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We have investigated the effect of F12 geminals on the basis set convergence of harmonic frequencies calculated using two representative double-hybrid density functionals, namely B2GP-PLYP and revDSD-PBEP86-D4. Like previously found for energetics [N. Mehta and J. M. L. Martin, \textit{J. Chem. Theor. Comput.} \textbf{18}, 5978--5991 (2022)] one sees an acceleration by two zeta steps, such that even the cc-pVDZ-F12 basis set is quite close to the complete basis set (CBS) limit. However, the basis set convergence problem is not as acute as for energetics, and compared to experimental harmonic frequencies, conventional orbital calculations with augmented triple zeta quality basis set are acceptably close to the CBS limit, and can be carried out using analytical second derivatives. An efficient implementation of double hybrid-F12 analytical derivatives would make the F12 approach attractive in the sense that even an $spd$ orbital basis set would be adequate. For the accurate revDSD-PBEP86-D4 functional, the role of differing local correlation terms (Perdew-Zunger 1981 vs. VWN5) in different electronic structure programs has been investigated: while optimal double hybrid parameters and performance statistics for energetics as well as frequencies differ slightly between the two implementations, these differences are insignificant for practical purposes., Can. J. Chem., minor revision (WATOC 2022 special issue)

Following earlier work [Mehta, N.; Martin, J. M. L.; J. Chem. Theory Comput. 2022, 18, acs.jctc.2c00426] that showed how the slow basis set convergence of double hybrid density functional theory can be obviated by the use of F12 explicit correlation in the GLPT2 step (second order G\"orling-Levy perturbation theory), we demonstrate here, for the very large and chemically diverse GMTKN55 benchmark suite, and using the B2GP-PLYP-D3BJ functional as a proof of principle, that the CPU time scaling of this step can be reduced (asymptotically linearized) using the PNO-L (pair natural orbitals, localized) approximation, at negligible cost in accuracy., Comment: Published version [Open Access CC:BY 4.0]

The S66 non-covalent interactions are studied through localized coupled-cluster methods and general LNO-CCSD(T)-based composite schemes. Very small RMS deviations (\leq 0.05 kcal/mol) for the low-cost composite approaches from the SILVER reference interaction energies of S66 indicate that we can safely avoid carrying out the largest basis set calculations with veryVeryTight thresholds, and apply instead additivity corrections in smaller basis sets. Interestingly, the counterpoise corrections do not have an appreciable effect on the composite schemes. These findings may prove useful for intermolecular and intramolecular NCIs of larger systems., 6 pages, AIP Conference Proceedings, in press (ICCMSE-2021)

We propose here a DFT-based diagnostic for static correlation %TAEX[TPSS@HF - HF] which effectively measures how different the DFT and HF exchange energies for a given HF density are. This and %TAEcorr[TPSS] are two cost-effective a priori estimates for the adequacy of the importance of static correlation. %TAEX[TPSS@HF - HF] contains nearly the same information as the earlier A diagnostic, but may be more intuitive to understand. Principal component and variable clustering analysis of a large number of static correlation diagnostics reveals much of the variation is explained by just two components, and almost all of it by four; these are blocked by four variable clusters (single excitations; correlation entropy; double excitations; pragmatic energetics)., 5 pages, AIP Conference Proceedings, in press (ICCMSE-2021)

The total atomization energy of a molecule is the thermochemical cognate of the heat of formation in the gas phase, its most fundamental thermochemical property. We decompose it into different components and provide a survey of them. It emerges that the connected triple excitations contribution is the third most important one, about an order of magnitude less important than the "big two" contributions (mean-field Hartree-Fock and valence CCSD correlation), but 1-2 orders of magnitude more important than the remainder. For the 200 total atomization energies of small molecules in the W4-17 benchmark, we have investigated the basis set convergence of the connected triple excitations contribution (T). Achieving basis set convergence for the valence triple excitations energy is much easier than for the valence singles and doubles correlation energy. Using reference data obtained from spdfghi and spdfghik basis sets, we show that extrapolation from quintuple-zeta and sextuple-zeta yields values within about 0.004 kcal/mol RMS. Convergence to within about 0.01 kcal/mol is achievable with quadruple- and quintuple-zeta basis sets, and to within about 0.05 kcal/mol with triple- and quadruple-zeta basis sets. It appears that radial flexibility in the basis set is more important here than adding angular momenta L: apparently, replacing nZaPa basis sets with truncations of 7ZaPa at L=n gains about one angular momentum for small values of n. We end the article with a brief outlook for the future of accurate electronic structure calculations., Comment: chapter for upcoming Springer book "Quantum Science-Frontier of Chemistry and Physics", edited by Taku Onishi. Revised version with additional background sections requested by editor

While the inclusion of the nonlocal correlation in fifth rung "double hybrid" functionals is definitely beneficial, one might rightfully ask whether its evaluation in the basis of Kohn-Sham (KS) orbitals has additional value compared to the use of Hartree-Fock reference orbitals (in a type of multilevel scheme). We have investigated this question for a very large and chemically diverse dataset, GMTKN55. We conclude that KS reference orbitals are undoubtedly beneficial, but the benefit is not as large as one might intuitively expect., Comment: 4 pages, AIP Conference Proceedings, in press (ICCMSE-2021)

