How to compute isomerization energies of organic molecules with quantum chemical methods

The reaction energies for 34 typical organic isomerizations including oxygen and nitrogen heteroatoms are investigated with modern quantum chemical methods that have the perspective of also being applicable to large systems. The experimental reaction enthalpies are corrected for vibrational and thermal effects, and the thus derived "experimental" reaction energies are compared to corresponding theoretical data. A series of standard AO basis sets in combination with second-order perturbation theory (MP2, SCS-MP2), conventional density functionals (e.g., PBE, TPSS, B3-LYP, MPW1K, BMK), and new perturbative functionals (B2-PLYP, mPW2-PLYP) are tested. In three cases, obvious errors of the experimental values could be detected, and accurate coupled-cluster [CCSD(T)] reference values have been used instead. It is found that only triple-zeta quality AO basis sets provide results close enough to the basis set limit and that sets like the popular 6-31G(d) should be avoided in accurate work. Augmentation of small basis sets with diffuse functions has a notable effect in B3-LYP calculations that is attributed to intramolecular basis set superposition error and covers basic deficiencies of the functional. The new methods based on perturbation theory (SCS-MP2, X2-PLYP) are found to be clearly superior to many other approaches; that is, they provide mean absolute deviations of less than 1.2 kcal mol-1 and only a few (<10%) outliers. The best performance in the group of conventional functionals is found for the highly parametrized BMK hybrid meta-GGA. Contrary to accepted opinion, hybrid density functionals offer no real advantage over simple GGAs. For reasonably large AO basis sets, results of poor quality are obtained with the popular B3-LYP functional that cannot be recommended for thermochemical applications in organic chemistry. The results of this study are complementary to often used benchmarks based on atomization energies and should guide chemists in their search for accurate and efficient computational thermochemistry methods.     

Testing the performance of density functionals for the calculation of energetic properties of complex-forming radical-molecule reactions

The performance of some popular and some more recent density functional methods for the calculation of energies of stationary points on the potential surfaces of radical-molecule reactions was examined. The functionals studied are B3-LYP, BH&H, BH&H-LYP, MPW1K, MPWB1K, TPSS, TPSSh, BB1K, M05 and M05-2X, in conjunction with nine different AO basis sets. The reaction energies, barrier heights and the relative energies of the pre-and post-reaction complexes were compared with those obtained at the CCSD(T)/CBS limit for the reactions of OH radicals with HOOH and CH₃OOH. Very poor barrier heights are provided by the B3-LYP, TPSS and TPSSh functionals. The best overall performance was obtained with the BB1K, MPW1K and MPWB1K functionals. In these reactions all of the studied functionals provide converged results only if they are used with large basis sets like aug-cc-pVTZ and def2-TZVP. The data show that before relying on a functional for a specific reaction, it is desirable to make some test calculations on the performance. The same functional can predict some relative energies very well and some others very poorly even in systems including chemically similar reactants.     

Semiempirical double-hybrid density functional with improved description of long-range correlation

The recently proposed new family of "double-hybrid" density functionals [Grimme, S. J. Chem. Phys. 2006, 124, 34108] replaces a fraction of the semi-local correlation energy by a non-local correlation energy expression that employs the Kohn-Sham orbitals in second-order many-body perturbation theory. These functionals have provided results of high accuracy over a wide range of properties but fail to accurately describe long-range van der Waals interactions. In this work, a distance-dependent scaling factor for the non-local correlation energy is introduced to address this problem, and two new double-hybrid density functionals are proposed. The new functionals are optimized with the finite cc-pVTZ basis on training sets of atomization energies and intermolecular interaction energies. They are compared against (scaled) second-order M?ller-Plesset perturbation theories and popular density functionals including the hybrid-GGA functional B3-LYP and the first double-hybrid functional (B2-PLYP). Tests are performed on an extensive set including reaction energies, barrier heights, weakly interacting complexes, transition-metal systems, molecular geometries, and harmonic vibrational frequencies. Within the cc-pVTZ atomic orbital basis, we have demonstrated the ability to find a parametrization scheme which is simultaneously able to describe thermochemistry and weakly bound systems with a satisfactory degree of accuracy.     

