Free energies for biological electron transfer from QM/MM calculation: method, application and critical assessment

Computer simulations of biological electron transfer reactions are reviewed with a focus on the calculation of reaction free energy (driving force) and reorganization free energy. Then a mixed quantum mechanical/molecular mechanical (QM/MM) approach is described which is designed for computation of these quantities for pure electron transfer reactions with large donor-acceptor separation distances. The method is applied to intra-protein electron transfer in Ru(bpy)(2)(im)His33 cytochrome c and the results compared to experimental data. Several modeling aspects which are important for successful calculation of free energies with QM/MM are discussed in detail.     

Reaction mechanism of Ru(II) piano‐stool complexes: Umbrella sampling QM/MM MD study

Biologically relevant interactions of piano‐stool ruthenium(II) complexes with ds‐DNA are studied in this article by hybrid quantum mechanics—molecular mechanics (QM/MM) computational technique. The whole reaction mechanism is divided into three phases: (i) hydration of the [Ru^II(η⁶‐benzene)(en)Cl]⁺ complex, (ii) monoadduct formation between the resulting aqua‐Ru(II) complex and N7 position of one of the guanines in the ds‐DNA oligomer, and (iii) formation of the intrastrand Ru(II) bridge (cross‐link) between two adjacent guanines. Free energy profiles of all the reactions are explored by QM/MM MD umbrella sampling approach where the Ru(II) complex and two guanines represent a quantum core, which is described by density functional theory methods. The combined QM/MM scheme is realized by our own software, which was developed to couple several quantum chemical programs (in this study Gaussian 09) and Amber 11 package. Calculated free energy barriers of the both ruthenium hydration and Ru(II)‐N7(G) DNA binding process are in good agreement with experimentally measured rate constants. Then, this method was used to study the possibility of cross‐link formation. One feasible pathway leading to Ru(II) guanine‐guanine cross‐link with synchronous releasing of the benzene ligand is predicted. The cross‐linking is an exergonic process with the energy barrier lower than for the monoadduct reaction of Ru(II) complex with ds‐DNA. © 2014 Wiley Periodicals, Inc.     

Quantum chemical calculations of reduction potentials of AnO2(2+)/AnO2+ (An = U, Np, Pu, Am) and Fe3+/Fe2+ couples

The reduction potentials of the AnO(2)(H(2)O)(5)(2+)/AnO(2)(H(2)O)(5)(+) couple (An = U, Np, Pu, and Am) and Fe(H(2)O)(6)(3+) to Fe(H(2)O)(6)(2+) in aqueous solution were calculated at MP2, CASPT2, and CCSD(T) levels of theory. Spin-orbit effects for all species were estimated at the CASSCF level. Solvation of the hydrated metal cations was modeled both by polarizable conductor model (PCM) calculation and by solvating the solutes with over one thousand TIP3P water molecules in the QM/MM framework. The redox reaction energy calculated by QM/MM method agreed well with the PCM method after corrections using the classical Born formula for the contribution from the rest of the solvation sphere and correction for dynamic response of solvent polarization in the MM region. Calculated reduction potentials inclusive of spin-orbit effect, zero-point energy, thermal corrections, entropy effect, and PCM solvation energy were found to be comparable with experimental data. The difference between CASPT2 calculated and experimental reduction energies were less than 35 kJ/mol in all cases, which ensures that CASPT2 (and CCSD(T)) calculations provide reasonable estimates of the thermochemistry of these reactions.     

Photodriven electron and energy transfer from a light-harvesting metallodendrimer

Intermolecular electron and energy transfer from a light-harvesting metallodendrimer [Ru[bpy(C-450)(4)](3)](2+), where bpy(C-450)(4) is a 2,2'-bipyridine derivative containing 4 coumarin-450 units connected together through aryl ether linkages, is observed in acetonitrile solutions at room temperature. The model complex [Ru(dmb)(3)](2+), where dmb is 4,4'-dimethyl-2,2'-bipyridine, is included for quantitative comparison. The excited states of both compounds are metal-to-ligand charge transfer in nature and participate in excited-state electron and triplet energy transfer processes. Quenching constants were determined from luminescence and time-resolved absorption experiments at constant ionic strength. [Ru[bpy(C-450)(4)](3)](2+) displays significantly slower quenching rates to molecular oxygen and methyl viologen relative to the other processes investigated. Triplet energy transfer from [Ru[bpy(C-450)(4)](3)](2+) to 9-methylanthracene is quantitatively indistinguishable from [Ru(dmb)(3)](2+) while reductive electron transfer from phenothiazine was slightly faster in the former. With the exception of dioxygen quenching, our results indicate that the current dendritic structure is ineffective in shielding the core from bimolecular electron and triplet energy transfer reactions. Electrochemical measurements of [Ru[bpy(C-450)(4)](3)](2+) reveal irreversible oxidative processes at potentials slightly negative to the Ru(III/II) potential that are assigned to oxidations in the dendritic structure. Excited-state oxidative electron-transfer reactions facilitate this process resulting in the reduction of ground-state Ru(III) to Ru(II) and the trapping of the methyl viologen radical cation (MV(*+)) when methyl viologen serves as the quencher. This process generates a minimum of 9 MV(*+)'s for every [Ru[bpy(C-450)(4)](3)](2+) molecule and disassembles the metallodendrimer, resulting in the production of a [Ru(dmb)(3)](2+)-like species and "free" C-450-like dyes.     

