Time-dependent density functional theory study of absorption spectra of metallocenes Yong L. Li a , Lei Han b , Ye Mei c , John Z.H. Zhang c,d, * a School of Chemistry and Chemical Engineering, Nanjing University, 22 Hankou Road, Nanjing 210093, China b Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences, 345 Lingling Road, Shanghai 200032, China c State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai 200062, China d Department of Chemistry, New York University, New York, NY 10003, United States article info Article history: Received 2 September 2009 In final form 9 October 2009 Available online 13 October 2009 abstract Extensive TDDFT calculations with various combinations of functionals are carried out to compute low- lying excited states of ferrocene. The combined functional and basis set approach TD-PBE0/6-311++G(d,p) is found to be well-behaved in the calculation of excited states. This choice of functional/basis set can give correct ground-state geometries, excitation energies, absorption spectra, and correct symmetry sequence of low level unoccupied molecular orbitals. This method is applied to the calculation of excitation ener- gies of bis(benzene)chromium and four derivatives of ferrocene and the results are accurate within 0.3 eV. The current study implies that the combination TD-PBE0/6-311++G(d,p) can be used to compute excited state properties of other transition metal complexes. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction Time-dependent density functional theory (TDDFT) provides an efficient means for computing excited states of chemicals, such as dye molecules and metallorganic compounds [1–7]. Metallocenes, especially ferrocene, are the most interesting prototypes of this type of compounds and have attracted significant interest [8]. TDDFT method is considered to be reliably accurate for calculating transition metal complex [9–12]. Although configuration methods such as CASSCF [13], CASPT2 [14], etc. could provide more accurate results, but their applications are limited because they either re- quire much experience to deal with pitfalls such as the notorious intruder states [15] or need much more computer times. It is thus desirable to study excited state properties of metallocenes based on TDDFT approach. Of particular interest for us is to investigate the dependence of the computed molecular properties on specific functionals and basis sizes. It is known that the TDDFT may give relatively larger errors in predicting the d–d transition. In such cases, the method DSCF performs better [10]. But we will see that results from TDDFT are also acceptable. For all major transition types of metal centered (MC) metallorganic compounds, metal to ligand charge transfer (MLCT) and ligand to metal charge transfer (LMCT) are of valence type [10]. They can be reliably predicted by TDDFT than the Rydberg type transitions which are hard to be dealt with using TDDFT. The first attempt to predict absorption spectrum of ferrocene is by Boulet et al. [5]. In that work, they used several functionals including B3LYP and calculated the first four excitations of D 5d fer- rocene. Although the hybrid B3LYP functional is most popular to calculate diverse properties of various molecules, it has been noted that B3LYP is not ideal in calculating excited state properties of molecules [7,16] despite continued use of it [2,4,6]. We think it is important to perform a comparison study of existing functionals in their prediction of excited state properties molecules. It is also known that larger basis set does not necessarily result in more accurate results in DFT calculation [17]. It is thus possible to em- ploy just moderate basis size to obtain results as accurate as that obtained from other post-Hartree–Fock methods such as CI, many-body perturbation etc. In those methods, large orbitals are needed. In our study we found that triple-f diffuse 6-311++G(d,p) [18] is sufficient to balance the accuracy and efficiency. Another issue concerned is the symmetry sequence of virtual orbitals that are sensitive to functionals used, although they all give the same energy sequence for occupied orbitals. Even in two previous works, the reported symmetries of virtual orbitals are dif- ferent [19,20]. As we will see below, different functionals and com- bined with pseudopotential would give different symmetry sequences of virtual orbitals. This difference of symmetry of virtual orbitals could confuse the specification of the transition type, and may be one of the resources of deviations of calculated excitation energies from experimental values. 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.10.026 * Corresponding author. Address: Department of Chemistry, New York Univer- sity, New York, NY 10003, United States. E-mail address: john.zhang@nyu.edu (J.Z.H. Zhang). Chemical Physics Letters 482 (2009) 217–222 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett