Electron Donor States Research Articles

(Invited) Atomic-Scale Modeling of Charge-Transfer Kinetics at LixCoO2 Cathode-Electrolyte Interfaces

In the search for Li-ion batteries with improved performance, interface engineering is a comparably underexplored area with significant opportunities for innovation. Ion transport across interfaces is, for instance, a significant bottleneck for fast charging/discharging. At electrode interfaces, it is often essential to capture the coupled motion of ions and electrons in order to provide accurate computational input for interfacial design. In this work we employ the recently proposed theory of coupled ion-electron transfer kinetics[1,2] in conjugation with constrained and constant-potential density functional theory to examine Li+ transfer across battery electrolyte-cathode interfaces at the atomic scale. Here, we focus on the common Li x CoO2 intercalation-type cathode material and liquid-state organic electrolytes. We establish trends in transport kinetics for different states-of-charge (SOC, i.e., varied degree of lithiation, x), types of electrolytes, and counterions that closely reproduces experimentally observed trends. From our modeling, we can identify a few key descriptors to predict performance metrics in Li-ion transport of a given electrolyte-cathode combination. These include the Li-ion free energy of adsorption, the free energies of reorganization of the cathode material and electrolyte upon the addition/removal of electrons, as well as the electronic coupling between electron acceptor and donor states. As these quantities can be relatively straightforwardly estimated for any given electrode-electrolyte pair, we envisage broad applications of our modeling approach in the interfacial design for batteries and related fields.[1] Fraggedakis et al., Electrochimica Acta, 367, 137432 (2021)[2] Bazant, Faraday Discussion, 246, 60 (2023)

Reduction-Assisted Calcination Enhances the Photocatalytic Activity of ZnO and WO3 Nanoparticles in Biomass Conversion.

Rising energy needs and environmental issues have prompted the creation of effective and affordable photocatalysts for converting biomass. Utilizing abundant biomass, oxidation of 5-hydroxymethylfurfural (HMF) emerges as a method for generating high-value chemicals from biomass, offering an alternative to fossil fuels. We synthesized defect-engineered metal oxides (ZnO and WO3) by calcination with NaBH4 as a reducing agent. Atomic-level analyses identified oxygen vacancy defects induced by the reduction of metal ions within the metal oxide nanoparticles. Further analysis showed an unchanged band gap but an up to 4-fold increase in current density. This enhancement is attributed to the trapping of electrons in defect sites created during the calcination process. The formation of new electron donor states hindered photogenerated electron-hole recombination, enhancing the photocatalytic efficiency of the metal oxide. The photocatalytic degradation yield of HMF was over 95%, and the selective organic products 2,5-diformylfuran (DFF) and 2,5-furandicarboxylic acid (FDCA) were obtained without byproducts. Kinetic studies demonstrated that the photocatalytic conversion reaction rates were accelerated by up to 3.5-fold. Improved photocatalytic activity for HMF oxidation was achieved by introducing oxygen vacancy defects upon the reduction of metal ions within the metal oxides. Our results provide a promising approach for designing efficient photocatalysts.

Oxygen Driven Defect Engineering of Monolayer MoS2 for Tunable Electronic, Optoelectronic, and Electrochemical Devices

AbstractMolybdenum disulfide (MoS2), a two‐dimensional (2D) semiconducting material harbors intrinsic defects that can be harnessed to achieve tuneable electronic, optoelectronic, and electrochemical devices. However, achieving precise control over defect formation within monolayer MoS2, remains a notable challenge. Here, an in‐situ defect engineering approach for monolayer MoS2 using a pressure‐dependent chemical vapor deposition (CVD) process is presented. Monolayer MoS2 grown in a low pressure CVD conditions (LP‐MoS2) produces sulfur vacancy (Vs) induced defect‐rich crystals primarily attributed to the oxygen‐deficient growth conditions. Conversely, atmospheric pressure CVD‐grown MoS2 (AP‐MoS2) passivates these defects with oxygen from ambient conditions. This disparity in defect profiles profoundly impacts crucial functional properties and device performance. AP‐MoS2 shows a drastically enhanced photoluminescence, which is significantly quenched in LP‐MoS2 attributed to in‐gap electron donor states induced by the Vs defects. However, the n‐doping induced in LP‐MoS2 generates enhanced photoresponsivity and detectivity in fabricated photodetectors compared to the AP‐MoS2‐based devices. Defect‐rich LP‐MoS2 outperforms AP‐MoS2 as channel layers of field‐effect transistors (FETs), as well as electrocatalytic material for hydrogen evolution reaction (HER). This work presents a single‐step CVD approach for in situ defect engineering in monolayer MoS2 and presents a pathway to control defects in other monolayer 2D materials.

