## 1. Introduction

The invention of photosynthetic oxygen evolution in 4.6 billion years of the history of the earth allowed for the development of oxygenic atmosphere that forms the basis of life activities. Green plants, algae, and cyanobacteria powered by solar energy convert carbon dioxide and water into molecular oxygen and organic matter. This process is catalyzed by a huge membrane pigment–protein complex enzyme in photosystem II (PSII) [

1]. The core machinery for oxygen evolution is Mn

_{4}CaO

_{5} cluster (catalytic site) located in photosystem II (PS II) protein complex [

2]. The oxygen evolution proceeds, removing four electrons and four protons (H

^{+}) from the two substrate water molecules at the Mn

_{4}CaO

_{5} cluster of the oxygen-evolving complex (OEC) of PSII [

3,

4]. The two ligand water molecules, W1 and W2, are located at the dangling Mn4 site in the Mn

_{4}CaO

_{5} cluster, while another two water ligands (W3 and W4) are located at the Ca

^{2+} site [

5]. The structure of the multi-sub-unit pigment–protein complex (PSII) has been studied extensively by X-ray diffraction (XRD), with a resolution ranging from 3.8 to 1.9 Å using synchrotron radiation (SR) X-ray sources [

6,

7,

8,

9,

10,

11]. The structure of PSII from different photosynthetic organisms has been revealed by both cryoelectron microscopy and X-ray crystallography [

2,

7,

12,

13,

14,

15]. The PSII electron transfer process is divided into ‘acceptor’ and ‘donor’ sides. The acceptor side receives an electron from the reduced P

_{680}*, hence oxidizing it to P

_{680}^{+} (estimated reduction potential of 1.2 V). The P

_{680}^{+} formed is reduced from the ‘donor’ side by oxidizing the Mn

_{4}CaO

_{5} cluster [

16]. The OEC is oxidized successively by P

_{680}^{+} four times, then resets itself to the most reduced state after it converts water into molecular oxygen. The redox-active tyrosine residue of D1 subunit called tyrosine ‘Z’ (Tyr

_{Z}) electrically links the OEC to P

_{680} [

17,

18,

19]. The catalytic mechanism of the OEC is still unresolved. The oxidation states of the Mn ions and how they change along the catalytic site is not clear. The manganese cluster undergoes four successive oxidations, progressing through a series of different net valence states (so-called S

_{i} states, where i = 0–4, i denotes the stored oxidizing equivalents). The oxidation state of the OEC, S

_{i}, increases as electron transfer occurs. Oxygen evolved in the

${\mathrm{S}}_{3}\to {\mathrm{S}}_{0}$ transition while proton release is noticed with stoichiometry 1:0:1:2 for

${\mathrm{S}}_{0}\to {\mathrm{S}}_{1}\to {\mathrm{S}}_{2}\to {\mathrm{S}}_{3}\to {\mathrm{S}}_{0}$ [

5]. The S

_{0} and S

_{2} states of the catalytic site have a net unpaired spin ½ arising from anti-ferromagnetic couplings of the Mn ions, which makes them paramagnetic and thus can be studied using electron paramagnetic resonance (EPR) spectroscopy. The S

_{2} (and S

_{0}) states yield Mn-derived hyperfine structured, so-called multiline (ML) signals (included over 20 resolved lines hence called ‘multiline’), centered on

$g$ ≈ 2 at low temperatures [

20,

21,

22]. The Mn ions are exchange coupled in all Kok cycle S-states [

23]. This is mainly anti-ferromagnetic—the spins oppose each other. S

_{0} and S

_{2} have a net spin ½ ground state. This effective single electron spin interacts with all Mn nuclei (each Mn ion has nuclear spin

$\mathrm{I}=\frac{5}{2}$), giving rise to a nuclear hyperfine (HF)-structured ML pattern through the nuclear HF couplings

${\mathrm{A}}_{\mathrm{i}}$. In the exchange-coupled system, these are given by

${\mathrm{A}}_{\mathrm{i}}={\rho}_{\mathrm{i}}{\mathrm{A}}_{\mathrm{i}\left(\mathrm{ion}\right)}$, where

