Investigation of the Benzene–Naphthalene and Naphthalene–Naphthalene Potential Energy Surfaces: DFT/CCSD(T) Correction Scheme

The potential energy surfaces of the naphthalene dimer and benzene–naphthalene complexes are investigated using the recently developed DFT/CCSD(T) correction scheme [J. Chem. Phys. 2008 , 128, 114 102]. One and three minima are located on the PES of the benzene–naphthalene and the naphthalene dimer complexes, respectively, all of which are of the parallel‐displaced type. The stabilities of benzene–naphthalene and the naphthalene dimer are ?4.2 and ?6.2 kcal mol^?1, respectively. Unlike the benzene dimer, where the T‐shaped complex is the global minimum, the lowest‐energy T‐shaped structure is about 0.2 and 1.6 kcal mol^?1 above the global minimum on the benzene–naphthalene and the naphthalene dimer potential energy surfaces, respectively.     

Intermolecular interaction between hexafluorobenzene and benzene: Ab initio calculations including CCSD(T) level electron correlation correction

The intermolecular interaction energy of hexafluorobenzene-benzene has been calculated with the ARS-E model (a model chemistry for the evaluation of the intermolecular interaction energy between aromatic systems using extrapolation), which was formerly called the AIMI model. The CCSD(T) interaction energy at the basis-set limit has been estimated from the MP2 interaction energy at the basis-set limit and the CCSD(T) correction term obtained using a medium-sized basis set. The slipped-parallel (Cs) complex has the largest (most negative) interaction energy (-5.38 kcal/mol). The sandwich (C6v) complex is slightly less stable (-5.07 kcal/mol). The interaction energies of two T-shaped (C2v) complexes are very small (-1.74 and -0.88 kcal/mol). The calculated interaction energy of the slipped-parallel complex is about twice as large as that of the benzene dimer. The dispersion interaction is found to be the major source of attraction in the complex, although electrostatic interaction also contributes to the attraction. The dispersion interaction increases the relative stability of the slipped-parallel benzene dimer and the hexafluorobenzene-benzene complex compared to T-shaped ones. The electrostatic interaction is repulsive in the slipped-parallel benzene dimer, whereas it stabilizes the slipped-parallel hexafluorobenzene-benzene complex. Both electrostatic and dispersion interactions stabilize the slipped-parallel hexafluorobenzene-benzene complex, which is the cause of the preference of the slipped-parallel orientation and the larger interaction energy of the complex compared to the benzene dimer.     

Geometries and stabilities of various configurations of benzene dimer: details of novel V-shaped structure revealed

Benzene dimer configurations namely T-shaped, parallel-displaced, sandwich, and V-shaped that were proposed by experimental studies are investigated using second- and fourth-order Møller–Plesset perturbation theory. The MP2 method with aug-cc-pVDZ and aug-cc-pVTZ basis sets unequivocally shows that the parallel-displaced configuration is considerably more stable than T-shaped structure. On the other hand, the MP4(SDTQ)/aug-cc-pVDZ level predicts that the T-shaped and parallel-displaced configurations are nearly isoenergetic, which is parallel to the previous results of estimated CCSD(T)/CBS level reported recently. The lowest energy T-shaped configuration is stabilized by 0.17 kcal/mol over the parallel-displaced configuration at the MP4(SDTQ)/aug-cc-pVDZ level. Although the structures of all the four different types of configurations are found to be stable at both MP2 and full MP4 methods, the V-shaped configuration is the least stable among them. The calculated interaction energy of ?2.3 kcal/mol for the lowest energy T-shaped structure at the MP4(SDTQ)/aug-cc-pVDZ level is in good agreement with the experimental value of ?2.4 ± 0.4 kcal/mol. We conclude that the MP4(SDTQ) with a reasonably good basis set can be used for systems involving π–π interactions to obtain qualitative and quantitative results.     

