Van der Waals interactions in aromatic systems: structure and energetics of dimers and trimers of pyridine.

Full geometry optimizations at the dispersion-corrected DFT-BLYP level of theory were carried out for dimers and trimers of pyridine. The DFT-D interaction energies were checked against results from single-point SCS-MP2/aug-cc-pVTZ calculations. Three stacked structures and a planar H-bonded dimer were found to be very close in energy (interaction energies in the range from -3.4 to -4.0 kcal mol(-1)). Two T-shaped geometries are higher lying, by about 1 kcal mol(-1), which is explained by the more favorable electrostatic interactions in the stacked and H-bonded arrangements. The DFT-D approach has proved to be a reliable and efficient tool to explore the conformational space of aromatic van der Waals complexes and furthermore provides interaction energies with errors of less than 10-20 % of DeltaE. Comparisons with previous results obtained by using only partially optimized model geometries strongly indicate that unconstrained optimizations are mandatory in such weakly bonded low-symmetry systems.     

Scope and limitations of the SCS-MP2 method for stacking and hydrogen bonding interactions

Fluorobenzenes are pi-acceptor synthons that form pi-stacked structures in molecular crystals as well as in artificial DNAs. We investigate the competition between hydrogen bonding and pi-stacking in dimers consisting of the nucleobase mimic 2-pyridone (2PY) and all fluorobenzenes from 1-fluorobenzene to hexafluorobenzene (n-FB, with n = 1-6). We contrast the results of high level ab initio calculations with those obtained using ultraviolet (UV) and infrared (IR) laser spectroscopy of isolated and supersonically cooled dimers. The 2PY.n-FB complexes with n = 1-5 prefer double hydrogen bonding over pi-stacking, as diagnosed from the UV absorption and IR laser depletion spectra, which both show features characteristic of doubly H-bonded complexes. The 2-pyridone.hexafluorobenzene dimer is the only pi-stacked dimer, exhibiting a homogeneously broadened UV spectrum and no IR bands characteristic for H-bonded species. MP2 (second-order M?ller-Plesset perturbation theory) calculations overestimate the pi-stacked dimer binding energies by about 10 kJ/mol and disagree with the experimental observations. In contrast, the MP2 treatment of the H-bonded dimers appears to be quite accurate. Grimme's spin-component-scaled MP2 approach (SCS-MP2) is an improvement over MP2 for the pi-stacked dimers, reducing the binding energy by approximately 10 kJ/mol. When applied to explicitly correlated MP2 theory (SCS-MP2-R12 approach), agreement with the corresponding coupled-cluster binding energies [at the CCSD(T) level] is very good for the pi-stacked dimers, within +/- 1 kJ/mol for the 2PY complexes with 1-fluorobenzene, 1,2-difluorobenzene, 1,2,4,5-tetrafluorobenzene, pentafluorobenzene and hexafluorobenzene. Unfortunately, the SCS-MP2 approach also reduces the binding energy of the H-bonded species, leading to disagreement with both coupled-cluster theory and experiment. The SCS-MP2-R12 binding energies follow the SCS-MP2 binding energies closely, being about 0.5 and 0.7 kJ/mol larger for the H-bonded and pi-stacked forms, respectively, in an augmented correlation-consistent polarized valence quadruple-zeta basis. It seems that the SCS-MP2 and SCS-MP2-R12 methods cannot provide sufficient accuracy to replace the CCSD(T) method for intermolecular interactions where H-bonding and pi-stacking are competitive.     