${\mathrm{A}}_{\mathrm{i}\left(\mathrm{ion}\right)}$ is ‘isolated ion’ HF value. The projection coefficients are dimensionless and sum 1 for the whole Mn cluster [

24]. An estimate of this HF value can be obtained from a single determinant quantum chemical calculation on the geometry-optimized S

_{2} state Mn cluster [

25]. The

${\rho}_{\mathrm{i}}$ (projection of the total spin onto

${\mathrm{Mn}}_{\mathrm{i}}$) is the projection coefficient arising from the coupling in the system within the S

_{T} = ½ manifold. Since the OEC is a sufficiently strongly exchanged coupled system, it is therefore the effective Mn HF interaction’s ‘spin projected’ values that are seen, not the intrinsic ‘single’ ion value. The spin projections reflect the contribution of each Mn ion to a total spin state. The pulsed electron–electron double resonance (PELDOR) measurements carried out between the S

_{2} ML signal and Try

_{D} (situated ≈30 Å from the OEC) radical dipole/dipole interaction are consistent with the data of Jin et al. [

25] and Kurashinge et al. [

26], with

ρ_{1} ≈ 2,

ρ_{2} ≈ −1.2,

ρ_{3} +

ρ_{4} ≈ 0.2 [

27]. Therefore, the HF couplings seen from the Mn

^{III} is ≈ twice that from Mn

^{IV} and much more anisotropic. Since the dominant line spacing of the ML signal is ≈90 G (250 MHz) and the width of the ML signal is ≈1800 G (5.5 GHz), it means that one coupling must be large since two Mn couplings are small. This is because, in first order

Here, the A

_{i eff} are effective, ≈angularly averaged HF values. The

${\rho}_{\mathrm{i}}$ can be described as a measure of electron density of each Mn ion in the cluster or describe the contribution of each of the Mn ions in the Mn

_{4}CaO

_{5} cluster to a total spin state. All the four Mn contribute to the ML signal through its HF interactions in the OEC. The total width is determined by the contributions from individual Mn ions. The effective spin Hamiltonian describing ground state S

_{T} = ½ is

The first term in Equation (2) represents the total electron Zeeman term, while the second term represents HF terms, and the last term the nuclear quadrupole.

Casey et al. [

28], discovered another S

_{2} state signal formed by ≈140 K illumination of PSII samples, also attributed to the manganese cluster and called the

$g4.1$ signal, centered near

$g$ ≈ 4.10, which can appear with or without the presence of the ML signal [

29]. Following its initial discovery by Casey et al., it was subsequently shown that the ML signal to

$g$4.1 inter-conversion could be stimulated by near infrared (NIR) illumination at about 140 K in PSII centers already in the S

_{2} state [

30]. It is likely that some NIR was present in the illuminations originally used by Casey et al. The ‘ground’ state

$g$4.1 signal has been proposed to arise from a rhombic spin

$\frac{5}{2}$ center [

31] or near axial spin

$\frac{3}{2}$ center [

32].

A strong focus in this paper has been on the ‘ground’ state

$g$4.1 signal, whether it is a rhombic

$\frac{5}{2}$ spin state signal or an axial

$\frac{3}{2}$ spin state signal. A quartet state is when an ion has three unpaired electrons with the total spin of

$\frac{3}{2}$ (see

Figure 1). This state with an odd number of electrons is a Kramers system and the electronic states are at least doubly degenerate (±

$\frac{1}{2}$ and ±

$\frac{3}{2}$) in the absence of external magnetic fields. These Kramers doublets are degenerate states for any molecule with an odd number of electrons (±

$\frac{1}{2}$, ±

$\frac{3}{2}$, ±

$\frac{5}{2}$, ±

$\frac{7}{2}\dots .$). The zero-field splitting’s (ZFS) and deviation from regular symmetry produce two Kramers doublets:

m_{s} = ±

$\frac{1}{2}$ and

m_{s} = ±

$\frac{3}{2}$. The Zeeman splittings also depend on the orientation of the magnetic field with respect to the molecule. The spin Hamiltonian for the EPR spectra becomes [

33]

The first term in the Hamiltonian (Equation (3)) represents the electron Zeeman term, while the second term is the ZFS interaction, with

E = 0 for axially symmetric. The degeneracy of the Kramers doublets is removed by the magnetic field along the external

z direction. The energy gap of the splitting is 2D (

Figure 1) between the two states, which are Kramers pairs, with D representing the energy of ZFS. These degenerate doublets undergo splitting when an external magnetic field is applied.

