The inclusion of electron correlation in intermolecular potentials: applications to the formamide dimer and liquid formamide

A test of the quality of the electrostatic properties and polarizabilities used in the nonempirical molecular orbital (NEMO) potential is carried out for formamide by calculating the molecular dipole moment and polarizability at the second-order M?ller–Plesset (MP2) level of theory. The molecular dipole moment is 11% lower at the MP2 level than at the Hartree–Fock (HF) level, whereas the isotropic part of the polarizability is increased by 36% by adding electron correlation and using a considerably larger basis set. The atomic charges, dipole moments and polarizabilities obtained at the HF level are rescaled to get the correct molecular properties at the MP2 level. The potential minimum for the cyclic dimer of formamide is −17.50 kcal/mol with the MP2-scaled properties and is significantly lower than other potentials give. Two intermolecular potentials are constructed and used in subsequent molecular dynamics simulations: one with the regular NEMO potential and the other with the rescaled MP2 properties. A damping of the electrostatic field at short intermolecular distances is included in the present NEMO model. The average energies for liquid formamide are lower for the MP2-scaled model and are in good agreement with experimental results. The lowering of the simulation energy for the MP2-scaled potential indicates the strong dispersive interactions in liquid formamide. Received: 20 March 2000 / Accepted: 18 April 2000 / Published online: 18 August 2000     

Substituent effects in the benzene dimer are due to direct interactions of the substituents with the unsubstituted benzene

The prevailing views of substituent effects in the sandwich configuration of the benzene dimer are flawed. For example, in the polar/pi model of Cozzi and co-workers (J. Am. Chem. Soc. 1992, 114, 5729), electron-withdrawing substituents enhance binding in the benzene dimer by withdrawing electron density from the pi-cloud of the substituted ring, reducing the repulsive electrostatic interaction with the nonsubstituted benzene. Conversely, electron-donating substituents donate excess electrons into the pi-system and diminish the pi-stacking interaction. We present computed interaction energies for the sandwich configuration of the benzene dimer and 24 substituted dimers, as well as sandwich complexes of substituted benzenes with perfluorobenzene. While the computed interaction energies correlate well with sigmam values for the substituents, interaction energies for related model systems demonstrate that this trend is independent of the substituted ring. Instead, the observed trends are consistent with direct electrostatic and dispersive interactions of the substituents with the unsubstituted ring.     

Study of specific ion-amino acid interactions through the use of local correlation methods

Specific ion effects, related to the hydration of ions and ion-solute interactions, play a fundamental part in many processes in chemistry and biology. Although intensively studied since the seminal studies of Franz Hofmeister and co-workers, their molecular origin has only recently started to be unveiled. In this work, we have investigated the interaction between halide anions and a selected set of amino acid residues in an attempt to identify the forces behind ion specificity. Two-dimensional potential energy surfaces have been calculated with the use of local second order M?ller-Plesset perturbation theory (LMP2), coupled with the COSMO model to describe solvent effects. The results show in great detail the impact of dispersion interactions, in particular for the heavier anions (Br(-) and I(-)). The obtained potential energy surfaces also hint at a greater mobility of iodide in the vicinity of a residue, which correlates well with its placing in the Hofmeister series.     

An ab initio study of intermolecular interactions of nitromethane dimer and nitromethane trimer

Different geometries of nitromethane dimer and nitromethane trimer have been fully optimized employing the density functional theory B3LYP method and the 6-31++G** basis set. Three-body interaction energy has been obtained with the ab initio supermolecular approach at the levels of MP2/6-31++G**//B3LYP/6-31++G** and MP2/aug-cc-pVDZ//B3LYP/6-31++G**. The internal rotation of methyl group induced by intermolecular interaction has been observed theoretically. For the optimized structures of nitromethane dimer, the strength of C--H...O--N H-bond ranges from -9.0 to -12.4 kJ mol(-1) at the MP2/aug-cc-pVDZ//B3LYP/6-31++G** level, and the B3LYP method underestimates the interaction strength compared with the MP2 method, while MP2/6-31++G**//B3LYP/6-31++G** calculated DeltaE(C) is within 2.5 kJ mol(-1) of the corresponding value at the MP4(SDTQ)/6-31G**//B3LYP/6-31++G** level. The analytic atom-atom intermolecular potential has been successfully regressed by using the MP2/6-31++G**//B3LYP/6-31++G** calculated interaction energies of nitromethane dimer. For the optimized structures of nitromethane trimer the three-body interaction energies occupy small percentage of corresponding total binding energies, but become important for the compressed nitromethane explosive. In addition, it has been discovered that the three-body interaction energy in the cyclic nitromethane trimer is more and more negative as intermolecular distances decrease from 2.2 to 1.7 A.     