Probing the effects of heterogeneity on delocalized pi...pi interaction energies

Dimers composed of benzene (Bz), 1,3,5-triazine (Tz), cyanogen (Cy) and diacetylene (Di) are used to examine the effects of heterogeneity at the molecular level and at the cluster level on pi...pi stacking energies. The MP2 complete basis set (CBS) limits for the interaction energies (E(int)) of these model systems were determined with extrapolation techniques designed for correlation consistent basis sets. CCSD(T) calculations were used to correct for higher-order correlation effects (deltaE(CCSD)(T)(MP2)) which were as large as +2.81 kcal mol(-1). The introduction of nitrogen atoms into the parallel-slipped dimers of the aforementioned molecules causes significant changes to E(int). The CCSD(T)/CBS E(int) for Di-Cy is -2.47 kcal mol(-1) which is substantially larger than either Cy-Cy (-1.69 kcal mol(-1)) or Di-Di (-1.42 kcal mol(-1)). Similarly, the heteroaromatic Bz-Tz dimer has an E(int) of -3.75 kcal mol(-1) which is much larger than either Tz-Tz (-3.03 kcal mol(-1)) or Bz-Bz (-2.78 kcal mol(-1)). Symmetry-adapted perturbation theory calculations reveal a correlation between the electrostatic component of E(int) and the large increase in the interaction energy for the mixed dimers. However, all components (exchange, induction, dispersion) must be considered to rationalize the observed trend. Another significant conclusion of this work is that basis-set superposition error has a negligible impact on the popular deltaE(CCSD)(T)(MP2) correction, which indicates that counterpoise corrections are not necessary when computing higher-order correlation effects on E(int). Spin-component-scaled MP2 (SCS-MP2 and SCSN-MP2) calculations with a correlation-consistent triple-zeta basis set reproduce the trends in the interaction energies despite overestimating the CCSD(T)/CBS E(int) of Bz-Tz by 20-30%.     

Furan-formic acid dimers: an ab initio and matrix isolation study

The dimers formed by formic acid (FA) and furan are investigated by ab initio methods and matrix isolation spectroscopy. Nine complexes with binding energies between -3.91 and -0.82 kcal/mol (MP2/6-311++G(d,p) + ZPE + BSSE) are identified. Another five weaker bound complexes are localized at lower level of theory only. The binding in the furan-FA dimers can be described in terms of OH...O, C=O...H, HO...H, CH...O, OH...pi, and CH...pi interactions. Therefore, the furan-FA complexes are classified in two types: (1) the dimers where the OH hydrogen of formic acid interacts with the furan molecule and (2) the dimers where the main interactions of FA with the furan molecule are via the less acidic CH hydrogen. Duning's and Pople's triple and double basis sets were used to study the dependence of the geometries and energies of the complexes from the basis set. BSSE (basis set superposition error) counterpoise corrections (CP) were included during the geometry optimizations of all dimers at the MP2/6-31G(d,p) level of theory. Matrix isolation spectroscopy allowed us to record the IR spectrum of aggregates between FA and furan. By comparison of the experimental IR spectrum with calculated IR spectra of a variety of complexes, it was possible to identify the most stable furan-FA dimer as the major product of the aggregation.     

Benzene-pyridine interactions predicted by the effective fragment potential method

The accurate representation of nitrogen-containing heterocycles is essential for modeling biological systems. In this study, the general effective fragment potential (EFP2) method is used to model dimers of benzene and pyridine, complexes for which high-level theoretical data -including large basis spin-component-scaled second-order perturbation theory (SCS-MP2), symmetry-adapted perturbation theory (SAPT), and coupled cluster with singles, doubles, and perturbative triples (CCSD(T))-are available. An extensive comparison of potential energy curves and components of the interaction energy is presented for sandwich, T-shaped, parallel displaced, and hydrogen-bonded structures of these dimers. EFP2 and CCSD(T) potential energy curves for the sandwich, T-shaped, and hydrogen-bonded dimers have an average root-mean-square deviation (RMSD) of 0.49 kcal/mol; EFP2 and SCS-MP2 curves for the parallel displaced dimers have an average RMSD of 0.52 kcal/mol. Additionally, results are presented from an EFP2 Monte Carlo/simulated annealing (MC/SA) computation to sample the potential energy surface of the benzene-pyridine and pyridine dimers.     

