Comprehensive Benchmark Study on the Calculation of ²⁹Si NMR Chemical Shifts

Abstract

A comprehensive and diverse benchmark set for the calculation of 29 Si NMR chemical shifts is presented. The SiS146 set includes 100 silicon containing compounds with 146 experimentally determined reference 29 Si NMR chemical shifts measured in nine different solvents in a range from −400 to +828 ppm. Silicon atoms bound to main group elements as well as transition metals with coordination numbers of 2−6 in various bonding patterns including multiple bonds and coordinative and aromatic bonding are represented. The performance of various common and specialized density functional approximations including (meta-)GGA, hybrid, and double-hybrid functionals in combination with different AO basis sets and for differently optimized geometries is evaluated. The role of scalar-relativistic effects is further investigated by inclusion of the zeroth order regular approximation (ZORA) method into the calculations. GGA density functional approximations (DFAs) are found to outperform hybrid DFAs with B97-D3 performing best with an MAD of 7.2 ppm for the subset including only light atoms (Z < 18), while TPSSh is the best tested hybrid functional with an MAD of 10.3 ppm. For 29 Si cores in the vicinity of heavier atoms, the application of ZORA proved indispensable. Inclusion of spin−orbit effects into the 29 Si NMR chemical shift calculation decreases the mean absolute deviations by up to 74% compared to calculations applying effective core potentials.

Dialkylboryl-Substituted Cyclic Disilenes Synthesized by Desilylation-Borylation of Trimethylsilyl-Substituted Disilenes

“…Conversely, the δSi for the SiMe3-substituted double bond silicon nuclei (87.9 ppm) is upfield-shifted compared to that of 3 (187.2). The substantial difference in the chemical shifts of the double bond silicon nuclei was reproduced qualitatively by the GIAO calculations of 5opt [73.1 (=SiSiMe3) and 237.7 (=Si(BBN•DMAP) ppm] and 3opt [209.1 (=SiSiMe3) and 136.2 (=Si(BBN) ppm] at the B97-D3/def2-TZVP [26] level of theory (Table S4). As Strohman, Kaupp et al have theoretically In the 29 Si NMR spectrum, two 29 Si resonances due to the unsaturated silicon nuclei [87.9 (=SiSiMe 3 ) and 195.2 (=Si(BBN•DMAP) ppm] were observed for 5.…”

“…Conversely, the δSi for the SiMe 3 -substituted double bond silicon nuclei (87.9 ppm) is upfield-shifted compared to that of 3 (187.2). The substantial difference in the chemical shifts of the double bond silicon nuclei was reproduced qualitatively by the GIAO calculations of 5 opt [73.1 (=SiSiMe 3 ) and 237.7 (=Si(BBN•DMAP) ppm] and 3 opt [209.1 (=SiSiMe 3 ) and 136.2 (=Si(BBN) ppm] at the B97-D3/def2-TZVP [26] level of theory (Table S4). As Strohman, Kaupp et al have theoretically shown that the large difference in δSi of the double bond Si nuclei in the unsymmetrically substituted disilenes is mainly due to the spatial extent and orientation of the occupied and unoccupied molecular orbitals around the Si=Si double bond [27], the remarkable change in the δSi of the double bond Si nuclei upon coordination of DMAP is consistent with the lack of the conjugation between the π(Si=Si) and 2p(B) orbitals.…”

Lithiated 1,3-Disilabicyclo[1.1.0]butanes Synthesized via Selective Cleavage of Exocyclic Si–Si Bonds on Bridgehead Silicon Atoms

“…The transition energies and oscillator strengths of the electron transition in hexane (Tables S5–S8) were calculated using a time-dependent hybrid DFT method (TD-DFT) at the B3LYP-D3/def2-TZVP (hexane) level of theory. The GIAO calculations for NMR chemical shifts (Table S6) were performed at the HCTH407/B1 (B1:6-311+G­(3d) [Si], 6-31G­(d) [other atoms] (benzene) or the B97-D3/def2-TZVP (benzene) level of theory. Natural bond orbital (NBO) analysis was performed using NBO 7.0 program (Tables S5).…”

Do Double Hybrid Functionals Benefit from Regularization in the PT2 term? Observations from an Extensive Benchmark

“…As such, DHDF theory resides on the seamline between DFT and wavefunction approaches. DHDFs are the most accurate DFT methods available to date for main group energetics, [6][7][8] transition metal catalysis, [9][10][11][12] electronic excitation spectroscopy, [13][14][15][16][17][18][19][20][21] external magnetic [22][23][24][25] and electric field 26,27 induced properties, and vibrational frequencies. 28 Its reliance on a second-order perturbation theory term for part of the correlation energy creates an Achilles' Heel for molecules with small band gaps, due to the presence of orbital energy differences in the denominator.…”