Benzene Dimer Research Articles

Potential Energy Surface for the Benzene Dimer and Perturbational Analysis of π−π Interactions

We present a complete 6-dimensional potential energy surface for the benzene dimer obtained using symmetry-adapted perturbation theory (SAPT) of intermolecular interactions based on Kohn-Sham's description of monomers. Ab initio calculations were performed for 491 dimer geometries in a triple-zeta-quality basis set supplemented by bond functions. An accurate analytic fit to the ab initio results has been developed and low-energy stationary points on the potential energy surface have been found. We have determined that there are three minima on the surface. Two of them, the tilted T-shape and the parallel-displaced, are nearly isoenergetic with interaction energies of -2.77 and -2.74 kcal/mol, respectively. The third minimum, a twisted edge-to-edge conformation, is significantly less attractive, with the interaction energy equal to -1.82 kcal/mol. Both the T-shape and sandwich geometries, sometimes assumed to be minima, are shown to be only saddle points. The potential energy surface is extremely flat between the two lowest minima, the barrier being only 0.10 kcal/mol above the global minimum. The second-virial coefficient obtained with the new potential agrees well with experimental results over a wide range of temperatures. The SAPT approach rigorously decomposes the interaction energy into physical components. The relative importance of these components has been analyzed.

Time-independent coupled cluster theory of the polarization propagator. Implementation and application of the singles and doubles model to dynamic polarizabilities and van der Waals constants†

Recently proposed time-independent coupled cluster theory of the polarization propagator [R. Moszynski, P. S. Żuchowski, and B. Jeziorski, Collect. Czech. Chem. Commun. 70, 1109, 2005] has been implemented at the single and double excitations (CCSD) level. The performance of the new approach was investigated by carrying out calculations of static and dynamic electric dipole polarizabilities for various molecules and by making a comparison with values obtained from other ab initio methods, including the full configuration interaction (FCI) technique. Our results show that the polarizabilities computed with the new approach are in a good agreement with the time-dependent CCSD and (when available) FCI values. The isotropic C 6 dispersion coefficients for several benchmark van der Waals complexes, e.g. dimers of helium, argon, water, and benzene, are also reported. They compare very well with existing experimental and best theoretical data. The new propagator, implemented already in the MOLPRO package, is computationally somewhat less demanding than the propagator of the time-dependent coupled cluster theory, and can be considered as an alternative to the latter in applications to large molecules and in studies of their interactions.

Formation of Trimer and Dimer Radical Cations of Methyl-Substituted Benzenes in γ-Irradiated Low-Temperature Matrices

Dimer and trimer radical cations of benzene, toluene, and xylenes were produced selectively after gamma-irradiation in low-temperature 2-methylpentane matrices with electron scavengers: oxygen (O(2)) and sec-butyl chloride (sec-BuCl). The charge resonance (CR) band of the trimer radical cation (M(3)(+)) produced via the corresponding dimer radical cation (M(2)(+)) is clearly seen in the solution containing O(2) as the temperature increases over a range from 80 to 90 K. In o-xylene solution, a fairly strong and distinct M(3)(+) CR absorption is observed; this is due to the large M(3)(+)/M(2)(+) relative extinction coefficient. All benzene derivatives show an equilibrium between dimer and trimer radical cations at approximately 90 K; however, the equilibrium constants of toluene and the xylenes are considerably lower than that of benzene. Formation of the trimer radical cation is inhibited in sec-BuCl, which has commonly been used as a low-temperature optical matrix for producing cationic species. An ab initio DFT method is applied to predict the geometry of M(3)(+), giving "slipped sandwich" (for benzene, m-xylene, and p-xylene) and "slipped fan-shaped" (toluene and o-xylene) structures as the most plausible geometries. The experimentally observed spectroscopic parameters reflect well those predicted by TD-DFT calculation based on geometry, suggesting strong dependence of the geometry of M(3)(+) on substitution patterns. This is the first report not only of direct spectroscopic observation of aromatic trimer radical cations in the condensed phase but also on the quantitative analysis of their equilibria.

