Correlation Consistent Composite Approach Research Articles

A QM/QM Multilayer Composite Methodology: The ONIOM Correlation Consistent Composite Approach (ONIOM-ccCA)

A QM/QM approach incorporating the correlation consistent composite approach (ccCA) into the ONIOM multilayer methodology has been implemented. This new multilayer composite scheme, ONIOM-ccCA, enables the accurate prediction of thermochemical properties for systems containing dozens-and potentially hundreds-of atoms. ONIOM-ccCA is used to predict the C-H bond dissociation energies of 18 anthracene and fluorene analogues, containing up to 43 atoms, to within 1.2 kcal mol(-1) of experimental values. Several density functional and basis set combinations are evaluated for use as the low level QM layer. The mean absolute deviation (1.2 kcal mol(-1)) using the most accurate ONIOM-ccCA method, ccCA:B3LYP/cc-pVTZ, is significantly lower than that of an earlier reported multilayer composite scheme [2.4 kcal mol(-1), Li, M.-J.; Liu, L.; Fu, Y.; Guo, Q.-X. J. Phys. Chem. B, 2005, 109, 13818]. Thus, through use of ONIOM-ccCA, accurate thermochemical calculations are now feasible for sizable molecular systems of chemical or biological interest.

Theoretical Studies on the Catalysis of the Reverse Water−Gas Shift Reaction Using First-Row Transition Metal β-Diketiminato Complexes

The reverse water-gas shift reaction CO(2) + H(2) --> H(2)O + CO has been investigated using a set of homogeneous catalyst models L'M(I) (L' = beta-diketiminate, C(3)N(2)H(5)(-); M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn). The thermodynamics of prototypical reaction pathways were simulated at two levels of theory: B3LYP/6-311+G(d) and B3LYP/aug-cc-pVTZ. The modeled catalytic reaction has been considered in the following steps: coordination of CO(2) by the catalyst to generate a carbon dioxide complex, L'M(CO(2)); scission of L'M(CO(2)) to yield L'M(CO) and L'M(O); L'M(O) hydrogenation to form L'M(H(2)O). The final products, H(2)O and CO, were obtained from the dissociation of L'M(H(2)O) and L'M(CO). All of the reactants, intermediates, and products were modeled, where different possible conformers and multiplicities were identified and considered as potential minima. The reaction enthalpy DeltaH, of all steps for each catalyst as a function of transition metal have been determined. The Mn and Fe catalysts show more thermodynamically accessible pathways than the other catalyst models studied. The overall reaction enthalpy has been determined not only by B3LYP/6-311+G(d) and B3LYP/aug-cc-pVTZ but also via a more rigorous ab initio electron-correlation-based approach, the correlation consistent Composite Approach (ccCA).

Activation of Carbon-Hydrogen and Hydrogen-Hydrogen Bonds by Copper-Nitrenes: A Comparison of Density Functional Theory with Single- and Multireference Correlation Consistent Composite Approaches.

The kinetics and thermodynamics of copper-mediated nitrene insertion into C-H and H-H bonds (the former of methane) have been studied using several levels of theory: B3LYP/6-311++G(d,p), B97-1/cc-pVTZ, PBE1KCIS/cc-pVTZ, and ccCA (correlation consistent Composite Approach). The results show no significant difference among the DFT methods. All three DFT methods predict the ground state of the copper-nitrene model complex, L'Cu(NH), to be a triplet, while single reference ccCA predicts the singlet to be the ground state. The contributions to the total ccCA energy indicate that the singlet state is favored at the MP2/CBS level of theory, while electron correlation beyond this level (CCSD(T)) favors a triplet state, resulting in a close energetic balance between the two states. A multireference ccCA method is applied to the nitrene active species and supports the assignment of a singlet ground state. In general, the largest difference in the model reaction cycles between DFT and ccCA methods is for processes involving radicals and bond dissociation.