σ/σ- And π/π-interactions are equally important: multilayered graphanes

The properties of single-sheet [n]graphanes, their double-layered forms (diamondoids), and their van der Waals (vdW) complexes (multilayered [n]graphanes) were studied for n = 10-97 at the dispersion-corrected density functional theory (DFT) level utilizing B97D with a 6-31G(d,p) basis set; for comparison, we also computed a series of structures at M06-2X/6-31G(d,p) as well as B3LYP-D3/6-31G(d,p) and evaluated SCS-MP2/cc-pVDZ single-point energies. The association energies for the vdW complexes reach 120 kcal mol(-1) already at 2 nm particle size ([97]graphane dimer), and graphanes adopt layered structures similar to that of graphenes. The association energies of multilayered graphanes per carbon atom are rather similar and independent of the number of layers (ca. 1.2 kcal mol(-1)). Graphanes show quantum confinement effects as the HOMO-LUMO gaps decrease from 8.2 eV for [10]graphane to 5.7 eV for [97]graphane, asymptotically approaching 5.4 eV previously obtained for bulk graphane. Similar trends were found for layered graphanes, where the differences in the electronic properties of double-sheet CH/σ vdW and double-layered CC/σ diamondoids vanish at particles sizes of 1 nm. For comparison, we studied the parent CC/π systems, i.e., the single- and double-sheet [n]graphenes (n = 10-130) for which the association energies demonstrate the same trends as in the case of [n]graphanes; in both cases the band gaps decrease with an increase in system size. The [112]graphene dimer (HOMO-LUMO gap = 0.5 eV) already approaches the 2D metallic properties of graphite.     

Corannulene as a Lewis base: computational modeling of protonation and lithium cation binding.

A computational modeling of the protonation of corannulene at B3LYP/6-311G(d,p)//B3LYP/6-311G(d,p) and of the binding of lithium cations to corannulene at B3LYP/6-311G(d,p)//B3LYP/6-31G(d,p) has been performed. A proton attaches preferentially to one carbon atom, forming a sigma-complex. The isomer protonated at the innermost (hub) carbon has the best total energy. Protonation at the outermost (rim) carbon and at the intermediate (bridgehead rim) carbon is less favorable by ca. 2 and 14 kcal mol(-)(1), respectively. Hydrogen-bridged isomers are transition states between the sigma-complexes; the corresponding activation energies vary from 10 to 26 kcal mol(-)(1). With an empirical correction obtained from calculations on benzene, naphthalene, and azulene, the best estimate for the proton affinity of corannulene is 203 kcal mol(-)(1). The lithium cation positions itself preferentially over a ring. There is a small energetic preference for the 6-ring over the 5-ring binding (up to 2 kcal mol(-)(1)) and of the convex face over the concave face (3-5 kcal mol(-)(1)). The Li-bridged complexes are transition states between the pi-face complexes. Movement of the Li(+) cation over either face is facile, and the activation energy does not exceed 6 kcal mol(-)(1) on the convex face and 2.2 kcal mol(-)(1) on the concave face. In contrast, the transition of Li(+) around the corannulene edge involves a high activation barrier (24 kcal mol(-)(1) with respect to the lowest energy pi-face complex). An easier concave/convex transformation and vice versa is the bowl-to-bowl inversion with an activation energy of 7-12 kcal mol(-)(1). The computed binding energy of Li(+) to corannulene is 44 kcal mol(-)(1). Calculations of the (7)Li NMR chemical shifts and nuclear independent chemical shifts (NICS) have been performed to analyze the aromaticity of the corannulene rings and its changes upon protonation.     

Intermolecular interactions of nitrobenzene-benzene complex and nitrobenzene dimer: significant stabilization of slipped-parallel orientation by dispersion interaction

The CCSD(T) level interaction energies of eight orientations of nitrobenzene-benzene complexes and nine orientations of nitrobenzene dimers at the basis set limit have been estimated. The calculated interaction energy of the most stable slipped-parallel (C(s)) nitrobenzene-benzene complex was -4.51 kcal/mol. That of the most stable slipped-parallel (antiparallel) (C(2h)) nitrobenzene dimer was -6.81 kcal/mol. The interaction energies of these complexes are significantly larger than that of the benzene dimer. The T-shaped complexes are substantially less stable. Although nitrobenzene has a polar nitro group, electrostatic interaction is always considerably weaker than the dispersion interaction. The dispersion interaction in these complexes is larger than that in the benzene dimer, which is the cause of the preference of the slipped-parallel orientation in these complexes.     

