Showing 1–50 of 98 results for author: Martin, J M

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

Authors: Vladimir Fishman, Jan M. L. Martin

Abstract: 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 gen… ▽ More 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. △ Less

Submitted 21 May, 2026; originally announced May 2026.

Comments: 33 pages draft; basis sets part of download package

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

Authors: Gregory H. Jones, Aditya Barman, Margarita Shepelenko, Jan M. L. Martin

Abstract: 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… ▽ More 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. △ Less

Submitted 25 June, 2026; v1 submitted 19 May, 2026; originally announced May 2026.

Comments: Revised MS for Chemical Physics Letters (minor revision)

Journal ref: Chem. Phys. Lett. 897, 142951 (2026)

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

Authors: Aditya Barman, Gregory H. Jones, Jan M. L. Martin

Abstract: 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 oppo… ▽ More 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. △ Less

Submitted 4 August, 2026; v1 submitted 19 May, 2026; originally announced May 2026.

Comments: CPL, in press (supporting information PDF appended; raw data included as .xlsx in source download)

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

Authors: Vladimir Fishman, Jan M. L. Martin, A. Daniel Boese

Abstract: 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 specie… ▽ More 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. △ Less

Submitted 30 June, 2026; v1 submitted 4 February, 2026; originally announced February 2026.

Comments: J. Phys. Chem. A, revised [Steve Scheiner festschrift]; sequel to https://doi.org/10.1021/acs.jctc.4c01512

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

Authors: Aditya Barman, Gregory H. Jones, Kaila E. Weflen, Margarita Shepelenko, Jan M. L. Martin

Abstract: 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 $T_3$--(… ▽ More 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. △ Less

Submitted 15 April, 2026; v1 submitted 5 January, 2026; originally announced January 2026.

Comments: J. Phys. Chem. A (John F. Stanton memorial issue), Open Access CC:BY

Journal ref: J. Phys. Chem. A 130, 2943-2955 (2026)

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

Authors: Gregory H. Jones, Kaila E. Weflen, Jan M. L. Martin

Abstract: 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 cha… ▽ More 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. △ Less

Submitted 4 June, 2026; v1 submitted 4 September, 2025; originally announced September 2025.

Comments: J. Phys. Chem. A 130, 4289-4298 (2026). [John F. Stanton memorial issue]. Open Access CC:BY

Journal ref: J. Phys. Chem. A 130, 4289-4298 (2026)

Prime Factorization Equation from a Tensor Network Perspective

Authors: Alejandro Mata Ali, Jorge Martínez Martín, Sergio Muñiz Subiñas, Miguel Franco Hernando, Javier Sedano, Ángel Miguel García-Vico

Abstract: This paper presents an exact and explicit tensor-network equation for the search of nontrivial divisors of a composite integer, together with an algorithm for its computation. The proposed method is based on the MeLoCoToN approach, which addresses combinatorial optimization problems through classical tensor networks. The presented tensor network tensorizes a binary multiplication circuit and proje… ▽ More This paper presents an exact and explicit tensor-network equation for the search of nontrivial divisors of a composite integer, together with an algorithm for its computation. The proposed method is based on the MeLoCoToN approach, which addresses combinatorial optimization problems through classical tensor networks. The presented tensor network tensorizes a binary multiplication circuit and projects its output onto the target integer to be factorized. Additionally, in order to make the algorithm more efficient, the number and dimension of the tensors and their contraction scheme are optimized, including a reduced auxiliary register that still preserves at least one valid factorization orientation. Finally, a series of tests on the algorithm are conducted, contracting the tensor network both exactly and approximately using tensor train compression, and evaluating its performance. △ Less

Submitted 30 April, 2026; v1 submitted 29 July, 2025; originally announced August 2025.

Comments: 17 pages, 12 figures, improved version with new demonstrations and better computational complexities

MSC Class: 65F99; 81P68; 94A60

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

Authors: Kaila E. Weflen, Megan R. Bentley, James H. Thorpe, Peter R. Franke, Jan M. L. Martin, Devin A. Matthews, John F. Stanton

Abstract: 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… ▽ More 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. △ Less

Submitted 14 May, 2025; v1 submitted 25 March, 2025; originally announced March 2025.

Comments: Published version, Open Access CC-BY 4.0. Senior author deceased March 21, 2025; last version approved by him, revised following referee comments

Journal ref: Journal of Physical Chemistry Letters 16, 5121-5127 (2025)

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

Authors: Emmanouil Semidalas, A. Daniel Boese, Jan M. L. Martin

Abstract: 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 cancellatio… ▽ More 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 $O(N^7)$. △ Less

Submitted 21 January, 2025; v1 submitted 18 November, 2024; originally announced November 2024.

Comments: Final published version, CC:BY Open Access

Journal ref: Chemical Physics Letters 863 (2025) 141874

Another Angle on Benchmarking Noncovalent Interactions

Authors: Vladimir Fishman, Michał Lesiuk, Jan M. L. Martin, A. Daniel Boese

Abstract: 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… ▽ More 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. △ Less

Submitted 26 February, 2025; v1 submitted 16 October, 2024; originally announced October 2024.

Comments: Published version in J. Chem. Theory Comput.; Open Access CC:BY 4.0

Journal ref: J. Chem. Theory Comput. 21, 2311-2324 (2025)

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

Authors: Jan M. L. Martin, Emmanouil Semidalas

Abstract: 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 e… ▽ More 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)$Λ$. △ Less

Submitted 2 October, 2024; originally announced October 2024.

Comments: 5 pages, ICCMSE-2024 conference proceedings

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

Authors: Vladimir Fishman, Emmanouil Semidalas, Margarita Shepelenko, Jan M. L. Martin

Abstract: 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 negligi… ▽ More 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). △ Less

Submitted 4 January, 2025; v1 submitted 19 August, 2024; originally announced August 2024.

Comments: Final published article under CC:BY license (Hans Lischka festschrift)

Journal ref: Journal of Computational Chemistry 46, e70006 (2025)

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

Authors: Nisha Mehta, Jan M. L. Martin

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

Submitted 16 January, 2025; v1 submitted 8 May, 2024; originally announced May 2024.

Comments: Final published version with inside journal cover. CC:BY open access. Special collection "Emerging Investigators" (Dr. Nisha Mehta is senior author)

Journal ref: Phys. Chem. Chem. Phys. 27, 1274-1283 (2025)

Basis set extrapolation from the vanishing counterpoise correction condition

Authors: Vladimir Fishman, Emmanouil Semidalas, Jan M. L. Martin

Abstract: 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 t… ▽ More 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. △ Less

Submitted 21 August, 2024; v1 submitted 7 May, 2024; originally announced May 2024.

Comments: J. Phys. Chem. A, ASAP (Gustavo E. Scuseria festschrift); CC:BY 4.0 Open Access

Journal ref: J. Phys. Chem. A 128, 7462-7470 (2024)

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

Authors: Emmanouil Semidalas, Amir Karton, Jan M. L. Martin

Abstract: 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 benc… ▽ More 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. △ Less

Submitted 11 April, 2024; v1 submitted 14 December, 2023; originally announced December 2023.

