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Hernández-Segura LI, Olvera-Rubalcava FA, Flores-Moreno R, Calaminici P, Köster AM. Exchange-correlation kernel for perturbation dependent auxiliary functions in auxiliary density perturbation theory. J Mol Model 2024; 30:302. [PMID: 39115689 PMCID: PMC11310252 DOI: 10.1007/s00894-024-06091-z] [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: 05/21/2024] [Accepted: 07/23/2024] [Indexed: 08/11/2024]
Abstract
CONTEXT Analytic exchange-correlation kernel formulations are of the outermost importance for density functional theory (DFT) perturbation calculations. In this paper, the working equation for the exchange-correlation kernel of the generalized gradient approximation (GGA) for perturbation dependent auxiliary functions is derived and discussed in the framework of auxiliary density functional theory (ADFT). The presented new formulation is extended to the unrestricted approach, too. A comprehensive discussion of the implementation of the GGA ADFT kernel, using either the native exchange-correlation functional implementations in deMon2k or the ones from the LibXC library, is given. Calculations with analytic exchange-correlation kernels are compared to their finite difference counterparts. The obtained results are in quantitative agreement. Nevertheless, analytic GGA ADFT kernel implementations show substantial improvement in the computational performance. Similar results are reported for analytic second derivatives of effective core potential (ECP) and model core potential (MCP) matrix elements when compared to their finite difference counterparts in molecular frequency analyses. METHOD All calculations are performed in the framework of ADFT as implemented in deMon2k. In the ADFT analytic frequency calculations, auxiliary density perturbation theory was used. The underlying two-center exchange-correlation kernel matrix elements are calculated by numerical integration either with analytic or finite difference kernel expressions. Validation calculations are performed with the VWN and PBE functionals employing DFT-optimized DZVP basis sets in conjunction with automatically generated GEN-A2 auxiliary density function sets. In the (Pt3Cu)n cluster benchmark calculations, the RPBE functional was used. For Pt atoms, the quasi-relativistic LANL2DZ effective core potential with the corresponding valence basis set was employed, whereas for Cu atoms, the all-electron DFT-optimized TZVP basis was applied. The auxiliary density was expanded by the automatically generated GEN-A2* auxiliary function set. We run all benchmark calculations in parallel on 24 cores.
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Affiliation(s)
- Luis I Hernández-Segura
- Chemistry Department, CINVESTAV, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Del. Gustavo A. Madero, Mexico City, C.P. 07360, Mexico.
| | - Flor A Olvera-Rubalcava
- Chemistry Department, CINVESTAV, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Del. Gustavo A. Madero, Mexico City, C.P. 07360, Mexico
| | - Roberto Flores-Moreno
- Departamento de Química, Universidad de Guadalajara, Blvd. Gral. Marcelino García Barragán 1421, Guadalajara, Jal., C.P. 44430, Mexico
| | - Patrizia Calaminici
- Chemistry Department, CINVESTAV, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Del. Gustavo A. Madero, Mexico City, C.P. 07360, Mexico
| | - Andreas M Köster
- Chemistry Department, CINVESTAV, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Del. Gustavo A. Madero, Mexico City, C.P. 07360, Mexico.
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Hernández-Segura LI, Köster AM. Efficient implementation of time-dependent auxiliary density functional theory. J Chem Phys 2023; 158:024108. [PMID: 36641386 DOI: 10.1063/5.0135263] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
The random phase approximation of time-dependent auxiliary density functional theory (TDADFT) is rederived from auxiliary density perturbation theory. Our exhaustive validation of TDADFT reveals an upshift of the excitation energies by ∼0.1 eV with respect to standard time-dependent density functional theory. For the computationally efficient implementation of TDADFT, floating point operation optimized three-center electron repulsion integral recurrence relations and their double asymptotic expansions are implemented into the Davidson solver. The computational efficiency of TDADFT is benchmarked with four sets of molecules comprising alkanes, fullerenes, DNA fragments, and zeolites. The results show that TDADFT has a computational scaling between 1.3 and 1.9 with respect to the number of basis functions, which is lower than the scaling of standard time-dependent density functional theory. Due to its computational simplifications, TDADFT is particularly well suited for Born-Oppenheimer molecular dynamics simulations. As illustrative examples, we present the temperature effects on the gas-phase absorption spectra of benzene, naphthalene, and anthracene.