Estimating the basis set superposition error in the CCSD(T)(F12) explicitly correlated method using the example of a water dimer

Changes in the basis set superposition errors upon transitioning from conventional CCSD(T) to the CCSD(T)(F12) explicitly correlated method is studied using the example of a water dimer. A comparison of the compensation errors for CCSD(T) and CCSD(T)(F12) reveals a substantial reduction in the superposition error upon use of the latter. Numerical experiments with water dimers show it is possible theoretically predict an equilibrium distance between oxygen atoms that is similar to the experimental data (2.946 Å), as is the predicted energy of dissociation of a dimer (5.4 ± 0.7 kcal/mol). It is found that the structural and energy parameters of hydrogen bonds in water dimers can be calculated precisely even with two-exponential correlation-consistent basis sets if we use the explicitly correlated approach and subsequently correct the basis set superposition error.     

Binding Energies of the π‐Stacked Anisole Dimer: New Molecular Beam—Laser Spectroscopy Experiments and CCSD(T) Calculations

Among noncovalent interactions, π–π stacking is a very important binding motif governed mainly by London dispersion. Despite its importance, for instance, for the structure of bio‐macromolecules, the direct experimental measurement of binding energies in π–π stacked complexes has been elusive for a long time. Only recently, an experimental value for the binding energy of the anisole dimer was presented, determined by velocity mapping ion imaging in a two‐photon resonant ionisation molecular beam experiment. However, in that paper, a discrepancy was already noted between the obtained experimental value and a theoretical estimate. Here, we present an accurate recalculation of the binding energy based on the combination of the CCSD(T)/CBS interaction energy and a DFT‐D3 vibrational analysis. This proves unambiguously that the previously reported experimental value is too high and a new series of measurements with a different, more sensitive apparatus was performed. The new experimental value of 1800±100 cm^?1 (5.15±0.29 kcal mol^?1) is close to the present theoretical prediction of 5.04±0.40 kcal mol^?1. Additional calculations of the properties of the cationic and excited states involved in the photodissociation of the dimer were used to identify and rationalise the difficulties encountered in the experimental work.     

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.     

Ab initio calculations of structures and interaction energies of toluene dimers including CCSD(T) level electron correlation correction

The intermolecular interaction energy of the toluene dimer has been calculated with the ARS-F model (a model chemistry for the evaluation of intermolecular interaction energy between ARomatic Systems using Feller's method), which was formerly called as the AIMI model III. 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 Moller-Plesset perturbation interaction energy at the basis set limit obtained by Feller's method and the CCSD(T) correction term obtained using a medium-size basis set. The cross (C(2)) dimer has the largest (most negative) interaction energy (-4.08 kcal/mol). The antiparallel (C(2h)) and parallel (C(S)) dimers (-3.77 and -3.41 kcal/mol, respectively) are slightly less stable. The dispersion interaction is found to be the major source of attraction in the toluene dimer. The dispersion interaction mainly determines the relative stability of the stacked three dimers. The electrostatic interaction of the stacked three dimers is repulsive. Although the T-shaped and slipped-parallel benzene dimers are nearly isoenergetic, the stacked toluene dimers are substantially more stable than the T-shaped toluene dimer (-2.62 kcal/mol). The large dispersion interaction in the stacked toluene dimers is the cause of their enhanced stability.     

Origin of attraction and directionality of the pi/pi interaction: model chemistry calculations of benzene dimer interaction.

A model chemistry for the evaluation of intermolecular interaction between aromatic molecules (AIMI Model) has been developed. The CCSD(T) interaction energy at the basis set limit has been estimated from the MP2 interaction energy near the basis set limit and the CCSD(T) correction term obtained by using a medium size basis set. The calculated interaction energies of the parallel, T-shaped,and slipped-parallel benzene dimers are -1.48, -2.46, and -2.48 kcal/mol, respectively. The substantial attractive interaction in benzene dimer, even where the molecules are well separated, shows that the major source of attraction is not short-range interactions such as charge-transfer but long-range interactions such as electrostatic and dispersion. The inclusion of electron correlation increases attraction significantly. The dispersion interaction is found to be the major source of attraction in the benzene dimer. The orientation dependence of the dimer interaction is mainly controlled by long-range interactions. Although electrostatic interaction is considerably weaker than dispersion interaction, it is highly orientation dependent. Dispersion and electrostatic interactions are both important for the directionality of the benzene dimer interaction.     