Comments: J. Phys. Chem. A 128, 1715-1724 (2024). PDF is CC:BY 4.0

Journal ref: J. Phys. Chem. A 128, 1715-1724 (2024)

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

Authors: Nisha Mehta, Jan M. L. Martin

Abstract: 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… ▽ More 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. △ Less

Submitted 4 April, 2024; v1 submitted 21 September, 2023; originally announced September 2023.

Comments: Final published manuscript (CC-BY Open Access); part of special correction in honor of Elfi Kraka

Journal ref: J. Comput. Chem. 45, 1017-1032 (2024)

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

Authors: Golokesh Santra, Margarita Shepelenko, Emmanouil Semidalas, Jan M. L. Martin

Abstract: 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 la… ▽ More 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. △ Less

Submitted 11 August, 2023; originally announced August 2023.

Comments: version updated from ResearchGate, now including 3-body contributions for water20

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

Authors: Emmanouil Semdalas, Jan M. L. Martin

Abstract: 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… ▽ More 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. △ Less

Submitted 22 September, 2023; v1 submitted 11 August, 2023; originally announced August 2023.

Comments: Molecular Physics, in press [Timothy J. Lee memorial issue]

Journal ref: Mol. Phys. 122, e2263593 (2024)

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

Authors: Maciej Spiegel, Emmanouil Semidalas, Jan M. L. Martin, Megan R. Bentley, John F. Stanton

Abstract: 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 some… ▽ More 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. △ Less

Submitted 22 August, 2023; v1 submitted 27 July, 2023; originally announced July 2023.

Comments: Mol. Phys., in press [Timothy J. Lee memorial issue]

Journal ref: Mol. Phys. 122, e2252114 (2024)

The importance of tight $f$ basis functions for heavy p-block oxides and halides: a parallel with tight $d$ functions in the second row

Authors: Nisha Mehta, Jan M. L. Martin

Abstract: It is well-known that both wavefunction ab initio and DFT calculations on second-row compounds exhibit anomalously slow basis set convergence unless the basis sets are augmented with additional `tight' (high-exponent) $d$ functions, as in the cc-pV($n+d$)Z and aug-cc-pV($n+d$)Z basis sets. This has been rationalized as being necessary for a better description of the low-lying $3d$ orbital, which a… ▽ More It is well-known that both wavefunction ab initio and DFT calculations on second-row compounds exhibit anomalously slow basis set convergence unless the basis sets are augmented with additional `tight' (high-exponent) $d$ functions, as in the cc-pV($n+d$)Z and aug-cc-pV($n+d$)Z basis sets. This has been rationalized as being necessary for a better description of the low-lying $3d$ orbital, which as the oxidation state increases sinks low enough to act as a back-donation acceptor from chalcogen and halogen lone pairs. This prompts the question whether a similar phenomenon exists for the isovalent compounds of the heavy p-block. We show that for the fourth and fifth row, this is the case, but this time for tight $f$ functions enhancing the description of the low-lying $4f$ and $5f$ Rydberg orbitals, respectively. In the third-row heavy $p$ block, the $4f$ orbitals are too far up, while the $4d$ orbitals are adequately covered by the basis functions already present to describe the $3d$ subvalence orbitals. △ Less

Submitted 25 April, 2023; v1 submitted 24 January, 2023; originally announced January 2023.

Comments: CC:BY 4.0 Open Access (Krishnan Raghavachari festschrift)

Journal ref: Journal of Physical Chemistry A 127 (9), 2104-2112 (2023)

A double-hybrid density functional based on good local physics with outstanding performance on the GMTKN55 database

Authors: Axel D. Becke, Golokesh Santra, Jan M. L. Martin

Abstract: In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and 157, 234102 (2022)] we compared two Kohn-Sham density functionals based on physical modelling and theory with the best density-functional power-series fits in the literature. The best error statistics reported to date for a hybrid functional on the GMTKN55 chemical database of Goerigk, Grimme, and coworkers [Phys. Chem. Chem.… ▽ More In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and 157, 234102 (2022)] we compared two Kohn-Sham density functionals based on physical modelling and theory with the best density-functional power-series fits in the literature. The best error statistics reported to date for a hybrid functional on the GMTKN55 chemical database of Goerigk, Grimme, and coworkers [Phys. Chem. Chem. Phys. 19, 32184 (2017)] were obtained. In the present work, additional second-order perturbation-theory terms are considered. The result is a 12-parameter double-hybrid (DH) density functional with the lowest GMTKN55 "WTMAD2" error yet seen for a DH functional. We call it "DH23". △ Less

Submitted 22 March, 2023; v1 submitted 3 January, 2023; originally announced January 2023.

Comments: 23 pages + supporting information, J. Chem. Phys., accepted

Journal ref: J. Chem. Phys. 158, 151103 (2023)

Is explicitly correlated double hybrid DFT advantageous for vibrational frequencies?

Authors: Nisha Mehta, Golokesh Santra, Jan M. L. Martin

Abstract: 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 ev… ▽ More 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. △ Less

Submitted 12 December, 2022; v1 submitted 6 November, 2022; originally announced November 2022.

Comments: Can. J. Chem., minor revision (WATOC 2022 special issue)

Performance of Localized-Orbital Coupled Cluster Approaches for the Conformational Energies of Longer n-alkane Chains

Authors: Golokesh Santra, Jan M. L. Martin

Abstract: We report an update and enhancement of the ACONFL (conformer energies of large alkanes [Ehlert, S.; Grimme, S.; Hansen, A. J. Phys. Chem. A 2022, 126, 3521-3535]) dataset. For the ACONF12 (n-dodecane) subset, we report basis set limit canonical CCSD(T) reference data obtained from MP2-F12/cc-pV{T,Q}Z-F12 extrapolation, [CCSD(F12*)-MP2-F12]/aug-cc-pVTZ-F12, and a (T) correction from conventional CC… ▽ More We report an update and enhancement of the ACONFL (conformer energies of large alkanes [Ehlert, S.; Grimme, S.; Hansen, A. J. Phys. Chem. A 2022, 126, 3521-3535]) dataset. For the ACONF12 (n-dodecane) subset, we report basis set limit canonical CCSD(T) reference data obtained from MP2-F12/cc-pV{T,Q}Z-F12 extrapolation, [CCSD(F12*)-MP2-F12]/aug-cc-pVTZ-F12, and a (T) correction from conventional CCSD(T)/aug-cc-pV{D,T}Z calculations. Then we explored the performance of a variety of single and composite localized-orbital CCSD(T) approximations, ultimately finding an affordable LNO-CCSD(T)-based post-MP2 correction that agrees to 0.008 kcal/mol MAD (mean absolute deviation) with the revised canonical reference data. In tandem with canonical MP2-F12/CBS extrapolation, this was then used to re-evaluate the ACONF16 and ACONF20 subsets for n-hexadecane and n-icosane, respectively. A revised ACONFL set was thus obtained. It was then used to assess the performance of different localized-orbital coupled cluster approaches, such as PNO-LCCSD(T) as implemented in MOLPRO, DLPNO-CCSD (T1) as implemented in ORCA, and LNO-CCSD(T) as implemented in MRCC, at their various accuracy settings. A three-tier LNO-CCSD(T)-based composite scheme disagrees by only 0.02 kcal/mol from the revised ACONFL reference data. When extrapolated to the complete PNO space limit, DLPNO-CCSD(T1, Tight) and a composite method are the best picks among all the localized coupled cluster methods tested for the dodecane conformers. Dispersion-corrected dRPA-based double hybrids perform remarkably well for the ACONFL set. While the revised reference data do not affect any conclusions on the less accurate methods, they may upend orderings for more accurate methods with error statistics on the same order as the difference between reference datasets. △ Less

Submitted 9 November, 2022; v1 submitted 7 September, 2022; originally announced September 2022.

