Featured paper by Gershom Martin
Journal of Physical Chemistry Letters, 2025
The fundamental non-Hermitian nature of the forms of the coupled-cluster (CC) theory widely used ... more The fundamental non-Hermitian nature of the forms of the coupled-cluster (CC) theory widely used in quantum chemistry has usually been viewed as a negative, but the present paper shows how this can be used to an 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 the full coupledcluster theory [which is equivalent to full configuration interaction (FCI)], the electronic wave function 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 the 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 application of this idea to excited states, open-shell systems, and symmetry-breaking problems and an extension of the method to the two-particle density are then proposed.
Chemical Physics Letters, 2025
• Post-CCSD(T) corrections for most of the S66 noncovalent interactions benchmark • For most syst... more • Post-CCSD(T) corrections for most of the S66 noncovalent interactions benchmark • For most systems, higher-order triples and connected quadruples nicely cancel • For 𝜋-stacking systems, however, higherorder triples are much more important • Hence, the cancellation breaks down, and CCSD(T) tends to overbind • This corroborates recent claims based on diffusion Monte Carlo • Simple estimation formulas for post-CCSD(T) contributions are proposed.
J. Chem. Theory Comput., 2025
For noncovalent interactions, the CCSD(T)coupled cluster method is widely regarded as the "gold s... more For noncovalent interactions, the CCSD(T)coupled cluster method is widely regarded as the "gold standard". With localized orbital approximations, benchmarks for ever larger complexes are being published, yet FN-DMC (fixed-node quantum Monte Carlo) intermolecular interaction energies diverge to a progressively larger degree from CCSD(T) as the system size grows, particularly when π-stacking is involved. Unfortunately, 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 going further into the coupled cluster expansion and comparing with CCSDT(Q) results for benzene and naphthalene dimers, we show that CCSD(T) does slightly overbind but not as strongly as suggested by the FN-DMC results.
Journal of Physical Chemistry A, 2024
Basis set extrapolations are typically rationalized either from analytical arguments involving th... 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.
Journal of Computational Chemistry, 2025
We have investigated the title question for both a subset of the W4-11 total atomization energies... 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 T4−(Q) especially so. In contrast, for atomization energies, the T3−(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 T3−(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).
Journal of Computational Chemistry, 2024
Partial charges are a central concept in general chemistry and chemical biology, yet dozens of di... more Partial charges are a central concept in general chemistry and chemical biology, yet dozens of different computational definitions exist. In prior work [Cho et al., Chem-PhysChem 21, 688-696 (2020)], we showed that these can be reduced to at most three 'principal components of ionicity'. The present study addressed the dependence of 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 sev
Journal of Physical Chemistry A, 2024
High-accuracy composite wave function methods like Weizmann-4 (W4) theory, high-accuracy extrapol... more High-accuracy composite wave function methods like Weizmann-4 (W4) theory, high-accuracy extrapolated ab initio thermochemistry (HEAT), and the Feller−Peterson−Dixon (FPD) approach enable sub-kJ/mol accuracy in gas-phase thermochemical properties. Their biggest computational bottleneck is the evaluation of the valence post-CCSD(T) correction term. We demonstrate here, for the W4-17 thermochemistry benchmark and subsets thereof, that the Λ coupled-cluster expansion converges more rapidly and smoothly than the regular coupled-cluster series. By means of CCSDT(Q) Λ and CCSDTQ(5) Λ , we can considerably (up to an order of magnitude) accelerate W4-and W4.3-type calculations without loss in accuracy, leading to the W4Λ and W4.3Λ computational thermochemistry protocols.
PCCP, 2022
The S66x8 noncovalent interactions benchmark has been re-evaluated at the ''sterling silver'' lev... 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 values differ by 0.1 kcal mol À1 RMS from the original Hobza benchmark and its revision by Brauer et al., but by only 0.04 kcal mol À1 RMS from the ''bronze'' level data in Kesharwani et al., Aust. J. Chem., 2018, 71, 238-248. 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(T 1) 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) À Tight(T)]. In contrast, PNO-LCCSD(T) works best with counterpoise, while performance with and without counterpoise is comparable for DLPNO-CCSD(T 1). Among more economical methods, the highest accuracies are seen for dRPA75-D3BJ, oB97M-V, oB97M(2), revDSD-PBEP86-D4, and DFT(SAPT) with a TDEXX or ATDEXX kernel.
Journal of Chemical Theory and Computation, 2023
We present correlation consistent basis sets for explicitly correlated (F12) calculations, denote... more We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. The cc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wis are [9s8p6d3f 2g] for the 3d-block elements and [7s7p6d3f 2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wis basis sets are evaluated on challenging test sets for metal− organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of maingroup elements; however, it is somewhat more significant for metal clusters.
