Abstracts

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N.V.Shokhirev, F.A.Walker.
The effect of axial ligand plane orientation on the contact and pseudocontact shifts of low-spin ferriheme proteins.
Journal of Biological Inorganic Chemistry. 3: (6) 581-594, 1998.

Abstract:

The effect of axial ligand nodal plane orientation on the contact and seudocontact shifts of a symmetrical low-spin octamethylferriheme center has been calculated as a function of the angle of the axial ligand. Simple Hückel techniques have been used to estimate the contact contribution, and values obtained from model hemes, together with counter-rotation of the g-tensor, have been used to estimate the pseudocontact contribution, for the eight beta-pyrrole methyl and four meso-H positions. It is found that the maximum and minimum contact shifts occur when the axial ligand is aligned at an angle of +/-15 degrees to the meso-H axes of the heme, rather than when the axial ligand plane lies along the porphyrin nitrogens, as assumed previously by some investigators. For systems having one planar axial ligand or two ligands in parallel planes, the contact and pseudocontact contributions at the meso-H positions are comparable in size (at least on the basis of simple Hückel estimates), while the contact contribution clearly dominates the isotropic shifts of the heme methyls. Allowing for the substituent effect of the 2,4-vinyls of protohemin, or the 2,4-thioethers of hemin c, as well as the average diamagnetic shifts of the heme methyls and meso-H, plots of the predicted shifts as a function of axial ligand nodal plane orientation have been constructed for hemin b- and c-containing proteins. Excellent agreement in the order of shifts, and reasonable agreement in the sizes of the observed shifts, is observed in the majority of the ferriheme proteins for which the methyl and meso-H resonances have been assigned and proton shifts reported. Plots have also been constructed for hemin c-containing proteins having the two axial ligand nodal planes oriented at relative angles of 40 degrees, 70 degrees, and 80 degrees. Excellent agreement in the order of shifts, and reasonable agreement in the magnitudes of the observed shifts, is observed in all cases of bacterial cytochromes which do not fit the plots that assume the ligands are in parallel planes, except one - the cytochrome c-552 of Nitrosomonas europae. Except for this case, where the order of the predicted methyl shifts at any angle of the axial ligands disagrees with the observed, the reasons can usually be attributed to a large dihedral angle between two axial ligand nodal planes, to strong H-bonding interactions involving His and/or CN- ligands, or to off-axis binding of one (or both) axial ligand(s). Ruffling of the porphyrin ring may also contribute to the contact shift in as yet undefined ways. Hence, despite the simplicity of the calculations, the agreement with observed data is highly satisfying and the concept of the importance of axial ligand plane orientation on the observed proton shifts of heme proteins is fully confirmed.

L.Banci, I.Bertini, C.Luchinat, R.Pierattelli, N.V.Shokhirev, F.A.Walker.
Analysis of the temperature dependence of the ¹H and ¹³C isotropic shifts of horse heart ferricytochrome c: Explanation of Curie and anti-Curie temperature dependence and nonlinear pseudocontact shifts in a common two-level framework.
Journal of the American Chemical Society. 120: (33) 8472-8479, 1998

Abstract:

The ¹H and ¹³C hyperfine shifts of the heme methyls of horse heart ferricytochrome c have been measured over the temperature range 278-328 K in order to interpret the "anomalous" temperature-dependence of the hyperfine shifts in terms of their pseudocontact and contact shifts. by taking advantage of the available pseudocontact shifts for protein nuclei measured at 303 and 323 K (Santos, H.; Turner, D. L. fur. J. Biochem. 1992, 206, 721-728), the metal- centered pseudocontact shifts have been analyzed in terms of a thermally accessible excited state lying 355-590 cm^-1 to higher energy which has a magnetic susceptibility tensor with the rhombic anisotropy, ((rh, which is rotated by 90 degrees to that of the ground state. The metal-centered pseudocontact shifts have been evaluated at all temperatures at which the chemical shifts were measured, and these calculated values were used to evaluate the contact shifts of each heme methyl for the two nuclei. The temperature dependence of the heme methyl contact shifts for both 1H and ¹³C, assuming a thermally accessible excited state, was then used to evaluate the spin density for the four beta-pyrrole heme carbons to which the methyls are attached. The ligand-centered pseudocontact shifts have been estimated and found to give a modest contribution to the experimental behavior. The ¹H and ¹³C data are highly self-consistent. The present analysis provides deep insight into the electron distribution on the porphyrin ring in low-spin Fe(III) hemes.

N.V.Shokhirev, F.A.Walker.
Co- and counterrotation of magnetic axes and axial ligands in low-spin ferriheme systems
Journal of the American Chemical Society. 120: (5) 981-990, 1998

Abstract:

The orientation of the principal axes of the g-tensor with respect to the relationship of axial ligand planes to the porphyrin nitrogens has been studied in the framework of the,one-electron crystal field model for tetragonal and rhombic low-spin d⁵ complexes such as ferriheme centers. All five d atomic orbitals were taken into account for two-different ground-state-electronic configurations, the "normal" (d_xy)²(d_xz, d_yz)³ and the "novel" (d_xz, d_yz)⁴ (d_xy)¹ configurations. The expressions for the g-tensor, g-values, and magnetic axes were derived on the basis of first-order perturbation theory. The conditions for co- and counterrotation of magnetic axes with rotation of planar axial ligands away from the porphyrin nitrogens toward the meso positions and beyond, as well as the order of g values, have been analyzed. It is found that counterrotation is the only possibility for the (d_xz, d_yz)⁴ (d_xy)⁴ configuration and that it is also by far more common for the (d_xy)²(dxz, dyz)³ electron configuration. The possibilities of nonlinear co-/counterrotation are also explored. The predictions of this treatment are then compared to experimental results obtained from single-crystal EPR, glassy sample ESEEM, and solution NMR spectroscopic studies. It is clear that the majority of experimental systems reported thus far follow the major predictions of this treatment: Most systems exhibit angle-for-angle (linear) counterrotation of the g or (tensor with rotation of planar axial ligands away for the N-Fe-N axes; Hence, knowing the structure of a model heme or heme protein, and in particular, the orientation of (fixed) axial ligand planes, one should be able to predict the approximate orientation of the in-plane magnetic axes. This knowledge provides a check on the values obtained in new solution NMR, single-crystal EPR or frozen solution ESEEM experiments.

