Molecular Vertical Excitation Energies Studied with First-Order RASSCF (RAS[1,1]): Balancing Covalent and Ionic Excited States

Abstract

RASSCF calculations of vertical excitation energies were carried out on a benchmark set of 19 organic molecules studied by Thiel and co-workers [ J. Chem. Phys. 2008 , 128 , 134110 ]. The best results, in comparison with the MS-CASPT2 results of Thiel, were obtained using a RASSCF space that contains at most one hole and one particle in the RAS1 and RAS3 spaces, respectively, which we denote as RAS[1,1]. This subset of configurations recovers mainly the effect of polarization and semi-internal electronic correlation that is only included in CASSCF in an averaged way. Adding all-external correlation by allowing double excitations from RAS1 and RAS2 into RAS3 did not improve the results, and indeed, they were slightly worse. The accuracy of the first-order RASSCF computations is demonstrated to be a function of whether the state of interest can be classified as covalent or ionic in the space of configurations built from orbitals localized onto atomic sites. For covalent states, polarization and semi-internal correlation effects are negligible (RAS[1,1]), while for ionic states, these effects are large (because of inherent diffusiveness of these states compared to the covalent states) and, thus, an acceptable agreement with MS-CASPT2 can be obtained using first-order RASSCF with the extra basis set involving 3p orbitals in most cases. However, for those ionic states that are quasi-degenerate with a Rydberg state or for nonlocal nπ* states, there remains a significant error resulting from all external correlation effects.

Scheme 1. Classification of RASSCF Configuations

Scheme 2. Summary of RASSCF Procedure Used

Scheme 3. Examples of Covalent and Ionic VB Structures for Hexatriene

Figure 1

List of molecules investigated for the benchmark of vertical excitation energies using CASSCF/RASSCF based the data set of Schreiber et al. A subset of the Thiel benchmark set is used rather than the full set due to unfavorable scaling of the RASSCF active space with the current approach.

Figure 2

Scatter plot of error (in blue) and its average (in red) on vertical excitation of all investigated excited states computed at CASSCF/RASSCF level compared MS-CASPT2 results of Schreiber et al. Rydberg states are not included.

Figure 3

Scatter plot of the error (in blue) and its average (in red) for the vertical excitation energies for covalent (top) and ionic (bottom) excited states. The comparison is done against MS-CASPT2 results of Schreiber et al. The Rydberg states are not included. (The three outliers in the last three columns correspond to the ethene V state which is a Rydberg–ionic mixture.)

Figure 4

Comparison of the mean standard error (in blue) and mean absolute error (in red) for the vertical excitation energies of the 19 molecules computed with different electronic structure method (see Tables S20–S22 in the Supporting Information for details). The values are compared to the theoretical best estimated (i.e., TBE-2) in the work of Silva-Junior et al. The statistics are done over 36 excited states for all methods, except for CC2/AVTZ and CC3/AVTZ where only 29 and 6 values were available for the current set of molecules, respectively.