Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds

Systematic Error Estimation for Chemical Reaction Energies

For a theoretical understanding of the reactivity of complex chemical systems, accurate relative energies between intermediates and transition states are required. Despite its popularity, density functional theory (DFT) often fails to provide sufficiently accurate data, especially for molecules containing transition metals. Due to the huge number of intermediates that need to be studied for all but the simplest chemical processes, DFT is, to date, the only method that is computationally feasible. Here, we present a Bayesian framework for DFT that allows for error estimation of calculated properties. Since the optimal choice of parameters in present-day density functionals is strongly system dependent, we advocate for a system-focused reparameterization. While, at first sight, this approach conflicts with the first-principles character of DFT that should make it, in principle, system independent, we deliberately introduce system dependence to be able to assign a stochastically meaningful error to the system-dependent parametrization, which makes it nonarbitrary. By reparameterizing a functional that was derived on a sound physical basis to a chemical system of interest, we obtain a functional that yields reliable confidence intervals for reaction energies. We demonstrate our approach on the example of catalytic nitrogen fixation.

An Evaluation of Gas Phase Enthalpies of Formation for Hydrogen-Oxygen (HxOy) Species

We have compiled gas phase enthalpies of formation for nine hydrogen-oxygen species (HxOy) and selected recommended values for H, O, OH, H2O, HO2, H2O2, O3, HO3, and H2O3. The compilation consists of values derived from experimental measurements, quantum chemical calculations, and prior evaluations. This work updates the recommended values in the NIST-JANAF (1985) and Gurvich et al. (1989) thermochemical tables for seven species. For two species, HO3 and H2O3 (important in atmospheric chemistry) and not found in prior thermochemical evaluations, we also provide supplementary data consisting of molecular geometries, vibrational frequencies, and torsional potentials which can be used to compute thermochemical functions. For all species, we also provide supplementary data consisting of zero point energies, vibrational frequencies, and ion reaction energetics.

The transition from the open minimum to the ring minimum on the ground state and on the lowest excited state of like symmetry in ozone: A configuration interaction study

The metastable ring structure of the ozone 1(1)A1 ground state, which theoretical calculations have shown to exist, has so far eluded experimental detection. An accurate prediction for the energy difference between this isomer and the lower open structure is therefore of interest, as is a prediction for the isomerization barrier between them, which results from interactions between the lowest two (1)A1 states. In the present work, valence correlated energies of the 1(1)A1 state and the 2(1)A1 state were calculated at the 1(1)A1 open minimum, the 1(1)A1 ring minimum, the transition state between these two minima, the minimum of the 2(1)A1 state, and the conical intersection between the two states. The geometries were determined at the full-valence multi-configuration self-consistent-field level. Configuration interaction (CI) expansions up to quadruple excitations were calculated with triple-zeta atomic basis sets. The CI expansions based on eight different reference configuration spaces were explored. To obtain some of the quadruple excitation energies, the method of Correlation Energy Extrapolation by Intrinsic Scaling was generalized to the simultaneous extrapolation for two states. This extrapolation method was shown to be very accurate. On the other hand, none of the CI expansions were found to have converged to millihartree (mh) accuracy at the quadruple excitation level. The data suggest that convergence to mh accuracy is probably attained at the sextuple excitation level. On the 1(1)A1 state, the present calculations yield the estimates of (ring minimum-open minimum) ∼45-50 mh and (transition state-open minimum) ∼85-90 mh. For the (2(1)A1-(1)A1) excitation energy, the estimate of ∼130-170 mh is found at the open minimum and 270-310 mh at the ring minimum. At the transition state, the difference (2(1)A1-(1)A1) is found to be between 1 and 10 mh. The geometry of the transition state on the 1(1)A1 surface and that of the minimum on the 2(1)A1 surface nearly coincide. More accurate predictions of the energy differences also require CI expansions to at least sextuple excitations with respect to the valence space. For every wave function considered, the omission of the correlations of the 2s oxygen orbitals, which is a widely used approximation, was found to cause errors of about ±10 mh with respect to the energy differences.

Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Benchmarks for Ground-State Properties

The semiempirical orthogonalization-corrected OMx methods (OM1, OM2, and OM3) go beyond the standard MNDO model by including additional interactions in the electronic structure calculation. When augmented with empirical dispersion corrections, the resulting OMx-Dn approaches offer a fast and robust treatment of noncovalent interactions. Here we evaluate the performance of the OMx and OMx-Dn methods for a variety of ground-state properties using a large and diverse collection of benchmark sets from the literature, with a total of 13035 original and derived reference data. Extensive comparisons are made with the results from established semiempirical methods (MNDO, AM1, PM3, PM6, and PM7) that also use the NDDO (neglect of diatomic differential overlap) integral approximation. Statistical evaluations show that the OMx and OMx-Dn methods outperform the other methods for most of the benchmark sets.

Acid-catalyzed carboxylic acid esterification and ester hydrolysis mechanism: acylium ion as a sharing active intermediate via a spontaneous trimolecular reaction based on density functional theory calculation and supported by electrospray ionization-mass spectrometry

By DFT calculation, we found that acid-catalyzed carboxylic acid esterification and ester hydrolysis are brief two-step reactions. First, the carboxylic acid hydroxyl-oxygen or ester alkyl-oxygen is protonated, which generates a highly active acylium ion. The protonation requires an activation energy (Ea) of 4-10 kcal mol(-1), and is the rate-controlling step of the esterification or hydrolysis. Sequentially, the acylium ion spontaneously reacts with two alcohol or two water molecules to form a neutral product molecule; this is a trimolecular reaction. The acylium ion is the highly active intermediate shared by esterification and hydrolysis. ESI-MS data for several typical carboxylic acids confirmed that their acylium ions are easily generated. For 2,4,6-trialkylbenzoic acid and its ester, the two unsubstituted carbons in the benzene ring are very easily protonated, and we have thus revealed the root of the success of Newman's method. Based on these results, the popular esterification and hydrolysis mechanism in organic chemistry textbooks is incorrect.

Hydrogen Abstraction from Fluorinated Ethyl Methyl Ether Systems by OH Radicals

A systematic computational investigation of hydrogen abstraction by OH from the full series of fluorinated ethyl methyl ethers (EME) containing at least one H and one F, C2HnX5-nOCHmX3-m (n=0–5, m=0–3; and n=m=0 not allowed), including 147 reactants and 469 transition states, has been carried out, employing the MP2/6-31G(d) level of theory. Results for optimized geometries, including evidence of intramolecular hydrogen bonding in transition states, and barrier heights are presented. Trends pertaining to the number of fluorines substituted, key bond lengths, barrier heights, and key bond angles were found with good correlations and were investigated. An increase in the number of F increases the barrier height of the reaction. An increase in some parameters such as C–H length of TS, relative change in C–H from reactants to TS, ∠COC of reactants, ∠HOH in the TS, and relative change in ∠HOH between TS and free water bond angle also correlates with increased barrier height. An increase in other parameters like C–H length in the reactants and hydrogen bonding can decrease the barrier height.

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules I. Reference Data at the CCSD(T) Complete Basis Set Limit

In designing organic materials for electronics applications, particularly for organic photovoltaics (OPV), the ionization potential (IP) of the donor and the electron affinity (EA) of the acceptor play key roles. This makes OPV design an appealing application for computational chemistry since IPs and EAs are readily calculable from most electronic structure methods. Unfortunately reliable, high-accuracy wave function methods, such as coupled cluster theory with single, double, and perturbative triples [CCSD(T)] in the complete basis set (CBS) limit are too expensive for routine applications to this problem for any but the smallest of systems. One solution is to calibrate approximate, less computationally expensive methods against a database of high-accuracy IP/EA values; however, to our knowledge, no such database exists for systems related to OPV design. The present work is the first of a multipart study whose overarching goal is to determine which computational methods can be used to reliably compute IPs and EAs of electron acceptors. This part introduces a database of 24 known organic electron acceptors and provides high-accuracy vertical IP and EA values expected to be within ±0.03 eV of the true non-relativistic, vertical CCSD(T)/CBS limit. Convergence of IP and EA values toward the CBS limit is studied systematically for the Hartree-Fock, MP2 correlation, and beyond-MP2 coupled cluster contributions to the focal point estimates.

Benchmarking Density Functionals on Structural Parameters of Small-/Medium-Sized Organic Molecules

In this Letter we report the error analysis of 59 exchange-correlation functionals in evaluating the structural parameters of small- and medium-sized organic molecules. From this analysis, recently developed double hybrids, such as xDH-PBE0, emerge as the most reliable methods, while global hybrids confirm their robustness in reproducing molecular structures. Notably the M06-L density functional is the only semilocal method reaching an accuracy comparable to hybrids'. A comparison with errors obtained on energetic databases (including thermochemistry, reaction barriers, and interaction energies) indicate that most of the functionals have a coherent behavior, showing low (or high) deviations on both energy and structure data sets. Only a few of them are more prone toward one of these two properties.