A theoretical study of singlet low-energy excited states of the benzene dimer

The singlet ground and low-energy excited states of the benzene dimer in D6h geometry are characterized using second order multireference perturbation theory (CASPT2). The counterpoise-corrected spectroscopic parameters of the benzene excimer are in quantitative agreement with experiment. The same method was used to compute a submanifold of the potential energy hypersurface of the first excited state of the benzene dimer, exhibiting two local minima in addition to a saddle point between them. This study demonstrates the suitability of CASPT2 to describe the benzene excimer and suggests that the method can be used to describe weak intermolecular interactions involving excited states.

An experimental value for the B1u C–H stretch mode in benzene

We here present experimental infrared spectra on two (C(6)H(6))(C(6)D(6)) benzene dimer isomers in the gas phase. The spectra show that the two benzene molecules in the dimer are symmetrically inequivalent and have distinct IR signatures. One of the two molecules is in a site of low symmetry, which leads to the IR activation of fundamental modes that are IR forbidden by symmetry in the monomer. In the spectra, all four fundamental C-H stretch modes of benzene are observed. Modes in the dimer are shifted up to 3 cm(-1) to the red, compared to the modes that are known for the monomer. For the nu(13) B(1u) C-H stretch fundamental mode of benzene, a first experimental value of 3015(+2) (-5) cm(-1) is determined, in excellent agreement with anharmonic frequency calculations presented here.

Magnitude and Physical Origin of Intermolecular Interactions of Aromatic Molecules: Recent Progress of Computational Studies

Intermolecular interactions of aromatic molecules ( π/π , OH/π , NH/π and cation/π interactions) are important in many fields of chemistry and biology. These interactions are important for crystal structures, stability of biological systems and their molecular recognition processes. Detailed information on the interactions of aromatic molecules is essential for improved material and drug design. However it is not an easy task to study the magnitude and physical origin of these interactions by experimental measurements only. Recent developments of computational methodologies and increasing computer performance enable us to study these interactions quatitatively by high-level ab initio molecular orbital calculations. High-level ab initio calculations are rapidly increasing our knowledge on the intermolecular interactions of aromatic molecules. This review attempts to introduce methodologies for studying weak intermolecular interactions by ab initio calculations and to summarize recent progress in quantitative analysis of intermolecular interactions of aromatic molecules. Keywords: Crystal structure, Intermolecular Perturbation Theory, Electron Correlation, benzene dimer, Naphthalene Dimer, Heteroatoms

DRF90: a polarizable force field

The direct reaction field (DRF) approach has proven to be a useful tool to investigate the influence of solvents on the quantum/classical behaviour of solute molecules. In this paper, we report the latest extension of this DRF approach, which consists of the gradient of the completely classical energy expressions of this otherwise QM/MM method. They can be used in (completely classical) molecular dynamics (MD) simulations and geometry optimizations, that can be followed by a number of single point QM/MM calculations on configurations obtained in these simulations/optimizations. We report all energy and gradient expressions, and results for a number of interesting (model) systems. They include geometry optimization of the benzene dimer as well as MD simulations of some solvents. The most stable configuration for the benzene dimer is shown to be the parallel-displaced form, which is slightly more stable (0.3 kcal/mol) than the T-shaped dimer.

Binding energies in benzene dimers: Nonlocal density functional calculations

The interaction energy and minimum energy structure for different geometries of the benzene dimer have been calculated using the recently developed nonlocal correlation energy functional for calculating dispersion interactions. The comparison of this straightforward and relatively quick density functional based method with recent calculations provides a promising first step to elucidate how the former, quicker method might be exploited in larger more complicated biological, organic, aromatic, and even infinite systems such as molecules physisorbed on surfaces and van der Waals crystals.

Interaction energies of monosubstituted benzene dimers via nonlocal density functional theory

We present density functional calculations for the interaction energy of monosubstituted benzene dimers. Our approach utilizes a recently developed fully nonlocal correlation energy functional, which has been applied to the pure benzene dimer and several other systems with promising results. The interaction energy as a function of monomer distance was calculated for four different substituents in a sandwich and two T-shaped configurations. In addition, we considered two methods for dealing with exchange, namely, using the revPBE generalized gradient functional as well as full Hartree-Fock. Our results are compared with other methods, such as Moller-Plesset and coupled-cluster calculations, thereby suggesting the usefulness of our approach. Since our density functional based method is considerably faster than other standard methods, it provides a computationally inexpensive alternative, which is of particular interest for larger systems where standard calculations are too expensive or infeasible.

