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

Dispersion corrected hartree-fock and density functional theory for organic crystal structure prediction

We present and evaluate dispersion corrected Hartree-Fock (HF) and Density Functional Theory (DFT) based quantum chemical methods for organic crystal structure prediction. The necessity of correcting for missing long-range electron correlation, also known as van der Waals (vdW) interaction, is pointed out and some methodological issues such as inclusion of three-body dispersion terms are discussed. One of the most efficient and widely used methods is the semi-classical dispersion correction D3. Its applicability for the calculation of sublimation energies is investigated for the benchmark set X23 consisting of 23 small organic crystals. For PBE-D3 the mean absolute deviation (MAD) is below the estimated experimental uncertainty of 1.3 kcal/mol. For two larger π-systems, the equilibrium crystal geometry is investigated and very good agreement with experimental data is found. Since these calculations are carried out with huge plane-wave basis sets they are rather time consuming and routinely applicable only to systems with less than about 200 atoms in the unit cell. Aiming at crystal structure prediction, which involves screening of many structures, a pre-sorting with faster methods is mandatory. Small, atom-centered basis sets can speed up the computation significantly but they suffer greatly from basis set errors. We present the recently developed geometrical counterpoise correction gCP. It is a fast semi-empirical method which corrects for most of the inter- and intramolecular basis set superposition error. For HF calculations with nearly minimal basis sets, we additionally correct for short-range basis incompleteness. We combine all three terms in the HF-3c denoted scheme which performs very well for the X23 sublimation energies with an MAD of only 1.5 kcal/mol, which is close to the huge basis set DFT-D3 result.

Ab initio calculations of the interaction between CO2 and the acetate ion

A series of ab initio calculations designed to investigate the interaction of CO(2) with acetate are presented. The lowest energy structure, AC-CO(2)-η(2), is predicted by CCSD(T)/aVTZ to be bound by -10.6 kcal/mol. Six of the bound complexes have binding energies on the order of -8 kcal/mol, but analysis shows that the η(1)-CT complex is fundamentally different from the others. The η(1)-CT complex is characterized by geometric distortion, large polarization and induction effects and charge transfer whereas the other five complexes have little geometric distortion and negligible charge transfer. The amount of charge that is transferred from the anion to the CO(2) in the η(1)-CT complex is estimated to be about half an electron by NPA, DMA, CHELPG, and Mulliken analyses, whereas the EDA-ALMO-CTA (B3LYP) approach predicts a charge transfer of 75 me(-). However, the transfer of this small amount of charge leads to an energy lowering of -56 kcal/mol, without which the complex would not be bound. The RI-MP2 geometries closely approximate those resulting from the CCSD optimizations, and the optimized second-order opposite spin (O2) method performs well for all the complexes except for the η(1)-CT complex. DFT methods do not reproduce all the ab initio geometries, binding energies and/or energy ordering of these complexes although the range-separated hybrid meta-GGA (M11) and nonlocal (VV10 and vdwDF10) functionals are shown to yield results significantly better than other functionals considered for this system. The fact that there is such variation among DFT methods has implications for DFT-based ab initio molecular dynamics simulations and for the parametrization of classical force fields based on DFT calculations.

Factors that distort the heme structure in Heme-Nitric Oxide/OXygen-Binding (H-NOX) protein domains. A theoretical study

DFT and dispersion-corrected DFT calculations were carried out to probe the factors that distort the heme structure in Heme-Nitric oxide/OXygen-binding (H-NOX) protein domains. Various model systems that include heme, heme+surrounding residues, and heme+surrounding residues+additional protein environment were examined; the latter system was calculated with a quantum mechanics/molecular mechanics (QM/MM) method. The computations were extended to a myoglobin (Mb) protein, in which the heme structure is quite planar, in contrast to that in H-NOX. The natural tendency of the heme is to be planar. The strong structural distortion in H-NOX is mainly brought about by the intermolecular interactions between the whole heme molecule (heme ring plus its peripheral substituents) and the surrounding residues, among which the polar residues (Tyr140, Pro115, Mse98) play major roles in distorting the heme structure. The two peripheral propionate substituents that are oriented on the same side of the heme plane can also make the molecule distort, but the distortion caused by this factor is not significant. In Mb, the surrounding residues considered are all nonpolar and do not cause a structural distortion. The different structural features of the heme macrocycle in the different proteins (H-NOX and Mb) are reproduced by the calculations. The dispersion correction is necessary, since it improves the calculated structures. The effects of the distortion on the binding affinity of the axial ligand to the heme were also examined.

Is it possible to derive quantitative information on polarization of electron density from the multipolar model?

The accuracy of electrostatic properties estimated from the Hansen-Coppens multipolar model was verified. Tests were carried out to determine whether the multipolar model is accurate enough to study changes of electrostatic properties under the influence of a crystal field. Perturbed and unperturbed electron densities of individual molecules of amino acids and dipeptides were obtained from cluster and perturbation theory calculations. This enabled the changes in electrostatic properties values caused by polarization of the electron density to be characterized. Multipolar models were then fitted to the subsequent theoretical electron densities. The study revealed that electrostatic properties obtained from the multipolar models are significantly different from those obtained directly from the theoretical densities. The electrostatic properties of isolated molecules are reproduced better by multipolar models than the electrostatic properties of molecules in a crystal. Changes of electrostatic properties caused by perturbation of electron density due to the crystal environment are barely described by the multipolar model. As a consequence, the electrostatic properties obtained from multipolar models fitted to the perturbed theoretical densities derived either from cluster or periodic calculations do not differ much from those estimated from multipolar models fitted to densities of isolated molecules. The main reason for this seems to be related to an inadequate description of electron-density polarization in the vicinity of the nuclei by the multipolar model.