Enhanced electron–phonon coupling by delocalizing phonon states for desirable interlayer transfer of excited charges in MoSSe/WS2 heterobilayer

Regulating the interlayer transfer of excited charges is challenging but crucial for high-efficiency photoelectric conversion devices based on semiconductor heterojunction. In this work, the interlayer transfer and recombination of excited charges are investigated for the heterobilayers based on monolayer MoSSe and WS2 by combining density functional theory calculation with nonadiabatic molecular dynamics simulation. Our results reveal that the heterobilayers possess type-II band alignments and the interface engineering from S–Se to S–S stacking configuration reverses the spatial distribution of valence and conduction bands from MoSSe and WS2 to WS2 and MoSSe layers, respectively, which produces interlayer transfer of excited charges in opposite direction. The interface engineering also causes the delocalization of out-of-plane phonon states from the WS2 layer to both WS2 and MoSSe layers. This delocalized character in S–S configuration facilitates the simultaneous coupling of out-of-plane phonon states with the localized donor and acceptor electronic states, accelerates the motion of interface atoms, and reduces the band energy differences, which synergistically promote interlayer transfer of excited charges. As a result, the interlayer transfer of excited charges in S–S configuration is faster than that in S–Se configuration. Our investigation demonstrates that delocalizing phonon states through interface engineering can regulate electron–phonon coupling and interlayer transfer of excited charges.

Electronic structure and terahertz intersubband absorption spectra of phosphorus donor in silicon using a variationally optimized diagonalization method

The electronic structure and terahertz (THz) intersubband absorption spectra of phosphorus (P) donor in silicon (Si) are theoretically investigated using a variationally optimized diagonalization method based on the three-dimensional (3D) nonorthogonal associated Laguerre basis set, the basis set of eigenfunctions of 3D hydrogen atom and the basis set of eigenfunctions of 3D isotropic harmonic oscillator. A fully analytical expression of the matrix elements of the Hamiltonian is derived. Due to the large band anisotropy of Si, the donor electron series appear in an anomalous energy-level order and interval of the orbital angular momentum. The donor electron energy levels with even a small number of basis functions are in excellent agreement with those reported in the previous literature. Compared to two different basis sets of eigenfunctions of 3D hydrogen atom and isotropic harmonic oscillator, my proposed variationally optimized diagonalization method based on the 3D nonorthogonal associated Laguerre basis set is proven to be more efficient and reliable in calculating highly accurate impurity states of anisotropic 3D materials. The intersubband absorption spectra of P donor electron involving transitions from the 1s to excited states are strongly dependent on the orientations of the valley and the polarization vector of the incident light, which results from the fact that the large band anisotropy of Si induces strong mixing of the donor electron states. Their absorption frequencies are found to fall into the THz part of the electromagnetic spectrum. These results show that P donor in Si provides a material platform that enables intersubband devices operating in the THz frequency domain. • A fully analytical expression of the matrix elements of the donor Hamiltonian is derived. • The donor electron energy levels are in excellent agreement with those reported in the previous literature. • The intersubband absorption spectra of P donor electron are strongly dependent on the orientations of the incident light polarization. • P donor in Si provides a material platform that enables optoelectronic devices operating in the THz frequency domain. • The 3D nonorthogonal Laguerre basis is more efficient and reliable in calculating impurity states of anisotropic 3D materials.

(Keynote) Photoinduced Charge Transfer from Quantum Dots Measured By Cyclic Voltammetry

Measuring and modulating charge transfer processes at quantum dot interfaces are crucial steps in the development of quantum dot photocatalysis. In this work, cyclic voltammetry under illumination is demonstrated to measure the rate of photoinduced charge transfer from CdS quantum dots by directly probing the changing oxidation states of a library of model charge acceptors. The voltammetry data demonstrates the presence of long-lived electron donor states generated by native photodoping of the QDs as well as the relationship between driving force and rate of charge transfer. Changes to the voltammograms under illumination follow mechanistic predictions from classic zone diagrams and electrochemical modeling allows for measurement of the rate of productive electron transfer, giving rate constants (104 M-1s-1) that are distinct from the ps dynamics measured by conventional optical spectroscopy methods and that are more closely connected to the quantum yield of photoinduced chemical transformations.