Photoredox vs. energy transfer in a Ru(II)-Fe(II) supramolecular complex built with an heteroditopic bipyridine-terpyridine ligand

A trinuclear [[Ru(II)(bpy)(2)(bpy-terpy)](2)Fe(II)](6+) complex (I) in which a Fe(II)-bis-terpyridine-like centre is covalently linked to two Ru(II)-tris-bipyridine-like moieties by a bridging bipyridine-terpyridine ligand has been synthesised and characterised. Its electrochemical, photophysical and photochemical properties have been investigated in CH(3)CN and compared with those of mononuclear model complexes. The cyclic voltammetry of (I) exhibits, in the positive region, two successive reversible oxidation processes, corresponding to the Fe(III)/Fe(II) and Ru(III)/Ru(II) redox couples. These systems are clearly separated (DeltaE(1/2) = 160 mV), demonstrating the lack of an electronic connection between the two subunits. The two oxidized forms of the complex, [[Ru(II)(bpy)(2)(bpy-terpy)](2)Fe(III)](7+) and [[Ru(III)(bpy)(2)(terpy-bpy)](2)Fe(III)](9+), obtained after two successive exhaustive electrolyses, are stable. (I) is poorly luminescent, indicating that the covalent linkage of the Ru(II)-tris-bipyridine to the Fe(II)-bis-terpyridine subunit leads to a strong quenching of the Ru(II)* excited state by energy transfer to the Fe(II) centre. Luminescence lifetime experiments show that the process occurs within 6 ns. The nature of the energy transfer process is discussed and an intramolecular energy exchange is proposed as a preferable deactivation pathway. Nevertheless this energy transfer can be efficiently quenched by an electron transfer process in the presence of a large excess of the 4-bromophenyl diazonium cation, playing the role of a sacrificial oxidant. Finally complete photoinduced oxidation of (I) has been performed by continuous photolysis experiments in the presence of a large excess of this sacrificial oxidant. The comparison with a mixture of the corresponding mononuclear model complexes has been made.     

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.     

Geometry optimization based on linear response free energy with quantum mechanical/molecular mechanical method: applications to Menshutkin-type and Claisen rearrangement reactions in aqueous solution

The authors present a method based on a linear response theory that allows one to optimize the geometries of quantum mechanical/molecular mechanical (QM/MM) systems on the free energy surfaces. Two different forms of linear response free energy functionals are introduced, and electronic wave functions of the QM region, as well as the responses of electrostatic and Lennard-Jones potentials between QM and MM regions, are self-consistently determined. The covariant matrix relating the QM charge distribution to the MM response is evaluated by molecular dynamics (MD) simulation of the MM system. The free energy gradients with respect to the QM atomic coordinates are also calculated using the MD trajectory results. They apply the present method to calculate the free energy profiles of Menshutkin-type reaction of NH3 with CH3Cl and Claisen rearrangement of allyl vinyl ether in aqueous solution. For the Menshutkin reaction, the free energy profile calculated with the modified linear response free energy functional is in good agreement with that by the free energy perturbation calculations. They examine the nonequilibrium solvation effect on the transmission coefficient and the kinetic isotope effect for the Claisen rearrangement.     

