A Prototype for Graphene Material Simulation: Structures and Interaction Potentials of Coronene Dimers

Graphene sheets are the building blocks of carbon nanotubes and a variety of functionalized nanomaterials. Methods to be used for computer-aided design of such materials or for the study of aromatic−aromatic interactions in biopolymers and other soft materials should be validated for smaller systems where reliable estimates of interaction energies are available. In this work, we first validated the M06-2X functional against the S22 database of noncovalent interaction energies of biological importance. We then applied the M06-2X functional to study aromatic−aromatic interactions in coronene dimers. We located six stationary points on the potential energy surface of coronene dimer, we calculated the potential energy curves for the sandwich, T-shaped, and parallel-displaced configurations of this prototype of aromatic−aromatic interactions, and we found that a parallel displaced configuration is the global minimum. The potential curves for the coronene dimers will aid the development of new force fields and potential energy functions that are computationally efficient and capable of modeling large graphene or aromatic clusters

Infinite-Basis Calculations of Binding Energies for the Hydrogen Bonded and Stacked Tetramers of Formic Acid and Formamide and Their Use for Validation of Hybrid DFT and ab Initio Methods

Benchmark stabilization energies for planar H-bonded and stacked structures of formic acid tetramers and formamide tetramers were determined as the sum of the infinite basis set limit of MP2 energies and a CCSD(T) correction term evaluated with the 6-31G*(0.25) basis set. The infinite basis (IB) set limit of MP2 energies was determined by two-point extrapolation using the aug-cc-pVXZ basis sets for X = D and T and separate extrapolation of the Hartree−Fock and correlation energies with new IB parameters for augmented basis sets determined here. Final stabilization energies (kcal/mol) for the tetramer studied are in the range of 4.6∼6.7 kcal/mol and they were used as reference data to test 14 density functionals. Among the tested DFT methods, PWB6K gives the best performance with an average error equal to only 30% of the average binding energy. In contrast, the popular B3LYP functional has an average error of 85%. We recommend the PWB6K method for exploring the potential energy surfaces of organic complexes and clusters and supramolecular assemblies

Density Functionals for Noncovalent Interaction Energies of Biological Importance

Forty density functionals and one wavefunction method are assessed against a recently published database of accurate noncovalent interaction energies of biological importance. The comparison shows that two newly developed density functional theory (DFT) methods, PWB6K and M05-2X, give the best performance for this benchmark database of 22 noncovalent complexes, including both hydrogen-bonding and dispersion-dominated complexes. In contrast, the more popular B3LYP and PBEh functionals fail to describe the interactions in the dispersion-dominated complexes. The local spin density approximation and BHandH functionals give good performance for dispersion-dominated interactions at the expense of a large error for hydrogen bonding. PWB6K and M05-2X constitute a new generation of DFT methods based on simultaneously optimized exchange and correlation functionals that include kinetic energy density in both the exchange and correlation functional, and the present study confirms that they have greatly improved performance for noncovalent interactions as compared to previous DFT methods. We interpret this as being due to an improved treatment of medium-range correlation effects by the exchange-correlation functional. We recommend the PWB6K and M05-2X methods for investigating large biological systems and soft materials

Global Potential Energy Surfaces with Correct Permutation Symmetry by Multiconfiguration Molecular Mechanics

In the framework of the previously developed multiconfiguration molecular mechanics (MCMM) method, we present a new algorithm for constructing global potential energy surfaces that are invariant with respect to the exchange of identical nuclei. We illustrate the new algorithm by its application to the HOH‘ ‘ + H‘ → OH + H‘H‘ ‘, OH‘ + HH‘ ‘, OH‘ ‘ + HH‘, HOH‘ + H‘ ‘, and H‘ ‘OH‘ + H reactions. As part of the MCMM methodology, the new scheme can be used to generate multidimensional global PESs for both small and large systems where a few reaction pathways need to be treated as symmetrically equivalent

Size-Selective Supramolecular Chemistry in a Hydrocarbon Nanoring

New-generation density functionals (M06-L and M06-2X) include an accurate treatment of medium-range correlation energy and have been applied to investigate host−guest interactions in supramolecular complexes in which a hydrocarbon nanoring, [6]paraphenyleneacetylene ([6]CPPA), acts as the host molecule. Guests include fullerenes and carbon nanotubes. The nature of the interactions has been discussed and analyzed. The size-selective supramolecular chemistry in the nanoring has been investigated by varying the size of the guest molecules and optimizing inclusion structures as large as C128H44. We found that the (5,5) armchair-type nanotube fits in the [6]CPPA hydrocarbon nanoring better than the (3,3) or (4,4) ones, and C70 is bound more strongly than C60. The predicted host−guest binding energies of the (4,4), (5,5), C60, and C70 structures are 24, 43, 25, and 28 kcal/mol, respectively

Benchmark Data for Interactions in Zeolite Model Complexes and Their Use for Assessment and Validation of Electronic Structure Methods

