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.     

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.     

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.     

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.     

Theoretical study on mesogenic core structures of nematic liquid crystalline compounds

The structures and intermolecular interaction energies of 10 dimers, included in the mesogenic core structures of typical liquid crystalline (LC) compounds, are obtained at the MP2/6-31G(d) level of theory. It is proved that the dispersion energy significantly contributes to the total interaction energy of these dimers. Even when bulky substituents are introduced into the core part, the interaction energy is still large. It is also revealed that when a long intermolecular distance is provided by a high steric repulsion originating from the linkage of two phenyl groups, the dispersion energy is significantly small. However, in this range of intermolecular distances, the electrostatic energy caused by a strong quadrupole-quadrupole attractive interaction plays a dominant role, and as a result, a rather stable dimer is formed. In all 10 dimers, the dispersion, electrostatic, and exchange-repulsion energies strongly depend on the geometrical orientation of the molecules. The calculated interaction energies of these dimers are also compared with the corresponding experimentally measured viscosities. The results suggest an explicit linear relationship between the interaction energies and viscosities.     

Differences in structure, energy, and spectrum between neutral, protonated, and deprotonated phenol dimers: comparison of various density functionals with ab initio theory

We have carried out extensive calculations for neutral, cationic protonated, anionic deprotonated phenol dimers. The structures and energetics of this system are determined by the delicate competition between H-bonding, H-π interaction and π-π interaction. Thus, the structures, binding energies and frequencies of the dimers are studied by using a variety of functionals of density functional theory (DFT) and M?ller-Plesset second order perturbation theory (MP2) with medium and extended basis sets. The binding energies are compared with those of highly reliable coupled cluster theory with single, double, and perturbative triple excitations (CCSD(T)) at the complete basis set (CBS) limit. The neutral phenol dimer is unique in the sense that its experimental rotational constants have been measured. The geometry of the neutral phenol dimer is governed by the hydrogen bond formed by two hydroxyl groups and the H-π interaction between two aromatic rings, while the structure of the protonated/deprotonated phenol dimers is additionally governed by the electrostatic and induction effects due to the short strong hydrogen bond (SSHB) and the charges populated in the aromatic rings in the ionic systems. Our salient finding is the substantial differences in structure between neutral, protonated, and deprotonated phenol dimers. This is because the neutral dimer involves in both H(π)···O and H(π)···π interactions, the protonated dimer involves in H(π)···π interactions, and the deprotonated dimer involves in a strong H(π)···O interaction. It is important to compare the reliability of diverse computational approaches employed in quantum chemistry on the basis of the calculational results of this system. MP2 calculations using a small cc-pVDZ basis set give reasonable structures, but those using extended basis sets predict wrong π-stacked structures due to the overestimation of the dispersion energies of the π-π interactions. A few new DFT functionals with the empirical dispersion give reliable results consistent with the CCSD(T)/CBS results. The binding energies of the neutral, cationic protonated, and anionic deprotonated phenol dimers are estimated to be more than 28.5, 118.2, and 118.3 kJ mol(-1), respectively. The energy components of the intermolecular interactions for the neutral, protonated and deprotonated dimers are analyzed.     

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 study of substituent effects in the interactions of dimethyl ether with aromatic rings

Ab initio calculations have been used to investigate the interaction energies of dimers of dimethyl ether with benzene, hexafluorobenzene, and several monosubstituted benzenes. The potential energy curves were explored at the MP2/aug-cc-pVDZ level for two basic configurations of the dimers, one in which the oxygen atom of the dimethyl ether was pointed towards the aromatic ring and the other in which the oxygen atom was pointed away from the aromatic ring. Once the optimum intermolecular distances between the dimethyl and the aromatic ring had been determined for each of the dimers in both configurations at the MP2/aug-cc-pVDZ level, single point energy calculations were performed at the MP2/aug-cc-pVTZ level. A CCSD(T) correction term to the energy was determined and this was combined with the MP2/aug-cc-pVTZ energies to estimate the CCSD(T)/aug-cc-pVTZ interaction energies of the dimers. The estimated CCSD(T)/aug-cc-pVTZ interaction energies are predicted to be attractive for all of the dimers in both configurations and dispersion interactions are found to be a large component of the stabilization of the dimers. For the dimers with the dimethyl ether oxygen pointing towards the aromatic ring, the strengths of interaction energies are found to increase as the aromatic ring becomes more electron deficient, while for the dimers with the dimethyl ether oxygen pointing away from the aromatic ring, they increase as the aromatic ring becomes more electron rich. In both cases, the trends can be explained in terms of the electrostatic potentials of the dimethyl ether and the aromatic rings.     

