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Xi ZK, Ding YH, Tian X. Building a New Platform for Significantly Improving Performance of Hartree-Fock and CCSD(T) Correlation Energy Based on Two-Point Complete Basis Set Extrapolation Schemes. J Phys Chem A 2024. [PMID: 38686765 DOI: 10.1021/acs.jpca.4c01712] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/02/2024]
Abstract
The leading cause of high expense in gold standard coupled cluster theory is that calculations of electronic energies converge exceedingly slowly with an increased basis set size. Extrapolation principally allows for achieving higher-quality outcomes at reduced costs. Numerous extrapolation formulas have been developed, with attempts to predict energies up to the complete basis set limit. Unfortunately, since the intricate shape of the function hinges on the molecular properties with the highest angular momentum of the basis set, the accuracy of the extrapolated energies highly depends on the fitted empirical parameters, which rely on the quality of the data sets for fitting. In this work, to overcome the extrapolation deficiency caused by the very limited data sets and smaller basis sets in the early stages, we constructed a new benchmark platform that includes a broader data set of 183 species (containing open-shell, closed-shell, ionic, and neutral species) and a larger basis set up to aug-cc-pV6Z. The newly optimized parameters can significantly improve the energy-predictive abilities of ten published formulas. Notably, all ten formulas perform quite similarly under the new platform with the reoptimized parameters. Finally, we built an online calculator for researchers to use for these extrapolation schemes. Our work would reignite the interest and applications of the underestimated formulas.
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Affiliation(s)
- Zhao-Kai Xi
- †Key Laboratory of Carbon Materials of Zhejiang Province, Wenzhou Key Lab of Advanced Energy Storage and Conversion, Zhejiang Province Key Lab of Leather Engineering, College of Chemistry and Materials Engineering, Wenzhou University, Wenzhou 325035, P. R. China
| | - Yi-Hong Ding
- Key Laboratory of Carbon Materials of Zhejiang Province, Wenzhou Key Lab of Advanced Energy Storage and Conversion, Zhejiang Province Key Lab of Leather Engineering, College of Chemistry and Materials Engineering, Wenzhou University, Wenzhou 325035, P. R. China
- Institute of Theoretical Chemistry, Jilin University, Changchun 130023, P. R. China
| | - Xiao Tian
- School of Mathematics and Science, Hebei GEO University, Shijiazhuang 050031, P. R. China
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Varandas AJC. Carbon-[ n]Triangulenes and Sila-[ n]Triangulenes: Which Are Planar? J Phys Chem A 2023. [PMID: 37256705 DOI: 10.1021/acs.jpca.3c01820] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Using our recently suggested concept of a quasi-molecule ("tile") and, in the case of the planarity here at stake, its generalization to larger than tetratomics, we explain why carbon [n]triangulenes tend to be planar, while hybrids, where just a few or even all a- or b-type carbon atoms are silicon-substituted (sila-[n]triangulenes), tend to be planar/nonplanar when compared with the unsubstituted carbon-[n]triangulenes. Because other spin states of the parent carbon- and sila-[n]triangulenes tend to correlate with the same tiles, it is conjectured that no structural changes are expected to depend on their spin state. Other polycyclic and sila-compounds are also discussed.
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Affiliation(s)
- A J C Varandas
- School of Physics and Physical Engineering, Qufu Normal University, Qufu 273165, P. R. China
- Department of Physics, Universidade Federal do Espí rito Santo, 29075-910 Vitória, Brazil
- Department of Chemistry and Coimbra Chemistry Centre, University of Coimbra 3004-535 Coimbra, Portugal
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Rocha CMR, Linnartz H, Varandas AJC. Reconciling spectroscopy with dynamics in global potential energy surfaces: the case of the astrophysically relevant SiC_{2}. J Chem Phys 2022; 157:104301. [DOI: 10.1063/5.0096364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
SiC_{2} is a fascinating molecule due to its unusual bonding and astrophysical importance. In this work, we report the first global potential energy surface (PES) for ground-state SiC_{2} using the combined-hyperbolic-inverse-power-representation (CHIPR) method and accurate ab initio energies. The calibration grid data is obtained via a general dual-level protocol developed afresh herein that entails both coupled-cluster and multireference configuration interaction energies jointly extrapolated to the complete basis set limit. Such an approach is specially devised to recover much of the spectroscopy from the PES, while still permitting a proper fragmentation of the system to allow for reaction dynamics studies. Besides describing accurately the valence strongly-bound region that includes both the cyclic global minimum and isomerization barriers, the final analytic PES form is shown to properly reproduce dissociation energies,diatomic potentials, and long-range interactions at all asymptotic channels, in addition to naturally reflect the correct permutational symmetry of the potential. Bound vibrational state calculations have been carried out, unveiling an excellent match of the available experimental data on c-SiC_{2}(^{1}A_{1}). To further exploit the global nature of the PES, exploratory quasi-classical trajectory calculations for the endothermic C2 +Si → SiC+C reaction are also performed, yielding thermalized rate coefficients for temperatures up to 5000 K. The results hint for the prominence of this reaction in the innermost layers of the circumstellar envelopes around carbon-rich stars, thence conceivably playing therein a key contribution to the gas-phase formation of SiC, and eventually, solid SiC dust.
