RESUMEN

ATOMIC is a midlevel thermochemistry protocol that uses Pople's concept of bond separation reactions (BSRs) as a theoretical framework to reduce computational demands in the evaluation of atomization energies and enthalpies of formation. Various composite models are available that approximate bond separation energies at the complete-basis-set limit of all-electron CCSD(T), each balancing computational cost with achievable accuracy. Evaluated energies are then combined with very high-level, precomputed atomization energies of all auxiliary molecules appearing in the BSR to obtain the atomization energy of the molecule under study. ATOMIC-2 is a new version of the protocol that retains the overall concept and all previously defined composite models but improves on ATOMIC-1 in various other ways: Geometry optimization and zero-point-energy evaluation are performed at the density functional level (PBE0-D3/6-311G(d)), which shows significant computational savings and better accuracy than the previously employed RI-MP2/cc-pVTZ. The BSR framework is improved, using more accurate complete-basis-set (CBS) extrapolations toward the Full CI limit for the atomization energies of all auxiliary molecules. Finally, and most importantly, an error and uncertainty model termed ATOMIC-2um is added that estimates average bias and uncertainty for each of the atomization energy contributions that arise from the simplified treatment of some contributions to bond separation energies (CCSD(T)) and the neglect of others (such as higher order, scalar relativistic, or diagonal Born-Oppenheimer corrections) or from residual error in the energies of auxiliary molecules. Large and diverse benchmarks including up to 1179 molecules are used to evaluate necessary reference data and to correlate the observed error for each of the contributions with appropriate proxies that are available without additional quantum-chemical calculations for a particular molecule and represent its size and type. The implementation of ATOMIC-2 considers neutral, closed-shell molecules containing H, C, N, O, and F atoms; compared to ATOMIC-1, the framework has been extended to cover a few challenging but rare bond topologies. In comparison to highly accurate reference data for 184 molecules taken from the ATcT database (V. 1.122r), regular ATOMIC-2 shows noticeable underbinding, but the bias-corrected protocol ATOMIC-2um is found to be more accurate than either ATOMIC-1 or standard Gaussian-4 theory, and the uncertainty model is consistent with statistics of actually observed errors. Problems arising from ambiguous or challenging Lewis-valence structures defining BSRs are discussed, and computational efficiency is demonstrated. Computer code is made available to perform ATOMIC-2um analyses.

RESUMEN

Density functionals are often used in ab initio thermochemistry to provide optimized geometries for single-point evaluations at a high level and to supply estimates of anharmonic zero-point energies (ZPEs). Their use is motivated by relatively high accuracy at a modest computational expense, but a thorough assessment of geometry-related error seems to be lacking. We have benchmarked 53 density functionals, focusing on approximations of the first four rungs and on relatively small basis sets for computational efficiency. Optimized geometries of 279 neutral first-row molecules (H, C, N, O, F) are judged by energy penalties relative to the best available geometries, using the composite model ATOMIC/B5 as energy probe. Only hybrid functionals provide good accuracy with root-mean-square errors around 0.1 kcal/mol and maximum errors below 1.0 kcal/mol, but not all of them do. Conspicuously, first-generation hybrids with few or no empirical parameters tend to perform better than highly parameterized ones. A number of them show good accuracy already with small basis sets (6-31G(d), 6-311G(d)). As is standard practice, anharmonic ZPEs are estimated from scaled harmonic values. Statistics of the latter show less performance variation among functionals than observed for geometry-related error, but they also indicate that ZPE error will generally dominate. We have selected PBE0-D3/6-311G(d) for the next version of the ATOMIC protocol (ATOMIC-2) and studied it in more detail. Empirical expressions have been calibrated to estimate bias corrections and 95% uncertainty intervals for both geometry-related error and scaled ZPEs.

