Communication: Density functional theory overcomes the failure of predicting intermolecular interaction energies

Analytical Derivatives of Symmetry-Adapted Perturbation Theory Corrections for Interaction-Induced Properties

A new approach that allows for the calculation of interaction-induced properties exclusively from the properties of monomers is presented. The method is derived in the spirit of the symmetry-adapted perturbation theory (SAPT). The interaction-induced property is presented in the first order of the molecular interaction operator, including the exchange effects. Test calculations of the interaction-induced dipole moment were carried out for a number of small nonpolar and polar atomic and molecular dimers. The numerical results show that the analytical first-order corrections proposed in this paper reproduce the finite-field treatment of the first-order corrections of SAPT. Compared to supermolecular approaches, the performance of the finite-field SAPT (up to the second order) constitutes an insightful alternative for calculations of interaction-induced properties.

Methyl-π Interactions. Nature of Bonding and Limits of Strength

Both methyl groups and benzene rings are exceedingly common, and they lie near one another in many chemical situations. DFT calculations are used to gauge the strength of the attractive forces between them, and to better understand the phenomena that underlie this attraction. Methane and benzene are taken as the starting point, and substituents of both electron-withdrawing and donating types are added to each. The interaction energy varies between 1.4 and 5.0 kcal/mol, depending upon the substituents placed on the two groups. The nature of the binding is analyzed via Atoms in Molecules (AIM), Natural Bond Orbital (NBO), Symmetry-Adapted Perturbation Theory (SAPT), nuclear magnetic resonance (NMR) chemical shifts, and electron density shift diagrams. While there is a sizable electrostatic component, it is dispersion that dominates these interactions, particularly the weaker ones. As such, these interactions cannot be categorized unambiguously as either H-bonds or tetrel bonds.

Competition Between Halogen Atom and Ring of Halobenzenes as Hydrogen Bond Electron Donor Sites

A halobenzene molecule contains several sites that are capable of acting in an electron-donating capacity within a H-bond. One set of such sites comprise the lone electron pairs of the halogen (X) atoms on the periphery of the ring. The π-electron system above the ring plane can also fulfill this function in many cases. DFT calculations are applied to compare and contrast the propensity of these two site types to engage in such a H-bond within the context of mono, di, tri, tetra, and hexasubstituted halobenzenes. The X atoms chosen for study comprise the full set: F, Cl, Br, and I. It is found that even when the electrostatic potential of the X lone pair is more negative than that above the ring, it is the latter position which is the preferred binding site of HCl in most cases. This preference switches over to the X lone pair only for higher order of substitution, with n=4 or 6. This pattern is explained in large measure by the higher contribution of dispersion when the proton donor is located above the ring.

Boosting Leaching of Spent Ternary Cathode via Strong Van Der Waals Force Beyond Hydrogen Bonding

Promoting the green and efficient recycling of critical metals in spent ternary batteries represents a crucial step in driving the reduce of resource dependence in the electric vehicle industry. However, the leaching progress of metals from spent cathodes generally requires high reaction temperatures and large usage of solvents. Herein, a strategy is proposed to strengthen the van der Waals forces between solvent components by constructing affinity interactions between functional groups (e.g., -OH and -COOH), which can significantly enhance the leaching kinetics of metals at a high solid-liquid ratio and low temperature (30 °C). The results demonstrate that the strong van der Waals force between ascorbic acid with -OH group and betaine ions with -COOH group can strengthen the nucleophilicity of the carbon atoms and reduce the specific C─C bond energy, thus enhancing the redox capability of the DESs. Encouragingly, the designed solvent shows an impressive leaching performance at a super high S/L ratio (1: 3) without external heating for the actual black mass under a scaled-up experiment.

The competitive strengths of hydrogen and halogen bonding to haloforms and their different spectroscopic markers

Haloforms (CX3H) are paired with halide anions and with neutral N-bases, and the properties of the ensuing hydrogen (HB) and halogen bond (XB) are examined by DFT calculations. The strength of either sort of interaction diminishes in the order F- > Cl- > Br- > I- > NH3 > NCH. The XB energy climbs rapidly as the haloform X atom grows larger, but the HB is much less sensitive to the identity of X. In most cases, the HB is energetically favored over the XB. Exceptions occur when CI3H is paired with any of the halides, where the XB is more stable. In both cases, the X-H stretching frequency is shifted to the red, but the magnitude of this shift is far larger in the HB case. The NMR chemical shielding of the proton is substantially reduced by formation of a HB, but undergoes a small increase within the XB. The C nucleus of the haloform suffers a large shielding drop within the HB, but its shielding change is far smaller within the context of a XB, and can be of either sign.

