Application of semiempirical long-range dispersion corrections to periodic systems in density functional theory

Ewald summation is used to apply semiempirical long-range dispersion corrections (Grimme, J Comput Chem 2006, 27, 1787; 2004, 25, 1463) to periodic systems in density functional theory. Using the parameters determined before for molecules and the Perdew-Burke-Ernzerhof functional, structure parameters and binding energies for solid methane, graphite, and vanadium pentoxide are determined in close agreement with observed values. For methane, a lattice constant a of 580 pm and a sublimation energy of 11 kJ mol(-1) are calculated. For the layered solids graphite and vanadia, the interlayer distances are 320 pm and 450 pm, respectively, whereas the graphite interlayer energy is -5.5 kJ mol(-1) per carbon atom and layer. Only when adding the semiempirical dispersion corrections, realistic values are obtained for the energies of adsorption of C(4) alkenes in microporous silica (-66 to -73 kJ mol(-1)) and the adsorption and chemisorption (alkoxide formation) of isobutene on acidic sites in the micropores of zeolite ferrierite (-78 to -94 kJ mol(-1)). As expected, errors due to missing self-interaction correction as in the energy for the proton transfer from the acidic site to the alkene forming a carbenium ion are not affected by the dispersion term. The adsorption and reaction energies are compared with the results from M?ller-Plesset second-order perturbation theory with basis set extrapolation.     

Local quantum chemistry: The local space approximation for Møller–Plesset perturbation theory

The local space approximation is an accurate technique for describing a relatively small cluster embedded within an extended system. It has previously been developed for the Hartree-Fock, local density functional, configuration interaction, and coupled cluster electronic structure methods. Here it is extended to Møller-Plesset perturbation theory. © 1995 John Wiley & Sons, Inc.     

The gaseous enthalpy of formation of the ionic liquid 1-butyl-3-methylimidazolium dicyanamide from combustion calorimetry, vapor pressure measurements, and ab initio calculations

Ionic liquids are attracting growing interest as alternatives to conventional molecular solvents. Experimental values of vapor pressure, enthalpy of vaporization, and enthalpy of formation of ionic liquids are the key thermodynamic quantities, which are required for the validation and development of the molecular modeling and ab initio methods toward this new class of solvents. In this work, the molar enthalpy of formation of the liquid 1-butyl-3-methylimidazolium dicyanamide, 206.2 +/- 2.5 kJ.mol-1, was measured by means of combustion calorimetry. The molar enthalpy of vaporization of 1-butyl-3-methylimidazolium dicyanamide, 157.2 +/- 1.1 kJ.mol-1, was obtained from the temperature dependence of the vapor pressure measured using the transpiration method. The latter method has been checked with measurements of 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide, where data are available from the effusion technique. The first experimental determination of the gaseous enthalpy of formation of the ionic liquid 1-butyl-3-methylimidazolium dicyanamide, 363.4 +/- 2.7 kJ.mol-1, from thermochemical measurements (combustion and transpiration) is presented. Ab initio calculations of the enthalpy of formation in the gaseous phase have been performed for 1-butyl-3-methylimidazolium dicyanamide using the G3MP2 theory. Excellent agreement with experimental results has been observed. The method developed opens a new way to obtain thermodynamic properties of ionic liquids which have not been available so far.     

Computational study of hydrogen binding by metal-organic framework-5

We report the results of quantum chemistry calculations on H(2) binding by the metal-organic framework-5 (MOF)-5. Density functional theory calculations were used to calculate the atomic positions, lattice constant, and effective atomic charges from the electrostatic potential for the MOF-5 crystal structure. Second-order M?ller-Plesset perturbation theory was used to calculate the binding energy of H(2) to benzene and H(2)-1,4-benzenedicarboxylate-H(2). To achieve the necessary accuracy, the large Dunning basis sets aug-cc-pVTZ, and aug-cc-pVQZ were used, and the results were extrapolated to the basis set limit. The binding energy results were 4.77 kJ/mol for benzene, 5.27 kJ/mol for H(2)-1,4-benzenedicarboxylate-H(2). We also estimate binding of 5.38 kJ/mol for Li-1,4-benzenedicarboxylate-Li and 6.86 kJ/mol at the zinc oxide corners using second-order M?ller-Plesset perturbation theory. In order to compare our theoretical calculations to the experimental hydrogen storage results, grand canonical Monte Carlo calculations were performed. The Monte Carlo simulations identify a high energy binding site at the corners that quickly saturated with 1.27 H(2) molecules at 78 K. At 300 K, a broad range of binding sites are observed.     