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Affiliation(s)
| | | | - António JC Varandas
- Departament of Chemistry, University of Coimbra Coimbra Chemistry Centre, Portugal
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Varandas AJC. From six to eight Π-electron bare rings of group-XIV elements and beyond: can planarity be deciphered from the "quasi-molecules" they embed? Phys Chem Chem Phys 2022; 24:8488-8507. [PMID: 35343978 DOI: 10.1039/d1cp04130d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Ab initio molecular orbital theory is used to study the structures of six and eight π-electron bare rings of group-XIV elements, and even larger [n]annulenes up to C18H18, including some of their mono-, di-, tri-, and tetra-anions. While some of the above rings are planar, others are nonplanar. A much spotlighted case is cyclo-octatetraene (C8H8), which is predicted to be nonplanar together with its heavier group-XIV analogues Si8H8 and Ge8H8, with the solely planar members of its family having the stoichiometric formulas C4Si4H8 and C4Ge4H8. A similar situation arises with the six π-electron bare rings, where benzene and substituted ones up to C3Si3H6 or so are planar, while others are not. However, the explanations encountered in the literature find support in ab initio calculations for such species, often rationalized from distinct calculated features. Using second-order Møller-Plesset perturbation theory and, when affordable (particularly tetratomics, which may allow even higher levels), the coupled-cluster method including single, double, and perturbative triple excitations, a common rationale is suggested based on a novel concept of quasi-molecules or the (3+4)-atom partition scheme. Any criticism of tautology is therefore avoided. The same analysis has also been successfully applied to even larger [n]annulenes, to their mixed family members involving silicon and germanium atoms, and to the C18 carbon ring. Furthermore, it has been extended to annulene anions to check the criteria of the popular Hückel rule for planarity and aromaticity. Exploratory work on cycloarenes is also reported. Besides a partial study of the involved potential energy surfaces, equilibrium geometries and harmonic vibrational frequencies have been calculated anew, for both the parent and the actual prototypes of the quasi-molecules.
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Affiliation(s)
- A J C Varandas
- School of Physics and Physical Engineering, Qufu Normal University, 273165 Qufu, China.,Department of Physics, Universidade Federal do Esp rito Santo, 29075-910 Vitória, Brazil.,Department of Chemistry, and Chemistry Centre, University of Coimbra, 3004-535 Coimbra, Portugal.
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Pansini FNN, Mota VC, Varandas AJC. Optimized Structural Data at the Complete Basis Set Limit via Successive Quadratic Minimizations. J Phys Chem A 2021; 125:10657-10666. [PMID: 34881905 DOI: 10.1021/acs.jpca.1c07596] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Two variants of a successive quadratic minimization method (SQM and c-SQM) are suggested to calculate the structural properties of molecular systems at the complete basis set (CBS) limit. When applied to H3+, H2O, CH2O, SH2, and SO2, they revealed CBS/(x1, x2) structural parameters that significantly surpass the raw ones calculated at the x2 basis set level. Such a performance has also been verified for the intricate case of the water dimer. Because the c-SQM method is system specific, thus showing somewhat enhanced results relative to the general SQM protocol, it can be of higher cost depending on the level of calibration used. Yet, it hardly surpasses the general quality of the results obtained with the cost-effective SQM method. Since the number of cycles required to reach convergence is relatively small, both schemes are simple to use and easily adaptable to any of the existing extrapolation schemes for the Hartree-Fock and correlation energies.
