Fragment interaction analysis based on local MP2

We have developed a fragment interaction analysis based on local MP2 (FILM) in the context of the fragment molecular orbital (FMO) scheme. The primary purpose of this work is to provide a tool for analyzing inter-fragment interaction associated with dispersion interactions in a large molecule such as protein and DNA. Our implementation of local MP2 (LMP2) is based on the algorithm developed by Pulay and Werner. A potential of FILM was demonstrated using the human immunodeficiency virus type 1 protease (HIV-1 PR) complexed with lopinavir (LPV). The total energy, binding affinity, and inter-fragment interaction energy (IFIE) by the FMO method using LMP2 were compared with those obtained by canonical MP2 and the site-specific information in dispersion interaction was obtained. It turned out that the FILM is a useful tool for analyzing the dispersion interaction between an amino acid residue and a specific site of a ligand.     

Possible improvements of the interaction energy calculated using minimal basis sets

Interaction energies for H₂O·H₂O, H₂O·F^– and H₂O·CH₄ have been calculated using the LCAO MO SCF method with minimal basis sets, and employing the counterpoise method to eliminate the basis set superposition error. The results compare favourably with those obtained using extended basis sets. It is shown that for H₂O·H₂O and for the benzene-carbonyl cyanide complex a large part of the dispersion energy can easily be obtained as a sum of bond-bond dispersion energies calculated from a London-type formula using experimental values of the bond polarizability tensors. By considering the interaction between a water and a glycine molecule it is also shown that the dispersion energy plays an important role in the hydration of organic molecules.On leave from the Quantum Chemistry Laboratory, Institute of Basic Problems of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland     

Basis set effects on the intermolecular interaction of the H2-H2 system obtained using ab initio molecular orbital calculations with the Møller-Plesset perturbation correction

The intermolecular interaction potential of the H₂-H₂ system was calculated by an ab initio molecular orbital method using several basis sets (up to 6-31 lG(3pd)) with inclusion of the electron correlation correction of the Møller-Plesset perturbation method and the basis set superposition error (BSSE) correction of the counterpoise method in order to evaluate the basis set effect. The calculated interaction energies depend strongly on the basis set used. Whereas the interaction energies of the repulsive and coulombic energy components calculated at the Hartree-Fock level are not affected by a change of basis set, the dispersion energy component depends strongly on the basis set used. Parameters of an exp-6-1 type non-bonding interaction potential were optimized on the basis of the MP4(SDTQ)/6-311G(3p) level intermolecular interaction energies of the H₂-H₂ system.     

Binding energy of gas molecule with two pyrazine molecules as organic linker in metal�Corganic framework: its theoretical evaluation and understanding of determining factors

We explored the interactions of gas molecules such as H₂, CH₄, C₂H₄, C₂H₆, CO₂, and CS₂ sandwiched by two pyrazine (Pz) molecules, which were employed as a model of organic linker in the Hofmann-type metal?Corganic framework (MOF). The MP2.5/aug-cc-pVTZ method was employed here, because this method presents almost the same binding energy as that calculated by the CCSD(T)/aug-cc-pVDZ with MP2.5-evaluated basis set extension effects to aug-cc-pVTZ basis set. The binding energy of the gas molecule increases in the order H₂?<?CH₄?<?CO₂?<?C₂H₄????C₂H₆?<?CS₂. The energy decomposition analysis of the interaction energy indicates that the electrostatic term presents the largest contribution to the interaction energy at the Hartree?CFock level. However, the dispersion interaction provides dominant contribution to the total binding energy at correlated level. We newly found a linear correlation between the z-component of polarizability of gas molecules and dispersion energy, where the z-axis was taken to be perpendicular to two Pz rings. These results are useful for understanding and predicting the binding energy of the gas molecule with the organic linkers of MOF.     