The resolution of the identity approximation applied to the correlation consistent composite approach

A new implementation of the correlation consistent composite approach (ccCA), denoted RI-ccCA, utilizing both the resolution of the identity (RI) and local methods is presented. A set of 102 molecules composed of first and second row, main group atoms is employed to compare total energies, atomization energies, and enthalpies of formation between the original ccCA implementation and those of RI-ccCA. Relative CPU time and disk space requirements of RI-ccCA as compared to ccCA, demonstrate that on the average, employing the RI approximation in ccCA affords CPU time savings over 70% and disk space requirements diminished by well over 90% without introducing significant error in energetic properties.

Accurate thermochemistry for transition metal complexes from first-principles calculations

The "correlation consistent Composite Approach" or ccCA is an ab initio model chemistry based on the single reference MP2 level of theory. By adjusting the basis set and level of theory of the core valence additive correction, ccCA is capable of reliable thermochemical predictions of inorganic and organometallic transition metal-containing molecules, as well as achieving chemical accuracy on main group species, with a mean absolute deviation of 0.89 kcal mol(-1) against the 147 enthalpies of formation in the G2/97 test set. For a set of 52 complexes containing elements Sc-Zn, ranging in size from diatomics to Ni(PF(3))(4) and Fe(C(5)H(2))(2), ccCA on average predicts enthalpies of formation to within +/-3 kcal mol(-1) of the experimental result with a mean absolute deviation of 2.85 kcal mol(-1) and a root mean square deviation of 3.77 kcal mol(-1). The ccCA methodology is a significant step toward quantitative theoretical modeling of transition metal thermodynamics.

Computation of potential energy surfaces with the multireference correlation consistent composite approach

A multireference composite method that is based on the correlation consistent Composite Approach (ccCA) is introduced. The developed approach, multireference ccCA, has been utilized to compute the potential energy surfaces (PESs) of N(2) and C(2), which provide rigorous tests for multireference composite methods due to the large multireference character that must be correctly described as the molecules dissociate. As well, PESs provide a stringent test of a composite method because all components of the method must work in harmony for an appropriate, smooth representation across the entire surface.

Towards the intrinsic error of the correlation consistent Composite Approach (ccCA)

The correlation consistent Composite Approach (ccCA) has been made more robust by (a) modifying the basis set used in computing B3LYP equilibrium geometries and harmonic vibrational frequencies so that the correlation consistent basis sets are used throughout ccCA; (b) separately extrapolating the MP2 and Hartree–Fock complete basis set limit energies; (c) uniformly treating unrestricted open shell wave functions; (d) utilizing newly recommended enthalpies of formation for C, B, Al, and Si atoms; and (e) using theoretically derived vibrational scale factors. This modified ccCA formulation has been used to compute the 454 energetic properties (enthalpies of formation, dissociation energies, ionization potentials, electron affinities, and proton affinities) in the G3/05 test set. This new formulation, which does not contain any optimized parameters, has a small systematic statistical bias (mean signed deviation of −0.20 kcal mol−1), and has a mean absolute deviation of 1.01 kcal mol−1 with the incorporation of modification d) or 0.99 kcal mol−1 without. This is compared to a G4(MP2) MAD of 1.04 kcal mol−1 and a G3(MP2) MAD of 1.39 kcal mol−1. These modifications result in minimal change with respect to the computational requirements of the current ccCA methodology. The ccCA model chemistry is the first MP2-based model chemistry to achieve an accuracy of ± 1.00 kcal mol−1 for the G3/05 training set without any optimized parameters, and it is the only MP2-based model chemistry uniformly applicable to systems comprised of elements from H to Kr.