Thermal-Driven Dynamic Shape Change of Bimetallic Nanoparticles Extends Hot Electron Lifetime of Pt/MoS2 Catalysts.

Using a combination of time-domain density functional theory and nonadiabatic (NA) molecular dynamics, we demonstrate that the replacement of noble Pt with cheap Sn in the Pt nanoparticles sensitized MoS2 greatly retards the photoexcited "hot" electron relaxation. The simulations show that Sn substitution causes significant geometry distortion associated with the Sn dopant detaching from the Pt nanoparticle base, which decreases the NA coupling and creates an isolated trap state distant from the electron donor state. Generally, smaller NA coupling delays "hot" electron relaxation. At the same time, the photoexcited electron on MoS2 first populates the nanoparticles state and then slowly goes to the trap state, following relaxation to the nanoparticle acceptor state over 1 ps. As a result, the "hot" electron lives over 3.5 times longer than that in pristine Pt/MoS2 system. The long-lived "hot" electron associated with the reduced cost establishes a novel concept for developing high-efficient and cost-effective photocatalysts and photovoltaics.

Three-state harmonic models for photoinduced charge transfer.

A widely used strategy for simulating the charge transfer between donor and acceptor electronic states in an all-atom anharmonic condensed-phase system is based on invoking linear response theory to describe the system in terms of an effective spin-boson model Hamiltonian. Extending this strategy to photoinduced charge transfer processes requires also taking into consideration the ground electronic state in addition to the excited donor and acceptor electronic states. In this paper, we revisit the problem of describing such nonequilibrium processes in terms of an effective three-state harmonic model. We do so within the framework of nonequilibrium Fermi's golden rule (NE-FGR) in the context of photoinduced charge transfer in the carotenoid-porphyrin-C60 (CPC60) molecular triad dissolved in explicit tetrahydrofuran (THF). To this end, we consider different ways for obtaining a three-state harmonic model from the equilibrium autocorrelation functions of the donor-acceptor, donor-ground, and acceptor-ground energy gaps, as obtained from all-atom molecular dynamics simulations of the CPC60/THF system. The quantum-mechanically exact time-dependent NE-FGR rate coefficients for two different charge transfer processes in two different triad conformations are then calculated using the effective three-state model Hamiltonians as well as a hierarchy of more approximate expressions that lead to the instantaneous Marcus theory limit. Our results show that the photoinduced charge transfer in CPC60/THF can be described accurately by the effective harmonic three-state models and that nuclear quantum effects are small in this system.

High content anion (S/Se/P) doping assisted by defect engineering with fast charge transfer kinetics for high-performance sodium ion capacitors

The rate-determining process for sodium storage in TiO2 is greatly depending on charge transfer happening in the electrode materials owing to its inferior diffusion coefficient and electronic conductivity. Apart from reducing the diffusion distance of ion/electron, the increasement of ionic/electronic mobility in the crystal lattice is also very important for charge transport. Here, an oxygen vacancy (OV) engineering assisted in high-content anion (S/Se/P) doping strategy to enhance charge transfer kinetics for ultrafast sodium-storage performance is proposed. Theoretical calculations indicate that OV-engineering evokes spontaneous S doping into the TiO2 phase and achieves high dopant concentration to bring about impurity state electron donor and electronic delocalization over S occupied sites, which can largely reduce the migration barrier of Na+. To realize the speculation, high-content anion doped anatase TiO2/C composites (9.82 at% for S in A-TiO2–x-S/C) are elaborately designed. The optimized A-TiO2–x-S/C anode exhibits extraordinarily high-rate capability with 209.6 mAh g−1 at 5000 mA g−1. The assembled sodium ion capacitors deliver an ultrahigh energy density of 150.1 Wh kg−1 at a power density of 150 W kg−1 when applied as anode materials. This work provides a new strategy to realize high content anion doping concentration, and enhances the charge transfer kinetics for TiO2, which delivers an efficient approach for the design of electrode materials with fast kinetic.