Dispersionless Nonhybrid Density Functional

A dispersion-corrected density functional theory (DFT+D) method has been developed. It includes a nonhybrid dispersionless generalized gradient approximation (GGA) functional paired with a literature-parametrized dispersion function. The functional's 9 adjustable parameters were optimized using a training set of 589 benchmark interaction energies. The resulting method performs better than other GGA-based DFT+D methods, giving a mean unsigned error of 0.33 kcal/mol. It even performs better than some more expensive meta-GGA or hybrid dispersion-corrected functionals. An important advantage of using the new functional is that its dispersion energy given by the D component is very close to the true dispersion energy at all intermolecular separations, whereas in other similarly accurate DFT+D approaches, such a dispersion contribution in the van der Waals minimum region is only a small fraction of the true value.

Ability of the Spectroscopic Properties of the P═Se Bond of a Base to Assess Noncovalent Bond Strength

The viability of the P═Se bond to serve as a monitor of the strength of a noncovalent bond was tested in the context of the (CH3)3PSe molecule. Density functional theory (DFT) computations paired this base with a collection of Lewis acids that spanned hydrogen, halogen, chalcogen, pnicogen, and tetrel bonding interactions and covered a wide range of bond strengths. A very strong linear correlation was observed between the interaction energy and the nuclear magnetic resonance (NMR) 1J(PSe) coupling constant, which could serve as an accurate indicator of bond strength. Also correlating very well with the interaction energy is the stretch of the P═Se bond caused by complexation and the red shift of its stretching frequency. Moderate correlations arise in the chemical shifts of the P and Se nuclei. The σ-hole depth on the Lewis acid is poorly correlated with the energetics, and the same is true for the full electrostatic contribution to the bond energy. Of the various components, it is the polarization energy that correlates most closely with the interaction energy.

Modulating the Competition between Different Atoms to Form Halogen Bonds

I and Br atoms are placed on opposite ends of a n-butyl group, with each allowed to form a halogen bond (XB) with NH3. DFT calculations show that the intrinsic preference of the nucleophile for the heavier I over Br can be reversed by the proper placement of substituents on the alkyl chain. A similar reversal occurs for NH2 and OH groups on the alkyl chain, where substituents make the O a better electron donor than N in an XB to an electrophilic ICCH. The highly mobile π-electron cloud of an aromatic ring makes such reversals much more difficult when the pair of competing atoms are placed on, or within, such a ring.

Participation of transition metal atoms in noncovalent bonds

The existence of halogen, chalcogen, pnicogen, and tetrel bonds as variants of noncovalent σ and π-hole bonds is now widely accepted, and many of their properties have been elucidated. The ability of the d-block transition metals to potentially act as Lewis acids in a similar capacity is examined systematically by DFT calculations. Metals examined span the entire range of the d-block from Group 3 to 12, and are selected from several rows of the periodic table. These atoms are placed in a variety of neutral MXn molecules, with X = Cl and O, and paired with a NH3 nucleophile. The resulting M⋯N bonds tend to be stronger than their p-block analogues, many of them with a substantial degree of covalency. The way in which the properties of these bonds is affected by the row and column of the periodic table from which the M atom is drawn, and the number and nature of ligands, is elucidated.

Spodium Bonding to Dicoordinated Group 12 Atoms

DFT calculations consider the interactions between linear MR2 and a series of N-bases, where M is Hg or Zn and its R substituents are CCH, CN, or NO2. NCH, NH3, and NMe3 were considered as three different N-bases. Zn forms stronger bonds with the N bases than does Hg, and they strengthen along with the electron-withdrawing power of the R substituent, varying over a wide range from 3.4 to 43.9 kcal/mol. Another factor contributing to the bond strength is the nucleophilicity of the base: NCH < NH3 < NMe3. All MR2 Lewis acids can bind at least two bases, which are situated along the R-M-R bisecting plane, fairly close to one another, with θ(N-M-N) angles between 67° and 117°. The presence of a more electron-withdrawing substituent R and more powerful nucleophile allows up to 4 bases to bind to M. The properties of these bonds place them along a continuum, some clearly noncovalent, while other contain a good deal of covalent character.

