Is spin-component scaled second-order Møller-Plesset perturbation theory an appropriate method for the study of noncovalent interactions in molecules?

Testing of the spin-component scaled second-order M?ller-Plesset (SCS-MP2) method for the computation of noncovalent interaction energies is done with a database of 165 biologically relevant complexes. The effects of the spin-scaling procedure (i.e., MP2 vs SCS-MP2), the basis set size, and the corrections for basis set superposition error (BSSE) are systematically examined. When using two-point basis set extrapolations for the correlation energy, augmentation of the atomic orbital basis with computationally costly diffuse functions is found to be obsolete. In general, SCS-MP2 also improves results for noncovalent interactions statistically on MP2, and significant outliers are removed. Moreover, it is shown that effects of BSSE and one-particle basis set incompleteness almost cancel each other in the case of triple-zeta sets (SCS-MP2/TZVPP or SCS-MP2/cc-pVTZ without counterpoise correction), which opens a practical route to efficient computations for large systems. We recommend SCS-MP2 as the preferred quantum chemical wave function based method for the noncovalent interactions in large biologically relevant systems when reasonable coupled-cluster with single and double and perturbative triple excitations (CCSD(T)) calculations cannot be performed anymore. A comparison to MP2 and CCSD(T) interaction energies for n-alkane dimers, however, indicates (and this also holds to a lesser extent for hydrogen-bonded systems) limitations of SCS-MP2 when treating chemically "saturated" interactions. The different behavior of second-order perturbation theory for saturated and for stacked pi-systems is discussed.     

Assessment of the performance of MP2 and MP2 variants for the treatment of noncovalent interactions

For many years, MP2 served as the principal method for the treatment of noncovalent interactions. Until recently, this was the only technique that could be used to produce reasonably accurate binding energies, with binding energy errors generally below ~35%, at a reasonable computational cost. The past decade has seen the development of many new methods with improved performance for noncovalent interactions, several of which are based on MP2. Here, we assess the performance of MP2, LMP2, MP2-F12, and LMP2-F12, as well as spin component scaled variants (SCS) of these methods, in terms of their abilities to produce accurate interaction energies for binding motifs commonly found in organic and biomolecular systems. Reference data from the newly developed S66 database of interaction energies are used for this assessment, and a further set of 38 complexes is used as a test set for SCS methods developed herein. The strongly basis set-dependent nature of MP2 is confirmed in this study, with the SCS technique greatly reducing this behavior. It is found in this work that the spin component scaling technique can effectively be used to dramatically improve the performance of MP2 and MP2 variants, with overall errors being reduced by factors of about 1.5-2. SCS versions of all MP2 variants tested here are shown to give similarly accurate overall results.     

The performance of MP2.5 and MP2.X methods for nonequilibrium geometries of molecular complexes

Here we test the performance of the newly developed MP2.5 and MP2.X methods in terms of their abilities to generate accurate binding energies for noncovalently bound complexes at points away from their minimum energy structures and in terms of the accuracy of their potential energy minima. The MP2.X method is a scaled version of MP2.5 that allows for the use of smaller basis sets for the most computationally demanding (MP3) term, significantly reducing its computational cost. MP2.5 and MP2.X binding energy errors are compared to those of the reference CCSD(T)/CBS method on the dissociation curves associated with the S66 dataset of noncovalent complexes (S66x8). It is found that both the MP2.5 and MP2.X methods produce binding energy errors, as well as potential energy minima, that are significantly more accurate than those of MP2 methods. Thus, these methods are appropriate choices when very high quality geometries of noncovalent complexes are required.     

