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Liu A, Zhang T, Hammes-Schiffer S, Li X. Multicomponent Cholesky Decomposition: Application to Nuclear-Electronic Orbital Theory. J Chem Theory Comput 2023; 19:6255-6262. [PMID: 37699735 DOI: 10.1021/acs.jctc.3c00686] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/14/2023]
Abstract
The Cholesky decomposition technique is commonly used to reduce the memory requirement for storing two-particle repulsion integrals in quantum chemistry calculations that use atomic orbital bases. However, when quantum methods use multicomponent bases, such as nuclear-electronic orbitals, additional challenges are introduced due to asymmetric two-particle integrals. This work proposes several multicomponent Cholesky decomposition methods for calculations using nuclear-electronic orbital density functional theory. To analyze the errors in different Cholesky decomposition components, benchmark calculations using water clusters are carried out. The largest benchmark calculation is a water cluster (H2O)27 where all 54 protons are treated quantum mechanically. This study provides energetic and complexity analyses to demonstrate the accuracy and performance of the proposed multicomponent Cholesky decomposition method.
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Affiliation(s)
- Aodong Liu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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2
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Banerjee S, Zhang T, Dyall KG, Li X. Relativistic resolution-of-the-identity with Cholesky integral decomposition. J Chem Phys 2023; 159:114119. [PMID: 37728204 DOI: 10.1063/5.0161871] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 08/28/2023] [Indexed: 09/21/2023] Open
Abstract
In this study, we present an efficient integral decomposition approach called the restricted-kinetic-balance resolution-of-the-identity (RKB-RI) algorithm, which utilizes a tunable RI method based on the Cholesky integral decomposition for in-core relativistic quantum chemistry calculations. The RKB-RI algorithm incorporates the restricted-kinetic-balance condition and offers a versatile framework for accurate computations. Notably, the Cholesky integral decomposition is employed not only to approximate symmetric large-component electron repulsion integrals but also those involving small-component basis functions. In addition to comprehensive error analysis, we investigate crucial conditions, such as the kinetic balance condition and variational stability, which underlie the applicability of Dirac relativistic electronic structure theory. We compare the computational cost of the RKB-RI approach with the full in-core method to assess its efficiency. To evaluate the accuracy and reliability of the RKB-RI method proposed in this work, we employ actinyl oxides as benchmark systems, leveraging their properties for validation purposes. This investigation provides valuable insights into the capabilities and performance of the RKB-RI algorithm and establishes its potential as a powerful tool in the field of relativistic quantum chemistry.
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Affiliation(s)
- Samragni Banerjee
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | | | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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3
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Bozkaya U, Ermiş B, Alagöz Y, Ünal A, Uyar AK. MacroQC 1.0: An electronic structure theory software for large-scale applications. J Chem Phys 2022; 156:044801. [DOI: 10.1063/5.0077823] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Uğur Bozkaya
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Betül Ermiş
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Yavuz Alagöz
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Aslı Ünal
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Ali Kaan Uyar
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
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Alagöz Y, Ünal A, Bozkaya U. Efficient implementations of the symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles method with the density-fitting approximation. J Chem Phys 2021; 155:114104. [PMID: 34551547 DOI: 10.1063/5.0061351] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Efficient implementations of the symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles (OCCD) method with the density-fitting approach, denoted by DF-OCCD(T) and DF-OCCD(T)Λ, are presented. The computational cost of the DF-OCCD(T) method is compared with that of the conventional OCCD(T). In the conventional OCCD(T) and OCCD(T)Λ methods, one needs to perform four-index integral transformations at each coupled-cluster doubles iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD(T) provides dramatically lower computational costs compared to OCCD(T), and there are more than 68-fold reductions in the computational time for the C5H12 molecule with the cc-pVTZ basis set. Our results show that the DF-OCCD(T) and DF-OCCD(T)Λ methods are very helpful for the study of single bond-breaking problems. Performances of the DF-OCCD(T) and DF-OCCD(T)Λ methods are noticeably better than that of the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for the potential energy surfaces of the molecules considered. Specifically, the DF-OCCD(T)Λ method provides dramatic improvements upon CCSD(T), and there are 8-14-fold reductions in nonparallelity errors. Overall, we conclude that the DF-OCCD(T)Λ method is very promising for the study of challenging chemical systems, where the CCSD(T) fails.
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Affiliation(s)
- Yavuz Alagöz
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Aslı Ünal
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Uğur Bozkaya
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
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Zhang T, Liu X, Valeev EF, Li X. Toward the Minimal Floating Operation Count Cholesky Decomposition of Electron Repulsion Integrals. J Phys Chem A 2021; 125:4258-4265. [PMID: 33970626 DOI: 10.1021/acs.jpca.1c02317] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
As quantum chemistry calculations deal with molecular systems of increasing size, the memory requirement to store electron-repulsion integrals (ERIs) greatly outpaces the physical memory available in computing hardware. The Cholesky decomposition of ERIs provides a convenient yet accurate technique to reduce the storage requirement of integrals. Recent developments of a two-step algorithm have drastically reduced the memory operation (MOP) count, leaving the floating operation (FLOP) count as the last frontier of cost reduction in the Cholesky ERI algorithm. In this report, we introduce a dynamic integral tracking, reusing, and compression/elimination protocol embedded in the two-step Cholesky ERI method. Benchmark studies suggest that this technique becomes particularly advantageous when the basis set consists of many computationally expensive high-angular-momentum basis functions. With this dynamic-ERI improvement, the Cholesky ERI approach proves to be a highly efficient algorithm with minimal FLOP and MOP count.
