1. Introduction

2. Results

2.4. Temperature dependence of the DEE rate constants

For the estimation of the effect of diffusion the following DEE kinetic scheme was considered (using tyrosine as an example):

where the first-order DEE rate wex is related to the second-order rate constant k_et as:

$${\mathrm{w}}_{\mathrm{e}\mathrm{x}}={\mathrm{k}}_{\mathrm{e}\mathrm{t}}\frac{{\mathrm{k}}_{-\mathrm{d}}}{{\mathrm{k}}_{\mathrm{d}}}$$

(19)

k_obs is the observable DEE rate constant, k_obs it is expressed through k_et and k_d as follows:

$${\mathrm{k}}_{\mathrm{o}\mathrm{b}\mathrm{s}}=\frac{{\mathrm{k}}_{\mathrm{e}\mathrm{t}}{\mathrm{k}}_{\mathrm{d}}}{2{\mathrm{k}}_{\mathrm{e}\mathrm{t}}+{\mathrm{k}}_{\mathrm{d}}}$$

(20)

The diffusion rate constant k_d was estimated by the Smoluchowski equation, taking into account the charges of the reactants:

$${\mathrm{k}}_{\mathrm{d}}=\frac{2}{3\mathsf{\eta }}·\frac{{\left({\mathrm{r}}_1+{\mathrm{r}}_2\right)}^2}{{\mathrm{r}}_1{\mathrm{r}}_2}·\frac{{\mathrm{w}}_{\mathrm{r}}}{\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{{\mathrm{w}}_{\mathrm{r}}}{\mathrm{R}\mathrm{T}}\right)-1}$$

(21)

where r₁, r₂ are the radii of the reagents; w_r is the work function of approach charged reactants to each other:

$${\mathrm{w}}_{\mathrm{r}}=\frac{{\mathrm{z}}_1{\mathrm{z}}_2{\mathrm{e}}^2{\mathrm{N}}_{\mathrm{A}}}{4\mathsf{\pi }{\mathsf{\epsilon }}_0\mathsf{\epsilon }\left({\mathrm{r}}_1+{\mathrm{r}}_2\right)}\mathrm{f}$$

(22)

we assume that the reactants approaches to the distance equal to the sum of their radii. The factor $f$ takes into account the ionic strength of the solution:

$$f={\left(1+\left(r_1+r_2\right)B\sqrt{\frac{\mu }{\epsilon T}}\right)}^{-1}$$

(23)

where B = (2N_Ae²/(ε₀k))^1/2 = 50.345 l^1/2K^1/2Å^-1M^-1/2.

The viscosity values of D₂O were taken from [51, 52], dielectric permittivity from [53]. The average elliptical radii of the reactants were used to estimate r₁ and r₂. An ellipsoid of the smallest volume was described around the molecule and the radius was expressed as [54]:

$$\frac{1}{\mathrm{r}}=\frac{\mathrm{F}\left(\mathsf{\phi },\mathsf{\alpha }\right)}{\sqrt{\left({\mathrm{a}}^2-{\mathrm{c}}^2\right)}}$$

(24)

where F(φ,α) is an elliptic integral of the first kind; φ = arcsin((a² – c²)^1/2/a); α = ((a² – c²)/(a² – b²))^1/2; a, b, c are the semiaxes of the ellipsoid, a ≥ b ≥ c.

The ellipsoid semiaxes were calculated using the algorithm N. Shor [55] with the molecular geometries of the crystal structures of DL-tyrosine [56], N-acetyl-L-tyrosine and guanosine-5'-monophosphate trihydrate [57]. The molecular radii found: r(GMP(-H)^-) = 4.18 Å, r(NacTyrO^-) = 3.82 Å, r(TyrO^-) = 3.06 Å, we assumed that the radii of the radicals do not differ from those of the corresponding diamagnetic particles.

When calculating w_r, the negatively charged carboxyl and phosphate groups in the reactants were taken into account: z(GMP(-H)^-) = -3, z(TyrO^-) = -2.

The k_et values calculated by Eq.(20) are given in the last columns of Table Error! Reference source not found.-Error! Reference source not found..

The first-order DEE rate constant w_ex depends on temperature as [1]:

$$w_{ex}\left(T\right)=\frac{k_0}{\sqrt{T}}exp\left(-\frac{\lambda }{4RT}\right)$$

(25)

The second-order DEE rate constant k_et is expressed as follows:

$$k_{et}=\frac{k_d}{k_{-d}}{k}_{ex}=K_A{w}_{ex}$$

(26)

The K_A in Eq. (26) is the equilibrium constant of pre-reaction complex formation; it depends on temperature as follows [58] :

$${\mathrm{K}}_{\mathrm{A}}=4\mathsf{\pi }{\mathrm{N}}_{\mathrm{A}}{\left({\mathrm{r}}_1+{\mathrm{r}}_2\right)}^2\mathsf{\delta }\mathrm{d}·\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{{\mathrm{w}}_{\mathrm{r}}}{\mathrm{R}\mathrm{T}}\right)={\mathrm{K}}_0\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{{\mathrm{w}}_{\mathrm{r}}}{\mathrm{R}\mathrm{T}}\right)$$

(27)

where $\delta d$ is the reaction zone thickness. Then the second-order rate constant k_et depends on temperature as:

$$k_{et}=\frac{K_0{k}_0}{\sqrt{T}}exp\left(-\frac{w_r}{RT}-\frac{\lambda }{4RT}\right)=\frac{A}{\sqrt{T}}exp\left(-\frac{w_r}{RT}-\frac{\lambda }{4RT}\right)$$

(28)

The work function w_r depends on the temperature through dependence on temperature of the D₂O dielectric permittivity, at each temperature w_r can be calculated by Eq. (22). To find the pre-exponent A and the reorganization energy λ, we plot the values of ln[k_et√Texp(w_r/RT)], where the k_et values are experimental ones, versus 1/T (Figure 3) and and approximated these points by linear dependence. The values of A and λ found from the approximation are given in Table 4.

