Density-functional theory-symmetry-adapted intermolecular perturbation theory with density fitting: A new efficient method to study intermolecular interaction energies

Attractive PHHP interactions revealed by state-of-the-art ab initio calculations

We report in this work a combined structural and state-of-the-art computational study of homopolar P-HH-P intermolecular contacts. Database surveys have shown the abundance of such surprisingly unexplored contacts, which are usually accompanied by other weak interactions in the solid state. By means of a detailed theoretical study utilizing SAPT(DFT), MP2, SCS-MP2, MP2C and CCSD(T) methods and both aug-cc-pVXZ and aug-cc-pCVXZ (X = D, T, Q, 5) basis sets as well as extrapolation to the CBS limit, we have shown that P-HH-P contacts are indeed attractive and considerably strong. SAPT(DFT) calculations have revealed the dispersive nature of the P-HH-P interaction with only minor contribution of the inductive term, whereas the first-order electrostatic term is clearly overbalanced by the first-order exchange energy. In general the computed interaction energies follow the trend: E ≈ E < E < E. Our results have also shown that the aug-cc-pVDZ (or aug-cc-pCVDZ) basis set is not yet well balanced and that the second-order dispersion energy term is the slowest converging among all SAPT(DFT) energy components. Compared to aug-cc-pVXZ basis sets, their core-correlation counterparts have a modest influence on all supermolecular interaction energies and a negligible influence on both the SAPT(DFT) interaction energy and its components.

Discerning Inter- and Intramolecular Vibrations of Sulfur Polyaromatic Compounds

Thiophenes are an important class of molecules in fields as diverse as petrochemistry, molecular electronics, and optoelectronics. Thiophenic submolecular motifs are thought to play a role in molecular association and nanoaggregation phenomena in both pure materials and natural and synthetic mixtures. Vibrational (infrared and Raman) spectroscopy provides the means to characterize these species. In this work far-infrared photoacoustic and low-frequency Raman spectra of a series of polycyclic aromatic hydrocarbons containing sulfur have been measured and interpreted using DFT calculations based on a perturbational-variational method coupled with potential truncation. The approach and outcomes illustrate how inter- and intramolecular vibrations for thiophenic systems in single and multicomponent mixtures can be discriminated. This work offers the perspective to search the inter- and intramolecular signatures of the main submolecular motifs and heteroelements postulated as being present in the asphaltenes.

Dispersion Interactions and the Stability of Amine Dimers

Weak, intermolecular interactions in amine dimers were studied by using the combination of a dispersionless density functional and a function that describes the dispersion contribution to the interaction energy. The validity of this method was shown by comparison of structural and energetic properties with data obtained with a conventional density functional and the coupled cluster method. The stability of amine dimers was shown to depend on the size, the shape, and the relative orientation of the alkyl substituents, and it was shown that the stabilization energy for large substituents is dominated by dispersion interactions. In contrast to traditional chemical explanations that attribute stability and condensed matter properties solely to hydrogen bonding and, thus, to the properties of the atoms forming the hydrogen bridge, we show that without dispersion interactions not even the stability and structure of the ammonia dimer can be correctly described. The stability of amine dimers depends crucially on the interaction between the non-polar alkyl groups, which is dominated by dispersion interactions. This interaction is also responsible for the energetic part of the free energy interaction used to describe hydrophobic interactions in liquid alkanes. The entropic part has its origin in the high degeneracy of the interaction energy for complexes of alkane molecules, which exist in a great variety of conformers, having their origin in internal rotations of the alkane chains.

Side Reactions with an Equilibrium Constraint: Detailed Mechanism of the Substitution Reaction of Tetraplatin with dGMP as a Starting Step of the Platinum(IV) Reduction Process

Two possible pathways of the substitution reaction within the reduction process of the Pt^IV(DACH)Cl₄ by dGMP are compared: associative reaction course and autocatalytic Basolo-Pearson mechanisms. Since two forms: single-protonated and fully deprotonated phosphate group of dGMP are present in equilibrium at neutral and mildly acidic solutions, consideration of a side reactions scheme with acido-basic equilibrium-constraint is a very important model for obtaining reliable results. The examined complexes are optimized at the B3LYP-GD3BJ/6-31G(d) level with the COSMO implicit solvation model and Klamt's radii used for cavity construction. Energy characteristics and thermodynamics for all reaction branches are determined using the B3LYP-GD3BJ/6-311++G(2df,2pd)/IEF-PCM/scaled-UAKS level with Wertz's entropy corrections. Rate constants are estimated for each individual branch according to Eyring's transition state theory (TST), averaged according to equilibrium constraint and compared with available experimental data. The determined reaction barriers of the autocatalytic pathway fairly correspond with experimental values. Furthermore, autocatalytic reaction of tetraplatin and its two analogues complexes [Pt^IV(en)Cl₄ and Pt^IV(NH₃)₂Cl₄] are explored and compared with measured data in order to examined general reaction descriptors.