J.H.Bowen, N.V.Shokhirev, A.M.Raitsimring, D.H.Buttlaire, F.A.Walker.
EPR studies of the dynamics of rotation of dioxygen in model cobalt(II) hemes and cobalt-containing hybrid hemoglobins
Journal of Physical Chemistry B. 101: (43) 8683-8691, 1997.

Abstract:

Earlier we showed that the shapes of the EPR spectra of cobalt(II) porphyrinate(nitrogen base)(dioxygen) complexes in fluid solution were sensitive to the rate of rotation about the Co-O bond (Walker, F. A.; Bowen, J. H. J. Am. Chem. Sec.1985, 107, 7632). We have now extended these studies to four metal-substituted hybrid hemoglobins in an attempt to determine whether EPR spectroscopy is sensitive to differences in the mobility of dioxygen in the alpha and beta subunits of the T and R quaternary states. For purposes of this study, [alpha(2)(CoO₂) beta(2)(FeO₂)] and [alpha(2)(FeO₂)beta(2) (CoO₂)] were used as R-state models and [alpha(2) (CoO₂)beta(2)(Zn)] and [alpha(2)(Zn)beta(2)(CoO2)] were used as T-state models. EPR spectra were recorded for samples of each of the above hybrids, equilibrated with 1 atm of O₂ gas, as a function of temperature. The ''progress toward averaging'' of the EPR signals of the Co-O₂-containing subunits was measured as the difference in field positions, Delta H, for the midpoint of the low- and high-field extrema of the derivative EPR spectra. A plot of Delta H vs temperature for each hybrid shows that the [alpha(2)(Zn)beta(2) (CoO₂)] hybrid is unique in averaging more slowly than the other three (all of which behave similarly), indicating more restricted rotation of dioxygen in T-state beta-chain pockets than in the heme distal O-₂-binding pockets of any other form. This finding is consistent with X-ray crystallographic data which show that valine Ell on the distal side of the T-state P-chain pocket partially blocks the dioxygen binding site (Perutz, M. F.; Fermi, G.; Luisi, B.; Shaanan, B.; Liddington, R. C. Ace. Chem. Res. 1987, 20, 309). Simulation of EPR spectra as a function of jump time provides semiquantitative estimates of the rate of dioxygen rotation in these mixed-metal hemoglobin-dioxygen samples; these rates are in the 1 x 10⁸ s^-1 range for three of the hybrids at 35-37 degrees C, and about one-third that value for T-state beta(CoO₂) centers. These results provide new insight into the highly dynamic nature of dioxygen bound to the metal centers of hemoglobin at physiological temperatures.

W.Naumann, N.V.Shokhirev, A.Szabo.
Exact asymptotic relaxation of pseudo-first-order reversible reactions.
Physical Review Letters. 79: (16) 3074-3077, 1997.

Abstract:

The relaxation kinetics of the diffusion-influenced reversible reaction A + B C is studied in the pseudo-first-order limit ([B] much greater than [A]) when A and C are static and the B's move independently with diffusion coefficient D. For the initial condition [A(0)] = 1, [C(0)]= 0, it is shown that the asymptotics of [A(t)] for t ( is given in d dimensions by (1 + K-cq[B])(-1) + K-eq(2)[B]/(1 + K-eq[B])(3) f(d)(t) with f(1)(t) = (( Dt)(-1/2), f(2)(t) = (4 ( Dt)(-1), and f(3)(t) = (4 ( Dt)(-3/2), and where K-eq is the equilibrium constant. by comparing with accurate simulations, this result is found to be exact for d = 1, and we predict that it is exact for higher dimensions.

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N.V.Shokhirev, T.K.Shokhireva, J.R.Polam, C.T.Watson, K.Raffii, U.Simonis, F.A.Walker
2D NMR investigations of the rotation of axial ligands in six-coordinate low-spin iron(III) and cobalt(III) tetraphenylporphyrinates having 2,6-disubstituted phenyl rings: Quantitation of rate constants from ¹H EXSY cross-peak intensities
Journal of Physical Chemistry A. 101: (15) 2778-2786, 1997.

Abstract:

Phase-sensitive NOESY/EXSY experiments have been utilized to measure the rates of axial ligand rotation for (tetramesitylporphyrinato)iron(m) and -cobalt(III) bis(2-methylimidazole), [(TMP)Fe(2-MeImH)(2)]+ClO^4- and [(TMP)Co(2-MelmH)(2)]+BF^4-, and several related complexes at various low temperatures. The derivations of the expressions for EXSY cross-peak volumes (Ernst, R. R.; Bodenhausen, G.; Wokaun, A, Principles of Magnetic Resonance in One and Two Dimensions; Clarendon Press: Oxford, U.K., 1992; chapters 6 and 9) as a function of mixing time tau(m), longitudinal relaxation time T-1, and chemical exchange rate constant, k, have been extended to the case of cyclic four-site chemical exchange having a single rate constant. Cross-peak volumes were fit to the expressions, and the rate constants were calculated using a computer fitting program developed in this laboratory. The dependence of the reliability of the rate constant on T-1, tau(m), and other experimental factors is discussed. The temperature dependence of the rate constants was used to calculate the activation enthalpy and entropy for these complexes and two others, [tetrakis(2,6-dichlorophenyl)porphyrinato]iron bis(2-methylimidazole) perchlorate, [(2,6-Cl-2)(4)(TPP)Fe(2-MeImH)(2)] +ClO4- and its 2,6-dibromophenyl analog, [(2,6-Br-2)(4)(TPP)Fe(2-MelmH)(2)] +ClO4-, as well as the bis(1,2-dimethylimidazole) complexes of(TMP)Co-III. The values of Delta H-double dagger are very similar for all Fe(III) complexes (46-51 kJ/mol), and Delta S-double dagger values are close to zero. Nevertheless, the combined differences in these activation parameters led to rate constants for ligand rotation at 25 degrees C ranging from 1.1 x 10⁵ (2,6-Br-2) to 1 x 10⁴ (TMP) s^-1. For the [(TMP)CoL(2)]+BF4- complexes where L = 2-MeImH and 1,2-Me(2)Im, the values of Delta H-double dagger are very similar but slightly smaller than those for the low-spin Fe(m) complexes, but the v alues of Delta S-double dagger are rather negative (-63 and -84 J/(mol K), respectively), which lead to rate constants at 25 degrees C of 14 and 5 s^-1, respectively. The difference in Delta S-double dagger and thus the 10³ difference in the rate constants for Fe(III) and Co(III) complexes probably indicates either steric hindrance to rotation of the 2-methyl group of the ''hindered'' ligand in the Co(III) complexes, where the Co-N-ax bond lengths are expected to be somewhat shorter than the corresponding Fe-N-ax bonds, or differences in solvation of the Co(III) complexes (BF4- anion) that lead to a more highly structured transition state than for those of the Fe(III) complexes (ClO4- anion). The methods developed for analysis of the EXSY data are general and could be used for any case of four-site chemical exchange with a single rate constant.

A.I.Burshtein, N.V.Shokhirev
Viscosity and free energy dependence of photochemical charge separation
Journal of Physical Chemistry A. 101: (1) 25-30, 1997.

Abstract:

Contrary to the conventional (''exponential'') model of contact charge creation and recombination, we consider here a recombination of a geminate ion pair occurring in a remote rectangular spherical layer. This simple model available for analytical solution enables one to discriminate between inner and outer generation of charges with respect to a thin recombination layer. In the slow diffusion limit, the qualitatively different viscosity and free energy dependencies of effective recombination rate are predicted for these alternative cases. The experimental verification of these predictions can provide clear evidence of noncontact electron transfer in liquid solutions.

F.A.Walker, H.Nasri H, I.Turowska-Tyrk, K.Mohanrao, C.T.Watson, N.V.Shokhirev, P.G.Debrunner, W.R.Scheidt.
p -Acid ligands in iron(III) porphyrinates. Characterization of low-spin bis(tert-butylisocyanide) (porphyrinato)iron(III) complexes having (d_xz,d_yz)⁴ (d_xy)¹ ground states.
Journal of The American Chemical Society. 118: (48) 12109-12118, 1996
Abstract:

The synthesis and characterization of isocyanide complexes of (porphyrinato)iron(III) species, [(Porph)Fe(t-BuNC)(2)]ClO4, Porph = OEP, TPP, are reported. The crystal structures of [(TPP)Fe(t-BuNC)(2)]ClO4 and [(OEP)Fe(t-BuNC)(2)]ClO4 have been determined. Consistent with the expected effect from the strong pi-acceptor character of the axial tert-butyl isocyanide ligands, the X-ray structure of the complex shows that the porphyrinate ring is strongly ruffled. The spectroscopic properties of these complexes suggest the possibility of ''blurring'' of the definitions of the electron configurations of low-spin Fe(III) macrocycles having (d(xy))¹ electronic ground states, with the extreme possibilities being low-spin Fe(III)-(macrocycle)(2-), with the unpaired electron localized in the d(xy) orbital of the metal, and low-spin Fe(II)-(macrocycle)(1-.), with the unpaired electron localized on the macrocycle. EPR spectroscopy of the TPP and OEP complexes shows that the g-values (g perpendicular to = 2.20-2.28, g parallel to = 1.94-1.83) are consistent with an electron configuration that is (d(xz)d(yz))⁴(d(xy))¹, the purest (d(xy))¹ ground state system with the most complete quenching of orbital angular momentum discovered thus far (Sigma g(2) as small as 13.5). Proton NMR spectra of [OEPFe(t-BuNC)(2)]ClO4 in CD2Cl2, recorded over the temperature range -100 to +37 degrees C, also support the (d(xy))¹ ground state, where ruffling of the porphyrinate ring makes it possible for unpaired electron spin delocalization to the 3a(2u)(pi) orbital of the porphyrinate ring. This orbital has very large electron density coefficients at the meso positions and hence explains the very large negative contact shift of the meso-H; its size indicates considerable (similar to 19%) spin delocalization from low-spin Fe(III) to the 3a(2u)(pi) orbital by porphyrin --> Fe pi donation. Mössbauer and IR spectral data are also consistent with the (d(xy))(1) ground state.

M.J.M.Nesset, N.V.Shokhirev, P.D.Enemark, S.E.Jacobson, F.A.Walker.
Models of the cytochromes. Redox properties and thermodynamic stabilities of complexes of ''hindered'' iron(III) and iron(II) tetraphenylporphyrinates with substituted pyridines and imidazoles
Inorganic Chemistry. 35: (18) 5188-5200, 1996.