Previously we studied [30] the temperature dependence of the DEE rate constant between the GMPH⁺ cation and the GMPH^++•, dication radical, the reorganization energy found for this reaction is λ = 0.79 ± 0.11 eV [21] and coincides with the value for GMP(-H)^- + GMP(-H)^• (see Table Error! Reference source not found.).

2.5. The Marcus cross-relation equation

To account for the effects of diffusion the following kinetic scheme of electron transfer was considered (for the radical GMP(-H)^• reduction by anion TyrO^- as an example):

where the first-order rate w₁₂ is related to the second-order rate constant k₁₂ as:

$$w^{12}=\frac{k_{-d}^{12}}{k_d^{12}}{k}^{12}$$

(29)

The observable second-order rate constant k_obs¹² is expressed through k¹² and k_d¹² as follows:

$$k_{obs}^{12}=\frac{k^{12}{k}_d^{12}}{k^{12}+k_d^{12}}$$

(30)

The rate constants k¹²(TyrO^-) and k¹²(NacTyrO^-) of GMP(-H)^• reduction by TyrO^- and NacTyrO^- respectively after correction for diffusion (k_d was calculated according Eq. (21)) are the following: k¹²(TyrO-) = 1.7*10⁸ M^-1s^-1 and k¹²(NacTyrO^-) = 1.8*10⁸ M^-1s^-1 [29]. Thus, the values of the reduction rate constants are very close.

The rate constant w¹² depends on the temperature as follows:

$$w^{12}=\frac{k_0}{\sqrt{T}}exp\left(-\frac{{\left({\Delta G}_{12}^{0\mathrm{\text{'}}}+{\lambda }_{12}\right)}^2}{4RT{\lambda }_{12}}\right)$$

(31)

where ΔG₁₂º’ is the driving force of the first-order redox reaction.

The equilibrium constant between the initial reactants and reaction products K₁₂ is expressed as:

$$K_{12}=exp\left(-\frac{{\Delta G}_{12}^0}{RT}\right)=K_A^{12}{K}_{12}\prime {\left(K_A^{21}\right)}^{-1}=exp\left(\frac{-{\Delta G}_{12}^{0^{\prime }}-w_{12}+w_{21}}{RT}\right)$$

(32)

here K_A¹² and K_A²¹ are the equilibrium constants of the formation of pre-reaction and post-reaction complexes, expressed by Eq. (27). Assuming the radii of radicals and corresponding diamagnetic particles are the same, the pre-exponents in Eq. (32) the factors K_A¹² and K_A²¹ can be shortened (reduced). The ΔG₁₂º value is expressed through standard electrode potentials, thus, ΔG₁₂º’ can be calculated.

The expression for the second-order electron transfer rate constant k¹² is given as follows:

$$k^{12}=K_A^{12}{w}^{12}=\frac{A_{12}}{\sqrt{T}}exp\left(-\frac{w_{12}}{RT}\right)exp\left(-\frac{{\left({\Delta G}_{12}^0-w_{12}+w_{21}+{\lambda }_{12}\right)}^2}{4RT{\lambda }_{12}}\right)$$

(33)

If the electron transfer occurs over a relatively long distance with a weak force interaction between the reactants, then one can assume that λ₁₂ = (λ₁₁ + λ₂₂)/2 that is the Marcus cross relation, where λ₁₁, λ₂₂ are the reorganization energies for the respective DEE reactions.

If we additionally assume the following ratio between the pre-exponents: A₁₂ = (A₁₁A₂₂)^1/2, then we can express k¹² through the temperature dependence parameters of the DEE rate constants. Thus, the cross-reaction rate constant k_calc¹² was calculated employing the following formula:

$$k_{calc}^{12}=\frac{\sqrt{A_{11}{A}_{22}}}{\sqrt{T}}exp\left(-\frac{w_{12}}{RT}\right)exp\left(-\frac{{\left({\Delta G}_{12}^0-w_{12}+w_{21}+\left({\lambda }_{11}+{\lambda }_{22}\right)/2\right)}^2}{2RT\left({\lambda }_{11}+{\lambda }_{22}\right)}\right)$$

(34)

2.5.1. Reactants parameters for the Marcus cross-relation calculations

The cross-relation calculations require the values of the difference of standard electrode potentials, the reorganization energy and the pre-exponent for the corresponding DEE reactions, as well as the radii of all reactants and products to calculate the work function. In all the cases, we assume that the radii of radicals and corresponding diamagnetic particles are the same.

If only the DEE rate constant at a certain temperature is known, we estimate the pre-exponent as: A₁₁ = 10¹¹ M^-1s^-1 and calculate the reorganization energy by Eq. (35).

$${\lambda }_{11}=-4w_r-4RT\ast ln\left(\frac{k_{11}\sqrt{T}}{A_{11}}\right)$$

(35)

All the parameters of the reactants are given in Table 5. The Z_red column shows the charge of the reduced form of each reactant. The structures of some reactants are shown in Figure 4.

The TyrO^•/TyrO^- case. The standard electrode potential is E° = 0.72 V [59]. The radius calculation is described above, the pre-exponent and reorganization energy for the DEE reaction were found experimentally in this work.

The NacTyrO^•/NacTyrO^- case. We use the value of the standard electrode potential for N-acetyltyrosine methyl ester at pH = 7, E₇ = 0.97 V [60]. pK_a(NacTyrOH) = 10.1, then Eº = 0.79 V. The calculation of the radius is described above; the pre-exponent and reorganization energy for the DEE reaction were found experimentally in this work.

The GMP(-H)^•/GMP(-H)^- case. The standard electrode potential of GMP at pH = 7, E₇ = 1.31 V [61], determined from photoinduced electron transfer reaction rates, that agrees well with that of guanosine at pH = 7, E₇ = 1.29 V [62], determined by pulsed radiolysis. The acidity constants of GMP [63] and its radical [64,65,66] are shown in Figure 4. For GMP(-H)^•/GMP(-H)^- the calculated potential is: Eº = 1.23 V.

