arXiv subjects

Jan M. L. Martin

Publications and source records attributed to Jan M. L. Martin.

At least 19 recordsLinked to original sources

arXiv2026

Intermolecular Interactions of Large Systems: Boron Nitrides, Acenes, and Coronenes

In a recent contribution [Fishman, V.; Lesiuk, M.; Martin, J.M.L.; Boese, A.D., J. Chem. Theory Comput. 2025, 21, 2311-2324], we introduced another angle at benchmarking non-covalent interactions by not just benchmarking interaction energies of different species, but by considering the evolution of interaction energies with increasing system size. Here, we extend the benchmark set to more species, such as electrostatically bound borazine dimers as well as the minima structures of parallel displaced acene and coronene dimers. While the minimum structures of the parallel displaced acene dimers yield similar results to previously published sandwich-structured acenes, the borazine dimers behave vastly different, yielding yet a more complete picture on non-covalent interactions and their scalability. In contrast, the polycyclic aromatic hydrocarbon structures -- coronenes sandwich-stacked and coronenes parallel displaced -- give results consistent with those obtained for both types of the polyacene series, resulting in an updated estimate for the coronene dimer energy.

physics.chem-ph↗

arXiv2026

A new open-shell CCSDTQ implementation and its application to the basis set convergence of post-CCSDT(Q) corrections in computational thermochemistry

We extend the CCSDTQ implementation in CFOUR to UHF and ROHF references and demonstrate its efficiency. We apply it to basis set convergence of post-CCSDT(Q) corrections for the W4-08 thermochemical dataset. Convergence of (Q)$_Λ$--(Q) is relatively rapid. For difficult species (e.g., B2, O3), CCSDTQ--CCSDT(Q)$_Λ$ may converge more slowly than (5)$_Λ$, but the effects and and basis-set trends oppose each other. Consequently, a single-shot CCCSDTQ(5)$_Λ$-CCSDT(Q)$_Λ$ correction appears most efficient. For radicals with bifurcating UHF solutions, energetics of the `less spin-contaminated' solution are clearly more well-behaved. Alternatives to a single-shot CCSDTQ(5)$_Λ$--CCSDT(Q)$_Λ$ correction are evaluating (5)$_Λ$ either in a truncated cc-pVDZ(p,s) basis set, or by means of frozen natural orbitals. Our best computed adiabatic electron affinity of ozone is in excellent agreement with experiment.

physics.chem-ph↗

arXiv2026

FNO-CCSDTQ(5)$_Λ$ as an economical alternative for connected quintuple excitations contributions in coupled cluster thermochemistry

Contributions from connected quintuple excitations in coupled cluster theory can reach the 0.5 kcal/mol range, important enough to matter in accurate computational thermochemistry, yet the very steep $\propto N^{12}$ CPU time scaling impedes routine evaluation. We show that for the differential contribution of quintuples, convergence of a frozen natural orbital (FNO) expansion with respect to the NO cutoff is rapid enough to make FNO-CCSDTQ(5)$_Λ$ with cutoffs of 0.0025 or 0.001 viable alternatives. A naive extrapolation to zero cutoff from \{0.005,0.0025\} works surprisingly well as a low-cost option. Interestingly, FNO convergence is definitely slower for second-row than for first-row compounds.

physics.chem-ph↗

arXiv2026

Toward an affordable density-based measure for the quality of a coupled cluster calculation