Calculation of excited-state properties using general coupled-cluster and configuration-interaction models

Using string-based algorithms excitation energies and analytic first derivatives for excited states have been implemented for general coupled-cluster (CC) models within CC linear-response (LR) theory which is equivalent to the equation-of-motion (EOM) CC approach for these quantities. Transition moments between the ground and excited states are also considered in the framework of linear-response theory. The presented procedures are applicable to both single-reference-type and multireference-type CC wave functions independently of the excitation manifold constituting the cluster operator and the space in which the effective Hamiltonian is diagonalized. The performance of different LR-CC/EOM-CC and configuration-interaction approaches for excited states is compared. The effect of higher excitations on excited-state properties is demonstrated in benchmark calculations for NH(2) and NH(3). As a first application, the stationary points of the S(1) surface of acetylene are characterized by high-accuracy calculations.     

Molecular structure of p-diisocyanobenzene from gas-phase electron diffraction and theoretical calculations and effects of intermolecular interactions in the crystal on the benzene ring geometry

In this study, the molecular structure of p-diisocyanobenzene has been determined by gas-phase electron diffraction and quantum chemical calculations. The electron diffraction intensities from a previous study by Colapietro et al. (J Mol Struct 125:19–32, 1984) have been reanalyzed using geometrical constraints and initial values of vibrational amplitudes from computations. The equilibrium structure of the molecule has D _2h symmetry, whereas the average geometry in the gaseous phase is best described by a non-planar model of C _2v symmetry. The lowering of symmetry is due to large-amplitude motion of the substituents out of the plane of the benzene ring. The non-planar model has an internal ring angle at the ipso position, ∠_aC2–C1–C6 = 120.6 ± 0.2°, about 1° smaller than that from the previous study, but consistent with the quantum chemical calculations. The mean length of the ring C–C bonds and the length of the triple bond are accurately determined as 〈r _g(C–C)〉 = 1.398 ± 0.003 Å and r _g(N≡C) = 1.177 ± 0.002 Å, respectively. Comparison with the gaseous isoelectronic molecules p-diethynylbenzene and p-dicyanobenzene shows that the differences in the mean lengths of the ring C–C bonds and in the lengths of the triple bonds determined by electron diffraction are equal or closely similar to the corresponding differences from quantum chemical calculations. The present experimental value of the ipso angle in free p-diisocyanobenzene is slightly, but significantly smaller than that obtained by X-ray crystallography. The difference is confirmed by computational modeling of the crystal structure and appears to be due to –N≡C···H–C intermolecular interactions in the crystal.     

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

State-of-the-art electronic structure methods have been applied to the simplest prototype of aromatic pi-pi interactions, the benzene dimer. By comparison to results with a large aug-cc-pVTZ basis set, we demonstrate that more modest basis sets such as aug-cc-pVDZ are sufficient for geometry optimizations of intermolecular parameters at the second-order M?ller-Plesset perturbation theory (MP2) level. However, basis sets even larger than aug-cc-pVTZ are important for accurate binding energies. The complete basis set MP2 binding energies, estimated by explicitly correlated MP2-R12/A techniques, are significantly larger in magnitude than previous estimates. When corrected for higher-order correlation effects via coupled cluster with singles, doubles, and perturbative triples [CCSD(T)], the binding energies D(e) (D(0)) for the sandwich, T-shaped, and parallel-displaced configurations are found to be 1.8 (2.0), 2.7 (2.4), and 2.8 (2.7) kcal mol(-1), respectively.     

Beyond the benzene dimer: an investigation of the additivity of pi-pi interactions

The benzene dimer is the simplest prototype of pi-pi interactions and has been used to understand the fundamental physics of these interactions as they are observed in more complex systems. In biological systems, however, aromatic rings are rarely found in isolated pairs; thus, it is important to understand whether aromatic pairs remain a good model of pi-pi interactions in clusters. In this study, ab initio methods are used to compute the binding energies of several benzene trimers and tetramers, most of them in 1D stacked configurations. The two-body terms change only slightly relative to the dimer, and except for the cyclic trimer, the three- and four-body terms are negligible. This indicates that aromatic clusters do not feature any large nonadditive effects in their binding energies, and polarization effects in benzene clusters do not greatly change the binding that would be anticipated from unperturbed benzene-benzene interactions, at least for the 1D stacked systems considered. Three-body effects are larger for the cyclic trimer, but for all systems considered, the computed binding energies are within 10% of what would be estimated from benzene dimer energies at the same geometries.     

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.     

Comparative performance of exchange and correlation density functionals in determining intermolecular interaction potentials of the methane dimer

We have calculated the interaction potentials of the methane dimer for the minimum-energy D(3d) conformation using the density functional theory (DFT) with 90 density functionals chosen from the combinations of nine exchange and 10 correlation functionals. Several hybrid functionals are also considered. While the performance of an exchange functional is related to the large reduced density gradient of the exchange enhancement factor, the correlation energy is determined by the low-density behavior of a correlation enhancement factor. Our calculations demonstrate that the correlation counterpart plays an equally important role as the exchange functional in determining the van der Waals interactions of the methane dimer. These observations can be utilized to better understand the seemingly unsystematic DFT interaction potentials for weakly bound systems.     

Electron and hole mobilities in polymorphs of benzene and naphthalene: role of intermolecular interactions

The hole and electron mobilities of the polymorphs of benzene and naphthalene crystals are estimated through quantum chemical calculations. The reorganization energy (lambda) and the charge-transfer matrix elements (Hmn) calculated for the two molecules reveal that these crystals can be used for dual applications, for both hole and electron conductance. The electron mobilities are five to eight times more than the hole mobilities for benzene while for naphthalene, the hole mobilities are almost an order magnitude more than the electron mobilities. The transfer matrices for both hole and electron conductance decrease monotonically with increase in the intermolecular distances. Calculations for various unique stacked dimers as determined from the radial distribution functions in both the crystals for the two molecules show strong dependence on the orientations of the rings and for similar intermolecular separations; Hmnhole is larger than Hmnelectron. The crystal mobilities are calculated from the weighted average over all the unique pair of molecules. The overall preference in a crystal for hole or electron mobility depends on the mutual competition of lambdahole/lambdaelectron and Hmnhole/Hmnelectron. From our microscopic understanding of essential parameters, specific dimers are identified from the crystalline solids of the two polymorphs and experimental strategies are suggested to enrich such pairs in aggregates for enhancing mobilities for these organic solids.     

A spectroscopically effective molecular mechanics model for the intermolecular interactions of the hydrogen-bonded N-methylacetamide dimer

An MP2/6-31+G¹ calculation of the N-methylacetamide dimer shows that it has two minimum energy structures, both hydrogen bonded with peptide planes roughly perpendicular to each other. A complete molecular mechanics optimization of the dimer has been done, using a model for the intermolecular interactions consisting of charges, atomic dipoles, and van der Waals interactions and the methodology of our spectroscopically determined force field for the intramolecular interactions. The two structures are satisfactorily reproduced, as are their interaction energies, their dipole moments, and, from the point of view of our goal of a spectroscopically accurate force field, their six intermolecular normal mode frequencies.     

The ground-state potential energy function of a beryllium dimer determined using the single-reference coupled-cluster approach

The accurate ground-state potential energy function of the beryllium dimer, Be(2), has been determined from large-scale ab initio calculations using the single-reference coupled-cluster approach in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. Results obtained with the conventional and explicitly-correlated coupled-cluster methods were compared. The scalar relativistic and adiabatic (the diagonal correction) effects were also discussed. The vibration-rotation energy levels of Be(2) were predicted and found to be as accurate as those determined from the empirical potential energy function [J. M. Merritt et al., Science, 2009, 324, 1548]. The potential energy function of Be(2) was determined in this study to have a minimum at 2.444 ? and the well depth of 935 cm(-1).     

Modeling pi-pi interactions with the effective fragment potential method: the benzene dimer and substituents

This study compares the results of the general effective fragment potential (EFP2) method to the results of a previous combined coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] and symmetry-adapted perturbation theory (SAPT) study [Sinnokrot and Sherrill, J. Am. Chem. Soc., 2004, 126, 7690] on substituent effects in pi-pi interactions. EFP2 is found to accurately model the binding energies of the benzene-benzene, benzene-phenol, benzene-toluene, benzene-fluorobenzene, and benzene-benzonitrile dimers, as compared with high-level methods [Sinnokrot and Sherrill, J. Am. Chem. Soc., 2004, 126, 7690], but at a fraction of the computational cost of CCSD(T). In addition, an EFP-based Monte Carlo/simulated annealing study was undertaken to examine the potential energy surface of the substituted dimers.