A CCSD(T) and ccCA study of mixed silicon hydrides and halides: Structures and thermochemistry

A set of 24 mixed silicon hydrides and halides (SiH n X m − n , where X = F, Cl; m = 1–4; and n = 0– m) has been investigated using; (1) CCSD(T) with the correlation consistent basis sets of double-through quintuple-ζ quality; (2) CCSD(T) with the augmented tight d form of the correlation consistent basis sets for the second row atoms (Si and Cl); and (3) the recently developed correlation consistent composite approach (ccCA). Optimized geometries and harmonic vibrational frequencies are reported, as well as enthalpies of formation, free energies of formation, and dissociation reaction enthalpies. Relativistic effects, including atomic spin-orbit coupling and scalar relativistic effects, and core-valence correlation, have been accounted for via the ccCA formulism. As demonstrated in previous studies, the tight d basis sets accelerate the convergence, as compared to the standard correlation consistent basis sets, of CCSD(T)-computed geometries and energetics of molecular species containing second row, main group atoms. The ccCA enthalpies of formation are shown to be similar and, on average, better than the corresponding CCSD(T) enthalpies of formation for the silicon species. Further, large DKH-CCSD(T) computations with explicit inclusion of core-valence and scalar relativistic effects have been performed to predict the enthalpies of formation of SiHF, SiHCl, SiH 2F, SiHF 2, SiH 2Cl, and SiHCl 2.

Performance of the correlation-consistent composite approach for sulfur species

The performance of the correlation-consistent composite approach (ccCA) model chemistry has been examined for a test set of sulfur-containing molecules which includes enthalpies of formation, bond dissociation enthalpies (BDEs), and isomerization energies. The ccCA method was compared with other model chemistries (G3, G3B3) and, overall, was found to be more accurate than both G3 and G3B3 for sulfur-containing species, and at a moderate increase in computational cost. The ccCA model chemistry resulted in a mean absolute deviation (MAD) of 3.6 kJ/mol for the enthalpy of formation test set as compared with 8.3 and 9.6 kJ/mol for G3 and G3B3, respectively. The 95% confidence interval in the enthalpies of formation, which corresponds to two times the root mean square of the deviation from experiment, for the ccCA model chemistry is±10.3 kJ/mol as compared with±23.2 and±27.5 kJ/mol for the G3 and G3B3 methods. For the BDEs, the MAD for ccCA is 2.6 kJ/mol as compared with 4.4 and 4.3 kJ/mol for G3 and G3B3, respectively. The 95% confidence interval for BDEs for the ccCA model chemistry is±7.0 kJ/mol as compared with±10.3 and±10.1 kJ/mol for G3 and G3B3, respectively. Three isomeric systems which have resulted in disagreement among prior theoretical studies, NSO/SNO, HOS/HSO, and FSSF/SSF2, were also examined using ccCA, and, in each case, ccCA correctly predicted the lowest isomer and agreed within 4 kJ/mol of previously reported values.

Accurate thermochemistry from quantum chemical calculations?

The answer to the title question is definitely “yes” – at least for fairly small molecules. Computational procedures, namely the Weizmann (Wn) and Gaussian-3 (G3) family of methods, the complete basis set extrapolation scheme (CBS-x), the “high accuracy extrapolated ab initio thermochemistry” (HEAT) as well as the “correlation consistent composite approach” (ccCA), aimed at energies with chemical accuracy or even better (sub kJ mol−1) are described and several applications illustrating the level of accuracy that can be achieved are presented.

Application of the Correlation Consistent Composite Approach (ccCA) to Third-Row (Ga-Kr) Molecules.

The correlation consistent composite approach (ccCA) has been applied to the G3/05 training set of 51 energetic properties for the atoms and molecules that contain the 4p elements, Ga-Kr. When atomic and molecular first-order spin orbit coupling corrections are added to open shell atoms and molecules, the ccCA has a mean absolute deviation from experiment (MAD) of 0.95 kcal mol(-1), an improvement of 0.10 kcal mol(-1) over G3 and G3X model chemistries. The performance of the ccCA on third-row-containing atoms and molecules is, therefore, commensurate in accuracy with previous studies on lighter main group elements H-Ar. While the typical methods used to compute theoretical molecular spin orbit corrections may go against the spirit of "black box" model chemistries, such corrections may be necessary for molecules containing heavy elements such as Ga-Kr. For example, when second-order spin orbit corrections are added to the atomic and molecular energies, the ccCA MAD is reduced to 0.88 kcal mol(-1).