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Affiliation(s)
- Luis I Hernández-Segura
- Departamento de Química, Cinvestav, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, CDMX C.P. 07360, Mexico
| | - Andreas M Köster
- Departamento de Química, Cinvestav, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, CDMX C.P. 07360, Mexico
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Carmona-Espíndola J. Photoabsorption spectra of helicenes. COMPUT THEOR CHEM 2021. [DOI: 10.1016/j.comptc.2021.113272] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Morrison AF, Epifanovsky E, Herbert JM. Double-buffered, heterogeneous CPU + GPU integral digestion algorithm for single-excitation calculations involving a large number of excited states. J Comput Chem 2018; 39:2173-2182. [PMID: 30368836 DOI: 10.1002/jcc.25531] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2018] [Revised: 05/12/2018] [Accepted: 06/14/2018] [Indexed: 01/29/2023]
Abstract
The most widely used quantum-chemical models for excited states are single-excitation theories, a category that includes configuration interaction with single substitutions, time-dependent density functional theory, and also a recently developed ab initio exciton model. When a large number of excited states are desired, these calculations incur a significant bottleneck in the "digestion" step in which two-electron integrals are contracted with density or density-like matrices. We present an implementation that moves this step onto graphical processing units (GPUs), and introduce a double-buffer scheme that minimizes latency by computing integrals on the central processing units (CPUs) concurrently with their digestion on the GPUs. An automatic code generation scheme simplifies the implementation of high-performance GPU kernels. For the exciton model, which requires separate excited-state calculations on each electronically coupled chromophore, the heterogeneous implementation described here results in speedups of 2-6× versus a CPU-only implementation. For traditional time-dependent density functional theory calculations, we obtain speedups of up to 5× when a large number of excited states is computed. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Adrian F Morrison
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio.,Q-Chem Inc., Pleasanton, California
| | | | - John M Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio
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Carmona-Espíndola J, Gázquez JL, Vela A, Trickey SB. Global hybrid exchange energy functional with correct asymptotic behavior of the corresponding potential. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1864-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Zuniga-Gutierrez B, Köster AM. Analytical GGA exchange–correlation kernel calculation in auxiliary density functional theory. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1125026] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
| | - Andreas M. Köster
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, México D.F., México
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Zhang X, Wang Y, Wang H, Lim A, Gantefoer G, Bowen KH, Reveles JU, Khanna SN. On the Existence of Designer Magnetic Superatoms. J Am Chem Soc 2013; 135:4856-61. [DOI: 10.1021/ja400830z] [Citation(s) in RCA: 96] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xinxing Zhang
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218,
United States
| | - Yi Wang
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218,
United States
| | - Haopeng Wang
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218,
United States
| | - Alane Lim
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218,
United States
| | - Gerd Gantefoer
- Department
of Physics, Universitaet Konstanz, Konstanz,
Germany
| | - Kit H. Bowen
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218,
United States
| | - J. Ulises Reveles
- Department of Physics, Virginia Commonwealth University, Richmond, Virginia
23284, United States
| | - Shiv N. Khanna
- Department of Physics, Virginia Commonwealth University, Richmond, Virginia
23284, United States
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Assessment of dressed time-dependent density-functional theory for the low-lying valence states of 28 organic chromophores. Chem Phys 2011. [DOI: 10.1016/j.chemphys.2011.03.019] [Citation(s) in RCA: 66] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Validation and application of auxiliary density perturbation theory and non-iterative approximation to coupled-perturbed Kohn–Sham approach for calculation of dipole–quadrupole polarizability. Chem Phys Lett 2011. [DOI: 10.1016/j.cplett.2011.05.032] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Carmona-Espíndola J, Flores-Moreno R, Köster AM. Time-dependent auxiliary density perturbation theory. J Chem Phys 2010; 133:084102. [DOI: 10.1063/1.3478551] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Shedge SV, Carmona-Espíndola J, Pal S, Köster AM. Comparison of the Auxiliary Density Perturbation Theory and the Noniterative Approximation to the Coupled Perturbed Kohn−Sham Method: Case Study of the Polarizabilities of Disubstituted Azoarene Molecules. J Phys Chem A 2010; 114:2357-64. [DOI: 10.1021/jp909966f] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sapana V. Shedge
- Theory Group, Physical Chemistry Division, National Chemical Laboratory, Pune 411 008, India
| | - Javier Carmona-Espíndola
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, México D.F. 07000, México
| | - Sourav Pal
- Theory Group, Physical Chemistry Division, National Chemical Laboratory, Pune 411 008, India
| | - Andreas M. Köster
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, México D.F. 07000, México
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Huix-Rotllant M, Natarajan B, Ipatov A, Muhavini Wawire C, Deutsch T, Casida ME. Assessment of noncollinear spin-flip Tamm–Dancoff approximation time-dependent density-functional theory for the photochemical ring-opening of oxirane. Phys Chem Chem Phys 2010; 12:12811-25. [DOI: 10.1039/c0cp00273a] [Citation(s) in RCA: 87] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Ipatov A, Cordova F, Doriol LJ, Casida ME. Excited-state spin-contamination in time-dependent density-functional theory for molecules with open-shell ground states. ACTA ACUST UNITED AC 2009. [DOI: 10.1016/j.theochem.2009.07.036] [Citation(s) in RCA: 71] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Dunlap BI. Variational, V-representable, and variable-occupation-number perturbation theories. J Chem Phys 2008; 129:244109. [DOI: 10.1063/1.3042143] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Foerster D. Elimination, in electronic structure calculations, of redundant orbital products. J Chem Phys 2008; 128:034108. [DOI: 10.1063/1.2821021] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Cordova F, Doriol LJ, Ipatov A, Casida ME, Filippi C, Vela A. Troubleshooting time-dependent density-functional theory for photochemical applications: Oxirane. J Chem Phys 2007; 127:164111. [DOI: 10.1063/1.2786997] [Citation(s) in RCA: 100] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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