Correlation of native point defects and photocatalytic activity of annealed ZnO nanoparticle studied by electron spin resonance and photoluminescence emission

In this paper, we investigate the origin of point defects revealed by electron spin resonance (ESR) and photoluminescence (PL) emission in correlation with the photocatalytic activity of ZnO nanocrystals subjected to thermal annealing at various temperatures. Two ESR signals at g ∼ 1.96 and ∼2.003 were consistently observed in all annealed ZnO samples. However, their relative intensities have changed, indicating that the point defect densities were influenced by the annealing temperature. Interestingly, when doping nanoZnO with Cr3+, the Q-band ESR measurements at T = 100 K did show that the g ∼ 1.96 signal was completely passivated, suggesting that the origin of the signal lies in the electrons located near the conduction band, i.e. at a shallow-donor level. The intensity of the g ∼ 2.003 signal decreased by rising the annealing temperature, and this is attributed to the depopulation of zinc interstitials through the thermally induced migration process and/or recombination with the zinc vacancies. The green PL emission line at ∼520 nm, which is dominant in the 700 °C annealed ZnO sample, shows a correlation with the ESR signal at g ∼ 1.96, whose origin is attributed to the radiative transition of the electron from the shallow donor level to the singly ionized zinc vacancy. Furthermore, the high density of the shallow donor electron states was found to be primarily responsible for the high photocatalytic activity in the degradation of methylene blue.

In Situ Observation of Two-Dimensional Electron Gas Creation at the Interface of an Atomic Layer-Deposited Al2O3/TiO2 Thin-Film Heterostructure

A two-dimensional electron gas (2DEG) was formed at the interface of an ultrathin Al2O3/TiO2 heterostructure that was fabricated using atomic layer deposition (ALD) at a low temperature (<300 °C) on a thermally oxidized SiO2/Si substrate. A high electron density (∼1014 cm–2) and mobility (∼4 cm2 V–1 s–1) were achieved, which are comparable to those of the epitaxial LaAlO3/SrTiO3 heterostructure. An in situ resistance measurement directly demonstrated that the resistance of the heterostructure interface dropped significantly with the injection of trimethylaluminum (TMA), indicating that oxygen vacancies were formed on the TiO2 surface during the TMA pulse in the ALD of Al2O3 films, such that they provide electron donor states to generate free electrons at the interface of the ultrathin Al2O3/TiO2 heterostructure. The activation energy of the electron donor states to move to the Ti 3d conduction band plays an essential role in the electrical characteristics of the 2DEG. Interestingly, the donor state level can be tailored by the control of TiO2 crystallinity, which eventually adjusts the electron density. The activation energy was decreased to less than 20 meV to generate ultrashallow donor states while improving the TiO2 crystallinity, such that the 2D electrons become readily delocalized, even at room temperature, to create a 2DEG.

Linear and nonlinear optical properties of a single dopant in GaN conical quantum dot with spherical cap

ABSTRACT The states of a single dopant centre in zinc-blende GaN-based conical quantum dots with spherical cap are theoretically investigated by analytically solving the corresponding effective mass equation taking advantage of the localisation of the ionised impurity at the cone apex. Nonlinear optical response is analysed through the calculation of the coefficients of optical absorption, relative refractive index change, and second and third harmonic generation, for the chosen set of allowed electron-donor states. The behaviour of the calculated optical quantities under changes in the geometry of the system due to variations in apical width and quantum dot radius is analysed and discussed.

Nano-Grain Ni/ZrO2 Functional Gradient Coating Fabricated by Double Pulses Electrodeposition with Enhanced High Temperature Corrosion Performance

Functional gradient materials (FGM) have many excellent properties, and high-performance gradient coating exhibits good prospective application. In this paper, the nano-grain Ni/ZrO2 gradient coating was prepared by double pulse electrodeposition (BP). The surface morphology, crystal structure and electrochemical corrosion resistance of the nano-grain Ni/ZrO2 coating and Ni coating, annealed at different temperatures (400–800 °C), have been compared. In the vertical direction to the substrate surface, the content of ZrO2 increases from 0% to 34.99%. X-ray diffraction (XRD) revealed that the average crystal size of Ni/ZrO2 gradient coating gradually increases from 13.75 to 27.75 nm, and the crystal structure is a face-centered cubic (FCC). The main crystal orientation faces are (111) and (200), while the (200) face exhibited a stronger preferred orientation. Compared with the Ni coating by scanning electron microscopy, the surface morphology of double pulse fabricated Ni/ZrO2 gradient coating was revealed as being smoother, denser, and having fewer pores, and the crystal particle size distribution became narrow. X-ray photoelectron spectroscopy (XPS) shows that the chemical binding states of elements Ni and Zr have been altered. The binding energies of 2p3/2 and 2p1/2 for Ni have been increased, resulting in a higher electron donor state of Ni. The binding energy of 3d5/2 and 3d3/2 of Zr4+ in ZrO2 is decreased, thus becoming better electron acceptors. Chemical bonding has been formed at the Ni/ZrO2 interface. This study demonstrated that double pulse electrodeposition is a promising fabrication method for functional gradient coatings for high temperature applications.

