Can the Counterpoise Correction for Basis Set Superposition Effect Be Justified?

Strategies to Obtain Reliable Energy Landscapes from Embedded Multireference Correlated Wavefunction Methods for Surface Reactions

Embedded correlated wavefunction (ECW) theory is a powerful tool for studying ground- and excited-state reaction mechanisms and associated energetics in heterogeneous catalysis. Several factors are important to obtaining reliable ECW energies, critically the construction of consistent active spaces (ASs) along reaction pathways when using a multireference correlated wavefunction (CW) method that relies on a subset of orbital spaces in the configuration interaction expansion to account for static electron correlation, e.g., complete AS self-consistent field theory, in addition to the adequate partitioning of the system into a cluster and environment, as well as the choice of a suitable basis set and number of states included in excited-state simulations. Here, we conducted a series of systematic studies to develop best-practice guidelines for ground- and excited-state ECW theory simulations, utilizing the decomposition of NH3 on Pd(111) as an example. We determine that ECW theory results are relatively insensitive to cluster size, the aug-cc-pVDZ basis set provides an adequate compromise between computational complexity and accuracy, and that a fixed-clean-surface approximation holds well for the derivation of the embedding potential. Additionally, we demonstrate that a merging approach, which involves generating ASs from the molecular fragments at each configuration, is preferable to a creeping approach, which utilizes ASs from adjacent structures as an initial guess, for the generation of consistent potential energy curves involving open-d-shell metal surfaces, and, finally, we show that it is essential to include bands of excited states in their entirety when simulating excited-state reaction pathways.

Structures and stability of I2 and ICl complexes with pyridine: Ab initio and DFT study

Theoretical investigation of thermodynamic stability and bonding features of possible isomers of the molecular and ionic complexes of pyridine with molecular iodine and iodine monochloride IX (X = I,Cl) is presented. M06-2X DFT functional is found to provide bond distances and dissociation energies which are close to those obtained at high-level ab initio CCSD(T)/aug-cc-pvtz//CCSD/aug-cc-pvtz benchmark computations for the most stable isomers, formed via donation of a lone pair of nitrogen atom of pyridine to the iodine atom. These isomers are by 23-33 kJ mol-1 (in case of I2) and by 39-56 kJ mol-1 (in case of ICl) more stable than other molecular complexes. T-shaped π-σ* bonded isomers turn out to be energetically comparable with van der Waals bound compounds. Among the ionic isomers, structures featuring [IPy2]+ cation with I3 - or ICl2 - counterions are more stable. Oligomerization favors ionic isomers starting from the tetrameric clusters of the composition (IX)4Py4.

Structural and Electronic Insights into 1-Ethyl-3-Methylimidazolium Bis(fluorosulfonyl)imide Ion Pair Conformers: Ab Initio DFT Study

An understanding of the nature of molecular interactions among the ion pairs of 1-ethyl-3-methylimidazolium bis(fluorosulfonyl)imide [EMI[FSI]] can offer a starting point and significant insight into the more dynamic and multiple interactions within the bulk liquid state. In this context, close inspection of ion pair conformers can offer insight into the effects in bulk [EMI][FSI] liquid. The current work, therefore, gives a detailed analysis of the [EMI][FSI] ion pair conformers through analysis of the interaction energies, stabilization energies, and natural orbital of the ion pair conformers. The structures of the cations, anions, and cation-anion ion pairs of the conformers are optimized systematically by the ωB97X-D method with the DGDZVP basis sets, considering both the empirical dispersion corrections and the presence of a polar solvent, and the most stable geometries are obtained. The [FSI]- anions, unlike [TFSI]- anions, exist at the top position with respect to imidazolium rings. The presence of out-of-plane interactions between the [EMI]+ and [FSI]- ions is in good agreement with the stronger interactions of the [FSI]- anions with alkyl group hydrogens. The presence of out-of-plane conformers could also be related to the interaction of the anion with the π clouds of the [EMI]+ ring. In the [EMI]+ cation, the aromatic ring is π-acidic due to the presence of a positive charge in the N1-C1-N2 ring, which leads to the presence of [FSI]- anion donor [EMI]+ π-acceptor type interactions. The [EMI]+ cation and [FSI]- anions tend to form multiple σ* and π* interactions but reduce the strength of the individual contributions from a potential (linear) maximum. For the ion pair [EMI][FSI], the absolute value of the interaction energies is lower than the normal hydrogen bond energy (50 kJ/mol), which indicates that there is a very weak electrostatic interaction between the [EMI]+ cations and [FSI]- anions. The weaker attraction between the [EMI]+ and [FSI]- ions is suggested to contribute to the larger diffusion coefficients of the ions.

Basis Set Superposition Errors Are Partly Basis Set Imbalances

When calculating fragment interaction energies by electronic structure methods employing medium-sized atom-centered basis sets, it is often observed that the effect is systematically overestimated. The common interpretation is that the systematic error arises because the basis set for the complex is more complete than for the isolated fragments, and this is denoted basis set superposition errors. It has been observed, however, that the interaction energy in some cases is underestimated, which defies the interpretation in terms of basis set completeness, and instead suggests that the effect partly is due to basis set imbalance. The imbalance can be removed by explicit optimization of the basis sets for each structure, and it is shown that this to a significant extent reduces the systematic overestimation attributed to basis set superposition error.

