1
|
Grotjahn R, Purnomo J, Jin D, Lutfi N, Furche F. Chemically Accurate Singlet-Triplet Gaps of Arylcarbenes from Local Hybrid Density Functionals. J Phys Chem A 2024; 128:6046-6060. [PMID: 39012067 DOI: 10.1021/acs.jpca.4c02852] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/17/2024]
Abstract
Singlet-triplet (ST) gaps are key descriptors of carbenes, because their properties and reactivity are strongly spin-dependent. However, the theoretical prediction of ST gaps is challenging and generally thought to require elaborate correlated wave function methods or double-hybrid density functionals. By evaluating two recent test sets of arylcarbenes (AC12 and AC18), we show that local hybrid functionals based on the "common t" local mixing function (LMF) model achieve mean absolute errors below 1 kcal/mol at a computational cost only slightly higher than that of global hybrid functionals. An analysis of correlation contributions to the ST gaps suggests that the accuracy of the common t-LMF model is mainly due to an improved description of nondynamical correlation which, unlike exchange, is not additive in each spin-channel. Although spin-nonadditivity can be achieved using the local spin polarization alone, using the "common", i.e., spin-unresolved, iso-orbital indicator t for constructing the LMF is found to be critical for consistent accuracy in ST gaps of arylcarbenes. The results support the view of LHs as vehicles to improve the description of nondynamical correlation rather than sophisticated exchange mixing approaches.
Collapse
Affiliation(s)
- Robin Grotjahn
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Justin Purnomo
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Dayun Jin
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Nicolas Lutfi
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Filipp Furche
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| |
Collapse
|
2
|
Richter R, Aschebrock T, Schelter I, Kümmel S. Meta-generalized gradient approximations in time dependent generalized Kohn-Sham theory: Importance of the current density correction. J Chem Phys 2023; 159:124117. [PMID: 38127400 DOI: 10.1063/5.0167972] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2023] [Accepted: 09/07/2023] [Indexed: 12/23/2023] Open
Abstract
We revisit the use of Meta-Generalized Gradient Approximations (mGGAs) in time-dependent density functional theory, reviewing conceptual questions and solving the generalized Kohn-Sham equations by real-time propagation. After discussing the technical aspects of using mGGAs in combination with pseudopotentials and comparing real-space and basis set results, we focus on investigating the importance of the current-density based gauge invariance correction. For the two modern mGGAs that we investigate in this work, TASK and r2SCAN, we observe that for some systems, the current density correction leads to negligible changes, but for others, it changes excitation energies by up to 40% and more than 0.8 eV. In the cases that we study, the agreement with the reference data is improved by the current density correction.
Collapse
Affiliation(s)
- Rian Richter
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| | - Thilo Aschebrock
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| | - Ingo Schelter
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| | - Stephan Kümmel
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| |
Collapse
|
3
|
Hofmann F, Kümmel S. Molecular excitations from meta-generalized gradient approximations in the Kohn-Sham scheme. J Chem Phys 2020; 153:114106. [PMID: 32962375 DOI: 10.1063/5.0023657] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
Meta-Generalized Gradient Approximations (meta-GGAs) can, in principle, include spatial and temporal nonlocality in time-dependent density functional theory at a much lower computational cost than functionals that use exact exchange. We here test whether a meta-GGA that has recently been developed with a focus on capturing nonlocal response properties and the particle number discontinuity can realize such features in practice. To this end, we extended the frequency-dependent Sternheimer formalism to the meta-GGA case. Using the Krieger-Li-Iafrate (KLI) approximation, we calculate the optical response for the selected paradigm molecular systems and compare the meta-GGA Kohn-Sham response to the one found with exact exchange and conventional (semi-)local functionals. We find that the new meta-GGA captures important properties of the nonlocal exchange response. The KLI approximation, however, emerges as a limiting factor in the evaluation of charge-transfer excitations.