We present benchmark binding energies for five zeolite model complexes, with four of the adsorbates bound noncovalently and one covalently. The binding energies were determined as the sum of the infinite-basis-set limit of Møller−Plesset second-order perturbation theory (MP2) energies and a CCSD(T) correction term evaluated with the aug-cc-pVDZ basis set. The basis set limit of MP2 energies was determined by two-point extrapolation using the aug-cc-pVXZ basis sets for X = D and T and separate extrapolation of the Hartree−Fock and correlation energies. We found that correlation contributions beyond MP2 to the final binding energies are small; their magnitude is in the range of 0.02−1.0 kcal/mol. For the MP2 method to describe the interactions in these zeolite model systems accurately, one needs to use a basis set at least the size of aug-cc-pVTZ in conjunction with counterpoise corrections. Final binding energies (kcal/mol) of the model complexes are in the range of 3.5−19.5 kcal/mol, and they were used as reference data to test 6 wave function methods and 41 density functionals. Among the tested density functional methods, M06-L/6-31+G(d,p) gives a mean unsigned error (MUE) without counterpoise correction of 0.87 kcal/mol. With counterpoise corrections, the M06-2X and M05-2X functionals give the best performance. The MUE with counterpoise corrections for the M06-2X/6-311+G(2df,2p)//MP2/6-311+G(2df,2p) level of theory is 0.39 kcal/mol. With the DFT/6-31+G(d,p) geometries and the 6-311+G(2df,2p) basis set, M05-2X and M06-2X give MUEs with counterpoise corrections of 0.40 and 0.52 kcal/mol, respectively. Tests against the binding energies of four complexes (two noncovalent and two covalent) of the adsoption of isobutene on a large 16T zeolite model cluster confirmed that M06-L, M06, M05-2X, and M06-2X are very promising quantum mechanical methods for hybrid quantum mechanical/molecular mechanical (QM/MM) simulations of zeolites. In fact the performance of these four Minnesota functionals, as compared to other high-quality functionals, is relatively even better for the larger 16T clusters than for the smaller 3T ones

Validation of Density Functionals for Adsorption Energies on Transition Metal Surfaces

The quantitative prediction of adsorption energies of radicals and molecules on surfaces is essential for the design and understanding of heterogeneous catalytic processes. A recent paper by Wellendorff et al. collected an experimental database of 39 reaction energies involving adsorption energies on transition metal surfaces that can be used as benchmarks for testing quantum mechanical electronic structure methods, and we compared the experimental data to Kohn–Sham density functional calculations with six exchange–correlation functionals. In this paper, we rearranged the data into two categories: open-shell radical adsorption reactions and closed-shell molecular adsorption reactions. We recalculated the adsorption energies with PBE, and we also calculated them with three functionals, M06-L, GAM, and MN15-L, that were not studied in the Wellendorff et al. paper; then we compared our results to the benchmark data. Of the nine functionals that have been compared to the databases, we find that BEEF-vdW, GAM, and RPBE perform best for the open-shell radical adsorption reactions, and MN15-L performs best for the closed-shell molecular adsorption, followed by BEEF-vdW and M06-L

Benchmark Databases for Nonbonded Interactions and Their Use To Test Density Functional Theory

We present four benchmark databases of binding energies for nonbonded complexes. Four types of nonbonded interactions are considered:  hydrogen bonding, charge transfer, dipole interactions, and weak interactions. We tested 44 DFT methods and 1 WFT method against the new databases; one of the DFT methods (PBE1KCIS) is new, and all of the other methods are from the literature. Among the tested methods, the PBE, PBE1PBE, B3P86, MPW1K, B97-1, and BHandHLYP functionals give the best performance for hydrogen bonding. MPWB1K, MP2, MPW1B95, MPW1K, and BHandHLYP give the best performances for charge-transfer interactions, and MPW3LYP, B97-1, PBE1KCIS, B98, and PBE1PBE give the best performance for dipole interactions. Finally, MP2, B97-1, MPWB1K, PBE1KCIS, and MPW1B95 give the best performance for weak interactions. Overall, MPWB1K is the best of all the tested DFT methods, with a relative error (highly averaged) of only 11%, and MPW1K, PBE1PBE, and B98 are the best of the tested DFT methods that do not contain kinetic energy density. Moving up the rungs of Jacob's ladder for nonempirical DFT, PBE improves significantly over the LSDA, and TPSS improve slightly over PBE (on average) for nonbonded interactions

B₂N₂O₄: Prediction of a Magnetic Ground State for a Light Main-Group Molecule

Cyclobutanetetrone, (CO)₄, has a triplet ground state. Here we predict, based on electronic structure calculations, that the B₂N₂O₄ molecule also has a triplet ground state and is therefore paramagnetic; the structure is an analogue of (CO)₄ in which the carbon ring is replaced by a (BN)₂ ring. Similar to (CO)₄, the triplet ground-state structure of B₂N₂O₄ is also thermodynamically unstable. Besides analysis of the molecular orbitals, we found that the partial atomic charges are good indicators for predicting magnetic ground states