Effects of vibrational averaging on coupled cluster calculations of spin–spin coupling constants for hydrocarbons

Abstract

We present vibrationally corrected nuclear spin–spin coupling constants for four hydrocarbons with different types of carbon–carbon bonds calculated with coupled cluster (CC) theory. First, we perform a systematic basis set investigation on acetylene for all of the four contributions (Fermi-contact, spin-dipole, para- and diamagnetic spin–orbit) to the spin–spin coupling constants and subsequently choose basis sets of sufficient flexibility to describe converged electronic properties. Then, in order to describe the effects of vibrational motion for the studied molecules we perform a Taylor expansion in the normal coordinates up to second order – a method that is well known for both its quality and efficiency – and rigorously estimate the resulting contribution for all types of spin–spin coupling constants. Combined, this allows us to obtain highly accurate benchmark estimates of the spin–spin coupling constants for acetylene, ethylene, ethane, and cyclopropane. This work provides one of the first systematic benchmarks of zero-point vibrational contributions to spin–spin coupling constants in poly-atomic molecules using the reliable CC theory and it is thus an important reference for further research within in-silico spin–spin coupling constant determination. We note that earlier computational estimates of zero-point vibrational effects agree well with those presented here (for acetylene, ethylene, and cyclopropane) while vibrational corrections for ethane are reported for the first time.

Keywords:

• coupled cluster
• spin–spin coupling
• hydrocarbons
• vibrational averaging

Acknowledgements

The authors thank Prof. Hans-Ullrich Siehl for the suggestion of investigating the considered hydrocarbons. This work has been supported by the Robert A. Welch Foundation (Grant F-1283) and the US National Science Foundation.

Notes

Notes

1. In an obvious C basis/H basis notation.

2. For example, for the one-bond ¹ J(CH) coupling in acetylene CAS, SOPPA, and DFT 30 give a coupling of 188, 185, and 205 Hz, respectively.

3. That is, { ⁿ J} _n>1.

4. For example, for ¹ J(CC) vibrational corrections of −10.26 Hz 33 and −10.0 Hz 30.

5. For example, for ¹ J(CC) in ethylene and cyclopropane vibrational contributions of 0.9 Hz 32 and 0.5 Hz 42 have been reported – both estimated using DFT.