Plane Waves Versus Correlation-Consistent Basis Sets: A Comparison of MP2 Non-Covalent Interaction Energies in the Complete Basis Set Limit

Second-order Møller-Plesset perturbation theory (MP2) is the most expedient wave function-based method for considering electron correlation in quantum chemical calculations and, as such, provides a cost-effective framework to assess the effects of basis sets on correlation energies, for which the complete basis set (CBS) limit can commonly only be obtained via extrapolation techniques. Software packages providing MP2 energies are commonly based on atom-centered bases with innate issues related to possible basis set superposition errors (BSSE), especially in the case of weakly bonded systems. Here, we present noncovalent interaction energies in the CBS limit, free of BSSE, for 20 dimer systems of the S22 data set obtained via a highly parallelized MP2 implementation in the plane-wave pseudopotential molecular dynamics package CPMD. The specificities related to plane waves for accurate and efficient calculations of gas-phase energies are discussed, and results are compared to the localized (aug-)cc-pV[D,T,Q,5]Z correlation-consistent bases as well as their extrapolated CBS estimates. We find that the BSSE-corrected aug-cc-pV5Z basis can provide MP2 energies highly consistent with the CBS plane wave values with a minimum mean absolute deviation of ∼0.05 kcal/mol without the application of any extrapolation scheme. In addition, we tested the performance of 13 different extrapolation schemes and found that the X-3 expression applied to the (aug-)cc-pVXZ bases provides the smallest deviations against CBS plane wave values if the extrapolation sequence is composed of points D and T, while ( X + 1 2 ) - 4 performs slightly better for TQ and Q5 extrapolations. Also, we propose A ( X - 1 2 ) - 3 + B ( X + 1 2 ) - 4 as a reliable alternative to extrapolate total energies from the DTQ, TQ5, or DTQ5 data points. In spite of the general good agreement between the values obtained from the two types of basis sets, it is noticed that differences between plane waves and (aug-)cc-pVXZ basis sets, extrapolated or not, tend to increase with the number of electrons, thus raising the question of whether these discrepancies could indeed limit the attainable accuracy for localized bases in the limit of large systems.

Reactions of a hydrogen atom with haloacetates in aqueous solutions: Computational evidence for proton-coupled electron transfer and competing mechanisms

A computational study of the mechanisms and kinetics of the aqueous reactions of a hydrogen atom with haloacetates is presented. Several mechanisms in the close competition are observed, such as proton-coupled electron transfer (PCET), hydrogen atom transfer (HAT), and halogen abstraction (XA). Computations predict that dechlorination takes place via PCET mechanisms and not via XA, as stated earlier, while XA is the fastest mechanism forIAc - . The reaction rate constants are reasonably well predicted within the theoretically most reliable canonical variational transition state theory with small curvature tunneling corrections and compared with the experimental ones. To reproduce the experimental rate constants of the debromination process it is necessary to include the PCET and XA cumulative values. Small curvature tunneling corrections to the rate constants are the highest for HAT and PCET mechanisms, up to 70 times larger than the Wigner, while variational effects for XA mechanisms are very small.

Photoelectron Velocity Map Imaging Spectroscopy of the Beryllium Trimer and Tetramer

Computational studies of small beryllium clusters (BeN) predict dramatic, nonmonotonic changes in the bonding mechanisms and per-atom cohesion energies with increasing N. To date, experimental tests of these quantum chemistry models are lacking for all but the Be2 molecule. In the present study, we report spectroscopic data for Be3 and Be4 obtained via anion photodetachment spectroscopy. The trimer is predicted to have D3h symmetric equilibrium structures for both the neutral molecule and the anion. Photodetachment spectra reveal transitions that originate from the X2A2″ ground state and the 12A1' electronically excited state. The state symmetries were assigned on the basis of anisotropic photoelectron angular distributions. The neutral and anionic forms of Be4 are predicted to be tetrahedral. Franck-Condon diagonal photodetachment was observed with a photoelectron angular distribution consistent with the expected Be4-X2A1 → Be4X1A1 transition. The electron affinities of Be3 and Be4 were determined to be 11363 ± 60 and 13052 ± 50 cm-1, respectively.

Ab Initio Approach to the Structure, Vibrational Properties, and Electron Binding Energies of H2S∙∙∙SO2

The present study employs high-level ab initio calculations to investigate the structure, vibrational frequencies, and electronic properties of H2S∙∙∙SO2. The analysis of vibrational frequencies reveals an intramolecular vibrational energy transfer phenomenon, where energy from the stretching modes of H2S is transferred to the ν1s mode of SO2. At the CCSD(T)/aug-cc-pVQZ level, the interaction energy between H2S and SO2 is predicted to be 2.78 kcal/mol. Electron propagator theory calculations yield a HOMO-LUMO gap of 8.24 eV for H2S∙∙∙SO2. Furthermore, by utilizing ab initio results for the adiabatic ionization energy and electron affinity, the electrophilicity of H2S∙∙∙SO2 is estimated to be 2.01 eV. This value is similar to the electrophilicity of SO2, suggesting comparable reactivity and chemical behavior. The non-covalent interaction (NCI) analysis of the H2S∙∙∙SO2 complex emphasizes the significant contribution of non-covalent van der Waals interactions in its energetic stabilization.

Quantifying Intramolecular Basis Set Superposition Errors

We show that medium-sized Gaussian basis sets lead to significant intramolecular basis set superposition errors at Hartree-Fock and density functional levels of theory, with artificial stabilization of compact over extended conformations for a 186 atom deca-peptide. Errors of ∼80 and ∼10 kJ/mol are observed, with polarized double zeta and polarized triple zeta quality basis sets, respectively. Two different procedures for taking the basis set superposition error into account are tested. While both reduce the error, it appears that polarized quadruple zeta basis sets are required to reduce the error below a few kJ/mol. Alternatively, the basis set superposition error can be eliminated using multiresolution methods based on Multiwavelets.

How proton transfer affects the helical parameters in DNA:DNA microhelices

Proton transfer reactions are a widespread phenomenon in many areas of the life sciences and it is one of the origins of the spontaneous point mutations during DNA replication. Because of its importance, many studies have been reported on these reactions. However, the present work is the first one focused on the structural geometrical changes by double proton transfer (DPT). Thus, different Watson-Crick (WC) pairs were optimized first in a simple model with one nucleoside base pair, and in a microhelix form with three nucleoside base pairs. The canonical and few tautomeric forms were considered in DNA:DNA microhelices with A-type and B-type helical forms. The stability of these structures and how the DPT process affects the main geometrical parameters was analyzed, in particular the deformation of the helical parameters. The M06-2X DFT method was used for this purpose. The purine/pyrimidine ring in the keto form appears easier to be deformed than when it is in the enol form. The weaker WC base pair formed with mixed microhelices than with nucleobases alone and the significant deformation of the helical and backbone parameters with the DPT appears to complicate this process in microhelices.Communicated by Ramaswamy H. Sarma.