Van der Waals corrections to density functional theory calculations: Methane, ethane, ethylene, benzene, formaldehyde, ammonia, water, PBE, and CPMD

Parameters are developed for a practical application of the empirical van der Waals (vdW) correction infrastructure available in the CPMD density functional theory (DFT) code. The binding energy, geometry, and potential energy surface (PES) are examined for methane, ethane, ethylene, formaldehyde, ammonia, three benzene dimer geometries, and three benzene–water geometries. The vdW corrected results compare favorably with MP2 and CCSD(T) calculations near the complete basis set limits, and with experimental results where they are available.

The Effect of Multiple Substituents on Sandwich and T‐Shaped π–π Interactions

Sandwich and T-shaped configurations of substituted benzene dimers were studied by second-order perturbation theory to determine how substituents tune pi-pi interactions. Remarkably, multiple substituents have an additive effect on the binding energy of sandwich dimers, except in some cases when substituents are aligned on top of each other. The energetics of substituted T-shaped configurations are more complex, but nevertheless a simple model that accounts for electrostatic and dispersion interactions (and direct contacts between substituents on one ring and hydrogen atoms on the other), provides a good match to the quantum mechanical results. These results provide insight into the manner by which substituents csan be utilized in supramolecular design.

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.

Hybrid density functional theory for π‐stacking interactions: Application to benzenes, pyridines, and DNA bases

The suitability of a hybrid density functional to qualitatively reproduce geometric and energetic details of parallel pi-stacked aromatic complexes is presented. The hybrid functional includes an ad hoc mixture of half the exact (HF) exchange with half of the uniform electron gas exchange, plus Lee, Yang, and Parr's expression for correlation energy. This functional, in combination with polarized, diffuse basis sets, gives a binding energy for the parallel-displaced benzene dimer in good agreement with the best available high-level calculations reported in the literature, and qualitatively reproduces the local MP2 potential energy surface of the parallel-displaced benzene dimer. This method was further critically compared to high-level calculations recently reported in the literature for a range of pi-stacked complexes, including monosubstituted benzene-benzene dimers, along with DNA and RNA bases, and generally agrees with MP2 and/or CCSD(T) results to within +/-2 kJ mol(-1). We also show that the resulting BH&H binding energy is closely related to the electron density in the intermolecular region. The net result is that the BH&H functional, presumably due to fortuitous cancellation of errors, provides a pragmatic, computationally efficient quantum mechanical tool for the study of large pi-stacked systems such as DNA.

Role of Electron Density and Magnetic Couplings on the Nucleus-Independent Chemical Shift (NICS) Profiles of [2.2]Paracyclophane and Related Species

The nucleus-independent chemical shifts (NICS) and electron density profiles along the inner and outer regions defined by the two stacked aromatic rings of [2.2]paracyclophane have been analyzed and compared to those of free benzene and p-xylene and benzene dimers taken as reference models. It is found that stacked aromatic rings show a reduction of the NICS indicator of aromaticity as compared to the same free aromatic systems. This decrease of the NICS values upon stacking is not due to an increase of the electron density in the inner region between the rings (as claimed in a previous work) but is related to the magnetic couplings between superimposed rings that affect this measure of local aromaticity. The increase of local aromaticity in superimposed aromatic rings indicated by NICS is not real but the result of the coupling between the magnetic fields generated by the two stacked rings. This result warns about the use of NICS as a descriptor of aromaticity for species having superimposed aromatic rings.

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.

