Showing 1–18 of 18 results for author: Karton, A

Accurate and scalable exchange-correlation with deep learning

Authors: Giulia Luise, Chin-Wei Huang, Thijs Vogels, Derk P. Kooi, Sebastian Ehlert, Stephanie Lanius, Klaas J. H. Giesbertz, Amir Karton, Deniz Gunceler, Stefano Battaglia, Gregor N. C. Simm, P. Bernát Szabó, Megan Stanley, Wessel P. Bruinsma, Lin Huang, Xinran Wei, José Garrido Torres, Abylay Katbashev, Rodrigo Chavez Zavaleta, Bálint Máté, Sékou-Oumar Kaba, Roberto Sordillo, Yingrong Chen, David B. Williams-Young, Christopher M. Bishop , et al. (3 additional authors not shown)

Abstract: Density Functional Theory (DFT) underpins much of modern computational chemistry and materials science. Yet, the reliability of DFT-derived predictions of experimentally measurable properties remains fundamentally limited by the need to approximate the unknown exchange-correlation (XC) functional. The traditional paradigm for improving accuracy has relied on increasingly elaborate hand-crafted fun… ▽ More Density Functional Theory (DFT) underpins much of modern computational chemistry and materials science. Yet, the reliability of DFT-derived predictions of experimentally measurable properties remains fundamentally limited by the need to approximate the unknown exchange-correlation (XC) functional. The traditional paradigm for improving accuracy has relied on increasingly elaborate hand-crafted functional forms. This approach has led to a longstanding trade-off between computational efficiency and accuracy, which remains insufficient for reliable predictive modelling of laboratory experiments. Here we introduce Skala, a deep learning-based XC functional that surpasses state-of-the-art hybrid functionals in accuracy across the main-group chemistry benchmark set GMTKN55 with an error of 2.8 kcal/mol, while retaining the lower computational cost characteristic of semi-local DFT. This demonstrated departure from the historical trade-off between accuracy and efficiency is enabled by learning non-local representations of electronic structure directly from data, bypassing the need for increasingly costly hand-engineered features. Leveraging an unprecedented volume of high-accuracy reference data from wavefunction-based methods, we establish that modern deep learning enables systematically improvable neural exchange-correlation models as training datasets expand, positioning first-principles simulations to become progressively more predictive. △ Less

Submitted 21 April, 2026; v1 submitted 17 June, 2025; originally announced June 2025.

Comments: The Skala model and inference code are available under MIT license at https://github.com/microsoft/skala

Accurate Chemistry Collection: Coupled cluster atomization energies for broad chemical space

Authors: Sebastian Ehlert, Jan Hermann, Thijs Vogels, Victor Garcia Satorras, Stephanie Lanius, Marwin Segler, Klaas J. H. Giesbertz, Derk P. Kooi, Kenji Takeda, Chin-Wei Huang, Giulia Luise, Rianne van den Berg, Paola Gori-Giorgi, Amir Karton

Abstract: Accurate thermochemical data with sub-chemical accuracy (within 1 kcal mol$^{-1}$ of the empirical ground truth) are essential for advancing computational chemistry methods. However, existing datasets that reach this level of accuracy remain limited in size or scope. This hinders the development of data-driven methods with predictive accuracy across the broad chemical space of closed-shell, neutra… ▽ More Accurate thermochemical data with sub-chemical accuracy (within 1 kcal mol$^{-1}$ of the empirical ground truth) are essential for advancing computational chemistry methods. However, existing datasets that reach this level of accuracy remain limited in size or scope. This hinders the development of data-driven methods with predictive accuracy across the broad chemical space of closed-shell, neutral molecules. Here we present Microsoft Research Accurate Chemistry Collection (MSR-ACC) and its first release, MSR-ACC/TAE25, comprising 73,040 total atomization energies at the CCSD(T)/CBS level obtained with the W1-F12 thermochemical protocol. The dataset is constructed to exhaustively cover the chemical space of closed-shell, charge-neutral, covalently bound equilibrium molecular structures containing up to 5 non-hydrogen atoms drawn from elements up to argon and lacking significant multireference character. The dataset and its canonical train and validation splits are openly available on Zenodo in the QCSchema format under the CDLA Permissive 2.0 license. This first release of MSR-ACC enables data-driven approaches for developing predictive computational chemistry methods with unprecedented accuracy and scope. △ Less

Submitted 16 February, 2026; v1 submitted 17 June, 2025; originally announced June 2025.