Comments: Revised MS submitted to JPC A: level of theory for reference calculations upgraded; many other changes

S66x8 Noncovalent Interactions Revisited: New Benchmark and Performance of Composite Localized Coupled-Cluster Methods

Authors: Golokesh Santra, Emmanouil Semidalas, Nisha Mehta, Amir Karton, Jan M. L. Martin

Abstract: The S66x8 noncovalent interactions benchmark has been re-evaluated at the "sterling silver" level, using explicitly correlated MP2-F12 near the complete basis set limit, CCSD(F12*)/aug-cc-pVTZ-F12, and a (T) correction from conventional CCSD(T)/sano-V{D,T}Z+ calculations. The revised reference value disagrees by 0.1 kcal/mol RMS with the original Hobza benchmark and its revision by Brauer et al, b… ▽ More The S66x8 noncovalent interactions benchmark has been re-evaluated at the "sterling silver" level, using explicitly correlated MP2-F12 near the complete basis set limit, CCSD(F12*)/aug-cc-pVTZ-F12, and a (T) correction from conventional CCSD(T)/sano-V{D,T}Z+ calculations. The revised reference value disagrees by 0.1 kcal/mol RMS with the original Hobza benchmark and its revision by Brauer et al, but by only 0.04 kcal/mol variety from the "bronze" level data in Kesharwani et al., Aust. J. Chem. 71, 238-248 (2018). We then used these to assess the performance of localized-orbital coupled cluster approaches with and without counterpoise corrections, such as PNO-LCCSD(T) as implemented in MOLPRO, DLPNO-CCSD (T1) as implemented in ORCA, and LNO-CCSD(T) as implemented in MRCC, for their respective "Normal", "Tight", and "very Tight" settings. We also considered composite approaches combining different basis sets and cutoffs. Furthermore, in order to isolate basis set convergence from domain truncation error, for the aug-cc-pVTZ basis set we compared PNO, DLPNO, and LNO approaches with canonical CCSD(T). We conclude that LNO-CCSD(T) with veryTight criteria performs very well for "raw" (CP-uncorrected), but struggles to reproduce counterpoise-corrected numbers even for veryVeryTight criteria: this means that accurate results can be obtained using either extrapolation from basis sets large enough to quench basis set superposition error (BSSE) such as aug-cc-pV{Q,5}Z, or using a composite scheme such as Tight{T,Q}+1.11[vvTight(T) - Tight(T)]. In contrast, PNO-LCCSD(T) works best with counterpoise, while performance with and without counterpoise is comparable for DLPNO-CCSD(T1). Among more economical methods, the highest accuracies are seen for dRPA75-D3BJ, ωB97M-V, ωB97M(2), revDSD-PBEP86-D4, and DFT(SAPT) with a TDEXX or ATDEXX kernel. △ Less

Submitted 27 October, 2022; v1 submitted 2 August, 2022; originally announced August 2022.

Comments: Final published version with CC license

Journal ref: Phys. Chem. Chem. Phys. 24, 25555-25570 (2022)

Reduced-scaling double hybrid DFT with rapid basis set convergence through localized pair natural orbital F12

Authors: Nisha Mehta, Jan M. L. Martin

Abstract: 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 Görling-Levy perturbation theory), we demonstrate here, for the very large and chemically diverse GMTKN55 benchmark su… ▽ More 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 Görling-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. △ Less

Submitted 30 September, 2022; v1 submitted 10 June, 2022; originally announced June 2022.

Comments: Published version [Open Access CC:BY 4.0]

Journal ref: Journal of Physical Chemistry Letters 13, 9332-9338 (2022)

Benefits of Range-separated Hybrid and Double-Hybrid Functionals for a Large and Diverse Dataset of Reaction Energies and Barrier Heights

Authors: Golokesh Santra, Rivka Calinsky, Jan M. L. Martin

Abstract: To better understand the thermochemical kinetics and mechanism of a specific chemical reaction, an accurate estimation of barrier heights (forward and reverse) and reaction energy are vital. Due to the large size of reactants and transition state structures involved in real-life mechanistic studies (e.g., enzymatically catalyzed reactions), DFT remains the workhorse for such calculations. In this… ▽ More To better understand the thermochemical kinetics and mechanism of a specific chemical reaction, an accurate estimation of barrier heights (forward and reverse) and reaction energy are vital. Due to the large size of reactants and transition state structures involved in real-life mechanistic studies (e.g., enzymatically catalyzed reactions), DFT remains the workhorse for such calculations. In this paper, we have assessed the performance of 88 density functionals for modeling the reaction energies and barrier heights on a large and chemically diverse dataset (BH9) composed of 449 organic chemistry reactions. We have shown that range-separated hybrid functionals perform better than the global hybris for BH9 barrier heights and reaction energies. Except for the PBE-based range-separated nonempirical double hybrids, the exchange term's range separation helps improve the performance for barrier heights and reaction energies. The sixteen-parameter Berkeley double hybrid, ωB97M(2), performs remarkably well for both properties. However, our minimally empirical range-separated double hybrid functionals offer marginally better accuracy than ωB97M(2) for BH9 barrier heights and reaction energies. △ Less

Submitted 28 July, 2022; v1 submitted 6 June, 2022; originally announced June 2022.

Comments: J. Phys. Chem. A, revised (Vincenzo Barone festschrift)

Journal ref: Journal of Physical Chemistry A 126, 5492-5505 (2022)

Explicitly correlated double hybrid DFT: a comprehensive analysis of the basis set convergence on the GMTKN55 database

Authors: Nisha Mehta, Jan M. L. Martin

Abstract: Double-hybrid density functional theory (DHDFT) offers a pathway to accuracies approaching composite wavefunction approaches like G4 theory. However, the GLPT2 (G{ö}rling 2nd order perturbation theory) term causes them to partially inherit the slow $\propto L^{-3}$ (with $L$ the maximum angular momentum) basis set convergence of correlated wavefunction methods. This could potentially be remedied b… ▽ More Double-hybrid density functional theory (DHDFT) offers a pathway to accuracies approaching composite wavefunction approaches like G4 theory. However, the GLPT2 (G{ö}rling 2nd order perturbation theory) term causes them to partially inherit the slow $\propto L^{-3}$ (with $L$ the maximum angular momentum) basis set convergence of correlated wavefunction methods. This could potentially be remedied by introducing F12 explicit correlation: we investigate the basis set convergence of both DHDFT and DHDFT-F12 for the large and chemically diverse GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) benchmark suite. The B2GP-PLYP-D3(BJ) and revDSD-PBEP86-D4 double hybrid density functionals (DHDFs) are investigated as test cases, together with orbital basis sets as large as aug-cc-pV5Z and F12 basis sets as large as cc-pV(Q+d)Z-F12. We show that F12 greatly accelerates basis set convergence of DHDFs, to the point that even the modest cc-pVDZ-F12 basis set is closer to the basis set limit than cc-pV(Q+d)Z or def2-QZVPP in orbital-based approaches, and in fact comparable in quality to cc-pV(5+d)Z. Somewhat surprisingly, aug-cc-pVDZ-F12 is not required even for the anionic subsets. In conclusion, DHDF-F12/VDZ-F12 eliminates concerns about basis set convergence in both the development and application of double-hybrid functionals. Mass storage and I/O bottlenecks for larger systems can be circumvented by localized pair natural orbital approximations, which also exhibit much gentler system size scaling. △ Less

Submitted 14 September, 2022; v1 submitted 25 April, 2022; originally announced April 2022.