RESUMEN

ATOMIC is a thermochemistry protocol geared toward larger molecules with first-row atoms. It implements Pople's concept of bond separation reactions in an ab initio fashion and so enhances the accuracy of midlevel composite models for atomization energies. Recently we have introduced ATOMIC(hc), a model for applications to hydrocarbons, that estimates bias and uncertainty for each of the components contributing to the ATOMIC bottom-of-the-well atomization energy ( Bakowies , D. J. Chem. Theory Comput. 2019 , 15 , 5230 - 5251 ). Here we scrutinize the remaining components of the ATOMIC protocol, including midlevel composite models to approximate the complete-basis set (CBS) limit of CCSD(T) as well as zero-point energies (ZPEs) and thermal enthalpy increments that are evaluated from scaled harmonic MP2 frequencies. Potential errors relating to imperfections in MP2 geometries and ZPEs are estimated using auxiliary information obtained from geometry optimizations and frequency calculations at the density functional (B3LYP) level. Overall corrections to and uncertainties of enthalpies of formation are obtained from summation and error propagation, respectively. The error and uncertainty model is validated with accurate data from the Active Thermochemical Tables (ATcT) and compared to earlier statistical assessments for the G3/99 benchmark. The proposed model is a welcome alternative to statistical assessment, first because it does not depend on comparison with experiment, second because it recognizes the expected scaling of error with system size, and third because it provides a detailed account of the importance of various contributions to overall error and uncertainty. The evaluation of ZPEs from scaled harmonic frequencies expectedly emerges as the leading source of uncertainty if highly accurate composite models are used to treat the electronic problem, but uncertainties are usually balanced with those arising from computationally more attractive B level (B1...B6) models to estimate the CBS limit of CCSD(T). ATOMIC(hc) enthalpies of formation, complete with uncertainty estimates, are reported for 161 hydrocarbons ranging in size from methane (CH4) to [8]circulene (C32H16) and tetra-tert-butyltetrahedrane (C20H36). Experimental data are available for 127 molecules but cannot be reconciled with theory in 37 cases. Theory helps to identify the more accurate among conflicting experimental values in 11 cases and emerges as a valuable complement to experiment also for larger molecules, provided that fair estimates of uncertainty are available.

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Research in ab initio quantum chemistry has produced an increasing number of thermochemistry protocols, serving different needs from benchmark-level accuracy for small molecules to "chemical accuracy" for larger molecules. While in experimental thermochemistry it is accepted standard to report results complete with intervals of 95% confidence, so far few of the most advanced theoretical approaches have followed suit, based on either statistical comparison to well-established experimental data or careful assessment of high level theoretical results for individual molecules. Here we report on the development of intrinsic uncertainty estimates for the ATOMIC protocol in applications to hydrocarbons. ATOMIC is a theoretical procedure geared toward larger molecules and based on the ab initio implementation of bond separation reactions (BSRs) to reduce errors of midlevel composite approaches. Each of the components contributing to the bottom-of-the-well atomization energy (EA,e) is scrutinized for possible error by comparison to a large number of very high-level results, including complete-basis-set estimates of CCSDT(Q) bond separation energies for 83 hydrocarbons up to the size of naphthalene. Some of the observations are the following: Post-CCSD(T) effects are sizable even for saturated aliphatic compounds but well-represented in a BSR model summing over bond contributions, while conjugated systems pose more problems. Another significant source of error is the complete-basis-set extrapolation of all-electron CCSD(T) contributions, which still carries an uncertainty of a few tenths of a kcal/mol for midsize molecules like benzene, even if based on large basis-set calculations (cc-pCV5Z, cc-pCV6Z). Scalar relativistic terms and diagonal Born-Oppenheimer corrections are of less concern, the former because they are well represented in a BSR model and the latter because they are small in general. Observations are cast into simple expressions that separate obvious bias from nonsystematic error, formulating the former as correction to and the latter as uncertainty of an ATOMIC result. The updated protocol, complete with uncertainties and termed ATOMIC(hc) ("hc" for hydrocarbons), is validated in comparisons with both experimental data from the Active Thermochemical Tables and high-level theoretical data generated in this work. Analysis of lower-level ATOMIC models and of further components needed to convert EA,e into enthalpies of formation will be reported separately.

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The reliability of popular density functionals was studied for the description of torsional profiles of 36 molecules: glyoxal, oxalyl halides, and their thiocarbonyl derivatives. HF and 18 functionals of varying complexity, from local density to range-separated hybrid approximations and double-hybrid, have been considered and benchmarked against CCSD(T)-level rotational profiles. For molecules containing heavy halogens, most functionals fail to reproduce barrier heights accurately and a number of functionals introduce spurious minima. Dispersion corrections show no improvement. Calibrated torsion-corrected atom-centered potentials rectify the shortcomings of PBE and also improve on σ-hole based intermolecular binding in dimers and crystals.