Large-scale symmetry-adapted perturbation theory computations via density fitting and Laplace transformation techniques: investigating the fundamental forces of DNA-intercalator interactions

Symmetry-adapted perturbation theory (SAPT) provides a means of probing the fundamental nature of intermolecular interactions. Low-orders of SAPT (here, SAPT0) are especially attractive since they provide qualitative (sometimes quantitative) results while remaining tractable for large systems. The application of density fitting and Laplace transformation techniques to SAPT0 can significantly reduce the expense associated with these computations and make even larger systems accessible. We present new factorizations of the SAPT0 equations with density-fitted two-electron integrals and the first application of Laplace transformations of energy denominators to SAPT. The improved scalability of the DF-SAPT0 implementation allows it to be applied to systems with more than 200 atoms and 2800 basis functions. The Laplace-transformed energy denominators are compared to analogous partial Cholesky decompositions of the energy denominator tensor. Application of our new DF-SAPT0 program to the intercalation of DNA by proflavine has allowed us to determine the nature of the proflavine-DNA interaction. Overall, the proflavine-DNA interaction contains important contributions from both electrostatics and dispersion. The energetics of the intercalator interaction are are dominated by the stacking interactions (two-thirds of the total), but contain important contributions from the intercalator-backbone interactions. It is hypothesized that the geometry of the complex will be determined by the interactions of the intercalator with the backbone, because by shifting toward one side of the backbone, the intercalator can form two long hydrogen-bonding type interactions. The long-range interactions between the intercalator and the next-nearest base pairs appear to be negligible, justifying the use of truncated DNA models in computational studies of intercalation interaction energies.

An automated approach for the parameterization of accurate intermolecular force-fields: pyridine as a case study

An automated protocol is proposed and validated, which integrates accurate quantum mechanical calculations with classical numerical simulations. Intermolecular force fields, (FF) suitable for molecular dynamics (MD) and Monte Carlo simulations, are parameterized through a novel iterative approach, fully based on quantum mechanical data, which has been automated and coded into the PICKY software, here presented. The whole procedure is tested and validated for pyridine, whose bulk phase, described through MD simulations performed with the specifically parameterized FF, is characterized by computing several of its thermodynamic, structural, and transport properties, comparing them with their experimental counterparts.

Noncanonical hydrogen bonding in nucleic acids. Benchmark evaluation of key base-phosphate interactions in folded RNA molecules using quantum-chemical calculations and molecular dynamics simulations

RNA molecules are stabilized by a wide range of noncanonical interactions that are not present in DNA. Among them, the recently classified base-phosphate (BPh) interactions belong to the most important ones. Twelve percent of nucleotides in the ribosomal crystal structures are involved in BPh interactions. BPh interactions are highly conserved and provide major constraints on RNA sequence evolution. Here we provide assessment of the energetics of BPh interactions using MP2 computations extrapolated to the complete basis set of atomic orbitals and corrected for higher-order electron correlation effects. The reference computations are compared with DFT-D and DFT-D3 approaches, the SAPT method, and the molecular mechanics force field. The computations, besides providing the basic benchmark for the BPh interactions, allow some refinements of the original classification, including identification of some potential doubly bonded BPh patterns. The reference computations are followed by analysis of some larger RNA fragments that consider the context of the BPh interactions. The computations demonstrate the complexity of interaction patterns utilizing the BPh interactions in real RNA structures. The BPh interactions are often involved in intricate interaction networks. We studied BPh interactions of protonated adenine that can contribute to catalysis of hairpin ribozyme, the key BPh interaction in the S-turn motif of the sarcin-ricin loop, which may predetermine the S-turn topology and complex BPh patterns from the glmS riboswitch. Finally, the structural stability of BPh interactions in explicit solvent molecular dynamics simulations is assessed. The simulations well preserve key BPh interactions and allow dissection of structurally/functionally important water-meditated BPh bridges, which could not be considered in earlier bioinformatics classification of BPh interactions.

Accurate Interaction Energies for Problematic Dispersion-Bound Complexes: Homogeneous Dimers of NCCN, P2, and PCCP

All intermolecular interactions involve London dispersion forces. The accurate treatment of dispersion is essential for the computation of realistic interaction potentials. In general, the most reliable method for computing intermolecular interactions is coupled-cluster singles and doubles with perturbative triples [CCSD(T)] in conjunction with a sufficiently flexible Gaussian atomic orbital basis set, a combination which is not routinely applicable due to its excessive computational demands (CPU time, memory, storage). Recently, many theoretical methods have been developed that attempt to account for dispersion in a more efficient manner. It is well-known that dispersion interactions are more difficult to compute in some systems than others; for example, π-π dispersion is notoriously difficult, while alkane-alkane dispersion is relatively simple to compute. In this work, numerous theoretical methods are tested for their ability to compute reliable interaction energies in particularly challenging systems, namely, the P2, PCCP, and NCCN dimers. Symmetry-adapted perturbation theory (SAPT) is applied to these dimers to demonstrate their sensitivity to the treatment of dispersion. Due to the small size of these systems, highly accurate CCSD(T) potential energy curves could be estimated at the complete basis set limit. Numerous theoretical methods are tested against the reliable CCSD(T) benchmarks. Methods using a treatment of dispersion that relies on time-dependent density functional theory (TDDFT) response functions are found to be the most reliable.