Chapter Three - Super-ccCA: Robust transition metal thermochemistry

Composite ab initio CBS-Q and G3 methods were used to calculate the bond dissociation energies (BDEs) of over 200 compounds listed in CRC Handbook of Chemistry and Physics (2002 ed.). It was found that these two methods agree with each other excellently in the calculation of BDEs, and they can predict BDEs within 10 kJ/mol of the experimental values. Using these two methods, it was found that among the examined compounds 161 experimental BDEs are valid because the standard deviation between the experimental and theoretical values for them is only 8.6 kJ/mol. Nevertheless, 40 BDEs listed in the Handbook may be highly inaccurate as the experimental and theoretical values for them differ by over 20 kJ/mol. Furthermore, 11 BDEs listed in the Handbook may be seriously flawed as the experimental and theoretical values for them differ by over 40 kJ/mol. Using the 161 cautiously validated experimental BDEs, we then assessed the performances of the standard density functional (DFT) methods including B3LYP, B3P86, B3PW91, and BH&HLYP in the calculation of BDEs. It was found that the BH&HLYP method performed poorly for the BDE calculations. B3LYP, B3P86, and B3PW91, however, performed reasonably well for the calculation of BDEs with standard deviations of about 12.1-18.0 kJ/mol. Nonetheless, all the DFT methods underestimated the BDEs by 4-17 kJ/mol in average. Sometimes, the underestimation by the DFT methods could be as high as 40-60 kJ/mol. Therefore, the DFT methods were more reliable for relative BDE calculations than for absolute BDE calculations. Finally, it was observed that the basis set effects on the BDEs calculated by the DFT methods were usually small except for the heteroatom-hydrogen BDEs.

Computational chemistry has led to the greater understanding of the molecular world, from the interaction of molecules, to the composition of molecular species and materials. Of the families of computational chemistry approaches available, the main families of electronic structure methods that are capable of accurate and/or reliable predictions of energetic, structural, and spectroscopic properties are ab initio methods and density functional theory (DFT). The focus of this dissertation is to improve the accuracy of predictions and computational efficiency (with respect to memory, disk space, and computer processing time) of some computational chemistry methods, which, in turn, can extend the size of molecule that can be addressed, and, for other methods, DFT, in particular, gain greater insight into which DFT methods are more reliable than others. Much, though not all, of the focus of this dissertation is upon transition metal species – species for which much less method development has been targeted or insight about method performance has been well established. The ab initio approach that has been targeted in this work is the correlation consistent composite approach (ccCA), which has proven to be a robust, ab initio computational method for main group and first row transition metal-containing molecules yielding, on average, accurate thermodynamic properties, i.e., within 1 kcal/mol of experiment for main group species and within 3 kcal/mol of experiment for first row transition metal molecules. In order to make ccCA applicable to systems containing any element from the periodic table, development of the method for second row transition metals and heavier elements, including lower p-block (5p and 6p) elements was pursued. The resulting method, the relativistic pseudopotential variant of ccCA (rp-ccCA), and its application are detailed for second row transition metals and lower p-block elements. Because of the computational cost of ab initio methods, DFT is a popular choice for the study of transition metals. Despite this, the most reliable density functionals for the prediction of energetic properties (e.g. enthalpy of formation, ionization potential, electron affinity, dissociation energy) of transition metal species, have not been clearly identified. The examination of DFT performance for first and second row transition metal thermochemistry (i.e., enthalpies of formation) was conducted and density functionals for the study of these species were identified. And, finally, to address the accuracy of spectroscopic and energetic properties, improvements for a series of density functionals have been established. In both DFT and ab initio methods, the harmonic approximation is typically employed. This neglect of anharmonic effects, such as those related to vibrational properties (e.g. zero-point vibrational energies, thermal contributions to enthalpy and entropy) of molecules, generally results in computational predictions that are not in agreement with experiment. To correct for the neglect of anharmonicity, scale factors can be applied to these vibrational properties, resulting in better alignment with experimental observations. Scale factors for DFT in conjunction with both the correlation and polarization consistent basis sets have been developed in this work.

Computational chemistry provides a powerful route to determine thermochemical properties. For transition metal thermochemistry, typically, high-level quantum methodologies are required. Ab initio composite methods – which aim to replicate the predictions possible from a high-level method/advanced basis set with predictions from a series of lower-level methods/basis sets to reduce computational cost – have proven to be effective for transition metal species, with better than chemical accuracy for transition metal energetics (<12 kJ mol−1), on average. While useful, to provide a more robust computational approach, Super ccCA (s-ccCA) is introduced herein and varies from its predecessor, ccCA, by utilising higher-level coupled-cluster corrections along with a spin–orbit contribution from a Breit-Pauli Hamiltonian. In this work, s-ccCA has been utilised for the prediction of dissociation energies of 3d and 4d molecules. A set of borides, sulphides and carbides in conjunction with three early first-row transition metals (Sc, Ti, V) and three second-row transition metals (Y, Zr, Nb) were studied with this new composite method. The energies calculated herein were compared with the experiment and shown to be in excellent agreement. The energetic predictions show that for cases where a balance of static and dynamic correlation is of paramount importance, s-ccCA offers an effective approach.