Evaluation of the performance of post-Hartree-Fock methods in terms of intermolecular distance in noncovalent complexes

Dissociation curves calculated using multiple correlated QM methods for 66 noncovalent complexes (?ezá? et al., J Chem Theory Comput 2011, 7, 2427) have allowed us to interpolate equilibrium intermolecular distances for each studied method. Comparison of these data with CCSD(T)/complete basis set reference geometries provides information on how these methods perform in geometry optimizations. The large set of systems considered here is necessary for reliable statistical evaluation of the results and assessment of the robustness of the studied methods. Our results show that advanced methods such as MP3 and CCSD provide significant improvement over MP2 only when empirical scaling is used. The best results can be achieved with spin component scaled CCSD optimized for noncovalent interactions, with a root mean square error of 0.4% of the equilibrium distance. Scaled MP3, the MP2.5 method, yields comparably good results (error 0.5%) while being substantially cheaper. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2012     

Performance of the DFT-D method, paired with the PCM implicit solvation model, for the computation of interaction energies of solvated complexes of biological interest

In this work we investigate the performance of the DFT method, augmented with an empirical dispersion function (DFT-D), paired with the PCM implicit solvation model, for the computation of noncovalent interaction energies of biologically-relevant, solvated model complexes. It is found that this method describes intermolecular interactions within water and ether (protein-like) environments with roughly the same accuracy as in the gas phase. Another important finding is that, when environmental effects are taken into account, the empirical dispersion term associated with the DFT-D method need be modified very little (or not at all), in order to obtain the optimum, most well balanced, performance.     

Application of polarizable ellipsoidal force field model to pnicogen bonds

Noncovalent interactions, such as hydrogen bonds and halogen bonds, are frequently used in drug designing and crystal engineering. Recently, a novel noncovalent pnicogen bonds have been identified as an important driving force in crystal structures with similar bonding mechanisms as hydrogen bond and halogen bond. Although the pnicogen bond is highly anisotropic, the pnicogen bond angles range from 160° to 180° due to the complicated substituent effects. To understand the anisotropic characters of pnicogen bond, a modification of the polarizable ellipsoidal force field (PEff) model previously used to define halogen bonds was proposed in this work. The potential energy surfaces (PESs) of mono‐ and polysubstituted PH₃–NH₃ complexes were calculated at CCSD(T), MP2, and density functional theory levels and were used to examine the modified PEff model. The results indicate that the modified PEff model can precisely characterize pnicogen bond. The root mean squared error of PES obtained with PEff model is less than 0.5 kcal/mol, compared with MP2 results. In addition, the modified PEff model may be applied to other noncovalent bond interactions, which is important to understand the role of intermolecular interactions in the self‐assembly structures. © 2015 Wiley Periodicals, Inc.     

Quantification of binding affinities of essential sugars with a tryptophan analogue and the ubiquitous role of C-H···π interactions

The role of noncovalent interactions in carbohydrate recognition by aromatic amino acids has long been reported. To develop a molecular understanding of noncovalent interactions in the recognition process, we have examined a series of binary complexes between 3-methylindole (3-MeIn) and sugars. In particular, the geometries and binding affinities of 3-MeIn with α/β-D-glucose, β-D-galactose, α-D-mannose and α/β-L-fucose are obtained using the MP2(full)/6-31G(d,p) and the M06/TZV2D//MP2/6-31G(d,p) level of theories. The conventional hydrogen bonding such as N-H···O and C-H···O as well as nonconventional O-H···π and C-H···π type of interactions is, in general, identified as responsible for the moderately strong interaction energies. Large variations in the position-orientations of 3-MeIn with respect to saccharide are noticed, within the same sugar family, as well as across different sugar series. Furthermore, complexes with large differences in their geometries are recognized as capable of exhibiting very similar interaction energies, underscoring the significance of exhaustive conformation sampling, as carried out in the present study. These observations are readily attributed to the differences in the efficiency of the type of interactions enlisted above. The highest and lowest interaction energies, upon inclusion of 50% BSSE correction, are found to be -16.02 and -6.22 kcal mol(-1), respectively, for α-D-glucose (1a) and α-L-fucose (5j). While more number of prominent conventional hydrogen bonding contacts remains as a characteristic feature of the strongly bound complexes, the lower end of the interaction energy spectrum is dominated by multiple C-H···π interactions. The complexes exhibiting as many as four C-H···π contacts are identified in the case of α/β-D-glucose, β-D-galactose, and α/β-L-fucose with an interaction energy hovering around -8 kcal mol(-1). The presence of effective C-H···π interactions is found to be dependent on the saccharide configuration as well as the area of the apolar patch constituted by the C-H groups. The study offers a comprehensive set of binary complexes, across different saccharides, which serves as an illustration of the significance and ubiquitous nature of C-H···π interactions in carbohydrate binding in saccharide-protein complexes.     