The Nature of the Binding of Au, Ag, and Pd to Benzene, Coronene, and Graphene: From Benchmark CCSD(T) Calculations to Plane-Wave DFT Calculations

The adsorption of Ag, Au, and Pd atoms on benzene, coronene, and graphene has been studied using post Hartree-Fock wave function theory (CCSD(T), MP2) and density functional theory (M06-2X, DFT-D3, PBE, vdW-DF) methods. The CCSD(T) benchmark binding energies for benzene-M (M = Pd, Au, Ag) complexes are 19.7, 4.2, and 2.3 kcal/mol, respectively. We found that the nature of binding of the three metals is different: While silver binds predominantly through dispersion interactions, the binding of palladium has a covalent character, and the binding of gold involves a subtle combination of charge transfer and dispersion interactions as well as relativistic effects. We demonstrate that the CCSD(T) benchmark binding energies for benzene-M complexes can be reproduced in plane-wave density functional theory calculations by including a fraction of the exact exchange and a nonempirical van der Waals correction (EE+vdW). Applying the EE+vdW method, we obtained binding energies for the graphene-M (M = Pd, Au, Ag) complexes of 17.4, 5.6, and 4.3 kcal/mol, respectively. The trends in binding energies found for the benzene-M complexes correspond to those in coronene and graphene complexes. DFT methods that use empirical corrections to account for the effects of vdW interactions significantly overestimate binding energies in some of the studied systems.     

Comparative DFT study of van der Waals complexes: rare-gas dimers, alkaline-earth dimers, zinc dimer, and zinc-rare-gas dimers

Recent interest in the application of density functional theory prompted us to test various functionals for the van der Waals interactions in the rare-gas dimers, the alkaline-earth metal dimers, zinc dimer, and zinc-rare-gas dimers. In the present study, we report such tests for 18 DFT functionals, including both some very recent functionals and some well-established older ones. We draw the following conclusions based on the mean errors in binding energies and complex geometries: (1) B97-1 gives the best performance for predicting the geometry of rare-gas dimers, whereas M05-2X and B97-1 give the best energetics for rare-gas dimers. (2) PWB6K gives the best performance for the prediction of the geometry of the alkaline-earth metal dimers, zinc dimers, and zinc-rare-gas dimers. M05-2X gives the best energetics for the metal dimers, whereas B97-1 gives the best energetics for the zinc-rare-gas dimers. (3) The M05 functional is unique in providing good accuracy for both covalent transition-metal dimers and van der Waals metal dimers. (4) The combined mean percentage unsigned error in geometries and energetics shows that M05-2X and MPWB1K are the overall best methods for the prediction of van der Waals interactions in metal and rare-gas van der Waals dimers.     

Further development and validation of empirical scoring functions for structure-based binding affinity prediction

New empirical scoring functions have been developed to estimate the binding affinity of a given protein-ligand complex with known three-dimensional structure. These scoring functions include terms accounting for van der Waals interaction, hydrogen bonding, deformation penalty, and hydrophobic effect. A special feature is that three different algorithms have been implemented to calculate the hydrophobic effect term, which results in three parallel scoring functions. All three scoring functions are calibrated through multivariate regression analysis of a set of 200 protein-ligand complexes and they reproduce the binding free energies of the entire training set with standard deviations of 2.2 kcal/mol, 2.1 kcal/mol, and 2.0 kcal/mol, respectively. These three scoring functions are further combined into a consensus scoring function, X-CSCORE. When tested on an independent set of 30 protein-ligand complexes, X-CSCORE is able to predict their binding free energies with a standard deviation of 2.2 kcal/mol. The potential application of X-CSCORE to molecular docking is also investigated. Our results show that this consensus scoring function improves the docking accuracy considerably when compared to the conventional force field computation used for molecular docking.     

High-level ab initio computations of structures and interaction energies of naphthalene dimers: origin of attraction and its directionality

The intermolecular interaction energies of naphthalene dimers have been calculated by using an aromatic intermolecular interaction model (a model chemistry for the evaluation of intermolecular interactions between aromatic molecules). The CCSD(T) (coupled cluster calculations with single and double substitutions with noniterative triple excitations) interaction energy at the basis set limit has been estimated from the second-order M?ller-Plesset perturbation interaction energy near saturation and the CCSD(T) correction term obtained using a medium-size basis set. The estimated interaction energies of the set of geometries explored in this work show that two structures emerge as being the lowest energy, and may effectively be considered as isoenergetic on the basis of the errors inherent in out extrapolation procedure. These structures are the slipped-parallel (Ci) structure (-5.73 kcal/mol) and the cross (D2d) structure (-5.28 kcal/mol). The T-shaped (C2v) and sandwich (D2h) dimers are substantially less stable (-4.34 and -3.78 kcal/mol, respectively). The dispersion interaction is found to be the major source of attraction in the naphthalene dimer. The electrostatic interaction is substantially smaller than the dispersion interaction. The large dispersion interaction is the cause of the large binding energies of the cross and slipped-parallel dimers.     