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

Converging ligand‐binding free energies obtained with free‐energy perturbations at the quantum mechanical level

In this article, the convergence of quantum mechanical (QM) free‐energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa‐acid deep‐cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158–224 atoms). We use single‐step exponential averaging (ssEA) and the non‐Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi‐empirical PM6‐DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free‐energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

QM/MM-PBSA method to estimate free energies for reactions in proteins

We have developed a method to estimate free energies of reactions in proteins, called QM/MM-PBSA. It estimates the internal energy of the reactive site by quantum mechanical (QM) calculations, whereas bonded, electrostatic, and van der Waals interactions with the surrounding protein are calculated at the molecular mechanics (MM) level. The electrostatic part of the solvation energy of the reactant and the product is estimated by solving the Poisson-Boltzmann (PB) equation, and the nonpolar part of the solvation energy is estimated from the change in solvent-accessible surface area (SA). Finally, the change in entropy is estimated from the vibrational frequencies. We test this method for five proton-transfer reactions in the active sites of [Ni,Fe] hydrogenase and copper nitrite reductase. We show that QM/MM-PBSA reproduces the results of a strict QM/MM free-energy perturbation method with a mean absolute deviation (MAD) of 8-10 kJ/mol if snapshots from molecular dynamics simulations are used and 4-14 kJ/mol if a single QM/MM structure is used. This is appreciably better than the original QM/MM results or if the QM energies are supplemented with a point-charge model, a self-consistent reaction field, or a PB model of the protein and the solvent, which give MADs of 22-36 kJ/mol for the same test set.     

Quantum mechanical/molecular mechanical study on the mechanism of the enzymatic Baeyer-Villiger reaction

We report a combined quantum mechanical/molecular mechanical (QM/MM) study on the mechanism of the enzymatic Baeyer-Villiger reaction catalyzed by cyclohexanone monooxygenase (CHMO). In QM/MM geometry optimizations and reaction path calculations, density functional theory (B3LYP/TZVP) is used to describe the QM region consisting of the substrate (cyclohexanone), the isoalloxazine ring of C4a-peroxyflavin, the side chain of Arg-329, and the nicotinamide ring and the adjacent ribose of NADP(+), while the remainder of the enzyme is represented by the CHARMM force field. QM/MM molecular dynamics simulations and free energy calculations at the semiempirical OM3/CHARMM level employ the same QM/MM partitioning. According to the QM/MM calculations, the enzyme-reactant complex contains an anionic deprotonated C4a-peroxyflavin that is stabilized by strong hydrogen bonds with the Arg-329 residue and the NADP(+) cofactor. The CHMO-catalyzed reaction proceeds via a Criegee intermediate having pronounced anionic character. The initial addition reaction has to overcome an energy barrier of about 9 kcal/mol. The formed Criegee intermediate occupies a shallow minimum on the QM/MM potential energy surface and can undergo fragmentation to the lactone product by surmounting a second energy barrier of about 7 kcal/mol. The transition state for the latter migration step is the highest point on the QM/MM energy profile. Gas-phase reoptimizations of the QM region lead to higher barriers and confirm the crucial role of the Arg-329 residue and the NADP(+) cofactor for the catalytic efficiency of CHMO. QM/MM calculations for the CHMO-catalyzed oxidation of 4-methylcyclohexanone reproduce and rationalize the experimentally observed (S)-enantioselectivity for this substrate, which is governed by the conformational preferences of the corresponding Criegee intermediate and the subsequent transition state for the migration step.     

Molecular dynamics and free energy perturbation study of hydride-ion transfer step in dihydrofolate reductase using combined quantum and molecular mechanical model

We used molecular dynamics simulation and free energy perturbation (FEP) methods to investigate the hydride-ion transfer step in the mechanism for the nicotinamide adenine dinucleotide phosphate (NADPH)-dependent reduction of a novel substrate by the enzyme dihydrofolate reductase (DHFR). The system is represented by a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1 semiempirical molecular orbital method for the reacting substrate and NADPH cofactor fragments, the AMBER force field for DHFR, and the TIP3P model for solvent water. The FEP calculations were performed for a number of choices for the QM system. The substrate, 8-methylpterin, was treated quantum mechanically in all the calculations, while the larger cofactor molecule was partitioned into various QM and MM regions with the addition of “link” atoms (F, CH₃, and H). Calculations were also carried out with the entire NADPH molecule treated by QM. The free energies of reaction and the net charges on the NADPH fragments were used to determine the most appropriate QM/MM model. The hydride-ion transfer was also carried out over several FEP pathways, and the QM and QM/MM component free energies thus calculated were found to be state functions (i.e., independent of pathway). A ca. 10 kcal/mol increase in free energy for the hydride-ion transfer with an activation barrier of ca. 30 kcal/mol was calculated. The increase in free energy on the hydride-ion transfer arose largely from the QM/MM component. Analysis of the QM/MM energy components suggests that, although a number of charged residues may contribute to the free energy change through long-range electrostatic interactions, the only interaction that can account for the 10 kcal/mol increase in free energy is the hydrogen bond between the carboxylate side chain of Glu30 (avian DHFR) and the activated (protonated) substrate. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 977–988, 1998     