Prediction of geometries and interaction energies of complexes formed by small molecules using semiempirical and ab initio methods

The accuracy of the semiempirical quantum mechanics methods (AM1 and PM3), and the ab initio methods (6-31G^** and MP2/6-31G^**) in predicting intermolecular geometries and interaction energies have been evaluated by detailed studies of 17 bimolecular complexes formed by small molecules. Comparisons between calculated and experimental geometries for 12 complexes are presented. It was found that AM1 gave reasonably good predictions of the geometries of complexes such as CH₄ · CH₄, which have very weak interactions, but it is not as good as other methods in predicting intermolecular geometry for complexes where hydrogen bonding interactions play an important role. This is consistent with its inability to reproduce the charge transfer in the formation of hydrogen bonds in these complexes.

PM3 is able to predict intermolecular geometries for most complexes, including those with hydrogen bonding; its major flaw is its tendency to overestimate the strength of the interactions between hydrogen atoms. Care should be taken therefore in using PM3 to study complicated molecular systems with multiple hydrogen atom interactions and the method's weakness in handling complexes in which electrostatic forces are important should also be noted.

Among ab initio methods, both the 6-31G^** and the MP2/6-31G^** were found to outperform AM1 and PM3 in prediction of intermolecular geometry. Both of these ab initio methods showed excellent consistency in geometry prediction for most of the complexes studied, although MP2/6-31G^** is better than 6-31G^**. It is noted that the MP2/6-31G^** did not produce the correct geometry for the CO₂· HF complex.

For 12 complexes for which experimental geometry data are available, AM1, PM3, 6-31G^**, and MP2/6-31G^** successfully predicted the geometry in 10, 12, 12, and 11 cases, respectively. The average errors given by AM1 in the predicted intermolecular distances were 0.264, 0.272, 0.091, and 0.061 Å, respectively. In comparison to the ab initio methods, AM1 and PM3 commonly underestimated the molecular interaction energy in such complexes by ˜ 1–2 kcal mol⁻¹.     

On the accuracy of DFT-SAPT, MP2, SCS-MP2, MP2C, and DFT+Disp methods for the interaction energies of endohedral complexes of the C(60) fullerene with a rare gas atom

Selected points on the potential energy surface for the complexes Rg@C(60) (Rg = He, Ne, Ar, Kr) are calculated with various theoretical methods, like symmetry-adapted perturbation theory with monomers described by density functional theory (DFT-SAPT), supermolecular M?ller-Plesset theory truncated on the second order (MP2), spin-component-scaled MP2 (SCS-MP2), supermolecular density functional theory with empirical dispersion correction (DFT+Disp), and the recently developed MP2C method that improves the MP2 method for long-range electron correlation effects. A stabilization of the endohedral complex is predicted by all methods, but the depth of the potential energy well is overestimated by the DFT+Disp and MP2 approaches. On the other hand, the MP2C model agrees well with DFT-SAPT, which serves as the reference. The performance of SCS-MP2 is mixed: it produces too low interaction energies for the two heavier guests, while its accuracy for He@C(60) and Ne@C(60) is similar to that of MP2C. Fitting formulas for the main interaction energy components, i.e. the dispersion and first-order repulsion energies are proposed, which are applicable for both endo- and exohedral cases. For all examined methods density fitting is used to evaluate two-electron repulsion integrals, which is indispensable to allow studies of noncovalent complexes of this size. It has been found that density-fitting auxiliary basis sets cannot be used in a black-box fashion for the calculation of the first-order SAPT electrostatic energy, and that the quality of these basis sets should be always carefully examined in order to avoid an unphysical long-range behavior.     