We propose two new diagnostics for the degree to which static correlation impacts the quality of a coupled cluster calculation. The first is the change in the Matito static correlation diagnostic $\overline{I_{ND}}$ between CCSD and CCSD(T), $ΔI_{ND}[\textrm{(T)}]=\overline{I_{ND}}[\textrm{CCSD(T)}]-\overline{I_{ND}}[\textrm{CCSD}]$. The second is the ratio of the same and of the corresponding change in the total correlation diagnostic $\overline{I_{T}}=\overline{I_{ND}}+\overline{I_{D}}$, i.e., $r_I[(T)]=ΔI_{ND}[\textrm{(T)}]/ΔI_{T}[\textrm{(T)}]$. The first diagnostic can be extended to higher-order improvements in the wave function, e.g., $ΔI_{ND}[\textrm{(Q)}]=\overline{I_{ND}}[\textrm{CCSDT(Q)}]-\overline{I_{ND}}[\textrm{CCSDT}]$. In general, a small $ΔI_{ND}$[\textrm{level$_1$}] value indicates that at this level$_1$ of theory, the density is converged and any further changes to the energy come from dynamical correlation, while larger $ΔI_{ND}$[\textrm{level$_2$}] indicates that the density is still not converged at level$_2$ and some static correlation remains. $r_I[(T)]$ is found to be a moderately good predictor for the importance of post-CCSD(T) correlation effects.

physics.chem-ph↗

arXiv2026

pANO-F12: An atomic natural orbital-inspired route to more compact basis sets for F12 explicitly correlated methods

Explicitly correlated methods such as MP2-F12 and CCSD(F12*) exhibit much faster basis set convergence (asymptotically $\propto L^{-7}$, with L the highest angular momentum) than orbital-only approaches. Yet it has been pointed out that cc-pVnZ-F12 basis sets themselves are substantially larger than the corresponding cc-pVnZ, and specifically that cc-pVDZ-F12 is the size of cc-pVTZ. One way to generate compact basis sets in an orbital-only context are Atomic Natural Orbital (ANO) basis sets [J. Almlöf and P. R. Taylor, JCP 86, 4070 (1987)]. However, obtaining the required first-order reduced density matrix while properly accounting for the F12 geminal is problematic. In this work, we show that an energy minimization-based contraction process under linear independence constraints yields `pseudo-ANO' (pANO) basis sets that are functionally equivalent in quality. Subsequently, we apply this recipe to obtain pANO-F12 basis sets from the same elements, then validate them for several thermochemical benchmarks and for the hypersensitive out-of-plane vibrations of benzene. We show that, unlike cc-pVnZ-F12, pANO-F12 exhibits the familiar shell structure seen in cc-pVnZ and ANO basis sets, and that pANO-F12 offers a route to more compact F12 basis sets more amenable to medium-sized systems, especially in conjunction with localized pair natural orbital approaches. Overall, the pANO approach is most beneficial for the smaller double-and triple-zeta basis sets, offering either superior performance to cc-pVnZ-F12 at same cost, or similar performance at lower cost.

physics.chem-ph↗

arXiv2026

Coupling between thermochemical contributions of subvalence correlation and of higher-order post-CCSD(T) correlation effects -- a step toward `W5 theory'

We consider the thermochemical impact of post-CCSD(T) contributions to the total atomization energy (TAE, the sum of all bond energies) of first- and second-row molecules, and specifically their coupling with the subvalence correlation contribution. In particular, we find large contributions from (Q) when there are several neighboring second-row atoms. Otherwise, both higher-order triples $T_3$--(T) and connected quadruples (Q) are important in systems with strong static correlation. Reoptimization of the reference geometry for core-valence correlation increases the calculated TAE across the board, most pronouncedly so for second-row compounds with neighboring second-row atoms. %just slightly increases the calculated TAE for all species, but more pronouncedly so if strong static correlation is present, as well as for second-row compounds, again especially with neighboring second-row atoms. We present a first proposal for a `W5 theory' protocol and compare computed TAEs for the W4-08 benchmark with prior reference values. For some key second-row species, the new values represent nontrivial revisions. Our predicted TAE$_0$ values (TAE at 0 K) agree well with the ATcT (active thermochemical tables) values, including for the very recent expansion of the ATcT network to boron, silicon, and sulfur compounds.