氯化亚铜在活性炭载体表面单层分散的密度泛函理论计算

 应用量子化学计算方法研究了活性炭载体表面CuCl活性组分的单层分散行为. 以C16H10,C13H9和C12H12原子簇模型模拟活性炭表面,用密度泛函理论中的B3LYP方法计算得到了CuCl在活性炭表面分散的活性位、稳定构型、相互作用能以及单层分散阈值. 结果表明,CuCl以铜端垂直附着在活性炭表面的顶位和桥位上,相互作用能为76.84～80.79 kJ/mol,单层分散阈值为0.471 g/g. 而XRD测得的单层分散阈值为0.467 g/g,与量子化学计算的结果一致; 按照密置单层模型计算得出的单层分散阈值为0.941 g/g,远大于实验测定结果. 因此,应用量子化学计算方法可以得到活性炭表面活性组分单层分散的丰富信息,并能确定活性组分的单层分散阈值.     

Investigation of the intermolecular interaction in the ethylene dimer by a modified CNDO method

The interaction energy of the ethylene dimer has been calculated for two orientations of the molecules in a modified CNDO method with consideration of the superposition error of the basis set. A comparison with the results of perturbationtheory calculations and nonempirical calculations has been made. The satisfactory agreement between these results and a significant improvement over the CNDO/2 method has been noted.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 5, pp. 529–535, September–October, 1985.     

Corrected small basis set Hartree‐Fock method for large systems

A quantum chemical method based on a Hartree‐Fock calculation with a small Gaussian AO basis set is presented. Its main area of application is the computation of structures, vibrational frequencies, and noncovalent interaction energies in huge molecular systems. The method is suggested as a partial replacement of semiempirical approaches or density functional theory (DFT) in particular when self‐interaction errors are acute. In order to get accurate results three physically plausible atom pair‐wise correction terms are applied for London dispersion interactions (D3 scheme), basis set superposition error (gCP scheme), and short‐ranged basis set incompleteness effects. In total nine global empirical parameters are used. This so‐called Hartee‐Fock‐3c (HF‐3c) method is tested for geometries of small organic molecules, interaction energies and geometries of noncovalently bound complexes, for supramolecular systems, and protein structures. In the majority of realistic test cases good results approaching large basis set DFT quality are obtained at a tiny fraction of computational cost. © 2013 Wiley Periodicals, Inc.     

Density functional theory augmented with an empirical dispersion term. Interaction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations

Standard density functional theory (DFT) is augmented with a damped empirical dispersion term. The damping function is optimized on a small, well balanced set of 22 van der Waals (vdW) complexes and verified on a validation set of 58 vdW complexes. Both sets contain biologically relevant molecules such as nucleic acid bases. Results are in remarkable agreement with reference high-level wave function data based on the CCSD(T) method. The geometries obtained by full gradient optimization are in very good agreement with the best available theoretical reference. In terms of the standard deviation and average errors, results including the empirical dispersion term are clearly superior to all pure density functionals investigated-B-LYP, B3-LYP, PBE, TPSS, TPSSh, and BH-LYP-and even surpass the MP2/cc-pVTZ method. The combination of empirical dispersion with the TPSS functional performs remarkably well. The most critical part of the empirical dispersion approach is the damping function. The damping parameters should be optimized for each density functional/basis set combination separately. To keep the method simple, we optimized mainly a single factor, s(R), scaling globally the vdW radii. For good results, a basis set of at least triple-zeta quality is required and diffuse functions are recommended, since the basis set superposition error seriously deteriorates the results. On average, the dispersion contribution to the interaction energy missing in the DFT functionals examined here is about 15 and 100% for the hydrogen-bonded and stacked complexes considered, respectively.     

A comparative effect of ring annelation on cation-benzene and anion-benzene

DFT/B3LYP calculations were carried out on several π-complexes formed by cations and anions with annelated benzene, respectively. The binding energies obtained with standard method were corrected by basis set superposition error (BSSE) and zero-point energy (ZPE) during the geometry optimization for all complexes at the same levels of theory, respectively. Some different aspects of the π–cation have been compared to those of π–anion, involving in binding energy changes in effect of ring annelation, the aromaticity of the ring upon complexation, Mulliken and NBO charge-transfer. The effect of BSSE correction during the optimization is very important in some π–anion complexes whether or not using diffuse functions in basis set, and results with at least one set of diffuse functions 6-31+G(d) basis set is a little better than results obtained by 6-31G(d, p) basis set for some π–anion especially for F⁻ complexes.     