Amide–π interactions between formamide and benzene

High‐level ab initio calculations have been carried out using a formamide–benzene model system to evaluate amide–π interactions. The interaction energies were estimated as a sum of the CCSD(T) correlation contribution and the HF energy at the complete basis set limit, for the geometries of the model structures at the energy minimum obtained by potential energy surface (PES) scans. NH/π geometry in a face‐on configuration was found to be the most attractive among the various geometries considered, with interaction energy of ?3.75 kcal/mol. An interaction energy of ?2.08 kcal/mol was calculated for the stacked N/Center type geometry, where the nitrogen atom of formamide points directly toward the center of the aromatic ring. The weakest C?O/π geometry, where a carbonyl oxygen atom points toward the plane of the aromatic ring, was found to have energy minimum at an intermolecular distance of 3.67 Å from the PES, with a repulsive interaction energy less than 1 kcal/mol. However, if there are simultaneous attractive interactions with other parts of the molecule besides the amide group, the weak repulsion could be easily overcome, to give a C?O/π geometry interaction. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Gibbs energy of activation for thermal isomerization of (1Z)‐acetaldehyde hydrazone and (1Z)‐acetaldehyde N,N‐dimethylhydrazone by Gaussian‐4 theory and CCSD(T)/CBS computations

In this article, we examined the Gibbs energy of activation for the Z/E thermal isomerization reaction of (1Z)‐acetaldehyde hydrazone and (1Z)‐acetaldehyde N,N‐dimethylhydrazone, at 298.15 K in the solvent of cyclohexane. We carried out computations employing both the Gaussian‐4 (G4) theory and the coupled cluster method using both single and double substitutions and triple excitations noniteratively, CCSD(T). The CCSD(T) energy is extrapolated to the complete basis set (CBS). We compared the calculated results to the available experimental observation. It appeared that both G4 and CCSD(T)/CBS computations overestimated the experimental value by as much as about 6 and 12 kcal/mol in the present two cases. We discussed possible sources of error and proposed the experimental kinetic data could be questionable. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Accurate ab initio binding energies of the benzene dimer

Accurate binding energies of the benzene dimer at the T and parallel displaced (PD) configurations were determined using the single- and double-coupled cluster method with perturbative triple correction (CCSD(T)) with correlation-consistent basis sets and an effective basis set extrapolation scheme recently devised. The difference between the estimated CCSD(T) basis set limit electronic binding energies for the T and PD shapes appears to amount to more than 0.3 kcal/mol, indicating the PD shape is a more stable configuration than the T shape for this dimer in the gas phase. This conclusion is further strengthened when a vibrational zero-point correction to the electronic binding energies of this dimer is made, which increases the difference between the two configurations to 0.4-0.5 kcal/mol. The binding energies of 2.4 and 2.8 kcal/mol for the T and PD configurations are in good accord with the previous experimental result from ionization potential measurement.     

Estimates of the ab initio limit for sulfur-pi interactions: the H2S-benzene dimer

The interaction between aromatic rings and sulfur atoms in the side chains of amino acids is a factor in the formation and stabilization of alpha-helices in proteins. We studied the H(2)S-benzene dimer as the simplest possible prototype of sulfur-pi interactions. High-quality potential energy curves were obtained using coupled-cluster theory with single, double, and perturbative triple substitutions (CCSD(T)) and a large, augmented quadruple-zeta basis set (aug-cc-pVQZ). The equilibrium intermonomer distance for the hydrogens-down C(2)(v) configuration is 3.8 A with an interaction energy of -2.74 kcal mol(-1). Extrapolating the binding energy to the complete basis set limit gives -2.81 kcal mol(-1). This binding energy is comparable to that of H(2)O-benzene or of the benzene dimer, and the equilibrium distance is in close agreement with experiment. Other orientations of the dimer were also considered at less complete levels of theory. A considerable reduction in binding for the sulfur-down configuration, together with an energy decomposition analysis, indicates that the attraction in H(2)S-benzene is best thought of as arising from a favorable electrostatic interaction between partially positive hydrogens in H(2)S with the negatively charged pi-cloud of the benzene.     