CH/pi interactions in methane clusters with polycyclic aromatic hydrocarbons

Geometries and interaction energies for methane clusters with naphthalene and pyrene were studied. Estimated CCSD(T) interaction energies for the clusters at the basis set limit were -1.92 and -2.50 kcal mol(-1), respectively. Dispersion is mainly responsible for the attraction. Electrostatic interaction is very small. Although the benzene-methane cluster prefers a monodentate structure, in which a C-H bond of the methane points toward the benzene, the methane clusters with the polycyclic aromatic hydrocarbons do not prefer monodentate structures. In the benzene-methane cluster, the weak electrostatic interaction stabilizes the monodentate structure. On the other hand the dispersion interaction controls the orientation of methane in the naphthalene and pyrene clusters. The dispersion interactions in these clusters are significantly larger than those in the benzene-methane cluster. The methane prefers the orientation which is suitable for stabilization by dispersion. Hydrogen atoms of the methane locate above the centers of hexagonal rings of the polycyclic aromatic hydrocarbons in the stable structures. The structures have a small steric repulsion and this positions them only a short distance from the aromatic plane. The large dispersion contribution to the attraction shows that interactions between carbon atoms are mainly responsible for the attraction, and that hydrogen atoms are not important for the attraction. This shows that the interactions between the methane and polycyclic aromatic hydrocarbons are not pi-hydrogen bonds.     

Origins of the stability of imidazole-imidazole, benzene-imidazole, and benzene-indole dimers: CCSD(T)/CBS and SAPT calculations

The respective structures and stabilities of imidazole-imidazole, benzene-imidazole, and benzene-indole dimers have been investigated using different DFT-D functional, MP2, CCSD(T), and SAPT levels of theory with a medium basis set. Comparative analysis of binding energies and structural parameters of the dimers points to a preference for stacking contact or hydrogen bond in an imidazole-imidazole dimer. In contrast, a T-shaped configuration with H-π interaction is maximally advantageous for benzene-imidazole and benzene-indole dimers. High-level ab initio calculations at the CCSD(T)/CBS and DFT-SAPT levels show that classical hydrogen-bonded tilted imidazole-imidazole dimer is a global minimum structure and that it has high electrostatic energy. However, for benzene-imidazole and benzene-indole dimers, the global minimum (N-H···π) structure has high electrostatic energy as well as dispersion energy.     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

F2 dimer: Improved intermolecular potential energy surface using ab initio calculations

A computational study on the intermolecular potential energy of 44 different orientations of F₂ dimers is presented. Basis set superposition error (BSSE) corrected potential energy surface is calculated using the supermolecular approach at CCSD(T) and QCISD(T) levels of theory. The interaction energies obtained using the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets are extrapolated to the complete basis set limit using the latest extrapolation scheme. The basis set effect is checked and it is found that the extrapolated intermolecular energies provide the best compromise between the accuracy and computational cost. Among 1320 energy points of F₂–F₂ system covering more relative orientations, the most stable structure of the dimers was obtained with a well depth of ?146.62 cm^?1 that related to cross configuration, and the most unstable structure is related to linear orientation with a well depth of ?52.63 cm^?1. The calculated second virial coefficients are in good agreement with experimental data. The latest extrapolation scheme of the complete basis set limit at the CCSD(T) level of theory is used to determine the intermolecular potential energy surface of the F₂ dimer. Comparing the results obtained by the latest scheme with those by older schemes show that the new approach provides the best compromise between accuracy and computational cost.     

Magnitude and orientation dependence of intermolecular interaction of perfluoropropane dimer studied by high-level ab initio calculations: comparison with propane dimer

