1
|
Gaikwad PB, Kim TD, Richer M, Lokhande RA, Sánchez-Díaz G, Limacher PA, Ayers PW, Miranda-Quintana RA. Coupled cluster-inspired geminal wavefunctions. J Chem Phys 2024; 160:144108. [PMID: 38597308 DOI: 10.1063/5.0202035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Accepted: 03/24/2024] [Indexed: 04/11/2024] Open
Abstract
Electron pairs have an illustrious history in chemistry, from powerful concepts to understanding structural stability and reactive changes to the promise of serving as building blocks of quantitative descriptions of the electronic structure of complex molecules and materials. However, traditionally, two-electron wavefunctions (geminals) have not enjoyed the popularity and widespread use of the more standard single-particle methods. This has changed recently, with a renewed interest in the development of geminal wavefunctions as an alternative to describing strongly correlated phenomena. Hence, there is a need to find geminal methods that are accurate, computationally tractable, and do not demand significant input from the user (particularly via cumbersome and often ill-behaved orbital optimization steps). Here, we propose new families of geminal wavefunctions inspired by the pair coupled cluster doubles ansatz. We present a new hierarchy of two-electron wavefunctions that extends the one-reference orbital idea to other geminals. Moreover, we show how to incorporate single-like excitations in this framework without leaving the quasiparticle picture. We explore the role of imposing seniority restrictions on these wavefunctions and benchmark these new methods on model strongly correlated systems.
Collapse
Affiliation(s)
- Pratiksha B Gaikwad
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - Taewon D Kim
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - M Richer
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Rugwed A Lokhande
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - Gabriela Sánchez-Díaz
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Peter A Limacher
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | | |
Collapse
|
2
|
Semidalas E, Karton A, Martin JML. W4Λ: Leveraging Λ Coupled-Cluster for Accurate Computational Thermochemistry Approaches. J Phys Chem A 2024; 128:1715-1724. [PMID: 38400740 PMCID: PMC10926103 DOI: 10.1021/acs.jpca.3c08158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2023] [Revised: 01/28/2024] [Accepted: 01/31/2024] [Indexed: 02/26/2024]
Abstract
High-accuracy composite wave function methods like Weizmann-4 (W4) theory, high-accuracy extrapolated ab initio thermochemistry (HEAT), and the Feller-Peterson-Dixon (FPD) approach enable sub-kJ/mol accuracy in gas-phase thermochemical properties. Their biggest computational bottleneck is the evaluation of the valence post-CCSD(T) correction term. We demonstrate here, for the W4-17 thermochemistry benchmark and subsets thereof, that the Λ coupled-cluster expansion converges more rapidly and smoothly than the regular coupled-cluster series. By means of CCSDT(Q)Λ and CCSDTQ(5)Λ, we can considerably (up to an order of magnitude) accelerate W4- and W4.3-type calculations without loss in accuracy, leading to the W4Λ and W4.3Λ computational thermochemistry protocols.
Collapse
Affiliation(s)
- Emmanouil Semidalas
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, 7610001 Reḥovot, Israel
| | - Amir Karton
- School
of Science and Technology, University of
New England, Armidale, New South Wales 2351, Australia
| | - Jan M. L. Martin
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, 7610001 Reḥovot, Israel
| |
Collapse
|
3
|
Xu X, Soriano-Agueda L, López X, Ramos-Cordoba E, Matito E. All-Purpose Measure of Electron Correlation for Multireference Diagnostics. J Chem Theory Comput 2024; 20:721-727. [PMID: 38157841 PMCID: PMC10809408 DOI: 10.1021/acs.jctc.3c01073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Revised: 11/24/2023] [Accepted: 11/27/2023] [Indexed: 01/03/2024]
Abstract
We present an analytical relationship between two natural orbital occupancy-based indices, I N D ¯ and INDmax, and two established electron correlation metrics: the leading term of a configuration interaction expansion, c0, and the D2 diagnostic. Numerical validation revealed that I N D ¯ and INDmax can effectively substitute for c0 and D2, respectively. These indices offer three distinct advantages: (i) they are universally applicable across all electronic structure methods, (ii) their interpretation is more intuitive, and (iii) they can be readily incorporated into the development of hybrid electronic structure methods. Additionally, we draw a distinction between correlation measures and correlation diagnostics, establishing MP2 and CCSD numerical thresholds for INDmax, which are to be used as a multireference diagnostic. Our findings further demonstrate that establishing thresholds for other electronic structure methods can be easily accomplished using small data sets.
Collapse
Affiliation(s)
- Xiang Xu
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Polimero
eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Luis Soriano-Agueda
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
| | - Xabier López
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Polimero
eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Eloy Ramos-Cordoba
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Polimero
eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072, 20080 Donostia, Euskadi, Spain
- Ikerbasque
Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
| | - Eduard Matito
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Ikerbasque
Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
| |
Collapse
|
4
|
Izsák R, Ivanov AV, Blunt NS, Holzmann N, Neese F. Measuring Electron Correlation: The Impact of Symmetry and Orbital Transformations. J Chem Theory Comput 2023; 19:2703-2720. [PMID: 37022051 PMCID: PMC10210250 DOI: 10.1021/acs.jctc.3c00122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Indexed: 04/07/2023]
Abstract
In this perspective, the various measures of electron correlation used in wave function theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behavior with respect to the choice of the N-electron and the one-electron basis. The impact of symmetry is discussed, and we emphasize that the distinction among determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wave function expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wave functions are discussed and the effect of orbital rotations on the multireference character is reviewed by analyzing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and N-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.