A polarizable dipole–dipole interaction model for evaluation of the interaction energies for NH···OC and CH···OC hydrogen‐bonded complexes

In this article, a polarizable dipole–dipole interaction model is established to estimate the equilibrium hydrogen bond distances and the interaction energies for hydrogen‐bonded complexes containing peptide amides and nucleic acid bases. We regard the chemical bonds N? H, C?O, and C? H as bond dipoles. The magnitude of the bond dipole moment varies according to its environment. We apply this polarizable dipole–dipole interaction model to a series of hydrogen‐bonded complexes containing the N? H···O?C and C? H···O?C hydrogen bonds, such as simple amide‐amide dimers, base‐base dimers, peptide‐base dimers, and β‐sheet models. We find that a simple two‐term function, only containing the permanent dipole–dipole interactions and the van der Waals interactions, can produce the equilibrium hydrogen bond distances compared favorably with those produced by the MP2/6‐31G(d) method, whereas the high‐quality counterpoise‐corrected (CP‐corrected) MP2/aug‐cc‐pVTZ interaction energies for the hydrogen‐bonded complexes can be well‐reproduced by a four‐term function which involves the permanent dipole–dipole interactions, the van der Waals interactions, the polarization contributions, and a corrected term. Based on the calculation results obtained from this polarizable dipole–dipole interaction model, the natures of the hydrogen bonding interactions in these hydrogen‐bonded complexes are further discussed. © 2013 Wiley Periodicals, Inc.     

Anion-aromatic bonding: a case for anion recognition by pi-acidic rings

The basis for unprecedented noncovalent bonding between anions and the aryl centroid of electron-deficient aromatic rings has been demonstrated by an ab initio study of the interaction between 1,3,5-triazine and the fluoride, chloride, and azide ion at the MP2 level of theory. Minima are also located corresponding to C[bond]H...X(-) hydrogen bonding, reactive complexes for nucleophilic attack on the triazine ring, and pi-stacking interactions (with azide). Trifluoro-1,3,5-triazine also participates in aryl centroid complexation and forms nucleophilic reactive complexes with anions. This novel mode of bonding suggests the development of new cyclophane-type receptors for the recognition of anions.     

An MP2 and DFT study of heterocyclic hydrogen complexes CnHmY-HX with n=2, m=4 or 5, Y=O, S or N and X=F or Cl

We present a theoretical study through MP2 ab initio molecular orbital calculations and B3LYP density functional theory with the 6-311++G(d,p) basis set of the heterocyclic hydrogen complexes, CnHmY-HX, where CnHmY = C2H4O, C2H5N and C2H4S, and X=F or Cl. This study aided in the elucidation the main changes in the structural, electronic and the vibrational properties in isolated species, due the hydrogen complexes formation, CnHmY-HX, revealing systematic tendencies in these chemical systems studied. The complexes has CS symmetry, with the HX subunit lying in the plane perpendicular to that of CYC nuclei of heterocyclic and acting as proton donor in forming a hydrogen bond to the heteroatom, Y. A weak secondary interaction between the CH2 groups of heterocyclics and the X atoms in HX causes a significant nonlinearity of the primary hydrogen bond. The hydrogen bond linearity deviations in these complexes due to secondary interactions are represented by theta angle. The MP2 intermolecular distances of complexes C2H5N-HF, C2H4O-HF and C2H4S-HF correspond the 1.652, 1.671 and 2.164 A, respectively, these results are in excellent agreement with experimental results of 1.700 and 2.193 A found for the last two complexes. In the same way, the MP2 values to theta angle, 14.7, 19.1 and 16.8 degrees, has a better reproduction in the experimental results of 16.5, 21.0 and 16.8 degrees, get to the C2H4O-HCl, C2H4S-HCl and C2H4S-HF complexes, respectively.     