Intermolecular interaction energies of 12 orientations of C(3)F(8) dimers were calculated with electron correlation correction by the second-order M?ller-Plesset perturbation method. The antiparallel C(2h) dimer has the largest interaction energy (-1.45 kcal/mol). Electron correlation correction increases the attraction considerably. Electrostatic energy is not large. Dispersion is mainly responsible for the attraction. Orientation dependence of the interaction energy of the C(3)F(8) dimer is substantially smaller than that of the C(3)H(8) dimer. The calculated interaction energy of the C(3)F(8) dimer at the potential minimum is 78% of that of the C(3)H(8) dimer (-1.85 kcal/mol), whereas the interaction energies of the CF(4) and C(2)F(6) dimers are larger than those of the CH(4) and C(2)H(6) dimers. The intermolecular separation in the C(3)F(8) dimer at the potential minimum is substantially larger than that in the C(3)H(8) dimer. The larger intermolecular separation due to the steric repulsion between fluorine atoms is the cause of the smaller interaction energy of the C(3)F(8) dimer at the potential minimum. The calculated intermolecular interaction energy potentials of the C(3)F(8) dimers using an all atom model OPLS-AA (OPLS all atom model) force field and a united atom model force field were compared with the ab initio calculations. Although the two force fields well reproduces the experimental vapor and liquid properties of perfluoroalkenes, the comparison shows that the united atom model underestimates the potential depth and orientation dependence of the interaction energy. The potentials obtained by the OPLS-AA force field are close to those obtained by the ab initio calculations.     

A quantum chemistry study of binding carotenoids in the bacterial light-harvesting complexes

Carotenoids play the dual function of light harvesting and photoprotection in photosynthetic organisms. Despite their functional importance, the molecular basis for binding of carotenoids in the photosynthetic proteins is poorly understood. We have discovered that all carotenoids are surrounded either by aromatic residues or by chlorophylls in all known crystal structures of the photosynthetic pigment-protein complexes. The intermolecular pi-pi stacking interactions between carotenoids and the surrounding aromatic residues in the light-harvesting complex II (LH-II) of Rhodospirillum molischianum were analyzed by high level ab initio electronic structure calculations. Intermolecular interaction energies were calculated with the second-order M?ller-Plesset perturbation method (MP2) using the modified 6-31G*(0.25) basis set with diffuse d-polarization by Hobza and co-workers. The MP2/6-31G*(0.25) calculations yield a total stabilization energy of -15.66 kcal/mol between the carotenoid molecule and the four surrounding aromatic residues (alpha-Trp-23, beta-Phe-20, beta-Phe-24, beta-Phe-27). It is thus concluded that pi-pi stacking interactions between carotenoids and the aromatic residues play an essential role in binding carotenoids in the LH-II complex of Rhodospirillum molischianum. The physical nature of the pi-pi stacking interactions was further analyzed, and the dispersion interactions were found to be the dominant intermolecular attraction force. There is also a substantial electrostatic contribution to the overall intermolecular stabilization energy.     

Understanding of assembly phenomena by aromatic-aromatic interactions: benzene dimer and the substituted systems

Interactions involving aromatic rings are important in molecular/biomolecular assembly and engineering. As a consequence, there have been a number of investigations on dimers involving benzene or other substituted pi systems. In this Feature Article, we examine the relevance of the magnitudes of their attractive and repulsive interaction energy components in governing the geometries of several pi-pi systems. The geometries and the associated binding energies were evaluated at the complete basis set (CBS) limit of coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)] using a least biased scheme for the given data set. The results for the benzene dimer indicate that the floppy T-shaped structure (center-to-center distance: 4.96 A, with an axial benzene off-centered above the facial benzene) is isoenergetic in zero-point-energy (ZPE) corrected binding energy (D0) to the displaced-stacked structure (vertical interplanar distance: 3.54 A). However, the T-shaped structure is likely to be slightly more stable (D0 approximately equal to 2.4-2.5 kcal/mol) if quadruple excitations are included in the coupled cluster calculations. The presence of substituents on the aromatic ring, irrespective of their electron withdrawing or donating nature, leads to an increase in the binding energy, and the displaced-stacked conformations are more stabilized than the T-shaped conformers. This explains the wide prevalence of displaced stacked structures in organic crystals. Despite that the dispersion energy is dominating, the substituent as well as the conformational effects are correlated to the electrostatic interaction. This electrostatic origin implies that the substituent effect would be reduced in polar solution, but important in apolar media, in particular, for assembling processes.     