A practical post-Hartree-Fock approach describing open-shell metal cluster-support interactions. Application to Cu3 adsorption on benzene/coronene

Current advances in synthesizing and characterizing atomically precise monodisperse metal clusters (AMCs) at the subnanometer scale have opened up fascinating possibilities in designing new heterogeneous (photo)catalysts as well as functional interfaces between AMCs and biologically relevant molecules. Understanding the nature of AMC-support interactions at molecular-level is essential for optimizing (photo)catalysts performance and designing novel ones with improved properties. Møller-Plesset second-order perturbation theory (MP2) is one of the most cost-efficient single-reference post-Hartree-Fock wave-function-based theories that can be applied to AMC-support interactions considering adequate molecular models of the support, and thus complementing state-of-the-art dispersion-corrected density functional theory. However, the resulting AMC-support interaction is typically overestimated with the MP2 method and must be corrected. The coupled MP2 (MP2C) scheme replacing the uncoupled Hartree-Fock dispersion energy by a coupled dispersion contribution, has been proven to describe accurately van-der-Waals (vdW)-dominated interactions between closed-shell AMCs and carbon-based supports. In this work, the accuracy of a MP2C-based scheme is evaluated in modelling open-shell AMC-cluster interactions that imply charge transfer or other strong attractive energy contributions beyond vdW forces. For this purpose, we consider the interaction of Cu3 with molecular models of graphene of increasing size (benzene and coronene). In this way, it is shown that subchemical precision (within 0.1 kcal mol-1) is achieved with the modified MP2C scheme, using the explicitly correlated coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)-F12] as a benchmark method. It is also revealed that the energy difference between uncoupled and coupled dispersion terms closely follows benchmark values of the repulsive intramonomer correlation contribution. The proposed open-shell MP2C-based approach is expected to be of general applicability to open-shell atomic or molecular species interacting with coronene for regions of the potential landscape where single-reference electronic structure descriptions suffice.

Halogen Bonding to the π-Systems of Polycyclic Aromatics

The propensity of the π-electron system lying above a polycyclic aromatic system to engage in a halogen bond is examined by DFT calculations. Prototype Lewis acid CF3I is placed above the planes of benzene, naphthalene, anthracene, phenanthrene, naphthacene, chrysene, triphenyl, pyrene, and coronene. The I atom positions itself some 3.3-3.4 Å above the polycyclic plane, and the associated interaction energy is about 4 kcal/mol. This quantity is a little smaller for benzene, but is roughly equal for the larger polycyclics. The energy only oscillates a little as the Lewis acid slides across the face of the polycyclic, preferring regions of higher π-electron density over minima of the electrostatic potential. The binding is dominated by dispersion which contributes half of the total interaction energy.

Anions as Lewis Acids in Noncovalent Bonds

The ability of an anion to serve as electron-accepting Lewis acid in a noncovalent bond is assessed via DFT calculations. NH3 is taken as the common base, and is paired with a host of ACln - anions, with central atom A=Ca, Sr, Mg, Te, Sb, Hg, Zn, Ag, Ga, Ti, Sn, I, and B. Each anion reacts through its σ or π-hole although the electrostatic potential of this hole is quite negative in most cases. Despite the contact between this negative hole and the negative region of the approaching nucleophile, the electrostatic component of the interaction energy of each bond is highly favorable, and accounts for more than half of the total attractive energy. The double negative charge of dianions precludes a stable complex with NH3.

Tetrel Bonding of the Carbenium Ion Forms a Pentacoordinate Carbon Atom

As a flat trigonal species, the CR3 + carbenium ion contains a pair of deep π-holes above and below its molecular plane. In the case of CH3 + a first base will form a covalent bond with the central C, making the combined species tetrahedral. Approach of a second base to the opposite side results in a longer but rather strong noncovalent tetrel bond (TB). While CMe3 + can also form a similar asymmetric complex with a pair of bases, it also has the capacity to form a pair of nearly equivalent TBs, such that the resulting symmetric trigonal bipyramid configuration is only slightly higher in energy. When the three substituents on the central C are phenyl rings, the symmetric configuration with two TBs predominates. These tetrel bonds are quite strong, reaching up to 20 kcal/mol. Adding OPH2 or OCH substituents to the phenyl rings permits the formation of intramolecular C⋅⋅O TBs to the central C, very similar in many respects to the case where these TBs are intermolecular.

