The layered transition metal dichalcogenide 1T-TiSe2 is of great research interest, having intriguing properties of charge density waves (CDWs) and superconductivity under doping or pressure. The monolayer form of 1T-TiSe2 also shows a CDW with a higher transition temperature than the bulk, indicating a stronger CDW interaction. By using the meta-generalized gradient approximation (metaGGA)-based model Bethe-Salpeter equation (mBSE) and many-body perturbation GW+BSE methods, we calculate the exciton binding energies and electron energy loss spectrum (EELS) for the 1T-TiSe2 monolayer under different in-plane biaxial strains. We find that even without strain the 1T-TiSe2 monolayer can have negative exciton energies at the Brillouin zone boundary point M, with a binding energy larger than the gap. The calculated EELS reinforces this picture, indicating exciton insulator (EI) states in 1T-TiSe2 monolayer even without strain. The Wannier-Mott formula calculations of exciton binding energy corroborate results from GW+BSE. Small compressive strain enhances the EI state, and for tensile strains slightly less than 3%, the EI state in this monolayer persists. At large tensile strains, the material makes a transition to a normal semiconductor. Our results provide important information for understanding the quantum nature of this two-dimensional material. Our results from the standard G0W0@PBE+SOC+U+BSE approach are not qualitatively different from those of a more computationally xc approach that employs a model BSE.

Ta2Ni3Te5, a layered transition metal chalcogenide with quasi-one-dimensional electronic states, exhibits rich topological and correlated phenomena. Using first-principles calculations, we explore Ta2Ni3Te5 nanoribbons, demonstrating tunable electronic and magnetic properties-ranging from metallic to semimetallic and semiconducting (band gaps of 29.7-60.8 meV), and from ferromagnetic to antiferromagnetic-controlled by edge (Ni or Ta), ribbon width, and H/F saturation. Additionally, GW and Bethe-Salpeter equation (BSE) calculations, complemented by metaGGA-based modified BSE, reveal that the Ta2Ni3Te5 monolayer is an excitonic insulator, with an exciton binding energy exceeding its band gap. These diverse properties position Ta2Ni3Te5 nanoribbons and monolayers as promising candidates for nanoelectronics, spintronics, and optoelectronics, motivating further experimental exploration.

The layered transition metal dichalcogenide 1T-TiSe_2 is of great research interest, having intriguing properties of charge density waves (CDW) and superconductivity under doping or pressurizing. The monolayer form of 1T-TiSe_2 also shows a CDW with a higher transition temperature T_c than the bulk, indicating a stronger CDW interaction. By using the meta-generalized gradient approximation (metaGGA)-based model Bethe-Salpeter Equation (BSE) and many-body perturbation GW+BSE methods, we calculate the exciton binding energies and electron energy loss spectrum (EELS) for the 1T-TiSe_2 monolayer under different in-plane biaxial strains. We find that even without strain the 1T-TiSe_2 monolayer can have negative exciton energies at the Brillouin zone boundary point M, with a binding energy larger than the gap. The calculated EELS reinforces this picture, indicating EI (exciton insulator) states in 1T-TiSe_2 monolayer even without strain. The Wannier-Mott formula calculations of exciton binding energy corroborate results from GW+BSE. Small compressive strains enhance the EI state, and for tensile strains slightly less than 3 material makes a transition to a normal semiconductor. Our results provide important information for understanding the quantum nature of this two-dimensional (2D) material. Our results from the standard G0W0@PBE+SOC+U+BSE approach are not qualitatively different from those of a more computationally efficient metaGGA-based SCAN+SOC+U+mBSE+f_xc^loc approach that employs a model BSE.

Are the vertical ionization energies from a bound electronic system, initially in its ground state, equal to minus the corresponding exact Kohn-Sham orbital energies of density functional theory (DFT)? This is known to be true for the first or lowest vertical ionization energy. We show that the correction from time-dependent DFT arises from the continuum and need not vanish. Recent work compared the experimental photoemission thresholds of the molecules Cu2O−, CuO−, CuO− 2 , and CuO3− with minus the corresponding orbital energies from a generalized gradient approximation (GGA) and its global and range-separated hybrids with exact exchange, finding striking differences which were attributed to self-interaction error, strong correlation, or both. Here we extend that work to include the local spin density approximation (LSDA), its Perdew-Zunger self-interaction correction with Fermi-L¨owdin localized orbitals (LSDASIC), a quasi-self-consistent locally scaled-down version of LSDA-SIC (QLSIC), and the Quantum Theory Project QTP02 range-separated hybrid functional, all but LSDA implemented in a generalized Kohn-Sham approach. QTP02 impressively yields a near equality for many sp-bonded molecules. But, for the copper oxide anions studied here, none of the tested methods reproduces the experimental photoemission thresholds.