Comments: 9 pages plus references, 6 figures, dataset on Zenodo; CHANGES: fixed abstract metadata

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)

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)

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)

The S66 noncovalent interactions benchmark reconsidered using explicitly correlated methods near the basis set limit

Authors: Manoj K. Kesharwani, Amir Karton, Nitai Sylvetsky, Jan M. L. Martin

Abstract: The S66 benchmark for noncovalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 "high-level corrections" are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the… ▽ More The S66 benchmark for noncovalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 "high-level corrections" are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the other hand. Implications for earlier benchmarks on the larger S66x8 problem set in particular, and for accurate calculations on noncovalent interactions in general, are discussed. At a slight cost in accuracy, (T) can be considerably accelerated by using sano-V{D,T}Z+ basis sets, while half-counterpoise CCSD(F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost. △ Less

Submitted 26 December, 2017; originally announced December 2017.

Comments: Australian Journal of Chemistry, in press [Graham S. Chandler special issue]

Toward a W4-F12 approach: Can explicitly correlated and orbital-based ab initio CCSD(T) limits be reconciled?

Authors: Nitai Sylvetsky, Kirk A. Peterson, Amir Karton, Jan M. L. Martin

Abstract: In the context of high-accuracy computational thermochemistry, the valence CCSD correlation component of molecular atomization energies present the most severe basis set convergence problem, followed by the (T) component. In the present paper, we make a detailed comparison, for an expanded version of the W4-11 thermochemistry benchmark, between on the one hand orbital-based CCSD/AV{5,6}Z+d and CCS… ▽ More In the context of high-accuracy computational thermochemistry, the valence CCSD correlation component of molecular atomization energies present the most severe basis set convergence problem, followed by the (T) component. In the present paper, we make a detailed comparison, for an expanded version of the W4-11 thermochemistry benchmark, between on the one hand orbital-based CCSD/AV{5,6}Z+d and CCSD/ACV{5,6}Z extrapolation, and on the other hand CCSD-F12b calculations with cc-pVQZ-F12 and cc-pV5Z-F12 basis sets. This latter basis set, now available for H--He, B--Ne, and Al--Ar, is shown to be very close to the basis set limit. Apparent differences (which can reach 0.35 kcal/mol for systems like CCl4) between orbital-based and CCSD-F12b basis set limits disappear if basis sets with additional radial flexibility, such as ACV{5,6}Z, are used for the orbital calculation. Counterpoise calculations reveal that, while TAEs with V5Z-F12 basis sets are nearly free of BSSE, orbital calculations have significant BSSE even with AV(6+d)Z basis sets, leading to non-negligible differences between raw and counterpoise-corrected extrapolated limits. This latter problem is greatly reduced by switching to ACV{5,6}Z core-valence basis sets, or simply adding an additional zeta to just the valence orbitals. Previous reports that all-electron approaches like HEAT lead to different CCSD(T) limits than valence limit+CV correction approaches like FPD and W4 theory can be rationalized in terms of the greater radial flexibility of core-valence basis sets. W4-F12 is found to agree slightly better than W4 with ATcT (active thermochemical tables) data, at a substantial saving in CPU time and especially I/O overhead. A W4-F12 calculation on benzene is presented as a proof of concept. △ Less

Submitted 11 May, 2016; originally announced May 2016.

