Emmanouil Semidalas

We investigated the energetics and bonding of lithium hydride clusters (LiH)n (n = 1–6) using a composite ab initio scheme inspired by W2 theory to achieve sub-kcal/mol accuracy. This approach combines CCSD(T) results extrapolated to the complete basis set limit with a rigorous treatment of core–valence correlation, scalar relativistic effects, and the diagonal Born–Oppenheimer correction. Our results show that while Hartree–Fock theory captures the primary electrostatic binding, correlation effects are crucial for determining the energetic preference of compact isomers over cyclic rings. A parallel density functional theory study shows that while standard hybrid functionals like B3LYP-D4 and M06-2X exhibit larger deviations, the double-hybrid revDSD-PBEP86-D4 functional closely matches our benchmarks, delivering sub-kcal/mol accuracy. Structural and chemical bonding analyses, including intrinsic bond orbital, nucleus-independent chemical shift, and many-body expansion (MBE) methods, reveal high ionic character and multi-center bonding (3c–2e and 4c–2e) within the (LiH)n clusters. MBE analysis of the interaction energy of the monocyclic clusters with respect to the LiH molecules reveals that the two- and three-body terms are consistently negative (stabilizing), while all higher-order terms are negligible. We find that σ-aromaticity in these systems is predominantly local and bond-centered. As the rings expand, the interior becomes magnetically decoupled from the σ-skeleton, precluding the formation of a global ring current. These results establish definitive benchmarks for the stability of prototypical electron-deficient clusters.

We present the development of local natural orbital (LNO)-based arbitrary order coupled cluster (CC) methods and a rigorous assessment of the beyond CCSD(T)-level correlation through LNO-CCSDTQ. Both the closed- and open-shell implementations inherit from our LNO family of methods the asymptotically linear-scaling framework, support for point group symmetry, multilevel embedding, as well as greatly reduced memory and disk use. The accuracy of LNO approximations and basis set completeness is benchmarked for thermochemistry and noncovalent interactions through CCSDTQ. Even for complicated atomizations and barrier heights, the CCSDT–CCSD(T), (Q), and especially the CCSDT(Q)–CCSD(T) contributions are obtained reliably within 85–95% relative and 0.05–0.1 kcal/mol absolute accuracy, already with the default LNO threshold set. Tightening LNO settings generally improves this performance, useful when aiming at high relative accuracy in even smaller effects, such as in noncovalent interactions or when pursuing the basis set limit of post-CCSD(T) atomization contributions. Thus, the LNO approximation greatly expands the reach of post-CCSD(T) methods, especially beyond a few atoms and small (double-ζ) basis sets, i.e., above ca. 100 orbitals. For example, via our multilevel approach, we report an unprecedented CCSDT(Q)–CCSD(T) reaction energy correction computation for a real-life enzyme reaction. Thus, LNO-based higher-order CC methods enable thermochemistry protocols aiming at kJ/mol accuracy for practical, 3D molecular systems that are much larger than previously accessible.

We present the development of local natural orbital (LNO) based arbitrary-order coupled-cluster (CC) methods, and rigorous assessment of the beyond CCSD(T)-level correlation through LNO-CCSDTQ. Both the closed-and open-shell implementations inherit from our LNO family of methods the asymptotically linear-scaling framework, support for point group symmetry, multi-level embedding, as well as greatly reduced memory and disk use. The accuracy of LNO approximations and basis set completeness is benchmarked for thermochemistry and non-covalent interactions through CCSDTQ. Even for complicated atomizations and barrier heights, the CCSDT−CCSD(T), (Q), and especially the CCSDT(Q)−CCSD(T) contributions are obtained reliably within 85-95% relative and 0.05-0.1 kcal/mol absolute accuracy, already with the default LNO threshold set. Tightening LNO settings generally improves this performance, useful when aiming at high relative accuracy in even smaller effects, such as in non-covalent interactions or when pursuing the basis set limit of post-CCSD(T) atomization contributions. Thus, the LNO approximation greatly expands the reach of post-CCSD(T) methods, especially beyond a few atoms and small (double-ζ) basis sets, i.e., above ca. 100 orbitals. For example, via our multi-level approach, we report an unprecedented CCSDT(Q)−CCSD(T) reaction energy correction computation for a real-life enzyme reaction. Thus, LNO-based higher-order CC methods enable thermochemistry protocols aiming at kJ/mol accuracy for practical, 3D molecular systems that are much larger than previously accessible.