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The ATOMIC protocol is a quantum-chemical thermochemistry protocol designed to obtain accurate atomization energies and derived heats of formation. It reduces errors of computationally tractable composite schemes through the use of bond separation reactions, which are implemented in a consistent ab initio framework. The present work explores possible simplification of previously introduced ATOMIC models. While coupled cluster calculations with singles and doubles excitations and perturbational treatments of connected triples excitations [CCSD(T)] are still required for high accuracy, basis-set truncations are possible in the CCSD-MP2 and CCSD(T)-CCSD components. The resulting models B4, B5, and B6 show root-mean-square (RMS) errors of only 0.21 to 0.46 kcal/mol for the AE set, which is a benchmark comprising complete-basis-set CCSD(T)(full) atomization energies of 73 neutral, closed-shell molecules composed of H, C, N, O, and F atoms. The evaluation of connected triples excitations can be avoided at medium levels of accuracy if the complete-basis-set MP2 energy is augmented with an empirically calibrated fraction of the difference between MP3 (or CCSD) and MP2 energies, calculated with small basis sets. The corresponding EMP3 and ECCSD models show RMS errors of 1.01 and 0.70 kcal/mol, respectively. Spin-component scaling is an option to rely entirely on the MP2 level of theory and still cut the RMS error of 4.38 kcal/mol by roughly a factor of 2 and achieve an accuracy comparable to accurate density functionals, such as M05-2X. The proposed new models are additionally tested with the HOF benchmark, a subset of G3/99 heats of formation that includes only neutral closed-shell molecules composed of H, C, N, O, and F atoms. The assessment shows that a number of experimental reference values are in error and should be replaced with more recent data. Results obtained with the new models are compared to original HOF (G3/99) reference data, to updated reference data, and to accurate ATOMIC/A theoretical data.

RESUMEN

The recently proposed ATOMIC protocol is a fully ab initio thermochemical protocol that rests upon the concept of bond separation reactions (BSRs) to correct for systematic errors of composite wave function approaches. It achieves high accuracy for atomization energies and derived heats of formation if basis set requirements for all contributing components are balanced carefully. The present work explores the potential of density functionals as possible replacements of composite wave function approaches in the ATOMIC protocol. Twenty density functionals are examined for their accuracy in thermochemical predictions based on calculated bond-separation energies and precomputed high-level data for the small parent molecules entering BSRs. The best density functionals outperform CCSD (coupled cluster with singles and doubles excitations), but none reaches the accuracy of well-balanced composite wave function approaches that consider quasiperturbational connected triples excitations at least with small basis sets. Some functionals show unexpected problems with bond separation reactions and are analyzed further with a model of empirically calibrated bond additivity corrections. Finally, the benefit of adding empirical dispersion terms to common density functionals is analyzed in the context of BSR-corrected thermochemistry.

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The recently proposed ATOMIC protocol is a fully ab initio thermochemical approach designed to provide accurate atomization energies for molecules with well-defined valence structures. It makes consistent use of the concept of bond-separation reactions to supply high-level precomputed bond increments which correct for errors of lower-level models. The present work extends the approach to the calculation of standard heats of formation and validates it by comparison to experimental and benchmark level ab initio data reported in the literature. Standard heats of formation (298 K) have been compiled for a large sample of 173 neutral molecules containing hydrogen and first-row atoms (C, N, O, F), resorting to several previous compilations and to the original experimental literature. Statistical evaluation shows that the simplest implementation of the ATOMIC protocol (composite model C) achieves an accuracy comparable to the popular Gaussian-3 approach and that composite models A and B perform better. Chemical accuracy (1-2 kcal/mol) is normally achieved even for larger systems with about 10 non-hydrogen atoms and for systems with charge-separated valence structures, bearing testimony to the robustness of the bond-separation reaction model. Effects of conformational averaging have been examined in detail for the series of n-alkanes, and our most refined composite model A reproduces experimental heats of formation quantitatively, provided that conformational averaging is properly accounted for. Several cases of larger discrepancy with respect to experiment are discussed, and potential weaknesses of the approach are identified.

RESUMEN

A theoretical composite approach, termed ATOMIC for Ab initio Thermochemistry using Optimal-balance Models with Isodesmic Corrections, is introduced for the calculation of molecular atomization energies and enthalpies of formation. Care is taken to achieve optimal balance in accuracy and cost between the various components contributing to high-level estimates of the fully correlated energy at the infinite-basis-set limit. To this end, the energy at the coupled-cluster level of theory including single, double, and quasiperturbational triple excitations is decomposed into Hartree-Fock, low-order correlation (MP2, CCSD), and connected-triples contributions and into valence-shell and core contributions. Statistical analyses for 73 representative neutral closed-shell molecules containing hydrogen and at least three first-row atoms (CNOF) are used to devise basis-set and extrapolation requirements for each of the eight components to maintain a given level of accuracy. Pople's concept of bond-separation reactions is implemented in an ab initio framework, providing for a complete set of high-level precomputed isodesmic corrections which can be used for any molecule for which a valence structure can be drawn. Use of these corrections is shown to lower basis-set requirements dramatically for each of the eight components of the composite model. A hierarchy of three levels is suggested for isodesmically corrected composite models which reproduce atomization energies at the reference level of theory to within 0.1 kcal/mol (A), 0.3 kcal/mol (B), and 1 kcal/mol (C). Large-scale statistical analysis shows that corrections beyond the CCSD(T) reference level of theory, including coupled-cluster theory with fully relaxed connected triple and quadruple excitations, first-order relativistic and diagonal Born-Oppenheimer corrections can normally be dealt with using a greatly simplified model that assumes thermoneutral bond-separation reactions and that reduces the estimate of these corrections to the simple task of adding up bond increments. Preliminary validation with experimental enthalpies of formation using the subset of neutral closed-shell (HCNOF) species contained in the G3/99 test set indicates that the ATOMIC protocol performs slightly better than the popular G3 approach. The newly introduced protocol does not require empirical calibration, however, and it is still efficient enough to be applied routinely to molecules with 10 or 20 nonhydrogen atoms.