Performance of dispersion-corrected density functional theory for the interactions in ionic liquids

Potential energy curves for the dissociation of cation-anion associates representing the building units of ionic liquids have been computed with dispersion corrected DFT methods. Non-local van der Waals density functionals (DFT-NL) for the first time as well as an atom pair-wise correction method (DFT-D3) have been tested. Reference data have been computed at the extrapolated MP2/CBS and estimated CCSD(T)/CBS levels of theory. The investigated systems are combined from two cations (1-butyl-3-methylimidazolium and tributyl(methyl)posphonium) and three anions (chloride, dicyanamide, acetate). We find substantial stabilization from London dispersion energy near equilibrium of 5-7 kcal mol(-1) (about 5-6% of the interaction energy). Equilibrium distances are shortened by 0.03-0.09 ? and fundamental (inter-fragment) vibrational frequencies (which are in the range 140-180 cm(-1)) are increased by typically 10 cm(-1) when dispersion corrections are made. The dispersion-corrected hybrid functional potentials are in general in excellent agreement with the corresponding CCSD(T) reference data (typical deviations of about 1-2%). The DFT-D3 method performs unexpectedly well presumably because of cancellation of errors between the dispersion coefficients of the cations and anions. Due to self-interaction error, semi-local density functionals exhibit severe SCF convergence problems, and provide artificial charge-transfer and inaccurate interaction energies for larger inter-fragment distances. Although these problems may be alleviated in condensed phase simulations by effective Coulomb screening, only dispersion-corrected hybrid functionals with larger amounts of Fock-exchange can in general be recommended for such ionic systems.     

Ab initio benchmark study for the oxidative addition of CH4 to Pd: importance of basis-set flexibility and polarization

To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order M?ller-Plesset perturbation theory, fourth-order M?ller-Plesset perturbation theory with single, double and quadruple excitations, coupled cluster theory with single and double excitations (CCSD), and with triple excitations treated perturbatively [CCSD(T)]) and hybrid density functional theory using the B3LYP functional, in combination with a hierarchical series of ten Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Counterpoise corrected relative energies of stationary points are converged to within 0.1-0.2 kcal/mol as a function of the basis-set size. Our best estimate of kinetic and thermodynamic parameters is -8.1 (-8.3) kcal/mol for the formation of the reactant complex, 5.8 (3.1) kcal/mol for the activation energy relative to the separate reactants, and 0.8 (-1.2) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). This agrees well with available experimental data. Our work highlights the importance of sufficient higher angular momentum polarization functions, f and g, for correctly describing metal-d-electron correlation and, thus, for obtaining reliable relative energies. We show that standard basis sets, such as LANL2DZ+1f for palladium, are not sufficiently polarized for this purpose and lead to erroneous CCSD(T) results. B3LYP is associated with smaller basis set superposition errors and shows faster convergence with basis-set size but yields relative energies (in particular, a reaction barrier) that are ca. 3.5 kcal/mol higher than the corresponding CCSD(T) values.     

Quantum Monte Carlo study of the reaction: Cl+CH3OH-->CH2OH+HCl

A theoretical study is reported of the Cl+CH3OH-->CH2OH+HCl reaction based on the diffusion Monte Carlo (DMC) variant of the quantum Monte Carlo method. Using a DMC trial function constructed as a product of Hartree-Fock and correlation functions, we have computed the barrier height, heat of reaction, atomization energies, and heats of formation of reagents and products. The DMC heat of reaction, atomization energies, and heats of formation are found to agree with experiment to within the error bounds of computation and experiment. M?ller-Plesset second order perturbation theory (MP2) and density functional theory, the latter in the B3LYP generalized gradient approximation, are found to overestimate the experimental heat of reaction. Intrinsic reaction coordinate calculations at the MP2 level of theory demonstrate that the reaction is predominantly direct, i.e., proceeds without formation of intermediates, which is consistent with a recent molecular beam experiment. The reaction barrier as determined from MP2 calculations is found to be 2.24 kcal/mol and by DMC it is computed to be 2.39(49) kcal/mol.     

环境污染物中碳氯键离解能的理论研究

利用六种密度泛函理论方法（B3LYP, B3P86, MPW1K, TPSS1KCIS, X3LYP, BMK）对碳氯键离解能进行理论计算,结果发现几种新发展的密度泛函(DFT)方法用于碳氯键离解能的计算比传统的B3LYP有较大的改善,其中对能量估算相对准确的B3P86方法对碳氯键离解能的计算精度最高,对17个分子中碳氯键离解能计算的平均绝对偏差为6.58 kJ/mol。最后运用B3P86方法对一系列环境危害较大,但可通过光化学降解和生物降解的氯代有机物的碳氯键离解能值进行预测,并讨论了影响碳氯键离解能的结构性质关系。     

Dispersion energy evaluated by using locally projected occupied and excited molecular orbitals for molecular interaction

The dispersion terms are evaluated with the perturbation theory based on the locally projected molecular orbitals. A series of model systems, including some of the S22 set, is examined, and the calculated binding energies are compared with the published results. The basis set dependence is also examined. The dispersion energy correction is evaluated by taking into account the double excitations only of the dispersion type electron configurations and is added to the 3rd order single excitation perturbation energy, which is a good approximation to the counterpoise (CP) corrected Hartree-Fock (HF) binding energy. The procedure is the approximate "CP corrected HF + D" method. It ensures that the evaluated binding energy is approximately free of the basis set superposition error without the CP procedure. If the augmented basis functions are used, the evaluated binding energies for the predominantly dispersion-bound systems, such as rare gas dimers and halogen bonded clusters, agree with those of the reference calculations within 1 kcal mol(-1) (4 kJ mol(-1)). The limitation of the present method is also discussed.     