Composite ab initio and density functional theory (DFT) methods were used to explore internal hydrogen-atom transfers in a variety of primary, secondary, and tertiary alkyl and functionalized radicals with implications for combustion environments. The composite ab initio method G3MP2B3 was found to achieve the most reasonable balance between accuracy and economy in modeling the energetics of these reactions. Increased alkyl substitution reduced barriers to isomerization by about 10 and 20 kJ mol(-1) for secondary and tertiary radical formation, respectively, relative to primary radical reactions and was relatively insensitive to the transition-state ring size (extent of H-atom internal shift). Reactions involving alkenyl and alkanoyl radicals were also explored. Hydrogen-atom transfers involving allylic radical formation demonstrated barrier heights that were 15-20 kJ mol(-1) lower than those in corresponding alkyl radicals, whereas those involving oxoallylic species (alpha-site radicals of aldehydes and ketones) were 20-40 kJ mol(-1) lower. In the cases of the alkyl radicals, enthalpies of activation were seen to scale with enthalpies of reaction. This correlation was not seen, however, in the cases of the allylic and oxoallylic radicals; this fact has significant implications in combustion chemistry and mechanism development, considering that such Evans-Polanyi correlations are widely used in estimating barrier heights for rate expressions.

CH and NH bond dissociation energies (BDEs) of various five‐ and six‐membered ring aromatic compounds were calculated using composite ab initio CBS‐Q, G3 and G3B3 methods. It was found that all these composite ab initio methods provided very similar BDEs, despite the fact that different geometries and different procedures in the extrapolation to complete incorporation of electron correlation and complete basis set limit were used. Therefore, the calculated BDEs should be reliable. In addition, we found interesting dependences of the CH BDEs on the bond angles, spins and charges. A good quantitative structure–activity relationship (QSAR) model for the CH BDEs of aromatic compounds was also established. Copyright © 2003 John Wiley &amp; Sons, Ltd.

Benchmark Accuracy in Thermochemistry, Kinetics, and Noncovalent Interactions

Prediction of Thermochemical Properties Across the Periodic Table

In celebration of the United Nations’ declaration of 2025 as the International Year of Quantum Science and Technology, marking 100 years since the development of quantum mechanics, this review highlights how accurate quantum mechanical calculations have transformed gas-phase thermochemistry. In particular, the developments of high-level composite ab initio methods over the past 30 years enable the calculations of thermochemical properties with confident chemical accuracy (i.e. with 95% confidence intervals ≤1 kcal mol−1) for molecules with up to 12 non-hydrogen atoms. Lower-level composite ab initio methods can be applied to molecules containing up to ~50 non-hydrogen atoms; however, they cannot achieve confident chemical accuracy in terms of 95% confidence intervals. Over the past three decades, hundreds of composite ab initio methods have been developed, covering different theoretical frameworks, levels of accuracy and computational costs. To guide users in selecting an appropriate composite ab initio method for a given system size and level of accuracy, we present a general approach for categorising the accuracy of these methods. This approach places composite ab initio methods on four rungs of Jacob’s Ladder. Lower rungs offer less accuracy but are applicable to larger systems, and higher rungs offer greater accuracy but are applicable to smaller systems. Each consecutive rung of this ladder represents an improvement in the treatment of the one-particle space, n-particle space, or both, leading toward the exact solution of the relativistic Schrödinger equation. The Jacob’s Ladder of composite ab initio methods can be considered as an extension to the Jacob’s Ladder of density functional theory (DFT), which leads from ‘Hartree Hell’ to the ‘Heaven’ of double-hybrid DFT methods.

A interpretation of stepwise bond dissociation energies of CH4

The C–H bond dissociation enthalpies (BDEs) of 27 N, O, S-containing mono-heterocyclic compounds were assessed by the composite high-level ab initio methods G4 and G3B3. After comparing the theoretical C–H BDEs of 32 N, O, S-containing heterocyclic compounds by using 10 density functional theory methods with experimental ones, we found that the BMK method provided the lowest root of mean square error of 7.2 kJ/mol. Subsequently, we calculated the C–H BDEs of oxygen-containing fused heterocyclic compounds at different positions by the BMK method. The results indicated that there are large BDE differences between the C(sp 3)–H bonds. In order to find the essence of the C–H BDE differences, NBO and molecular orbital analyses were conducted. In addition, the substituent effects on C–H BDEs in oxygen-containing fused heterocyclic compounds were discussed. Finally, we found two linear relationships between the BDEs and qO/e in the oxygen-containing fused heterocyclic compounds for different substituents, and the corresponding correlation coefficient squares (R 2) were 0.8551 and 0.9379, respectively.