Quantum-chemical study of interaction of gases with molecular fragment of carbon surface

The atom-atom potential method has been applied in ranking industrial gases in their affinity for carbon surfaces. From an analysis of the Coulombic induction, and dispersion contributions to the total energy, and also an analysis of the repulsion potentials, it has been found that the energy of dispersion interaction is a factor with a substantial influence on the affinity of the molecules for the matrix.Sorption and Fine Inorganic Synthesis Branch, Institute of General and Inorganic Chemistry, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 4, pp. 488–490, July–August, 1991. Original article submitted December 17, 1990.     

Halogen Interactions in Halogenated Oxindoles: Crystallographic and Computational Investigations of Intermolecular Interactions

X-ray structural determinations and computational studies were used to investigate halogen interactions in two halogenated oxindoles. Comparative analyses of the interaction energy and the interaction properties were carried out for Br···Br, C-H···Br, C-H···O and N-H···O interactions. Employing Møller–Plesset second-order perturbation theory (MP2) and density functional theory (DFT), the basis set superposition error (BSSE) corrected interaction energy (E_int(BSSE)) was determined using a supramolecular approach. The E_int(BSSE) results were compared with interaction energies obtained by Quantum Theory of Atoms in Molecules (QTAIM)-based methods. Reduced Density Gradient (RDG), QTAIM and Natural bond orbital (NBO) calculations provided insight into possible pathways for the intermolecular interactions examined. Comparative analysis employing the electron density at the bond critical points (BCP) and molecular electrostatic potential (MEP) showed that the interaction energies and the relative orientations of the monomers in the dimers may in part be understood in light of charge redistribution in these two compounds.     

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.     

A theoretical study of the C–HN hydrogen bond in the methane–ammonia complex

The C–HN hydrogen bond in the methane–ammonia complex is studied by determining its bond dissociation energy (BDE) and the n(N)→σ^*(C–H) interaction. At the MP2(Full)/6-311++G(3df,2p) level of theory with basis set superposition error (BSSE) correction, the BDE was determined to be 2.5 kJ mol⁻¹. The n(N)→σ^*(C–H) interaction at this level of theory was found to be 3.7 kJ mol⁻¹ by natural bond orbital (NBO) analysis. It was also found that the NBO values are in general higher than the BDE values with BSSE correction when they are compared at the same level of theory.     

Study of the hydrogen bond and of the proton transfer between two H2S molecules

The potential energy surface for the H₂S dimer is calculated as the sum of the SCF-MO-LCGO energy with a new, modified, basis set and the estimated dispersion energy. Proton affinities for SH^– and H₂S, and, as their difference, the energy of the proton transfer between two H₂S molecules, are also calculated. Despite the limited basis set used, the results are consistent with experimental data.This work was partly supported by the Polish Academy of Sciences within the project PAN-3.     

DFT study on the intermolecular interactions between Aun (n = 2–4) and thymine

Density functional B3LYP method with 6-31++G** basis set is applied to optimize the geometries of the luteolin, water and luteolin–(H₂O)_n complexes. The vibrational frequencies are also studied at the same level to analyze these complexes. We obtained four steady luteolin–H₂O, nine steady luteolin–(H₂O)₂ and ten steady luteolin–(H₂O)₃, respectively. Theories of atoms in molecules (AIM) and natural bond orbital (NBO) are used to investigate the hydrogen bonds involved in all the systems. The interaction energies of all the complexes corrected by basis set superposition error, are within −13.7 to −82.5 kJ/mol. The strong hydrogen bonding mainly contribute to the interaction energies, Natural bond orbital analysis is performed to reveal the origin of the interaction. All calculations also indicate that there are strong hydrogen bonding interactions in luteolin–(H₂O)_n complexes. The OH stretching modes of complexes are red-shifted relative to those of the monomer.     