New Transparent Magnetic Semiconductor NixCu1-xI which Can Perform as Either P-type or N-type and Success in the P-N Homojunction Diode.

A semiconductor that can be doped to be either p-type or n-type is of great importance, as p-n homojunctions are desirable for realizing various electronic devices and processes. However, because of pervasive doping asymmetry for wide band gap semiconductors, the achievement of both p-type and n-type in a single wide gap material is very difficult. Here, we report the success in developing a new transparent magnetic NixCu1-xI halide semiconductor that can be either p-type or n-type depending on Ni fraction in NixCu1-xI. For 0 ≤ x ≤ 0.10, NixCu1-xI films show p-type conductivity. For the range 0.15 ≤ x ≤ 0.35, NixCu1-xI films show an n-type character. The NixCu1-xI films are electrically conducting and optically transparent and show soft ferromagnetic behavior with an optimum conductivity of 42 S cm-1 (x = 0.03) and visible light transmission of 80%. Ultraviolet photoelectron spectroscopy studies on NixCu1-xI films reveal the systematic Fermi level shift toward the conduction band with respect to the valence band as a function Ni concentration. X-ray photoelectron spectroscopy analysis on Ni and I peak positions reveals Ni+2 valence for Ni in NixCu1-xI films, with signatures of Ni-I bonding. The observed p-type behavior originates from Cu vacancy, while the n-type character is identified to originate from the electron donor states generated by Ni incorporation in NixCu1-xI. The constructed homojunction with p-Ni0.0Cu1.0I/n-Ni0.16Cu0.84I shows a characteristic p-n junction behavior with a good rectification ratio of 2 × 102. This new type of NixCu1-xI transparent semiconductor with a tunable carrier type and magnetism may be a candidate for halide-based optoelectronic as well as spintronics development.

Vibrational energy redistribution during donor-acceptor electronic energy transfer: criteria to identify subsets of active normal modes.

Photoinduced electronic energy transfer in conjugated donor-acceptor systems is naturally accompanied by intramolecular vibrational energy redistributions accepting an excess of electronic energy. Herein, we simulate these processes in a covalently linked donor-acceptor molecular dyad system by using nonadiabatic excited state molecular dynamics simulations. We analyze different complementary criteria to systematically identify the subset of vibrational normal modes that actively participate on the donor → acceptor (S2→ S1) electronic relaxation. We analyze energy transfer coordinates in terms of state-specific normal modes defined according to the different potential energy surfaces (PESs) involved. On one hand, we identify those vibrations that contribute the most to the direction of the main driving force on the nuclei during electronic transitions, represented by the non-adiabatic derivative coupling vector between donor and acceptor electronic states. On the other hand, we monitor normal mode transient accumulations of excess energy and their intramolecular energy redistribution fluxes. We observe that the subset of active modes varies according to the PES on which they belong and these modes experience the most significant rearrangements and mixing. Whereas the nuclear motions that promote donor → acceptor energy funneling can be localized mainly on one or two normal modes of the S2 state, they become spread out across multiple normal modes of the S1 state following the energy transfer event.

An electrochemical investigation of interfacial electron uptake by the sulfur oxidizing bacterium Thioclava electrotropha ElOx9

Extracellular electron transfer (EET) allows microbes to acquire energy from solid state electron acceptors and donors, such as environmental minerals. This process can also be harnessed at electrode interfaces in bioelectrochemical technologies including microbial fuel cells, microbial electrosynthesis, bioremediation, and wastewater treatment. Improving the performance of these technologies will benefit from a better fundamental understanding of EET in diverse microbial systems. While the mechanisms of outward (i.e. microbe-to-anode) EET is relatively well characterized, specifically in a few metal-reducing bacteria, the reverse process of inward EET from redox-active minerals or cathodes to bacteria remains poorly understood. This knowledge gap stems, at least partly, from the lack of well-established model organisms and general difficulties associated with laboratory studies in existing model systems. Recently, a sulfur oxidizing marine microbe, Thioclava electrotropha ElOx9, was demonstrated to perform electron uptake from cathodes. However, a detailed analysis of the electron uptake pathways has yet to be established, and electrochemical characterization has been limited to aerobic conditions. Here, we report a detailed amperometric and voltammetric characterization of ElOx9 cells coupling cathodic electron uptake to reduction of nitrate as the sole electron acceptor, even in the absence of any added inorganic carbon source. By comparing this cellular activity to spent media controls and using medium exchange experiments, we demonstrate that one of the pathways by which ElOx9 facilitates inward EET is by a direct-contact mechanism through a redox center with a formal potential of −94 mV vs SHE, rather than soluble intermediate electron carriers. In addition to the implications for understanding microbial sulfur oxidation in marine environments, this study highlights the potential for ElOx9 to serve as a convenient and readily culturable model organism for understanding the molecular mechanisms of inward EET.