Abstract:

The Fe-III/Fe-II and Fe-II/Fe-I reduction potentials of a series of model hemes have been measured by cyclic voltammetry in dimethylformamide at 25 degrees C as a function of the concentration of added axial ligands. The six porphyrinate ligands utilized were tetraphenylporphyrin (TPP), tetramesitylporphyrin (TMP), and a series of ''hindered'' tetraphenylporphyrins having substituents (OCH3, F, Cl, Br) on both ortho positions of each of the four phenyl rings. The perchlorato salts of the iron(III) porphyrinates were utilized for the titrations. The axial ligands utilized were N-methylimidazole, 2-methylimidazole, and pyridines of basicities ranging in pK(a)(PyH(+)) from 9.7 to 1.1. From the electrochemical titration, the equilibrium constants (log beta(2) and some log beta(1)) of each iron porphyrinate with each ligand were determined. The values of log beta(2) for the iron(III) complexes decrease in the order Br > Cl > CH3 > OCH3 > H > F, while those for iron(II) decrease in the slightly modified order Br > Cl > CH3 > F > OCH3 > H. Rather than electronegativity or electron-donating/withdrawing characteristics, these results appear to follow primarily the physical size of the ortho substituents: The iron porphyrinates with the largest ortho substituents have the largest equilibrium constants. The hindered (TPP)Fe-II complexes are usually, but not always, more stable than the corresponding hindered (TPP)Fe-III complexes. For both (TPP)Fe-III and the hindered (TPP)Fe-III complexes, the slope of the correlation of log beta(2)(III) with the pK(a) of the conjugate acid of the pyridine ligand is 1.0. The equilibrium constants for hindered (TPP)Fe-II complexes, however, have virtually no dependence upon the base strength of the axial pyridines, while those for (TPP)Fe-II has a slight sensitivity, with a slope of 0.15. In contrast to common belief, 2-methylimidazole readily forms bis complexes with some iron(II) tetraphenylporphyrinates ((TMP)Fe-II, ((2,6-Cl-2)TPP)Fe-II, and ((2,6-Br-2)(4)(TPP)Fe-II), although it does not with (TPP)Fe-II and its (2,6-F-2)(4)- and (2,6-(OCH3)(2))(4)- counterparts. N-Methylimidazole is unique among the axial ligands of this study, in that the equilibrium constants for binding to both Fe(III) and Fe(II) are virtually identical for all porphyrinates studied.

A.I.Kruppa, M.B.Taraban, N.V.Shokhirev, S.A.Svarovsky, T.V.Leshina.
¹¹⁹Sn CIDNP: Calculations and experiment.
Chemical Physics Letters. 258: (1-2) 316-322, 1996.

Abstract:
¹¹⁹Sn CIDNP effects observed in the photolysis of 2-methylpropanoyltripropylstannane, Pr3SnC(O)CHMe(2), are in good agreement with those calculated in the frames of the diffusion model of radical pair (RP) theory. Simulations performed for arbitrary magnetic field strengths have shown that mainly S-T₀ transitions in RPs where the Zeeman term is comparable with the hyperfine interaction are responsible for CIDNP formation in the fields of modem NMR spectrometers (several tesla). CIDNP in lower magnetic fields result from S-T₊,T_- transitions in all RPs involving tin-centered radicals. In high fields these transitions lead to the appearance of net polarization in the RPs where the Zeeman term is well below the hyperfine interaction.

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T.H.Lay, L.N.Krasnoperov, C.A.Venanzi, J.W.Bozzelli, N.V.Shokhirev.
Ab initio study of alpha-chlorinated ethyl hydroperoxides CH₃CH₂OOH, CH₃CHClOOH, and CH₃CCl₂OOH: Conformational analysis, internal rotation barriers, vibrational frequencies, and thermodynamic properties
Journal of Physical Chemistry. 100: (20) 8240-8249, 1996.

Abstract:

Ab initio calculations were performed on CH₃CH₂OOH, CH₃CHClOOH, and CH₃CCl₂OOH molecules using the Gaussian92 system of programs. Geometries of stable rotational conformers and transition states for internal rotation were optimized at the RHF/6-31G* and MP2/6-31G* levels of theory. Harmonic vibrational frequencies were computed at the RHF/6-31G* level of theory. Potential barriers for internal rotations were calculated at the MP2/6-31G**/HF/6-31G* level. Parameters of the Fourier expansion of the hindrance potentials have been tabulated. Standard entropies (S degrees(298)) and heat capacities (C-p(T)'s, 300 less than or equal to T/K less than or equal to 1500) were calculated using the rigid-rotor-harmonic-oscillator approximation based on the information obtained from the ab initio studies. Contributions from hindered rotors were calculated by summation over the energy levels obtained by direct diagonalization of the Hamiltonian matrix of hindered internal rotations. Enthalpies of formation for these three molecules were calculated using isodesmic reactions. Enthalpies of formation were calculated to be Delta H degrees(298)(CH₃CH₂OOH) = -41.5 +/- 1.5 kcal mol(-1), Delta H degrees(f298)(CH3CHClOOH) = -50.9 +/- 3.4 kcal mol^-1, and Delta H degrees(f298)(CH3CCl2OOH) = -55.3 +/- 2.2 kcal mol(-1). Entropies (S degrees(298)) are calculated to be 76.1, 79.2 and 86.6 cal mol^-1 K-1 for CH₃CH₂OOH, CH₃CHClOOH, and CH₃CCl₂OOH, respectively.

T.Vesala, T.Ahonen, P.Hari, E.Krissinel, N.Shokhirev.
Analysis of stomatal CO₂ uptake by a three-dimensional cylindrically symmetric model.
New Phytologist. 132: (2) 235-245, 1996.