Highly accurate equilibrium structure of the C2h symmetric N1‐to‐O2 hydrogen‐bonded uracil‐dimer

The highly accurate ab initio equilibrium geometry of the hydrogen‐bonded uracil dimer is derived using a composite geometry extrapolation scheme based on all‐electron, complete basis set extrapolated Møller–Plesset perturbation theory using the jun‐pwCV[T,Q]Z basis sets combined with a valence CCSD(T)/cc‐pVTZ high‐level correction. Geometrical changes on dimerization are discussed and the performance of the several density functional approximations (among others SCAN, ωB97M‐V, DSD‐PBEP86‐D3(BJ), and DSD‐PBEP86‐NL) is evaluated. Orbital‐optimized MP2.5 is discussed as a reduced‐cost alternative to the CCSD(T) gradient in the composite scheme. A new reference interaction energy is calculated with explicitly correlated F12‐CCSD(T).     

Interactions of Molecules with cis and trans Double Bonds: A Theoretical Study of cis‐ and trans‐2‐Butene

Noncovalent interactions of cis‐ and trans‐2‐butene, as the smallest model systems of molecules with cis and trans double bonds, were studied to find potential differences in interactions of these molecules. The study was performed using quantum chemical methods including very accurate CCSD(T)/CBS method. We studied parallel and displaced parallel interactions in 2‐butene dimers, in butane dimers, and between 2‐butene and saturated butane. The results show the trend that interactions of 2‐butene with butane are the strongest, followed by interactions in butane dimers, whereas the interaction in 2‐butene dimers are the weakest. The strongest calculated interaction energy is between trans‐2‐butene and butane, with a CCSD(T)/CBS energy of ?2.80 kcal mol^?1. Interactions in cis‐2‐butene dimers are stronger than interactions in trans‐2‐butene dimers. Interestingly, some of the interactions involving 2‐butene are as strong as interactions in a benzene dimer. These insights into interactions of cis‐ and trans‐2‐butene can improve understanding of the properties and processes that involve molecules with cis and trans double bonds, such as fatty acids and polymers.     

Assessment of new meta and hybrid meta density functionals for predicting the geometry and binding energy of a challenging system: the dimer of H2S and benzene

Noncovalent interactions of a hydrogen bond donor with an aromatic pi system present a challenge for density functional theory, and most density functionals do not perform well for this kind of interaction. Here we test seven recent density functionals from our research group, along with the popular B3LYP functional, for the dimer of H 2S with benzene. The functionals considered include the four new meta and hybrid meta density functionals of the M06 suite, three slightly older hybrid meta functionals, and the B3LYP hybrid functional, and they were tested for their abilities to predict the dissociation energies of three conformations of the H 2S-benzene dimer and to reproduce the key geometric parameters of the equilibrium conformation of this dimer. All of the functionals tested except B3LYP correctly predict which of the three conformations of the dimer is the most stable. The functionals that are best able to reproduce the geometry of the equilibrium conformation of the dimer with a polarized triple-zeta basis set are M06-L, PWB6K, and MPWB1K, each having a mean unsigned relative error across the two experimentally verifiable geometric parameters of only 8%. The success of M06-L is very encouraging because it is a local functional, which reduces the cost for large simulations. The M05-2X functional yields the most accurate binding energy of a conformation of the dimer for which a binding energy calculated at the CCSD(T) level of theory is available; M05-2X gives a binding energy for the system with a difference of merely 0.02 kcal/mol from that obtained by the CCSD(T) calculation. The M06 functional performs well in both categories by yielding a good representation of the geometry of the equilibrium structure and by giving a binding energy that is only 0.19 kcal/mol different from that calculated by CCSD(T). We conclude that the new generation of density functionals should be useful for a variety of problems in biochemistry and materials where aromatic functional groups can serve as hydrogen bond acceptors.     