Density-fitted open-shell symmetry-adapted perturbation theory and application to π-stacking in benzene dimer cation and ionized DNA base pair steps

Symmetry-Adapted Perturbation Theory (SAPT) is one of the most popular approaches to energy component analysis of non-covalent interactions between closed-shell systems, yielding both accurate interaction energies and meaningful interaction energy components. In recent years, the full open-shell equations for SAPT up to second-order in the intermolecular interaction and zeroth-order in the intramolecular correlation (SAPT0) were published [P. S. Zuchowski et al., J. Chem. Phys. 129, 084101 (2008); M. Hapka et al., ibid. 137, 164104 (2012)]. Here, we utilize density-fitted electron repulsion integrals to produce an efficient computational implementation. This approach is used to examine the effect of ionization on π-π interactions. For the benzene dimer radical cation, comparison against reference values indicates a good performance for open-shell SAPT0, except in cases with substantial charge transfer. For π stacking between hydrogen-bonded pairs of nucleobases, dispersion interactions still dominate binding, in spite of the creation of a positive charge.

Perspective: Quantum mechanical methods in biochemistry and biophysics

In this perspective article, I discuss several research topics relevant to quantum mechanical (QM) methods in biophysical and biochemical applications. Due to the immense complexity of biological problems, the key is to develop methods that are able to strike the proper balance of computational efficiency and accuracy for the problem of interest. Therefore, in addition to the development of novel ab initio and density functional theory based QM methods for the study of reactive events that involve complex motifs such as transition metal clusters in metalloenzymes, it is equally important to develop inexpensive QM methods and advanced classical or quantal force fields to describe different physicochemical properties of biomolecules and their behaviors in complex environments. Maintaining a solid connection of these more approximate methods with rigorous QM methods is essential to their transferability and robustness. Comparison to diverse experimental observables helps validate computational models and mechanistic hypotheses as well as driving further development of computational methodologies.

Adsorption of Organic Molecules to van der Waals Materials: Comparison of Fluorographene and Fluorographite with Graphene and Graphite

Understanding strength and nature of noncovalent binding to surfaces imposes significant challenge both for computations and experiments. We explored the adsorption of five small nonpolar organic molecules (acetone, acetonitrile, dichloromethane, ethanol, ethyl acetate) to fluorographene and fluorographite using inverse gas chromatography and theoretical calculations, providing new insights into the strength and nature of adsorption of small organic molecules on these surfaces. The measured adsorption enthalpies on fluorographite range from -7 to -13 kcal/mol and are by 1-2 kcal/mol lower than those measured on graphene/graphite, which indicates higher affinity of organic adsorbates to fluorographene than to graphene. The dispersion-corrected functionals performed well, and the nonlocal vdW DFT functionals (particularly optB86b-vdW) achieved the best agreement with the experimental data. Computations show that the adsorption enthalpies are controlled by the interaction energy, which is dominated by London dispersion forces (∼70%). The calculations also show that bonding to structural features, like edges and steps, as well as defects does not significantly increase the adsorption enthalpies, which explains a low sensitivity of measured adsorption enthalpies to coverage. The adopted Langmuir model for fitting experimental data enabled determination of adsorption entropies. The adsorption on the fluorographene/fluorographite surface resulted in an entropy loss equal to approximately 40% of the gas phase entropy.

Noncovalent Interactions in Specific Recognition Motifs of Protein-DNA Complexes

In view of the importance of protein-DNA interactions in biological processes, we extracted from the Protein Data Bank several one-to-one complexes of amino acids with nucleotides that matched certain geometric and energetic specificity criteria and investigated them using quantum chemistry methods. The CCSD(T)/CBS interaction energies were used as a benchmark to compare the performance of the MP2.5, MP2-F12, DFT-D3, and PM6-D3H4 methods. All methods yielded good agreement with the reference values, with declining accuracy from MP2.5 to PM6-D3H4. Regardless of the site of interaction, the minima found after full optimization in implicit solvent with high dielectric constant were close to the structures experimentally detected in protein-DNA complexes. According to DFT-SAPT analysis, the nature of noncovalent interactions strongly depends on the type of amino acid. The negatively charged sugar-phosphate backbone of DNA heavily influences the strength of interactions and must be included in the computational model, especially in the case of interactions with charged amino acids.