Electrochromic hysteresis performance of a prussian blue film arising from electron-transfer control by a tris(2,2'-bipyridine)ruthenium(II)-doped WO(3) film as studied by a spectrocyclic voltammetry technique

A [Ru(bpy)(3)](2+) (bpy=2,2'-bipyridine)-doped WO(3) film was prepared as a base layer on a substrate by cathodic electrodeposition from a colloidal triad solution containing peroxotungstic acid (PTA), [Ru(bpy)(3)](2+), and poly(sodium 4-styrenesulfonate) (PSS). A Prussian blue (PB; Fe(II)-Fe(III)) film was cathodically electrodeposited on the [Ru(bpy)(3)](2+)-doped WO(3) film or neat WO(3) film from an aqueous Berlin brown (BB; Fe(III)-Fe(III)) colloid solution to yield a [Ru(bpy)(3)](2+)-doped WO(3)/PB bilayer film or WO(3)/PB bilayer film. For the spectrocyclic voltammogram (SCV) of the WO(3)/PB film, a redox response of Prussian white (PW; Fe(II)-Fe(II))/PB was observed at 0.11 V, however, further oxidation of PB to BB was not allowed by the interfacial n-type Schottky barrier between the WO(3) and PB layers. For the [Ru(bpy)(3)](2+)-doped WO(3)/PB film, any electrochemical response assigned to the redox of PB was not observed in the cyclic voltammogram, however, the in situ absorption spectral change recorded simultaneously showed the significant redox reactions based on PB. The SCV revealed that PW on the [Ru(bpy)(3)](2+)-doped WO(3) film is completely oxidized to PB by a geared reaction of Ru(II)/Ru(III) at 1.05 V, and that 32 % of PB formed is further oxidized to BB by the same geared reaction in the potential scan to 1.5 V. PB was completely re-reduced to PW by a geared reaction of H(x)WO(3)/WO(3) at -0.5 V in the reductive potential scan. These geared electrochemical reactions produced an electrochromic hysteresis performance of the PB film layered on the [Ru(bpy)(3)](2+)-doped WO(3) film.     

Electrochemical and photosensitized redox reactions of a prussian blue film layered on a WO3/[Ru(bpy)3]2+/polymer hybrid film.

A hybrid film of WO(3)/tris(2,2'-bipyridine)ruthenium(II) ([Ru(bpy)(3)](2+))/poly(sodium 4-styrenesulfonate) (PSS) (denoted as a WRP hybrid film) was prepared as a base layer on an indium tin oxide electrode substrate by cathodic electrodeposition from a colloidal ternary solution containing peroxotungstic acid, [Ru(bpy)(3)](2+), and PSS. Prussian blue, Fe(III) (4)[Fe(II)(CN)(6)](3) (Fe(II)-Fe(III)) was cathodically electrodeposited on the WRP hybrid film from a Berlin brown (Fe(III)-Fe(III)) colloidal solution to give a WRP/Fe(II)-Fe(III) bilayer film. Spectrocyclic voltammetry measurement of the WRP/Fe(II)-Fe(III) bilayer film reveals that Prussian white (Fe(II)-Fe(II)) is oxidized to Fe(II)-Fe(III) by electrogenerated Ru(III), and Fe(II)-Fe(III) is re-reduced to Fe(II)-Fe(II) by electrogenerated H(x)WO(3). Visible-light irradiation of the WRP hybrid film generates a small photocurrent (approximately 8 nA cm(-2)) at 0.4 V of an applied potential, whereas irradiation of the WRP/Fe(II)-Fe(II) bilayer film (Fe(II)-Fe(III) is electrochemically reduced to the Fe(II)-Fe(II) state) significantly generates a steady photoanodic current of 2.0-1.1 microA cm(-2) under the same conditions, thus demonstrating that the photoanodic current is produced by the layered Fe(II)-Fe(II) film. The photoaction spectrum of the bilayer film reveals that the photoanodic current is based on the photoexcitation of [Ru(bpy)(3)](2+). The photogeneration of Fe(II)-Fe(III) from Fe(II)-Fe(II) is shown by the absorption spectral change of the bilayer film on irradiation. These results corroborate the notion that Fe(II)-Fe(II) is oxidized by photogenerated Ru(III) to generate Fe(II)-Fe(III). However, the rate of photogeneration of Fe(II)-Fe(III) is slow, which could be ascribed to the fast back electron transfer (ET) from WO(3) to Ru(III), comparable with the forward ET from Fe(II)-Fe(II) to Ru(III). The fast back ET could be a crucial problem for the [Ru(bpy)(3)](2+)-sensitized reaction in the hybrid film.     