On the influence of basis sets and quantum chemical methods on the prediction accuracy of COSMO-RS

This paper examines how the accuracy of activity coefficients at infinite dilution calculated from the conductor-like screening model for real solvents (COSMO-RS) depends on the basis set and the quantum chemical method used. Activity coefficients at various temperatures serve as experimental parameters for optimising the COSMO-RS parameters. A modification of the electrostatic misfit term of the energy function of COSMO-RS is presented that leads to a slightly higher accuracy. COSMO-RS parameter sets for nine different systematically varied basis sets using the density functional theory with the BP86 functional show that at least a valence double-zeta basis set is necessary for good accuracy. Larger basis sets show no advantages. Investigations of eight different quantum chemical calculation methods using a valence triple-zeta basis set are documented. Hartree-Fock and local density approximations give relatively poor results. The gradient-corrected density functionals investigated and the B3LYP hybrid functional show practically identical accuracy. The most accurate parameterisation was obtained with MP2.     

The performance of B3-LYP density functional theory in describing SN2 reactions at saturated carbon

The performance of the B3-LYP variant of density functional theory when used in conjunction with the 6-31G(d) and 6-311 + G(3df, 2p) basis sets in describing the prototypical gas-phase S_N2 reactions of Cl⁻ + CH₃Cl and CH₃Br has been examined in detail. Reasonable values of the complexation energies (ΔH_comp) for the ion-molecule complexes formed in these reactions are obtained. However, the overall (ΔH_ovr^#) and central (ΔH_cent^#) barriers for these reactions calculated using the B3-LYP functional are significantly underestimated when compared with G2(+) or experimental results. This implies that the B3-LYP energies for the Cl(H₃C)Cl⁻ (D_3h) and Cl(H₃C)Br⁻ (C_3v) transition structures are relatively too low. The B3-LYP errors appear to be systematic, with similar errors being found for corresponding quantities for the two reactions examined.     

High-level ab initio versus DFT calculations on (H2O2)2 and H2O2–H2O complexes as prototypes of multiple hydrogen bond systems

The performance of B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91 density functionals to describe multiple hydrogen bond systems was studied. For this purpose we have chosen the dimers of hydrogen peroxide and the hydrogen peroxide–water complexes. The geometries and vibrational frequencies obtained with a 6-311+G(d,p) basis set were compared with those obtained at the MP2 level using the same basis set expansion. The corresponding dimerization energies were obtained using a 6-311+G(3df,2p) basis set and compared with those obtained using the G2(MP2) theory. Red shiftings of the OH donor stretching frequencies were predicted by all approaches investigated; however, in all cases, the DFT values were sizably larger than the MP2 ones. Similarly, the blue shifting of the torsion of the hydrogen peroxide subunit was larger when evaluated at the DFT level. All functionals reproduced the G2(MP2) relative stabilities of the different local minima quite well. With the exception of the B-LYP and B3-PW91 approaches, all functionals yielded binding energies which deviated from the G2(MP2) values by less than 0.5 kcal/mol, provided that G2-type basis sets were used and that the corresponding BSSE corrections were included. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1124–1135     

Ab initio and DFT predictions of infrared intensities and Raman activities

Relative infrared (IR) intensities and relative Raman activities have been computed for vibrations of test molecules, including from two to nine heavy atoms, using second-order Moller-Plesset perturbation theory (MP2), and three hybrid density functionals (B3LYP, M05, and M05-2X). The basis set convergence of vibrational properties is discussed. Our results demonstrate that B3LYP offers the most cost-effective choice for the prediction of molecular vibrational properties, but the predictions of another two tested hybrid functionals are very similar and in very good agreement with experimental data. MP2 shows good performance for the IR intensities, whereas the quality of prediction of the relative Raman activities should be characterized as only moderate. B3LYP calculations of the relative IR intensities using highly compact Sadlej's Z3PolX basis set retain the high accuracy of the more CPU expensive Sadlej's pVTZ and much more expensive aug-cc-pVTZ calculations. Relative Raman activities are more sensitive to basis set effects and require at least Sadlej's pVTZ to obtain quantitative results.     

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.     