Abstract:

A numerical model is introduced that solves the steady-state diffusion equation for a single stoma and the mesophyll surrounding. This system has cylindrical symmetry, and diffusive transport of carbon dioxide in the gas phase is coupled with transfer in mesophyll along with a photosynthetic sink rate and respiratory production rates. The mesophyll is treated as a continuously distributed liquid phase, and the photosynthetic rate is determined by the carbon dioxide concentration, the photosynthetic photon flux density and the chlorophyll concentration. Photorespiration is proportional to the photon flux density, and dark respiration is assumed to be constant. The model offers a rigorous way to investigate the roles of physics and geometrical structure in stomatal gas exchange. Lateral (radial) diffusion and differences between hypostomatous and needle-like leaves are analysed with special attention. To yield realistic stomatal behaviour, the model requires that the diffusion coefficient describing mesophyllic transport must be somewhat larger than carbon dioxide diffusivity in pure liquid water. The mesophyllic carbon dioxide concentration slopes sharply towards a constant value as a function of distance from the surface of a sub-stomatal cavity. The optimal placement of chlorophyll is close to the surface containing stomata.

N.V.Shokhirev, F.A.Walker.
Analysis of the temperature dependence of the H-1 contact shifts in low-spin Fe(III) model hemes and heme proteins: Explanation of ''Curie'' and ''anti-Curie'' behavior within the same molecule.
Journal of Physical Chemistry. 99: (50) 17795-17804 DEC 14 1995

Abstract:

The reasons that the temperature dependence of the NMR isotropic shifts of model ferrihemes and ferriheme proteins deviate from Curie behavior have been analyzed by considering the energies of the valence orbitals of the metal and the porphyrinate. For low-spin Fe(III), overlap of the e-symmetry pi orbitals of a symmetrical porphyrin ring and the d(p) orbitals of the metal produces two low-energy molecular orbitals that are mainly porphyrin in character and are filled and two high-energy (valence) molecular orbitals that are mainly metal in character and contain three electrons. The odd electron in the valence set thus gives rise to the spin delocalization that results in the observed contact shift pattern of these systems. Unsymmetrical substitution and/or presence of a planar axial ligand that is prevented from rotation removes the degeneracy of these e(p) orbitals, producing a system in which the energy separation between the two formerly degenerate pi orbitals, Delta E(pi), is of the order of only tens of cm^-1 for the former or quite large (several times k(B)T) for the latter. In either case, both orbitals are utilized for spin delocalization to a significant extent as the temperature is varied, according to their varying Boltzmann populations. Such a two-level system obeys a modified Curie law that takes into account the thermal population of the two levels as a function of temperature. In fact, the temperature dependence of some of the contact shifts of model hemes or heme proteins may show anti-Curie behavior if Delta E(pi) is large compared to k_BT at ambient emperatures. Such anti-Curie behavior has been observed for two of the heme methyl resonances of several cytochromes c and b(5) and cyanometmyoglobins or -hemoglobins, where the axial methionine pi-symmetry lone pair or histidine imidazole plane orientation, respectively, is believed to be the important factor in determining D E(p). Assuming reasonable energy separations of the two valence e(p) orbitals, from very small to quite large (similar to 1000 cm^-1), the expected temperature dependence of the contact shifts has been calculated for an assumed set of valence MO coefficients. These results have then been compared to the experimental isotropic shifts of several model heme systems having unsymmetrical substitution patterns and/or one fixed axial ligand and to several heme proteins. Using a computer program developed to fit the observed isotropic shifts to the two-level equation, D E(p) was estimated from the temperature dependence of the isotropic shifts of the protons of the beta-pyrrole substituents of the above-mentioned systems. In the case of the proteins investigated, Aplysia cyanometmyoglobin and cytochrome b(5), the values of D E(p), obtained from analysis of proton isotropic shifts are similar to those calculated from EPR g values measured at low temperatures, while for model hemins, the values of D E(p) obtained are smaller than those predicted and vary in accord with the expectations as to the rigidity, or lack thereof, of the orientation of at least one planar axial ligand, indicating that thermal averaging of the two levels due to rapid rotation (or libration) of the axial ligand is fast on the NMR time scale. This same two-level approach could be applied to any system in which there is a thermal equilibrium between two states separated by an energy within several factors of k_BT.

A.M.Raitsimring, P.Basu, N.V.Shokhirev, J.H.Enemark.
Epr Studies of Weakly Coupled Oxomolybdenum(V) and Low-Spin Iron(Iii) Porphyrin Centers. Applied Magnetic Resonance. 9: (2) 173-192, 1995.

Abstract:

Novel compounds containing two S=1/2 coupled spin centers (Mo(V) and low spin Fe(III)) have been investigated in detail by X- and Q-band EPR spectroscopy, spectral simulation and molecular modelling calculations. For one system with a Mo-Fe distance of similar to 9.4 Angstrom the dominant dipolar coupling allows distinction among structures that are consistent with molecular modelling calculations. For the second system with a Mo-Fe of similar to 7.9 Angstrom the exchange interaction is dominant (0.5 < J < 3.0 GHz). These coupled systems are preliminary benchmarks for using EPR to investigate the Mo-Fe interaction in sulfite oxidase.

P.Basu, N.V.Shokhirev, J.H.Enemark, F.A.Walker.
Nmr-Studies of Hindered Ligand Rotation, Magnetic-Anisotropy, Curie Behavior, Proton Spin Relaxation, and Ligand-Exchange In Some Novel Oxomolybdenum(V) Iron(Iii) Porphyrinate Complexes.
Journal of the American Chemical Society. 117: (35) 9042-9055, 1995.