An application of the novel quantum mechanical/molecular mechanical method combined with the theory of energy representation: An ionic dissociation of a water molecule in the supercritical water

A novel quantum chemical approach recently developed has been applied to an ionic dissociation of a water molecule (2H(2)O-->H(3)O(+)+OH(-)) in ambient and supercritical water. The method is based on the quantum mechanical/molecular mechanical (QM/MM) simulations combined with the theory of energy representation (QM/MM-ER), where the energy distribution function of MM solvent molecules around a QM solute serves as a fundamental variable to determine the hydration free energy of the solute according to the rigorous framework of the theory of energy representation. The density dependence of the dissociation free energy in the supercritical water has been investigated for the density range from 0.1 to 0.6 g/cm(3) with the temperature fixed at a constant. It has been found that the product ionic species significantly stabilizes in the high density region as compared with the low density. Consequently, the dissociation free energy decreases monotonically as the density increases. The decomposition of the hydration free energy has revealed that the entropic term (-TDeltaS) strongly depends on the density of the solution and dominates the behavior of the dissociation free energy with respect to the variation of the density. The increase in the entropic term in the low density region can be attributed to the decrease in the translational degrees of freedom brought about by the aggregation of solvent water molecules around the ionic solute.     

Metastable anions of dinitrobenzene: resonances for electron attachment and kinetic energy release

Attachment of free, low-energy electrons to dinitrobenzene (DNB) in the gas phase leads to DNB(-) as well as several fragment anions. DNB(-), (DNB-H)(-), (DNB-NO)(-), (DNB-2NO)(-), and (DNB-NO(2))(-) are found to undergo metastable (unimolecular) dissociation. A rich pattern of resonances in the yield of these metastable reactions versus electron energy is observed; some resonances are highly isomer-specific. Most metastable reactions are accompanied by large average kinetic energy releases (KER) that range from 0.5 to 1.32 eV, typical of complex rearrangement reactions, but (1,3-DNB-H)(-) features a resonance with a KER of only 0.06 eV for loss of NO. (1,3-DNB-NO)(-) offers a rare example of a sequential metastable reaction, namely, loss of NO followed by loss of CO to yield C(5)H(4)O(-) with a large KER of 1.32 eV. The G4(MP2) method is applied to compute adiabatic electron affinities and reaction energies for several of the observed metastable channels.     

Redox properties of undoped 5 nm diamond nanoparticles

This paper demonstrates the promoting effects of 5 nm undoped detonation diamond nanoparticles on redox reactions in solution. An enhancement in faradaic current for the redox couples Ru(NH(3))(6)(3+/2+) and Fe(CN)(6)(4-/3-) was observed for a gold electrode modified with a drop-coated layer of nanodiamond (ND), in comparison to the bare gold electrode. The ND layer was also found to promote oxygen reduction. Surface modification of the ND powders by heating in air or in a hydrogen flow resulted in oxygenated and hydrogenated forms of the ND, respectively. Oxygenated ND was found to exhibit the greatest electrochemical activity and hydrogenated ND the least. Differential pulse voltammetry of electrode-immobilised ND layers in the absence of solution redox species revealed oxidation and reduction peaks that could be attributed to direct electron transfer (ET) reactions of the ND particles themselves. It is hypothesised that ND consists of an insulating sp(3) diamond core with a surface that has significant delocalised pi character due to unsatisfied surface atoms and C[double bond, length as m-dash]O bond formation. At the nanoscale surface properties of the particles dominate over those of the bulk, allowing ET to occur between these essentially insulating particles and a redox species in solution or an underlying electrode. We speculate that reversible reduction of the ND may occur via electron injection into available surface states at well-defined reduction potentials and allow the ND particles to act as a source and sink of electrons for the promotion of solution redox reactions.     

Theoretical modeling of the heme group with a hybrid QM/MM method

The quality of the results obtained in calculations with the hybrid QM/MM method IMOMM on systems where the heme group is partitioned in QM and MM regions is evaluated through the performance of calculations on the 4‐coordinate [Fe(P)] (P = porphyrin), the 5‐coordinate [Fe(P)(1−(Me)Im)] (Im = imidazole) and the 6‐coordinate [Fe(P)(1−(Me)Im)(O₂)] systems. The results are compared with those obtained from much more expensive pure quantum mechanics calculations on model systems. Three different properties are analyzed—namely, the optimized geometries, the binding energies of the axial ligands to the heme group, and the energy cost of the biochemically relevant out‐of‐plane displacement of the iron atom. Agreement is especially good in the case of optimized geometries and energy cost of out‐of‐plane displacements, with larger discrepancies in the case of binding energies. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 282–294, 2000