Protein-ligand interaction energies with dispersion corrected density functional theory and high-level wave function based methods

With dispersion-corrected density functional theory (DFT-D3) intermolecular interaction energies for a diverse set of noncovalently bound protein-ligand complexes from the Protein Data Bank are calculated. The focus is on major contacts occurring between the drug molecule and the binding site. Generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are used. DFT-D3 interaction energies are benchmarked against the best available wave function based results that are provided by the estimated complete basis set (CBS) limit of the local pair natural orbital coupled-electron pair approximation (LPNO-CEPA/1) and compared to MP2 and semiempirical data. The size of the complexes and their interaction energies (ΔE(PL)) varies between 50 and 300 atoms and from -1 to -65 kcal/mol, respectively. Basis set effects are considered by applying extended sets of triple- to quadruple-ζ quality. Computed total ΔE(PL) values show a good correlation with the dispersion contribution despite the fact that the protein-ligand complexes contain many hydrogen bonds. It is concluded that an adequate, for example, asymptotically correct, treatment of dispersion interactions is necessary for the realistic modeling of protein-ligand binding. Inclusion of the dispersion correction drastically reduces the dependence of the computed interaction energies on the density functional compared to uncorrected DFT results. DFT-D3 methods provide results that are consistent with LPNO-CEPA/1 and MP2, the differences of about 1-2 kcal/mol on average (<5% of ΔE(PL)) being on the order of their accuracy, while dispersion-corrected semiempirical AM1 and PM3 approaches show a deviating behavior. The DFT-D3 results are found to depend insignificantly on the choice of the short-range damping model. We propose to use DFT-D3 as an essential ingredient in a QM/MM approach for advanced virtual screening approaches of protein-ligand interactions to be combined with similarly "first-principle" accounts for the estimation of solvation and entropic effects.     

Treating dispersion effects in extended systems by hybrid MP2:DFT calculations--protonation of isobutene in zeolite ferrierite

We propose use of a hybrid method to study problems that involve both bond rearrangements and van-der-Waals interactions. The method combines second-order M?ller-Plesset perturbation theory (MP2) calculations for the reaction site with density functional theory (DFT) calculations for a large system under periodic boundary conditions. Hybrid MP2:DFT structure optimisation for a cluster embedded in the periodic model is the first of three steps in a multi-level approach. The second step is extrapolation of the MP2 energy to the complete basis set limit. The third step is extrapolating the high-level (MP2) correction to the limiting case of the full periodic structure. This is done by calculating the MP2 correction for a series of cluster models of increasing size, fitting an analytic expression to these energy corrections, and applying the fitted expression to the full periodic structure. We assume that, up to a constant, the high-level correction is described by a damped dispersion expression. Combining the results of all three steps yields an estimate of the MP2 reaction energy for the full periodic system at the complete basis set level. The method is designed for a reaction between a small or medium sized substrate molecule and a very large chemical system. For adsorption of isobutene in zeolite H-ferrierite, the energies obtained for the formation of different structures, the pi-complex, the isobutoxide, the tert-butoxide, and the tert-butyl carbenium ion, are -78, -73, -48, and -21 kJ mol(-1), respectively. This corresponds to corrections of the pure DFT (PBE functional) results by -62, -70, -67, and -29 kJ mol(-1), respectively. Hence, the MP2 corrections are substantial and, perhaps more importantly, not the same for the different hydrocarbon species in the zeolite. Coupled-cluster (CCSD(T)) calculations change the MP2 energies by -4 kJ mol(-1) (tert-butyl cation) or less (below +/-1 kJ mol(-1) for the other species).     

Model of peptide bond-aromatic ring interaction: correlated ab initio quantum chemical study

Aromatic ring-peptide bond interactions (modeled as benzene and formamide, N-methylformamide and N-methylacetamide) are studied by means of advanced computational chemistry methods: second-order M?ller-Plesset (MP2), coupled-cluster single and double excitation model [CCSD(T)], and density functional theory with dispersion (DFT-D). The geometrical preferences of these interactions as well as their interaction energy content, in both parallel and T-shaped arrangements, are investigated. The stabilization energy reaches a value of over 5 kcal/mol for the N-methylformamide-benzene complex at the CCSD(T)/complete basis set (CBS) level. Decomposition of interaction energy by the DFT-symmetry-adapted perturbation treatment (SAPT) technique shows that the parallel and T-shaped arrangements, although similar in their total interaction energies, differ significantly in the proportion of electrostatic and dispersion terms.     