A mechanistic study of carbonyl activation under solvent-free conditions: evidence drawn from the synthesis of imidazoles

An assembly of carbonyls held together by weak-bond interactions (Constitutional Dynamic Chemistry) results in bulk polarisation. Molecules participate in reactions in a cycle rather than as individual moieties leading to higher reaction rates.

Beyond energies: geometry predictions with the XYG3 type of doubly hybrid density functionals

The scaled mean absolute deviations (s-MADs) of the optimized geometric parameters for covalent bondings (the CCse set), nonbonded interactions (the S22G30 set) and the transition state structures (the TSG36 set), with Tot referring to the averaged s-MAD for general performances.

Successful application of the DBLOC method to the hydroxylation of camphor by cytochrome p450

The activation barrier for the hydroxylation of camphor by cytochrome P450 was computed using a mixed quantum mechanics/molecular mechanics (QM/MM) model of the full protein-ligand system and a fully QM calculation using a cluster model of the active site at the B3LYP/LACVP*/LACV3P** level of theory, which consisted of B3LYP/LACV3P** single point energies computed at B3LYP/LACVP* optimized geometries. From the QM/MM calculation, a barrier height of 17.5 kcal/mol was obtained, while the experimental value was known to be less than or equal to 10 kcal/mol. This process was repeated using the D3 correction for hybrid DFT in order to investigate whether the inadequate treatment of dispersion interaction was responsible for the overestimation of the barrier. While the D3 correction does reduce the computed barrier to 13.3 kcal/mol, it was still in disagreement with experiment. After application of a series of transition metal optimized localized orbital corrections (DBLOC) and without any refitting of parameters, the barrier was further reduced to 10.0 kcal/mol, which was consistent with the experimental results. The DBLOC method to CH bond activation in methane monooxygenase (MMO) was also applied, as a second, independent test. The barrier in MMO was known, by experiment, to be 15.4 kcal/mol. After application of the DBLOC corrections to the MMO barrier compute by B3LYP, in a previous study, and accounting for dispersion with Grimme's D3 method, the unsigned deviation from experiment was improved from 3.2 to 2.3 kcal/mol. These results suggested that the combination of dispersion plus localized orbital corrections could yield significant quantitative improvements in modeling the catalytic chemistry of transition-metal containing enzymes, within the limitations of the statistical errors of the model, which appear to be on the order of approximately 2 kcal/mole.

Benchmark Databases for Nonbonded Interactions and Their Use To Test Density Functional Theory

We present four benchmark databases of binding energies for nonbonded complexes. Four types of nonbonded interactions are considered:  hydrogen bonding, charge transfer, dipole interactions, and weak interactions. We tested 44 DFT methods and 1 WFT method against the new databases; one of the DFT methods (PBE1KCIS) is new, and all of the other methods are from the literature. Among the tested methods, the PBE, PBE1PBE, B3P86, MPW1K, B97-1, and BHandHLYP functionals give the best performance for hydrogen bonding. MPWB1K, MP2, MPW1B95, MPW1K, and BHandHLYP give the best performances for charge-transfer interactions, and MPW3LYP, B97-1, PBE1KCIS, B98, and PBE1PBE give the best performance for dipole interactions. Finally, MP2, B97-1, MPWB1K, PBE1KCIS, and MPW1B95 give the best performance for weak interactions. Overall, MPWB1K is the best of all the tested DFT methods, with a relative error (highly averaged) of only 11%, and MPW1K, PBE1PBE, and B98 are the best of the tested DFT methods that do not contain kinetic energy density. Moving up the rungs of Jacob's ladder for nonempirical DFT, PBE improves significantly over the LSDA, and TPSS improve slightly over PBE (on average) for nonbonded interactions.

First UHF Implementation of the Incremental Scheme for Open-Shell Systems

The incremental scheme makes it possible to compute CCSD(T) correlation energies to high accuracy for large systems. We present the first extension of this fully automated black-box approach to open-shell systems using an Unrestricted Hartree-Fock (UHF) wave function, extending the efficient domain-specific basis set approach to handle open-shell references. We test our approach on a set of organic and metal organic structures and molecular clusters and demonstrate standard deviations from canonical CCSD(T) values of only 1.35 kJ/mol using a triple ζ basis set. We find that the incremental scheme is significantly more cost-effective than the canonical implementation even for relatively small systems and that the ease of parallelization makes it possible to perform high-level calculations on large systems in a few hours on inexpensive computers. We show that the approximations that make our approach widely applicable are significantly smaller than both the basis set incompleteness error and the intrinsic error of the CCSD(T) method, and we further demonstrate that incremental energies can be reliably used in extrapolation schemes to obtain near complete basis set limit CCSD(T) reaction energies for large systems.