Comments: Journal of Chemical Physics, in press

Journal ref: Journal of Chemical Physics 144, 214101 (2016)

The CH3CHOO `Criegee Intermediate' and its anion: Isomers, Infrared spectra, and W3-F12 energetics

Authors: Marcus Kettner, Amir Karton, Allan McKinley, Duncan Wild

Abstract: For the CH3CHOO Criegee intermediates (ethanal-oxide) and analogous anions, we obtain heats of formations and electron affinities at CCSDT(Q)/CBS level of theory by means of the high-level W3-F12 thermochemical protocol. The electron affinities amount to 0.20 eV and 0.35 eV for the cis and trans isomer, respectively. Neutral cis and trans isomers are separated by 14.1 kJ/mol, the anions are almost… ▽ More For the CH3CHOO Criegee intermediates (ethanal-oxide) and analogous anions, we obtain heats of formations and electron affinities at CCSDT(Q)/CBS level of theory by means of the high-level W3-F12 thermochemical protocol. The electron affinities amount to 0.20 eV and 0.35 eV for the cis and trans isomer, respectively. Neutral cis and trans isomers are separated by 14.1 kJ/mol, the anions are almost isoenergetic (0.4 kJ/mol separation). Harmonic vibrational frequencies are presented at CCSD(T)/aug'-cc-pVTZ level of theory. Since the synthesis of these species in gas-phase experiments might be possible in the near future, we include a predicted photoelectron spectrum. △ Less

Submitted 5 January, 2015; v1 submitted 2 January, 2015; originally announced January 2015.

Comments: arXiv admin note: substantial text overlap with arXiv:1309.2554

Sneaking Up On The Criegee Intermediate From Below: Predicted Photoelectron Spectrum Of The CH_2OO^- Anion And W3-F12 Electron Affinity Of CH_2OO

Authors: Amir Karton, Marcus Kettner, Duncan Andrew Wild

Abstract: High level ab initio calculations were undertaken on the CH$_2$OO anion and neutral species to predict the electron affinity and anion photoelectron spectrum. The electron affinity of CH$_2$OO, 0.567 eV, and barrier height for dissociation of CH$_2$OO$^-$ to O$^-$ and CH$_2$O, 16.5 kJ mol$^{-1}$, are obtained by means of the W3-F12 thermochemical protocol. Two major geometric differences between t… ▽ More High level ab initio calculations were undertaken on the CH$_2$OO anion and neutral species to predict the electron affinity and anion photoelectron spectrum. The electron affinity of CH$_2$OO, 0.567 eV, and barrier height for dissociation of CH$_2$OO$^-$ to O$^-$ and CH$_2$O, 16.5 kJ mol$^{-1}$, are obtained by means of the W3-F12 thermochemical protocol. Two major geometric differences between the anion and neutral, being the dihedral angle of the terminal hydrogen atoms with respect to C-O-O plane, and the O-O bond length, are reflected in the predicted spectrum as pronounced vibrational progressions. △ Less

Submitted 11 September, 2013; v1 submitted 10 September, 2013; originally announced September 2013.

Journal ref: Chem.Phys.Let. 585 (2013) 15-20

Performance of W4 theory for spectroscopic constants and electrical properties of small molecules

Authors: Amir Karton, Jan M. L. Martin

Abstract: Accurate spectroscopic constants and electrical properties of small molecules are determined by means of W4 and post-W4 theories. For a set of 28 first- and second-row diatomic molecules for which very accurate experimental spectroscopic constants are available, W4 theory affords near-spectroscopic or better predictions. Specifically, the root-mean-square deviations (RMSD) from experiment are 0.04… ▽ More Accurate spectroscopic constants and electrical properties of small molecules are determined by means of W4 and post-W4 theories. For a set of 28 first- and second-row diatomic molecules for which very accurate experimental spectroscopic constants are available, W4 theory affords near-spectroscopic or better predictions. Specifically, the root-mean-square deviations (RMSD) from experiment are 0.04 pm for the equilibrium bond distances (r_e), 1.03 cm^{-1} for the harmonic frequencies (ω_e), 0.20 cm^{-1} for the first anharmonicity constants (ω_e x_e), 0.10 cm^{-1} for the second anharmonicity constants (ω_e y_e), and 0.001 cm^{-1} for the vibration-rotation coupling constants (α_e). Higher-order connected triples, \hat{T}_3-(T), improve agreement with experiment for the hydride systems, but their inclusion (in the absence of \hat{T}_4) tends to worsen agreement with experiment for the nonhydride systems. Connected quadruple excitations, \hat{T}_4, have significant and systematic effects on r_e, ω_e, and ω_e x_e, in particular they universally increase r_e (by up to 0.5 pm), universally reduce ω_e (by up to 32 cm^{-1}), and universally increase ω_e x_e (by up to 1 cm^{-1}). Connected quintuple excitations, \hat{T}_5, are spectroscopically significant for ω_e of the nonhydride systems, affecting ω_e by up to 4 cm^{-1}. The triatomic molecules H_2O, CO_2, and O_3, as well as the pathologically multireference BN and BeO diatomics, are also considered. The asymmetric stretch of ozone represents a severe challenge to W4 theory, in particular the connected quadruple contribution converges very slowly with the basis set size. Finally, the importance of post-CCSD(T) correlation effects for electrical properties, namely dipole moments (μ), polarizabilities (α), and first hyperpolarizabilities (β) is evaluated. △ Less