The GMPH^++•/GMPH⁺ case. The standard electrode potential E° = 1.55 V, calculated from E⁷ = 1.29 V [62]. The pre-exponent and reorganization energy for the DEE reaction were found earlier [30]. Average elliptical radius r = 4.19 Å, calculated by the method described above, the geometry was taken from the crystal structure of guanosine-5'-monophosphate trihydrate [57]

The NacTrpH^+•/NacTrpH case, we use the value of the standard electrode potential for tryptophan, E° = 1.15 V [59]. The DEE rate constant at 25°C is k₁₁ = 9*10⁸ M^-1s^-1 was determined experimentally by CIDNP with microsecond resolution [38]. After correction for diffusion by Eq. (20) one has: k₁₁ = 1.3*10⁹ M^-1s^-1. The mean elliptical radius r = 3.83 Å was calculated by the method described above, geometry from was taken from the NacTrpH crystal structure [67]. We assume that A₁₁/√T = 10¹¹ M^-1s^-1, then λ = 0.45 eV.

The ClO₂^•/ClO₂^- case. The standard electrode potential E° = 0.934 V [68]. The DEE constant at 25°C is k₁₁ = 3.3*10⁴ M^-1s^-1, determined from a cross relation with parameters A₁₁/√T = 10¹¹ M^-1s^-1, r = 1.5 Å [69]. Then λ₁₁ = 1.53 eV.

The N₃^•/N₃^- case. The standard electrode potential E° = 1.33 V [68]. The DEE rate constant at 25°C k₁₁ = 3.7*10⁶ M^-1s^-1, determined from a cross relation with parameters A₁₁/√T = 10¹¹ M^-1s^-1, r = 2 Å [69]. Then λ₁₁ = 1.05 eV.

The NO₂^•/NO₂^- case. The standard electrode potential E° = 1.04 V [68]. The DEE rate constant at 25°C k₁₁ = 580 M^-1s^-1, determined experimentally by isotopic substitution [70]. We assume that A₁₁/√T = 10¹¹ M^-1s^-1, then λ = 1.95 eV. The radius r = 1.9 Å [69].

The [IrCl₆]^2-/[IrCl₆]^3- case. The standard electrode potential E° = 0.892 V [71]. The DEE constant at 25°C k₁₁ = 2.3*10⁵ M^-1s^-1, determined experimentally by isotopic substitution [72]. We assume that A₁₁/√T = 10¹¹ M^-1s^-1. Radius r = 4.4 Å [73], DEE rate constant measured at μ = 0.1 M. Then λ = 1.04 eV.

The CysS^•/CysS^- case. The standard electrode potential E° = 0.76 V [74]. The DEE rate constant at 25°C k₁₁ = 5.4*10³ M^-1s^-1, determined from the Marcus cross relation with parameters A₁₁/√T = 10¹¹ M^-1s^-1, r = 3.0 Å, the k₁₂ cross-reaction rate constant was measured at μ = 0.1 M [74]. Then λ = 1.48 eV.

The TEMPO⁺/TEMPO^• case. The standard electrode potential E° = 0.745 V [75]. The DEE rate constant at 25°C k_obs = 8.6*10⁷ M^-1s^-1, determined experimentally by line broadening in the EPR spectrum [76]. After correction for diffusion by Eq. (20), k₁₁ = 8.8*10⁷ M^-1s^-1. We assume that A₁₁/√T = 10¹¹ M^-1s^-1. Then λ = 0.72 eV. The radius r = 3.67 Å [76].

Figure 5. Structures of N-acetyltryptophan (NacTrpH), guanosine-5'-monophosphate cation (GMPH⁺), cysteine anion (CysS^-), stable free radical TEMPO – (2,2,6,6-tetramethylpiperidin-1-yl)oxyl.

Figure 5. Structures of N-acetyltryptophan (NacTrpH), guanosine-5'-monophosphate cation (GMPH⁺), cysteine anion (CysS^-), stable free radical TEMPO – (2,2,6,6-tetramethylpiperidin-1-yl)oxyl.

Table 5. Parameters of the reactants for the Marcus cross-relation calculations.

Table 5. Parameters of the reactants for the Marcus cross-relation calculations.

DEE reaction	E°, V	ln(A)	λ, eV	r, Å	Zred
GMP(-H)- + GMP(-H)•	1.23	31.7	0.82	4.18	-3
GMPH+ + GMPH++•	1.55	29.2	0.79	4.19	0
NacTyrO- + NacTyrO•	0.79	27.0	0.50	3.82	-2
TyrO- + TyrO•	0.72	30.2	0.81	3.06	-2
ClO2- + ClO2•	0.934	28.2	1.53	1.5	-1
N3- + N3•	1.33	28.2	1.05	2.0	-1
NO2• + NO2-	1.04	28.2	1.95	1.9	-1
[IrCl6]2- + [IrCl6]3-	0.892	28.2	1.04	4.4	-3
TEMPO• + TEMPO+	0.745	28.2	0.72	3.67	0
CysS- + CysS•	0.76	28.2	1.57	3.0	-2
NacTrpH + NacTrpH+•	1.15	28.2	0.45	3.83	0