Comments: published version in JCTC: Open Access with Creative Commons license

Journal ref: J. Chem. Theory Comput. 18, 5978-5991 (2022)

Automatic generation of complementary auxiliary basis sets (CABS) for explicitly correlated methods

Authors: Emmanouil Semidalas, Jan M. L. Martin

Abstract: Explicitly correlated calculations, aside from the orbital basis set, typically require three auxiliary basis sets: JK (Coulomb-exchange fitting), RI-MP2 (resolution of the identity MP2), and CABS (complementary auxiliary basis set). If unavailable for the orbital basis set and chemical elements of interest, the first two can be auto-generated on the fly using existing algorithms, but not the thir… ▽ More Explicitly correlated calculations, aside from the orbital basis set, typically require three auxiliary basis sets: JK (Coulomb-exchange fitting), RI-MP2 (resolution of the identity MP2), and CABS (complementary auxiliary basis set). If unavailable for the orbital basis set and chemical elements of interest, the first two can be auto-generated on the fly using existing algorithms, but not the third. In this paper, we present a quite simple algorithm named autoCABS; a Python implementation under a free software license is offered at Github. For the cc-pVnZ-F12 (n=D,T,Q,5) and the W4-08 thermochemical benchmark, we demonstrate that autoCABS-generated CABS basis sets are comparable in quality to purpose-optimized OptRI basis sets from the literature, and that the quality difference becomes entirely negligible as n increases. △ Less

Submitted 13 June, 2022; v1 submitted 14 April, 2022; originally announced April 2022.

Comments: 18 pages; new section on harmonic frequencies added

Journal ref: Journal of Computational Chemistry 43, 1690-1700 (2022)

MP2-F12 basis set convergence near the complete basis set limit: are $h$ functions sufficient?

Authors: Nisha Mehta, Jan M. L. Martin

Abstract: We have investigated the title question for the W4-08 thermochemical benchmark using partial-wave truncations of a large reference (REF) basis set, as well as for standard F12-optimized basis sets. With the REF basis set, the root mean square (RMS) contribution of i functions to the total atomization energies (TAEs) is about 0.01 kcal/mol, the largest individual contributions being 0.04 kcal/mol f… ▽ More We have investigated the title question for the W4-08 thermochemical benchmark using partial-wave truncations of a large reference (REF) basis set, as well as for standard F12-optimized basis sets. With the REF basis set, the root mean square (RMS) contribution of i functions to the total atomization energies (TAEs) is about 0.01 kcal/mol, the largest individual contributions being 0.04 kcal/mol for \ce{P2} and \ce{P4}. However, even for these cases, basis set extrapolation from \{g,h\} basis sets adequately addresses the problem. Using basis sets insufficiently saturated in the $spdfgh$ angular momenta may lead to exaggerated $i$ function contributions. For extrapolation from $spdfg$ and $spdfgh$ basis sets, basis set convergence appears to be quite close to the theoretical asymptotic $\propto L^{-7}$ behavior. We hence conclude that $h$ functions are sufficient even for highly demanding F12 applications. With one-parameter extrapolation, $spdf$ and $spdfg$ basis sets are adequate, with aug-cc-pV\{T,Q\}Z-F12 yielding RMSD=0.03 kcal/mol. A limited exploration of CCSD(F12*) and CCSD-F12b suggests our conclusions are applicable to higher-level F12 methods as well. △ Less

Submitted 2 July, 2022; v1 submitted 7 April, 2022; originally announced April 2022.

Comments: Final version: Open Access ACS AuthorChoice CC:BY 4.0

Journal ref: J. Phys. Chem. A 126, 3964-3971 (2022)

Electron Correlation: Nature's Weird and Wonderful Chemical Glue

Authors: Jan M. L. Martin

Abstract: It can be argued that electron correlation, as a concept, deserves the same prominence in general chemistry as molecular orbital theory. We show how it acts as Nature's "chemical glue" at both the molecular and supramolecular levels. Electron correlation can be presented in a general chemistry course in an at least somewhat intuitive manner. We also propose a simple classification of correlation e… ▽ More It can be argued that electron correlation, as a concept, deserves the same prominence in general chemistry as molecular orbital theory. We show how it acts as Nature's "chemical glue" at both the molecular and supramolecular levels. Electron correlation can be presented in a general chemistry course in an at least somewhat intuitive manner. We also propose a simple classification of correlation effects based on their length scales and the size of the orbital gap (relative to the two-electron integrals). In the discussion, we also show how DFT can shed light on wavefunction theory, and conversely. We discuss two types of "honorary valence orbitals", one related to small core-valence gaps, the other to the ability of empty 3d orbitals in 2nd row elements to act as backbonding acceptors. Finally, we show why the pursuit of absolute total energies for their own sake becomes a sterile exercise, and why atomization energies are a more realistic "fix point". △ Less

Submitted 7 January, 2022; v1 submitted 8 December, 2021; originally announced December 2021.

Comments: Israel Journal of Chemistry, Early View (2022) [Perspective Article for special issue "Rosarium Philosophorum" dedicated to computational chemistry] (CC-BY Open Access)

The MOBH35 metal-organic barrier heights reconsidered: performance of local-orbital coupled cluster approaches in different static correlation regimes

Authors: Emmanouil Semidalas, Jan M. L. Martin

Abstract: We have revisited the MOBH35 (Metal-Organic Barrier Heights, 35 reactions) benchmark [Iron, M. A.; Janes, T. J. Phys. Chem. A 2019, 123 (17), 3761-3781; ibid. 2019, 123, 6379-6380] for realistic organometallic catalytic reactions, using both canonical CCSD(T) and localized orbital approximations to it. For low levels of static correlation, all of DLPNO-CCSD(T), PNO-LCCSD(T), and LNO-CCSD(T) perfor… ▽ More We have revisited the MOBH35 (Metal-Organic Barrier Heights, 35 reactions) benchmark [Iron, M. A.; Janes, T. J. Phys. Chem. A 2019, 123 (17), 3761-3781; ibid. 2019, 123, 6379-6380] for realistic organometallic catalytic reactions, using both canonical CCSD(T) and localized orbital approximations to it. For low levels of static correlation, all of DLPNO-CCSD(T), PNO-LCCSD(T), and LNO-CCSD(T) perform well; for moderately strong levels of static correlation, DLPNO-CCSD(T) and (T1) may break down catastrophically, and PNO-LCCSD(T) is vulnerable as well. In contrast, LNO-CCSD(T) converges smoothly to the canonical CCSD(T) answer with increasingly tight convergence settings. The only two reactions for which our revised MOBH35 reference values differ substantially from the original ones are reaction 9 and to a lesser extent 8, both involving iron. For the purpose of evaluating DFT methods for MOBH35, it would be best to excise reaction 9 entirely as its severe level of static correlation is just too demanding a test. The magnitude of the difference between DLPNO-CCSD(T) and DLPNO-CCSD(T1) is a reasonably good predictor for errors in DLPNO-CCSD(T1) compared to canonical CCSD(T); [...] △ Less

Submitted 20 January, 2022; v1 submitted 8 November, 2021; originally announced November 2021.

