Cyclic and ladder hydrogen bonded cyanamide oligomers: a density functional theory and many-body analysis approach

This work reports hydrogen bonding interaction in cyclic and ladder oligomers using density functional theory method. Many-body analysis technique has been used to study the nature of interactions between different molecules and their contribution to the binding energy of a respective hydrogen bonded oligomers. Hydrogen bonds in cyclic trimer to pentamer are stronger than those in corresponding ladder structures. Cyanamide monomer shows the lowest energy at B3LYP/aug-cc-pvdz level among different methods used here with the same basis set. The geometrical parameters for cyanamide monomer obtained at B3LYP/aug-cc-pvdz level are in excellent agreement with the experimental determinations. Cyclic structures are more stable than the ladder. In cyclic oligomers not only total two-body energies, but higher body energies also contribute significantly to the binding energy of a respective complex whereas in ladder, only total two-body energies contribute significantly and higher-body energies are almost negligible for cyanamide trimer to pentamer.     

The Generalized Energy‐Based Fragmentation Approach with an Improved Fragmentation Scheme: Benchmark Results and Illustrative Applications

We propose an improved fragmentation scheme for the generalized energy‐based fragmentation (GEBF) approach, which improves the accuracy of the GEBF approach in total energy calculations and intermolecular interactions. The main modification is to introduce some two‐fragment‐centered primitive subsystems, which are neglected in the previous GEBF implementation. Numerical calculations demonstrate that the present GEBF approach can provide more accurate ground‐state energies and intermolecular interactions. The present GEBF approach with the M06‐2X functional and the cc‐pVTZ basis set are employed to investigate the structures and binding energies in two dimeric species, which are related to pseudopolymorphism of a phenyleneethynylene‐based π‐conjugated molecule. A comparison of the binding free energies in a dimeric species and its corresponding model without C? H???F contacts reveal that the substitution of fluorine atoms weakens the binding of monomers in the dimeric species formed by intermolecular O? H???O hydrogen bonds, but strengthens the binding in the dimer formed by the π–π stacking interaction. Therefore, the C? H???F contacts in these two dimeric species are demonstrated to play a less significant role.     

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.     

Many-body interaction in glycine-(water)3 complex using density functional theory method

Various configurations were investigated to find the most stable structures of glycine-(water)3 complex. Five different optimized conformers of glycine-(water)3 complex are obtained from density functional theory calculations using 6-311++G* basis set. Relaxation energy and many body interaction energies (two, three, and four body) are also calculated for these conformers. Out of the five conformers, the most stable conformer has the BSSE corrected total energy -513.917 967 7 Hartree and binding energy -27.28 Kcal/mol. It has been found that the relaxation energies, two body energies and three body energies have significant contribution to the total binding energy whereas four body energies are very small. The chemical hardness and chemical potential also confirmed the stability of the conformer having lowest total energy.     

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.     

Assessment of the pairwise additive approximation and evaluation of many-body terms for water clusters

We have tested the ability of four commonly used density functionals (three of which are semilocal and one of which is nonlocal) to outperform accurate pairwise additive approximations in the prediction of binding energies for a series of water clusters ranging in size from dimer to pentamer. Comparison to results obtained with the Weizmann-1 (W1) level of wave function theory shows that while all density functionals are capable of outperforming the accurate pairwise data, the choice of basis set used is crucial to the performance of the method, and if a poor choice of basis set is made the errors obtained with density functional theory (DFT) can be larger than those obtained with the simple pairwise approximation. We have also compared the binding energies and many-body terms determined with DFT to those obtained with W1, and have found that all semilocal functionals have significant errors in the many-body components of the full interactions energy. Despite this limitation, however, we have found that, of the four functionals tested, PBE1W/MG3S is the most accurate for predicting the binding energies of the clusters.     

Theoretical study on intermolecular interaction of epoxyethane dimer

Ab initio calculations at Hartree–Fock and fourth‐order Mø ller–Plesset (MP4) correlation correction levels with 6‐31G* basis set have been performed on the epoxyethane dimer. Dimer binding energies have been corrected for the basis set superposition error (BSSE) and the zero‐point energy. The greatest corrected dimer binding energy is −8.36 kJ/mol at the MP4/6‐31G*//HF/6‐31G* level. The natural bond orbital analysis has been performed to trace the origin of the weak interactions that stabilize dimer. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 94–98, 2000     