Nature and Strength of Weak O⋅⋅⋅O Interactions in Nitryl Halide Dimers

The use of real space functions and molecular graphs has pushed some chemists to wonder: Are interactions between negatively charged oxygen atoms possible? In this contribution we analyze whether there is a real interaction between oxygen atoms in nitryl halide dimers (XNO₂ )₂ (X=F, Cl, Br and I) and in tetranitromethane and derivatives. Based on ab-initio and density functional theories (DFT) methods, we show these complexes are weakly stabilized. Energy decomposition analyses based on local molecular orbitals (LMOEDA) and interacting quantum atoms (IQA) reveal both dispersion and exchange play a crucial role in the stabilization of these complexes. Electron charge density and IQA analyses indicate that the oxygen atoms are connected by privileged exchange channels. In addition, electrostatic interactions between O and N atoms are also vital for the stabilization of the complexes. Finally, a reasonable explanation is given for the dynamic behavior of nitryl groups in tetranitromethane and derivatives.

Systematic Evaluation of Counterpoise Correction in Density Functional Theory

A widespread belief persists that the Boys-Bernardi function counterpoise (CP) procedure "overcorrects" supramolecular interaction energies for the effects of basis-set superposition error. To the extent that this is true for correlated wave function methods, it is usually an artifact of low-quality basis sets. The question has not been considered systematically in the context of density functional theory, however, where basis-set convergence is generally less problematic. We present a systematic assessment of the CP procedure for a representative set of functionals and basis sets, considering both benchmark data sets of small dimers and larger supramolecular complexes. The latter include layered composite polymers with ∼150 atoms and ligand-protein models with ∼300 atoms. Provided that CP correction is used, we find that intermolecular interaction energies of nearly complete-basis quality can be obtained using only double-ζ basis sets. This is less expensive as compared to triple-ζ basis sets without CP correction. CP-corrected interaction energies are less sensitive to the presence of diffuse basis functions as compared to uncorrected energies, which is important because diffuse functions are expensive and often numerically problematic for large systems. Our results upend the conventional wisdom that CP "overcorrects" for basis-set incompleteness. In small basis sets, CP correction is mandatory in order to demonstrate that the results do not rest on error cancellation.

Unusual In-plane Aromaticity Facilitates Intramolecular Hydrogen Transfer in Long-Bonded cis-Isonitrosyl Methoxide

The hydrogen-atom transfer from methoxy radical to nitric oxide, leading to the formation of formaldehyde and nitroxyl, represents a secondary reaction of photodissociation of methyl nitrite, which is used as rocket fuel. In this study, we explored the potential energy profile of the hydrogen-atom transfer using the electronic structure calculations at the DLPNO-CCSD(T)/aug-cc-pVTZ level of theory for two isomeric forms (cis and trans) of the pre-reaction complex. The cis-oriented pre-reaction complex has a weak elongated O─O bond, which gets further elongated in the hydrogen transfer transition state. This O─O bond stabilizes the pre-reaction complex by 32.9 kJ/mol. The O─O-induced stabilization is even greater for the transition state (48.2 kJ/mol), which was unexpected because of the larger O─O distance in the transition state structure. To address this paradox, we performed the electronic structure analysis of the reaction participants using the valence bond (VB) theory, natural resonance theory, topological analysis of the electron density and its derivatives, and analysis of the electron localization function distribution. This combined analysis led to the conclusion that the cis-transition state for hydrogen transfer, instead of being directly stabilized by the O─O interaction, gained substantial stabilization from the in-plane five-center six-electron aromaticity.

Anion Binding Based on Hg3 Anticrowns as Multidentate Lewis Acidic Hosts

We present herein a combined structural and computational analysis of the anion binding capabilities of perfluorinated polymercuramacrocycles. The Cambridge Structural Database (CSD) has been explored to find the coordination preference of these cyclic systems toward specific Lewis bases, both anionic and neutral. Interaction energies with different electron-rich species have been computed and further decomposed into chemically meaningful terms by means of energy decomposition analysis. Furthermore, we have investigated, by means of the natural resonance theory and natural bond orbital analyses how the orbitals involved in the interaction are key in determining the final geometry of the adduct. Finally, a generalization of the findings in terms of the molecular orbital theory has allowed us to understand the formation of the pseudo-octahedral second coordination sphere in linear Hg(II) complexes.

Demarcating Noncovalent and Covalent Bond Territories: Imine-CO2 Complexes and Cooperative CO2 Capture

Chemical bond territory is rich with covalently bonded molecules wherein a strong bond is formed by equal or unequal sharing of a quantum of electrons. The noncovalent version of the bonding scenarios expands the chemical bonding territory to a weak domain wherein the interplay of electrostatic and π-effects, dipole-dipole, dipole-induced dipole, and induced dipole-induced dipole interactions, and hydrophobic effects occur. Here we study both the covalent and noncovalent interactive behavior of cyclic and acyclic imine-based functional molecules (XN) with CO₂. All parent XN systems preferred the formation of noncovalent (nc) complex XN···CO₂, while more saturated such systems (XN') produced both nc and covalent (c) complexes XN'⁺-(CO₂)^-. In all such cases, crossover from an nc to c complex is clearly demarcated with the identification of a transition state (ts). The complexes XN'···CO₂ and XN'⁺-(CO₂)^- are bond stretch isomers, and they define the weak and strong bonding territories, respectively, while the ts appears as the demarcation point of the two territories. Cluster formation of XN with CO₂ reinforces the interaction between them, and all become covalent clusters of general formula (XN⁺-(CO₂)^-)_n. The positive cooperativity associated with the NH···OC hydrogen bond formation between any two XN'⁺-(CO₂)^- units strengthened the N-C coordinate covalent bond and led to massive stabilization of the cluster. For instance, the stabilizing interaction between the XN unit with CO₂ is increased from 2-7 kcal/mol range in a monomer complex to 14-31 kcal/mol range for the octamer cluster (XN'⁺-(CO₂)^-)₈. The cooperativity effect compensates for the large reduction in the entropy of cluster formation. Several imine systems showed the exergonic formation of the cluster and are predicted as potential candidates for CO₂ capture and conversion.