Comments: J. Chem. Theor. Comput. 18, ASAP (2022). CC:BY 4.0. Dedicated to the memory of Shimon Vega (1943-2021)

Journal ref: J. Chem. Theor. Comput. 18, 883-898 (2022)

The S66 Noncovalent Interaction Benchmark Re-examined: Composite Localized Coupled Cluster Approaches

Authors: Emmanouil Semidalas, Golokesh Santra, Nisha Mehta, Jan M. L. Martin

Abstract: 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 i… ▽ More 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. △ Less

Submitted 14 November, 2021; v1 submitted 2 November, 2021; originally announced November 2021.

Comments: 6 pages, AIP Conference Proceedings, in press (ICCMSE-2021)

Journal ref: AIP Conference Proceedings 2611, 020016 (2022)

Does GLPT2 Offer Any Actual Benefit Over Conventional HF-MP2 In the Context of Double-Hybrid Density Functionals?

Authors: Golokesh Santra, Jan M. L. Martin

Abstract: 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, GM… ▽ More 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. △ Less

Submitted 14 November, 2021; v1 submitted 2 November, 2021; originally announced November 2021.

Comments: 4 pages, AIP Conference Proceedings, in press (ICCMSE-2021)

Journal ref: AIP Conference Proceedings 2611, 020015 (2022)

An Exchange-Based Diagnostic for Static Correlation

Authors: Jan M. L. Martin, Golokesh Santra, Emmanouil Semidalas

Abstract: 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 ma… ▽ More 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). △ Less

Submitted 14 November, 2021; v1 submitted 2 November, 2021; originally announced November 2021.

Comments: 5 pages, AIP Conference Proceedings, in press (ICCMSE-2021)

Journal ref: AIP Conference Proceedings 2611, 020014 (2022)

Surprisingly Good Performance of XYG3 Family Functionals Using Scaled KS-MP3 Correlation

Authors: Golokesh Santra, Emmanouil Semidalas, Jan M. L. Martin

Abstract: By adding a GLPT3 (third-order Görling-Levy perturbation theory, or KS-MP3) term E3 to the XYG7 form for a double hybrid, we are able to bring down WTMAD2 (weighted total mean absolute deviation) for the very large and chemically diverse GMTKN55 benchmark to an unprecedented 1.17 kcal/mol, competitive with much costlier composite wavefunction ab initio approaches. Intriguingly: (a) the introductio… ▽ More By adding a GLPT3 (third-order Görling-Levy perturbation theory, or KS-MP3) term E3 to the XYG7 form for a double hybrid, we are able to bring down WTMAD2 (weighted total mean absolute deviation) for the very large and chemically diverse GMTKN55 benchmark to an unprecedented 1.17 kcal/mol, competitive with much costlier composite wavefunction ab initio approaches. Intriguingly: (a) the introduction of E3 makes an empirical dispersion correction redundant; (b) GGA or mGGA semilocal correlation functionals offer no advantage over LDA in this framework; (c) if a dispersion correction is retained, then simple Slater exchange leads to no significant loss in accuracy. It is possible to create a 6-parameter functional with WTMAD2=1.42 that has no post-LDA DFT components and no dispersion correction in the final energy. △ Less

Submitted 14 September, 2021; v1 submitted 29 August, 2021; originally announced August 2021.

Journal ref: J. Phys. Chem. Lett 12, 9368-9376 (2021)

Basis set convergence and extrapolation of connected triple excitation contributions (T) in computational thermochemistry: the W4-17 benchmark with up to k functions

Authors: Jan M. L. Martin

Abstract: 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" contribut… ▽ More 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. △ Less

Submitted 25 June, 2021; v1 submitted 26 March, 2021; originally announced March 2021.

Comments: 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

Journal ref: Chapter 8 in "Quantum Science", Ed. Taku Onishi, Springer, 2022, pp. 467-496

Prototypical pi-pi dimers re-examined by means of high-level CCSDT(Q) composite ab inito methods

Authors: Amir Karton, Jan M. L. Martin

Abstract: The benzene...ethene and parallel-displaced (PD) benzene...benzene dimers are the most fundamental systems involving p-p stacking interactions. Several high-level ab initio investigations calculated the binding energies of these dimers at the CCSD(T)/CBS level of theory using various approaches such as reduced virtual orbital spaces and/or MP2-based basis set corrections. Here we obtain CCSDT(Q) b… ▽ More The benzene...ethene and parallel-displaced (PD) benzene...benzene dimers are the most fundamental systems involving p-p stacking interactions. Several high-level ab initio investigations calculated the binding energies of these dimers at the CCSD(T)/CBS level of theory using various approaches such as reduced virtual orbital spaces and/or MP2-based basis set corrections. Here we obtain CCSDT(Q) binding energies using a Weizmann-3-type approach. In particular, we extrapolate the SCF, CCSD, and (T) components using large heavy-atom augmented Gaussian basis sets (namely, SCF/jul-cc-pV{5,6}Z, CCSD/jul-cc-pV{Q,5}Z, and (T)/jul-cc-pV{T,Q}Z). We consider post-CCSD(T) contributions up to CCSDT(Q), inner-shell, scalar-relativistic, and Born-Oppenheimer corrections. Overall, our best relativistic, all-electron CCSDT(Q) binding energies are Delta Ee,all,rel = 1.234 (benzene...ethene) and 2.550 (benzene...benzene PD), Delta H0 = 0.949 (benzene...ethene) and 2.310 (benzene...benzene PD), and Delta H298 = 0.130 (benzene...ethene) and 1.461 (benzene...benzene PD) kcal/mol. Important conclusions are reached regarding the basis set convergence of the SCF, CCSD, (T), and post-CCSD(T) components. Explicitly correlated calculations are used as a sanity check on the conventional binding energies. Overall, post-CCSD(T) contributions are destabilizing by 0.028 (benzene...ethene) and 0.058(benzene...benzene) kcal/mol, thus they cannot be neglected if 0.1 kcal/mol accuracy is sought. △ Less

Submitted 5 March, 2021; originally announced March 2021.