Submitted 24 August, 2010; originally announced August 2010.

Comments: Journal of Chemical Physics, in press

Performance of ab initio and density functional methods for conformational equilibria of CnH2n+2 alkane isomers (n=2-8)

Authors: David Gruzman, Amir Karton, Jan M. L. Martin

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

Submitted 17 July, 2009; originally announced July 2009.

Comments: J. Phys. Chem. A, revised [Walter Thiel festschrift]

Journal ref: Journal of Physical Chemistry A 113, 11974-11983 (2009)

Benchmark thermochemistry of the C_nH_{2n+2} alkane isomers (n=2--8) and performance of DFT and composite ab initio methods for dispersion-driven isomeric equilibria

Authors: Amir Karton, David Gruzman, Jan M. L. Martin

Abstract: The thermochemistry of linear and branched alkanes with up to eight carbons has been reexamined by means of W4, W3.2lite and W1h theories. `Quasi-W4' atomization energies have been obtained via isodesmic and hypohomodesmotic reactions. Our best atomization energies at 0 K (in kcal/mol) are: 1220.04 n-butane, 1497.01 n-pentane, 1774.15 n-hexane, 2051.17 n-heptane, 2328.30 n-octane, 1221.73 isobut… ▽ More The thermochemistry of linear and branched alkanes with up to eight carbons has been reexamined by means of W4, W3.2lite and W1h theories. `Quasi-W4' atomization energies have been obtained via isodesmic and hypohomodesmotic reactions. Our best atomization energies at 0 K (in kcal/mol) are: 1220.04 n-butane, 1497.01 n-pentane, 1774.15 n-hexane, 2051.17 n-heptane, 2328.30 n-octane, 1221.73 isobutane, 1498.27 isopentane, 1501.01 neopentane, 1775.22 isohexane, 1774.61 3-methylpentane, 1775.67 diisopropyl, 1777.27 neohexane, 2052.43 isoheptane, 2054.41 neoheptane, 2330.67 isooctane, and 2330.81 hexamethylethane. Our best estimates for $ΔH^\circ_{f,298K}$ are: -30.00 n-butane, -34.84 n-pentane, -39.84 n-hexane, -44.74 n-heptane, -49.71 n-octane, -32.01 isobutane, -36.49 isopentane, -39.69 neopentane, -41.42 isohexane, -40.72 3-methylpentane, -42.08 diisopropyl, -43.77 neohexane, -46.43 isoheptane, -48.84 neoheptane, -53.29 isooctane, and -53.68 hexamethylethane. These are in excellent agreement (typically better than 1 kJ/mol) with the experimental heats of formation at 298 K obtained from the CCCBDB and/or NIST Chemistry WebBook databases. However, at 0 K a large discrepancy between theory and experiment (1.1 kcal/mol) is observed for only neopentane. This deviation is mainly due to the erroneous heat content function for neopentane used in calculating the 0 K CCCBDB value. The thermochemistry of these systems, especially of the larger alkanes, is an extremely difficult test for density functional methods. A posteriori corrections for dispersion are essential. Particularly for the atomization energies, the B2GP-PLYP and B2K-PLYP double-hybrids, and the PW6B95 hybrid-meta GGA clearly outperform other DFT functionals. △ Less

Submitted 20 May, 2009; originally announced May 2009.