Behavior of counterpoise correction in many-body molecular clusters of organic compounds: Hartree-Fock interaction energy perspective

The counterpoise (CP) correction by Boys and Bernardi has been well accepted as a reliable strategy to account for basis set superposition error (BSSE) in intermolecular complexes. The behavior of the CP correction was thoroughly studied in individual molecules of molecular complexes. This work studies the performance of the CP correction in many‐body clusters including three‐body clusters of organic compounds in the 3B‐69 dataset. Additionally, we used crystal structures of polymorphs of benzene, aspirin, and oxalyl dihydrazide (ODH) to construct a many‐body cluster dataset, abbreviated as the MBC‐36 dataset, consisting of two, four and eight molecules, and 16 molecules in the case of benzene. A series of Dunning's basis sets—cc‐pXZ and aug‐cc‐pXZ (X = D and T)—were used to predict CP‐corrected Hartree–Fock (HF) interaction energies of the 3B‐69 and MBC‐36 datasets. The CP‐corrected interaction energies were found to be basis‐set independent, whereas the non‐CP corrected interaction energies were found not to a follow a smooth exponential fitting as previously found for electronic energies of individual molecules. This observation was attributed to the presence of non‐additive induction forces in some clusters. Two 2 × 2 × 2 supercells of benzene polymorphs were constructed to explore the local nature of BSSE effects. A cut‐off radius of 10 Å was demonstrated to be sufficient to fully recover these effects. Although the behavior of CP correction was found to be non‐conventional in many‐body clusters of organic compounds, the use of a small basis set such as cc‐pVDZ showed excellent performance in the prediction of HF interaction energies.

Thermodynamically Stable Cationic Dimers in Carboxyl-Functionalized Ionic Liquids: The Paradoxical Case of "Anti-Electrostatic" Hydrogen Bonding

We show that carboxyl-functionalized ionic liquids (ILs) form doubly hydrogen-bonded cationic dimers (c⁺=c⁺) despite the repulsive forces between ions of like charge and competing hydrogen bonds between cation and anion (c⁺–a⁻). This structural motif as known for formic acid, the archetype of double hydrogen bridges, is present in the solid state of the IL 1−(carboxymethyl)pyridinium bis(trifluoromethylsulfonyl)imide [HOOC−CH₂−py][NTf₂]. By means of quantum chemical calculations, we explored different hydrogen-bonded isomers of neutral (HOOC–(CH₂)_n–py⁺)₂(NTf₂⁻)₂, single-charged (HOOC–(CH₂)_n–py⁺)₂(NTf₂⁻), and double-charged (HOOC– (CH₂)_n−py⁺)₂ complexes for demonstrating the paradoxical case of “anti-electrostatic” hydrogen bonding (AEHB) between ions of like charge. For the pure doubly hydrogen-bonded cationic dimers (HOOC– (CH₂)_n−py⁺)₂, we report robust kinetic stability for n = 1–4. At n = 5, hydrogen bonding and dispersion fully compensate for the repulsive Coulomb forces between the cations, allowing for the quantification of the two equivalent hydrogen bonds and dispersion interaction in the order of 58.5 and 11 kJmol⁻¹, respectively. For n = 6–8, we calculated negative free energies for temperatures below 47, 80, and 114 K, respectively. Quantum cluster equilibrium (QCE) theory predicts the equilibria between cationic monomers and dimers by considering the intermolecular interaction between the species, leading to thermodynamic stability at even higher temperatures. We rationalize the H-bond characteristics of the cationic dimers by the natural bond orbital (NBO) approach, emphasizing the strong correlation between NBO-based and spectroscopic descriptors, such as NMR chemical shifts and vibrational frequencies.

Guanidine as a strong CO2 adsorbent: a DFT study on cooperative CO2 adsorption

Among the various carbon capture and storage (CCS) technologies, the direct air capture (DAC) of CO2 by engineered chemical reactions on suitable adsorbents has attained more attention in recent times. Guanidine (G) is one of such promising adsorbent molecules for CO2 capture. Recently Lee et al. (Phys. Chem. Chem. Phys., 2015, 17, 10925-10933) reported an interaction energy (ΔE) of -5.5 kcal mol-1 for the GCO2 complex at the CCSD(T)/CBS level, which was one of the best non-covalent interactions observed for CO2 among several functional molecules. Here we show that the non-covalent GCO2 complex can transform to a strongly interacting G-CO2 covalent complex under the influence of multiple molecules of G and CO2. The study, conducted at M06-2X/6-311++G** level density functional theory, shows ΔE = -5.7 kcal mol-1 for GCO2 with an NC distance of 2.688 Å while almost a five-fold increase in ΔE (-27.5 kcal mol-1) is observed for the (G-CO2)8 cluster wherein the N-C distance is 1.444 Å. All the (G-CO2)n clusters (n = 2-10) show a strong N-CO2 covalent interaction with the N-C distance gradually decreasing from 1.479 Å for n = 2 to 1.444 Å for n = 8 ≅ 9, 10. The N-CO2 bonding gives (G+)-(CO2-) zwitterion character for G-CO2 and the charge-separated units preferred a cyclic arrangement in (G-CO2)n clusters due to the support of three strong intermolecular OHN hydrogen bonds from every CO2. The OHN interaction is also enhanced with an increase in the size of the cluster up to n = 8. The high ΔE is attributed to the large cooperativity associated with the N-CO2 and OHN interactions. The quantum theory of atoms in molecules (QTAIM) analysis confirms the nature and strength of such interactions, and finds that the total interaction energy is directly related to the sum of the electron density at the bond critical points of N-CO2 and OHN interactions. Further, molecular electrostatic potential analysis shows that the cyclic cluster is stabilized due to the delocalization of charges accumulated on the (G+)-(CO2-) zwitterion via multiple OHN interactions. The cyclic (G-CO2)n cluster formation is a highly exergonic process, which reveals the high CO2 adsorption capability of guanidine.