Semi-local density functional approximations are widely used. None of them can capture the long-range van der Waals (vdW) attraction between separated subsystems, but they differ remarkably in the extent to which they capture intermediate-range vdW effects responsible for equilibrium bonds between neighboring small closed-shell subsystems. The local density approximation (LDA) often overestimates this effect, while the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) underestimates it. The strongly-constrained and appropriately normed (SCAN) meta-GGA often estimates it well. All of these semi-local functionals require an additive non-local correction such as the revised Vydrov-Van Voorhis 2010 (rVV10) to capture the long-range part. This work reports adsorption energies and the corresponding geometry of the aromatic thiophene (C$_4$H$_4$S) bound to transition metal surfaces. The adsorption process requires a genuine interplay of covalent and weak binding and requires a simultaneously accurate description of surface and adsorption energies with the correct prediction of the adsorption site. All these quantities must come from well balanced short and long-range correlation effects for a universally applicable method for weak interactions with chemical accuracy.

We analyzed various possibilities to improve upon the SCAN meta-generalized gradient approximation density functional obeying all known properties of the exact functional that can be satisfied at this level of approximation. We examined the necessity of locally satisfying a strongly tightened lower bound for the exchange energy density in single-orbital regions, the nature of the error cancellation between the exchange and correlation parts in two-electron regions, and the effect of the fourth-order term in the gradient expansion of the correlation energy density. We have concluded that the functional can be modified to separately reproduce the exchange and correlation energies of the helium atom by locally releasing the strongly tightened lower bound for the exchange energy density in single-orbital regions, but this leads to an unbalanced improvement in the single-orbital electron densities. Therefore, we decided to keep the FX ≤ 1.174 exact condition for any single-orbital density, where FX is the exchange enhancement factor. However, we observed a general improvement in the single-orbital electron densities by revising the correlation functional form to follow the second-order gradient expansion in a wider range. Our new revSCAN functional provides more-accurate atomization energies for the systems with multireference character, compared to the SCAN functional. The nonlocal VV10 dispersion-corrected revSCAN functional yields more-accurate noncovalent interaction energies than the VV10-corrected SCAN functional. Furthermore, its global hybrid version with 25% of exact exchange, called revSCAN0, generally performs better than the similar SCAN0 for reaction barrier heights. Here, we also analyzed the possibility of the construction of a local hybrid from the SCAN exchange and a specific locally bounded nonconventional exact exchange energy density. We predict compatibility problems since this nonconventional exact exchange energy density does not really obey the strongly tightened lower bound for the exchange energy density in single-orbital regions.

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 density's 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.

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.

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.

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.

While most molecules and solids are spin-unpolarized, most chemically-active atoms are partly spin-polarized. As a result, the errors of the spin-dependence of a density functional are much more troublesome for atomization energies than they are for typical reaction or formation energies. This observation explains why the atomization energy errors of approximate functionals do not correlate with their other errors, and why the errors of atomization energies for a given functional can be radically reduced by fitting the energies of the atoms. We present an illustrative example from the recent nonempirical construction of the SCAN meta-generalized gradient approximation.

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.

A correct description of the anion-π interaction is essential for the design of selective anion receptors and channels and important for advances in the field of supramolecular chemistry. However, it is challenging to do accurate, precise, and efficient calculations of this interaction, which are lacking in the literature. In this article, by testing sets of 20 binary anion-π complexes of fluoride, chloride, bromide, nitrate, or carbonate ions with hexafluorobenzene, 1,3,5-trifluorobenzene, 2,4,6-trifluoro-1,3,5-triazine, or 1,3,5-triazine and 30 ternary π-anion-π' sandwich complexes composed from the same monomers, we suggest domain-based local-pair natural orbital coupled cluster energies extrapolated to the complete basis-set limit as reference values. We give a detailed explanation of the origin of anion-π interactions, using the permanent quadrupole moments, static dipole polarizabilities, and electrostatic potential maps. We use symmetry-adapted perturbation theory (SAPT) to calculate the components of the anion-π interaction energies. We examine the performance of the direct random phase approximation (dRPA), the second-order screened exchange (SOSEX), local-pair natural-orbital (LPNO) coupled electron pair approximation (CEPA), and several dispersion-corrected density functionals (including generalized gradient approximation (GGA), meta-GGA, and double hybrid density functional). The LPNO-CEPA/1 results show the best agreement with the reference results. The dRPA method is only slightly less accurate and precise than the LPNO-CEPA/1, but it is considerably more efficient (6-17 times faster) for the binary complexes studied in this paper. For 30 ternary π-anion-π' sandwich complexes, we give dRPA interaction energies as reference values. The double hybrid functionals are much more efficient but less accurate and precise than dRPA. The dispersion-corrected double hybrid PWPB95-D3(BJ) and B2PLYP-D3(BJ) functionals perform better than the GGA and meta-GGA functionals for the present test set.

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 Dunning's 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.

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(2 df , 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 (O3 Carb )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 γ L -turn, a structural water molecule can stabilize a polyproline II helix of a proline-rich sequence, a β-sheet, or more likely random coils.

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.

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.

Computationally-efficient semilocal approximations of density functional theory at the level of the local spin density approximation (LSDA) or generalized gradient approximation (GGA) poorly describe weak interactions. We show improved descriptions for weak bonds (without loss of accuracy for strong ones) from a newly-developed semilocal meta-GGA (MGGA), by applying it to molecules, surfaces, and solids. We argue that this improvement comes from using the right MGGA dimensionless ingredient to recognize all types of orbital overlap.