If the ZFS is greater than the applied microwave quantum (

$E=hv$), then the transition

$+\frac{1}{2}\leftrightarrow +\frac{3}{2}$ will not be accessible, while the lower one (

$-\frac{1}{2}\leftrightarrow -\frac{3}{2}$) will require very high magnetic fields to be observed. These leave

$-\frac{1}{2}\leftrightarrow +\frac{1}{2}$ as the only transition that can be observed under any amount of ZFS. Therefore, only a

$g\approx $ 2 transition will be visible if the parallel external magnetic field is applied parallel to the molecular ZFS axis (

Figure 1). If the external magnetic field is applied perpendicular (

Figure 2) to the molecular symmetry axis, the splitting’s of the Kramers doublets will be different from when the field is applied parallel due to the Zeeman interaction. Here, the states

$\pm \frac{1}{2}$ and

$\pm \frac{3}{2}$ mix instead of forming the simple Kramers doublets, forming new states with combination of both the

$\frac{1}{2}$ and

$\frac{3}{2}$ states, which splits differently from the earlier case during the Zeeman interaction. The transitions occur around

$g$ = 4 and the

$g$4.1 peak will be visible (

Figure 2).

An ion with five unpaired d electrons (high spin) has total spin =

$\frac{5}{2}$, and the

m_{s} can be

$+\frac{5}{2}$,

$+\frac{3}{2}$,

$+\frac{1}{2}$,

$-\frac{1}{2}$,

$-\frac{3}{2}$,

$-\frac{5}{2}$. These electrons, in both tetrahedral and octahedral symmetry, occupy the d orbitals as follows: two occupy the degenerate

e_{g} orbitals while the remaining three occupy the triply degenerate

t_{2g} orbitals. This means the ground state orbitals are nondegenerate, and any excited state will involve the promotion of an electron from

t_{2g} to

e_{g} orbitals or from

e_{g} to

t_{2g} orbitals. Since the orbitals are non-degenerate, as opposed to the quartet state above, then spin orbit coupling will be negligible and hence the ZFS would be quite small. Nonetheless the spin degeneracy is still removed in this kind of complex, with direct electron dipole spin–spin couplings or higher order spin–orbit perturbations modifying the spin Hamiltonian as follows [

33]:

The first term in the Hamiltonian (Equation (4)) represents the electronic Zeeman term, while the second term represents the direct electron dipole spin–spin couplings or higher order spin–orbit perturbations. Ŝ is the fictitious spin. This results in the splitting of the rhombic

$\frac{5}{2}$ spin state into three Kramers doublets (

m_{s} = ±

$\frac{1}{2}$,

m_{s} = ±

$\frac{3}{2}$, and

m_{s} = ±

$\frac{5}{2}$). The three Kramers doublets have three groups of states, with all the transitions except

$-\frac{1}{2}\leftrightarrow +\frac{1}{2}$ with

$g$ = 2 being forbidden by ∆

m_{s} = ±1 selection rule. The degeneracy is removed when a magnetic field is applied, with the splitting produced proportional to the applied magnetic field because it occurs in first order perturbation [

34].

For a pure rhombic system, only the terms

${\u015c}_{x}^{2}-{\u015c}_{y}^{2}$ are significant in ZFS, and the three Kramers doublets are once again split into three degenerate pairs. The pair with splitting energy W = 0 (

Figure 3) is characterized by

$g$ = 4.286, which is independent of orientation, i.e., isotropic [

34]. The two other pairs (upper and lower) have anisotropic (dependent on orientation) transitions, with

$g$ = 9.678, 0.857, and 0.607 values [

34].

Figure 3 below shows the energy level-splitting diagram associated with the pure rhombic spin

$\frac{5}{2}$- state. This is characterized by the quasi-isotropic EPR transition at

$g\approx 4.2-4.3$. This spin species is examined here as the possible basis for OEC resonances in the S

_{2} state.