Efficient charge transport in surface engineered TiO2 nanoparticulate photoanodes leading to improved performance in quantum dot sensitized solar cells

Cold argon plasma treated TiO2 nanoparticulate photoanodes have been utilized for fabrication of quantum dot sensitized solar cells (QDSSCs). After plasma treatment the TiO2 nanoparticles got assembled in a closely spaced manner with increase in surface roughness factor owing to surface etching by the highly energetic ions, electron and radicals present in the plasma output. The photoanodes possess high inter-particle contact delivering fast charge carrier transport network minimizing the loss of charge carriers. The increase in conductivity was probed through conducting-AFM measurements. This morphological variation significantly inhibits the interfacial recombination by 3.5 times at the TiO2/NC/electrolyte interface as confirmed through electrochemical impedance spectroscopy. Moreover, the increase in Ti3+ as suggested by X-ray photoelectron spectroscopy also contributes in the enhancement of conductivity providing additional electron donor states. The power conversion efficiency increased from 3.65% to 5.01% for CdSe0.4S0.6 alloy nanocrystals (NCs) sensitized solar cells utilizing these plasma treated TiO2 photoanodes. Thus our strategy paves promising direction for the efficiency enhancements in QDSSC devices.

Stabilities and electronic properties of vacancy-doped Ti2CO2

The stabilities and electronic properties of vacancy-doped Ti2CO2 have been investigated by a first-principles method. The formation energies of carbon (C) vacancies are relatively small. And they change from negative to positive as the defect concentration of C vacancies increases. Atomic-vacancy-induced defect states appear in the band structure of defective Ti2CO2. The Fermi energy of C vacancy (VC)-doped Ti2CO2 shifts upward compared with that of perfect Ti2CO2, making VC-doped Ti2CO2 exhibit metallic character. A localized defect state of oxygen vacancy (VO)-doped Ti2CO2 occurs in the midgap of pristine Ti2CO2. And as the defect concentration decreases, the VO-induced band becomes more localized with nearly flat band dispersion. The defective state of VO-doped Ti2CO2 acts as an electron donor state when Ti2CO2 is used as a semiconducting material. Further, the stabilities and electronic properties of different C and O divacancy configurations are explored. Investigation of the C divacancy (V2C) in a 4 × 4 × 1 Ti2CO2 supercell indicates that the C vacancy configuration distribution has little influence on the electronic conductivity of V2C-doped Ti2CO2. Hence it is possible to modulate the electrical conductivity of Ti2CO2 by adjusting the C vacancy concentration. Investigation of the O divacancy (V2O) suggests that the O vacancy configuration distribution changes the electronic band structure at the Fermi level of V2O-doped Ti2CO2.

Exact Solution of the Problem of Bound Electronic States in Graphene

In graphene with a gap in the electronic spectrum, the problem of bound states of an electron in the field of an impurity ion with the charge Z is considered. Parameter Z is the effective ion charge; it includes the permittivity of graphene. Analytical solution of the Schrodinger equation in the problem under consideration leads to a formula which contains two numbers determining the quantum state of the electron: the total pseudospin moment and the radial quantum number. The sign of the effective screening ion charge Z determines the positions of levels near the conduction or valence band of graphene. Accordingly, the energy levels can be interpreted as donor or acceptor electronic states in the gap.

Vibrational control of molecular electron transfer reactions

ABSTRACTVibrational motions promote molecular electron transfer (ET) reactions by bringing electron donor and electron acceptor electronic states to fleeting resonance, and by modulating the donor-to-acceptor electronic coupling. The main experimental signature of molecular motion effects on the ET rate is the temperature dependence of the rate, which gives information about the overall free energy activation barrier for the ET reaction. Another approach to probing the vibrational control of ET reactions is to excite specific electron-transfer-active vibrational motions by external infrared (IR) fields. This type of experimental probe is potentially more specific than thermal excitation and recent experiments have shown that molecular ET rates can be perturbed by mode-specific IR driving. We review the theory and experiments of vibrational control of ET rates, and discuss future challenges that need to be tackled in order to achieve the mode-specific tuning of rates.