Comments: J. Chem. Phys., accepted with minor revision

Journal ref: J. Chem. Phys. 154, 124117 (2021)

Exploring Avenues Beyond Revised DSD Functionals: II. Random-Phase Approximation and scaled MP3 corrections

Authors: Golokesh Santra, Emmanouil Semidalas, Jan M. L. Martin

Abstract: For revDSD double hybrids, the Görling-Levy second-order perturbation theory component is an Achilles' Heel when applied to systems with significant near-degeneracy ("static") correlation. We have explored its replacement by the direct random phase approximation (dRPA), inspired by the SCS-dRPA75 functional of Kállay and coworkers. The addition to the final energy of both a D4 empirical dispersion… ▽ More For revDSD double hybrids, the Görling-Levy second-order perturbation theory component is an Achilles' Heel when applied to systems with significant near-degeneracy ("static") correlation. We have explored its replacement by the direct random phase approximation (dRPA), inspired by the SCS-dRPA75 functional of Kállay and coworkers. The addition to the final energy of both a D4 empirical dispersion correction, and of a semilocal correlation component lead, to significant improvements, with DSD-PBEdRPA75-D4 approaching the performance of revDSD-PBEP86-D4 and the Berkeley $ω$B97M(2). This form appears to be fairly insensitive to the choice of semilocal functional, but does exhibit stronger basis set sensitivity than the PT2-based double hybrids (due to much larger prefactors for the nonlocal correlation). As an alternative, we explored adding an MP3-like correction term (in a medium-sized basis sets) to a range-separated $ω$DSD-PBEP86-D4 double hybrid, and found it to have significantly lower WTMAD2 (weighted mean absolute deviation) for the large and chemically diverse GMTKN55 benchmark suite; the added computational cost can be mitigated through density fitting techniques. △ Less

Submitted 22 May, 2021; v1 submitted 9 February, 2021; originally announced February 2021.

Comments: J. Phys. Chem. A 125, ASAP (2021) Creative Commons License

Journal ref: J. Phys. Chem. A 125, 4628-4638 (2021)

Exploring Avenues Beyond Revised DSD Functionals: I. range separation, with xDSD as a special case

Authors: Golokesh Santra, Minsik Cho, Jan M. L. Martin

Abstract: We have explored the use of range separation as a possible avenue for further improvement on our revDSD minimally empirical double hybrid functionals. Such $ω$DSD functionals encompass the XYG3 type of double hybrid (i.e., xDSD) as a special case for $ω$->0. As in our previous studies, the large and chemically diverse GMTKN55 benchmark suite was used for evaluation. Especially when using the D4 ra… ▽ More We have explored the use of range separation as a possible avenue for further improvement on our revDSD minimally empirical double hybrid functionals. Such $ω$DSD functionals encompass the XYG3 type of double hybrid (i.e., xDSD) as a special case for $ω$->0. As in our previous studies, the large and chemically diverse GMTKN55 benchmark suite was used for evaluation. Especially when using the D4 rather than D3BJ dispersion model, xDSD has a slight performance advantage in WTMAD2. As found previously, PBEP86 is the winning combination for the semilocal parts. xDSDn-PBEP86-D4 marginally outperforms the previous 'best in class' $ω$B97M(2) Berkeley double hybrid, but without range separation and using fewer than half the number of empirical parameters. Range separation turns out to offer only marginal further improvements on GMTKN55 itself. While $ω$B97M(2) still yields better performance for small-molecule thermochemistry, this is outweighed in WTMAD2 by superior performance of the new functionals for conformer equilibria. Results for two external test sets with pronounced static correlation effects may indicate that range-separated double hybrids are more resilient to such effects. △ Less

Submitted 22 May, 2021; v1 submitted 9 February, 2021; originally announced February 2021.

Comments: J. Phys. Chem. A 125, ASAP (2021) Creative Commons License (1st of two papers back-to-back)

Journal ref: J. Phys. Chem. A 125, 4614-4627 (2021)

What types of chemical problems benefit from density-corrected DFT? A probe using an extensive and chemically diverse test suite

Authors: Golokesh Santra, Jan M. L. Martin

Abstract: For the large and chemically diverse GMTKN55 benchmark suite, we have studied the performance of density-corrected density functional theory (HF-DFT), compared to self-consistent DFT, for several pure and hybrid GGA and meta-GGA exchange-correlation (XC) functionals (PBE, BLYP, TPSS, SCAN) as a function of the percentage of HF exchange in the hybrid. The D4 empirical dispersion correction has been… ▽ More For the large and chemically diverse GMTKN55 benchmark suite, we have studied the performance of density-corrected density functional theory (HF-DFT), compared to self-consistent DFT, for several pure and hybrid GGA and meta-GGA exchange-correlation (XC) functionals (PBE, BLYP, TPSS, SCAN) as a function of the percentage of HF exchange in the hybrid. The D4 empirical dispersion correction has been added throughout. For subsets dominated by dynamical correlation -- particularly noncovalent interaction subsets -- HF-DFT is highly beneficial, particularly at low HF exchange percentages. For subsets with significant static correlation (i.e., where a Hartree-Fock determinant is not a good zero-order wavefunction), HF-DFT may do more harm than good. While the self-consistent series show optima at or near 37.5% (i.e., 3/8) for all four XC functionals -- consistent with Grimme's proposal of the PBE38 functional -- HF-BnLYP-D4, HF-PBEn-D4, and HF-TPSSn-D4 all exhibit minima nearer 25% (i.e., 1/4). Intriguingly, for HF-SCANn-D4, the minimum is near 10%, but the weighted mean absolute error (WTMAD2) for GMTKN55 is only barely lower than that of HF-SCAN-D4 (i.e., where the post-HF step is a pure meta-GGA). The latter becomes an attractive option, only slightly more costly than pure Hartree-Fock, and devoid of adjustable parameters other than the three in the dispersion correction. Moreover, its WTMAD2 is only surpassed by the highly empirical M06-2X and by the combinatorically optimized empirical range-separated hybrids wB97X-V and wB97M-V. △ Less

Submitted 24 February, 2021; v1 submitted 4 October, 2020; originally announced October 2020.

Comments: Journal of Chemical Theory and Computation (2021)

Journal ref: J. Chem. Theory Comput. 17, 1368-1379 (2021)

Canonical and DLPNO-based composite wavefunction methods parametrized against large and chemically diverse training sets. 2. Correlation consistent basis sets, core-valence correlation, and F12 alternatives

Authors: Emmanouil Semidalas, Jan M. L. Martin

Abstract: A hierarchy of wavefunction composite methods (cWFT), based on G4- type cWFT methods available for elements H through Rn, was recently reported by Semidalas and Martin [J. Chem. Theor. Comput. 2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Moller-Plesset correction and replacing the Weigend-Ahlrichs def2-mZVPP(D) basis sets used in t… ▽ More A hierarchy of wavefunction composite methods (cWFT), based on G4- type cWFT methods available for elements H through Rn, was recently reported by Semidalas and Martin [J. Chem. Theor. Comput. 2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Moller-Plesset correction and replacing the Weigend-Ahlrichs def2-mZVPP(D) basis sets used in the aforementioned paper with complete basis set extrapolation from augmented correlation consistent core-valence triple-zeta, aug-cc-pwCVTZ(-PP), and quadruple-zeta, aug-cc-pwCVQZ(-PP), basis sets, thus creating cc-G4- type methods. For the large and chemically diverse GMTKN55 benchmark suite, they represent a substantial further improvement and bring WTMAD2 (weighted mean absolute deviation) down below 1 kcal/mol. Intriguingly, the lion's share of the improvement comes from better capture of valence correlation; the inclusion of core-valence correlation is almost an order of magnitude less important. These robust correlation consistent cWFT methods approach the CCSD(T) complete basis limit with just one or a few fitted parameters. Particularly the DLPNO variants such as cc-G4-T-DLPNO are applicable to fairly large molecules at modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component. △ Less

Submitted 17 November, 2020; v1 submitted 4 August, 2020; originally announced August 2020.