Performance of the correlation consistent composite approach for transition states: A comparison to G3B theory

The correlation consistent composite approach (ccCA) was applied to the prediction of reaction barrier heights (i.e., transition state energy relative to reactants and products) for a standard benchmark set of reactions comprised of both hydrogen transfer reactions and nonhydrogen transfer reactions (i.e., heavy-atom transfer, SN2, and unimolecular reactions). The ccCA method was compared against G3B for the same set of reactions. Error metrics indicate that ccCA achieves "chemical accuracy" with a mean unsigned error (MUE) of 0.89 kcal/mol with respect to the benchmark data for barrier heights; G3B has a mean unsigned error of 1.94 kcal/mol. Further, the greater accuracy of ccCA for predicted reaction barriers is compared to other benchmarked literature methods, including density functional (BB1K, MUE=1.16 kcal/mol) and wavefunction-based [QCISD(T), MUE=1.10 kcal/mol] methods.

Computationals-Block Thermochemistry with the Correlation Consistent Composite Approach

The correlation consistent composite approach (ccCA) is a model chemistry that has been shown to accurately compute gas-phase enthalpies of formation for alkali and alkaline earth metal oxides and hydroxides (Ho, D. S.; DeYonker, N. J.; Wilson, A. K.; Cundari, T. R. J. Phys. Chem. A 2006, 110, 9767). The ccCA results contrast to more widely used model chemistries where calculated enthalpies of formation for such species can be in error by up to 90 kcal mol-1. In this study, we have applied ccCA to a more general set of 42 s-block molecules and compared the ccCA DeltaHf values to values obtained using the G3 and G3B model chemistries. Included in this training set are water complexes such as Na(H2O)n+ where n = 1 - 4, dimers and trimers of ionic compounds such as (LiCl)2 and (LiCl)3, and the largest ccCA computation to date: Be(acac)2, BeC10H14O4. Problems with the G3 model chemistries seem to be isolated to metal-oxygen bonded systems and Be-containing systems, as G3 and G3B still perform quite well with a 2.7 and 2.6 kcal mol-1 mean absolute deviation (MAD), respectively, for gas-phase enthalpies of formation. The MAD of the ccCA is only 2.2 kcal mol-1 for enthalpies of formation (DeltaHf) for all compounds studied herein. While this MAD is roughly double that found for a ccCA study of >350 main group (i.e., p-block) compounds, it is commensurate with typical experimental uncertainties for s-block complexes. Some molecules where G3/G3B and ccCA computed DeltaHf values deviate significantly from experiment, such as (LiCl)3, NaCN, and MgF, are inviting candidates for new experimental and high-level theoretical studies.

Quantitative Computational Thermochemistry of Transition Metal Species

The correlation consistent Composite Approach (ccCA), which has been shown to achieve chemical accuracy (+/-1 kcal mol-1) for a large benchmark set of main group and s-block metal compounds, is used to compute enthalpies of formation for a set of 17 3d transition metal species. The training set includes a variety of metals, ligands, and bonding types. Using the correlation consistent basis sets for the 3d transition metals, we find that gas-phase enthalpies of formation can be efficiently calculated for inorganic and organometallic molecules with ccCA. However, until the reliability of gas-phase transition metal thermochemistry is improved, both experimentally and theoretically, a large experimental training set where uncertainties are near +/-1 kcal mol-1 (akin to commonly used main group benchmarking sets) remains an ambitious goal. For now, an average deviation of +/-3 kcal mol-1 appears to be the initial goal of "chemical accuracy" for ab initio transition metal model chemistries. The ccCA is also compared to a more robust but relatively expensive composite approach primarily utilizing large basis set coupled cluster computations. For a smaller training set of eight molecules, ccCA has a mean absolute deviation (MAD) of 3.4 kcal mol-1 versus the large basis set coupled-cluster-based model chemistry, which has a MAD of 3.1 kcal mol-1. However, the agreement for transition metal complexes is more system dependent than observed in previous benchmark studies of composite methods and main group compounds.