In silico analysis of interaction pattern switching in ligand⋯receptor binding in Golgi α-mannosidase II induced by the protonated states of inhibitors

Different binding modes for charge-neutral and protonated inhibitor forms in Golgi α-mannosidase II active sites may influence their biological activities.

B–H⋯π: a nonclassical hydrogen bond or dispersion contact?

Quantum mechanical calculations disprove the attractive electrostatic nature of B–H⋯π motif and define it as dispersion-driven contact.

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 .

Adsorption of molecular hydrogen on coronene with a new potential energy surface

Adsorption of molecular hydrogen on coronene studied with a new potential energy surface. Path integral Monte Carlo and basin-hopping calculations have been performed to investigate energies and structures of the corresponding (H₂)_N-coronene clusters.

A theoretical study of complexes formed between cations and curved aromatic systems: electrostatics does not always control cation–π interaction

Cation–π interactions in curved aromatic systems are not controlled by electrostatics; induction and dispersion dominate in most cases studied.

Size-dependent conformational change in halogen–π interaction: from benzene to graphene

Diatomic halogen molecules (Cl₂, Br₂) favor the stacked conformation on graphene, while they favor the edge-to-face conformation on benzene.

Multi-spectroscopic and theoretical analyses on the diphenyl ether–tert-butyl alcohol complex in the electronic ground and electronically excited state

Multi-spectroscopic and theoretical investigations on the isolated diphenyl ether–tert-butyl alcohol complex – an ideal benchmark system for theory with strongly competing OH–O and OH–π binding motifs.

Halogen-π Interactions between Benzene and X2/CX4 (X = Cl, Br): Assessment of Various Density Functionals with Respect to CCSD(T)

Various types of interactions between halogen (X) and π moiety (X-π interaction) including halogen bonding play important roles in forming the structures of biological, supramolecular, and nanomaterial systems containing halogens and aromatic rings. Furthermore, halogen molecules such as X₂ and CX₄ (X = Cl/Br) can be intercalated in graphite and bilayer graphene for doping and graphene functionalization/modification. Due to the X-π interactions, though recently highly studied, their structures are still hardly predictable. Here, using the coupled-cluster with single, double, and noniterative triple excitations (CCSD(T)), the Møller-Plesset second-order perturbation theory (MP2), and various flavors of density functional theory (DFT) methods, we study complexes of benzene (Bz) with halogen-containing molecules X₂ and CX₄ (X = Cl/Br) and analyze various components of the interaction energy using symmetry adapted perturbation theory (SAPT). As for the lowest energy conformers (S1), X₂-Bz is found to have the T-shaped structure where the electropositive X atom-end of X₂ is pointing to the electronegative midpoint of CC bond of the Bz ring, and CX₄-Bz has the stacked structure. In addition to this CX₄-Bz (S1), other low energy conformers of X₂-Bz (S2/S3) and CX₄-Bz (S2) are stabilized primarily by the dispersion interaction, whereas the electrostatic interaction is substantial. Most of the density functionals show noticeable deviations from the CCSD(T) complete basis set (CBS) limit binding energies, especially in the case of strongly halogen-bonded conformers of X₂-Bz (S1), whereas the deviations are relatively small for CX₄-Bz where the dispersion is more important. The halogen bond shows highly anisotropic electron density around halogen atoms and the DFT results are very sensitive to basis set. The unsatisfactory performance of many density functionals could be mainly due to less accurate exchange. This is evidenced from the good performance by the dispersion corrected hybrid and double hybrid functionals. B2GP-PLYP-D3 and PBE0-TS(Tkatchenko-Scheffler)/D3 are well suited to describe the X-π interactions adequately, close to the CCSD(T)/CBS binding energies (within ∼1 kJ/mol). This understanding would be useful to study diverse X-π interaction driven structures such as halogen containing compounds intercalated between 2-dimensional layers.