Localized orbital coupled cluster theory has recently emerged as an nonempirical alternative to DFT for large systems. Intuitively, one might expect such methods to perform less well for highly delocalized systems. In the present work, we apply both canonical CCSD(T) and a variety of localized approximations thereto to a set of expanded porphyrins -- systems that can switch between H��ckel, figure-eight, and M��bius topologies under external stimuli. Both minima and isomerization transition states are considered. We find that M��bius(-like) structures have much stronger static correlation character than the remaining structures, and that this causes significant errors in DLPNO-CCSD(T) and even DLPNO-CCSD(T1) approaches, unless TightPNO cutoffs are employed. If sub-kcal/mol reproduction of canonical relative energies is required even for M��bius-type systems (or other systems plagued by strong static correlation), then Nagy and Kallay's LNO-CCSD(T) method with "tight" settings can provide that, at much greater computational expense than either the PNO-LCCSD(T) or DLPNO-LCCSD(T) approaches but with still a much gentler CPU time scaling than canonical approaches. We would propose the present POLYPYR21 dataset as a benchmark for localized orbital methods, or more broadly, for the ability of lower-level methods to handle energetics with strongly varying degrees of static correlation., 27 pages; revised version. J. Chem. Theory. Comput., ASAP (2020)

Electronic coupling matrix elements are important to the theoretical description of electron transfer processes. However, they are notoriously difficult to obtain accurately from time-dependent density functional theory (TDDFT). Here, we use the HAB11 benchmark dataset of coupling matrix elements to assess whether TDDFT using optimally tuned range-separated hybrid functionals, already known to be successful for the description of charge transfer excitation energies, also allows for an improved accuracy in the prediction of coupling matrix elements. We find that this approach outperforms all previous TDDFT calculations, based on semi-local, hybrid or non-tuned range-separated hybrid functionals, with a remaining average deviation as low as ∼12%. We discuss potential sources for the remaining error.

Conformational energies of n-butane, n-pentane, and n-hexane have been calculated at the CCSD(T) level and at or near the basis set limit. Post-CCSD(T) contribution were considered and found to be unimportant. The data thus obtained were used to assess the performance of a variety of density functional methods. Double-hybrid functionals like B2GP-PLYP and B2K-PLYP, especially with a small Grimme-type empirical dispersion correction, are capable of rendering conformational energies of CCSD(T) quality. These were then used as a `secondary standard' for a larger sample of alkanes, including isopentane and the branched hexanes as well as key isomers of heptane and octane. Popular DFT functionals like B3LYP, B3PW91, BLYP, PBE, and PBE0 tend to overestimate conformer energies without dispersion correction, while the M06 family severely underestimates GG interaction energies. Grimme-type dispersion corrections for these overcorrect and lead to qualitatively wrong conformer orderings. All of these functionals also exhibit deficiencies in the conformer geometries, particularly the backbone torsion angles. The PW6B95 and, to a lesser extent, BMK functionals are relatively free of these deficiencies. Performance of these methods is further investigated to derive conformer ensemble corrections to the enthalpy function, $H_{298}-H_0$, and the Gibbs energy function, ${\rm gef}(T)\equiv - [G(T)-H_0]/T$, of these alkanes. While $H_{298}-H_0$ is only moderately sensitive to the level of theory, ${\rm gef}(T)$ exhibits more pronounced sensitivity. Once again, double hybrids acquit themselves very well., J. Phys. Chem. A, revised [Walter Thiel festschrift]

In this 2nd chapter of the book Quantum Mechanical Prediction of Thermochemical Data" (ed. Jerzy Cioslowski, Kluwer, 2001; ISBN 0-7923-7077-5), we review the nonempirical computational thermochemistry methods W1 and W2 theory and their variants. The chapter is made available online following a change in publisher E-print policy., Comment: 32 pages: differs only in minor formatting details from published book chapter. Posted online following purchase of Kluwer by Springer and move to "Romeo Green" policy

From large basis set coupled cluster calculations and a minor empirical adjustment, an anharmonic force field for silane has been derived that is consistently of spectroscopic quality ($\pm 1 cm^{-1}$ on vibrational fundamentals) for all isotopomers of silane studied. Inner-shell polarization functions have an appreciable effect on computed properties and even on anharmonic corrections. From large basis set coupled cluster calculations and extrapolations to the infinite-basis set limit, we obtain TAE_0=303.80 \pm 0.18 kcal/mol, which includes an anharmonic zero-point energy (19.59 kcal/mol), inner-shell correlation (-0.36 kcal/mol), scalar relativistic corrections (-0.70 kcal/mol), and atomic spin-orbit corrections (-0.43 kcal/mol). In combination with the recently revised \HVSI{0}, we obtain $\Delta H^{\circ}_{f,0}[SiH_4(g)]=9.9 \pm 0.4 kcal/mol$, in between the two established experimental values., Comment: Mol. Phys., in press

By judicious use of extrapolations to the 1-particle basis set limit and $n$-particle calibration techniques, total atomization energies of molecules with up to four heavy atoms can be obtained with calibration accuracy (1 kJ/mol or better, on average) without any empirical correction. For the SCF energy a 3-point geometric extrapolation is the method of choice. For the MP2 correlation energy, a 2-point $A+B/(l+1/2)^3$ extrapolation is recommended, while for CCSD and CCSD(T) correlation energies we prefer the 3-point $A+B/(l+1/2)^C$ formula. Addition of high-exponent `inner polarization functions' to second-row atoms is essential for reliable results. For the highest accuracy, accounts are required of inner-shell correlation, atomic spin-orbit splitting, anharmonicity in the zero-point energy, and scalar relativistic effects., 43 pages, in upcoming NATO ASI volume "Energetics of stable molecules and reactive intermediates" (ed. M. E. Minas da Piedade)