Conformational and thermodynamic properties of gaseous levulinic acid

Molecular modeling is used to determine low-energy conformational structures and thermodynamic properties of levulinic acid in the gas phase. Structure and IR vibrational frequencies are obtained using density functional and M?ller-Plesset perturbation theories. Electronic energies are computed using G3//B3LYP and CBS-QB3 model chemistries. Computed anharmonic frequencies are consistent with reported experimental data. Population analysis shows a boat- and a chainlike structure to be most abundant at 298 K, with increasing proportions of two other conformers at higher temperatures. Population mean distribution values for thermodynamic quantities are derived. At 298 K and 1 atm, the enthalpy of formation, entropy, and heat capacity are -613.1 ± 1.0 kJ·mol(-1), 407.4 J·mol(-1)·K(-1), and 132.3 J·mol(-1)·K(-1), respectively.     

Si~2Cl~6分子的内旋转能垒和振动基频的理论研究

用从头算方法HF/6-31G^*^*和密度函方法B3LYP/6-31G^*^*,对Si~2Cl~6分子的平衡几何构型进行优化,优化的结果与实验结果吻合得较好.并用上述两种不同的方法计算Si~2Cl~6分子的内旋转能垒,结果分别为8.786和6.694kJ/mol,其中DFT方法的计算结果与实验结果4.18kJ/mol吻合得较好.对Si~2Cl~6分子的振动基频进行计算.用HF/6-31G^*^*SQM力场所计算的频率理论值与实验值的平均误差为7.3cm^-^1,用B3LYP/6-31G^*^*未标度的力场所计算的频率理论值与实验值的平均误差为6.0cm^-^1.该密度泛函方法(B3LYP/~6-31G^*^*)的理论计算值比用HF/6-31G^*^*标度后的SQM力场计算的频率与实验值(除Si--Si键扭转振动基频之外的11条振动基频)吻合得更好.并给出了Si--Si键扭转振动基频的预测值。     

The dimerization of SnCl2(g): mass spectrometric and theoretical studies

The vaporization of SnCl2(s) was investigated in the temperature range between 382 and 504 K by the use of Knudsen effusion mass spectrometry. The Sn+, SnCl+, SnCl2+, Sn2Cl3+, and Sn2Cl4+ ions were detected in the mass spectrum of the equilibrium vapor. The SnCl2(g) and Sn2Cl4(g) gaseous species were identified, and their partial pressures were determined. The structure and vibrational properties of both species and corresponding fragmentation products were studied applying density functional theory and second-order M?ller-Plesset perturbation theoretical approaches. Molecular parameters yielded thermodynamic functions by the use of statistical thermodynamics. The sublimation enthalpies of SnCl2(g) and Sn2Cl4(g) at 298 K resulting from the second- and third-law methods are evaluated as 130.9 +/- 6.2 kJ mol(-1) and 155.8 +/- 7.3 kJ mol(-1), respectively. The enthalpy changes of the dissociation reactions Sn2Cl4(g) = 2 SnCl2(g) were obtained as delta(d)H degrees(298) = 106.8 +/- 6.2 kJ mol(-1). The corresponding theoretical value amounts to 103.4 kJ mol(-1). The change of monomer properties due to the dimerization reaction is also discussed.     

A benchmark for non-covalent interactions in solids

A benchmark for non-covalent interactions in solids (C21) based on the experimental sublimation enthalpies and geometries of 21 molecular crystals is presented. Thermal and zero-point effects are carefully accounted for and reference lattice energies and thermal pressures are provided, which allow dispersion-corrected density functionals to be assessed in a straightforward way. Other thermal corrections to the sublimation enthalpy (the 2RT term) are reexamined. We compare the recently implemented exchange-hole dipole moment (XDM) model with other approaches in the literature to find that XDM roughly doubles the accuracy of DFT-D2 and non-local functionals in computed lattice energies (4.8 kJ/mol mean absolute error) while, at the same time, predicting cell geometries within less than 2% of the experimental result on average. The XDM model of dispersion interactions is confirmed as a very promising approach in solid-state applications.     

An alternative approach for the calculation of correlation energy in periodic systems: a hybrid MP2(B3LYP) study of the He-MgO(100) interaction

A practical and efficient method for exploiting second order Rayleigh-Schr?dinger perturbation theory to approximate the correlation energy contribution to the London dispersion interaction is presented. The correlation energy is estimated as the M?ller-Plesset contribution computed using single particle orbitals from hybrid exchange density functional theory as the reference state.