Transition from covalent to noncovalent bonding between tetrel atoms

The strength and nature of the bonding between tetrel (T) atoms in R2T⋯TR2 is examined by quantum calculations. T atoms cover the range of Group 14 atoms from C to Pb, and substituents R include Cl, F, and NH2. Systems vary from electrically neutral to both positive and negative overall charged radicals. There is a steady weakening progression in T-T bond strength as the tetrel atom grows larger, transitioning smoothly from a strong covalent to a much weaker noncovalent bond for the larger T atoms. The latter have some of the characteristics of a ditetrel bond, but there are also significant deviations from a classic bond of this type. The T2Cl4- anions are more strongly bonded than the corresponding cations, which are in turn stronger than the neutrals.

Wolfium bonds in homodimers of MX4Y (M = Mo, W; X = F, Cl, Br; Y = O, S, Se)

The term "wolfium bond" has been recently introduced to describe the noncovalent attraction between an atom of group 6 and a nucleophile via a σ-hole binding site. Crystal structures commonly contain a motif wherein two MX4Y units are arranged in close proximity, where M represents either Mo or W, and X and Y refer to halogen and chalcogen atoms respectively. DFT calculations were thus applied to a wide range of homodimers of these molecules so as to assess their preferred arrangements, and to characterize the types of bonding that are present in each in a systematic manner. The most stable Dual-X configuration is symmetric and contains a pair of equivalent M⋯X bonds. The interaction energies range from -8 to -29 kcal mol-1, and are largest for X = F, Y = O, and M = W. The X electron donor is replaced by Y, and the two wolfium bonds are reduced to one, in the less stable Mono-Y structure, with interaction energies between -2 and -10 kcal mol-1. There is some question as to whether the weaker bonds of this type constitute true wolfium bonds.

Influence of Internal Angular Arrangement on Pnicogen Bond Strength

The three Z-X covalent bonds of a ZX3 unit (Z = P, As, Sb, Bi) are normally arranged in a pyramidal structure. Quantum chemical calculations show that pnicogen bonds (ZBs) to the central Z are weakened if ZX3 is flattened, as in the opening of an umbrella. The partial closing of the umbrella has the opposite effect of substantially strengthening these ZBs, even amounting to a 2- or 3-fold magnification in certain cases. The strongest such bonds, wherein Sb and Bi are in a strained configuration within a ZO3CH model system, have interaction energies of 20 kcal/mol with an NH3 base. Most of these systems, whether flattened or more pyramidal, are capable of engaging in three ZBs simultaneously, despite a certain amount of negative cooperativity.

Transition between the Noncovalency and Covalency of σ-Hole Bonds

The properties of the bond between a N-ligand and a Lewis acid containing a σ-hole are studied by quantum chemical methods. Interactions considered include pnicogen bonds involving SbX5, PX5, and PX3, where X represents any of the halogen atoms F, Cl, Br, or I. Also studied are the tetrel bonds of PbX4 and SiX4, as well as the chalcogen bond involving TeOX4. Both NH3 and NCH are applied as two possible bases of differing potency. Some of the bonds are very strong with interaction energies easily exceeding 25 kcal/mol and with AIM bond critical point densities much higher than 0.04 au, suggesting their classification as coordinate covalent bonds. The pentavalent SbX5 and PX5 fall into this category when combined with NH3, as does TeOX4. Although the tetrel bonds involving PbX4 are only slightly weaker, they are probably better viewed as a strong noncovalent bond on the cusp of covalency. Changing the internal bonding of hypervalent SbX5 to the more conventional SbX3 weakens the interaction to a classical noncovalent pnicogen bond. Reducing the base nucleophilicity from NH3 to NCH weakens the bonds so that they are clearly noncovalent.

