N-Heterocyclic Carbenes: A Benchmark Study on their Singlet-Triplet Energy Gap as a Critical Molecular Descriptor

Abstract

N-heterocyclic carbenes (NHCs) are used extensively in modern chemistry and materials science. The in-depth understanding of their electronic structure and their metal complexes remains an important topic of research and of experimental and theoretical interest. Herein, the adiabatic singlet-triplet gap as a superior, quantifiable critical descriptor, sensitive to the nature and the structural diversity of the NHCs, for a successful rationalization of experimental observations and computationally extracted trends is established. The choice is supported by a benchmark study on the electronic structures of NHCs, using high-level ab initio methods, that is, complete active space self-consistent field, n-electron valence second-order perturbation theory, multireference configuration interaction + singles + doubles, and domain-based local pair natural orbital-coupled cluster method with single-, double-, and perturbative triple excitations along with density functional theory methods such as BP86, M06, and M06-L, B3LYP, PBE0, TPSSh, CAM-B3LYP, and B2PLYP. In contrast to the adiabatic singlet-triplet (S-T) gap preferred as descriptor, the highest occupied molecular orbital-lowest unoccupied molecular orbital gap or the S-T vertical gap that has been used in the past occasionally leads to controversial results; some of these are critically discussed below. Extrapolation of these ideas to a group of copper-NHC complexes is also described.

Keywords: N ‐heterocyclic carbenes; ab initio; HOMO–LUMO gaps; density functional theories; singlet–triplet gaps.

Figure 1

Prototype NHC structure, featuring the imidazole backbone and two methyl groups as wingtips.

Figure 2

NHC structures derived from 1 by the replacement of the Me wingtips with bulkier tBu, (1 ^tBu ); Ph, (1 ^Ph ); mesityl (Mes)(1 ^Mes ); and diisopropylphenyl (DiPP), (1 ^DiPP ).

Figure 3

Optimized geometries of analogs of 1, at the M06‐L/def2‐TZVPP level of theory. ‘S’ and ‘T’ denote the ground singlet and the first excited triplet states, respectively.

Figure 4

Calculated molecular structures of the N‐heterocyclic carbenes and borylenes molecules.

Figure 5

Adiabatic S–T gap for molecules 1‐11 using a series of DFT methods and the def2‐TZVPP basis set. The gap is given both in eV and kcal/mol.

Figure 6

Relative (adiabatic) S–T gaps for 3 (right) and two derivatives (3a and 3b) of it (left, middle). The optimized geometries for all singlet (black lines, down) and triplet (red lines, up) states are also shown, calculated by the BP86/def2‐TZVPP method.

Figure 7

Vertical S–T gap for molecules 1‐11 calculated via a series of methodologies using the def2‐TZVPP basis set. The M06‐L geometries have been used for the CASSCF, NEVPT2, MRCISD, and DLPNO‐CCSD(T). The respective DFT values from M06‐L and B2PLYP are given for comparison purposes.

Figure 8

Adiabatic S–T gap for molecules 1‐11 calculated via DFT (M06‐L), MRCISD + Q, NEVPT2, and DLPNO‐CCSD(T) (both at def2‐TZVPP and CBS) methods, using the M06‐L/def2‐TZVPP optimized geometries.

Figure 9

Model calculated compounds featuring the abovementioned NHCs 1, 8, and 11.

Figure 10

Schematic presentation of the S–T gaps of the model compounds, along with their optimised geometries at the M06‐L/def2‐TZVPP level of theory. The S–T gaps are obtained via the DLPNO‐CCSD(T)/def2‐TZVPP. For each complex, the left arrow represents the vertical excitation, while the right one the adiabatic excitation.