Comments: J. Chem. Theor. Comput., ASAP (Open Access under CC)

Journal ref: J. Chem. Theory Comput. 16, 7507-7524 (2020)

Canonical and DLPNO-based G4(MP2)XK-inspired composite wavefunction methods parametrized against large and chemically diverse training sets: Are they more accurate and/or robust than double hybrid DFT?

Authors: Emmanouil Semidalas, Jan M. L. Martin

Abstract: The large and chemically diverse GMTKN55 benchmark was used as a training set for parametrizing composite wave function thermochemistry protocols akin to G4(MP2)XK theory (Chan et al, JCTC 2019, 15, 4478-4484). Even after reparametrization, the GMTKN55 WTMAD2 (weighted mean absolute deviation, type 2) for G4(MP2)-XK is actually inferior to that of the best rung-4 DFT functional, wB97M-V. By increa… ▽ More The large and chemically diverse GMTKN55 benchmark was used as a training set for parametrizing composite wave function thermochemistry protocols akin to G4(MP2)XK theory (Chan et al, JCTC 2019, 15, 4478-4484). Even after reparametrization, the GMTKN55 WTMAD2 (weighted mean absolute deviation, type 2) for G4(MP2)-XK is actually inferior to that of the best rung-4 DFT functional, wB97M-V. By increasing the basis set for the MP2 part to def2-QZVPPD, we were able to substantially improve performance at modest cost (if an RI-MP2 approximation is made), with WTMAD2 for this G4(MP2)-XK-D method now comparable to the better rung-5 functionals (albeit at greater cost). A three-tier approach with a scaled MP3/def2-TZVPP intermediate step, however, leads to a G4(MP3)-D method that is markedly superior to even the best double hybrids wB97M(2) and revDSD-PBEP86-D4. Evaluating the CCSD(T) component with a triple-zeta, rather than split-valence, basis set yields only a modest further improvement that is incommensurate with the drastic increase in computational cost. G4(MP3)-D and G4(MP2)- XK-D have about 40% better WTMAD2, at similar or lower computational cost, than their counterparts G4 and G4(MP2), respectively: detailed comparison reveals that the difference lies in larger molecules due to basis set incompleteness error. An E2/ {T,Q} extrapolation and a CCSD(T)/def2-TZVP step provided the G4-T method of high accuracy and with just three fitted parameters. Using KS orbitals in MP2 leads to the G4(MP3|KS)-D method, which entirely eliminates the CCSD(T) step and has no steps costlier than scaled MP3; this shows a path forward to further improvements in double-hybrid density functional methods. G4-T-DLPNO, a variant in which post-MP2 corrections are evaluated at the DLPNO- CCSD(T) level, achieves nearly the accuracy of G4-T but is applicable to much larger systems. △ Less

Submitted 8 June, 2020; originally announced June 2020.

Comments: J. Chem. Theor. Comp., ASAP (2020). CC:BY 4.0 Open Access article

Journal ref: Journal of Chemical Theory and Computation 16, 4238-4255 (2020)

Energetics of (H2O)20 Isomers by means of F12 Canonical and Localized Coupled Cluster Methods

Authors: Nitai Sylvetsky, Jan M. L. Martin

Abstract: We consider the performance of combined PNO-F12 approaches for the dissociation energy of water clusters as large as (H2O)20 by comparison to canonical CCSD(T)/CBS reference values obtained through n-body decomposition of post-MP2 corrections. We find that PNO-LCCSD(T)-F12b approaches with "Tight" cutoffs are generally capable of reproducing canonical CCSD(T) interaction energies to within ~0.25%… ▽ More We consider the performance of combined PNO-F12 approaches for the dissociation energy of water clusters as large as (H2O)20 by comparison to canonical CCSD(T)/CBS reference values obtained through n-body decomposition of post-MP2 corrections. We find that PNO-LCCSD(T)-F12b approaches with "Tight" cutoffs are generally capable of reproducing canonical CCSD(T) interaction energies to within ~0.25% and isomerization energies to ~1.5%, while requiring only a fraction of the canonical computational cost. However, basis set convergence patterns and effect of counterpoise corrections are more erratic than for canonical calculations, highlighting the need for canonical benchmarks on closely related systems. △ Less

Submitted 29 June, 2020; v1 submitted 5 February, 2020; originally announced February 2020.

Comments: AIP Conference Proceedings, in press [ICCMSE-2020 issue]

Journal ref: AIP Conference Proceedings 2343, 020003 (2021)

Performance of Localized Coupled Cluster Methods in a Moderately Strong Correlation Regime: Hückel-Möbius Interconversions in Expanded Porphyrins

Authors: Nitai Sylvetsky, Ambar Banerjee, Mercedes Alonso, Jan M. L. Martin

Abstract: 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 Hückel, figure-… ▽ More 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 Hückel, figure-eight, and Möbius topologies under external stimuli. Both minima and isomerization transition states are considered. We find that Möbius(-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 Möbius-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. △ Less

Submitted 11 May, 2020; v1 submitted 23 January, 2020; originally announced January 2020.

Comments: 27 pages; revised version. J. Chem. Theory. Comput., ASAP (2020)

Journal ref: J. Chem. Theory Comput. 16, 3641-3653 (2020)

Empirical Double-Hybrid Density Functional Theory: A 'Third Way' In Between WFT and DFT

Authors: Jan M. L. Martin, Golokesh Santra

Abstract: Double hybrid density functional theory arguably sits on the seamline between wavefunction methods and DFT: it represents a special case of Rung 5 on the "Jacobs Ladder" of John P. Perdew. For large and chemically diverse benchmarks such as GMTKN55, empirical double hybrid functionals with dispersion corrections can achieve accuracies approaching wavefunction methods at a cost not greatly dissimil… ▽ More Double hybrid density functional theory arguably sits on the seamline between wavefunction methods and DFT: it represents a special case of Rung 5 on the "Jacobs Ladder" of John P. Perdew. For large and chemically diverse benchmarks such as GMTKN55, empirical double hybrid functionals with dispersion corrections can achieve accuracies approaching wavefunction methods at a cost not greatly dissimilar to hybrid DFT approaches, provided RI-MP2 and/or another MP2 acceleration techniques are available in the electronic structure code. Only a half-dozen or fewer empirical parameters are required. For vibrational frequencies, accuracies intermediate between CCSD and CCSD(T) can be achieved, and performance for other properties is encouraging as well. Organometallic reactions can likewise be treated well, provided static correlation is not too strong. Further prospects are discussed, including range-separated and RPA-based approaches. △ Less

Submitted 26 December, 2019; v1 submitted 3 November, 2019; originally announced November 2019.