We present the development of local natural orbital (LNO) based arbitrary-order coupled-cluster (CC) methods, and rigorous assessment of the beyond CCSD(T)-level correlation through LNO-CCSDTQ. Both the closed-and open-shell implementations inherit from our LNO family of methods the asymptotically linear-scaling framework, support for point group symmetry, multi-level embedding, as well as greatly reduced memory and disk use. The accuracy of LNO approximations and basis set completeness is benchmarked for thermochemistry and non-covalent interactions through CCSDTQ. Even for complicated atomizations and barrier heights, the CCSDT−CCSD(T), (Q), and especially the CCSDT(Q)−CCSD(T) contributions are obtained reliably within 85-95% relative and 0.05-0.1 kcal/mol absolute accuracy, already with the default LNO threshold set. Tightening LNO settings generally improves this performance, useful when aiming at high relative accuracy in even smaller effects, such as in non-covalent interactions or when pursuing the basis set limit of post-CCSD(T) atomization contributions. Thus, the LNO approximation greatly expands the reach of post-CCSD(T) methods, especially beyond a few atoms and small (double-ζ) basis sets, i.e., above ca. 100 orbitals. For example, via our multi-level approach, we report an unprecedented CCSDT(Q)−CCSD(T) reaction energy correction computation for a real-life enzyme reaction. Thus, LNO-based higher-order CC methods enable thermochemistry protocols aiming at kJ/mol accuracy for practical, 3D molecular systems that are much larger than previously accessible.

We have investigated the title question for both a subset of the W4‐11 total atomization energies benchmark, and for the A24x8 noncovalent interactions benchmark. Overall, counterpoise corrections to post‐CCSD(T) contributions are about two orders of magnitude less important than those to the CCSD(T) interaction energy. Counterpoise corrections for connected quadruple substitutions (Q) are negligible, and or especially so. In contrast, for atomization energies, the counterpoise correction can reach about 0.05 kcal/mol for small basis sets like cc‐pVDZ, thought it rapidly tapers off with cc‐pVTZ and especially aug‐cc‐pVTZ basis sets. It is reduced to insignificance by the extrapolation of applied in both W4 and HEAT thermochemistry protocols. In noncovalent dimers, the differential BSSE on post‐CCSD(T) correlation contributions is negligible even in basis sets as small as the unpolarized split‐valence cc‐pVDZ(no d).

While limited coupled cluster theory is \textit{formally} nonvariational, it is not broadly appreciated whether this is a major issue \textit{in practice}. We carried out a detailed comparison with \textit{de facto} full CI energies for a relatively large and diverse set of molecules. Fully iterative limited CC methods such as CCSDT, CCSDTQ, CCSDTQ5 do represent practical upper bounds to the FCI energy. While quasiperturbative approaches such as CCSD(T) and especially CCSDT(Q) may significantly over-correlate molecules if there is significant static correlation, this is much less of an issue with Lambda approaches such as CCSDT(Q)$Λ$.

Basis set extrapolations are typically rationalized either from analytical arguments involving the partial-wave or principal expansions of the correlation energy in helium-like systems or from fitting extrapolation parameters to reference energetics for a small(ish) training set. Seeking to avoid both, we explore a third alternative: extracting extrapolation parameters from the requirement that the BSSE (basis set superposition error) should vanish at the complete basis set limit. We find this to be a viable approach provided that the underlying basis sets are not too small and reasonably well balanced. For basis sets not augmented by diffuse functions, BSSE minimization and energy fitting yield quite similar parameters.

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.

We present correlationconsistent basis sets for explicitly correlated(F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. Thecc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contractedto [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wisare [9s8p6d3f2g] for the 3d-blockelements and [7s7p6d3f2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wisbasis sets are evaluated on challenging test sets for metal-organicbarrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). InF12 calculations, they are found to be about as close to the completebasis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). Whileour basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexesthat contain only one or two transition metals among dozens of main-groupelements; however, it is somewhat more significant for metal clusters.