Collapse
Affiliation(s)
- Róbert Izsák
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Aleksei V. Ivanov
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nick S. Blunt
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nicole Holzmann
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Frank Neese
- Max-Planck
Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| |
Collapse
|
5
|
Mehta N, Martin JML. The Importance of Tight f Basis Functions for Heavy p-Block Oxides and Halides: A Parallel With Tight d functions in the Second Row. J Phys Chem A 2023; 127:2104-2112. [PMID: 36854651 PMCID: PMC10009808 DOI: 10.1021/acs.jpca.3c00544] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/02/2023]
Abstract
It is well-known that both wave function ab initio and DFT calculations on second-row compounds exhibit anomalously slow basis set convergence unless the basis sets are augmented with additional "tight" (high-exponent) d functions, as in the cc-pV(n+d)Z and aug-cc-pV(n+d)Z basis sets. This has been rationalized as being necessary for a better description of the low-lying 3d orbital, which as the oxidation state increases sinks low enough to act as a back-donation acceptor from chalcogen and halogen lone pairs. This prompts the question whether a similar phenomenon exists for the isovalent compounds of the heavy p-block. We show that for the fourth and fifth row, this is the case, but this time for tight f functions enhancing the description of the low-lying 4f and 5f Rydberg orbitals, respectively. In the third-row heavy p block, the 4f orbitals are too far up, while the 4d orbitals are adequately covered by the basis functions already present to describe the 3d subvalence orbitals.
Collapse
Affiliation(s)
- Nisha Mehta
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, 76100 Reḥovot, Israel
| | - Jan M L Martin
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, 76100 Reḥovot, Israel
| |
Collapse
|
6
|
Mehta N, Martin JML. MP2-F12 Basis Set Convergence near the Complete Basis Set Limit: Are h Functions Sufficient? J Phys Chem A 2022; 126:3964-3971. [PMID: 35687124 PMCID: PMC9234959 DOI: 10.1021/acs.jpca.2c02494] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
We have investigated
the title question for the W4-08 thermochemical
benchmark using l-saturated truncations of a large
reference (REF) basis set, as well as for standard F12-optimized basis
sets. With the REF basis set, the root-mean-square (RMS) contribution
of i functions to the MP2-F12 total atomization energies
(TAEs) is about 0.01 kcal/mol, the largest individual contributions
being 0.04 kcal/mol for P2 and P4. However,
even for these cases, basis set extrapolation from {g,h} basis sets adequately addresses the problem.
Using basis sets insufficiently saturated in the spdfgh angular momenta may lead to exaggerated i function
contributions. For extrapolation from spdfg and spdfgh basis sets, basis set convergence appears to be quite
close to the theoretical asymptotic ∝ L–7 behavior. We hence conclude that h functions are sufficient even for highly demanding F12 applications.
With one-parameter extrapolation, spdf and spdfg basis sets are adequate, aug-cc-pV{T,Q}Z-F12 yielding
a RMSD = 0.03 kcal/mol. A limited exploration of CCSD(F12*) and CCSD-F12b
suggests our conclusions are applicable to higher-level F12 methods
as well.
Collapse
Affiliation(s)
- Nisha Mehta
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Reḥovot, 7610001, Israel
| | - Jan M L Martin
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Reḥovot, 7610001, Israel
| |
Collapse
|
7
|
Santra G, Martin JML. Do Double-Hybrid Functionals Benefit from Regularization in the PT2 Term? Observations from an Extensive Benchmark. J Phys Chem Lett 2022; 13:3499-3506. [PMID: 35417181 PMCID: PMC9036584 DOI: 10.1021/acs.jpclett.2c00718] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
We put to the test a recent suggestion [Shee, J., et al. J. Phys. Chem. Lett. 2021, 12 (50), 12084-12097] that MP2 regularization might improve the performance of double-hybrid density functionals. Using the very large and chemically diverse GMTKN55 benchmark, we find that κ-regularization is indeed beneficial at lower percentages of Hartree-Fock exchange, especially if spin-component scaling is not applied [such as in B2GP-PLYP or ωB97M(2)]. This benefit dwindles for DSD and DOD functionals and vanishes entirely in the ∼70% HF exchange region optimal for them.
Collapse
|
8
|
Prokopiou G, Hartstein M, Govind N, Kronik L. Optimal Tuning Perspective of Range-Separated Double Hybrid Functionals. J Chem Theory Comput 2022; 18:2331-2340. [PMID: 35369687 PMCID: PMC9009176 DOI: 10.1021/acs.jctc.2c00082] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2022] [Indexed: 11/29/2022]
Abstract
We study the optimal tuning of the free parameters in range-separated double hybrid functionals, based on enforcing the exact conditions of piecewise linearity and spin constancy. We find that introducing the range separation in both the exchange and the correlation terms allows for the minimization of both fractional charge and fractional spin errors for singlet atoms. The optimal set of parameters is system specific, underlining the importance of the tuning procedure. We test the performance of the resulting optimally tuned functionals for the dissociation curves of diatomic molecules. We find that they recover the correct dissociation curve for the one-electron system, H2+, and improve the dissociation curves of many-electron molecules such as H2 and Li2, but they also yield a nonphysical maximum and only converge to the correct dissociation limit at very large distances.
Collapse
Affiliation(s)
- Georgia Prokopiou
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Michal Hartstein
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Niranjan Govind
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Leeor Kronik
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| |
Collapse
|