Abstract:

A detailed H-1 NMR study has been carried out on the novel porphyrinatoiron(III)-Mo(V) complexes {tri-p-tolyl[2,3-[((hydrotris(3,5-dimethylpyrazolyl)borato) oxomolybdenum) dioxy]phenyl] porphyrinato}bis(L) iron-(III)chloride, [Fe(2,3-Mo-TTP)L₂]Cl-+(-), where L = N-methylimidazole (NMeIm), imidazole (ImH), or 4-(dimethylamino)pyridine (4DAP), and [Fe(3,4-Mo-TTP) (NMeIm)(2)]Cl-+(-). Each of these compounds contains two S =1/2 metal centers. In the 2,3-isomer, rotation of one of the axial ligands bound to the iron atom is prevented by the bulky (hydrotris(pyrazolyl)borato) oxomolybdenum substituent, as evidenced by the observation of eight unique pyrrole-H resonances that do not coalesce over most of the liquid range of the CD₂Cl₂ solvent (-90 to +30 degrees C). Moreover, the slow electron spin relaxation time of oxomolybdenum(V) allows this center to function as a ''dipolar relaxation agent'' that provides a sensitive measure of the distance between the Mo(V)(V) center and each of the pyrrole protons of the low-spin iron(III) porphyrinate. Combination of results from measurement of the T(1)s of the eight pyrrole protons, the COSY coupling pattern, NOEs between protons not in the same pyrrole ring, and analysis of the effect of the orientation of the nodal plane of the nonrotating axial ligand on the rhombic dipolar contribution to the isotropic shift led to a complete and unambiguous assignment of these resonances. Theoretical analysis of the observed shifts and their temperature dependence made it possible to map the unpaired electron spin density at the beta-pyrrole positions, and thereby the unpaired electron spin density distribution in the pi orbital into which the unpaired electron is preferentially delocalized, and to calculate the approximate energy separation, Delta E(pi), between it and its e(pi) counterpart. Thermal population of the higher-energy orbital accounts for the non-zero intercepts of the Curie plots of the pyrrole-H resonances. Comparison to other systems, including the 3,4-MoO complex, demonstrates the large, dominating effect of a fixed axial ligand plane in determining the spread of the pyrrole-H resonances. The results demonstrate the relatively small effect of the orientation df the p(pi) orbital of the planar ligand on the in-plane magnetic anisotropy, and its much larger effect on spin d elocalization via the contact interaction. Thus, we conclude that it is likely that the spread of the methyl resonances in ferricytochromes b₂ and c and other low-spin ferriheme proteins is controlled largely by the effect of the orientation of the pp orbital of the strongest p donor ligand on the contact shift, rather than on the in-plane magnetic anisotropy created simultaneously by that same pp orbital and manifested in the dipolar term. Rates of axial ligand (L) exchange for [Fe(2,3-Mo-TTP)L₂]Cl-+(-) (for L =NMeIm and 4DAP) have also been measured. It is found that the ligand on the same side of the porphyrinate plane (syn) as the bulky oxomolybdenum(V) group exchanges much more slowly than the one on the opposite side of the porphyrinate plane (anti).

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V.V.Korolev, V.V.Bolotsky, N.V.Shokhirev, E.B.Krissinel, V.A.Bagryansky, N.M.Bazhin.
Diffusion of Molecular-Oxygen In Glassy Matrices, Studied by Luminescence Quenching
Chemical Physics. 196: (1-2) 317-325, 1995.

Abstract:

Oxygen diffusion in low temperature squalane glasses was studied by phenanthrene phosphorescence quenching and anthracene fluorescence quenching in geminate pairs (anthracene...O₂). The oxygen mobility can be described by continuous diffusion. Anthracene fluorescence quenching in geminate pairs allow to measure diffusion coefficients till 10^-23 cm²/s.

T.Vesala, K.Hameri, T.Ahonen, M.Kulmala, P.Harip, T.Pohja, E.Krissinel, N.Shokhirev, A.A.Lushnikov.
Experimental and Numerical Analysis of Stomatal Absorption of Sulfur Dioxide and Transpiration by Pine Needles.
Atmospheric Environment. 29: (7) 825-836 APR 1995.

Abstract:

We present the experimental results of flow chamber measurements on SO₂ dry deposition, and of separate field measurements on transpiration of Scots pine (Pinus sylvestris L) twigs under typical northerly summertime conditions. These results are interpreted by a numerical model, which solves the steady-state diffusion equation for a single stoma approximated to have cylindrical symmetry. An analytical method to estimate the maximal effect of interference (merging concentration fields of adjacent stomata) between stomatal pores is introduced. As a result, a functional pore radius is found to be of order of 2-3 mum, which is significantly smaller than the maximal anatomical size of stomatal aperture. This indicates that stomata are capable to transfer vapours to different degrees. If the obtained estimates for needle resistances are divided by a factor of 4, the leaf area index of local pine canopy, the bulk stomatal resistance for SO₂ is of the order of 200-300 s m^-1.

N.V.Shokhirev, E.B.Krissinel.
Simple Analytical Approach To The Description of Flash-Cidnp Formation For Ion Radicals
Chemical Physics Letters. 236: (3) 247-252, 1995.

Abstract:

The simple analytical expressions for the stationary bimolecular rate constants of recombination of charged radicals in external magnetic field were obtained for the case of high magnetic field, stepwise exchange integral and contact recombination. A comparison of the analytical and the precise numerical calculations shows good accuracy of the proposed approach. Also discussed is the non-trivial influence of solvent polarity and viscosity on the rate constants via singlet-triplet conversion efficiency.

P.A.Frantsuzov, N.V.Shokhirev, A.A.Zharikov.
Nonstationary Kinetics of Noncontact Electron Transfer
Chemical Physics Letters. 236: (1-2) 30-36, 1995.

Abstract:

The behavior of nonstationary kinetics of noncontact transfer has been studied on a step-wise model admitting an exact solution. The existence of an intermediate kinetic stage in essentially nonstationary noncontact reactions has been shown.

