Pál D. Mezei

Construction and application of a new dual-hybrid random phase approximation.

The direct random phase approximation (dRPA) combined with Kohn-Sham reference orbitals is among the most promising tools in computational chemistry and applicable in many areas of chemistry and physics. The reason for this is that it scales as N(4) with the system size, which is a considerable advantage over the accurate ab initio wave function methods like standard coupled-cluster. dRPA also yields a considerably more accurate description of thermodynamic and electronic properties than standard density-functional theory methods. It is also able to describe strong static electron correlation effects even in large systems with a small or vanishing band gap missed by common single-reference methods. However, dRPA has several flaws due to its self-correlation error. In order to obtain accurate and precise reaction energies, barriers and noncovalent intra- and intermolecular interactions, we construct a new dual-hybrid dRPA (hybridization of exact and semilocal exchange in both the energy and the orbitals) and test the performance of this new functional on isogyric, isodesmic, hypohomodesmotic, homodesmotic, and hyperhomodesmotic reaction classes. We also use a test set of 14 Diels-Alder reactions, six atomization energies (AE6), 38 hydrocarbon atomization energies, and 100 reaction barrier heights (DBH24, HT-BH38, and NHT-BH38). For noncovalent complexes, we use the NCCE31 and S22 test sets. To test the intramolecular interactions, we use a set of alkane, cysteine, phenylalanine-glycine-glycine tripeptide, and monosaccharide conformers. We also discuss the delocalization and static correlation errors. We show that a universally accurate description of chemical properties can be provided by a large, 75% exact exchange mixing both in the calculation of the reference orbitals and the final energy.

Electron density errors and density-driven exchange-correlation energy errors in approximate density functional calculations

Since its formal introduction, density functional theory has achieved many successes in the fields of molecular and solid-state chemistry. According to its central theorems, the ground state of a many-electron system is fully described by its electron density, and the exact functional minimizes the energy at the exact electron density. For many years of density functional development, it was assumed that the improvements in the energy are accompanied by the improvements in the density, and the approximations approach the exact functional. In a recent analysis ( Medvedev et al. Science 2017 , 355 , 49 - 52 .), it has been pointed out for 14 first row (Be-Ne) atoms and cations with 2, 4, or 10 electrons that the nowadays popular flexible but physically less rigorous approximate density functionals may provide large errors in the calculated electron densities despite the accurate energies. Although far-reaching conclusions have been drawn in this work, the methodology used by the authors may need improvements. Most importantly, their benchmark set was biased toward small atomic cations with compressed, high electron densities. In our paper, we construct a molecular test set with chemically relevant densities and analyze the performance of several density functional approximations including the less-investigated double hybrids. We apply an intensive error measure for the density, its gradient, and its Laplacian and examine how the errors in the density propagate into the semilocal exchange-correlation energy. While we have confirmed the broad conclusions of Medvedev et al., our different way of analyzing the data has led to conclusions that differ in detail. Finally, seeking for a rationale behind the global hybrid or double hybrid methods from the densitys point of view, we also analyze the role of the exact exchange and second-order perturbative correlation mixing in PBE-based global hybrid and double hybrid functional forms.

Accurate Diels-Alder Reaction Energies from Efficient Density Functional Calculations

We assess the performance of the semilocal PBE functional; its global hybrid variants; the highly parametrized empirical M06-2X and M08-SO; the range separated rCAM-B3LYP and MCY3; the atom-pairwise or nonlocal dispersion corrected semilocal PBE and TPSS; the dispersion corrected range-separated ωB97X-D; the dispersion corrected double hybrids such as PWPB95-D3; the direct random phase approximation, dRPA, with Hartree-Fock, Perdew-Burke-Ernzerhof, and Perdew-Burke-Ernzerhof hybrid reference orbitals and the RPAX2 method based on a Perdew-Burke-Ernzerhof exchange reference orbitals for the Diels-Alder, DARC; and self-interaction error sensitive, SIE11, reaction energy test sets with large, augmented correlation consistent valence basis sets. The dRPA energies for the DARC test set are extrapolated to the complete basis set limit. CCSD(T)/CBS energies were used as a reference. The standard global hybrid functionals show general improvements over the typical endothermic energy error of semilocal functionals, but despite the increased accuracy the precision of the methods increases only slightly, and thus all reaction energies are simply shifted into the exothermic direction. Dispersion corrections give mixed results for the DARC test set. Vydrov-Van Voorhis 10 correction to the reaction energies gives superior quality results compared to the too-small D3 correction. Functionals parametrized for energies of noncovalent interactions like M08-SO give reasonable results without any dispersion correction. The dRPA method that seamlessly and theoretically correctly includes noncovalent interaction energies gives excellent results with properly chosen reference orbitals. As the results for the SIE11 test set and H2(+) dissociation show that the dRPA methods suffer from delocalization error, good reaction energies for the DARC test set from a given method do not prove that the method is free from delocalization error. The RPAX2 method shows good performance for the DARC, the SIE11 test sets, and for the H2(+) and H2 potential energy curves showing no one-electron self-interaction error and reduced static correlation errors at the same time. We also suggest simplified DARC6 and SIE9 test sets for future benchmarking.

