Trends in Strong Chemical Bonding in C₂, CN, CN^–, CO, N₂, NO, NO⁺, and O₂

Abstract

The strong chemical bonds between C, N, and O play a central role in chemistry, and their formation and cleavage are critical steps in very many catalytic processes. The close-lying molecular orbital energies and large correlation effects pose a challenge to electronic structure calculations and have led to different bonding interpretations, most notably for C. One way to approach this problem is by strict benchmark comparison of related systems. This work reports reference electronic structures and computed bond dissociation enthalpies D for C, CN, CN, CO, N, NO, NO, O and related systems C and C at chemical accuracy (∼1 kcal/mol or 4 kJ/mol) using CCSD(T)/aug-cc-pV5Z, with additional benchmarks of HF, MP2, CCSD, explicitly correlated F12 methods, and four density functionals. Very large correlation and basis set effects are responsible for up to 93% of total D. The order of the molecular orbitals 1π and 3σ changes, as seen in textbooks, depending on total and effective nuclear charge. Linear trends are observed in 2σ-2σ orbital splitting (R = 0.91) and in D of C, C, and C (R = 0.99). The correlation component of D of C is by far the largest (∼93%) due to a poor HF description. Importantly, density functional theory fails massively in describing this series consistently in both limits of effective nuclear charge, and Hartree-Fock exchange or meta functionals do not remedy this 100 kJ/mol error, which should thus be addressed in future density functional developments as it affects very many studies involving cleavage or formation of these bonds.

Accuracy of theoretical catalysis from a model of iron-catalyzed ammonia synthesis

“…2; numbers and errors in Supplementary Tables 7 and 8). HF lacks correlation energy in the Löwdin definition and thus underestimates the experimental D 0 by more than 200 kJ mol −1 on average for the five bonds, but clearly most for the strong triple bond of N 2 , as found previously 22,36 . The local density method PWLDA displays a MAE of 78 kJ mol −1 but with an opposite tendency of strong over-binding (MSE =+78 kJ mol −1 ) ( Supplementary Tables 7/8), which is also well-known and illustrates the original rationale for mixing local DFT and HF exchange in hybrids 37 .…”

“…All the methods MP2, CAMB3LYP, CCSD(T), CCSD, PW6B95, M06-2×, B3LYP, and B3LYP* are within chemical accuracy (4 kJ mol −1 ) for the net process. CCSD(T) includes the essential electron correlation and performs at chemical accuracy, as expected since the applied basis set is saturated within this window of accuracy 22,36 . The zeropoint energy corrections provide most of the correction of the electronic energies to enable comparison to experiment, with a minor additional contribution from thermal enthalpy of~RT (~2.5 kJ mol −1 ) at 298 K. At higher temperature where real processes take place, these corrections become larger but are derived from the same (BP86) frequency calculation representing the geometry optimization and thus do not differentially affect method performance.…”

“…The quantum mechanical goldstandard CCSD(T) agrees well with most of the experimental values, but for Fe-NH 3 there is disagreement of 36 kJ mol −1 between experiment and CCSD(T), i.e., one of the numbers is less accurate, and thus both numbers may be considered when evaluating the DFT methods for this particular enthalpy. Major changes in static correlation effects upon ligand dissociation could plausibly cause CCSD(T) to fail, but generally CCSD(T) achieves chemical accuracy with the applied basis set 22 .…”

“…However, the most important catalytic processes commonly involve transition metals with unpaired d-electrons whose treatment depends critically on the type of DFT applied and multiple steps having very distinct changes in electronic structure 5,21 . Strong double and triple bonds that are often broken during catalysis (e.g., N 2 , CO, O 2 ) pose an additional challenge to DFT, as the error in electron correlation typically scales with the bond strength 22 . Despite this, many theoretical studies of transition metal catalysis routinely use a single popular functional such as RPBE or B3LYP for all steps as the basis for conclusions, with assumptions of accuracy largely extrapolated from previous onestep benchmarks [23][24][25] .…”

Performance of Density Functional Theory for Transition Metal Oxygen Bonds

“…This basis set is saturated to within 2-3 kJ/mol in terms of errors in BDEs as shown from previous work. [40,56]…”