Comments: (J. Phys. Chem. A, in press)

Journal ref: Journal of Physical Chemistry A 113, 8434-8447 (2009)

Atomization energies of the carbon clusters Cn (n=2--10) revisited by means of W4 theory as well as density functional, Gn, and CBS methods

Authors: Amir Karton, Alex Tarnopolsky, Jan M. L. Martin

Abstract: The thermochemistry of the carbon clusters C$_n$ (n=2--10) has been revisited by means of W4 theory and W3.2lite theory. Particularly the larger clusters exhibit very pronounced post-CCSD(T) correlation effects. Despite this, our best calculated total atomization energies agree surprisingly well with 1991 estimates obtained from scaled CCD(ST)/6-31G* data. Accurately reproducing the small single… ▽ More The thermochemistry of the carbon clusters C$_n$ (n=2--10) has been revisited by means of W4 theory and W3.2lite theory. Particularly the larger clusters exhibit very pronounced post-CCSD(T) correlation effects. Despite this, our best calculated total atomization energies agree surprisingly well with 1991 estimates obtained from scaled CCD(ST)/6-31G* data. Accurately reproducing the small singlet-triplet splitting in C$_2$ requires inclusion of connected quintuple and sextuple excitations. Post-CCSD(T) correlation effects in C$_4$ stabilize the linear form. Linear/cyclic equilibria in C$_6$, C$_8$, and C$_{10}$ are not strongly affected by connected quadruples, but they are affected by higher-order triples, which favor polyacetylenic rings but disfavor cumulenic ones. Near the CCSD(T) basis set limit, C$_{10}$ does undergo bond angle alternation in the bottom-of-the-well structure, although it is expected to be absent in the vibrationally averaged structure. The thermochemistry of these systems, and particularly the longer linear chains, is a particularly difficult test for density functional methods. Particularly for the smaller chains and the rings, double-hybrid functionals clearly outperform convential DFT functionals for these systems. Among compound thermochemistry schemes, G4 clearly outperforms the other members of the G$n$ family. Our best estimates for total atomization energies at 0 K should be reliable to 1 kJ/mol up to C$_5$ inclusive, and to better than 1 kcal/mol up to C$_9$ inclusive. △ Less

Submitted 19 December, 2008; originally announced December 2008.

Comments: [Mol. Phys., in press (Henry F. Schaefer III Festschrift)]

Journal ref: Molecular Physics 107, 977-990 (2009)

W4 thermochemistry of P_2 and P_4. Is the CODATA heat of formation of phosphorus atom correct?

Authors: Amir Karton, Jan M. L. Martin

Abstract: The high-accuracy W4 computational thermochemistry protocol, and several post-W4 methods, have been applied to the P$_2$ and P$_4$ molecules. Contrary to previous studies, we find the experimental thermochemistry to be fundamentally sound. The reaction enthalpy for P$_4\to 2$P$_2$ has a very significant contribution from post-CCSD(T) correlation effects. We derive a gas-phase heat of formation f… ▽ More The high-accuracy W4 computational thermochemistry protocol, and several post-W4 methods, have been applied to the P$_2$ and P$_4$ molecules. Contrary to previous studies, we find the experimental thermochemistry to be fundamentally sound. The reaction enthalpy for P$_4\to 2$P$_2$ has a very significant contribution from post-CCSD(T) correlation effects. We derive a gas-phase heat of formation for the phosphorus atom of $ΔH^\circ_{f,0}$[P(g)]=75.54$\pm$0.1 kcal/mol and $ΔH^\circ_{f,298}$[P(g)]=75.74$\pm$0.1 kcal/mol, in the upper half of the CODATA uncertainty interval. △ Less

Submitted 28 June, 2007; originally announced June 2007.