Reference Determinant Dependence of the Random Phase Approximation in 3d Transition Metal Chemistry

Without extensive fitting, accurate prediction of transition metal chemistry is a challenge for semilocal and hybrid density funcitonals. The Random Phase Approximation (RPA) has been shown to yield superior results to semilocal functionals for main group thermochemistry, but much less is known about its performance for transition metals. We have therefore analyzed the behavior of reaction energies, barrier heights, and ligand dissociation energies obtained with RPA and compare our results to several semilocal and hybrid functionals. Particular attention is paid to the reference determinant dependence of RPA. We find that typically the results do not vary much between semilocal or hybrid functionals as a reference, as long as the fraction of exact exchange (EXX) mixing in the hybrid functional is small. For large fractions of EXX mixing, however, the Hartree-Fock-like nature of the determinant can severely degrade the performance. Overall, RPA systematically reduces the errors of semilocal functionals and delivers excellent performance from a single reference determinant for inherently multireference reactions. The behavior of dual hybrids that combine RPA correlation with a hybrid exchange energy was also explored, but ultimately did not lead to a systematic improvement compared to traditional RPA for these systems. We rationalize this conclusion by decomposing the contributions to the reaction energies, and briefly discuss the possible implications for double-hybrid functionals based on RPA. The correlation between EXX mixing and spin-symmetry breaking is also discussed.

Accurate Complete Basis Set Extrapolation of Direct Random Phase Correlation Energies.

The direct random phase approximation (dRPA) is a promising way to obtain improvements upon the standard semilocal density functional results in many aspects of computational chemistry. In this paper, we address the slow convergence of the calculated dRPA correlation energy with the increase of the quality and size of the popular Gaussian-type Dunnings correlation consistent aug-cc-pVXZ split valence atomic basis set family. The cardinal number X controls the size of the basis set, and we use X = 3-6 in this study. It is known that even the very expensive X = 6 basis sets lead to large errors for the dRPA correlation energy, and thus complete basis set extrapolation is necessary. We study the basis set convergence of the dRPA correlation energies on a set of 65 hydrocarbon isomers from CH4 to C6H6. We calculate the iterative density fitted dRPA correlation energies using an efficient algorithm based on the CC-like form of the equations using the self-consistent HF orbitals. We test the popular inverse cubic, the optimized exponential, and inverse power formulas for complete basis set extrapolation. We have found that the optimized inverse power based extrapolation delivers the best energies. Further analysis showed that the optimal exponent depends on the molecular structure, and the most efficient two-point energy extrapolations that use X = 3 and 4 can be improved considerably by considering the atomic composition and hybridization states of the atoms in the molecules. Our results also show that the optimized exponents that yield accurate X = 3 and 4 extrapolated dRPA energies for atoms or small molecules might be inaccurate for larger molecules.

Construction of a Spin-Component Scaled Dual-Hybrid Random Phase Approximation

Recently, we have constructed a dual-hybrid direct random phase approximation method, called dRPA75, and demonstrated its good performance on reaction energies, barrier heights, and noncovalent interactions of main-group elements. However, this method has also shown significant but quite systematic errors in the computed atomization energies. In this paper, we suggest a constrained spin-component scaling formalism for the dRPA75 method (SCS-dRPA75) in order to overcome the large error in the computed atomization energies, preserving the good performance of this method on spin-unpolarized systems at the same time. The SCS-dRPA75 method with the aug-cc-pVTZ basis set results in an average error lower than 1.5 kcal mol-1 for the entire n-homodesmotic hierarchy of hydrocarbon reactions (RC0-RC5 test sets). The overall performance of this method is better than the related direct random phase approximation-based double-hybrid PWRB95 method on open-shell systems of main-group elements (from the GMTKN30 database) and comparable to the best O(N4)-scaling opposite-spin second-order perturbation theory-based double-hybrid methods like PWPB95-D3 and to the O(N5)-scaling RPAX2@PBEx method, which also includes exchange interactions. Furthermore, it gives well-balanced performance on many types of barrier heights similarly to the best O(N5)-scaling second-order perturbation theory-based or spin-component scaled second-order perturbation theory-based double-hybrid methods such as XYG3 or DSD-PBEhB95. Finally, we show that the SCS-dRPA75 method has reduced self-interaction and delocalization errors compared to the parent dRPA75 method and a slightly smaller static correlation error than the related PWRB95 method.