Computational study of the reactions of methanol with the hydroperoxyl and methyl radicals. 1. Accurate thermochemistry and barrier heights

The reactions of CH(3)OH with the HO(2) and CH(3) radicals are important in the combustion of methanol and are prototypes for reactions of heavier alcohols in biofuels. The reaction energies and barrier heights for these reaction systems are computed with CCSD(T) theory extrapolated to the complete basis set limit using correlation-consistent basis sets, both augmented and unaugmented, and further refined by including a fully coupled treatment of the connected triple excitations, a second-order perturbative treatment of quadruple excitations (by CCSDT(2)(Q)), core-valence corrections, and scalar relativistic effects. It is shown that the M08-HX and M08-SO hybrid meta-GGA density functionals can achieve sub-kcal mol(-1) agreement with the high-level ab initio results, identifying these functionals as important potential candidates for direct dynamics studies on the rates of these and homologous reaction systems.     

H3PAuR型单核Au(Ⅰ)配合物的结构和非线性光学系数的量子化学计算比较

采用量子化学ab initio和DFT中的不同方法和基组对H3PAuR型单核Au(Ⅰ)配合物结构和二阶NLO系数进行计算, 探讨不同计算方法和Au基组对计算结果产生的影响. 对计算结果分析表明, 不同计算方法对Au(Ⅰ)配合物结构和二阶NLO系数影响较大, 其中用考虑电子相关效应的DFT-B3LYP和MP2方法优化得到的Au—P配键长比用HF方法的短, 相应的二阶NLO系数比HF方法的大2倍左右; 同一计算方法下, Au基组中d轨道个数增加优化得到的Au—P配键键长减小; 随着Au基组的增大, 前线分子轨道能级差减小, 其中SDD和CEP-121G基组之间的变化更明显. 基组变化对分子二阶NLO系数的影响较小, 多数分子Au取不同基组计算的βμ值相差在10%以内.     

Assessment of multicoefficient correlation methods, second-order Møller-Plesset perturbation theory, and density functional theory for H3O(+)(H2O)n (n = 1-5) and OH(-)(H2O)n (n = 1-4)

We have assessed the ability of 52 methods including 15 multicoefficient correlation methods (MCCMs), two complete basis set (CBS) methods, second-order M?ller-Plesset perturbation theory (MP2) with 5 basis sets, the popular B3LYP hybrid functional with 6 basis sets, and 24 combinations of local density functional and basis set to accurately reproduce reaction energies obtained at the Weizmann-1 level of theory for hydronium, hydroxide, and pure water clusters. The three best methods overall are BMC-CCSD, G3SX(MP3), and M06-L/aug-cc-pVTZ. If only microsolvated ion data is included, M06-L/aug-cc-pVTZ is the best method; it has errors only half as large as the other density functionals. The deviations between the three best performing methods are larger for the larger hydronium- and hydroxide-containing clusters, despite a decrease in the average reaction energy, making it impossible to determine which of the three methods is overall the best, so they might be ranked in order of increasing cost, with BMC-CCSD least expensive, followed by M06-L/aug-cc-pVTZ. However, the cost for M06-L will increase more slowly as cluster size increases. This study shows that the M06-L functional is very promising for condensed-phase simulations of the transport of hydronium and hydroxide ions in aqueous solution.     

Theoretical study of mixed LiLnX4 (Ln = La, Dy; X = F, Cl, Br, I) rare earth/alkali halide complexes

The structure, bonding and vibrational properties of the mixed LiLnX4 (Ln = La, Dy; X = F, Cl, Br, I) rare earth/alkali halide complexes were studied using various quantum chemical methods (HF, MP2 and the Becke3-Lee-Yang-Parr exchange-correlation density functional) in conjunction with polarized triple-zeta valence basis sets and quasi-relativistic effective core potentials for the heavy atoms. Our comparative study indicated the superiority of MP2 theory while the HF and B3-LYP methods as well as less sophisticated basis sets failed for the correct energetic relations. In particular, f polarization functions on Li and X proved to be important for the Li...X interaction in the complexes. From the three characteristic structures of such complexes, possessing 1-(C3v), 2-(C2v), or 3-fold coordination (C3v) between the alkali metal and the bridging halide atoms, the bi- and tridentate forms are located considerably lower on the potential energy surface then the monodentate isomer. Therefore only the bi- and tridentate isomers have chemical relevance. The monodentate isomer is only a high-lying local minimum in the case of X = F. For X = Cl, Br, and I this structure is found to be a second-order saddle point. The bidentate structure was found to be the global minimum for the systems with X = F, Cl, and Br. However, the relative stability with respect to the tridentate structure is very small (1-5 kJ/mol) for the heavier halide derivatives and the relative order is reversed in the case of the iodides. The energy difference between the three structures and the dissociation energy decrease in the row F to I. The ionic bonding in the complexes was characterized by natural charges and a topological analysis of the electron density distribution according to Bader's theorem. Variation of the geometrical and bonding characteristics between the lanthanum and dysprosium complexes reflects the effect of "lanthanide contraction". The calculated vibrational data indicate that infrared spectroscopy may be an effective tool for experimental investigation and characterization of LiLnX4 molecules.     