PO2X…PX3/PH2X(X=F,Cl, Br,CH3, NH2)复合物中π-hole磷键作用的电子密度拓扑分析

磷键作为一种新型的分子键合力,因在晶体工程和超分子合成等方面的重要作用而越来越多地引起科研工作者的广泛关注。本文采用量子化学从头算和电子密度拓扑分析等方法,在MP2/aug-cc-pVTZ理论水平上,对PO₂X…PX₃和PO₂X…PH₂X (X = F, Cl, Br, CH₃, NH₂) π型复合物的结构和磷键性质进行了理论研究。研究表明:π-hole磷键复合物存在A和B两种稳定构型,分别以P…P和P…X磷键作用为主。分子中原子(AIM)、非共价作用(NCI)、电子定域函数(ELF)及适应性自然密度划分(AdNDP)分析表明,不同取代基对该类磷键作用的性质产生很大影响:当取代基为给电子基(CH₃, NH₂)时,磷键具有明显的共价作用特征;当取代基为吸电子基(F, Cl, Br)时,构型和取代基不同的磷键分别表现为非共价、部分共价或共价作用特征。自然键轨道(NBO)分析指出,分子间磷键的Wiberg键级的数值越大,磷键的共价性越强,磷键的作用强度越大。构型B的电荷转移主要是PX₃/PH₂X中X原子上的孤对电子转移到PO₂X中π^*(P=O)反键空轨道。     

Ab initio investigation of the complexes between bromobenzene and several electron donors: some insights into the magnitude and nature of halogen bonding interactions

Halogen bonding, a specific intermolecular noncovalent interaction, plays crucial roles in fields as diverse as molecular recognition, crystal engineering, and biological systems. This paper presents an ab initio investigation of a series of dimeric complexes formed between bromobenzene and several electron donors. Such small model systems are selected to mimic halogen bonding interactions found within crystal structures as well as within biological molecules. In all cases, the intermolecular distances are shown to be equal to or below sums of van der Waals radii of the atoms involved. Halogen bonding energies, calculated at the MP2/aug-cc-pVDZ level, span over a wide range, from -1.52 to -15.53 kcal/mol. The interactions become comparable to, or even prevail over, classical hydrogen bonding. For charge-assisted halogen bonds, calculations have shown that the strength decreases in the order OH- > F- > HCO2- > Cl- > Br-, while for neutral systems, their relative strengths attenuate in the order H2CS > H2CO > NH3 > H2S > H2O. These results agree with those of the quantum theory of atoms in molecules (QTAIM) since bond critical points (BCPs) are identified for these halogen bonds. The QTAIM analysis also suggests that strong halogen bonds are more covalent in nature, while weak ones are mostly electrostatic interactions. The electron densities at the BCPs are recommended as a good measure of the halogen bond strength. Finally, natural bond orbital (NBO) analysis has been applied to gain more insights into the origin of halogen bonding interactions.     

Interplay between edge-to-face aromatic and hydrogen-bonding interactions

The interplay between two important noncovalent interactions involving aromatic rings is studied by means of MP2/6-31++G** ab initio calculations. They indicate that synergistic effects are present in complexes where edge-to-face aromatic interactions and hydrogen-bonding interactions coexist. These synergistic effects have been studied bu using the atoms in molecules theory and the molecular interaction potential with polarization partition scheme. Experimental evidence for such interactions has been obtained from the Cambridge Structural Database.     

Hydrocarbons as proton donors in C–H⋯N and C–H⋯S hydrogen bonds

C–H?N and C–H?S hydrogen bonds were analyzed in complexes where acetylene, ethylene, methane and their derivatives are proton donors while ammonia and hydrogen sulfide are proton acceptors. Ab initio calculations were performed to analyze those interactions; MP2 method was applied and the following basis sets were used: 6-311++G(d,p), aug-cc-pVDZ and aug-cc-pVTZ. The results showed that hydrogen bonds for complexes with ammonia are systematically stronger than such interactions in complexes with hydrogen sulfide. If the fluorine substituted hydrocarbons are considered then F-substituents enhance the strength of hydrogen bonding. For a few complexes, mainly those where carbon atom in proton donating C–H bond possesses sp³ hybridization, the blue-shifting hydrogen bonds were detected. Additionally, Quantum Theory of ‘Atoms in Molecules’ and Natural Bond Orbitals method were applied to analyze H-bond interactions.     