Adsorption, Dissociation, and Dehydrogenation of Water Monomer and Water Dimer on the Smallest 3D Aluminum Particle. The O-H Dissociation Barrier Disappears for the Dimer

We present a detailed mechanistic study on the interaction and reaction of water monomer and water dimer with the smallest 3D aluminum particle (Al₆) by employing density functional and explicitly correlated coupled cluster CCSD(T)-F12 theories. Water adsorption, dissociation, and dehydrogenation are considered. For the monomer reaction, where core-valence correlation and an extrapolation to the complete basis set limit is allowed for, our coupled cluster calculations predict the O-H dissociation barrier of about 2 kcal/mol. For the dimer reaction, two distinct reaction paths are identified, initiated by forming separate dimer complexes wherein (H₂O)₂ adsorbs mainly via the oxygen atom of the donor H₂O molecule. The key O-H dissociation transition states of the dimer reaction involve a concerted migration of two H atoms resulting in the dissociation of the donor molecule and formation of the OH-water complex adsorbed on the metal cluster's surface. The most remarkable feature of both dimer reaction energy profiles is the lack of the overall energy barrier for the (rate-determining) O-H dissociation. The hydrogen bond acceptor molecule is suggested to have an extra catalytic effect on the O-H dissociation barrier of the hydrogen bond donor molecule by removing this barrier. A similar effect on the dehydrogenation step is indicated.

Assessing Ion-Water Interactions in the AMOEBA Force Field Using Energy Decomposition Analysis of Electronic Structure Calculations

AMOEBA is a molecular mechanics force field that addresses some of the shortcomings of a fixed partial charge model, by including permanent atomic point multipoles through quadrupoles, as well as many-body polarization through the use of point inducible dipoles. In this work, we investigate how well AMOEBA formulates its non-bonded interactions, and how it implicitly incorporates quantum mechanical effects such as charge penetration (CP) and charge transfer (CT), for water-water and water-ion interactions. We find that AMOEBA's total interaction energies, as a function of distance and over angular scans for the water dimer and for a range of water-monovalent cations, agree well with an advanced density functional theory (DFT) model, whereas the water-halides and water-divalent cations show significant disagreement with the DFT result, especially in the compressed region when the two fragments overlap. We use a second-generation energy decomposition analysis (EDA) scheme based on absolutely localized molecular orbitals (ALMOs) to show that in the best cases AMOEBA relies on cancellation of errors by softening of the van der Waals (vdW) wall to balance permanent electrostatics that are too unfavorable, thereby compensating for the missing CP effect. CT, as another important stabilizing effect not explicitly taken into account in AMOEBA, is also found to be incorporated by the softened vdW interaction. For the water-halides and water-divalent cations, this compensatory approach is not as well executed by AMOEBA over all distances and angles, wherein permanent electrostatics remains too unfavorable and polarization is overdamped in the former while overestimated in the latter. We conclude that the DFT-based EDA approach can help refine a next-generation AMOEBA model that either realizes a better cancellation of errors for problematic cases like those illustrated here, or serves to guide the parametrization of explicit functional forms for short-range contributions from CP and/or CT.

Molecular energies from an incremental fragmentation method

The systematic molecular fragmentation method by Collins and Deev [J. Chem. Phys. 125, 104104 (2006)] has been used to calculate total energies and relative conformational energies for a number of small and extended molecular systems. In contrast to the original approach by Collins, we have tested the accuracy of the fragmentation method by utilising an incremental scheme in which the energies at the lowest level of the fragmentation are calculated on an accurate quantum chemistry level while lower-cost methods are used to correct the low-level energies through a high-level fragmentation. In this work, the fragment energies at the lowest level of fragmentation were calculated using the random-phase approximation (RPA) and two recently developed extensions to the RPA while the incremental corrections at higher levels of the fragmentation were calculated using standard density functional theory (DFT) methods. The complete incremental fragmentation method has been shown to reproduce the supermolecule results with a very good accuracy, almost independent on the molecular type, size, or type of decomposition. The fragmentation method has also been used in conjunction with the DFT-SAPT (symmetry-adapted perturbation theory) method which enables a breakdown of the total nonbonding energy contributions into individual interaction energy terms. Finally, the potential problems of the method connected with the use of capping hydrogen atoms are analysed and two possible solutions are supplied.