physics.chem-ph↗

arXiv2025

Exploiting a Shortcoming of Coupled-Cluster Theory: The Extent of non-Hermiticity as a Diagnostic Indicator of Computational Accuracy

The fundamental non-Hermitian nature of the forms of coupled-cluster (CC) theory widely used in quantum chemistry has usually been viewed as a negative, but the present letter shows how this can be used to advantage. Specifically, the non-symmetric nature of the reduced one-particle density matrix (in the molecular orbital basis) is advocated as a diagnostic indicator of computational quality. In the limit of full coupled-cluster theory (which is equivalent to full configuration interaction (FCI)), the electronic wavefunction and correlation energy are exact within a given one-particle basis set and the symmetric character of the exact density matrix is recovered. The extent of the density matrix asymmetry is shown to provide a measure of ``how difficult the problem is'' (like the well-known T$_1$ diagnostic), but its variation with level of theory also gives information about ``how well this particular method works'', irrespective of the difficulty of the problem at hand. The proposed diagnostic is described and applied to a select group of small molecules, and an example of its overall utility for the practicing quantum chemist is illustrated through its application to the beryllium dimer (Be$_2$). Future applications of this idea to excited states, open-shell systems, symmetry-breaking problems and extension of the method to the two-particle density are then proposed.

physics.chem-ph↗

arXiv2025

Another Angle on Benchmarking Noncovalent Interactions

For noncovalent interactions (NCIs), the CCSD(T) coupled cluster method is widely regarded as the `gold standard'. With localized orbital approximations, benchmarks for ever larger NCI complexes are being published; yet tantalizing evidence from quantum Monte Carlo (QMC) results appears to indicate that as the system size grows, CCSD(T) overbinds NCIs by progressively larger amounts, particularly when $π$-stacking is involved. Alas, post-CCSD(T) methods like CCSDT(Q) are cost-prohibitive, which requires us to consider alternative means of estimating post-CCSD(T) contributions. In this work, we take a step back by considering the evolution of the correlation energy with respect to the number of subunits for such $π$-stacked sequences as acene dimers and alkadiene dimers. We show it to be almost perfectly linear, and propose the slope of the line as a probe for the behavior of a given electron correlation method. By comparison with rank-reduced CCSDT(Q) results for benzene and naphthalene dimers, we show that while CCSD(T) does slightly overbind, it does not at the level suggested by the QMC results.

physics.chem-ph↗

arXiv2025

Post-CCSD(T) corrections in the S66 noncovalent interactions benchmark

For noncovalent interactions, it is generally assumed that CCSD(T) is nearly the exact solution within the 1-particle basis set. For the S66 noncovalent interactions benchmark, we present for the majority of species CCSDT and CCSDT(Q) corrections with a polarized double-zeta basis set. For hydrogen bonds, pure London complexes, and mixed-influence complexes, CCSD(T) benefits from error cancellation between (usually repulsive) higher-order triples, $T_3 - (T)$, and (almost universally attractive) connected quadruples, (Q). For $π$-stacking complexes, this cancellation starts breaking down and CCSD(T) overbinds; CCSD(T)$_Λ$ corrects the problem at the expense of London complexes. A fairly simple two-parameter model predicts CCSDT(Q)--CCSD(T) differences to 0.01 kcal/mol RMS, requiring no calculations that scale more steeply than $O(N^7)$.

physics.chem-ph↗

arXiv2025

Exploring the Influence of (n-1)d Subvalence Correlation and of Spin-Orbit Coupling on Chalcogen Bonding

