Intermolecular Interaction Energy Calculations Research Articles

Enhanced Layered-Herringbone Packing due to Long Alkyl Chain Substitution in Solution-Processable Organic Semiconductors

Herein, we report the stabilization and modulation of layered-herringbone (LHB) packing, which is known to afford high-performance organic thin-film transistors, based on crystal structure analyses and calculations of intermolecular interaction energies for alkyl-substituted organic semiconductor (OSC) crystals. We systematically investigated the alkyl chain-length dependence of the crystal structures, solvent solubilities, and thermal characteristics for three series of symmetrically and asymmetrically alkyl-substituted benzothieno[3,2-b][1]benzothiophenes (BTBTs). All the series exhibit LHB packing when the BTBTs are substituted with relatively long alkyl chains (−CnH2n+1), i.e., n ≥ 4 for monoalkylated, n ≥ 6 for dialkylated, and n ≥ 5 for phenyl-alkylated BTBTs. LHB packing is also evident in the nonsubstituted and diethyl-substituted BTBTs, although those substituted with short alkyl chains generally did not feature LHB packing because of their lack of interchain ordering. The density functional theo...

Intermolecular interactions in molecular crystals: what's in a name?

Structure-property relationships are the key to modern crystal engineering, and for molecular crystals this requires both a thorough understanding of intermolecular interactions, and the subsequent use of this to create solids with desired properties. There has been a rapid increase in publications aimed at furthering this understanding, especially the importance of non-canonical interactions such as halogen, chalcogen, pnicogen, and tetrel bonds. Here we show how all of these interactions - and hydrogen bonds - can be readily understood through their common origin in the redistribution of electron density that results from chemical bonding. This redistribution is directly linked to the molecular electrostatic potential, to qualitative concepts such as electrostatic complementarity, and to the calculation of quantitative intermolecular interaction energies. Visualization of these energies, along with their electrostatic and dispersion components, sheds light on the architecture of molecular crystals, in turn providing a link to actual crystal properties.

Surface Adsorption from the Exchange-Hole Dipole Moment Dispersion Model.

The accurate calculation of intermolecular interaction energies with density functional theory requires methods that include a treatment of long-range, nonlocal dispersion correlation. In this work, we explore the ability of the exchange-hole dipole moment (XDM) dispersion correction to model molecular surface adsorption. Adsorption energies are calculated for six small aromatic molecules (benzene, furan, pyridine, thiophene, thiophenol, and benzenediamine) and the four DNA nucleobases (adenine, thymine, guanine, and cytosine) on the (111) surfaces of the three coinage metals (copper, silver, and gold). For benzene, where the experimental reference data is most precise, the mean absolute error in the computed absorption energies is 0.04 eV. For the other aromatic molecules, the computed binding energies are found to be within 0.09 eV of the available reference data, on average, which is well below the expected experimental uncertainties for temperature-programmed desorption measurements. Unlike other dispersion-corrected functionals, adequate performance does not require changes to the canonical XDM implementation, and the good performance of XDM is explained in terms of the behavior of the exchange hole. Additionally, the base functional employed (B86bPBE) is also optimal for molecular studies, making B86bPBE-XDM an excellent candidate for studying chemistry on material surfaces. Finally, the noncovalent interaction (NCI) plot technique is shown to detect adsorption effects in real space on the order of tenths of an eV.

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.

Defining the contributions of permanent electrostatics, Pauli repulsion, and dispersion in density functional theory calculations of intermolecular interaction energies.

In energy decomposition analysis of Kohn-Sham density functional theory calculations, the so-called frozen (or pre-polarization) interaction energy contains contributions from permanent electrostatics, dispersion, and Pauli repulsion. The standard classical approach to separate them suffers from several well-known limitations. We introduce an alternative scheme that employs valid antisymmetric electronic wavefunctions throughout and is based on the identification of individual fragment contributions to the initial supersystem wavefunction as determined by an energetic optimality criterion. The density deformations identified with individual fragments upon formation of the initial supersystem wavefunction are analyzed along with the distance dependence of the new and classical terms for test cases that include the neon dimer, ammonia borane, water-Na(+), water-Cl(-), and the naphthalene dimer.

Benzo[e]pyrimido[5,4-b][1,4]diazepin-6(11H)-one derivatives as Aurora A kinase inhibitors: LQTA-QSAR analysis and detailed systematic validation of the developed model.