3. Discussion

4. Materials and Methods

5. Conclusions.

References

1. Marcus, R.A.; Sutin, N. Electron transfers in chemistry and biology. Biochimica et Biophysica Acta (BBA)-Reviews on Bioenergetics 1985, 811, 265–322. [Google Scholar] [CrossRef]
2. Zerk, T.J.; Saouma, C.T.; Mayer, J.M.; Tolman, W.B. Low Reorganization Energy for Electron Self-Exchange by a Formally Copper (III, II) Redox Couple. Inorganic chemistry 2019, 58, 14151–14158. [Google Scholar] [CrossRef]
3. Xie, B.; Wilson, L.J.; Stanbury, D.M. Cross-Electron-Transfer Reactions of the [CuII/I(bite)]2+/+ Redox Couple. Inorganic Chemistry 2001, 40, 3606–3614. [Google Scholar] [CrossRef] [PubMed]
4. Ganesan, M.; Sivasubramanian, V.K.; Rajagopal, S.; Ramaraj, R. Electron transfer reactions of organic sulfoxides with photochemically generated ruthenium(III)–polypyridyl complexes. Tetrahedron 2004, 60, 1921–1929. [Google Scholar] [CrossRef]
5. Meyer, T.J.; Taube, H. Electron-transfer reactions of ruthenium ammines. Inorganic Chemistry 1968, 7, 2369–2379. [Google Scholar] [CrossRef]
6. Dwyer, F.P.; Sargeson, A.M. The Rate of Electron Transfer Between the Tris-(Ethylenediamine)-Cobalt (II) and Cobalt (III) Ions. The Journal of Physical Chemistry 1961, 65, 1892–1894. [Google Scholar] [CrossRef]
7. Krishnamurty, K.V.; Waiil, A.C. Kinetics of the Vanadium(II)-Vanadium(III) Isotopic Exchange Reaction. Journal of the American Chemical Society 1958, 80, 5921–5924. [Google Scholar] [CrossRef]
8. Grampp, G.; Landgraf, S.; Rasmussen, K. Electron self-exchange kinetics between 2,3-dicyano-5,6-dichloro-p-benzoquinone (DDQ) and its radical anion. Part 1. Solvent dynamical effects. Journal of the Chemical Society, Perkin Transactions 2 1999, 9, 1897–1899. [Google Scholar] [CrossRef]
9. Grampp, G.; Rasmussen, K. Solvent dynamical effects on the electron self-exchange rate of the TEMPO/TEMPO⁺ Couple (TEMPO= 2, 2, 6, 6-Tetramethyl-1-Piperidinyloxy Radical) Part I. ESR-Linebroadening measurements at T= 298 K. Physical Chemistry Chemical Physics 2002, 4, 5546–5549. [Google Scholar] [CrossRef]
10. Mladenova, B.; Kattnig, D.R.; Kaiser, C.; Schäfer, J.; Lambert, C.; Grampp, G. n. Investigations of the Degenerate Intramolecular Charge Exchange in Symmetric Organic Mixed Valence Compounds: Solvent Dynamics of Bis (triarylamine) paracyclophane Redox Systems. The Journal of Physical Chemistry C 2015, 119, 8547–8553. [Google Scholar] [CrossRef]
11. Grampp, G.; Mladenova, B.Y.; Kattnig, D.; Landgraf, S. ESR and ENDOR investigations of the degenerate electron exchange reactions of various viologens in solution. Solvent dynamical effects. Applied Magnetic Resonance 2006, 30, 145–164. [Google Scholar] [CrossRef]
12. Chan, M.-S.; Wahl, A.C. Rate of electron exchange between iron, ruthenium, and osmium complexes containing 1, 10-phenanthroline, 2, 2'-bipyridyl, or their derivatives from nuclear magnetic resonance studies. The Journal of Physical Chemistry 1978, 82, 2542–2549. [Google Scholar] [CrossRef]
13. Koval, C.A.; Margerum, D.W. Determination of the self-exchange electron-transfer rate constant for a copper (III/II) tripeptide complex by proton NMR line broadening. Inorganic Chemistry 1981, 20, 2311–2318. [Google Scholar] [CrossRef]
14. Parker, J.F.; Choi, J.-P.; Wang, W.; Murray, R.W. Electron Self-exchange Dynamics of the Nanoparticle Couple [Au25(SC2Ph)18]0/1− By Nuclear Magnetic Resonance Line-Broadening. The Journal of Physical Chemistry C 2008, 112, 13976–13981. [Google Scholar] [CrossRef]
15. Closs, G.L.; Miller, R.J. Laser flash photolysis with NMR detection. Microsecond time-resolved CIDNP: separation of geminate and random-phase processes. J. Am. Chem. Soc. 1979, 101, 1639–41. [Google Scholar] [CrossRef]
16. Closs, G.L.; Miller, R.J.; Redwine, O.D. Time-resolved CIDNP: applications to radical and biradical chemistry. Acc. Chem. Res. 1985, 18, 196–202. [Google Scholar] [CrossRef]
17. Morozova, O.B.; Yurkovskaya, A.V.; Tsentalovich, Y.P.; Forbes, M.D.E.; Hore, P.J.; Sagdeev, R.Z. Time resolved CIDNP study of electron transfer reactions in proteins and model compounds. Mol. Phys. 2002, 100, 1187–1195. [Google Scholar] [CrossRef]
18. Morozova, O.B.; Yurkovskaya, A.V.; Tsentalovich, Y.P.; Forbes, M.D.E.; Sagdeev, R.Z. Time-Resolved CIDNP Study of Intramolecular Charge Transfer in the Dipeptide Tryptophan-Tyrosine. J. Phys. Chem. B 2002, 106, 1455–1460. [Google Scholar] [CrossRef]
19. Goez, M.; Kuprov, I.; Hore, P.J. Increasing the sensitivity of time-resolved photo-CIDNP experiments by multiple laser flashes and temporary storage in the rotating frame. J. Magn. Reson. 2005, 177, 139–145. [Google Scholar] [CrossRef] [PubMed]