RESUMEN

A new two-point scheme is proposed for the extrapolation of electron correlation energies obtained with small basis sets. Using the series of correlation-consistent polarized valence basis sets, cc-pVXZ, the basis set truncation error is expressed as deltaE(X) proportional, variant(X + xi(i))(-gamma). The angular momentum offset xi(i) captures differences in effective rates of convergence previously observed for first-row molecules. It is based on simple electron counts and tends to values close to 0 for hydrogen-rich compounds and values closer to 1 for pure first-row compounds containing several electronegative atoms. The formula is motivated theoretically by the structure of correlation-consistent basis sets which include basis functions up to angular momentum L = X-1 for hydrogen and helium and up to L = X for first-row atoms. It contains three parameters which are calibrated against a large set of 105 reference molecules (H, C, N, O, F) for extrapolations of MP2 and CCSD valence-shell correlation energies from double- and triple-zeta (DT) and triple- and quadruple-zeta (TQ) basis sets. The new model is shown to be three to five times more accurate than previous two-point schemes using a single parameter, and (TQ) extrapolations are found to reproduce a small set of available R12 reference data better than even (56) extrapolations using the conventional asymptotic limit formula deltaE(X) proportional, variantX(-3). Applications to a small selection of boron compounds and to neon show very satisfactory results as well. Limitations of the model are discussed.

RESUMEN

The electron correlation energy of two-electron atoms is known to converge asymptotically as approximately (L+1)(-3) to the complete basis set limit, where L is the maximum angular momentum quantum number included in the basis set. Numerical evidence has established a similar asymptotic convergence approximately X(-3) with the cardinal number X of correlation-consistent basis sets cc-pVXZ for coupled cluster singles and doubles (CCSD) and second order perturbation theory (MP2) calculations of molecules. The main focus of this article is to probe for deviations from asymptotic convergence behavior for practical values of X by defining a trial function X(-beta) that for an effective exponent beta=beta(eff)(X,X+1,X+N) provides the correct energy E(X+N), when extrapolating from results for two smaller basis sets, E(X) and E(X+1). This analysis is first applied to "model" expansions available from analytical theory, and then to a large body of finite basis set results (X=D,T,Q,5,6) for 105 molecules containing H, C, N, O, and F, complemented by a smaller set of 14 molecules for which accurate complete basis set limits are available from MP2-R12 and CCSD-R12 calculations. beta(eff) is generally found to vary monotonically with the target of extrapolation, X+N, making results for large but finite basis sets a useful addition to the limited number of cases where complete basis set limits are available. Significant differences in effective convergence behavior are observed between MP2 and CCSD (valence) correlation energies, between hydrogen-rich and hydrogen-free molecules, and, for He, between partial-wave expansions and correlation-consistent basis sets. Deviations from asymptotic convergence behavior tend to get smaller as X increases, but not always monotonically, and are still quite noticeable even for X=5. Finally, correlation contributions to atomization energies (rather than total energies) exhibit a much larger variation of effective convergence behavior, and extrapolations from small basis sets are found to be particularly erratic for molecules containing several electronegative atoms. Observed effects are discussed in the light of results known from analytical theory. A carefully calibrated protocol for extrapolations to the complete basis set limit is presented, based on a single "optimal" exponent beta(opt)(X,X+1,infinity) for the entire set of molecules, and compared to similar approaches reported in the literature.

RESUMEN

Computation based on molecular models is playing an increasingly important role in biology, biological chemistry, and biophysics. Since only a very limited number of properties of biomolecular systems is actually accessible to measurement by experimental means, computer simulation can complement experiment by providing not only averages, but also distributions and time series of any definable quantity, for example, conformational distributions or interactions between parts of systems. Present day biomolecular modeling is limited in its application by four main problems: 1) the force-field problem, 2) the search (sampling) problem, 3) the ensemble (sampling) problem, and 4) the experimental problem. These four problems are discussed and illustrated by practical examples. Perspectives are also outlined for pushing forward the limitations of biomolecular modeling.