The World of Non-Covalent Interactions: 2006

The review focusses on the fundamental importance of non-covalent interactions in nature by illustrating specific examples from chemistry, physics and the biosciences. Laser spectroscopic methods and both ab initio and molecular modelling procedures used for the study of non-covalent interactions in molecular clusters are briefly outlined. The role of structure and geometry, stabilization energy, potential and free energy surfaces for molecular clusters is extensively discussed in the light of the most advanced ab initio computational results for the CCSD(T) method, extrapolated to the CBS limit. The most important types of non-covalent complexes are classified and several small and medium size non-covalent systems, including H-bonded and improper H-bonded complexes, nucleic acid base pairs, and peptides and proteins are discussed with some detail. Finally, we evaluate the interpretation of experimental results in comparison with state of the art theoretical models: this is illustrated for phenol...Ar, the benzene dimer and nucleic acid base pairs. A review with 270 references.

Evaluation of DFT methods for computing the interaction energies of homomolecular and heteromolecular dimers of monosubstituted benzene

AbstractWe present density functional theory (DFT) interaction energies for the sandwich and T‐shaped conformers of substituted benzene dimers. The DFT functionals studied include TPSS, HCTH407, B3LYP, and X3LYP. We also include Hartree–Fock (HF) and second‐order Møller–Plesset perturbation theory calculations (MP2), as well as calculations using a new functional, P3LYP, which includes PBE and HF exchange and LYP correlation. Although DFT methods do not explicitly account for the dispersion interactions important in the benzene–dimer interactions, we find that our new method, P3LYP, as well as HCTH407 and TPSS, match MP2 and CCSD(T) calculations much better than the hybrid methods B3LYP and X3LYP methods do. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

A fast correlated electronic structure method for computing interaction energies of large van der Waals complexes applied to the fullerene–porphyrin dimer

A new implementation of the scaled opposite spin Møller-Plesset (SOS-MP2) method is briefly described, which exploits the locality and sparsity of expansion coefficients and as a result has computational costs that increase approximately quadratically with molecular size. The performance of SOS-MP2 for describing stacked pi-complexes is carefully investigated using the benzene, ethylene, uracil, and naphthalene dimers as model systems. It is demonstrated that counterpoise-corrected SOS-MP2 results, extrapolated towards the complete basis set (CBS) limit using a two-point extrapolation scheme, can yield association energies that are reasonably close to the best available numbers, when the single scale factor is chosen as 1.55 for extrapolating results at the cc-pVDZ and cc-pVTZ levels. This methodology yields an interaction energy for the fullerene-tetraphenylporphyrin dimer of -31.47 kcal mol(-1) while Hartree-Fock (HF) with the cc-pVTZ basis finds the dimer at the same geometry is unbound by +10.83 kcal mol(-1). This implies that the net binding is a result of substantial correlation effects, presumably long-range London dispersions.

Calculation of intermolecular interactions in the benzene dimer using coupled-cluster and local electron correlation methods

Potential energy curves for the parallel-displaced, T-shaped and sandwich structures of the benzene dimer are computed with density fitted local second-order Møller-Plesset perturbation theory (DF-LMP2) as well as with the spin-component scaled (SCS) variant of DF-LMP2. While DF-LMP2 strongly overestimates the dispersion interaction, in common with canonical MP2, the DF-SCS-LMP2 interaction energies are in excellent agreement with the best available literature values along the entire potential energy curves. The DF-SCS-LMP2 dissociation energies for the three structures are also compared with new complete basis set estimates of the interaction energies obtained from accurate coupled cluster (CCSD(T)) and DF-SCS-MP2 calculations. Since LMP2 is essentially free of basis set superposition errors, counterpoise corrections are not required. As a result, DF-SCS-LMP2 is computationally inexpensive and represents an attractive method for the study of larger pi-stacked systems such as truncated sections of DNA.

Quantum Mechanical Calculations for Benzene Dimer Energies: Present Problems and Future Challenges

Factors influencing quantum mechanical calculations of nonbonded interactions between organic molecules are still imperfectly understood. Much effort has gone into efforts to calculate the structures and binding energies of stable benzene dimers. However, little experimental evidence is available for comparison with theoretical results. As a benchmark for assessing the reliability and accuracy of such calculations, the benzene crystal structure seems a more suitable target than the elusive dimer structures.