20. Morozova, O.B.; Korchak, S.E.; Sagdeev, R.Z.; Yurkovskaya, A.V. Time-Resolved Chemically Induced Dynamic Nuclear Polarization Studies of Structure and Reactivity of Methionine Radical Cations in Aqueous Solution as a Function of pH. J. Phys. Chem. A 2005, 109, 10459–10466. [Google Scholar] [CrossRef]
21. Kuprov, I.; Goez, M.; Abbott, P.A.; Hore, P.J. Design and performance of a microsecond time-resolved photo-chemically induced dynamic nuclear polarization add-on for a high-field nuclear magnetic resonance spectrometer. Rev. Sci. Instrum. 2005, 76, 084103/1-084103/7. [Google Scholar] [CrossRef]
22. Wörner, J.; Chen, J.; Bacher, A.; Weber, S. Non-classical disproportionation revealed by photo-chemically induced dynamic nuclear polarization NMR. Magn. Reson. 2021, 2, 281–290. [Google Scholar] [CrossRef]
23. Pompe, N.; Illarionov, B.; Fischer, M.; Bacher, A.; Weber, S. Completing the Picture: Determination of 13C Hyperfine Coupling Constants of Flavin Semiquinone Radicals by Photochemically Induced Dynamic Nuclear Polarization Spectroscopy. J. Phys. Chem. Lett. 2022, 13, 5160–5167. [Google Scholar] [CrossRef] [PubMed]
24. Goez, M. The Degenerate Electron Exchange between N, N-Dimethylanilines and their Radical Cations. Zeitschrift für Physikalische Chemie 1990, 169, 133–145. [Google Scholar] [CrossRef]
25. Schael, F.; Löhmannsröben, H.-G. The deactivation of singlet excited all-trans-1, 6-diphenylhexa-1, 3, 5-triene by intermolecular charge transfer processes. 1. Mechanisms of fluorescence quenching and of triplet and cation formation. Chemical physics 1996, 206, (1-2), 193-210.
26. Closs, G.L.; Sitzmann, E.V. Measurements of degenerate radical ion-neutral molecule electron exchange by microsecond time-resolved CIDNP. Determination of relative hyperfine coupling constants of radical cations of chlorophylls and derivatives. J. Am. Chem. Soc. 1981, 103, 3217–19. [Google Scholar] [CrossRef]
27. Yurkovskaya, A.V.; Snytnikova, O.A.; Morozova, O.B.; Tsentalovich, Y.P.; Sagdeev, R.Z. Time-resolved CIDNP and laser flash photolysis study of the photoreaction between triplet 2, 2′-dipyridyl and guanosine-5′-monophosphate in water. Physical chemistry chemical physics 2003, 5, 3653–3659. [Google Scholar] [CrossRef]
28. Tsentalovich, Y.P.; Morozova, O.B.; Yurkovskaya, A.V.; Hore, P.J.; Sagdeev, R.Z. Time-Resolved CIDNP and Laser Flash Photolysis Study of the Photoreactions of N-Acetyl Histidine with 2,2'-Dipyridyl in Aqueous Solution. J. Phys. Chem. A 2000, 104, 6912–6916. [Google Scholar] [CrossRef]
29. Morozova, O.B.; Kiryutin, A.S.; Sagdeev, R.Z.; Yurkovskaya, A.V. Electron transfer between guanosine radical and amino acids in aqueous solution. 1. Reduction of guanosine radical by tyrosine. The Journal of Physical Chemistry B 2007, 111, 7439–7448. [Google Scholar] [CrossRef]
30. Geniman, M.; Panov, M.; Morozova, O.; Kiryutin, A.; Fishman, N.; Yurkovskaya, A. Temperature dependence of the degenerate electron exchange between guanosine-5′-monophosphate cation and its short-lived radical dication in aqueous solution. Russian Chemical Bulletin 2021, 70, 2375–2381. [Google Scholar] [CrossRef]
31. Gottlieb, H.; Kotlyar, V.; Nudelman, A. NMR Chemical Shifts of Common Laboratory Solvents as Trace Impurities. The Journal of organic chemistry 1997, 62, 7512–7515. [Google Scholar] [CrossRef]
32. Kaptein, R. Simple rules for chemically induced dynamic nuclear polarization. J. Chem. Soc. Chem Commun. 1971, (14), 732–733. [Google Scholar] [CrossRef]
33. Adhikary, A.; Kumar, A.; Becker, D.; Sevilla, M.D. The Guanine Cation Radical:  Investigation of Deprotonation States by ESR and DFT. The Journal of Physical Chemistry B 2006, 110, 24171–24180. [Google Scholar] [CrossRef] [PubMed]
34. Tomkiewicz, M.; McAlpine, R.D.; Cocivera, M. Photooxidation and Decarboxylation of Tyrosine Studied by E.P.R. and C.I.D.N.P. Techniques. Canadian Journal of Chemistry 1972, 50, 3849–3856. [Google Scholar] [CrossRef]
35. Mezzetti, A.; Maniero, A.L.; Brustolon, M.; Giacometti, G.; Brunel, L.C. A tyrosyl radical in an irradiated single crystal of N-acetyl-L-tyrosine studied by X-band cw-EPR, high-frequency EPR, and ENDOR spectroscopies. The Journal of Physical Chemistry A 1999, 103, 9636–9643. [Google Scholar] [CrossRef]
36. Vollenweider, J.-K.; Fischer, H.; Hennig, J.; Leuschner, R. Time-resolved CIDNP in laser flash photolysis of aliphatic ketones. A quantitative analysis. Chemical physics 1985, 97, (2-3), 217-234.
37. Mulazzani, Q.G.; Emmi, S.; Fuochi, P.G.; Venturi, M.; Hoffman, M.Z.; Simic, M.G. One-electron reduction of aromatic nitrogen heterocycles in aqueous solution. 2,2'-Bipyridine and 1,10-phenanthroline. The Journal of Physical Chemistry 1979, 10, 1582–1590. [Google Scholar] [CrossRef]