Beyond Born-Mayer: Improved Models for Short-Range Repulsion in ab Initio Force Fields

Short-range repulsion within intermolecular force fields is conventionally described by either Lennard-Jones (A/r(12)) or Born-Mayer (A exp(-Br)) forms. Despite their widespread use, these simple functional forms are often unable to describe the interaction energy accurately over a broad range of intermolecular distances, thus creating challenges in the development of ab initio force fields and potentially leading to decreased accuracy and transferability. Herein, we derive a novel short-range functional form based on a simple Slater-like model of overlapping atomic densities and an iterated stockholder atom (ISA) partitioning of the molecular electron density. We demonstrate that this Slater-ISA methodology yields a more accurate, transferable, and robust description of the short-range interactions at minimal additional computational cost compared to standard Lennard-Jones or Born-Mayer approaches. Finally, we show how this methodology can be adapted to yield the standard Born-Mayer functional form while still retaining many of the advantages of the Slater-ISA approach.

Challenging Dogmas: Hydrogen Bond Revisited

Hydrogen bond directionality in the water dimer is explained on the basis of symmetry-adapted intermolecular perturbation theory which directly separates the intermolecular interaction energy into four physically interpretable components: electrostatics, exchange-repulsion, dispersion, and induction. Analysis of these four main contributions to the binding energy allows a deeper understanding of the dominant factors ruling the mutual arrangement of the two monomers. A preference for the linear configuration is shown to be due to a subtle interplay of all four energy components. While the first-order terms, electrostatic and exchange-repulsion, almost perfectly cancel each other near the equilibrium geometry of the dimer, the importance of the second- and higher-order terms, induction and dispersion, becomes evident.

Chemical accuracy from quantum Monte Carlo for the benzene dimer

We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is -2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.

Character of intermolecular interaction in pyridine-argon complex: Ab initio potential energy surface, internal dynamics, and interrelations between SAPT energy components

The pyridine-Ar (PAr) van der Waals (vdW) complex is studied using a high level ab initio method. Its structure, binding energy, and intermolecular vibrational states are determined from the analytical potential energy surface constructed from interaction energy (IE) values computed at the coupled cluster level of theory with single, double, and perturbatively included triple excitations with the augmented correlation consistent polarized valence double-ζ (aug-cc-pVDZ) basis set complemented by midbond functions. The structure of the complex at its global minimum with Ar at a distance of 3.509 Å from the pyridine plane and shifted by 0.218 Å from the center of mass towards nitrogen agrees well with the corresponding equilibrium structure derived previously from the rotational spectrum of PAr. The PAr binding energy De of 392 cm(-1) is close to that of 387 cm(-1) calculated earlier at the same ab initio level for the prototypical benzene-Ar (BAr) complex. However, under an extension of the basis set, De for PAr becomes slightly lower than De for BAr. The ab initio vdW vibrational energy levels allow us to estimate the reliability of the methods for the determination of the vdW fundamentals from the rotational spectra. To disclose the character of the intermolecular interaction in PAr, the symmetry-adapted perturbation theory (SAPT) is employed for the analysis of different physical contributions to IE. It is found that SAPT components of IE can be approximately expressed in the binding region by only two of them: the exchange repulsion and dispersion energy. The total induction effect is negligible. The interrelations between various SAPT components found for PAr are fulfilled for a few other complexes involving aromatic molecules and Ar or Ne, which indicates that they are valid for all rare gas (Rg) atoms and aromatics.

Energy Decomposition Analysis with a Stable Charge-Transfer Term for Interpreting Intermolecular Interactions

Many schemes for decomposing quantum-chemical calculations of intermolecular interaction energies into physically meaningful components can be found in the literature, but the definition of the charge-transfer (CT) contribution has proven particularly vexing to define in a satisfactory way and typically depends strongly on the choice of basis set. This is problematic, especially in cases of dative bonding and for open-shell complexes involving cation radicals, for which one might expect significant CT. Here, we analyze CT interactions predicted by several popular energy decomposition analyses and ultimately recommend the definition afforded by constrained density functional theory (cDFT), as it is scarcely dependent on basis set and provides results that are in accord with chemical intuition in simple cases, and in quantitative agreement with experimental estimates of the CT energy, where available. For open-shell complexes, the cDFT approach affords CT energies that are in line with trends expected based on ionization potentials and electron affinities whereas some other definitions afford unreasonably large CT energies in large-gap systems, which are sometimes artificially offset by underestimation of van der Waals interactions by density functional theory. Our recommended energy decomposition analysis is a composite approach, in which cDFT is used to define the CT component of the interaction energy and symmetry-adapted perturbation theory (SAPT) defines the electrostatic, polarization, Pauli repulsion, and van der Waals contributions. SAPT/cDFT provides a stable and physically motivated energy decomposition that, when combined with a new implementation of open-shell SAPT, can be applied to supramolecular complexes involving molecules, ions, and/or radicals.