Collapse
Affiliation(s)
- Fabian Hofmann
- Theoretical Physics IV, University of Bayreuth, D-95440 Bayreuth, Germany
| | - Stephan Kümmel
- Theoretical Physics IV, University of Bayreuth, D-95440 Bayreuth, Germany
| |
Collapse
|
4
|
Yamamoto Y, Salcedo A, Diaz CM, Alam MS, Baruah T, Zope RR. Assessing the effect of regularization on the molecular properties predicted by SCAN and self-interaction corrected SCAN meta-GGA. Phys Chem Chem Phys 2020; 22:18060-18070. [PMID: 32760934 DOI: 10.1039/d0cp02717k] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Recent regularization of the SCAN meta-GGA functional (rSCAN) has simplified the numerical complexities of the SCAN functional, alleviating SCAN's stringent demand on the numerical integration grids to some extent. The regularization of rSCAN, however, results in the breaking of some constraints such as the uniform electron gas limit, the slowly varying density limit, and coordinate scaling of the iso-orbital indicator. Here, we assess the effects of regularization on the electronic, structural, vibrational, and magnetic properties of molecules by comparing the SCAN and rSCAN predictions. The properties studied include atomic energies, atomization energies, ionization potentials, electron affinities, barrier heights, infrared intensities, dissociation and reaction energies, spin moments of molecular magnets, and isomer ordering of water clusters. Our results show that rSCAN requires less dense numerical grids and gives very similar results to those of SCAN for all properties examined with the exception of atomization energies, which are worsened in rSCAN. We also examine the performance of self-interaction-corrected (SIC) rSCAN with respect to SIC-SCAN using the Perdew-Zunger (PZ) SIC method. The PZSIC method uses orbital densities to compute one-electron self-interaction errors and places an even more stringent demand on numerical grids. Our results show that SIC-rSCAN gives marginally better performance than SIC-SCAN for almost all properties studied in this work with numerical grids that are on average half or less as dense as that needed for SIC-SCAN.
Collapse
Affiliation(s)
- Yoh Yamamoto
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA.
| | - Alan Salcedo
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA.
| | - Carlos M Diaz
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA. and Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Md Shamsul Alam
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA. and Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA. and Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R Zope
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA. and Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| |
Collapse
|
5
|
How does SCAN compare to PBE in the framework of parameter-free spin-opposite-scaled double-hybrids? Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2019.136898] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
6
|
Lou P, Lee JY. Origin of structural stability of ScH 3 molecular nanowires and their chemical-bonding behavior: Correlation effects of the Sc 3d electrons. J Chem Phys 2019; 150:184307. [PMID: 31091917 DOI: 10.1063/1.5093446] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
A new stable transition-metal trihydride (ScH3) molecular nanowire was recently reported by Li et al. [J. Am. Chem. Soc. 139, 6290-6293 (2017)]. Of the two typical structures (T-ScH3 and O-ScH3), T-ScH3 is more stable than O-ScH3. However, the reason why O-ScH3 is less stable than T-ScH3 was not known. Using Perdew-Burke-Ernzerhof (PBE), PBE+U, SCAN, and HSE06, as well as crystal orbital Hamilton populations (COHPs), we investigate the orbital-projected band structures and chemical bonding of T-ScH3 and O-ScH3. It is found that the energies calculated by PBE, SCAN, and HSE06 indeed reveal that T-ScH3 is more stable than O-ScH3, and there is no occupied antibonding state at the Fermi level of the COHP curves of T-ScH3, supporting the stable Sc-H bonding of T-ScH3. To the contrary, the Sc-H bonding of O-ScH3 is unstable because there exist occupied antibonding states at the Fermi level of the COHP curves of O-ScH3. We found that the results of PBE+U are consistent with those of PBE, SCAN, and HSE06 in the case of U < Uc. However, when U > Uc, the results of PBE+U are opposite to those of PBE, SCAN, and HSE06.
