Fermi Contact Spin Density Calculations of Aromatic Radicals

The Gaussian-weighted operator derived by Rassolov and Chipman (RC operator) is applied to the spin density of large organic pi-radicals using B3LYP and PBE0 density functionals and compared to the performance of the delta-function operator. The influence of the basis sets is examined. It is shown that both the delta-function operator and the RC operator provide comparable spin densities with the basis sets ext-6-311++G** and ext-6-311++G(2d,2p). An optimum range parameter of 0.25 or 0.35 a(0) is appropriate for the RC operator with the extended basis sets. For standard basis sets 6-311++G** and 6-311++G(2d,2p), the delta-function operator may yield considerable errors for heavy atoms due to the deficiency of the basis sets near the nuclei. To a large extent, however, this deficiency can be cured with the RC operator. With the same range parameter of 0.25 or 0.35 a(0) previously recommended, the errors are significantly reduced with respect to the delta-function method. If a relatively larger range parameter of 0.45 a(0) is used, a further improvement can be obtained and the spin densities at the B3LYP/6-311++G** or B3LYP/6-311++G(2d,2p) level of methods are similar to the ones at the B3LYP/ext-6-311++G** or B3LYP/ext-6-311++G(2d,2p) level of methods. Generally, the UB3LYP/6-311++G** and the UB3LYP/ext-6-311++G** methods are able to provide satisfactory spin densities. For some anions, the B3LYP/6-311++G(2d,2p) and the B3LYP/ext-6-311++G(2d,2p) methods are needed to achieve better agreement with the experiment. It is demonstrated that the B3LYP functional combined with the standard Pople-type basis sets 6-311++G** and 6-311++G(2d,2p), which are designed for conventional electronic structure calculations, serves as an efficient and reliable method for the calculation of spin densities of large organic radicals when the Rassolov-Chipman operator is utilized, while the delta-function operator may lead to far less reliable results. An optimum range parameter of 0.45 a(0) is recommended.