Predictions of solvation and vaporization enthalpies. 1.n-alkane +n-alkane solutions

A simple method for the calculation of the enthalpy of solvation is presented and demonstrated for 35 n-alkane + n-alkane solutions at 25°C. There is a good agreement between the predicted and experimental values. The calculation was based on the separation of the solvation enthalpy into the cavity formation and solute-solvent interaction contributions. The former term was determined from the activation enthalpy of the solvent viscous flow and solute molar volume while the latter on the basis of the dispersion energy using van der Waals diameters for n-propyl group. The procedure was also successful in prediction of the vaporization enthalpy of C₅–C₁₇ n-alkanes.     

Analysis of the interaction energy in the Cu+-H2O and Cl−-H2O systems,with CP corrections to the BSSE of the separate terms,and MC simulations of the aqueous systems with and without CP corrections

The interaction energyE of the systems Cu⁺-H₂O and Cl^–-H₂O has been computed over a wide range of distances and orientations with the MINI-1 basis set in the SCF approximation. The interaction energy has been decomposed according to the Kitaura-Morokuma scheme, with and without counterpoise (CP) corrections to the basis set superposition error. The importance of this correction is analysed by its effect upon Monte Carlo calculations of the Cu⁺-water and Cl^–-water systems, using two-body potentials without and with CP corrections. The effect of CP corrections on theE analysis is similar to that found in other systems of analogous composition (of the general type ion plus neutral ligands), but with significant differences in the details. The effect of the CP corrections to the interaction potential, and then on the results of the Monte Carlo simulations, is small for the Cu⁺ ion, but remarkable for the Cl^– ion.     

State to state rotational integral cross sections and rate coefficients of HCP collision with He at low temperature

We report coupled-cluster [CCSD(T)] ab initio calculations of the two-dimensional interaction potential energy surface of the HCP–He complex. The aug-cc-pVTZ and aug-cc-pVQZ gaussian basis sets are used. HCP is held fixed at its linear equilibrium ground vibrational level with the corresponding [H–C] and [C–P] bond lengths set to the values 2.016 bohrs and 2.914 bohrs, respectively. Our calculations are corrected for basis set superposition errors (BSSE). The PES obtained with the above triple zeta basis set has two minima located 22.018 cm⁻¹ and 14.808 cm⁻¹ below the HCP+He dissociation limit. These well depths are shifted to 23.505 cm⁻¹ and 15.949 cm⁻¹, respectively, when the quadruple zeta basis set is used. Our PESs are fitted on a basis of Legendre polynomial functions and state to state rotational integral cross sections of the HCP collision with He are calculated in the close-coupling (CC) approximation. Downward rate coefficients are inferred at low temperature () by averaging the cross sections over a Maxwell–Boltzmann velocity distribution. An analysis of our results shows that for kinetic energies greater than 60 cm⁻¹, the 0→2 transition dominates. The numbers derived here may be very useful for astrophysical observations.     

Removal of dependencies from nearly complete basis sets. Calculations on the helium dimer

A method is devised for dealing with almost linearly dependent basis sets that contain large sets of bond functions. Using the largest of such basis sets, LARSAT, the second-order Møller-Plesset polarization dispersion energy of the helium dimer is calculated to be - 17.08 K at R = 5.6 bohrs. MR-SDCI calculations, employing a set of 37 reference configurations, were performed for the helium dimer with several basis sets at 4.0 and 5.6 bohrs. Size-extensivity corrections were included to take into account the R dependency of the size-extensivity error in MR-SDCI calculations. The He₂ interaction energies computed with basis LARSAT are - 10.92 K at 5.6 bohrs and 295.1 K at 4.0 bohrs. The 37-MR-SDCI calculations with basis LARSAT almost reproduce the He₂ full configuration interaction (CI) interaction energies computed with the same basis, at notably smaller cost. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 805–815, 1997