Torsional Potentials of Glyoxal, Oxalyl Halides, and Their Thiocarbonyl Derivatives: Challenges for Popular Density Functional Approximations

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree-Fock Methods Corrected with Atom-Centered Potentials

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

Explaining and Fixing DFT Failures for Torsional Barriers

Most torsional barriers are predicted with high accuracies (about 1 kJ/mol) by standard semilocal functionals, but a small subset was found to have much larger errors. We created a database of almost 300 carbon-carbon torsional barriers, including 12 poorly behaved barriers, that stem from the Y═C-X group, where Y is O or S and X is a halide. Functionals with enhanced exchange mixing (about 50%) worked well for all barriers. We found that poor actors have delocalization errors caused by hyperconjugation. These problematic calculations are density-sensitive (i.e., DFT predictions change noticeably with the density), and using HF densities (HF-DFT) fixes these issues. For example, conventional B3LYP performs as accurately as exchange-enhanced functionals if the HF density is used. For long-chain conjugated molecules, HF-DFT can be much better than exchange-enhanced functionals. We suggest that HF-PBE0 has the best overall performance.

Difficulties of Popular Density Functionals to Describe the Conformational Isomerism in Iodoacetic Acid

Matrix isolation studies in solid argon and neon at 4.2 K reveal that iodoacetic acid initially only exists as its ground state (c,x) conformer with an almost perpendicular I-C-C═O dihedral angle, but UV irradiation in the 240-255 nm range leads to population of the 0.8 kcal mol^-1 less stable (c,c) isomer. The latter structure exhibits a close 3.23 Å contact of the iodine and carbonyl oxygen atoms decidedly below the sum of their van der Waals radii (3.50 Å). Increasing the matrix temperature by only a few Kelvin triggers the thermal back reaction of (c,c) to (c,x) and leads to an estimated upper limit of 0.38 kcal mol^-1 for the associated torsional barrier. While wave function methods including completely uncorrelated Hartree-Fock theory have no problem to identify (c,c) as a proper minimum, many popular density functionals fail to describe the C-C torsional potential in cis-iodoacetic acid qualitatively correct. We assessed the performance of 12 density functionals of different levels of sophistication, namely, the BLYP, PBE, TPSS, B3LYP, BHandHLYP, PBE0, M06-2X, CAM-B3LYP, ωB97X-D3, B2-PLYP, B2GP-PLYP, and DSD-PBEP86 methods, against accurate extrapolated CCSD(T)/CBS(T-Q)//MP2/def2-TZVPP energies and found that almost all of them yield acceptable relative energies. Still, even some of the best performers fail to find a reasonably deep minimum in the region of the (c,c) conformer, and addition of the empirical D3-dispersion correction does not remedy the qualitative shortcoming. Instead, inclusion of a sufficient amount of (long-range) exact exchange and likely a proper treatment of medium-range correlation effects all along the torsional coordinate play an important role in the proper description of the sub-van der Waals iodine-oxygen contact. More modern, recommended functionals do not suffer from the described shortcoming.

Quantum-chemistry-aided identification, synthesis and experimental validation of model systems for conformationally controlled reaction studies: separation of the conformers of 2,3-dibromobuta-1,3-diene in the gas phase

The Diels-Alder cycloaddition, in which a diene reacts with a dienophile to form a cyclic compound, counts among the most important tools in organic synthesis. Achieving a precise understanding of its mechanistic details on the quantum level requires new experimental and theoretical methods. Here, we present an experimental approach that separates different diene conformers in a molecular beam as a prerequisite for the investigation of their individual cycloaddition reaction kinetics and dynamics under single-collision conditions in the gas phase. A low- and high-level quantum-chemistry-based screening of more than one hundred dienes identified 2,3-dibromobutadiene (DBB) as an optimal candidate for efficient separation of its gauche and s-trans conformers by electrostatic deflection. A preparation method for DBB was developed which enabled the generation of dense molecular beams of this compound. The theoretical predictions of the molecular properties of DBB were validated by the successful separation of the conformers in the molecular beam. A marked difference in photofragment ion yields of the two conformers upon femtosecond-laser pulse ionization was observed, pointing at a pronounced conformer-specific fragmentation dynamics of ionized DBB. Our work sets the stage for a rigorous examination of mechanistic models of cycloaddition reactions under controlled conditions in the gas phase.

A Trip to the Density Functional Theory Zoo: Warnings and Recommendations for the User

This account is written for general users of density functional theory (DFT) methods as well as experimental researchers who are new to the field and would like to conduct such calculations. Its main emphasis lies on how to find a way through the confusing ‘zoo’ of DFT by addressing common misconceptions and highlighting those modern methods that should ideally be used in calculations of energetic properties and geometries. A particular focus is on highly popular methods and the important fact that popularity does not imply accuracy. In this context, we present a new analysis of the openly available data published in Swart and co-workers’ famous annual ‘DFT poll’ (http://www.marcelswart.eu/dft-poll/) to demonstrate the existing communication gap between the DFT user and developer communities. We show that despite considerable methodological advances in the field, the perception of some parts of the user community regarding their favourite approaches has changed little. It is hoped that this account makes a contribution towards changing this status and that users are inspired to adjust their current computational protocols to accommodate strategies that are based on proven robustness, accuracy, and efficiency rather than popularity.