Experimental Observation of Anharmonic Coupling of the Heme-Doming and Iron−Ligand Out-of-Plane Vibrational Modes Confirmed by Density Functional Theory

Classical Correlation Model of Resonance Raman Spectroscopy

A classical correlation model (CCM), based on forces instead of potentials, is developed and applied to resonance Raman scattering to provide a foundation for further advances in understanding the effects of fields and vibronic perturbations on the optical properties of materials by a simple, yet versatile, description. The model consists of a charge connected by a classical spring to a surface and driven by an external electric field. The spring represents the charge cloud of the electrons and the transition strength, and the surface represents the nucleus or molecule. Molecular vibrations are assumed to be many-body effects that change the configuration and hence modify the spring constant directly, as opposed to all previous classical models of Raman scattering, and opposed to the anisotropic bond model (ABM) of nonlinear optics, by adding anharmonic terms to the potential. The resulting expression agrees exactly with quantum mechanical models of resonance Raman scattering in the limit of weak electron-phonon coupling, and it agrees well when the coupling becomes strong. The result is a classical derivation of Kramers-Heisenberg-Dirac scattering theory. We show that the difference between classical and quantum approaches lies only in the interpretation of the prefactor. In particular, the Raman excitation profile shows excellent agreement with all other methods of calculation. By comparing complementary classical and quantum solutions of the same complex system, understanding of both is enhanced.

Excited-state vibrational coherence in methanol solution of Zn(II) tetrakis(N-methylpyridyl)porphyrin: charge-dependent intermolecular mode frequencies and implications for electron-transfer dynamics in photosynthetic reaction centers

The nature of the intermolecular vibrational modes between the redox-active chromophores and the protein medium in the photosynthetic reaction center is central to an understanding of the structural origin of the quantum efficiency of the light-driven charge-separation reactions that result in storage of solar energy. In recent work on this issue, we have characterized the low-frequency vibrational coherence of Zn(II) meso-tetrakis(N-methylpyridyl)porphyrin (ZnTMPyP) and compared it to that from bacteriochlorophyll a in polar solution and in the small light-harvesting subunits B820 and B777. The charge-transfer character of ZnTMPyP's π* excited states afford us the opportunity to characterize how the intermolecular vibrational modes and potential with the surrounding medium are affected by the charge on the porphyrin macrocycle. The excited-state vibrational coherence observed with Q-band (S(1) state) excitation at 625 nm of ZnTMPyP in methanol solution contains dominant contributions from a pair of rapidly damped (effective damping time γ < 400 fs) components that are assigned to the hindered translational and librational porphyrin-solvent intermolecular modes. The 256 cm(-1) mean frequency of the intermolecular modes is significantly higher than that observed previously in the ground state, 79 cm(-1), with Soret-band excitation at 420 nm [Dillman et al., J. Phys. Chem. B. 2009, 113, 6127-6139]. The increased mode frequency arises from the activation of the ion-dipole and ion-induced-dipole terms in the intermolecular potential. In the ground state, the π-electron density of ZnTMPyP is mostly confined to the region of the porphyrin macrocycle. In the excited state, the π-electron density is extensively delocalized from the porphyrin out to two of the peripheral N-methylpyridyl rings, each of which carries a single formal charge. The charge-dependent terms contribute to a significant stabilization of the equilibrium geometry of the porphyrin-solvent complex in the excited state. In the photosynthetic reaction center, these terms will play an important role in trapping the charged products of the forward, charge-separation reactions, and the location of the bacteriopheophytin acceptor in a nonpolar region of the structure enhances the rate of the secondary charge-separation reaction.

Investigations of vibrational coherence in the low-frequency region of ferric heme proteins