Revisiting stacking interactions in tetrathiafulvalene and selected derivatives using tight-binding quantum chemical calculations and local coupled-cluster method

The engineering of supramolecular architectures needs accurate descriptions of the intermolecular interactions in crystal structures. Tetrathiafulvalene (TTF) is an effective building block used in the construction of promising functional materials. The parallel packing of the neutral TTF-TTF system was studied previously using the high-level quantum chemical method, advancing it as a valuable model system. The recently developed tight-binding quantum chemical method GFN2-xTB and local coupled-cluster method DLPNO-CCSD(T) were used to investigate the stacking interactions of TTF and selected derivatives deposited in the Cambridge Structural Database. Using the interaction energy of the TTF-TTF dimer calculated at the CCSD(T)/CBS level as the reference, the accuracies of the two methods are investigated. The energy decomposition analysis within the DLPNO-CCSD(T) framework reveals the importance of dispersion interaction in the TTF-related stacking systems. The dispersion interaction density plot vividly shows the magnitude and distribution of the dispersion interaction, providing a revealing insight into the stacking interactions in crystal structures. The results show that the GFN2-xTB and DLPNO-CCSD(T) methods could achieve accuracy at an affordable computational cost, which would be valuable in understanding the nature of parallel stacking in supramolecular systems.

First-principles calculations of hybrid inorganic-organic interfaces: from state-of-the-art to best practice

The computational characterization of inorganic-organic hybrid interfaces is arguably one of the technically most challenging applications of density functional theory. Due to the fundamentally different electronic properties of the inorganic and the organic components of a hybrid interface, the proper choice of the electronic structure method, of the algorithms to solve these methods, and of the parameters that enter these algorithms is highly non-trivial. In fact, computational choices that work well for one of the components often perform poorly for the other. As a consequence, default settings for one materials class are typically inadequate for the hybrid system, which makes calculations employing such settings inefficient and sometimes even prone to erroneous results. To address this issue, we discuss how to choose appropriate atomistic representations for the system under investigation, we highlight the role of the exchange-correlation functional and the van der Waals correction employed in the calculation and we provide tips and tricks how to efficiently converge the self-consistent field cycle and to obtain accurate geometries. We particularly focus on potentially unexpected pitfalls and the errors they incur. As a summary, we provide a list of best practice rules for interface simulations that should especially serve as a useful starting point for less experienced users and newcomers to the field.

Post-complete-basis-set extrapolation of conventional and explicitly correlated coupled-cluster energies: can the convergence to the CBS limit be diagnosed?

We assess benchmark correlation energies for 130 systems in test sets A24 and TS-106 both with the canonical CCSD(T) and explicitly correlated CCSD(T)-F12 methods. Aiming at enhanced accuracy, the calculated raw energies from both sets are CBS extrapolated to the complete basis set (CBS) limit and subsequently post-CBS extrapolated. Attention is focused at total energies, since their accuracy reflects on that of the interaction energies. Using up to triple-ζ basis sets for CBS and an additional quadruple-ζ for post-CBS, the mean and standard unsigned deviations with canonical CCSD(T) theory are 0.257 ± 0.25 kcal mol^-1, while the corresponding values for CCSD(T)-F12 in its F12a and F12b variants with specialized basis sets up to VQZ-F12 are 0.170 ± 0.13 kcal mol^-1 and 0.048 ± 0.04 kcal mol^-1. Although these show gains at post-CBS level that vary from 0.08 to 0.20 kcal mol^-1 relative to their CCSD(T)/VXZ analogues, the convergence is somewhat less clear when extending the basis up to V5Z-F12, the highest-rung available: 0.220 ± 0.17 kcal mol^-1 and 0.142 ± 0.08 kcal mol^-1, in the same order. An explanation for the up to one order of magnitude smaller deviations in energy differences is detailed. Based on energy differences involving basis set pairs employed for extrapolating to the CBS limit, a convergence diagnostic is also suggested. Arising from irregularities in the basis set that directly correlate with non-dynamical correlation, the new diagnostic may complement popular ones that feature other aspects of correlation.

Canonical and explicitly-correlated coupled cluster correlation energies of sub-kJ mol-1 accuracy via cost-effective hybrid-post-CBS extrapolation

Cost-effectiveness and accuracy are two basic pillars in electronic structure calculations. While cost-effectiveness enhances applicability, high accuracy is sustained when employing advanced computational tools. With the gold standard method of ab initio quantum chemistry at the focal point, canonical CCSD(T) and modern explicitly correlated CCSD(T)-F12 calculations are employed hand in hand to develop accurate hybrid post-CBS extrapolation schemes, which are validated using popular training sets involving a total of 130 molecules. By using raw valence-only calculations at CCSD(T)/VDZ and CCSD(T)/VQZ-F12 levels of theory, the novel scheme leads to the prediction of absolute energies that differ on average (-0.170 ± 0.224) kcal mol-1 from the highest affordable CCSD(T)-F12b/V(Q,5)Z-F12 extrapolations, but only (-0.048 ± 0.228) kcal mol-1 from the post-CBS extrapolated values based on CBS(D,T), CBS(D,Q) and CBS(T,Q) energies. From the cost-effectiveness standpoint, the approach is a kind of pseudo one-point extrapolation scheme since its cost is basically that of the highest-rung raw energy where it is based. Variants that imply no additional cost are also discussed, emerging h-pCBS(dt,dq)ab as the most effective. The approach can also be used with PNO-based local correlation methods that gained popularity due to allowing coupled-cluster calculations even for large molecules at reduced computational cost, namely local PNO-CCSD(T) and PNO-CCSD(T)-F12b. To gauge the approach performance, both the hydrogen molecule and the O-C2H5 torsion path of ethyl-methyl-ether, an extra molecule here considered with presupposed existence in astrophysical objects, are also studied. Additionally, the nonbonding interactions in the A24 test set are revisited per se. The results show that the title approach may be useful in high-accuracy quantum chemistry, with further improvements requiring the inclusion of contributions beyond the theory here employed such as the ones due to relativistic and nonadiabatic effects.