First-Principles Prediction of Enthalpies of Formation for Polycyclic Aromatic Hydrocarbons and Derivatives

In this article, the first-principles prediction of enthalpies of formation is demonstrated for 669 polycyclic aromatic hydrocarbon (PAH) compounds and a number of related functionalized molecules. It is shown that by extrapolating density functional theory calculations to a large basis set limit and then applying a group based correction scheme that good results may be obtained. Specifically, a mean unsigned deviation and root mean squared deviation from the experimental enthalpies of formation data of 5.0 and 6.4 kJ/mol, respectively, are obtained using this scheme. This computational scheme is economical to compute and straightforward to apply, while yielding results of reasonable reliability. The results are also compared for a smaller set of molecules to the predictions given by the G3B3 and G3MP2B3 variants of the Gaussian-3 model chemistry with a mean unsigned deviation and root mean squared deviation from the experimental enthalpies of formation of 4.5 and 4.8 kJ/mol, respectively.

Systematic Improvement of Density Functionals through Parameter-Free Hybridization Schemes

It is suggested here that the ultimate accuracy of DFT methods arises from the type of hybridization scheme followed. This idea can be cast into a mathematical formulation utilizing an integrand connecting the noninteracting and the interacting particle system. We consider two previously developed models for it, dubbed as HYB0 and QIDH, and assess a large number of exchange-correlation functionals against the AE6, G2/148, and S22 reference data sets. An interesting consequence of these hybridization schemes is that the error bars, including the standard deviation, are found to markedly decrease with respect to the density-based (nonhybrid) case. This improvement is substantially better than variations due to the underlying density functional used. We thus finally hypothesize about the universal character of the HYB0 and QIDH models.

Exploring Sustainable Rocket Fuels: [Imidazolyl-Amine-BH2](+)-Cation-Based Ionic Liquids as Replacements for Toxic Hydrazine Derivatives

The application of hypergolic ionic liquids as propellant fuels is a newly emerging area in the fields of chemistry and propulsion science. Herein, a new class of [imidazolyl-amine-BH2](+)-cation-based ionic liquids, which included fuel-rich anions, such as dicyanamide (N(CN)2(-)) and cyanoborohydride (BH3CN(-)) anions, were synthesized and characterized. As expected, all of the ionic liquids exhibited spontaneous combustion upon contact with the oxidizer 100 % HNO3. The densities of these ionic liquids varied from 0.99-1.12 g cm(-3), and the heats of formation, predicted based on Gaussian 09 calculations, were between -707.7 and 241.8 kJ mol(-1). Among them, the salt of compound 5, that is, (1-allyl-1H-imidazole-3-yl)-(trimethylamine)-dihydroboronium dicyanamide, exhibited the lowest viscosity (168 MPa s), good thermal properties (Tg <-70 °C, Td >130 °C), and the shortest ignition-delay time (18 ms) with 100 % HNO3. These ionic fuels, as "green" replacements for toxic hydrazine-derivatives, may have potential applications as bipropellant formulations.

London dispersion in molecular chemistry--reconsidering steric effects

London dispersion, which constitutes the attractive part of the famous van der Waals potential, has long been underappreciated in molecular chemistry as an important element of structural stability, and thus affects chemical reactivity and catalysis. This negligence is due to the common notion that dispersion is weak, which is only true for one pair of interacting atoms. For increasingly larger structures, the overall dispersion contribution grows rapidly and can amount to tens of kcal mol(-1) . This Review collects and emphasizes the importance of inter- and intramolecular dispersion for molecules consisting mostly of first row atoms. The synergy of experiment and theory has now reached a stage where dispersion effects can be examined in fine detail. This forces us to reconsider our perception of steric hindrance and stereoelectronic effects. The quantitation of dispersion energy donors will improve our ability to design sophisticated molecular structures and much better catalysts.

A systematic way for the cost reduction of density fitting methods

We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of three-center two-electron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of the computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of three-center Coulomb integrals is a bottleneck.