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Affiliation(s)
- Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaolin Liu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States.,Pacific Northwest National Laboratory, Richland, Washington 99354, United States
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Bozkaya U, Ünal A, Alagöz Y. Energy and analytic gradients for the orbital-optimized coupled-cluster doubles method with the density-fitting approximation: An efficient implementation. J Chem Phys 2020; 153:244115. [PMID: 33380091 DOI: 10.1063/5.0035811] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Efficient implementations of the orbital-optimized coupled-cluster doubles (or simply "optimized CCD," OCCD, for short) method and its analytic energy gradients with the density-fitting (DF) approach, denoted by DF-OCCD, are presented. In addition to the DF approach, the Cholesky-decomposed variant (CD-OCCD) is also implemented for energy computations. The computational cost of the DF-OCCD method (available in a plugin version of the DFOCC module of PSI4) is compared with that of the conventional OCCD (from the Q-CHEM package). The OCCD computations were performed with the Q-CHEM package in which OCCD are denoted by OD. In the conventional OCCD method, one needs to perform four-index integral transformations at each of the CCD iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD provides dramatically lower computational costs compared to OCCD, and there are almost eightfold reductions in the computational time for the C6H14 molecule with the cc-pVTZ basis set. For open-shell geometries, interaction energies, and hydrogen transfer reactions, DF-OCCD provides significant improvements upon DF-CCD. Furthermore, the performance of the DF-OCCD method is substantially better for harmonic vibrational frequencies in the case of symmetry-breaking problems. Moreover, several factors make DF-OCCD more attractive compared to CCSD: (1) for DF-OCCD, there is no need for orbital relaxation contributions in analytic gradient computations; (2) active spaces can readily be incorporated into DF-OCCD; (3) DF-OCCD provides accurate vibrational frequencies when symmetry-breaking problems are observed; (4) in its response function, DF-OCCD avoids artificial poles; hence, excited-state molecular properties can be computed via linear response theory; and (5) symmetric and asymmetric triples corrections based on DF-OCCD [DF-OCCD(T)] have a significantly better performance in near degeneracy regions.
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Affiliation(s)
- Uğur Bozkaya
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Aslı Ünal
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Yavuz Alagöz
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
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Servan SA, Ünal A, Hamarat B, Bozkaya U. Assessment of the Density-Fitted Second-Order Quasidegenerate Perturbation Theory for Transition Energies: Accurate Computations of Singlet-Triplet Gaps for Charge-Transfer Compounds. J Phys Chem A 2020; 124:6889-6898. [PMID: 32786988 DOI: 10.1021/acs.jpca.0c04555] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Organic light-emitting diodes (OLEDs) have been of significant interest because of their superior performance and low cost of production. Thermally activated delayed fluorescence (TADF) has attracted significant interest in the OLED technology because it improves the efficiency of OLEDs by harvesting triplet excitons. Therefore, the accurate computation of singlet-triplet transition energies (ΔES1-T1) of charge-transfer molecules is very important. However, the accurate computation of the ΔES1-T1 values is a challenging problem for single-reference methods because of the multireference character of excited states. In this research, an assessment of density-fitted second-order quasidegenerate perturbation theory (DF-QDPT2) [Bozkaya, U.; J. Chem. Theory Comput. 2019, 15, 4415-4429] for singlet-triplet transition energies (ΔES1-T1) of charge-transfer compounds is presented. The performance of the DF-QDPT2 method has been compared with those of several density-functional theory functionals, such as B3LYP, PBE0, M06-2X, ωB97X-D, and MN15; density-fitted state-averaged CASSCF (DF-SA-CASSCF); and single-state single-reference second-order perturbation theory (SS-SR-CASPT2) methods. For the TADF molecules considered, the DF-QDPT2 method provides a mean absolute error (MAE) of 0.13 eV, while the MAE values of DF-SA-CASSCF and SS-SR-CASPT2 are 0.65 and 0.74 eV, respectively. The performances of B3LYP and PBE0 are slightly better than that of DF-QDPT2, while M06-2X and ωB97X-D provide noticeably higher errors compared with DF-QDPT2. Furthermore, the standard CASSCF without state-averaging yields dramatic errors with an MAE value of 3.0 eV. Our results demonstrate that eigenvalues of the DF-QDPT2-effective Hamiltonian can be reliably used for the prediction of singlet-triplet transition energies, while eigenvalues of DF-CASSCF/DF-SA-CASSCF fail to provide accurate predictions. Overall, we conclude that the DF-QDPT2 method emerges as a very useful tool for the computation of excited-state properties.
