computational cost of exact change, we present a range-separated algorithm to compute electron repulsion integrals for Gaussian-type crystal basis. The algorithm splits the full-range Coulomb interactions into short-range and long-range parts, which are, respectively, computed in real and reciprocal space. This approach significantly reduces the overall computational cost, as integrals can be efficiently computed in both regions. The algorithm can efficiently handle large numbers of k points with limited central processing unit (CPU) and memory resources. As a demonstration, we performed an all-electron k-point Hartree-Fock calculation for LiH crystal with one million Gaussian basis functions, which was completed on a desktop computer in 1400 CPU hours.
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Affiliation(s)
- Qiming Sun
- Quantum Engine LLC, Lacey, Washington 98516, USA
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