38. Tsentalovich, Y.P.; Morozova, O.B.; Yurkovskaya, A.V.; Hore, P. Kinetics and Mechanism of the Photochemical Reaction of 2, 2 ‘-Dipyridyl with Tryptophan in Water: Time-Resolved CIDNP and Laser Flash Photolysis Study. The Journal of Physical Chemistry A 1999, 103, 5362–5368. [Google Scholar] [CrossRef]
39. Läufer, M. Increasing the time resolution of flash CIDNP by numerical analysis: photoreduction of anthraquinone by N, N-dimethylaniline. Chemical physics letters 1986, 127, 136–140. [Google Scholar] [CrossRef]
40. Goez, M. Evaluation of flash CIDNP experiments by iterative reconvolution. Chemical Physics Letters 1990, 165, 11–14. [Google Scholar] [CrossRef]
41. Morozova, O.B.; Tsentalovich, Y.P.; Yurkovskaya, A.V.; Sagdeev, R.Z. Consecutive biradicals during the photolysis of 2,12-dihydroxy-2,12-dimethylcyclododecanone: low- and high-field chemically induced dynamic nuclear polarizations (CIDNP) study. J. Phys. Chem. A 1998, 102, 3492–3497. [Google Scholar] [CrossRef]
42. Morozova, O.B.; Yurkovskaya, A.V.; Tsentalovich, Y.P.; Sagdeev, R.Z.; Wu, T.; Forbes, M.D.E. Study of Consecutive Biradicals from 2-Hydroxy-2,12-dimethylcyclododecanone by TR-CIDNP, TREPR, and Laser Flash Photolysis. J. Phys. Chem. A 1997, 101, 8803–8808. [Google Scholar] [CrossRef]
43. Morozova, O.B.; Yurkovskaya, A.V.; Tsentalovich, Y.P.; Vieth, H.-M. 1H and 13C Nuclear Polarization in Consecutive Biradicals during the Photolysis of 2,2,12,12-Tetramethylcyclododecanone. J. Phys. Chem. A 1997, 101, 399–406. [Google Scholar] [CrossRef]
44. Tsentalovich, Y.P.; Forbes, M.D.E.; Morozova, O.B.; Plotnikov, I.A.; McCaffrey, V.P.; Yurkovskaya, A.V. Spin and Molecular Dynamics in Acyl-Containing Biradicals: Time-Resolved Electron Paramagnetic Resonance and Laser Flash Photolysis Study. J. Phys. Chem. A 2002, 106, 7121–7129. [Google Scholar] [CrossRef]
45. Tsentalovich, Y.P.; Morozova, O.B.; Avdievich, N.I.; Ananchenko, G.S.; Yurkovskaya, A.V.; Ball, J.D.; Forbes, M.D.E. Influence of Molecular Structure on the Rate of Intersystem Crossing in Flexible Biradicals. J. Phys. Chem. A 1997, 101, 8809–8816. [Google Scholar] [CrossRef]
46. Tsentalovich, Y.P.; Yurkovskaya, A.V.; Sagdeev, R.Z.; Obynochny, A.A.; Purtov, P.A.; Shargorodsky, A.A. Kinetics of Nuclear-Polarization in the Geminate Recombination of Biradicals. Chem. Phys. 1989, 139, (2-3), 307-315.
47. Yurkovskaya, A.; Grosse, S.; Dvinskikh, S.; Morozova, O.; Vieth, H.-M. Spin and molecular dynamics of biradicals as studied by low field nuclear polarization at variable temperature. J. Phys. Chem. A 1999, 103, 980–988. [Google Scholar] [CrossRef]
48. Yurkovskaya, A.V.; Morozova, O.B.; Sagdeev, R.Z.; Dvinskih, S.V.; Buntkowsky, G.; Vieth, H.-M. The influence of scavenging on CIDNP field dependences in biradicals during the photolysis of large-ring cycloalkanones. Chem. Phys. 1995, 197, 157–66. [Google Scholar] [CrossRef]
49. Babenko, S.V.; Kruppa, A.I. Probing the inclusion complexes of short-lived radicals with β-cyclodextrin by CIDNP. Journal of Inclusion Phenomena and Macrocyclic Chemistry 2019, 95, 321–330. [Google Scholar] [CrossRef]
50. Tsentalovich, Y.P.; Morozova, O.B.; Yurkovskaya, A.V.; Hore, P.J.; Sagdeev, R.Z. Time-Resolved CIDNP and Laser Flash Photolysis Study of the Photoreactions of N-Acetyl Histidine with 2,2‘-Dipyridyl in Aqueous Solution. The Journal of Physical Chemistry A 2000, 104, 6912–6916. [Google Scholar] [CrossRef]
51. Hardy, R.C.; Cottington, R.L. Viscosity of deuterium oxide and water in the range 5 to 125°C. J. Res. Natl. Bur. Stand 1949, 42, 573. [Google Scholar] [CrossRef]
52. Nikol’skii, B.P.R.V.A. Spravochnik khimika [Chemist’s Handbook]. Khimiya: Moscow—Leningrad, 1962; Vol. 1, p 1075.
53. Malmberg, C.G. Dielectric constant of deuterium oxide. Journal of Research of the National Bureau of Standards 1958, 60, 609–612. [Google Scholar] [CrossRef]
54. German, E.; Kuznetsov, A. Outer sphere energy of reorganization in charge transfer processes. Electrochimica Acta 1981, 26, 1595–1608. [Google Scholar] [CrossRef]
55. Shor, N.; Berezovskii, O. Algorithms to construct a minimum-volume invariant ellipsoid for a stable dynamic system. Cybernetics and Systems Analysis 1995, 31, 421–427. [Google Scholar] [CrossRef]
56. Mostad, A.; Rømming, C.; Graver, H.; Husebye, S.; Klæboe, P.; Swahn, C. Crystal-structure of DL-tyrosine. Acta Chem. Scand 1973, 27, 401–410. [Google Scholar] [CrossRef]
57. Emerson, J.; Sundaralingam, M. Zwitterionic character of guanosine 5'-monophosphate (5'-GMP): Redetermination of the structure of 5'-GMP trihydrate. Acta Crystallographica Section B: Structural Crystallography and Crystal Chemistry 1980, 36, 1510–1513. [Google Scholar] [CrossRef]
58. Brunschwig, B.S.; Creutz, C.; Macartney, D.H.; Sham, T.; Sutin, N. The role of inner-sphere configuration changes in electron-exchange reactions of metal complexes. Faraday Discussions of the Chemical Society 1982, 74, 113–127. [Google Scholar] [CrossRef]