DFT study on cooperativity in the interactions of hydrazoic acid clusters

Density functional theory at the B3LYP level with the 6‐311G** basis set is performed to calculate the systems consisting of up to four hydrazoic acid molecules. The dimers are found to exhibit cyclic and chain structures with N … H contacts at ca. 2.1–2.7 Å. However, there are only cyclic structures with N … H contacts at ca. 2.0–2.3 Å and 2.0–2.1 Å in the trimer and tetramer, respectively. Hydrogen bond distances in the trimer and tetramer are shorter than those in the cyclic dimer as a result of the stronger interaction between molecules. The contribution of cooperative effect to the interaction energy is significant. After the correction of the basis set superposition error and zero‐point energy, the binding energies are ?10.69, ?29.34, and ?54.26 kJ·mol^?1 for the most stable dimer, trimer, and tetramer, respectively. The calculated IR shifts for N? H stretching mode increase with the size of the cluster growths, reaching more than 200 cm^?1 in the tetramer. For the most stable clusters, the transition from the monomer to dimer, dimer to trimer, and trimer to tetramer involve changes of ?14.40, ?25.68, and ?31.88 kJ·mol^?1 for the enthalpies at 298.15 K and 1atm, respectively. We also perform Mulliken populations analysis and find the Mulliken populations on intermolecular N … H increasing in the sequence of the dimer, trimer, and tetramer. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 279–286, 2003     

Perturbative calculation of the Hartree–Fock interaction energy using orthogonalized orbitals

A many‐body perturbation theory based on the partitioning of the dimer Hamiltonian, formulated in an orthogonalized basis set, is used for the calculation of interaction energies at the Hartree–Fock (HF) level. Numerical results for the (HF)₂ and (H₂O)₂ systems in selected geometries are presented. The interaction‐energy components are compared with the results obtained from the standard supermolecular approach and the intermolecular perturbation theory based on the biorthogonal basis set. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 81–88, 1999     

An ab initio benchmark study of hydrogen bonded formamide dimers

The five singly and doubly hydrogen bonded dimers of formamide are calculated at the correlated level by using resolution of identity M?ller-Plesset second-order perturbation theory (RIMP2) and the coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] method. All structures are optimized with the Dunning aug-cc-pVTZ and aug-cc-pVQZ basis sets. The binding energies are extrapolated to the complete basis set (CBS) limit by using the aug-cc-pVXZ (X = D, T, Q) basis set series. The effect of extending the basis set to aug-cc-pV5Z on the geometries and binding energies is studied for the centrosymmetric doubly N-H...O bonded dimer FA1 and the doubly C-H...O bonded dimer FA5. The MP2 CBS limits range from -5.19 kcal/mol for FA5 to -14.80 kcal/mol for the FA1 dimer. The DeltaCCSD(T) corrections to the MP2 CBS limit binding energies calculated with the 6-31+G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets are mutually consistent to within < or =0.03 kcal/mol. The DeltaCCSD(T) correction increases the binding energy of the C-H...O bonded FA5 dimer by 0.4 kcal/mol or approximately 9% over the distance range +/-0.5 Angstrom relative to the potential minimum. This implies that the ubiquitous long-range C-H...O interactions in proteins are stronger than hitherto calculated.     

Model chemistry calculations of thiophene dimer interactions: origin of pi-stacking

The intermolecular interaction energies of thiophene dimers have been calculated by using an aromatic intermolecular interaction (AIMI) model (a model chemistry for the evaluation of intermolecular interactions between aromatic molecules). 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 and perpendicular thiophene dimers are -1.71 and -3.12 kcal/mol, respectively. The substantial attractive interaction in the thiophene 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 rather long-range interactions such as electrostatic and dispersion. The inclusion of electron correlation increases the attraction significantly. The dispersion interaction is found to be the major source of attraction in the thiophene dimer. The calculated total interaction energy of the thiophene dimer is highly orientation dependent. Although electrostatic interaction is substantially weaker than dispersion interaction, it is highly orientation dependent, and therefore electrostatic interaction play an important role in the orientation dependence of the total interaction energy. The large attractive interaction in the perpendicular dimer is the cause of the preference for the herringbone structure in the crystals of nonsubstituted oligothiophenes (alpha-terthienyls), and the steric repulsion between the beta-substituents is the cause of the pi-stacked structure in the crystals of some beta-substituted oligothiophenes.     

1,2,3-三氮杂苯－(水)3复合物多体相互作用

The interaction between 1,2,3-triazine and three water molecules was studied using density functional theory B3LYP method at 6-31-t＋＋G^＊＊ basis set. Various structures for 1,2,3-triazine-（water）n （n= 1, 2, 3） complex were investigated and the different lower energy structures were reported. Many-body analysis was also carded out to obtain relaxation energy and many-body interaction energy （two, three, and four-body）, and the most stable conformer has the basis set superposition error corrected interaction energy of -- 102.61 kJ/mol. The relaxation energy, two- and three-body interactions have significant contribution to the total interaction energy whereas four-body interaction was very small for 1,2,3-triazine-（water）3 complex.     

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 M?ller-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.     

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.     