H.M.Tan, U.Simonis, N.V.Shokhirev, F.A.Walker.
Substituent Effects On The Choice of The Orbital Preferred For Electron-Spin Delocalization in 2 Paramagnetic Low-Spin Iron(III) Porphyrins - Mapping the Spin-Density Distribution at the Pyrrole Positions by ¹h Cosy and Noesy Techniques.
Journal of The American Chemical Society. 116:(13) 5784-5790, 1994.

Abstract:

In order to elucidate the distribution of unpaired electron spin density within the porphyrin Ir orbitals of two unsymmetrically substituted derivatives of (tetraphenylporphyrinato)iron(III), [(p-Cl)(p-NEt(2))(3) TPPFe(N-MeIm)(2)]-Cl and [(p-NEt(2))(p-Cl)(3)TPPFe(N-MeIm)(2)]Cl(NEt(2) = diethylamino; N-MeIm = N-methylimidazole), ¹H COSY and NOESY spectra were acquired. The cross peak patterns observed in the 2-D maps of these complexes allow assignment of the proton resonances in the same pyrrole ring (H-a,H-b and H-c,H-d) and of those that are closest to each other in adjacent pyrrole rings (H-b,H-c). Using these assignments, it is possible to delineate the pattern of unpaired electron spin delocalization in the porphyrin ring. This pattern can be unambiguously correlated to the relative electronic effects of the two types of phenyl substituents present, thereby permitting the electron-donating or -withdrawing effects of other substituents to be predicted. In order to test if the pattern of delocalized spin density derived from the 2-D NMR studies can be modeled, simple Hückel molecular orbital calculations were performed. Although only intended to provide a qualitative understanding of the effects of electron-donating and -withdrawing substituents, these most basic calculations provided significant results. Using well-established Hückel parameters, together with lowering or raising the energy of the p, orbital of one meso-carbon atom to account for the electronic nature of the unique substituent, an electron density distribution was obtained that fully supports the ¹H resonance assignments based on the cross peaks observed in the COSY and NOESY maps of these complexes. This indicates that more sophisticated theoretical calculations may lead to a quantitative description of the effects of porphyrin substituents on the pattern of spin delocalization in synthetic and naturally occurring hemes and their byproducts. In support of this conclusion, it should be noted that even the simplest Hückel calculations described herein have already proved valuable in explaining the pattern of spin delocalization observed in the substrate-bound form of the enzyme heme oxygenase, which catalyzes the stereospecific alpha-meso bridge cleavage of hemin to yield biliverdin-IX alpha (Hernandez, G.; Wilks, A.; Paolesse, R.; Smith, K. M.; Ortiz de Montellano, P. R.; La Mar, G. N. Biochemistry, in press).

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A.I.Kalugin, V.V.Konovalov, N.V.Shokhirev, A.M.Raitsimring.
Photoelectron Injection Into Dilute Electrolyte Solutions.1. Methodology.
Journal of Electroanalytical Chemistry. 359:(1-2) 63-80, 1993.

Abstract:

A general algorithm for the numerical solution that describes the diffusion and reactions of particles in an arbitrary potential was used to calculate the photodiffusion currents in dilute electrolyte solutions in terms of the exact Gouy-Chapman expression for the diffusion potential f(x). The solution has been obtained for the simplest case when the product of the capture of solvated electrons, generated by photoinjection, is a neutral radical. The limited applicability of the exponential approximation of the phi(x) potential has been demonstrated. When the electrolyte solution is dilute, the characteristic time of the return of solvated electrons e(s)(-) to the electrode increases by 3-6 orders of magnitude within the negative potential range. Thus, when the scavenger concentration is 10^-4-10^-3 M, it can fully capture e_s^-. The calculation results have been compared with those of experiments performed in diluted aqueous solutions of NaF (10^-3 - 1 M) at wavelengths of l = 428-193 nm. The mean distances determined between e_s^- and the photoelectrode are in fair agreement with the previous data obtained for concentrated aqueous electrolyte solutions. We have also found the mean distances, photoinjection threshold and full photoinjected charge in methanol. The effect of the intensity of light on the value of photo-induced charge has also been demonstrated.

N.V.Shokhirev, A.A.Zharikov, E.Krissinel.
Analytical Treatment of Magnetic-Field Effects In Contact Geminate Recombination of Radical-Ion Pairs In Solutions of Arbitrary Polarity.
Journal of Chemical Physics. 99:(4) 2643-2653, 1993.

Abstract:

Geminate recombination of radical ion pairs in the presence of magnetic field is considered on the assumption of a contact reaction and exchange and diffusion character of the reagent motion. Analytical expressions for recombination probabilities for arbitrary magnitude of inter-particle Coulomb interaction are obtained. For the case of high magnetic fields, the influence of a medium polarity and viscosity, the initial separation in a pair and the scavenging reactions rate on recombination probability and CIDNP is studied.

A.A.Zharikov, N.V.Shokhirev
The Influence of Solvent Polarity and Viscosity on Magnetic Effects in Geminate Recombination - Balance Approximation.
Zeitschrift für Physikalische Chemie - International Journal of Research In Physical Chemistry & Chemical Physics. 177:37-61, Part 1, 1992.

Abstract:

The influence of a magnetic field on the geminate recombination of ion-radicals in solutions is studied within the framework of a balance approximation. In the model, the motion in a pair is described by the isotropic diffusion in the Coulomb potential. It is assumed that the transitions between the spin states occur outside the strong exchange zone and are described in terms of rate constants. The effect of the medium polarity and viscosity on the magnitude of the magnetic field effect is studied. It is shown that S-T+(T-) transitions at the point of intersection of energy terms make a considerable contribution to the magnetic effect and may cause a change of the sign of the magnetic field effect at high viscosities. The influence of these transitions on the magnetic field effect in media of different viscosity is investigated theoretically and numerically.