59. Harriman, A. Further comments on the redox potentials of tryptophan and tyrosine. Journal of Physical Chemistry 1987, 91, 6102–6104. [Google Scholar] [CrossRef]
60. Mahmoudi, L.; Kissner, R.; Nauser, T.; Koppenol, W.H. Electrode Potentials of l-Tryptophan, l-Tyrosine, 3-Nitro-l-tyrosine, 2,3-Difluoro-l-tyrosine, and 2,3,5-Trifluoro-l-tyrosine. Biochemistry 2016, 55, 2849–2856. [Google Scholar] [CrossRef]
61. Fukuzumi, S.; Miyao, H.; Ohkubo, K.; Suenobu, T. Electron-transfer oxidation properties of DNA bases and DNA oligomers. The Journal of Physical Chemistry A 2005, 109, 3285–3294. [Google Scholar] [CrossRef]
62. Steenken, S.; Jovanovic, S.V. How Easily Oxidizable Is DNA? One-Electron Reduction Potentials of Adenosine and Guanosine Radicals in Aqueous Solution. J. Am. Chem. Soc. 1997, 119, 617–618. [Google Scholar] [CrossRef]
63. Asimov, I. Data for Biochemical Research (Dawson, RMC.; Elliott, Daphne C.; Elliott, WH.; Jones, KM; eds.). In ACS Publications: 1960.
64. Candeias, L.; Steenken, S. Structure and acid-base properties of one-electron-oxidized deoxyguanosine, guanosine, and 1-methylguanosine. Journal of the American Chemical Society 1989, 111, 1094–1099. [Google Scholar] [CrossRef]
65. Morozova, O.B.; Fishman, N.N.; Yurkovskaya, A.V. Kinetics of reversible protonation of transient neutral guanine radical in neutral aqueous solution. ChemPhysChem 2018, 19, 2696–2702. [Google Scholar] [CrossRef]
66. Saprygina, N.N.; Morozova, O.B.; Abramova, T.V.; Grampp, G. n.; Yurkovskaya, A.V. Oxidation of Purine Nucleotides by Triplet 3, 3′, 4, 4′-Benzophenone Tetracarboxylic Acid in Aqueous Solution: pH-Dependence. The Journal of Physical Chemistry A 2014, 118, 4966–4974. [Google Scholar] [CrossRef] [PubMed]
67. Sun, H.; Oldfield, E. Tryptophan Chemical Shift in Peptides and Proteins:  A Solid State Carbon-13 Nuclear Magnetic Resonance Spectroscopic and Quantum Chemical Investigation. Journal of the American Chemical Society 2004, 126, 4726–4734. [Google Scholar] [CrossRef] [PubMed]
68. Stanbury, D.M. Reduction Potentials Involving Inorganic Free Radicals in Aqueous Solution. In Advances in Inorganic Chemistry, Sykes, A.G. Ed. Academic Press: 1989; Vol. 33, pp 69-138.
69. Awad, H.H.; Stanbury, D.M. Electron transfer between azide and chlorine dioxide: the effect of solvent barrier nonadditivity. Journal of the American Chemical Society 1993, 115, 3636–3642. [Google Scholar] [CrossRef]
70. Stanbury, D.M.; DeMaine, M.M.; Goodloe, G. Reactive dissolution of nitrogen dioxide in aqueous 15NO2-: the first experimental determination of a main-group electron-exchange rate in solution. Journal of the American Chemical Society 1989, 111, 5496–5498. [Google Scholar] [CrossRef]
71. Margerum, D.W.; Chellappa, K.L.; Bossu, F.P.; Burce, G.L. Characterization of a readily accessible copper(III)-peptide complex. Journal of the American Chemical Society 1975, 97, 6894–6896. [Google Scholar] [CrossRef]
72. Hurwitz, P.; Kustin, K. Kinetic study of the reaction IrCl₆^2–+ IrBr₆^3– ⇌ IrCl₆^3–+ IrBr₆^2–. Transactions of the Faraday Society 1966, 62, 427–432. [Google Scholar] [CrossRef]
73. Stanbury, D.M.; Lednicky, L.A. Outer-sphere electron-transfer reactions involving the chlorite/chlorine dioxide couple. Activation barriers for bent triatomic species. Journal of the American Chemical Society 1984, 106, 2847–2853. [Google Scholar] [CrossRef]
74. Hung, M.; Stanbury, D.M. Catalytic and Direct Oxidation of Cysteine by Octacyanomolybdate(V). Inorganic Chemistry 2005, 44, 3541–3550. [Google Scholar] [CrossRef]
75. Gerken, J.B.; Pang, Y.Q.; Lauber, M.B.; Stahl, S.S. Structural Effects on the pH-Dependent Redox Properties of Organic Nitroxyls: Pourbaix Diagrams for TEMPO, ABNO, and Three TEMPO Analogs. The Journal of Organic Chemistry 2018, 83, 7323–7330. [Google Scholar] [CrossRef]
76. Grampp, G.; Rasmussen, K. Solvent dynamical effects on the electron self-exchange rate of the TEMPO˙/TEMPO+ couple (TEMPO = 2,2,6,6-tetramethyl-1-piperidinyloxy radical) Part I. ESR-linebroadening measurements at T = 298 K. Phys. Chem. Chem. Phys. 2002, 4, 5546–5549. [Google Scholar] [CrossRef]
77. Lipari, G.; Szabo, A. Model-free approach to the interpretation of nuclear magnetic resonance relaxation in macromolecules. 1. Theory and range of validity. J. Am. Chem. Soc. 1982, 104, 4546–59. [Google Scholar] [CrossRef]
78. Lipari, G.; Szabo, A. Model-free approach to the interpretation of nuclear magnetic resonance relaxation in macromolecules. 2. Analysis of experimental results. J. Am. Chem. Soc. 1982, 104, 4559–70. [Google Scholar] [CrossRef]