Magnitude and nature of interactions in benzene-X (X=ethylene and acetylene) in the gas phase: significantly different CH/pi interaction of acetylene as compared with those of ethylene and methane

The accurate interaction energies of the CH/pi interaction in the benzene-X clusters (X = ethylene and acetylene) were experimentally and theoretically determined. Two-color multiphoton ionization spectroscopy was applied, and the binding energies in the neutral ground state of the clusters were evaluated from the dissociation threshold measurements of the cluster cations. The experimental binding energies of the clusters (D0) were 1.4+/-0.2 and 2.7+/-0.2 kcal/mol, respectively. Estimated CCSD(T) interaction energies for the clusters at the basis set limit (De) were 2.2 and 2.8 kcal/mol, respectively. Calculated D0 values (1.7 and 2.4 kcal/mol, respectively) are close to the experimental values. Large electron correlation contributions (Ecorr=-3.6 and -2.8 kcal/mol, respectively) show that dispersion is the major source of the attraction in both clusters. The electrostatic interaction in the ethylene cluster is very small (-0.38 kcal/mol), as in the case of the benzene-methane cluster, whereas the electrostatic interaction in the acetylene cluster is large (-1.70 kcal/mol). The shifts of the S1-S0 transition also suggest that the ethylene cluster is a van der Waals-type cluster, but the acetylene cluster is a pi-hydrogen-bonded cluster. The nature of the CH/pi interaction of the "activated" alkyne C-H bond is significantly different from that of the "nonactivated" (or typical) alkane and alkene C-H bonds.     

Competition between van der Waals and hydrogen bonding interactions: structure of the trans-1-naphthol/N(2) cluster

The excitation energy in the multiphoton ionization spectrum of the trans-1-naphthol/N(2) cluster shows only a small red shift with respect to isolated naphthol, indicating a van der Waals pi-bound structure rather than a hydrogen-bonded one. To confirm this interpretation, high-level electronic structure calculations were performed for several pi- and hydrogen-bonded isomers of this cluster. The calculations were carried out at the second order M?ller-Plesset (MP2) level of perturbation theory with the family of correlation consistent basis sets up to quintuple-zeta quality including corrections for the basis set superposition error and extrapolation to the MP2 complete basis set (CBS) limit. We report the optimal geometries, vibrational frequencies, and binding energies (D(e)), also corrected for harmonic zero-point energies (D(0)), for three energetically low-lying isomers. In all calculations the lowest energy structure was found to be an isomer with the N(2) molecule bound to the pi-system of the naphthol ring carrying the OH group. In the CBS limit its dissociation energy was computed to be D(0) = 2.67 kcal/mol (934 cm(-1)) as compared to D(0) = 1.28 kcal/mol (448 cm(-1)) for the H-bound structure. The electronic structure calculations therefore confirm the assignment of the experimental electronic spectrum corresponding to a van der Waals pi-bound structure. The energetic stabilization of the pi-bound isomer with respect to the hydrogen-bonded one is rather unexpected when compared with previous findings in related systems, in particular phenol/N(2).     