Heavy pnicogen atoms as electron donors in sigma-hole bonds

DFT calculations evaluate the strength of σ-hole bonds formed by ZH3 and ZMe3 (Z = N, P, As, Sb) acting as electron donor. Bond types considered include H-bond, halogen, chalcogen, pnicogen, and tetrel bond to perfluorinated Lewis acids FH, FBr, F2Se F3As, F4Ge, respectively, as well as their monofluorinated analogues. All of the Z atoms can engage in bonds of at least moderate strength, varying from 3 to more than 40 kcal mol-1. In most cases, N forms the strongest bonds, but the falloff from P to Sb is quite mild. However, this pattern is not characteristic of all cases, as for example in the halogen bonds, where the heavier Z atoms are comparable to, or even stronger than N. Most of the bonds are strengthened by replacing the three H atoms of ZH3 by methyl groups, better simulating the situation that would be generally encountered. Structural and NMR shielding data ought to facilitate the identification of these bonds within crystals or in solution.

Competition between Binding to Various Sites of Substituted Imidazoliums

The imidazolium cation has a number of different sites that can interact with a nucleophile. Adding a halogen atom (X) or a chalcogen (YH) group introduces the possibility of an NX···nuc halogen or NY···nuc chalcogen bond, which competes against the various H-bonds (NH and CH donors) as well as the lone pair···π interaction wherein the nucleophile lies above the plane of the cation. Substituted imidazoliums are paired with the NH₃ base, and the various different complexes are evaluated by density functional theory (DFT) calculations. The strength of XB and YB increases quickly along with the size and polarizability of the X/Y atom, and this sort of bond is the strongest for the heavier Br, I, Se, and Te atoms, followed by the NH···N H-bond, but this order reverses for Cl and S. The various CH···N H-bonds are comparable to one another and to the lone pair···π bond, all with interaction energies of 10-13 kcal/mol, values which show very little dependence upon the substituent placed on the imidazolium.

Superfluid helium droplet-mediated surface-deposition of neutral and charged silver atomic species

Experimental and theoretical work has delivered evidence of the helium nanodroplet-mediated synthesis and soft-landing of metal nanoparticles, nanowires, clusters, and single atoms on solid supports. Recent experimental advances have allowed the formation of charged metal clusters into multiply charged helium nanodroplets. The impact of the charge of immersed metal species in helium nanodroplet-mediated surface deposition is proved by considering silver atoms and cations at zero-temperature graphene as the support. By combining high-level ab initio intermolecular interaction theory with a full quantum description of the superfluid helium nanodroplet motion, evidence is presented that the fundamental mechanism of soft-deposition is preserved in spite of the much stronger interaction of charged species with surfaces, with high-density fluctuations in the helium droplet playing an essential role in braking them. Corroboration is also presented that the soft-landing becomes favored as the helium nanodroplet size increases.

Enhancement of Halogen Bond Strength by Intramolecular H-Bonds

Quantum calculations study the potential of an intramolecular H-bond between the halogen atom (X) of a halobenzene and a substituent placed ortho to it, to amplify the ability of X to engage in a halogen bond (XB) with a Lewis base. H-bonding substituents NH₂, CH₂CH₂OH, CH₂OH, OH, and COOH were added to halobenzenes (X = Cl, Br, I). The amino group had little effect, but those containing OH increased the CX···N XB energy to a NH₃ nucleophile by about 0.5 kcal/mol; the increment associated with COOH is larger, nearly 2 kcal/mol. These energy increments were approximately doubled if two such H-bonding substituents are present. Combining a pair of ortho COOH groups with an electron-withdrawing NO₂ group in the para position has a particularly large effect, raising the XB energy by about 4 kcal/mol, which can amount to as much as a 4-fold magnification.

How great is the stabilization of crowded polyphenylbiphenyls by London dispersion?

Decaphenylbiphenyl (1) and 2,2',4,4',6,6'-hexaphenylbiphenyl (2) are bulky molecules expected to be greatly destabilized by steric crowding. Herein, through a combined experimental and computational approach, we evaluate the molecular energetics of crowded biphenyls. This is complemented by the study of phase equilibria for 1 and 2. Compound 1 shows a rich phase behavior, displaying an unusual interconversion between two polymorphs. Surprisingly, the polymorph with distorted molecules of C₁ symmetry is found to have the highest melting point and to be the one that is preferentially formed. The thermodynamic results also indicate that the polymorph displaying the more regular D₂ molecular geometry has larger heat capacity and is probably the more stable at lower temperatures. The melting and sublimation data clearly reveal the weakening of cohesive forces in crowded biphenyls due to the lower molecular surface area. The experimental quantification of the intramolecular interactions in 1 and 2 indicated, using homodesmotic reactions, a molecular stabilization of about 30 kJ mol^-1. We attribute the origin of this stabilization in both compounds to the existence of two parallel-displaced π⋯π interactions between the ortho-phenyl substituents on each side of the central biphenyl. Computational calculations with dispersion-corrected DFT methods underestimate the stabilization in 1, unless the steric crowding is well balanced in a homodesmotic scheme. This work demonstrates that London dispersion forces are important in crowded aromatic systems, making these molecules considerably more stable than previously thought.