Comments: Israel Journal of Chemistry, EarlyView (2020); 19 pages, Open Access

Journal ref: Israel Journal of Chemistry 60, 787-804 (2020)

Some Observations on the Performance of the Most Recent Exchange-Correlation Functionals for the Large and Chemically Diverse GMTKN55 Benchmark

Authors: Golokesh Santra, Jan M. L. Martin

Abstract: Benchmarks that span a broad swath of chemical space, such as GMTKN55, are very useful for assessing progress in the quest for more universal DFT functionals. We find that the WTMAD2 metrics for a great number of functionals show a clear "Jacob's Ladder hierarchy"; that the "combinatorial" development strategy of Head-Gordon and coworkers generates "best on rung" performers; that the quality of th… ▽ More Benchmarks that span a broad swath of chemical space, such as GMTKN55, are very useful for assessing progress in the quest for more universal DFT functionals. We find that the WTMAD2 metrics for a great number of functionals show a clear "Jacob's Ladder hierarchy"; that the "combinatorial" development strategy of Head-Gordon and coworkers generates "best on rung" performers; that the quality of the nonlocal dispersion correction becomes more important as functionals become more accurate for nondispersion properties; that fitting against small, unrepresentative benchmark sets leads to underperforming functionals; and that ωB97M(2) is currently the best DFT functional of any kind, but that revDSD-D4 functionals are able to reach similar performance using fewer parameters, and that revDOD-D4 in addition permits reduced-scaling algorithms. If one seeks a range-separated hybrid (RSH) GGA that also performs well for optical excitation energies, CAM-QTP-01 may be a viable option. The D4 dispersion model, with its partial charge dependence, appears to be clearly superior to D3BJ and even possibly NL. Should one require a double hybrid without dispersion model, noDispSD-SCAN is a viable option. Performance for the MOBH35 transition metal benchmark is different: the best double hybrids are competitive but not superior to ωB97M-V, which offers the best performance compromise for mixed main group-transition metal problems. △ Less

Submitted 3 June, 2019; v1 submitted 15 May, 2019; originally announced May 2019.

Comments: 5 pages (ICCMSE-2019 conference proceedings), AIP Conference Proceedings, in press

Journal ref: AIP Conference Proceedings 2186, 030004 (2019)

Coupled Cluster Benchmark of New Density Functionals and Domain Pair Natural Orbital Methods: Mechanisms of Hydroarylation and Oxidative Coupling Catalyzed by Ru(II) Chloride Carbonyls

Authors: Irena Efremenko, Jan M. L. Martin

Abstract: In the present work, we tested the performance of several new functionals for studying the mechanisms of concurrent reaction of hydroarylation and oxidative coupling catalyzed by Ru(II) chloride carbonyls. We find that DLPNO-CCSD(T) is an acceptable substitute for full canonical CCSD(T) calculations; that the recent ωB97X-V and ωB97M-V functionals exhibit superior performance to commonly used DFT… ▽ More In the present work, we tested the performance of several new functionals for studying the mechanisms of concurrent reaction of hydroarylation and oxidative coupling catalyzed by Ru(II) chloride carbonyls. We find that DLPNO-CCSD(T) is an acceptable substitute for full canonical CCSD(T) calculations; that the recent ωB97X-V and ωB97M-V functionals exhibit superior performance to commonly used DFT functionals; and that the revised DSD-PBEP86 double hybrid represents an improvement over the original, even though transition metals were not involved in its parametrization. △ Less

Submitted 29 May, 2019; v1 submitted 15 May, 2019; originally announced May 2019.

Comments: 5 pages (ICCMSE-2019 conference proceedings)

Journal ref: AIP Conference Proceedings 2186, 030005 (2019)

A Simple Model For Scalar Relativistic Corrections To Molecular Total Atomization Energies

Authors: Jan M. L. Martin, Nitai Sylvetsky

Abstract: Scalar relativistic corrections to atomization energies of 1st-and 2nd-row molecules can be rationalized in terms of a simple additive model, linear in changes in atomic s populations. In a sample of 200 first-and second-row molecules, such a model can account for over 98% of the variance (99% for the first-row subset). The remaining error can be halved again by adding a term involving the change… ▽ More Scalar relativistic corrections to atomization energies of 1st-and 2nd-row molecules can be rationalized in terms of a simple additive model, linear in changes in atomic s populations. In a sample of 200 first-and second-row molecules, such a model can account for over 98% of the variance (99% for the first-row subset). The remaining error can be halved again by adding a term involving the change in atomic p populations: those coefficients need not be fitted but can be fixed from atomic electron affinity calculations. This model allows a fairly accurate a priori estimate for the importance of scalar relativistic corrections on a reaction energy, at essentially zero computational cost. While this is not a substitute for explicit calculation of Douglas-Kroll-Hess (DKH) or exact two-component (X2C) relativistic corrections, the model offers an interpretative tool for the chemical analysis of scalar relativistic contributions to reaction energies. △ Less

Submitted 25 July, 2018; originally announced July 2018.

Comments: Molecular Physics, submitted (SANIBEL special issue)

Do CCSD and approximate CCSD-F12 variants converge to the same basis set limits? The case of atomization energies

Authors: Manoj K. Kesharwani, Nitai Sylvetsky, Andreas Köhn, David P. Tew, Jan M. L. Martin

Abstract: While the title question is a clear 'yes' from purely theoretical arguments, the case is less clear for practical calculations with finite (one-particle) basis sets. To shed further light on this issue, the basis set limits of CCSD (coupled cluster theory with all single and double excitations) and of different approximate implementations of CCSD-F12 (explicitly correlated CCSD) have been investig… ▽ More While the title question is a clear 'yes' from purely theoretical arguments, the case is less clear for practical calculations with finite (one-particle) basis sets. To shed further light on this issue, the basis set limits of CCSD (coupled cluster theory with all single and double excitations) and of different approximate implementations of CCSD-F12 (explicitly correlated CCSD) have been investigated on detail for the W4-17 thermochemical benchmark. Near the CBS ([1-particle] complete basis set) limit, CCSD and CCSD(F12*) agree to within their respective uncertainties (about \pm0.04 kcal/mol) due to residual basis set incompleteness error, but a nontrivial difference remains between CCSD-F12b and CCSD(F12*), which is roughly proportional to the degree of static correlation. The observed basis set convergence behavior results from the superposition of a rapidly converging, attractive, CCSD[F12]--CCSD-F12b difference (consisting mostly of third-order terms), and a more slowly converging, repulsive, fourth-order difference between CCSD(F12*) and CCSD[F12]. For accurate thermochemistry, we recommend CCSD(F12*) over CCSD-F12b if at all possible. There are some indications that the nZaPa family of basis sets exhibits somewhat smoother convergence than the correlation consistent family. △ Less

Submitted 17 September, 2018; v1 submitted 16 July, 2018; originally announced July 2018.

Comments: (J. Chem. Phys., revised)

Journal ref: J. Chem. Phys. 149, 154109 (2018)

Prediction of electronic couplings for molecular charge transfer using optimally-tuned range-separated hybrid functionals

Authors: Debashree Manna, Jochen Blumberger, Jan M. L. Martin, Leeor Kronik

Abstract: 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… ▽ More 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. △ Less

Submitted 5 June, 2018; originally announced June 2018.

Comments: Mol. Phys., in press (Michael Baer festschrift)

Journal ref: Molecular Physics 116, 2497-2505 (2018)