We present SPOCK.CI, a selecting direct multireference spin-orbit configuration interaction (MRSOCI) program based on configuration state functions. It constitutes an extension of the spin-free density functional theory/multireference configuration interaction (DFT/MRCI) code by Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] and includes spin-orbit interaction on the same footing with electron correlation. Key features of SPOCK.CI are a fast determination of coupling coefficients between configuration state functions, the use of a nonempirical effective one-electron spin-orbit atomic mean-field Hamiltonian, the application of a resolution-of-the-identity approximation to computationally expensive spin-free four-index integrals, and the use of an efficient multiroot Davidson diagonalization scheme for the complex Hamiltonian matrix. SPOCK.CI can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRSOCI). The application of these techniques and approximations makes it possible to compute spin-dependent properties of large molecules in ground and electronically excited states efficiently and with high confidence. Second-order properties such as phosphorescence rates are known to converge very slowly when evaluated perturbationally by sum-over-state approaches. We have investigated the performance of SPOCK.CI on these properties in three case studies on -pyran-4-thione, dithiosuccinimide, and free-base porphin. In particular, we have studied the dependence of the computed phosphorescence lifetimes on various technical parameters of the MRSOCI wave function such as the size of the configuration space, selection of single excitations, diagonalization thresholds, etc. The results are compared to the outcome of extensive quasidegenerate perturbation theory (QDPT) calculations as well as experiment. In all three cases, the MRSOCI approach is found to be superior to the QDPT expansion and yields results in very good agreement with experimental findings. For molecules up to the size of free-base porphin, MRSOCI calculations can easily be run on a single-processor personal computer. Total CPU times for the evaluation of the electronic excitation spectrum and the phosphorescence lifetime of this molecule are below 40 h.
REFERENCES
Note a typo in Table 2 of Ref. 37. The first case (, , ) should read .
In the actual implementation always wave functions are employed, irrespective of the irreducible representation of the spatial part. Before multiplying the spatial integrals with the spin factor, the latter is converted to a matrix element of the appropriate Cartesian spin operator by means of the scaled -symbol approach (Ref. 37).
The axis passes through the N–H bonds of free-base porphin and the axis is perpendicular to the molecular plane.
In the original publication, this sublevel is denoted because the and axes had been interchanged.
In metalloporphyrins of symmetry, the latter two orbitals even form a degenerate pair .
For being Hermitian, the matrix has to be symmetric while has to be skew symmetric. From this it easily follows that is symmetric.