Collapse
Affiliation(s)
- Ping Lou
- Department of Chemistry, Sungkyunkwan University, Suwon 440-746, South Korea
| | - Jin Yong Lee
- Department of Chemistry, Sungkyunkwan University, Suwon 440-746, South Korea
| |
Collapse
|
7
|
Carmona-Espíndola J, Gázquez JL, Vela A, Trickey SB. Generalized Gradient Approximation Exchange Energy Functional with Near-Best Semilocal Performance. J Chem Theory Comput 2018; 15:303-310. [PMID: 30481469 DOI: 10.1021/acs.jctc.8b00998] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
We develop and validate a nonempirical generalized gradient approximation (GGA) exchange (X) density functional that performs as well as the SCAN (strongly constrained and appropriately normed) meta-GGA on standard thermochemistry tests. Additionally, the new functional (NCAP, nearly correct asymptotic potential) yields Kohn-Sham eigenvalues that are useful approximations of the density functional theory (DFT) ionization potential theorem values by inclusion of a systematic derivative discontinuity shift of the X potential. NCAP also enables time-dependent DFT (TD-DFT) calculations of good-quality polarizabilities, hyper-polarizabilities, and one-Fermion excited states without modification (calculated or ad hoc) of the long-range behavior of the exchange potential or other patches. NCAP is constructed by reconsidering the imposition of the asymptotic correctness of the X potential (-1/ r) as a constraint. Inclusion of derivative discontinuity and approximate integer self-interaction correction treatments along with first-principles determination of the effective second-order gradient expansion coefficient yields a major advance over our earlier correct asymptotic potential functional [CAP; J. Chem. Phys. 2015 , 142 , 054105 ]. The new functional reduces a spurious bump in the CAP atomic exchange potential and moves it to distances irrelevantly far from the nucleus (outside the tail of essentially all practical basis functions). It therefore has nearly correct atomic exchange-potential behavior out to rather large finite distances r from the nucleus but eventually goes as - c/ r with an estimated value for the constant c of around 0.3, so as to achieve other important properties of exact DFT exchange within the restrictions of the GGA form. We illustrate the results with the Ne atom optimized effective potentials and with standard molecular benchmark test data sets for thermochemical, structural, and response properties.
Collapse
Affiliation(s)
- Javier Carmona-Espíndola
- Departamento de Química , CONACYT-Universidad Autónoma Metropolitana-Iztapalapa , Av. San Rafael Atlixco 186 , Ciudad de México 09340 , México
| | - José L Gázquez
- Departamento de Química , Universidad Autónoma Metropolitana-Iztapalapa , Av. San Rafael Atlixco 186 , Ciudad de México 09340 , México
| | - Alberto Vela
- Departamento de Química , Centro de Investigación y de Estudios Avanzados , Av. Instituto Politécnico Nacional 2508 , Ciudad de México 07360 , México
| | - S B Trickey
- Quantum Theory Project, Department of Physics and Deptartment of Chemistry , University of Florida , P.O. Box 118435, Gainesville , Florida 32611-8435 , United States
| |
Collapse
|
8
|
Hait D, Head-Gordon M. Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number. J Phys Chem Lett 2018; 9:6280-6288. [PMID: 30339010 DOI: 10.1021/acs.jpclett.8b02417] [Citation(s) in RCA: 65] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Approximate functionals used in practical density functional theory (DFT) deviate from the piecewise linear behavior of the exact functional for fractional charges. This deviation causes excess charge delocalization, which leads to incorrect densities, molecular properties, barrier heights, band gaps, and excitation energies. We present a simple delocalization function for characterizing this error and find it to be almost perfectly linear vs the fractional electron number for systems spanning in size from the H atom to the C12H14 polyene. This causes the delocalization energy error to be a quadratic polynomial in the fractional electron number, which permits us to assess the comparative performance of 47 popular and recent functionals through the curvature. The quadratic form further suggests that information about a single fractional charge is sufficient to eliminate the principal source of delocalization error. Generalizing traditional two-point information like ionization potentials or electron affinities to account for a third, fractional charge-based data point could therefore permit fitting/tuning of functionals with lower delocalization error.
Collapse
Affiliation(s)
- Diptarka Hait
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry , University of California , Berkeley , California 94720 , United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry , University of California , Berkeley , California 94720 , United States
- Chemical Sciences Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| |
Collapse
|