Aurora kinases are sub-divided into Aurora A, Aurora B, and Aurora C kinases that are considered as prospective targets for a new class of anticancer drugs. In this work, a 4-D-QSAR model using an LQTA-QSAR approach with previously reported 31 derivatives of benzo[e]pyrimido[5,4 -b][1,4]diazepin -6(11H)-one as potent Aurora kinase A inhibitors has been created. Instead of single conformation, the conformational ensemble profile generated for each ligand by using trajectories and topology information retrieved from molecular dynamics simulations from GROMACS package were aligned and used for the calculation of intermolecular interaction energies at each grid point. The descriptors generated on the basis of these Coulomb and Lennard-Jones potentials as independent variables were used to perform a PLS analysis using biological activity as dependent variable. A good predictive model was generated with nine field descriptors and five latent variables. The model showed [Formula: see text]; [Formula: see text] and [Formula: see text]. This model was further validated systematically by using different validation parameters. This 4D-QSAR model gave valuable information to recognize features essential to adapt and develop novel potential Aurora kinase inhibitors.

The same number of optimized parameters scheme for determining intermolecular interaction energies.

We propose the Same Number Of Optimized Parameters (SNOOP) scheme as an alternative to the counterpoise method for treating basis set superposition errors in calculations of intermolecular interaction energies. The key point of the SNOOP scheme is to enforce that the number of optimized wave function parameters for the noninteracting system is the same as for the interacting system. This ensures a delicate balance between the quality of the monomer and dimer finite basis set calculations. We compare the SNOOP scheme to the uncorrected and counterpoise schemes theoretically as well as numerically. Numerical results for second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster with single, double, and approximate triple excitations (CCSD(T)) show that the SNOOP scheme in general outperforms the uncorrected and counterpoise approaches. Furthermore, we show that SNOOP interaction energies calculated using a given basis set are of similar quality as those determined by basis set extrapolation of counterpoise-corrected results obtained at a similar computational cost.

Differential Cocrystallization Behavior of Isomeric Pyridine Carboxamides toward Antitubercular Drug Pyrazinoic Acid

Pyrazinoic acid, the active form of the antitubercular pro-drug Pyrazinamide, is an amphiprotic molecule containing carboxylic acid and pyridine groups and therefore can form both salts and cocrystals with relevant partner molecules. Cocrystallization of pyrazinoic acid with isomeric pyridine carboxamide series resulted in a dimorphic mixed-ionic complex with isonicotinamide and in eutectics with nicotinamide and picolinamide, respectively. It is observed that with alteration of the carboxamide position, steric and electrostatic compatibility issues between molecules of the combination emerge and affect intermolecular interactions and supramolecular growth, thus leading to either cocrystal or eutectic for different pyrazinoic acid–pyridine carboxamide combinations. Intermolecular interaction energy calculations have been performed to understand the role of underlying energetics on the formation of cocrystal/eutectic in different combinations. On the other hand, two molecular salts with piperazine and cyto...

Energy frameworks: insights into interaction anisotropy and the mechanical properties of molecular crystals.

We present an approach to understanding crystal packing via 'energy frameworks', that combines efficient calculation of accurate intermolecular interaction energies with a novel graphical representation of their magnitude. In this manner intriguing questions, such as why some crystals bend with an applied force while others break, and why one polymorph of a drug exhibits exceptional tabletability compared to others, can be addressed in terms of the anisotropy of the topology of pairwise intermolecular interaction energies. This approach is applied to a sample of organic molecular crystals with known bending, shearing and brittle behaviour, to illustrate its use in rationalising their mechanical behaviour at a molecular level.

Pressure-Induced Conformational Change in Organic Semiconductors: Triggering a Reversible Phase Transition in Rubrene

A high-pressure polymorph of the organic semiconductor rubrene was obtained above 6.0 GPa by hydrostatic compression of the triclinic form. In the high-pressure phase, rubrene adopts an unexpected and previously unobserved conformation, which is ca. 70 kJ/mol less stable than the planar one observed in the ambient-pressure phase and is characterized by a unique “double twisting” of the tetracene core and “scissoring” of the lateral phenyl groups, which favor the formation of C–H···π contacts. The evolution of the structure as a function of pressure is monitored and quantified by Hirshfeld surfaces analysis and calculations of lattice and intermolecular interaction energies. The isosymmetric single-crystal-to-single-crystal transition is fully reversible and is primarily driven by a reduction in molecular volume.