Structures and interaction energies of stacked graphene-nucleobase complexes

The noncovalent interactions of nucleobases and hydrogen-bonded (Watson-Crick) base-pairs on graphene are investigated with the DFT-D method, i.e., all-electron density functional theory (DFT) in generalized gradient approximation (GGA) combined with an empirical correction for dispersion (van der Waals) interactions. Full geometry optimization is performed for complexes with graphene sheet models of increasing size (up to C(150)H(30)). Large Gaussian basis sets of at least polarized triple-zeta quality are employed. The interaction energies are extrapolated to infinite lateral size of the sheets. Comparisons are made with B2PLYP-D and SCS-MP2 single point energies for coronene and C(54)H(18) substrates. The contributions to the binding (Pauli exchange repulsion, electrostatic and induction, dispersion) are analyzed. At a frozen inter-fragment distance, the interaction energy surface of the rigid C(96)H(24) and base monomers is explored in three dimensions (two lateral and one rotational). Methodologically and also regarding the results of an energy decomposition analysis, the complexes behave like other pi-stacked systems examined previously. The sequence obtained for the interaction energy of bases with graphene (G > A > T > C > U) is the same for all methods and supports recent experimental findings. The absolute values are rather large (about -20 to -25 kcal mol(-1)) but in the expected range for pi-systems of that size. The relatively short equilibrium inter-plane distance (about 3 A) is consistent with atomic force microscopy results of monolayer guanine and adenine on graphite. In graphene ... Watson-Crick pair complexes, the bases lie differently from their isolated energy minima leading to geometrical anti-cooperativity. Together with an electronic contribution of 2 and 6%, this adds up to total binding anti-cooperativities of 7 and 12% for AT and CG, respectively, on C(96)H(24). Hydrogen bonds themselves are merely affected by binding on graphene.     

Reliable structures and energetics for two new delocalized pi...pi prototypes: cyanogen dimer and diacetylene dimer

Two new prototype delocalized pi[dot dot dot]pi complexes are introduced: the dimers of cyanogen, (N[triple bond]C-C[triple bond]N)(2), and diacetylene, (HC[triple bond]C-C[triple bond]CH)(2). These dimers have properties similar to larger delocalized pi...pi systems such as benzene dimer but are small enough that they can be probed in far greater detail with high accuracy electronic structure methods. Parallel-slipped and T-shaped structures of both cyanogen dimer and diacetylene dimer have been optimized with 15 different procedures. The effects of basis set size, theoretical method, counterpoise correction, and the rigid monomer approximation on the structure and energetics of each dimer have been examined. MP2 and CCSD(T) optimized geometries for all four dimer structures are reported, as well as estimates of the CCSD(T) complete basis set (CBS) interaction energy for every optimized geometry. The data reported here suggest that future optimizations of delocalized pi[dot dot dot]pi clusters should be carried out with basis sets of triple-zeta quality. Larger basis sets and the expensive counterpoise correction to the molecular geometry are not necessary. The rigid monomer approximation has very little effect on structure and energetics of these dimers and may be used without consequence. Due to a consistent cancellation of errors, optimization with the MP2 method leads to CCSD(T)/CBS interaction energies that are within 0.2 kcal mol(-1) of those for structures optimized with the CCSD(T) method. Future studies that aim to resolve structures separated by a few tenths of a kcal mol(-1) should consider the effects of optimization with the CCSD(T) method.     

Intercalators. 1. Nature of stacking interactions between intercalators (ethidium, daunomycin, ellipticine, and 4',6-diaminide-2-phenylindole) and DNA base pairs. Ab initio quantum chemical, density functional theory, and empirical potential study

Properties of isolated intercalators (ethidium (E), daunomycin (D), ellipticine (EL), and 4,6'-diaminide-2-phenylindole (DAPI)) and their stacking interactions with adenine...thymine (AT) and guanine...cytosine (GC) nucleic acid base pairs were investigated by means of a nonempirical correlated ab initio method. All intercalators exhibit large charge delocalization, and none of them (including the DAPI dication) exhibits a site with dominant charge. All intercalators have large polarizability and are good electron acceptors, while base pairs are good electron donors. MP2/6-31G*(0.25) stabilization energies of intercalator...base pair complexes are large (E...AT, 22.4 kcal/mol; D...GC, 17.8 kcal/mol; EL...GC, 18.2 kcal/mol; DAPI...GC, 21.1 kcal/mol) and are well reproduced by modified AMBER potential (van der Waals radii of intercalator atoms are enlarged and their energy depths are increased). Standard AMBER potential underestimates binding, especially for DAPI-containing complexes. Because the DAPI dication is the best electron acceptor (among all intercalators studied), this difference is explained by the importance of the charge-transfer term, which is not included in the AMBER potential. For the neutral EL molecule, the standard AMBER force field provides correct results. The Hartree-Fock and DFT/B3LYP methods, not covering the dispersion energy, fail completely to reveal any energy minimum at the potential energy curve of the E...AT complex, and these methods thus cannot be recommended for a study of intercalation process. On the other hand, an approximate version of the DFT method, which was extended to cover London dispersion energy, yields for all complexes very good stabilization energies that are well comparable with referenced ab initio data. Besides the vertical dependence of the interaction, an energy twist dependence of the interaction energy was also investigated by a reference correlated ab initio method and empirical potentials. It is concluded that, despite the cationic (E +1, D +1, DAPI +2) or polar (EL) character of the intercalators investigated, it is the dispersion energy which predominantly contributes to the stability of intercalator...base pair complexes. Any procedure which does not cover dispersion energy is thus not suitable for studying the process of intercalation.     