Neutral and cation 1,2-dichloropropane molecular structures and energies investigated by DFT and ab initio methods

Quantum chemistry plays a key role in exploring the chemical properties of highly reactive chlorine polyfluoride compounds (ClFn). Here, we investigate the thermochemical properties of ClFn species (n=2-6) by means of high-level thermochemical procedures approximating the CCSDT(Q) and CCSDTQ5 energies at the complete basis set limit. We consider total atomization energies (TAEs), Cl-F bond dissociation energies (BDEs), F2 elimination energies (F2 elim.), ionization potentials (IPs), and electron affinities (EAs). The TAEs have significant contributions from post-CCSD(T) correlation effects. The higher-order triple excitations, CCSDT-CCSD(T), are negative and amount to -0.338 (ClF2), -0.727 (ClF3), -0.903 (ClF4), -1.335 (ClF5), and -1.946 (ClF6) kcal/mol. However, the contributions from quadruple (and, where available, also quintuple) excitations are much larger and positive and amount to +1.335 (ClF2), +1.387 (ClF3), +2.367 (ClF4), +2.399 (ClF5), and +3.432 (ClF6) kcal/mol. Thus, the contributions from post-CCSD(T) excitations exceed the threshold of chemical accuracy in nearly all cases. Due to their increasing hyper-valency and multireference character, the ClFn series provides an interesting and challenging test case for both density functional theory and low-level composite ab initio procedures. Here, we highlight the limitations in achieving overall chemical accuracy across all DFT and most composite ab initio procedures.

The hydrazine derivatives have been regarded as the important building blocks in organic chemistry for the synthesis of organic N-containing compounds. It is important to understand the structure-activity relationship of the thermodynamics of N-N bonds, in particular, their strength as measured by using the homolytic bond dissociation enthalpies (BDEs). We calculated the N-N BDEs of 13 organonitrogen compounds by eight composite high-level ab initio methods including G3, G3B3, G4, G4MP2, CBS-QB3, ROCBS-QB3, CBS-Q, and CBS-APNO. Then 25 density functional theory (DFT) methods were selected for calculating the N-N BDEs of 58 organonitrogen compounds. The M05-2X method can provide the most accurate results with the smallest root-mean-square error (RMSE) of 8.9 kJ/mol. Subsequently, the N-N BDE predictions of different hydrazine derivatives including cycloalkylhydrazines, N-heterocyclic hydrazines, arylhydrazines, and hydrazides as well as the substituent effects were investigated in detail by using the M05-2X method. In addition, the analysis including the natural bond orbital (NBO) as well as the energies of frontier orbitals were performed in order to further understand the essence of the N-N BDE change patterns.

The C–H bond dissociation enthalpies (BDEs) of the 26 N, O, S-containing mono-heterocyclic compounds were evaluated using the composite high-level ab initio methods G3 and G4. The C–H BDEs for 32 heterocyclic compounds were calculated using 8 types of density functional theory (DFT) methods. Comparing with the experimental values, the BMK method gave the lowest root mean square error (RMSE) of 7.2 kJ/mol. Therefore, the C–H BDEs of N-fused-heterocyclic compounds at different positions were investigated by the BMK method. By NBO analysis two linear relationships between the C–H BDEs of quinoline and isoquinoline with natural charges qC/e in molecules and with natural charges qC/e in radicals were found. The substituent effects on C(α)–H BDEs in N-fused-heterocyclic compounds were also discussed. It was found that there are two linear relationships between the C(α)–H BDEs of quinoline and isoquinoline derivatives with natural charges qC(α)/e for the EDGs and CEGs substituents.

The C‒H bond dissociation enthalpies (BDEs) of 26 N, O, S-containing mono-heterocyclic compounds were assessed by the composite high-level ab initio methods G4 and CBS-QB3. In addition, the C‒H BDEs of 32 heterocyclic compounds were evaluated by 13 density functional theory methods. The BMK method showed the lowest root mean square error of 7.2 kJ/mol and the correlation coefficient (R2) was 0.9874 after being compared with the experimental values. Subsequently, we used this method to study the C‒H BDE values of the different positions as well as the substituent effects on benzene and heterocycles in sulfur-containing fused heterocyclic compounds. Both the natural charge distributions of benzo[b]thiophene and benzothiazole and natural spin densities of benzo[b]thiophene derivative radicals were conducted by NBO analysis for further understanding the essence of the C‒H bond.