Quasi 4D-QSAR and 3D-QSAR study of the pan class I phosphoinositide-3-kinase (PI3K) inhibitors

The class I phosphoinositide-3-kinases (PI3Ks) is currently investigated and attracted as a promising target toward anticancer therapies. The quasi 4D-QSAR model is developed by a training set of 30 pan class I PI3K inhibitors. This methodology is based on the generation of a conformational ensemble profile for each compound instead of only one conformation, followed by the calculation of intermolecular interaction energies at each grid point considering probes and all aligned conformations resulting from molecular dynamic simulations. A comparison of the proposed methodology with comparative molecular field analysis (CoMFA) formalism has been performed. This paradigm explores jointly the main features of CoMFA and 4D-QSAR models. The best 4D-QSAR model is checked for free from chance correlation, reliability and robustness by leave-N-out cross-validation and Y-randomization in addition to analysis of the independent test set. Statistical parameters of the best 4D-QSAR model are R 2 = 0.871, q LOO 2 = 0.661, and R Pred 2 = 0.751. The results of the suggested model are in good agreement with docking study that was previously reported by Rewcastle et al. (J Med Chem 54:7105–7126, 2011).

Estimation of mesogenic character of disubstituted pyridine derivatives on the basis of intermolecular interaction energy calculations

Two pyridine derivative “2-(4-butoxyphenyl)-5-hexyl pyridine” (Cpd 1) and “3-(4-butoxyphenyl)-6-hexyl pyridine” (Cpd 2) differing only in the relative position of nitrogen have been examined quantum mechanically to understand the possible reason of their different mesogenic character. The studies include geometry optimization, evaluation of interaction energy between a molecular pair at minimum energy configuration and tendency of ordering at various interacting conditions. It has been found that in Cpd 1, the phenyl and pyridine rings are almost coplanar with the butoxy tail while Cpd 2 differs significantly from planarity. Cpd 1 therefore stacks more closely than Cpd 2. An attempt has been made to correlate the results of intermolecular interaction energy calculation with the mesogenic behavior of the respective molecules.

A theoretical discussion on the relationships among molecular packings, intermolecular interactions, and electron transport properties for naphthalene tetracarboxylic diimide derivatives

Three naphthalene tetracarboxylic diimide derivatives 1–3 with high electron mobilities and long-term ambient stabilities were investigated employing Marcus–Levich–Jortner formalism at the density functional theory (DFT) level. The complicated relationships among molecular packings, intermolecular interactions, and transport properties for these compounds were focused on and analyzed through investigating the sensitivities of transfer integrals to intermolecular relative orientations, the optimizations of the major transport pathways and the calculations of intermolecular interaction energies by using dispersion-corrected DFT. The results show that the transfer integrals are sensitive to the subtle changes of relative orientations of molecules, especially for core-chlorinated compounds, and there is an interplay between intermolecular interaction and molecular packing. It is found that the transfer integrals associated with the molecular packing motifs of these systems determine their electron mobilities. Interestingly, further discussions on band structures, the anisotropies and temperature dependences of mobilities, and the comparisons of mobilities before and after optimization indicate that the intermolecular packing motifs in the film state may be different from those in the crystalline state for 2. Finally, we hope that our conjecture would facilitate the future design and preparation of high-performance charge-transport materials.

The use of unsymmetrical one-range addition theorems of Slater type orbitals for the calculation of intermolecular Coulomb interaction energy

The formulae at Hartree–Fock level are derived for the energy of Coulomb interaction between molecules containing any number of closed and open shells. These formulae are expressed in terms of linear combination coefficients of molecular orbitals and multicenter integrals of Slater type orbitals and interaction potentials produced by the charges of the molecules. As an example of application, by the use of unsymmetrical one-range addition theorems of Slater type orbitals the Hartree–Fock–Roothaan calculations have been performed for the energy of interaction produced by the ground states of two molecules H2O.

Influence of Intermolecular Interactions on the Structure of Copper Phthalocyanine Layers on Passivated Semiconductor Surfaces

The surface structures of copper phthalocyanine (CuPc) thin films deposited on sulphur-passivated and plane perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA)-covered InAs(100) surfaces have been studied by low energy electron diffraction (LEED) and van der Waals (vdW) intermolecular interaction energy calculations. The annealing to <TEX>$300^{\circ}C$</TEX> and <TEX>$450^{\circ}C$</TEX> of <TEX>$(NH_4)_2S_x$</TEX>-treated InAs(100) substrates produces a (<TEX>$1{\times}1$</TEX>) and (<TEX>$2{\times}1$</TEX>) S-passivated surface respectively. The CuPc deposition onto the PTCDA-covered InAs(100) surface leads to a ring-like diffraction pattern, indicating that the 2D ordered overlayer exists and the structure is dominantly determined by the intermolecular interactions rather than substrate-molecule interactions. However, no ordered LEED patterns were observed for the CuPc on S-passivated InAs(100) surface. The intermolecular interaction energy calculations have been carried out to rationalise this structural difference. In the case of CuPc unit cells on PTCDA layer, the planar layered CuPc structure is more stable than the <TEX>$\alpha$</TEX>-herringbone structure, consistent with the experimental LEED results. For CuPc unit cells on a S-(<TEX>$1{\times}1$</TEX>) layer, however, the <TEX>$\alpha$</TEX>-herringbone structure is more stable than the planar layered structure, consistent with the absence of diffraction pattern. The results show that the lattice structure during the initial stages of thin film growth is influenced strongly by the intermolecular interactions at the interface.