This article presents a comprehensive computational investigation into chalcogen bonding interactions, focusing specifically on elucidating the role of subvalence (n$-$1)d and (n$-$1)sp correlation. The incorporation of inner-shell (n$-$1)d correlation leads to a decrease in interaction energies for chalcogen-bonded systems (at least those studied herein), contradicting the observations regarding halogen bonding documented by Kesharwani et al. in \textit{J. Phys. Chem. A}, \textbf{2018}, 122 (8), 2184-2197. The significance of (n$-$1)sp subvalence correlation appears to be lower by an order of magnitude. Notably, among the various components of interaction energies computed at the PNO-LCCSD(T) or DF-CCSD levels, we identify the PNO-LMP2 or DF-MP2 component of the (n$-$1)d correlation as predominant. Furthermore, we delve into the impact of second-order spin-orbit coupling (SOC2) on these interactions. Specifically, for the Te complexes, SOC2 effects rival (n$-$1)d correlation in importance; for the Se complexes, SOC2 is much less important. Generally, SOC2 stabilizes monomers more than dimers, resulting in reduced binding of the latter. Notably, at equilibrium and stretched geometries, SOC2 and (n$-$1)d destabilize the complex; however, at compressed geometries, they exhibit opposing effects, with (n$-$1)d becoming stabilizing.

physics.chem-ph↗

arXiv2025

Does basis set superposition error significantly affect post-CCSD(T) corrections?

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 $(Q)_Λ- (Q)$ or $T_4 - (Q)$ especially so. In contrast, for atomization energies, the $T_3-(T)$ counterpoise correction can reach about 0.05 \kcalmol~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 $T_3-(T)$ 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).

physics.chem-ph↗

arXiv2024

How `Nonvariational' Are Approximate Coupled Cluster Methods In Practice?

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)$Λ$.

physics.chem-ph↗

arXiv2024

Basis set extrapolation from the vanishing counterpoise correction condition

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.

physics.chem-ph↗

arXiv2024

W4$Λ$: leveraging $Λ$ coupled cluster for accurate computational thermochemistry approaches

High-accuracy composite wavefunction methods like Weizmann-4 (W4) theory, high-accuracy extrapolated \textit{ab initio} thermochemistry (HEAT), and Feller-Peterson-Dixon (FPD) 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 lambda 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 W4$Λ$ and W4.3$Λ$ computational thermochemistry protocols.

physics.chem-ph↗

arXiv2024

On the sensitivity of computed partial charges toward basis set and (exchange-)correlation treatment

Partial charges are a central concept in general chemistry and chemical biology, yet dozens of different computational definitions exist. In prior work [M. Cho et al., \textit{ChemPhysChem} {\bf 21}, 688-696 (2020)], we showed that these can be reduced to at most three `principal components of ionicity'. The present study addressed the dependance on computed partial charges $q$ on 1-particle basis set and (for WFT methods) $n$-particle correlation treatment or (for DFT methods) exchange-correlation functional, for several representative partial charge definitions such as QTAIM, Hirshfeld, Hirshfeld-I, HLY (electrostatic), NPA, and APT. Our findings show that semi-empirical double hybrids can closely approach the CCSD(T) `gold standard' for this property. In fact, owing to an error compensation in MP2, CCSD partial charges are further away from CCSD(T) than is MP2. The non-local correlation is important, especially when there is a substantial amount of non-local exchange. Employing range separation provides no clear advantage, while global hybrids with 20-30\% Hartree-Fock exchange exhibit the best performance across all charge types. Basis set convergence analysis shows that an augmented triple-zeta haVTZ+d basis set is sufficient for Hirshfeld, Hirshfeld-I, HLY, and APT methods. In contrast, QTAIM and NPA display slower basis set convergence. It is noteworthy that for both NPA and QTAIM, HF exhibits the slowest basis set convergence when contrasted with the correlation components of MP2 and CCSD. Triples corrections in CCSD(T), denoted as CCSD(T)-CCSD, exhibit even faster basis set convergence.

physics.chem-ph↗

arXiv2023

Can G4-like Composite Ab Initio Methods Accurately Predict Vibrational Harmonic Frequencies?