Highly accurate benchmark calculations of the interaction energies in the complexes C6H6···C6X6 (X = F,Cl, Br,and I)

Different from the case of the benzene dimer, the differences between the interaction energies are always less than 0.50 kcal/mol for face‐to‐face eclipsed, face‐to‐face staggered, and parallel‐displaced configurations of all investigated complexes C₆H₆···C₆X₆ (X = F, Cl, Br, and I). Hence, it is a great challenge for quantum chemists to accurately calculate the interaction energies for the three configurations of the complexes C₆H₆···C₆X₆. This work demonstrates that results obtained with the PBE0 density functional combined with the D3 dispersion correction (PBE0‐D3) and the basis set def2‐TZVPP are in excellent agreement with the estimates of the coupled‐cluster singles, doubles, and perturbative triples [CCSD(T)] complete basis set (CBS) limit. The other finding in this study is that, in comparison with the gold‐standard CCSD(T)/CBS benchmark, the spin‐component scaled (SCS) zeroth‐order symmetry‐adapted perturbation theory (SAPT0), when paired with the basis set aug‐cc‐pVDZ, performs also very well, and its performance is even better than that of the PBE0‐D3/def2‐TZVPP method or the conventional SAPT/aug‐cc‐pVQZ method. The findings of this study are very significant because both PBE0‐D3/def2‐TZVPP and SCS‐SAPT0/aug‐cc‐pVDZ can deal with the systems with more than 200 atoms.     

A benchmark quantum chemical study of the stacking interaction between larger polycondensed aromatic hydrocarbons

Large-scale electronic structure calculations were performed for the interaction energy between coronene, C₂₄H₁₂ with circumcoronene, C₅₄H₁₈, and between two circumcoronene molecules, in order to get a picture of the interaction between larger graphene sheets. Most calculations were performed at the SCS-MP2 level but we have corrected them for higher-order correlation effects using a calculation on the coronene-circumcoronene system at the quadratic CI, QCISD(T) level. Our best estimate for the interaction energy between coronene and circumcoronene is 32.1?kcal/mol. We estimate the binding of coronene on a graphite surface to be 37.4 or 1.56?kcal/mol per carbon atom (67.5?meV/C atom). This is also our estimate for the exfoliation energy of graphite. It is higher than most previous theoretical estimates. The SCS-MP2 method which reproduces the CCSD(T) and QCISD(T) values very well for smaller aromatic hydrocarbons, e.g., for the benzene dimer, increasingly overestimates dispersion as the bandgap (the HOMO-LUMO separation) decreases. The barrier to the sliding motion of coronene on circumcoronene is 0.45?kcal/mol, and for two circumcoronene molecules 1.85?kcal/mol (0.018 and 0.034?kcal/mol per C atom, respectively). This means that larger graphenes cannot easily glide over each other.     

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.     

Three-dimensional potential energy surface of selected carbohydrates' CH/π dispersion interactions calculated by high-level quantum mechanical methods

In this study we present the first systematic computational three‐dimensional scan of carbohydrate hydrophobic patches for the ability to interact through CH/π dispersion interactions. The carbohydrates β‐d‐ glucopyranose, β‐d‐ mannopyranose and α‐l‐ fucopyranose were studied in a complex with a benzene molecule, which served as a model of the CH/π interaction in carbohydrate/protein complexes. The 3D relaxed scans were performed at the SCC‐DFTB‐D level with 3 757 grid points for both carbohydrate hydrophobic sides. The interaction energy of all grid points was recalculated at the DFT‐D BP/def2‐TZVPP level. The results obtained clearly show highly delimited and separated areas around each CH group, with an interaction energy up to ?5.40 kcal mol^?1. The results also show that with increasing H???π distance these delimited areas merge and form one larger region, which covers all hydrogen atoms on that specific carbohydrate side. Simultaneously, the interaction becomes weaker with an energy of ?2.5 kcal mol^?1. All local energy minima were optimized at the DFT‐D BP/def2‐TZVPP level and the interaction energies of these complexes were refined by use of the high‐level ab initio computation at the CCSD(T)/CBS level. Results obtained from the optimization suggest that the CH group hydrogen atoms are not equivalent and the interaction energy at the CCSD(T)/CBS level range from ?3.54 to ?5.40 kcal mol^?1. These results also reveal that the optimal H???π distance for the CH/π dispersion interaction is approximately (2.310±0.030) Å, and the angle defined as carbon‐hydrogen‐benzene geometrical centre is (180±30)°. These results reveal that whereas the dispersion interactions with the lowest interaction energies are quite strictly located in space, the slightly higher interaction energy regions adopt a much larger space.