Converging free energy estimates: MM-PB(GB)SA studies on the protein-protein complex Ras-Raf

Estimating protein-protein interaction energies is a very challenging task for current simulation protocols. Here, absolute binding free energies are reported for the complex H-Ras/C-Raf1 using the MM-PB(GB)SA approach, testing the internal consistency and model dependence of the results. Averaging gas-phase energies (MM), solvation free energies as determined by Generalized Born models (GB/SA), and entropic contributions calculated by normal mode analysis for snapshots obtained from 10 ns explicit-solvent molecular dynamics in general results in an overestimation of the binding affinity when a solvent-accessible surface area-dependent model is used to estimate the nonpolar solvation contribution. Applying the sum of a cavity solvation free energy and explicitly modeled solute-solvent van der Waals interaction energies instead provides less negative estimates for the nonpolar solvation contribution. When the polar contribution to the solvation free energy is determined by solving the Poisson-Boltzmann equation (PB) instead, the calculated binding affinity strongly depends on the atomic radii set chosen. For three GB models investigated, different absolute deviations from PB energies were found for the unbound proteins and the complex. As an alternative to normal-mode calculations, quasiharmonic analyses have been performed to estimate entropic contributions due to changes of solute flexibility upon binding. However, such entropy estimates do not converge after 10 ns of simulation time, indicating that sampling issues may limit the applicability of this approach. Finally, binding free energies estimated from snapshots of the unbound proteins extracted from the complex trajectory result in an underestimate of binding affinity. This points to the need to exercise caution in applying the computationally cheaper "one-trajectory-alternative" to systems where there may be significant changes in flexibility and structure due to binding. The best estimate for the binding free energy of Ras-Raf obtained in this study of -8.3 kcal mol(-1) is in good agreement with the experimental result of -9.6 kcal mol(-1), however, further probing the transferability of the applied protocol that led to this result is necessary.     

Two-step evaluation of binding energy and potential energy surface of van der Waals complexes

Evaluation of intermolecular distance and binding energy (BE) of van der Waals complex/cluster at ab initio level of theory is computationally demanding when many monomers are involved. Starting from MP2 energy, we reached a two-step evaluation method of BE of van der Waals complex/cluster through reasonable approximations; BE = BE(HF) + sum Mi> Mj{BE (Mi- Mj)(MP2 or MP2.5) - BE(Mi-Mj)(HF)} where HF represents the Hartree-Fock calculation, Mi, Mj, etc. are interacting monomers, and MP2.5 represents the arithmetic mean of MP2 and MP3. The first term is the usual BE of the complex/cluster evaluated at the HF level. The second term is the sum of the difference in two-body BE between the correlated and HF levels of theory. This equation was applied to various van der Waals complexes consisting of up-to-four monomers at MP2 and MP2.5 levels of theory. We found that this method is capable of providing precise estimate of the BE and reproducing well the potential energy surface of van der Waals complexes/clusters; the maximum error of the BE is less than 1 kcal/mol and 1% in most cases except for several limited cases. The origins of error in these cases are discussed in detail.     

Noncovalent complexes between dimethyl ether and formic acid--an ab initio and matrix isolation study.

The complexes formed by noncovalent interactions between formic acid and dimethyl ether are investigated by ab initio methods and characterized by matrix isolation spectroscopy. Six complexes with binding energies between -2.26 and -7.97 kcal mol(-1) (MP2/cc-pVTZ+zero point vibrational energy+basis set superposition erros) are identified. The two strongest bound complexes are, within a range of 0.3 kcal mol(-1), isoenergetic. The binding in these six dimers can be described in terms of OH...O, C=O...H, C-O...H and CH...O interactions. Matrix isolation spectroscopy allowed to characterize the two strongest bound complexes by their infrared spectra.