Comments: Mol. Phys., in press (Peter Pulay issue)

Journal ref: Molecular Physics 105, 2499 (2007)

Basis set convergence of post-CCSD contributions to molecular atomization energies

Authors: Amir Karton, Peter R. Taylor, Jan M. L. Martin

Abstract: Basis set convergence of correlation effects on molecular atomization energies beyond the CCSD (coupled cluster with singles and doubles) approximation has been studied near the one-particle basis set limit. Quasiperturbative connected triple excitations, (T), converge more rapidly than $L^{-3}$ (where $L$ is the highest angular momentum represented in the basis set), while higher-order connecte… ▽ More Basis set convergence of correlation effects on molecular atomization energies beyond the CCSD (coupled cluster with singles and doubles) approximation has been studied near the one-particle basis set limit. Quasiperturbative connected triple excitations, (T), converge more rapidly than $L^{-3}$ (where $L$ is the highest angular momentum represented in the basis set), while higher-order connected triples, $T_3-(T)$, converge more slowly -- empirically, $\propto L^{-5/2}$. Quasiperturbative connected quadruple excitations, (Q), converge smoothly as $\propto L^{-3}$ starting with the cc-pVTZ basis set, while the cc-pVDZ basis set causes overshooting of the contribution in highly polar systems. Higher-order connected quadruples display only weak, but somewhat erratic, basis set dependence. Connected quintuple excitations converge very rapidly with the basis set, to the point where even an unpolarized double-zeta basis set yields useful numbers. In cases where fully iterative CCSDTQ5 (coupled cluster up to connected quintuples) calculations are not an option, CCSDTQ(5) (i.e., coupled cluster up to connected quadruples plus a quasiperturbative connected quintuples correction) cannot be relied upon in the presence of significant nondynamical correlation, whereas CCSDTQ(5)$_Λ$ represents a viable alternative. Connected quadruples corrections to the core-valence contribution are thermochemically significant in some systems. [...] We conclude that ``$3σ\leq 1$ kJ/mol'' thermochemistry is feasible with current technology, but that the more ambitious goal of $\pm$10 cm$^{-1}$ accuracy is illusory, at least for atomization energies. △ Less

Submitted 12 June, 2007; originally announced June 2007.

Comments: (J. Chem. Phys., in press)

Journal ref: Journal of Chemical Physics 127, 064104 (2007)

The lowest singlet-triplet excitation energy of BN: a converged coupled cluster perspective

Authors: Amir Karton, Jan M. L. Martin

Abstract: The notoriously small $X ^3Π-a ^1Σ^+$ excitation energy of the BN diatomic has been calculated using high-order coupled cluster methods. Convergence has been established in both the 1-particle basis set and the coupled cluster expansion. Explicit inclusion of connected quadruple excitations $\hat{T}_4$ is required for even semiquantitative agreement with the limit value, while connected quintupl… ▽ More The notoriously small $X ^3Π-a ^1Σ^+$ excitation energy of the BN diatomic has been calculated using high-order coupled cluster methods. Convergence has been established in both the 1-particle basis set and the coupled cluster expansion. Explicit inclusion of connected quadruple excitations $\hat{T}_4$ is required for even semiquantitative agreement with the limit value, while connected quintuple excitations $\hat{T}_5$ still have an effect of about 60 cm$^{-1}$. Still higher excitations only account for about 10 cm$^{-1}$. Inclusion of inner-shell correlation further reduces $T_e$ by about 60 cm$^{-1}$ at the CCSDT, and 85 cm$^{-1}$ at the CCSDTQ level. Our best estimate, $T_e$=183$\pm$40 cm$^{-1}$, is in excellent agreement with earlier calculations and experiment, albeit with a smaller (and conservative) uncertainty. The dissociation energy of BN($X ^3Π$) is $D_e$=105.74$\pm$0.16 kcal/mol and $D_0$=103.57$\pm$0.16 kcal/mol. △ Less

Submitted 15 August, 2006; originally announced August 2006.