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Affiliation(s)
- F N N Pansini
- Departamento de Física, Universidade Federal do Espírito Santo, 29075-910 Vitória, Brazil
| | - V C Mota
- Departamento de Física, Universidade Federal do Espírito Santo, 29075-910 Vitória, Brazil
| | - A J C Varandas
- Departamento de Física, Universidade Federal do Espírito Santo, 29075-910 Vitória, Brazil.,School of Physics and Physical Engineering, Qufu Normal University, 273165 Qufu, People's Republic of China.,Department of Chemistry, Coimbra Chemistry Centre, University of Coimbra, 3004-535 Coimbra, Portugal
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Varandas AJC. Post-complete-basis-set extrapolation of conventional and explicitly correlated coupled-cluster energies: can the convergence to the CBS limit be diagnosed? Phys Chem Chem Phys 2021; 23:8717-8730. [PMID: 33876031 DOI: 10.1039/d1cp00538c] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We assess benchmark correlation energies for 130 systems in test sets A24 and TS-106 both with the canonical CCSD(T) and explicitly correlated CCSD(T)-F12 methods. Aiming at enhanced accuracy, the calculated raw energies from both sets are CBS extrapolated to the complete basis set (CBS) limit and subsequently post-CBS extrapolated. Attention is focused at total energies, since their accuracy reflects on that of the interaction energies. Using up to triple-ζ basis sets for CBS and an additional quadruple-ζ for post-CBS, the mean and standard unsigned deviations with canonical CCSD(T) theory are 0.257 ± 0.25 kcal mol-1, while the corresponding values for CCSD(T)-F12 in its F12a and F12b variants with specialized basis sets up to VQZ-F12 are 0.170 ± 0.13 kcal mol-1 and 0.048 ± 0.04 kcal mol-1. Although these show gains at post-CBS level that vary from 0.08 to 0.20 kcal mol-1 relative to their CCSD(T)/VXZ analogues, the convergence is somewhat less clear when extending the basis up to V5Z-F12, the highest-rung available: 0.220 ± 0.17 kcal mol-1 and 0.142 ± 0.08 kcal mol-1, in the same order. An explanation for the up to one order of magnitude smaller deviations in energy differences is detailed. Based on energy differences involving basis set pairs employed for extrapolating to the CBS limit, a convergence diagnostic is also suggested. Arising from irregularities in the basis set that directly correlate with non-dynamical correlation, the new diagnostic may complement popular ones that feature other aspects of correlation.
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Affiliation(s)
- A J C Varandas
- School of Physics and Physical Engineering, Qufu Normal University, 273165 Qufu, China
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Varandas AJC. Canonical and explicitly-correlated coupled cluster correlation energies of sub-kJ mol -1 accuracy via cost-effective hybrid-post-CBS extrapolation. Phys Chem Chem Phys 2021; 23:9571-9584. [PMID: 33885095 DOI: 10.1039/d1cp00357g] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Cost-effectiveness and accuracy are two basic pillars in electronic structure calculations. While cost-effectiveness enhances applicability, high accuracy is sustained when employing advanced computational tools. With the gold standard method of ab initio quantum chemistry at the focal point, canonical CCSD(T) and modern explicitly correlated CCSD(T)-F12 calculations are employed hand in hand to develop accurate hybrid post-CBS extrapolation schemes, which are validated using popular training sets involving a total of 130 molecules. By using raw valence-only calculations at CCSD(T)/VDZ and CCSD(T)/VQZ-F12 levels of theory, the novel scheme leads to the prediction of absolute energies that differ on average (-0.170 ± 0.224) kcal mol-1 from the highest affordable CCSD(T)-F12b/V(Q,5)Z-F12 extrapolations, but only (-0.048 ± 0.228) kcal mol-1 from the post-CBS extrapolated values based on CBS(D,T), CBS(D,Q) and CBS(T,Q) energies. From the cost-effectiveness standpoint, the approach is a kind of pseudo one-point extrapolation scheme since its cost is basically that of the highest-rung raw energy where it is based. Variants that imply no additional cost are also discussed, emerging h-pCBS(dt,dq)ab as the most effective. The approach can also be used with PNO-based local correlation methods that gained popularity due to allowing coupled-cluster calculations even for large molecules at reduced computational cost, namely local PNO-CCSD(T) and PNO-CCSD(T)-F12b. To gauge the approach performance, both the hydrogen molecule and the O-C2H5 torsion path of ethyl-methyl-ether, an extra molecule here considered with presupposed existence in astrophysical objects, are also studied. Additionally, the nonbonding interactions in the A24 test set are revisited per se. The results show that the title approach may be useful in high-accuracy quantum chemistry, with further improvements requiring the inclusion of contributions beyond the theory here employed such as the ones due to relativistic and nonadiabatic effects.
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Affiliation(s)
- A J C Varandas
- School of Physics and Physical Engineering, Qufu Normal University, 273165 Qufu, China
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