79. Morozova, O.B.; Kiryutin, A.S.; Yurkovskaya, A.V. Electron transfer between guanosine radicals and amino acids in aqueous solution. II. Reduction of guanosine radicals by tryptophan. The Journal of Physical Chemistry B 2008, 112, 2747–2754. [Google Scholar] [CrossRef] [PubMed]
80. Morozova, O.B.; Kaptein, R.; Yurkovskaya, A.V. Reduction of Guanosyl Radical by Cysteine and Cysteine-Glycine Studied by Time-Resolved CIDNP. The Journal of Physical Chemistry B 2012, 116, 8058–8063. [Google Scholar] [CrossRef] [PubMed]
81. Napolitano, M.J.; Stewart, D.J.; Margerum, D.W. Chlorine Dioxide Oxidation of Guanosine 5 ‘-Monophosphate. Chemical research in toxicology 2006, 19, 1451–1458. [Google Scholar] [CrossRef]
82. Faraggi, M.; Broitman, F.; Trent, J.B.; Klapper, M.H. One-Electron Oxidation Reactions of Some Purine and Pyrimidine Bases in Aqueous Solutions. Electrochemical and Pulse Radiolysis Studies. The Journal of Physical Chemistry 1996, 100, 14751–14761. [Google Scholar] [CrossRef]
83. Napolitano, M.J.; Green, B.J.; Nicoson, J.S.; Margerum, D.W. Chlorine Dioxide Oxidations of Tyrosine, N-Acetyltyrosine, and Dopa. Chemical Research in Toxicology 2005, 18, 501–508. [Google Scholar] [CrossRef]
84. Land, E.J.; Prütz, W. Reaction of azide radicals with amino acids and proteins. International Journal of Radiation Biology and Related Studies in Physics, Chemistry and Medicine 1979, 36, 75–83. [Google Scholar] [CrossRef]
85. Prütz, W.A.; Mönig, H.; Butler, J.; Land, E.J. Reactions of nitrogen dioxide in aqueous model systems: Oxidation of tyrosine units in peptides and proteins. Archives of Biochemistry and Biophysics 1985, 243, 125–134. [Google Scholar] [CrossRef]
86. Song, N. Mechanisms and Kinetics of Proton-Coupled Electron-Transfer Oxidation of Phenols. 2011.
87. Pattison, D.I.; Lam, M.; Shinde, S.S.; Anderson, R.F.; Davies, M.J. The nitroxide TEMPO is an efficient scavenger of protein radicals: Cellular and kinetic studies. Free Radical Biology and Medicine 2012, 53, 1664–1674. [Google Scholar] [CrossRef]
88. Marcus, R.A. Electron transfer reactions in chemistry: theory and experiment (Nobel lecture). Angewandte Chemie International Edition in English 1993, 32, 1111–1121. [Google Scholar] [CrossRef]
89. Weinstock, I.A. Outer-Sphere Oxidation of the Superoxide Radical Anion. Inorganic Chemistry 2008, 47, 404–406. [Google Scholar] [CrossRef] [PubMed]
90. Chou, M.; Creutz, C.; Sutin, N. Rate constants and activation parameters for outer-sphere electron-transfer reactions and comparisons with the predictions of Marcus theory. Journal of the American Chemical Society 1977, 99, 5615–5623. [Google Scholar] [CrossRef]
91. Weaver, M.J.; Yee, E.L. Activation parameters for homogeneous outer-sphere electron-transfer reactions. Comparisons between self-exchange and cross reactions using Marcus' theory. Inorganic Chemistry 1980, 19, 1936–1945. [Google Scholar] [CrossRef]
92. Hupp, J.T.; Weaver, M.J. Electrochemical and homogeneous exchange kinetics for transition-metal aqua couples: anomalous behavior of hexaaquairon(III/II). Inorganic Chemistry 1983, 22, 2557–2564. [Google Scholar] [CrossRef]
93. Eberson, L. Electron-transfer reactions in organic chemistry. In Advances in physical organic chemistry, Elsevier: 1982; Vol. 18, pp 79-185.
94. Nelsen, S.F.; Ramm, M.T.; Ismagilov, R.F.; Nagy, M.A.; Trieber, D.A.; Powell, D.R.; Chen, X.; Gengler, J.J.; Qu, Q.; Brandt, J.L.; Pladziewicz, J.R. Estimation of Self-Exchange Electron Transfer Rate Constants for Organic Compounds from Stopped-Flow Studies. Journal of the American Chemical Society 1997, 119, 5900–5907. [Google Scholar] [CrossRef]
95. Grampp, G.; Landgraf, S.; Sabou, D.; Dvoranova, D. Application of Marcus cross-relation to mixed inorganic–organic redox couples. A stopped-flow study of the oxidation of N, N, N′, N′-tetramethyl-p-phenylenediamine with various oxidants. Journal of the Chemical Society, Perkin Transactions 2 2002, (1), 178-180.
96. Sutin, N. Theory of Electron Transfer Reactions: Insights and Hindsights. Progress in Inorganic Chemistry: An Appreciation of Henry Taube 1983, 441-498.
97. Marcus, R. On the theory of oxidation-reduction reactions involving electron transfer. III. Applications to data on the rates of organic redox reactions. The Journal of Chemical Physics 1957, 26, 872–877. [Google Scholar] [CrossRef]
98. Morozova, O.B.; Ivanov, K.L. Time-Resolved Chemically Induced Dynamic Nuclear Polarization of Biologically Important Molecules. ChemPhysChem 2019, 20, 197–215. [Google Scholar] [CrossRef]
99. Raiford, D.S.; Fisk, C.L.; Becker, E.D. Calibration of methanol and ethylene glycol nuclear magnetic resonance thermometers. Analytical Chemistry 1979, 51, 2050–2051. [Google Scholar] [CrossRef]
100. Nelson, D.L.; Lehninger, A.L.; Cox, M.M. Lehninger principles of biochemistry. Macmillan: 2008.