Theoretical study of the pyrolysis of methyltrichlorosilane in the gas phase. 2. Reaction paths and transition states

The kinetics for the previously proposed 114-reaction mechanism for the chemical vapor deposition (CVD) process that leads from methyltrichlorosilane (MTS) to silicon carbide (SiC) are examined. Among the 114 reactions, 41 are predicted to proceed with no intervening barrier. For the remaining 73 reactions, transition states and their corresponding barrier heights have been explored using second-order perturbation theory (MP2) with the aug-cc-pVDZ basis set. Final energies for the reaction barriers were obtained using both MP2 with the aug-cc-pVTZ basis set and coupled cluster theory (CCSD(T)) with the aug-cc-pVDZ basis set. CCSD(T)/aug-cc-pVTZ energies were estimated by assuming additivity of basis set and correlation effects. Partition functions for the computation of thermodynamic properties of the transition states were calculated with MP2/aug-cc-pVDZ. Forward and reverse Gibbs free energy barriers were obtained at 11 temperatures ranging from 0 to 2000 K. Important reaction pathways are illustrated at 0 and 1400 K.     

Conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete

The conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete are determined within the isodesmic, homodesmotic, and hyperhomodesmotic models. Optimum equilibrium geometries, harmonic vibrational frequencies, and corresponding electronic energies and zero-point vibrational energies are computed for all pertinent molecular systems using SCF theory, second-order perturbation theory, and density functional theory and employing the correlation consistent basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ. Single-point fourth-order perturbation theory, CCSD, and CCSD(T) calculations employing the cc-pVTZ and the cc-pVQZ basis sets are computed using the MP2/cc-pVTZ and MP2/cc-pVQZ optimized geometries, respectfully, to ascertain the contribution of higher order correlation. Three DFT functionals, B3LYP, wB97XD, and M06-2X, are employed to determine whether they can yield results similar to those obtained at the CCSD(T) level.     

Activation energies of pericyclic reactions: performance of DFT, MP2, and CBS-QB3 methods for the prediction of activation barriers and reaction energetics of 1,3-dipolar cycloadditions, and revised activation enthalpies for a standard set of hydrocarbon pericyclic reactions

Activation barriers and reaction energetics for the three main classes of 1,3-dipolar cycloadditions, including nine different reactions, were evaluated with the MPW1K and B3LYP density functional methods, MP2, and the multicomponent CBS-QB3 method. The CBS-QB3 values were used as standards for 1,3-dipolar cycloaddition activation barriers and reaction energetics, and the density functional theory (DFT) and MP2 methods were benchmarked against these values. The MPW1K/6-31G* method and basis set performs best for activation barriers, with a mean absolute deviation (MAD) value of 1.1 kcal/mol. The B3LYP/6-31G* method and basis set performs best for reaction enthalpies, with a MAD value of 2.4 kcal/mol, while the MPW1K method shows large errors for reaction energetics. The MP2 method gives the expected systematic underestimation of barriers. Concerted and nearly synchronous transition structures are predicted by all DFT and MP2 methods. Also reported are revised estimated 0 K experimental activation enthalpies for a standard set of hydrocarbon pericyclic reactions and updated comparisons to experiment for DFT, ab initio, and multicomponent methods. B3LYP and MPW1K methods with MAD values of 1.5 and 2.1 kcal/mol, respectively, fortuitously outperform the multicomponent CBS-QB3 method, which has a MAD value of 2.3. The MAD value of the O3LYP functional improves to 2.4 kcal/mol from the previously reported 3.0 kcal/mol.