Intermolecular interactions of formic acid with benzene: Energy decomposition analyses with ab initio MP2 and double‐hybrid density functional computations

The intermolecular interactions of formic acid (HCOOH) with benzene (C₆H₆) have been investigated using localized molecular orbital energy decomposition analyses (LMO‐EDA) with ab initio MP2 and several double‐hybrid density functionals. The molecular geometries of five HCOOH…C₆H₆ complexes and corresponding benchmark total interaction energies at the CCSD(T)/CBS level are taken from literature (Zhao et al., J. Chem. Theory Comput. 2009, 5, 2726). According to the results of LMO‐EDA with the MP2 method, the dispersion energies are found to be as important as the electrostatic energies for the total interaction energies of the five HCOOH…C₆H₆ complexes. Based on LMO‐EDA with the double‐hybrid density functionals of B2PLYP, B2K‐PLYP, B2T‐PLYP, and B2GP‐PLYP computations, two new parameters for the framework of B2PLYP are extrapolated. These two new parameters are tested with other 10 complexes involving C₆H₆ (Crittenden, J. Phys. Chem. A 2009, 113, 1663), and they perform well on predicting the corresponding total interaction energies. Interestingly, these two new parameters for the framework of B2PLYP also perform well on the noncovalent complexation energies database (NCCE31/05) developed by Truhlar's group (Zhao and Truhlar, J. Phys. Chem. A 2005, 109, 5656). Therefore, these two new parameters appear to be suitable for investigating the noncovalent interactions, and they are denoted as B2N‐PLYP, where N stands for the noncovalent interaction. This study is expected to provide new insight into the derivation of double‐hybrid density functionals for studying the noncovalent interactions. © 2013 Wiley Periodicals, Inc.     

Strength and nature of hydrogen bonding interactions in mono- and di-hydrated formamide complexes

In this work, mono- and di-hydrated complexes of the formamide were studied. The calculations were performed at the MP2/6-311++G(d,p) level of approximation. The atoms in molecules theory (AIM), based on the topological properties of the electronic density distribution, was used to characterize the different types of bonds. The analysis of the hydrogen bonds (H-bonds) in the most stable mono- and di-hydrated formamide complexes shows a mutual reinforcement of the interactions, and some of these complexes can be considered as "bifunctional hydrogen bonding hydration complexes". In addition, we analyzed how the strength and the nature of the interactions, in mono-hydrated complexes, are modified by the presence of a second water molecule in di-hydrated formamide complexes. Structural changes, cooperativity, and electron density redistributions demonstrate that the H-bonds are stronger in the di-hydrated complexes than in the corresponding mono-hydrated complexes, wherein the σ- and π-electron delocalization were found. To explain the nature of such interactions, we carried out the atoms in molecules theory in conjunction with reduced variational space self-consistent field (RVS) decomposition analysis. On the basis of the local Virial theorem, the characteristics of the local electron energy density components at the bond critical points (BCPs) (the 1/4? (2)ρ(b) component of electron energy density and the kinetic energy density) were analyzed. These parameters were used in conjunction with the electron density and the Laplacian of the electron density to analyze the characteristics of the interactions. The analysis of the interaction energy components for the systems considered indicates that the strengthening of the hydrogen bonds is manifested by an increased contribution of the electrostatic energy component represented by the kinetic energy density at the BCP.     

Ab initio study of chiral recognition in the propylene imine.hydrogen peroxide complex

High level ab initio calculations were employed to study the chiral recognition effect in several chiral molecular pairs that consist of the propylene imine and hydrogen peroxide molecules. The potential energy surfaces for the complexes formed between S-cis-1,2-propylene imine and the two enantiomeric forms of hydrogen peroxide were constructed, using the calculated interaction energies at different separations and orientations. The energy calculations were done using the MOLPRO suite of programs with CCSD(T)/cc-pVDZ. The energies were counterpoise corrected at every point to eliminate the basis set superposition error. Complete geometry optimizations were further carried out for the molecular complexes consisting of the cis- or trans-propylene imine isomers and the two enantiomeric forms of hydrogen peroxide. The geometry optimizations were done using the Gaussian 98 and 03 suites of programs, with MP2/aug-cc-pVDZ being the highest level used. Altogether, eight stable complexes were identified, and the corresponding dissociation energies were calculated with MP2/aug-cc-pVTZ. The largest chirodiastaltic energy is found at 0.74 kcal mol(-1) for the (syn)trans-propylene imine.hydrogen peroxide complexes, where hydrogen peroxide acts as a hydrogen donor and is on the opposite side of the ring from the methyl group. The rotational constants, dipole moments, and harmonic frequencies of the complexes are presented to assist future spectroscopic investigations.