Assessing the Applicability of the Geometric Counterpoise Correction in B2PLYP/Double-ζ Calculations for Thermochemistry, Kinetics, and Noncovalent Interactions

We present a proof-of-concept study of the suitability of Kruse and Grimme’s geometric counterpoise correction (gCP) for basis set superposition errors (BSSEs) in double-hybrid density functional calculations with a double-ζ basis set. The gCP approach only requires geometrical information as an input and no orbital/density information is needed. Therefore, this correction is practically free of any additional cost. gCP is trained against the Boys and Bernardi counterpoise correction across a set of 528 noncovalently bound dimers. We investigate the suitability of the approach for the B2PLYP/def2-SVP level of theory, and reveal error compensation effects—missing London dispersion and the BSSE—associated with B2PLYP/def2-SVP calculations, and present B2PLYP-gCP-D3(BJ)/def2-SVP with the reparametrised DFT-D3(BJ) and gCP corrections as a more balanced alternative. Benchmarking results on the S66x8 benchmark set for noncovalent interactions and the GMTKN55 database for main-group thermochemistry, kinetics, and noncovalent interactions show a statistical improvement of the B2PLYP-gCP-D3(BJ) scheme over plain B2PLYP and B2PLYP-D3(BJ). B2PLYP-D3(BJ) shows significant overestimation of interaction energies, barrier heights with larger deviations from the reference values, and wrong relative stabilities in conformers, all of which can be associated with BSSE. We find that the gCP-corrected method represents a significant improvement over B2PLYP-D3(BJ), particularly for intramolecular noncovalent interactions. These findings encourage future developments of efficient double-hybrid DFT strategies that can be applied when double-hybrid calculations with large basis sets are not feasible due to system size.

Occurrence and stability of lone pair-π and OH-π interactions between water and nucleobases in functional RNAs

We identified over 1000 instances of water-nucleobase stacking contacts in a variety of RNA molecules from a non-redundant set of crystal structures with resolution ≤3.0 Å. Such contacts may be of either the lone pair-π (lp-π) or the OH-π type, in nature. The distribution of the distances of the water oxygen from the nucleobase plane peaks at 3.5 Å for A, G and C, and approximately at 3.1-3.2 Å for U. Quantum mechanics (QM) calculations confirm, as expected, that the optimal energy is reached at a shorter distance for the lp-π interaction as compared to the OH-π one (3.0 versus 3.5 Å). The preference of each nucleobase for either type of interaction closely correlates with its electrostatic potential map. Furthermore, QM calculations show that for all the nucleobases a favorable interaction, of either the lp-π or the OH-π type, can be established at virtually any position of the water molecule above the nucleobase skeleton, which is consistent with the uniform projection of the OW atoms over the nucleobases ring we observed in the experimental occurrences. Finally, molecular dynamics simulations of a model system for the characterization of water-nucleobase stacking contacts confirm the stability of these interactions also under dynamic conditions.

Improved Basis-Set Incompleteness Potentials for Accurate Density-Functional Theory Calculations in Large Systems

The accurate calculation of chemical properties using density-functional theory (DFT) requires the use of a nearly complete basis set. In chemical systems involving hundreds to thousands of atoms, the cost of the calculations place practical limitations on the number of basis functions that can be used. Therefore, in most practical applications of DFT to large systems, there exists a basis-set incompleteness error (BSIE). In this article, we present the next iteration of the basis-set incompleteness potentials (BSIPs), one-electron potentials designed to correct for basis-set incompleteness error. The ultimate goal associated with the development of BSIPs is to allow the calculation of molecular properties using DFT with near-complete-basis-set results at a computational cost that is similar to a small basis set calculation. In this work, we develop BSIPs for 10 atoms in the first and second rows (H, B-F, Si-Cl) and 15 common basis sets of the Pople, Dunning, Karlsruhe, and Huzinaga types. Our new BSIPs are constructed to minimize BSIE in the calculation of reaction energies, barrier heights, noncovalent binding energies, and intermolecular distances. The BSIPs were obtained using a training set of 15 944 data points. The fitting approach employed a regularized linear least-squares method with variable selection (the LASSO method), which results in a much better fit to the training data than our previous BSIPs while, at the same time, reducing the computational cost of BSIP development. The proposed BSIPs are tested on various benchmark sets and demonstrate excellent performance in practice. Our new BSIPs are also transferable; i.e., they can be used to correct BSIE in calculations that employ density functionals other than the one used in the BSIP development (B3LYP). Finally, BSIPs can be used in any quantum chemistry program that have implemented effective-core potentials without changes to the software.