Comments: J. Chem. Phys., in press

Journal ref: J. Chem. Phys. 125, 144313 (2006)

W4 theory for computational thermochemistry: in pursuit of confident sub-kJ/mol predictions

Authors: Amir Karton, Elena Rabinovich, Jan M. L. Martin, Branko Ruscic

Abstract: In an attempt to improve on our earlier W3 theory [J. Chem. Phys. {\bf 120}, 4129 (2004)] we consider such refinements as more accurate estimates for the contribution of connected quadruple excitations ($\hat{T}_4$), inclusion of connected quintuple excitations ($\hat{T}_5$), diagonal Born-Oppenheimer corrections (DBOC), and improved basis set extrapolation procedures. Revised experimental data… ▽ More In an attempt to improve on our earlier W3 theory [J. Chem. Phys. {\bf 120}, 4129 (2004)] we consider such refinements as more accurate estimates for the contribution of connected quadruple excitations ($\hat{T}_4$), inclusion of connected quintuple excitations ($\hat{T}_5$), diagonal Born-Oppenheimer corrections (DBOC), and improved basis set extrapolation procedures. Revised experimental data for validation purposes were obtained from the latest version of the ATcT (Active Thermochemical Tables) Thermochemical Network. We found that the CCSDTQ$-$CCSDT(Q) difference converges quite rapidly with the basis set, and that the formula 1.10[CCSDT(Q)/cc-pVTZ+CCSDTQ/cc-pVDZ$-$CCSDT(Q)/cc-pVDZ] offers a very reliable as well as fairly cost-effective estimate of the basis set limit $\hat{T}_4$ contribution. The largest $\hat{T}_5$ contribution found in the present work is on the order of 0.5 kcal/mol (for ozone). DBOC corrections are significant at the 0.1 kcal/mol level in hydride systems. . Based on the accumulated experience, a new computational thermochemistry protocol for first-and second-row main-group systems, to be known as W4 theory, is proposed. Our W4 atomization energies for a number of key species are in excellent agreement (better than 0.1 kcal/mol on average, 95% confidence intervals narrower than 1 kJ/mol) with the latest experimental data obtained from Active Thermochemical Tables. A simple {\em a priori} estimate for the importance of post-CCSD(T) correlation contributions (and hence a pessimistic estimate for the error in a W2-type calculation) is proposed. △ Less

Submitted 11 August, 2006; originally announced August 2006.

Comments: J. Chem. Phys., in press; electronic supporting information available at http://theochem.weizmann.ac.il/web/papers/w4.html

Journal ref: J. Chem. Phys. 125, 144108 (2006)

Comment on: "Estimating the Hartree-Fock limit from finite basis set calculations" [Jensen F (2005) Theor Chem Acc 113:267]

Authors: Amir Karton, Jan M. L. Martin

Abstract: We demonstrate that a minor modification of the extrapolation proposed by Jensen [(2005): Theor Chem Acc 113:267] yields very reliable estimates of the Hartree-Fock limit in conjunction with correlation consistent basis sets. Specifically, a two-point extrapolation of the form $E_{HF,L}=E_{HF,\infty}+A(L+1)\exp(-9\sqrt{L})$ yields HF limits $E_{HF,\infty}$ with an RMS error of 0.1 millihartree u… ▽ More We demonstrate that a minor modification of the extrapolation proposed by Jensen [(2005): Theor Chem Acc 113:267] yields very reliable estimates of the Hartree-Fock limit in conjunction with correlation consistent basis sets. Specifically, a two-point extrapolation of the form $E_{HF,L}=E_{HF,\infty}+A(L+1)\exp(-9\sqrt{L})$ yields HF limits $E_{HF,\infty}$ with an RMS error of 0.1 millihartree using aug-cc-pVQZ and aug-cc-pV5Z basis sets, and of 0.01 millihartree using aug-cc-pV5Z and aug-cc-pV6Z basis sets. △ Less

Submitted 26 September, 2005; originally announced September 2005.

Comments: Theoretical Chemistry Accounts, in press

Journal ref: Theoretical Chemistry Accounts 115, 330-333 (2006)