Femtosecond coherence spectroscopy is applied to a series of ferric heme protein samples. The low-frequency vibrational spectra that are revealed show dominant oscillations near 40 cm(-1). MbCN is taken as a typical example of a histidine-ligated, six-coordinate, ferric heme and a comprehensive spectroscopic analysis is carried out. The results of this analysis reveal a new heme photoproduct species, absorbing near 418 nm, which is consistent with the photolysis of the His(93) axial ligand. The photoproduct undergoes subsequent rebinding/recovery with a time constant of approximately 4 ps. The photoproduct lineshapes are consistent with a photolysis quantum yield of 75-100%, although the observation of a relatively strong six-coordinate heme coherence near 252 cm(-1) (assigned to nu(9) in the MbCN Raman spectrum) suggests that the 75% lower limit is much more likely. The phase and amplitude excitation profiles of the low-frequency mode at 40 cm(-1) suggest that this mode is strongly coupled to the MbCN photoproduct species and it is assigned to the doming mode of the transient penta-coordinated material. The absolute phase of the 40 cm(-1) mode is found to be pi/2 on the red side of 418 nm and it jumps to 3pi/2 as excitation is tuned to the blue side of 418 nm. The absolute phase of the 40 cm(-1) signal is not explained by the standard theory for resonant impulsive stimulated Raman scattering. New mechanisms that give a dominant momentum impulse to the resonant wavepacket, rather than a coordinate displacement, are discussed. The possibilities of heme iron atom recoil after photolysis, as well as ultrafast nonradiative decay, are explored as potential ways to generate the strong momentum impulse needed to understand the phase properties of the 40 cm(-1) mode.

Laser control of vibrational excitation in carboxyhemoglobin: A quantum wave packet study

A coherent control algorithm is applied to obtain complex-shaped infrared laser pulses for the selective vibrational excitation of carbon monoxide at the active site of carbonmonoxyhemoglobin, modeled by the six-coordinated iron-porphyrin-imidazole-CO complex. The influence of the distal histidine is taken into account by an additional imidazole molecule. Density-functional theory is employed to calculate a multidimensional ground-state potential energy surface, and the vibrational dynamics as well as the laser interaction is described by quantum wave-packet calculations. At each instant in time, the optimal electric field is calculated and used for the subsequent quantum dynamics. The results presented show that the control scheme is applicable to complex systems and that it yields laser pulses with complex time-frequency structures, which, nevertheless, have a clear physical interpretation.

Correct interpretation of heme protein spectra allows distinguishing between the heme and the protein dynamics

It is shown by using the vibronic approach that the iron displacement out of the porphyrin plane in deoxyheme proteins intermixes the porphyrin pi and axial iron-histidine sigma electronic subsystems. This intermixing explains the substantial coupling of the iron-histidine vibration to the heme Soret excitation, the appearance of the iron-histidine band in the corresponding resonance Raman spectra, and a number of other experimental data, including the dependence of the iron-histidine vibrational frequency on the extent of the iron displacement out of the porphyrin plane. This dependence implies that there is an anharmonic coupling between the corresponding vibrations, which is shown to be the cause of the specific temperature dependence of the iron-histidine band. The anharmonic coupling and the dependence of the dipole transition moment of the charge transfer optical absorption band III on the iron-porphyrin distance cause the anomalous temperature and pressure dependencies of this band. It is shown that the change in both the magnitude and the distribution of the iron-porphyrin distance is expected to affect the band III intensity. Consequently, the stationarity of the band III intensity can be considered as a signature of the stationarity of the iron-porphyrin distance and its distribution in deoxyheme proteins, whereas the band III position and width could be also affected by the change in the protein electric field, caused by the protein globule dynamics.

Spin-dependent mechanism for diatomic ligand binding to heme

The nature of diatomic ligand recombination in heme proteins is elucidated by using a Landau-Zener model for the electronic coupling in the recombination rate constant. The model is developed by means of explicit potential energy surfaces calculated by using density functional theory (DFT). The interaction of all possible spin states of the three common diatomic ligands, CO, NO, and O2, and high-spin heme iron is compared. The electronic coupling, rebinding barrier, and Landau-Zener force terms can be obtained and used to demonstrate significant differences among the ligands. In particular the intermediate spin states of NO (S = 32) and O2 (S = 1) are shown to be bound states. Rapid recombination occurs from these bound states in agreement with experimental data. The slower phases of O2 recombination can be explained by the presence of two higher spin states, S = 2 and S = 3, which have a small and relatively large barrier to ligand recombination, respectively. By contrast, the intermediate spin state for CO is not a bound state, and the only recombination pathway for CO involves direct recombination from the S = 2 state. This process is significantly slower according to the Landau-Zener model. Quantitative estimates of the parameters used in the rate constants provide a complete description that explains rebinding rates that range from femtoseconds to milliseconds at ambient temperature.