Journal of Chemical Physics, 2023
In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and 157, 234102 (2022)] we c... 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 density functional with the lowest GMTKN55 "WTMAD2" error (1.76 kcal/mol) yet seen for any hybrid or double-hybrid density-functional approximation. We call it "DH23".
Journal of Physical Chemistry A, 2023
It is well-known that both wave function ab initio and DFT calculations on second-row compounds e... more It is well-known that both wave function 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.
JPC Letters, 2022
/acs.jctc.2c00426] that showed how the slow basis set convergence of the double hybrid density fu... more /acs.jctc.2c00426] that showed how the slow basis set convergence of the double hybrid density functional theory can be obviated by the use of F12 explicit correlation in the GLPT2 step (second order Gorling-Levy perturbation theory), we demonstrate here for the very large and chemically diverse GMTKN55 benchmark suite that the CPU time scaling of this step can be reduced (asymptotically linearized) using the localized pair natural orbital (PNO-L) approximation at negligible cost in accuracy.
J. Chem. Theory Comput., 2022
Double-hybrid density functional theory (DHDFT) offers a pathway to accuracy approaching composit... more Double-hybrid density functional theory (DHDFT) offers a pathway to accuracy approaching composite wavefunction approaches such as G4 theory. However, the Gorling−Levy second-order perturbation theory (GLPT2) term causes them to partially inherit the slow ∝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 (where GLPT2 is replaced by GLPT2-F12) for the large and chemically diverse general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) benchmark suite. The B2GP-PLYP-D3(BJ) and revDSD-PBEP86-D4 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-pVQZ-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-QZVPPD 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 applications 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.
J. Phys. Chem. A, 2022
To better understand the thermochemical kinetics and mechanism of a specific chemical reaction, a... 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 energies is vital. Because of the large size of reactants and transition state structures involved in real-life mechanistic studies (e.g., enzymatically catalyzed reactions), density functional theory remains the workhorse for such calculations. In this paper, we have assessed the performance of 91 density functionals for modeling the reaction energies and barrier heights on a large and chemically diverse data set (BH9) composed of 449 organic chemistry reactions. We have shown that range-separated hybrid functionals perform better than the global hybrids for BH9 barrier heights and reaction energies. Except for the PBE-based range-separated nonempirical double hybrids, range separation of the exchange term helps improve the performance for barrier heights and reaction energies. The 16-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.
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Journal of Physical Chemistry B, 2022
Recent quantum chemical computations demonstrated the electron-acceptance behavior of this highly... more Recent quantum chemical computations demonstrated the electron-acceptance behavior of this highly reactive cyclo[18]carbon (C 18) ring with piperidine (pip). The C 18 −pip complexation exhibited a double-well potential along the N−C reaction coordinate, forming a van der Waals (vdW) adduct and a more stable, strong covalent/dative bond (DB) complex by overcoming a low activation barrier. By means of direct dynamical computations using canonical variational transition state theory (CVT), including the small-curvature tunneling (SCT), we show the conspicuous role of heavy atom quantum mechanical tunneling (QMT) in the transformation of vdW to DB complex in the solvent phase near absolute zero. Below 50 K, the reaction is entirely driven by QMT, while at 30 K, the QMT rate is too rapid (k T ∼ 0.02 s −1), corresponding to a half-life time of 38 s, indicating that the vdW adduct will have a fleeting existence. We also explored the QMT rates of other cyclo[n]carbon−pip systems. This study sheds light on the decisive role of QMT in the covalent/DB formation of the C 18 −pip complex at cryogenic temperatures.
Journal of Chemical Theory and Computation, 2022
for realistic organometallic catalytic reactions, using both canonical CCSD(T) and localized orbi... more 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 (T 1) 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 density functional theory (DFT) methods for MOBH35, it would be best to remove reaction 9 entirely as its severe level of static correlation makes it just too demanding for a test. The magnitude of the difference between DLPNO-CCSD(T) and DLPNO-CCSD(T 1) is a reasonably good predictor for errors in DLPNO-CCSD(T 1) compared to canonical CCSD(T); otherwise, monitoring all of T 1 , D 1 , max|t i A |, and 1/(ε LUMO − ε HOMO) should provide adequate warning for potential problems. Our conclusions are not specific to the def2-SVP basis set but are largely conserved for the larger def2-TZVPP, as they are for the smaller def2-SV(P): the latter may be an economical choice for calibrating against canonical CCSD(T). Finally, diagnostics for static correlation are statistically clustered into groups corresponding to (1) importance of single excitations in the wavefunction; (2a) the small band gap, weakly separated from (2b) correlation entropy; and (3) thermochemical importance of correlation energy, as well as the slope of the DFT reaction energy with respect to the percentage of HF exchange. Finally, a variable reduction analysis reveals that much information on the multireference character is provided by T 1 , I ND /I tot , and the exchange-based diagnostic A 100 [TPSS].