The correlation-consistent composite approach: Application to the G3/99 test set

The correlation-consistent composite approach (ccCA), an ab initio composite technique for computing atomic and molecular energies, recently has been shown to successfully reproduce experimental data for a number of systems. The ccCA is applied to the G3/99 test set, which includes 223 enthalpies of formation, 88 adiabatic ionization potentials, 58 adiabatic electron affinities, and 8 adiabatic proton affinities. Improvements on the original ccCA formalism include replacing the small basis set quadratic configuration interaction computation with a coupled cluster computation, employing a correction for scalar relativistic effects, utilizing the tight-d forms of the second-row correlation-consistent basis sets, and revisiting the basis set chosen for geometry optimization. With two types of complete basis set extrapolation of MP2 energies, ccCA results in an almost zero mean deviation for the G3/99 set (with a best value of -0.10 kcal mol(-1)), and a 0.96 kcal mol(-1) mean absolute deviation, which is equivalent to the accuracy of the G3X model chemistry. There are no optimized or empirical parameters included in the computation of ccCA energies. Except for a few systems to be discussed, ccCA performs as well as or better than Gn methods for most systems containing first-row atoms, while for systems containing second-row atoms, ccCA is an improvement over Gn model chemistries.

Accurate Enthalpies of Formation of Alkali and Alkaline Earth Metal Oxides and Hydroxides: Assessment of the Correlation Consistent Composite Approach (ccCA)

Computing the enthalpies of formation for alkali metal and alkaline earth metal oxides (M(x)O) and hydroxides [M(OH)(n)] using the Gaussian-n (Gn) and Weismann-n (Wn) ab initio model chemistries is difficult due to an improper treatment of core-valence electron correlation effects. Using a new model chemistry called the correlation consistent Composite Approach (ccCA), enthalpies of formation were determined for eight different alkali/alkaline earth metal oxides and hydroxides. Unlike the Gn and Wn model chemistries, which must be modified to properly account for core-valence electron correlation, the standard implementations of the ccCA provide acceptable results, and all enthalpies of formation obtained with the ccCA are within the accepted range of recommended values.

The correlation consistent composite approach (ccCA): An alternative to the Gaussian-n methods

An alternative to the Gaussian-n (G1, G2, and G3) composite methods of computing molecular energies is proposed and is named the "correlation consistent composite approach" (ccCA, ccCA-CBS-1, ccCA-CBS-2). This approach uses the correlation consistent polarized valence (cc-pVXZ) basis sets. The G2-1 test set of 48 enthalpies of formation (DeltaHf), 38 adiabatic ionization potentials (IPs), 25 adiabatic electron affinities (EAs), and 8 adiabatic proton affinities (PAs) are computed using this approach, as well as the DeltaHf values of 30 more systems. Equilibrium molecular geometries and vibrational frequencies are obtained using B3LYP density functional theory. When applying the ccCA-CBS method with the cc-pVXZ series of basis sets augmented with diffuse functions, mean absolute deviations within the G2-1 test set compared to experiment are 1.33 kcal mol(-1) for DeltaHf,0.81 kcal mol(-1) for IPs, 1.02 kcal mol(-1) for EAs, and 1.51 kcal mol(-1) for PAs, without including the "high-level correction" (HLC) contained in the original Gn methods. Whereas the HLC originated in the Gaussian-1 method as an isogyric correction, it evolved into a fitted parameter that minimized the error of the composite methods, eliminating its physical meaning. Recomputing the G1 and G3 enthalpies of formation without the HLC reveals a systematic trend where most DeltaHf values are significantly higher than experimental values. By extrapolating electronic energies to the complete basis set (CBS) limit and adding G3-like corrections for the core-valence and infinite-order electron correlation effects, ccCA-CBS-2 often underestimates the experimental DeltaHf, especially for larger systems. This is desired as inclusion of relativistic and atomic spin-orbit effects subsequently improves theoretical DeltaHf values to give a 0.81 kcal mol(-1) mean absolute deviation with ccCA-CBS-2. The ccCA-CBS method is a viable "black box" method that can be used on systems with at least 10-15 heavy atoms.