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We present the latest version of the Groningen Molecular Simulation program package, GROMOS05. It has been developed for the dynamical modelling of (bio)molecules using the methods of molecular dynamics, stochastic dynamics, and energy minimization. An overview of GROMOS05 is given, highlighting features not present in the last major release, GROMOS96. The organization of the program package is outlined and the included analysis package GROMOS++ is described. Finally, some applications illustrating the various available functionalities are presented.

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The conformational spaces of five oligomers of tetrahydrofuran-based carbopeptoids in chloroform and dimethyl sulfoxide were investigated through nine molecular dynamics simulations. Prompted by nuclear magnetic resonance experiments that indicated various stable folds for some but not all of these carbopeptoids, their folding behaviour was investigated as a function of stereochemistry, chain length and solvent. The conformational distributions of these molecules were analysed in terms of occurrence of hydrogen bonds, backbone torsional-angle distributions, conformational clustering and solute configurational entropy. While a cis-linkage across the tetrahydrofuran ring favours right-handed helical structures, a trans-linkage results in a larger conformational variability. Intra-solute hydrogen bonding is reduced with increasing chain length and with increasing solvent polarity. Solute configurational entropies confirm the picture obtained: they are smaller for cis- than for trans-linked peptides, for chloroform than for dimethyl sulfoxide as solvent and for shorter peptide chains. The simulations provide an atomic picture of molecular conformational variability that is consistent with the available experimental data.

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Circular dichroism spectra of two beta-peptides, i.e. peptides composed of beta-amino acids, calculated using ensembles of configurations obtained by molecular dynamics simulation are presented. The calculations were based on 200 ns simulations of a beta-heptapeptide in methanol at 298 K and 340 K and a 50 ns simulation of a beta-hexapeptide in methanol at 340 K. In the simulations the peptides sampled both folded (helical) and unfolded structures. Trajectory structures with common backbone conformations were identified and grouped into clusters. The CD spectra were calculated for individual structures, based on peptide-group dipole transition moments obtained from semi-empirical molecular orbital theory and using the so-called matrix method. The single-structure spectra were then averaged over entire trajectories and over clusters of structures. Although certain features of the experimental CD spectra of the beta-peptides are reproduced by the trajectory-average spectra, there exist clear differences between the two sets of spectra in both wavelength and peak intensities. The analysis of individual contributions to the average spectra shows that, in general, the interpretation of a CD signal in terms of a single structure is not possible. Moreover, there is a large variation in the CD spectra calculated for a set of individual structures that belong to the same cluster, even when a structurally tight clustering criterion is used. This indicates that the CD spectra of these peptides are very sensitive to small local structural differences.

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A computational approach based on Delaunay triangulation is presented to identify internal water molecules in proteins and to capture pathways of exchange with the bulk. The implemented procedure is computationally efficient and can easily be applied to long molecular dynamics trajectories of protein simulations. In an application to fatty acid-binding protein in apo-form and with bound palmitate, several protein orifices known from crystal structures have been confirmed to be major portals of solvent exchange. Differences between the two forms of the protein are observed and discussed.

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Two molecular dynamics simulations of 5 ns each have been carried out for rat intestinal fatty acid binding protein, in apo-form and with bound palmitate. The fatty acid and a number of water molecules are encapsulated in a large interior cavity of the barrel-shaped protein. The simulations are compared to experimental data and analyzed in terms of root mean square deviations, atomic B-factors, secondary structure elements, hydrogen bond patterns, and distance constraints derived from nuclear Overhauser experiments. Excellent agreement is found between simulated and experimental solution structures of holo-FABP, but a number of differences are observed for the apo-form. The ligand in holo-FABP shows considerable displacement after about 1.5 ns and displays significant configurational entropy. A novel computational approach has been employed to identify internal water and to capture exchange pathways. Orifices in the portal and gap regions of the protein, discussed in the experimental literature, have been confirmed as major openings for solvent exchange between the internal cavity and bulk water. A third opening on the opposite side of the barrel experiences significant exchange but it does not provide a pathway for further passage to the central cavity. Internal water is characterized in terms of density distributions, interaction energies, mobility, protein contact times, and water molecule coordination. A number of differences are observed between the apo and holo-forms and related to differences in the protein structure. Solvent inside apo-FABP, for example, shows characteristics of a water droplet, while solvent in holo-FABP benefits from interactions with the ligand headgroup and slightly stronger interactions with protein residues.

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