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Affiliation(s)
| | - Aslı Ünal
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Büşra Hamarat
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
| | - Uğur Bozkaya
- Department of Chemistry, Hacettepe University, Ankara 06800, Turkey
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Lew-Yee JFH, Flores-Moreno R, Morales JL, M Del Campo J. Asymmetric Density Fitting with Modified Cholesky Decomposition Applied to Second-Order Electron Propagator. J Chem Theory Comput 2020; 16:1597-1605. [PMID: 31967819 DOI: 10.1021/acs.jctc.9b01215] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Computation of molecular orbital electron repulsion integrals (MO-ERIs) as a transformation from atomic orbital ERIs (AO-ERIs) is the bottleneck of second-order electron propagator calculations when a single orbital is studied. In this contribution, asymmetric density fitting is combined with modified Cholesky decomposition to generate efficiently the required MO-ERIs. The key point of the presented algorithms is to keep track of integrals through partial contractions performed on three-center AO-ERIs; these contractions are stored in RAM instead of the AO-ERIs. Two implementations are provided, an in-core, which reduces the arithmetic and memory scaling factors as compared to the four-center AO-ERIs contraction method, and a semidirect, which overcomes memory limitations by evaluating antisymmetrized MO-ERIs in batches. On the numerical side, the proposed approach is fast and stable. The bad effects due to ill conditioning, namely, several negative and close to zero eigenvalues due to machine round off errors of the matrix associated with the density fitting process, are effectively controlled by means of a modified Cholesky factorization that avoids the matrix inversion needed to perform the asymmetrical density fitting implementation. The numerical experience presented shows that the in-core implementation is highly competitive to perform calculations on medium and large basis sets, while the semidirect implementation has small variations in time by changes in the available memory. The general applicability is illustrated on a set of selected relatively large-size molecules.
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Affiliation(s)
- Juan Felipe Huan Lew-Yee
- Departamento de Fı́sica y Quı́mica Teórica, Facultad de Quı́mica, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
| | - Roberto Flores-Moreno
- Departamento de Quı́mica, Universidad de Guadalajara, Blvd. Marcelino García Barragán 1421, Guadalajara Jalisco 44430, Mexico
| | - José Luis Morales
- Facultad de Quı́mica, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
| | - Jorge M Del Campo
- Departamento de Fı́sica y Quı́mica Teórica, Facultad de Quı́mica, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
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9
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Abstract
![]()
We
introduce a new variant of the complete active space second-order
perturbation theory (CASPT2) method that performs similarly to multistate
CASPT2 (MS-CASPT2) in regions of the potential energy surface where
the electronic states are energetically well separated and is akin
to extended MS-CASPT2 (XMS-CASPT2) in case the underlying zeroth-order
references are near-degenerate. Our approach follows a recipe analogous
to that of XMS-CASPT2 to ensure approximate invariance under unitary
transformations of the model states and a dynamic weighting scheme
to smoothly interpolate the Fock operator between state-specific and
state-average regimes. The resulting extended dynamically weighted
CASPT2 (XDW-CASPT2) methodology possesses the most desirable features
of both MS-CASPT2 and XMS-CASPT2, that is, the ability to provide
accurate transition energies and correctly describe avoided crossings
and conical intersections. The reliability of XDW-CASPT2 is assessed
on a number of molecular systems. First, we consider the dissociation
of lithium fluoride, highlighting the distinctive characteristics
of the new approach. Second, the invariance of the theory is investigated
by studying the conical intersection of the distorted allene molecule.
Finally, the relative accuracy in the calculation of vertical excitation
energies is benchmarked on a set of 26 organic compounds. We found
that XDW-CASPT2, albeit being only approximately invariant, produces
smooth potential energy surfaces around conical intersections and
avoided crossings, performing equally well to the strictly invariant
XMS-CASPT2 method. The accuracy of vertical transition energies is
almost identical to MS-CASPT2, with a mean absolute deviation of 0.01–0.02
eV, in contrast to 0.12 eV for XMS-CASPT2.
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Affiliation(s)
- Stefano Battaglia
- Department of Chemistry-BMC, Uppsala University, P.O. Box 576, SE-75123 Uppsala, Sweden
| | - Roland Lindh
- Department of Chemistry-BMC, Uppsala University, P.O. Box 576, SE-75123 Uppsala, Sweden
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Oliveira VP, Kraka E, Machado FBC. Pushing 3c–4e Bonds to the Limit: A Coupled Cluster Study of Stepwise Fluorination of First-Row Atoms. Inorg Chem 2019; 58:14777-14789. [DOI: 10.1021/acs.inorgchem.9b02458] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Vytor P. Oliveira
- Instituto Tecnológico de Aeronáutica (ITA), Departamento de Química, São José dos Campos, 12228-900 São Paulo, Brazil
| | - Elfi Kraka
- Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, Texas 75275-0314, United States
| | - Francisco B. C. Machado
- Instituto Tecnológico de Aeronáutica (ITA), Departamento de Química, São José dos Campos, 12228-900 São Paulo, Brazil
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