A.A.Zharikov, N.V.Shokhirev.
Upper and Lower Bounds for The Rate-Constant of Bimolecular Reactions - Integral Approximation Method.
Chemical Physics Letters. 190:(5) 423-429, 1992

Abstract:

A method for the calculation of rate constants of bimolecular reactions for an arbitrary type of spherically isotropic transfer probabilities and the interaction potentials between reagents has been developed. On the basis of this method, an integral representation of upper and lower bounds for quenching radius is proposed. It has been shown that a relative deviation of the upper from the lower estimate cannot exceed 20%. Comparison with the available analytical results shows good accuracy of the approximations in the description of the viscosity dependence of quenching radius.

A.I.Burshtein, A.A.Zharikov, N.V.Shokhirev
Static and Contact Electron-Transfer Within Photoinduced Geminate Ion-Pairs
Journal of Chemical Physics. 96:(3) 1951-1956, 1992.

Abstract:

The quantum yield and a time of ion pair separation were calculated at any viscosity of solution and arbitrary distance between them at initial moment when geminate charge recombination starts. The results are compared with those obtained in a contact approximation and in a frame of "exponential model." The way is proposed how to use experimental data on back electron transfer to answer the questions where the ions were born and how long an exchange interaction is between them.

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O.B.Spirina, N.V.Shokhirev
Semi-Empirical Method For Calculation of Potential Surfaces of Radical Reactions of CH₄ + CH^.₃ --> CH^.₃ + CH₄ In The Basis of Boundary Orbitals
Teoreticheskaya I Eksperimentalnaya Khimiya. 27:(4) 499-506, 1991

Abstract:

A semiempirical approach in terms of the ZDO method is suggested to described potential energy surface (PES) of some radical reactions with a bounded basis including only frontier (single-filled) molecular orbitals of radicals depending on the geometric parameters with allowance for all the possible configuration. The methods for a choice of parameters are analyzed. The developed approach has been used to calculate the PES of CH₄ + CH^.₃ --> CH^.₃ + CH₄ reaction some points of which are checked up by the nonempiric method allowing for correlation energy according to perturbation theory. Relaxation energies are calculated. One-site parameters are found from the nonempiric consideration of CH₃⁺, CH₃ and CH₃^- energy, two-site ones - from simulation of CH₄ ® CH₃ + H and C₂H₆ ® 2CH₃ reactions in terms of the same one-orbital approximation. Energy parameters of the considered reactions are over-estimated by 10% while geometric ones - by 15%. The Hartree-Fock solutions and the solutions allowing for Cl have been also comparatively analyzed; the changes in spin and charge densities on the reaction centers have been considered.

A.I.Burshtein, A.A.Zharikov, N.V.Shokhirev, O.B.Spirina, E.B.Krissinel
Kinetic and Diffusional Control of Geminate Recombination
Journal of Chemical Physics. 95:(11) 8013-8021, 1991

Abstract:

A study is presented of geminate recombination and separation kinetics and their rates in liquid solutions. Applicability limits are proposed for the "exponential model" of this process, which is widely used for interpreting experimental data on back-electron transfer following photoionization. It is proved that this model qualitatively contradicts an analytical description of the process in polar media. A numerical experiment shows that the exponential model may be used only for nonpolar media of moderate viscosity. In this case the separation rate is linearly connected with the recombination constant and may be used to check the energy gap law characteristic for electron transfer.

A.A.Zharikov, N.V.Shokhirev
Analytical Treatment of The Contact Geminate Charge Recombination In Solutions of An Arbitrary Polarity
Chemical Physics Letters. 186:(2-3) 253-263, 1991.

Abstract:

The case of contact reactions of charged particles is considered. For pairs generated in contact, a closed analytical expression for the geminate recombination is derived. The comparison with numerical solution of the Smoluchowski equation demonstrates high accuracy of the approximation. The transition from the non-exponential quasineutral regime to the exponential one with decreasing solvent polarity is analysed.

N.V.Shokhirev, E.C.Korolenko, M.B.Taraban, T.V.Leshina
Anomalous Magnetic Effects - The Role of Association In The Recombination of Singlet Radical Pairs In Liquids
Chemical Physics. 154:(2) 237-244, 1991.

Abstract:

The magnetic field effects (MFEs) reported earlier on the recombination products ratio in the reactions of benzyl chloride with triethylgermylsodium (triethylgermylpotassium) have been analyzed. The experimentally observed MFEs prove to be much larger than those calculated under the assumption of a free diffusive radical pair motion. A model involving the associated radical pair (RP) state is proposed to explain the MFEs in the reactions studied. The calculations performed within the framework of the exponential model with a nuclear spin I = 1/2 provide for a quantitative description of the experimentally observed MFE field dependences. The comparison of the experimental and calculated resul ts shows that the experimental product yield ratio field dependences most probably correspond to the situation of a relatively short-lived (lifetime congruent-to 1 ns) associated RP state with a small effective exchange interaction.

V.S.Bashurova, K.P.Koutzenogil, A.Yu.Pusep, N.V.Shokhirev.
Determination of Atmospheric Aerosol Size Distribution-Functions From Screen Diffusion Battery Data - Mathematical Aspects
Journal of Aerosol Science. 22: (3) 373-388, 1991

Abstract:

This paper considers the mathematical aspects of the reconstruction of size distribution functions of fine atmospheric aerosol from screen-type diffusion battery (SDB) measurements. It is shown that the problem of reconstruction may be successfully solved using Tikhonov's regularization method of the second order. A series of experimental data is considered, and the spectra obtained are classified. The bimodal size distribution is proved to exist in the highly dispersed fraction of atmospheric aerosol. The reliability of the solutions is analysed; it is found that, for the existing characteristics of the SDB, it is impossible to determine more than two modes. Recommendations on the planning of SDB experiments are given.

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