Benchmark of the Extension of Frozen-Density Embedding Theory to Nonvariational Correlated Methods: The Embedded-MP2 Case

The extension of the frozen-density embedding theory for nonvariational methods [J. Chem. Theory Comput. 2020, 16, 6880] was utilized to evaluate intermolecular interaction energies for complexes in the Zhao-Truhlar basis set. In the applied method (FDET-MP2-FAT-LDA), the same auxiliary system is used to evaluate the correlation energy by means of the second-order Møller-Plesset perturbation theory (MP2), as in our previous work [J. Chem. Phys. 2019, 150, 121101]. Local density approximation is used for E_xcT^nad[ρ_A,ρ_B] in both cases. Additionally, the contribution to the energy due to the neglected correlation potential was evaluated and analyzed. The domain of applicability of the local density approximation for E_xcT^nad[ρ_A,ρ_B] was determined based on deviations from the interaction energies from the conventional MP2 calculations. The local density approximation for E_xcT^nad[ρ_A,ρ_B] performs well for hydrogen- or dipole-bound complexes. The relative errors in the interaction energy lie within 3-30%. While for charge-transfer complexes, this approximation fails consistently, and for other types of complexes, the performance of this approximation is not systematic. The sources of error are discussed in detail.

Dataset of noncovalent intermolecular interaction energy curves for 24 small high-spin open-shell dimers

We introduce a dataset of 24 interaction energy curves of open-shell noncovalent dimers, referred to as the O24 × 5 dataset. The dataset consists of high-spin dimers up to 11 atoms selected to assure diversity with respect to interaction types: dispersion, electrostatics, and induction. The benchmark interaction energies are obtained at the restricted open-shell CCSD(T) level of theory with complete basis set extrapolation (from aug-cc-pVQZ to aug-cc-pV5Z). We have analyzed the performance of selected wave function methods MP2, CCSD, and CCSD(T) as well as the F12a and F12b variants of coupled-cluster theory. In addition, we have tested dispersion-corrected density functional theory methods based on the PBE exchange-correlation model. The O24 × 5 dataset is a challenge to approximate methods due to the wide range of interaction energy strengths it spans. For the dispersion-dominated and mixed-type subsets, any tested method that does not include the triples contribution yields errors on the order of tens of percent. The electrostatic subset is less demanding with errors that are typically an order of magnitude smaller than the mixed and dispersion-dominated subsets.

Explaining and Fixing DFT Failures for Torsional Barriers

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

Ab Initio Extended Hartree-Fock plus Dispersion Method Applied to Dimers with Hundreds of Atoms

The Hartree-Fock plus dispersion plus first-order correlation (HFDc⁽¹⁾) method consists in augmenting the HF interaction energy by the correlation part of the first-order interaction energy and the second-order dispersion and exchange-dispersion energies. All of the augmentation terms are computed using the symmetry-adapted perturbation theory based on density functional theory description of monomers [SAPT(DFT)]; thus, HFDc⁽¹⁾ is a fully ab initio method. A partly empirical version of this method, HFD_asc⁽¹⁾, uses a damped asymptotic expansion for the dispersion plus exchange-dispersion term fitted to SAPT(DFT) ab initio values. The HFDc⁽¹⁾ interaction energies for dimers in the S22, S66, S66x8, NCCE31, IonHB, and UD-ARL benchmark data sets are more accurate than those given by most ab initio methods with comparable costs. HFDc⁽¹⁾ can be used routinely for dimers with nearly 200 atoms, such as included in the S12L benchmark set, giving results comparable to those obtained by the most expensive methods applicable.