Intermolecular interactions in nitrogen-containing aromatic systems

π–π and CH···N interactions are vital in biological systems. In this study, stacking and hydrogen-bonded interactions in pyrazine and triazine dimers were investigated by density functional theory combined with symmetry-adapted perturbation theory (DFT-SAPT) and counterpoise (CP)-corrected supermolecular MP2, SCS-MP2, B3LYP-D and CCSD(T) calculations. All interaction energies were computed using the optimized structures at the CP-corrected SCS/aug-cc-pVDZ level, which gave 1–2 kJ/mol lower interaction energies than the ones computed at the MP2 level. For both dimers, doubly hydrogen-bonded and cross-(displaced) stacked orientations were found to be the lowest energy ones. The reference CCSD(T) calculations favored the former structure in both dimer systems, whereas MP2 and SCS-MP2 located the latter as the lowest energy isomer. In particular, the former was found to be lower in energy than the latter by 2.28 and 1.01 kJ/mol at the CCSD(T)/aug-cc-pVDZ level for pyrazine and triazine, respectively. B3LYP-D produced interaction energies in agreement with the CCSD(T) at the equilibrium geometries, but it overestimates them at the short range and underestimates at the long intermonomer separations. Furthermore, it tends to give smaller equilibrium distances compared to the CCSD(T). DFT-SAPT method was in a good agreement with the reference CCSD(T) calculations. This suggests that DFT-SAPT can be employed to compute the full potential energy surface of these dimers. Moreover, DFT-SAPT calculations showed that the electrostatic and dispersion contributions are the most important energy components stabilizing these dimers. The present study aims to show which theoretical method is the most promising one for the investigation of intermolecular interactions dominated by π–π and CH···N. Therefore, the findings obtained in this study can be used to unravel the structures of nucleic acid bases and other systems stabilized by π–π and CH···N interactions.     

Origin of attraction, magnitude, and directionality of interactions in benzene complexes with pyridinium cations

Geometries and interaction energies of benzene complexes with pyridine, pyridinium, N-methylpyridinium were studied by ab initio molecular orbital calculations. Estimated CCSD(T) interaction energies of the complexes at the basis set limit were -3.04, -14.77, and -9.36 kcal/mol, respectively. The interactions in the pyridinium and N-methylpyridinium complexes should be categorized into a cation/pi interaction, because the electrostatic and induction interactions greatly contribute to the attraction. On the other hand, the interaction in the pyridine complex is a pi/pi interaction. The dispersion interaction is mainly responsible for the attraction in the benzene-pyridine complex. Short-range interactions including charge-transfer interactions are not important for the attraction in the three complexes. The most stable pyridinium complex has a T-shaped structure, in which the N-H bond points toward the benzene, while the N-methylpyridinium complex prefers a slipped-parallel structure. The benzene-pyridine complex has two nearly isoenergetic (Slipped-parallel and T-shaped) structures.     

Theoretical evaluation of the nature and strength of the F������F intermolecular interactions present in fluorinated hydrocarbons

The nature, strength and directionality of C?CF···F interactions were theoretically evaluated on all symmetry unique dimers present in the CF₄, C₂F₄ and C₆F₆ crystals and on CF₄, CHF₃, CH₂F₂ and CH₃F model dimers placed in two different geometries. On each dimer, the interaction energy was computed at the MP2/aug-cc-pVDZ level, and also an Atoms in Molecule analysis of the dimer electron density was done to find all intermolecular bonds. The characterization was completed by computing the energy components of the dimer interaction energy, using the SAPT method. The results show that in most dimers found in the CF₄, C₂F₄ and C₆F₆ crystals, there are more than one C?CF···F intermolecular bond and sometimes even a C?CF···?? intermolecular bond. By selecting dimers presenting one C?CF···F bond, the following strength can be estimated for a single C?CF···F bond: ?0.21?kcal/mol in C(sp³) atoms, ?0.25?kcal/mol in C(non-aromatic sp²), ?0.41?kcal/mol in C(aromatic sp²). The interaction energy of the dimer grows almost linearly with the number of C?CF···F bonds present. The relative orientation of the C?CF···F bond affects the bond strength. The SAPT calculations indicate that in collinear dimers, C?CF···F interactions are strongly dominated by the dispersion energetic component, while when in non-collinear conformations the electrostatic component can be as important as the dispersion one.     

Theoretical studies on hydroquinone-benzene clusters

High-level ab initio calculations were carried out to evaluate the interaction between the hydroquinone and benzene molecules. The intermolecular interaction energy was calculated using the M?ller-Plesset second-order perturbation theory at the complete basis set limit and also at the coupled cluster theory with single, double, and perturbatively triple excitations. The calculated binding energy is larger than the benzene dimer interaction energy. The T-shaped cluster (T-a) and the parallel conformation (P-a) are calculated to be nearly isoenergetic. Owing to the large energy gain in the attraction by electron correlation, the dispersion interaction is important for the attraction.