Dimerization of Acetic Acid in the Gas Phase-NMR Experiments and Quantum-Chemical Calculations

Due to the nature of the carboxylic group, acetic acid can serve as both a donor and acceptor of a hydrogen bond. Gaseous acetic acid is known to form cyclic dimers with two strong hydrogen bonds. However, trimeric and various oligomeric structures have also been hypothesized to exist in both the gas and liquid phases of acetic acid. In this work, a combination of gas-phase NMR experiments and advanced computational approaches were employed in order to validate the basic dimerization model of gaseous acetic acid. The gas-phase experiments performed in a glass tube revealed interactions of acetic acid with the glass surface. On the other hand, variable-temperature and variable-pressure NMR parameters obtained for acetic acid in a polymer insert provided thermodynamic parameters that were in excellent agreement with the MP2 (the second order Møller–Plesset perturbation theory) and CCSD(T) (coupled cluster with single, double and perturbative triple excitation) calculations based on the basic dimerization model. A slight disparity between the theoretical dimerization model and the experimental data was revealed only at low temperatures. This observation might indicate the presence of other, entropically disfavored, supramolecular structures at low temperatures.

Reaction pathways and kinetics study on a syngas combustion system: CO + HO2 in an H2O environment

The reaction between CO and HO2 plays a significant role in syngas combustion. In this work, the catalytic effect of single-molecule water on this reaction is theoretically investigated at the CCSD(T)/aug-cc-pV(D,T,Q)Z and CCSD(T)-F12a/jun-cc-pVTZ levels in combination with the M062X/aug-cc-pVTZ level. Firstly, the potential energy surface (PES) of CO + HO2 (water-free) is revisited. The major products CO2 + OH are formed via a cis- or a trans-transition state (TS) channel and the formation of HCO + O2 is minor. In the presence of water, the title reaction has three different pre-reactive complexes (i.e., RC2: COHO2 + H2O, RC3: COH2O + HO2, and RC4: HO2H2O + CO), depending on the initial hydrogen bond formation. Compared to the water-free process, the reaction barriers of the water-assisted process are reduced considerably, due to more stable cyclic TSs and complexes. The rate constants for the bimolecular reaction pathways CO + HO2, RC2, RC3, and RC4 are further calculated using conventional transition state theory (TST) with Eckart asymmetric tunneling correction. For reaction CO + HO2, our calculations are in good agreement with the literature. In addition, the effective rate constants for the water-assisted process decrease by 1-2 orders of magnitude compared to the water-free one at a temperature below 600 K. In particular, the effective rate constants for the water-assisted and water-free processes are 1.55 × 10-28 and 3.86 × 10-26 cm3 molecule-1 s-1 at 300 K, respectively. This implies that the contribution of a single molecule water-assisted process is small and cannot accelerate the title reaction.

Basis set convergence of binding energy with and without CP-correction utilizing PBE0 method: A benchmark study of X2 (X=Ge, As, Se, Sc, Ti, V, Cr, Mn, Co, Cu, Zn)

A DFT study of homonuclear X2 ([Formula: see text], As, Se, Sc, Ti, V, Cr, Mn, Fe, Co, Cu, Zn) is presented using PBEO exchange (xc) functional which is a mixing of Perdew–Burke–Ernzerhof (PBE) and Hartree Fock (HF) exchange energy. However, we used cc-pVXZ and aug-cc-pVXZ basis sets where X is maximum angular momentum number in basis set. Convergence pattern of binding energy with respect to basis set was observed. Two-point extrapolations to complete basis set (CBS) limit were applied to speed up convergence and decrease the basis set incompleteness error (BSIE). Counterpoise correction (CP) method was utilized to alleviate basis set superposition errors (BSSE). Both CP-corrected and uncorrected binding energies were obtained and compared with the experimental and theoretical binding energy values in literature.

On the Use of Popular Basis Sets: Impact of the Intramolecular Basis Set Superposition Error

The magnitude of intramolecular basis set superposition error (BSSE) is revealed via computing systematic trends in molecular properties. This type of error is largely neglected in the study of the chemical properties of small molecules and it has historically been analyzed just in the study of large molecules and processes dominated by non-covalent interactions (typically dimerization or molecular complexation and recognition events). In this work we try to provide proof of the broader prevalence of this error, which permeates all types of electronic structure calculations, particularly when employing insufficiently large basis sets.

A full additive QM/MM scheme for the computation of molecular crystals with extension to many-body expansions

An additive quantum mechanics/molecular mechanics (QM/MM) model for the theoretical investigation of molecular crystals (AC-QM/MM) is presented. At the one-body level, a single molecule is chosen as the QM region. The MM region around it consists of a finite cluster of explicit MM atoms, represented by point charges and Lennard-Jones potentials, with additional background charges to mimic periodic electrostatics. Cluster charges are QM-derived and calculated self-consistently to ensure a polarizable embedding. We have also considered the extension to many-body QM corrections, calculating the interactions of a central molecule to neighboring units in the crystal. Full gradient expressions have been derived, also including symmetry information. The scheme allows for the calculation of molecular properties as well as unconstrained optimizations of the molecular geometry and cell parameters with respect to the lattice energy. Benchmarking the approach with the X23 reference set confirms the convergence pattern of the many-body extension although a comparison to plane-wave density functional theory reveals a systematic overestimation of cohesive energies by 6-16 kJ mol^-1. While the scheme primarily aims to provide an inexpensive and flexible way to model a molecule in a crystal environment, it can also be used to reach highly accurate cohesive energies by the straightforward application of wave function correlated approaches. Calculations with local coupled cluster with singles, doubles, and perturbative triples, albeit limited to numerical gradients, show an impressive agreement with experimental estimates for small molecular crystals.