## 2. Results and Discussion

The difference spectra for the ML signals, and $g$4.1 and ‘$g2$’ NIR signals were obtained by subtracting the appropriate background, or pre-NIR illumination spectra, from the ≈140 K NIR illuminated spectra.

The ML signal (

Figure 4) that resulted exhibited even more HF structured detail compared to the ML signal generated from the ≈240 K illumination. This suggests that the ML signal generated by ≈240 K illumination here (and likely generally) is not a strictly uniform species with regards to factors contributing to fine spectral detail. The resultant spectrum obtained in

Figure 5 was obtained after subtracting the ≈140 K NIR ML difference spectrum from ≈240 K ML difference spectrum, which represents the amount of ML signal lost (≈35%) when re-illuminating the sample at ≈140 K with NIR light to photo-induce the

$g$4.1 signal. It is evident from the two spectra that the ML signal generated at ≈240 K illumination had more overall intensity than the one remaining after ≈140 K NIR illumination. This suggests that the

$g$4.1 signal (be it ‘ground’ or ‘excited’ state) was formed at low temperature illumination (approximately ≈140 K) by inter-conversion of a sub population of S

_{2} ML centers. Re-conversion back to ML signal centers occurs by dark adaptation at higher temperatures, ≈240 K for PSII core samples and 200 K for PS II membrane samples [

29]. This is all consistent with the original observation of ML signal to

$g$4.1 inter-conversion stimulated by near infrared illumination at about 140 K temperatures in PSII membrane centers [

30]. The procedure was repeated at several microwave powers of (0.2 mW, 1 mW) at 6 K in order to check for power saturation effects, and at a range of temperatures (5, 8, 15, and 20 K, with other parameters held constant). The ML signals generated at various temperatures showed some differences in the signal intensity (beyond expected Curie effects), with the maximum signal intensity observed at 6 K, with some decrease of the signal intensity at 5 K. The origin(s) of these effects, if real, was not pursued further here.

The 140 K NIR illuminated-minus-annealed spectrum for PSIINoAdds core sample.

Figure 6 shows the ≈240 K green illuminated

$g$4.1 difference spectrum. It was observed between 1000 and 2200 G in the magnetic field axis at X band.

To isolate the ‘pure’ spectrum of the

$g$4.1 species generated by NIR turnover, we subtracted from the 140 K NIR-illuminated

$g$4.1 (

Figure 7) an appropriately scaled amount of the 240 K green illuminated

$g$4.1 (

Figure 6, about 65% of the signal that did not interconvert) to obtained the spectrum in

Figure 8.

#### Simulation of X-Band CW-EPR-Generated $g$4.1 Signal of ≈140 K NIR-Illuminated PSII Core Samples

The

$g$4.1 signal experimental spectrum together with best fit simulation as a 5/2 state is shown in

Figure 9.

Table 1 lists the simulation parameters; the matrix diagonalization method was used.

Figure 9 shows the best fit simulation, which suggests that

$g$4.1 signal may originate from the spin 5/2 state. This is unlikely to be strictly accurate but given that no HF structure is resolved on any of the excited state, spin > ½ signals, it is a reasonable, minimal assumption. No plausible fit to the

$g$4.1 signal could be found with rhombic symmetry and a spin 3/2 state, but interestingly

Figure 10 shows that such a species may have been present, with one predicted up-field feature around 2200 G and the other possibly overlapping with the spin 5/2

$g$4.1 signal. Thus, the spin ½ and spin 3/2 states expected to accompany the easily visible spin 5/2 state arising from NIR turnover may have been present. It is a unique feature of the spin 5/2 system in rhombic symmetry that all three principal axis transitions were near co-incident at X band, making this signal easily seen. For other spin states in the manifold of this system, the principal axis transitions were generally well separated in the EPR spectrum and harder to identify (and thus quantitate). Hence, the data support an X-band CW-EPR-generated

$g$4.1 signal as originating from a near rhombic spin 5/2 of the S

_{2} state of the PSII manganese cluster. Therefore, the conclusion that can be drawn from the ≈140 K NIR-illuminated PSII core samples is that, in addition to a clear rhombic spin 5/2 state, the NIR turnover likely generated a g≈2 signal (S = 1/2) as indicated in

Figure 5 and a spin 3/2 system (

Figure 10), although temperature dependence studies of the latter two were not performed.