Conformational properties of propargyloxy-calix[4]arene tricarboxamides: NMR and DFT studies on the O-through-the-annulus rotation

The size limit of substituents allowing O-through-the-annulus rotation of substituted calix[4]arenes was further extended to the propargyloxy group in 24-propargyloxy-25,26,27-tris(N,N-dimethylcarbamoylmethoxy)-p-tert-butylcalix[4]arene by demonstrating its free but slow motion affording equilibrium between the partial cone and 1,2-alternate conformers. The effect of solvent and upper rim substituents R1 on the conformational inversion was investigated by means of 1H NMR. The rotational isomerisation of the parent (R1 = H) analogue could not unambiguously be detected. The experimental results were supported by comprehensive density functional theory studies.

Application of a Dual-Hybrid Direct Random Phase Approximation to Water Clusters

In water clusters, there is a delicate balance of van der Waals interactions and hydrogen bonds. Although semilocal and nonlocal density functional approximations have been recently routinely applied to water in various phases, the accurate description of hydrogen bonds remains a challenge. The most popular density functional approaches fail to predict the correct ordering of the energies of water clusters. To illustrate the required accuracy, the CCSD(T) complete basis set extrapolated dissociation energy difference between the two lowest energy hexamer structures is 0.06 kcal mol(-1) per monomer. In this work, we assessed interaction energies in neutral and ionic water clusters with various density functionals with or without van der Waals correction. Generally, van der Waals approximations play a significant role in clusters with increasing size, while hybrid functionals improve the description of hydrogen bonds. Despite these general trends, none of the tested density functional approximations with or without van der Waals correction and exact exchange mixing can lead to a uniform performance for neutral and ionic water clusters. The recently constructed dual-hybrid dRPA75 approximation is a successful combination of exact and semilocal exchange, and nonlocal correlation in its energy, while utilizing a high fraction of exact exchange. We have shown that the dRPA75 method has a systematic error, which can be efficiently compensated for by the aug-cc-pVTZ basis set for small- and medium-sized water clusters.

Features of the interactions between the methyl-CpG motif and the arginine residues on the surface of MBD proteins

Recognition of the methylated regions of the DNA plays an important role in the epigenetic processes. We analyze the interactions between the methylated DNA and the methyl-CpG-binding proteins using two models. The first model was built from a methylated or non-methylated cytosine, a guanine and an arginine residue in the experimental arrangement. We applied the M06L density functional method with a small, polarized double-ζ basis set for the geometry optimizations, and the MP2 method with polarized triple-ζ basis set for the energy calculations. The second model was built from two methylcytosines, guanines, guanidinium groups plus an additional carboxyl group in the experimental arrangement. We applied the B3LYP method with a small, polarized double-ζ basis set for the geometry optimizations and thermal corrections. The single-point energies were obtained from dual-hybrid dRPA75 and dRPA@PBE0 calculations supplemented by a moderately large polarized triple-ζ basis set. The hydration effects were modeled by adding explicit water molecules. These calculations revealed that the hydrophobic interaction has the largest contribution to the Gibbs interaction energy and turns the arginine side chains into hydrogen bonding position. Our results show that the translation of the protein along the DNA double helix is sterically hindered by the contact of its arginine side chains with the methyl groups of the methyl cytosines. This supports a hopping mechanism for the searching movement of the protein along the DNA.

Unified picture for the conformation and stabilization of the O -glycosidic linkage in glycopeptide model structures

Glycoproteins play a central role in the immune response. In this study, we focus on the core of the common O-linked mucin-type glycopeptides. It has been observed that glycosylation stabilizes the protein in a stiffened, extended structure. We provide a unified picture for the conformation and stabilization of the O-glycosidic linkage using O-(2-acetylamino-2-deoxy-α- or -β-d-galacto- or -mannopyranosyl)-N-acetyl-l-serinamide model structures. We have calculated equilibrium geometries of the model structures with the B3LYP/6-31G(2df,p) method suggested in the Gaussian-4 theory. According to the relative energies, we confirm that the GalNAc-Ser linkage is more stable than its mannose analogues. The natural preference for the α-GalNAc-Ser over the β-GalNAc-Ser anomers can be explained by entropic effects. We explored the hydrogen bonding patterns on the carbohydrate unit calculating highly accurate dRPA@PBE0.25 and dRPA75 energies and found that in some cases, the acetamido group can be fixed by hydrogen bonding from the (O3Carb)H atom, but in most of the cases, it can rotate more freely. The torsion angles in the glycosidic linkage show that the linkage is stiffened more in the α-anomers and the most in the α-GalNAc-Ser structure because of the steric strains in the axial position and by two or three intramolecular hydrogen bonds. We also found that although, in our gas-phase model geometries, the peptide backbone prefers to be in a γL-turn, a structural water molecule can stabilize a polyproline II helix of a proline-rich sequence, a β-sheet, or more likely random coils.