The interplay and strength of the π⋯HF, C⋯HF, F⋯HF and F⋯HC hydrogen bonds upon the formation of multimolecular complexes based on C2H2⋯HF and C2H4⋯HF small dimers

The conception of this theoretical research was idealized aiming to unveil the intermolecular structures of complexes formed by acetylene or ethylene and hydrofluoric acid. At light of computational calculations by using the B3LYP/6-311++G(d,p) method, the geometries of the C₂H₂⋯(HF), C₂H₂⋯2(HF), C₂H₂⋯4(HF), C₂H₄⋯(HF), C₂H₄⋯2(HF) and C₂H₄⋯4(HF) hydrogen-bonded complexes were fully optimized. Moreover, the Post-Hartree-Fock calculations MP2/6-311++G(d,p), MP2/aug-cc-pVTZ, MP4(SDQ)/6-311++G(d,p) and CCSD/6-311++G(d,p) also were also used. The infrared spectra were analyzed in order to identify the new vibrational modes and frequencies of the proton donors shifted to red region. Through the modeling of charge-fluxes on the basis of the Quantum Theory of Atoms In Molecules (QTAIM) and, by contradicting the expectation of the hydrofluorination mechanisms of acetylene or ethylene, C⋯HF was recognized as a new type of hydrogen bond instead of the already well known π⋯H. The calculations of the Natural Bonding Orbital (NBO) and Charges derived from the Electrostatic Potential Grid-based (ChElPG) were also applied to interpret the shifting frequencies as well as measuring of the punctual charge-transfer after the formation of the complexes. Finally, the determination of the stabilization energy was carried out through the arguments of the Fock matrix in NBO basis and through the supermolecule approach. Also it is worthwhile to notice that some algebraic formulations were used for determining the electronic cooperative effect (CE).

A Tautomeric λ3/λ5-Phosphane Pair and Its Ambiphilic Reactivity

The central phosphorus atom of a novel hydroxyl-functionalized triarylphosphane was shown to reversibly insert into one of the molecule's O-H bonds, which forms the basis for a tautomeric λ³/λ⁵-phosphane equilibrium. For the first time, this equilibrium was detected for a λ³-triarylphosphane and the underlying dynamic process was elucidated by NMR spectroscopy. On the basis of reactivity studies, a nucleophilic character was assigned to the minor species present in solution, the λ³-phosphane. Upon methylation, for example, the λ³-form was selectively removed from the equilibrium and converted to the corresponding phosphonium salt. However, upon generation of an alkoxide via proton abstraction, the electrophilic character of the λ⁵-phosphane in the equilibrium became evident since the alkoxide was found to attack the molecule's phosphorus atom. This intramolecular reaction led to the selective formation of a new anionic λ⁶-hydridospirophosphane.

α-methylation and α-fluorination electronic effects on the regioselectivity of carbonyl groups of uracil by H and triel bonds in the interaction of U, T and 5FU with HCl and TrH3 (Tr = B, Al)

Quantum chemical calculations at the ωB97XD/6-311++G(d,p) level of theory have been executed to investigate the effect of substituents via hydrogen-bonded and triel-bonded complexes between uracil (U), thymine (T) and 5-fluorouracil (5FU) with HCl for the former complexes, and with BH₃ and AlH₃ for the latter complexes. These calculations are supported by single-point energy calculations at MP2/6-311++G(d,p) and CCSD/6-31 + G(d,p) levels of theory, Natural Bond Orbital (NBO) and Molecular Electrostatic Potentials (MEPs) analyses, and global/local reactivity descriptors. The results reveal that triel-bonded complexes are strongly bounded than hydrogen-bonded ones, and Al-containing dimers stronger than B-containing ones. In addition, as the central triel atom grows in size, B-containing dimers (B-O triel bond) are accompanied by weak B-H⋯O unconventional H-bonds. According to local reactivity descriptors, the B-O triel bond is hard-hard interaction that indicates that the association is primarily charge controlled, while the Al-O triel bond is soft-soft interaction that is primarily orbital controlled. In both Hydrogen as well as triel-bonded complexes, the α-methylation slightly overestimates the binding strength of U, while the α-fluorination exerts the opposite role by underestimating the binding strength of U. In overall, the effect of substituents on the bond strength and thus on the regioselectivity is very small, suggesting a competition between the two carbonyl groups in terms of structures and binding energies.

Comparing the performances of various density functionals for modelling the mechanisms and kinetics of bimolecular free radical reactions in aqueous solution

We systematically tested the performances of 18 density functionals for the mechanisms and kinetics of reactions of the α-hydroxyisopropyl radical with 9 organic substrates.

Quantitative Assessment of Tetrel Bonding Utilizing Vibrational Spectroscopy

A set of 35 representative neutral and charged tetrel complexes was investigated with the objective of finding the factors that influence the strength of tetrel bonding involving single bonded C, Si, and Ge donors and double bonded C or Si donors. For the first time, we introduced an intrinsic bond strength measure for tetrel bonding, derived from calculated vibrational spectroscopy data obtained at the CCSD(T)/aug-cc-pVTZ level of theory and used this measure to rationalize and order the tetrel bonds. Our study revealed that the strength of tetrel bonds is affected by several factors, such as the magnitude of the σ-hole in the tetrel atom, the negative electrostatic potential at the lone pair of the tetrel-acceptor, the positive charge at the peripheral hydrogen of the tetrel-donor, the exchange-repulsion between the lone pair orbitals of the peripheral atoms of the tetrel-donor and the heteroatom of the tetrel-acceptor, and the stabilization brought about by electron delocalization. Thus, focusing on just one or two of these factors, in particular, the σ-hole description can only lead to an incomplete picture. Tetrel bonding covers a range of -1.4 to -26 kcal/mol, which can be strengthened by substituting the peripheral ligands with electron-withdrawing substituents and by positively charged tetrel-donors or negatively charged tetrel-acceptors.

Density Functional Theory for Microwave Spectroscopy of Noncovalent Complexes: A Benchmark Study

In this work, we compare the results obtained with 89 computational methods for predicting noncovalent bond lengths in weakly bound complexes. Evaluations for the performance in noncovalent interaction energies and covalent bond lengths obtained from five other data sets are included. The overall best performing density functional is the ωB97M-V method, achieving balanced results across all three categories. For noncovalent geometries, the best methods include B97M-V, B3LYP-D3(BJ) and DSD-PBEPBE-D3(BJ). The effects of systematic improvement of the density functional approximation and of dispersion corrections are also discussed.