Dispersionless Density Functional Theory

A new density functional (DF) method is proposed for calculations of intermolecular interaction energies. The exchange-correlation functional was optimized in such a way that the method recovers the interaction energies with the dispersion (including exchange-dispersion) component subtracted and therefore our approach is named the dispersionless DF (dlDF) method. The dlDF method is shown to predict very well the dispersionless part of the interaction energy for all types of intermolecular interactions. Thus, if combined with a dispersion component, computed ab initio or from a simple function fitted to ab initio values, it provides accurate and physically justified interaction energies in the whole range of intermolecular separations. Our dispersion function is significantly more accurate than the published ones.

Extension of the Hartree−Fock Plus Dispersion Method by First-Order Correlation Effects

The Hartree−Fock plus dispersion (HFD) method for calculations of intermolecular interaction energies has been extended by the addition of the correlation part of the first-order interaction energy computed from Kohn−Sham determinants of monomers. This extension increases the computational requirements of the HFD approach only insignificantly and at the same time reduces the uncertainties of the interaction energies several times for most of the investigated systems. Thus, the proposed method becomes an attractive computational tool for investigating interactions of very large molecules at the HF-level costs.

Accurate Calculations of Intermolecular Interaction Energies Using Explicitly Correlated Coupled Cluster Wave Functions and a Dispersion-Weighted MP2 Method

Explicitly correlated coupled-cluster calculations of intermolecular interaction energies for the S22 benchmark set of Jurecka, Sponer, Cerny, and Hobza (Chem. Phys. Phys. Chem. 2006, 8, 1985) are presented. Results obtained with the recently proposed CCSD(T)-F12a method and augmented double-zeta basis sets are found to be in very close agreement with basis set extrapolated conventional CCSD(T) results. Furthermore, we propose a dispersion-weighted MP2 (DW-MP2) approximation that combines the good accuracy of MP2 for complexes with predominately electrostatic bonding and SCS-MP2 for dispersion-dominated ones. The MP2-F12 and SCS-MP2-F12 correlation energies are weighted by a switching function that depends on the relative HF and correlation contributions to the interaction energy. For the S22 set, this yields a mean absolute deviation of 0.2 kcal/mol from the CCSD(T)-F12a results. The method, which allows obtaining accurate results at low cost, is also tested for a number of dimers that are not in the training set.

Weak intermolecular H-bonds as a tool to design 2D self-organized molecular architectures: Tailoring a “Scottish Tartan” open network

We show here that weak intermolecular H-bonds ( E = 2–3 kcal/mol) can be used as an efficient tool to design supramolecular self-organized 2D periodic networks. These weak attractive and directional forces can take place when the molecules bear weakly acidic hydrogen atoms (such as aromatic CH) and electron-attracting groups (such as NO 2). We demonstrate the versatility of using weak H-bonds to tailor 2D networks with a simple model molecule, an adequately substituted benzene derivative bearing a nitro group, two aliphatic chains, but deprived of strongly acidic H atom (such as OH, NH, etc.). We show by means of scanning tunnelling microscopy (STM) that this compound self-assembles on Au(1 1 1) into a 2D open network through multiple intermolecular weak H-bonds between aromatic H-atoms and the O-atoms of the NO 2 groups. The prominent role of weak H-bonds in the 2D arrangement of this molecule on gold is supported by ab initio calculations of intermolecular interaction energies ( E = 3.1 kcal/mol) and H-bond lengths ( L = 2.55 Å). Based on both experimental and theoretical results, we propose a 2D model where molecules first interlock to each other into quartets through eight weak H-bonds and then into quartets-of-quartets through interchain Van der Waals interactions, the final packing being reminiscent of a Scottish Tartan. It is worth noting that such an arrangement leaves a square-shape central cavity (1.1 × 1.1 nm 2) in the unit cell thus providing opportunities towards guest–host systems of a new type.

Long- and intermediate-range interaction between two ground state hydrogen atoms

Perturbation theory in the polarization approximation has been employed, without using the multipole expansion for the interaction Hamiltonian, to calculate the second- and third-order interaction energies of two ground state hydrogen atoms for internuclear separations R - 4(2) 12 a.u. Using recently computed variational energies for H-H and H-H, the values of higher order corrections to the interaction energy have been estimated. The accuracy of several approximations commonly used in calculations of inter-molecular interaction energies has been tested.