Multiconfigurational Second-Order Perturbation Theory with Frozen Natural Orbitals Extended to the Treatment of Photochemical Problems

Abstract

A new flavor of the frozen natural orbital complete active space second-order perturbation theory method (FNO-CASPT2, Aquilante et al., J. Chem. Phys. 131, 034113) is proposed herein. In this new implementation, the virtual space in Cholesky decomposition-based CASPT2 computations (CD-CASPT2) is truncated by excluding those orbitals that contribute the least toward preserving a predefined value of the trace of an approximate density matrix, as that represents a measure of the amount of dynamic correlation retained in the model. In this way, the amount of correlation included is practically constant at all nuclear arrangements, thus allowing for the computation of smooth electronic states surfaces and energy gradients-essential requirements for theoretical studies in photochemistry. The method has been benchmarked for a series of relevant biochromophores for which large speed-ups have been recorded while retaining the accuracy achieved in the corresponding CD-CASPT2 calculations. Both vertical excitation energies and gradient calculations have been carried out to establish general guidelines as to how much correlation needs to be retained in the calculation for the results to be consistent with the CD-CASPT2 findings. Our results feature errors within a tenth of an eV for the most difficult cases and have been validated to be used for gradient computations where an up to 3-fold speed-up is observed depending on the size of the system and the basis set employed.

Assessment of the Potential Energy Hypersurfaces in Thymine within Multiconfigurational Theory: CASSCF vs. CASPT2

“…Instead, the presence of a twisted minimum along the decay path, previously reported in the literature [34,63], appears to be the main structure hampering the barrierless route towards the 1 (ππ*/S 0 ) CI . This relates to what has also been found for PSB-3, where the dynamically correlated CASPT2 displays a more stable minimum under the planar minimum described by CASSCF [63]. Lower values of r favor this situation in which thymine finds itself to be stranded in a shallow minimum.…”

“…Figure 1 displays these structures for thymine, the system under study in the present work. They correspond to two different excited state minima, one planar [11] and one partially twisted or "boat-like" found in more correlated computations or solvated environments [24,34,63,64], and an "ethene-like" CI [65,66] connecting the 1 (ππ*) and ground states. The CI is usually employed to rationalize the ultrafast decay of thymine [8] and the extremely low fluorescence quantum yields recorded experimentally [62], and was initially reported in the pioneering study of Perun et al [22].…”

“…This would drastically reduce the role of the 1 (n O π*) state in the photo-process, in contrast to what has been reported in MRCIS and CASSCF non-diabatic molecular dynamics studies [26,93,95], where a vast fraction of the excited state population ends up trapped in the 1 (n O π*) state in the sub-ps timescale. This incidence is related to the likely overestimated role of the 1 (n O π*) PEH in MRCIS/CASSCF, where this state is proposed to be the main responsible of the ultrafast deactivation, and points towards an uneven treatment of the 1 (n O π*) and 1 (ππ*) states, which are described quite differently with methods lacking dynamic correlation like CASSCF [63,81], and that has motivated studies in the literature to assess the importance of the dynamic correlation in the overall photochemical picture [19,72]. This is further assessed in Figure 5, where an energy diagram of the involvement of the 1 (n O π*) state at both CASSCF//CASSCF and CASPT2//CASPT2 levels is shown, together with the energy profile arisen from the CASPT2//CASSCF protocol.…”

“…Their overall RMS compared to ANO-L 432/21 is~0.004, showing how covalent states such as 1 (n O π*) show a lesser dependence on the dynamic correlation included in the model than that found for the 1 (ππ*) state (cf . Table S48) [63]. It can therefore be concluded that 6-31G* provides a reasonable description of the PEH and will be the basis set used to test the adequacy of the CASPT2//CASSCF protocol against CASPT2//CASPT2.…”

“…A similar behavior is observed when the geometry optimizations are carried out at the CASPT2 level, with the sole difference that the minimum found along the hypersurface can be slightly twisted or "boat-like" 1 (ππ*) min-twisted (cf. Figure 1) [17,34,63]. The conclusions derived from those studies seem to be dependent on the strategy used, highlighting the additional insights provided by more sophisticated MEP techniques to map PEHs, while stressing the need for computing experimental observables derived from accurate PEHs to be able to unambiguously compare face-to-face with the experiment [17,73].…”