Illumination with 660-nm light shifts the in vitro equilibrium between the two towards approximately 85% Pfr and triggers a physiological response in vivo, whereas illumination with 730-nm light yields about 99% Pr and cancels the physiological effect⁵.The kinetics of the Pr → Pfr phototransformation has been extensively studied by a variety of time-resolved spectroscopic techniques,^6–14 and a number of metastable intermediates states with lifetimes in the micro to millisecond regime and distinctive absorption characteristics (λ_max) have thereby been identified.

In later studies resonance Raman (RR) techniques, which offer a means to investigate the in situ structure of chromophores in proteins, have been used to probe the conformation of PΦB at different stages of the photocycle.^16–20

By calculating ground and excited-state potential energy surfaces (PES) taking into account both concerted (Z,syn → E,anti) and stepwise (Z → E followed by syn → anti) reaction pathways, we will in particular herein be able to present valuable new information with regard to the nature and starting of the syn → anti isomerization (photochemical isomerization simultaneously with Z → E or thermal isomerization after Z → E).

It should here be pointed out that the above studies^25–27,30 were carried out using multiconfigurational complete active space self-consistent field (CASSCF) methods, which constitute the most appropriate theoretical framework for the modeling of photochemical reactions.³¹

However, such methods are inevitably marred by substantial computational demands, rendering them inapplicable to a molecular system as large as PΦB.

Actually, even subjecting to CASSCF calculations a simplified PΦB model comprising only rings C and D is a prohibitively difficult task if many points on a PES are of interest (an active space consisting of 12 electrons and 12 orbitals is a recent estimate³² of the practical limit for asymmetric molecules).

The density functional theory (DFT)-based approach undertaken in this work, on the other hand, enables the necessary calculations, but provides a less accurate description in regions where two potential energy surfaces come close in energy.

None of the conclusions emerging from the present work is however affected by this shortcoming.

Ground-state geometries were optimized using the B3LYP hybrid density functional^37–39 in conjunction with the 6-31G(d) basis set, excited-state geometries were optimized using the ab initio configuration interaction singles (CIS) method within the frozen-core approximation and employing the same basis set.

Vertical and adiabatic excitation energies were calculated on the basis of B3LYP ground-state and CIS excited-state geometries, respectively, using the Gaussian 03 implementation⁴⁰ of time-dependent density functional theory (TD-DFT).⁴¹

The TD-DFT single point calculations were carried out with the B3LYP functional, and made use of the 6-31G(d) basis set unless otherwise explicitly noted.

Next, basis set effects on excitation energies were investigated by calculating vertical excitation energies for the S₁ and S₂ states of PΦB1 in Z,syn, E,syn, Z,anti, and E,anti configurations using the 6-31G(d), 6-31G(d,p), 6-31+G(d), and 6-311+G(d,p) basis set.

Subsequently, zero-point vibrational energy (ZPVE) corrections and thermal corrections to Gibbs free energies (G_corr) for optimized S₀, S₁, and S₂ structures of PΦB1 (Z,syn, E,syn, Z,anti, and E,anti) were obtained through B3LYP/6-31G(d) and CIS/6-31G(d) frequency calculations, respectively.

Finally, S₀, S₁, and S₂ PES for PΦB1 taking into account variation in C13C14−C15C16 and C14−C15C16−C17 dihedrals were computed employing 99 ‘grid points’, each combining one value from C13C14−C15C16 = {−0, −30, −60, −75, −90, −105, −120, −150, −180°} with one value from C14−C15C16−C17 = {0, 30, 45, 60, 75, 90, 105, 120, 135, 150, 180°}.

At each point, B3LYP/6-31G(d) and CIS/6-31G(d) geometry optimizations were carried out relaxing all other degrees of freedom.

In order to obtain more accurate excited-state energies, TD-B3LYP/6-31G(d) single point calculations were then performed on the optimized CIS geometries.

On the basis of the initial ‘benchmark’ calculations (commented upon in detail below), neither ZPVE nor thermal corrections for these grid point were accounted for.

It should be noted that the use of DFT for optimizing ground-state structures and CIS − a Hartree–Fock (HF)-based method − for optimizing excited-state structures to some extent results in an unbalanced description of the PES.

By subjecting the optimized S₁ geometries of PΦB1 to TD-B3LYP/6-31G(d) single point calculations, wavelengths of maximum emission were obtained as well (Table 1).

In order to gain some insight into the intrinsic mechanism governing the PΦB C15-Z,syn → C15-E,anti isomerization responsible for the photoactivation of phytochrome, we have in the present study subjected a simplified PΦB model to quantum chemical calculations.