A theoretical study on the intermolecular interaction of energetic system-Nitromethane dimer

Three optimized geometries of nitromethane dimer have been obtained at the HF/6-31G level.Dimer binding energies have been corrected for the basis set superposition error (BSSE) and the zero point energy.Computed results indicate that the cyclic structure of (CH3NO2)2 is the most stable of three optimized geometries,whose corrected binding energyis 17.29 kJ mol-1 at the MP4SDTQ/6-31G//HF/6-31G level.In the optimized structures of nitromethane dimer,the inter-molecular hydrogen bond has not been found; and the charge-transfer interaction between CH3NO2 subsystems is weak; and the correlation interaction energy makes a little contribution to the intermolecular interaction energy of the dimer.     

Characterization of the potential energy surfaces of two small but challenging noncovalent dimers: (P2)2 and (PCCP)2

This work characterizes eight stationary points of the P₂ dimer and six stationary points of the PCCP dimer, including a newly identified minimum on both potential energy surfaces. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with the second‐order Møller–Plesset (MP2) electronic structure method and six different basis sets: aug‐cc‐pVXZ, aug‐cc‐pV(X+d)Z, and aug‐cc‐pCVXZ where X = T, Q. A new L‐shaped structure with C₂ symmetry is the only minimum for the P₂ dimer at the MP2 level of theory with these basis sets. The previously reported parallel‐slipped structure with C_2h symmetry and a newly identified cross configuration with D₂ symmetry are the only minima for the PCCP dimer. Single point energies were also computed using the canonical MP2 and CCSD(T) methods as well as the explicitly correlated MP2‐F12 and CCSD(T)‐F12 methods and the aug‐cc‐pVXZ (X = D, T, Q, 5) basis sets. The energetics obtained with the explicitly correlated methods were very similar to the canonical results for the larger basis sets. Extrapolations were performed to estimate the complete basis set (CBS) limit MP2 and CCSD(T) binding energies. MP2 and MP2‐F12 significantly overbind the P₂ and PCCP dimers relative to the CCSD(T) and CCSD(T)‐F12 binding energies by as much as 1.5 kcal mol^?1 for the former and 5.0 kcal mol^?1 for the latter at the CBS limit. The dominant attractive component of the interaction energy for each dimer configuration was dispersion according to several symmetry‐adapted perturbation theory analyses. © 2014 Wiley Periodicals, Inc.     

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.     

Theoretical Study on Intermolecular Interactions and Thermodynamic Properties of Nitroamine Dimers

Ab initio self-consistent field(SCF) and Mφller-Plesset correlation correction methods employing 6-31G^** basis set have been applied to the optimizations of nitroamine dimers.The binding energies have been corrected for the basis set superposition error (BSSE) and the zero-point energy.Theree optimized dimers have been obtained.The BSSE corrected binding energy of the most stable dimer is predicted to be -31.85kJ/mol at the MP4/6-31G^**//MP2/6-31G^** level.The energy barriers of the Walden conversion for -NH2 group are 19.7kJ/mol and 18.3kJ/mol for monomer and the most stable dimer,respectively.The molecular interaction makes the internal rotation around N1-N2 even more difficult.The thermodynamic properties of nitroamine and its dimers at different temperatures have been calculated on the basis of vibrational analyses.The change of the Gibbs free energy for the aggregation from monomer to the most stable dimer at standard pressure and 298.2 K is predicted to be 14.05kJ/mol.     

Rapid evaluation of the binding energies between peptide amide and DNA base

The binding energies and the equilibrium hydrogen bond distances as well as the potential energy curves of 20 hydrogen‐bonded amide–base dimers are evaluated from the analytic potential energy function established in our laboratory recently. The analytic potential energy function is used to calculate the N? H···N, N? H···O?C, C? H···N, and C? H···O?C dipole–dipole attractive interaction energies and C?O···O?C, N? H···H? N, and N? H···H? C dipole–dipole repulsive interaction energies in the 20 dimers composed of DNA bases adenine, guanine, cytosine, or thymine and peptide amide. The calculation results show that the potential energy curves obtained from the analytic potential energy function are in good agreement with those obtained from MP2/6‐311+G** calculations by including the basis set superposition error (BSSE) correction. For all the 20 dimers, the analytic potential energy function yields the binding energies of the MP2/6‐311+G** with BSSE correction within the error limits of 0.50 kcal/mol for 19 dimers, only one difference is larger than 0.50 kcal/mol and the difference is only 0.61 kcal/mol. The analytic potential energy function produces the equilibrium hydrogen bond distances of the MP2/6‐311+G** with BSSE correction within the error limits of 0.030 Å for all the 20 dimers. The analytic potential energy function is further applied to four more complicated DNA base‐peptide amide systems involving amino acid side chain and β‐sheet. The values of the binding energies and equilibrium hydrogen bond distances obtained from the analytic potential energy function are also in good agreement with those obtained from MP2 calculations with the BSSE correction. These results demonstrate that the analytic potential energy function can be used to evaluate the binding energies in hydrogen‐bonded peptide amide–DNA base dimers quickly and accurately. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011