Journal of Physical Chemistry Letters, 2021
By adding a GLPT3 (third-order Gorling-Levy perturbation theory, or KS-MP3) term E 3 to the XYG7 ... more By adding a GLPT3 (third-order Gorling-Levy perturbation theory, or KS-MP3) term E 3 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 wave function ab initio approaches. Intriguingly, (a) the introduction of E 3 makes an empirical dispersion correction redundant; (b) generalized gradient approximation (GGA) or meta-GGA semilocal correlation functionals offer no advantage over the local density approximation (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 six-parameter functional with WTMAD2 = 1.42 that has no post-LDA density functional theory components and no dispersion correction in the final energy.
Journal of Physical Chemistry A, 2021
We have evaluated a set of accurate canonical CCSD(T) energies for stationary points on the poten... more We have evaluated a set of accurate canonical CCSD(T) energies for stationary points on the potential energy surface for Ru(II, III) chloride carbonyl catalysis of two competing reactions between benzene and methyl acrylate (MA), namely, hydroarylation and oxidative coupling. We have then applied this set to evaluate the performance of localized orbital coupled-cluster methods and several new and common density functionals. We find that (a) DLPNO-CCSD(T) with TightPNO cutoffs is an acceptable substitute for full canonical CCSD(T) calculations on this system; (b) for the closed-shell systems where it could be applied, LNO-CCSD(T) with tight convergence criteria is very close to the canonical results; (c) the recent ωB97X-V and ωB97M-V functionals exhibit superior performance to commonly used DFT functionals in both closed-and open-shell calculations; (d) the revDSD-PBEP86 revision of the DSD-PBEP86 double hybrid represents an improvement over the original, even though transition metals were not involved in its parametrization; and (e) DSD-SCAN and DOD-SCAN show comparable efficiency. Most tested (meta)-GGA and hybrid density functionals perform better for open-shell than for closed-shell complexes; this is not the case for the double hybrids considered.
Israel Journal of Chemistry, 2022
[Perspective article] It can be argued that electron correlation, as a concept, deserves the same... more [Perspective article] 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".
Journal of Chemical Theory and Computation, 2020
A hierarchy of wavefunction composite methods (cWFT), based on G4-type cWFT methods available for... more A hierarchy of wavefunction composite methods (cWFT), based on G4-type cWFT methods available for elements H through Rn, was recently reported by the present authors [J. Chem. Theor. Comput. 2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Møller−Plesset correction and replacing the Weigend−Ahlrichs def2-mZVPP(D) basis sets used with complete basis set extrap-olation from augmented correlation-consistent core−valence triple-ζ, aug-cc-pwCVTZ(-PP), and quadruple-ζ, 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 a modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component. ■ INTRODUCTION Composite wavefunction theoretical (cWFT) methods continue to be a mainstay for reaching kcal/mol level "chemical accuracy" for reaction energies. Some of the well-established approaches include the Gaussian-n (Gn), 1−7 CBS-QB3, 8,9 multicoefficient correlation methods (MCCM), 10−12 the correlation-consistent composite approach (ccCA), 13−15 and, in sub-kcal/mol accuracy regimes, the Weizmann-n variants , 16−23 the HEAT-n methods, 24−26 and the Feller− Peterson−Dixon (FPD) 27−29 approach. All of these share a canonical coupled-cluster CCSD(T) 30,31 component. One step toward the pursuit of accurate low-cost cWFTs was a recent DLPNO-CCSD(T)-based method (DLPNO-ccCA) 32 suitable for the elements of the first and second rows of the PTE; it was parametrized to the small G2/97 training set 33,34 of 148 small closed-shell species, the largest organic molecule in it being benzene. The above methods, in their original form, focused on light elements. Very recently, Chan, Karton, and Raghavachari (CKR) 35 extended the applicability of G4(MP2) to the entire spd blocks of H-Rn through a switch to Weigend−Ahlrichs/ Karlsruhe/def2-type basis sets. 36 When we applied this G4(MP2)-XK to the larger and more chemically diverse GMTKN55 benchmark suitegeneral main-group thermochemistry, kinetics, and noncovalent interactions, with 55 problem sets 37 entailing with almost 2500 unique calculations on systems as large as 81 atomswe were astonished to find 38 WTMAD2, weighted mean absolute deviation type 2, values inferior to the best available double-hybrid 39 (see refs 40−43 for reviews) density functional theory (DFT) functionals, 43,44 which reach WTMAD2 values in the 2.2−2.3 kcal/mol range. As it turned out, by refitting to GMTKN55 and carefully monitoring statistical significance of empirical parameters, we were able to develop 38 a new family of cWFT methods using def2 basis sets: in particular, G4-T and G4-T-DLPNO methods reached WTMAD2 values of just 1.51 and 1.66
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Featured paper by Gershom Martin