Minimally empirical G4-like composite wavefunction theories [E. Semidalas and J. M. L. Martin, \textit{J. Chem. Theory Comput.} {\bf 16}, 4238-4255 and 7507-7524 (2020)] trained against the large and chemically diverse GMTKN55 benchmark suite have demonstrated both accuracy and cost-effectiveness in predicting thermochemistry, barrier heights, and noncovalent interaction energies. Here, we assess the spectroscopic accuracy of top-performing methods: G4-\textit{n}, cc-G4-\textit{n}, and G4-\textit{n}-F12, and validate them against explicitly correlated coupled cluster CCSD(T*)(F12*) harmonic vibrational frequencies and experimental data from the HFREQ2014 dataset, of small first- and second-row polyatomics. G4-T is three times more accurate than plain CCSD(T)/def2-TZVP, while G4-T$_{\rm ano}$ is two times superior to CCSD(T)/ano-pVTZ. Combining CCSD(T)/ano-pVTZ with MP2-F12 in a parameter-free composite scheme results to a root-mean-square deviation of ~5 cm$^{-1}$ relative to experiment, comparable to CCSD(T) at the complete basis set limit. Application to the harmonic frequencies of benzene reveals a significant advantage of composites with ANO basis sets -- MP2/ano-pV\textit{m}Z and [CCSD(T)-MP2]/ano-pVTZ (\textit{m} = Q or 5) -- over similar protocols based on CCSD(T)/def2-TZVP. Overall, G4-type composite energy schemes, particularly when combined with ANO basis sets in CCSD(T), are accurate and comparatively inexpensive tools for computational vibrational spectroscopy.

physics.chem-ph↗

arXiv2023

Post-CCSD(T) corrections to bond distances and vibrational frequencies: the power of $Λ$

The importance of post-CCSD(T) corrections as high as CCSDTQ56 for ground-state spectroscopic constants ($D_e$, $ω_e$, $ω_ex_e$, and $α_e$) has been surveyed for a sample of two dozen mostly heavy-atom diatomics spanning a broad range of static correlation strength. While CCSD(T) is known to be an unusually felicitous `Pauling point' between accuracy and computational cost, performance leaves something to be desired for molecules with strong static correlation. We find CCSDT(Q)$_Λ$ to be the next `sweet spot' up, of comparable or superior quality to the much more expensive CCSDTQ. A similar comparison applies to CCSDTQ(5)$_Λ$ vs. CCSDTQ5, while CCSDTQ5(6)$_Λ$ is essentially indistinguishable from CCSDTQ56. A composite of CCSD(T)-X2C/ACV5Z-X2C with [CCSDT(Q)$_Λ$ -- CCSD(T)]/cc-pVTZ or even cc-pVDZ basis sets appears highly effective for computational vibrational spectroscopy. Unlike CCSDT(Q) which breaks down for the ozone vibrational frequencies, CCSDT(Q)$_Λ$ handles them gracefully.

physics.chem-ph↗

arXiv2023

Is valence CCSD(T) enough for the binding of water clusters? The isomers of (H$_2$O)$_6$ and (H$_2$O)$_{20}$ as a case study

Benchmark calculations on noncovalent interactions typically exclude correlation effects beyond valence CCSD(T) owing to their steep computational cost scaling. In this work, we consider their importance for water clusters, specifically, eight isomers of (H$_2$O)$_6$ and four Wales-Hodges isomers of (H$_2$O)$_{20}$. Higher order connected triples, $T_3$--(T), reduce dissociation energies of the latter by about 0.4 kcal/mol, but this is more than compensated by an increase of up to 0.85 kcal/mol due to connected quadruple excitations. In general, higher-order correlation effects favor more compact isomers over more `spread-out' ones. We also consider additional small effects for balance: scalar relativistics reduce binding in (H$_2$O)$_{20}$ by ca. --0.4 kcal/mol, which fortuitously is compensated by the ca. 0.55 kcal/mol diagonal Born-Oppenheimer correction. Core-valence correlation has the greatest impact, at ca. 1.3 kcal/mol for the icosamer.

physics.chem-ph↗