Dispersion Energy from Local Polarizability Density

A simple nonlocal functional for calculation of dispersion energies is proposed. Compared to a similar formula used earlier, we introduced a regularization to remove its singularities and used a dynamic polarizability density similar to those in the so-called van der Waals density functionals. The performance of the new functional is tested on dispersion energies for a set of representative dimers, and it is found that it is significantly more accurate than published nonlocal functionals.

Does a pair of methane molecules aggregate in water?

Molecular dynamics (MD) simulations of methane-water mixtures were performed using ab initio force fields for the CH₄-H₂O, H₂O-H₂O, and CH₄-CH₄ interactions. Both methane and water molecules were polarizable. From these calculations, the potential of mean force (PMF) between two methane molecules was extracted. Our results are compared with PMFs from a density-functional-theory (DFT) based Born-Oppenheimer type MD (BOMD) simulation, from a Monte Carlo (MC) simulation with ab initio-based force fields, and from MD simulations with empirical force fields. Our PMF is qualitatively similar to that obtained from the simulations with empirical force fields but differs significantly from those resulting from the DFT-BOMD and MC simulations. The depth of the PMF global minimum obtained in the present work is in a much better agreement with the experimental estimate than the result of the DFT-BOMD simulation, possibly due to the inability of DFT to describe the dispersion interactions and the lack of extensive sampling in the BOMD simulations. Our work indicates that, for a pair of methane molecules, there are configurations where the solvent increases the attraction between the solutes, but there are also conformations in which the solvent causes a weak net repulsion. On average, the methane molecules are more likely to be in the configuration where they are separated by a water molecule than in the one in which they are in contact even though the minimum of the PMF at the latter configuration is deeper than that at the former. Finally, we found that the water structure around methane solutes does not show a greater tetrahedral ordering than in neat bulk water.

Spectroscopy of a rotating hydrogen molecule in carbon nanotubes

Computing the energy levels of molecular hydrogen rotating in carbon nanotubes of increasing size.

The nature of three-body interactions in DFT: Exchange and polarization effects

We propose a physically motivated decomposition of density functional theory (DFT) 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar₂-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems, range-separated DFAs achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component, although semilocal and global hybrid DFAs appear to imitate it in the short range.

Spatial quenching of a molecular charge-transfer process in a quantum fluid: the Csx-C60 reaction in superfluid helium nanodroplets

A recent experimental study [Renzler et al., J. Chem. Phys., 2016, 145, 181101] on superfluid helium nanodroplets reported different reactivities for Cs atoms and Cs₂ dimers with C₆₀ fullerenes inside helium droplets. Alkali metal atoms and clusters are heliophobic, therefore typically residing on the droplet surface, while fullerenes are fully immersed into the droplet. In this theoretical study, which combines standard methods of computational chemistry with orbital-free helium density functional theory, we show that the experimental findings can be interpreted in the light of a quenched electron-transfer reaction between the fullerene and the alkali dopant, which is additionally hindered by a reaction barrier stemming from the necessary extrusion of helium upon approach of the two reactants.

Quantum confinement of molecular deuterium clusters in carbon nanotubes: ab initio evidence for hexagonal close packing

This study shows ab initio evidence for hexagonal close packing of D₂ molecules in carbon nanotubes, with a = 3.6 Å and .

Range-Separated meta-GGA Functional Designed for Noncovalent Interactions

The accuracy of applying density functional theory to noncovalent interactions is hindered by errors arising from low-density regions of interaction-induced change in the density gradient, error compensation between correlation and exchange functionals, and dispersion double counting. A new exchange-correlation functional designed for noncovalent interactions is proposed to address these problems. The functional consists of the range-separated PBEsol exchange considered in two variants, pure and hybrid, and the semilocal correlation functional of Modrzejewski et al. (J. Chem. Phys. 2012, 137, 204121) designed with the constraint satisfaction technique to smoothly connect with a dispersion term. Two variants of dispersion correction are appended to the correlation functional: the atom-atom pairwise additive DFT-D3 model and the density-dependent many-body dispersion with self-consistent screening (MBD-rsSCS). From these building blocks, a set of four functionals is created to systematically examine the role of pure versus hybrid exchange and the underlying models for dispersion. The new functional is extensively tested on benchmark sets with diverse nature and size. Truly outstanding performance is demonstrated for water clusters of varying size, ionic hydrogen bonds, and thermochemistry of isodesmic n-alkane fragmentation reactions. The merits of each component of the new functional are discussed.