Spin Unrestricted Nonradiative Relaxation Dynamics of Cobalt-Doped

Article pubs.acs.org/JPCC

Spin Unrestricted Nonradiative Relaxation Dynamics of CobaltDoped Anatase Nanowire Stephanie J. Jensen,†,⊥ Talgat M. Inerbaev,‡,§ Aisulu U. Abuova,‡ and Dmitri S. Kilin*,∥,⊥ †

Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109, United States Faculty of Physics and Technical Sciences, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan § National University of Science and Technology “MISIS”, Moscow, 119049 Russian Federation ∥ Department of Chemistry and Biochemistry, North Dakota State University, Fargo, North Dakota 58108, United States ⊥ Department of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States ‡

S Supporting Information *

ABSTRACT: Spin-resolved charge transfer dynamics at the interface of a Co(NH3)2-doped (001) anatase TiO2 nanowire and liquid water calculations based on density functional theory and density matrix formalism are considered. Three models with the same stoichiometry but different electronic structure are explored. While one model had no change to electron count and spin count (neutral model), the other two models were assigned a charge of 2+, one in a doublet and the other a quartet spin configuration. Co2+ is the most probable state for dopant in all models and Co acts as an electron acceptor. The optical absorption spectra show a rather unique pattern post 400 nm where the α and β absorptions happen independently at different frequency ranges. Essentially, the relaxation dynamics can be controlled as when an α electron is excited, there is a near zero probability of a β electron also undergoing an excitation and vice versa. The isolated exemption is between 400 and 650 nm in the neutral model. All the models absorb light in the visible range, while the electrons and holes have drastic differences in relaxation rates. The spatial charge separation occurs upon excitation and subsequent trapping, designating the considered system a prospect for electrochemical cell applications. (2+) models trap states more effectively slow down electron relaxation, making the charged models slightly better options for application compared to the neutral model.

1. INTRODUCTION Titanium dioxide (TiO2) has received considerable attention due to its numerous applications in many important fields, such as catalysis, sensors, corrosion, coatings, and solar cells.1−8 Among these applications, energy harvesting directly from sunlight is a desirable approach toward fulfilling the need for clean energy with minimal environmental impact. TiO2 has three major structure forms: anatase, rutile, and brookite. We investigate the titania polymorph of anatase since it has generally shown higher photocatalytic activity than rutile and has a bandgap of about 3.2 eV.9 While the rutile phase is the most stable for bulk, anatase appears to be more stable for TiO2 nanoparticles.10−12 Nanosized structures offer unique characteristics that are greatly influenced by their diameters,13 crystallographic orientations,14 surface passivation,15 presence of metal, nonmetal ion implants,16,17 and reduced titania.18 The photocatalytic activity of pure titania photocatalysts is in most cases found to be rather small and, moreover, limited to illumination by ultraviolet light.16,19 Despite this, a number of studies have focused on catalytic reaction with TiO2 as a support material. Modifying TiO2 by introducing various transition metals into its lattice is deemed to be a good method because it was found effective for energy band reconstruction and band gap narrowing.20 Currently, most of © 2017 American Chemical Society

the developed photocatalyst systems utilize efficient but expensive noble-metal-based cocatalysts such as Pt, Au, Pd, Rh, Ru, and Ag to achieve high photocatalytic activity.21−35 Unfortunately, the above noble-metal cocatalysts are too scarce and expensive to be used for large-scale energy production. Therefore, the development of noble-metal free cocatalysts with high efficiency and low cost is highly desirable. In recent years, many kinds of novel cocatalysts constructed from cheap and earth-abundant elements have been developed for assisting photocatalytic water splitting.36−46 For example, Cu-TiO2 catalyzes H2 and CH4 photogeneration from mixtures of methanol/ethanol and water,39,40 and Co-TiO2 and Fe-Co codoped TiO2 catalyzes the Fischer−Tropsch reaction,41−43 ethane oxidative dehydrogenation,44 and ethanol steam reforming.45 Fe and N codoped TiO2 nanoparticles assist dibenzothiophene photo-oxidation.46 Sun et al. have recently shown that cobalt-doped TiO2 contains trapping states, or states involved in relaxation, where the electron/hole is trapped for a noticeable amount of time.47 These states are expected to Received: May 9, 2017 Revised: June 23, 2017 Published: June 26, 2017 16110

DOI: 10.1021/acs.jpcc.7b04263 J. Phys. Chem. C 2017, 121, 16110−16125

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The Journal of Physical Chemistry C

computational methods to explore charge transfer states introduced to wet anatase surfaces upon transition metal doping.86−89 Energy and charge transfer processes may occur in the ultrafast and coherent regime at times shorter than dephasing time. Such regimes are expected, for example, in systems with sparse energy states. In contrast, systems with dense energy states, such as semiconductor surfaces, can manifest coherent behavior only at ultrashort time scales due to faster dephasing. However, in present studies of charge transfer for photocatalysis, one primarily focuses on mechanisms of population relaxation. Spin-unrestricted electronic structure90 was found useful in describing materials with spin polarization, including TiO2 doped by transition metals,91 as well as vanadium,92 and TiO2 with oxygen vacancy converting Ti4+ to Ti3+ resulting in a local magnetic moment at Ti3+ ions.93 An approximate treatment can be pursued in the basis of spin-collinear density functional theory.94,95 Most transition-metal compounds exhibit open shell nonsinglet configurations, necessitating special treatment of electrons with α/β spin projections. By separate treatment of electronic states with the α/β spin components one is able to describe a broader range of materials, identify new channels of relaxation and charge transfer, and provide knowledge for rational design of new materials in solar energy harvesting and information storage. For this methodology, named spin-resolved electron dynamics approach (SREDA), spin-polarized DFT is used as the basis to implement nonadiabatic charge relaxation dynamics.96 In this work, we theoretically investigate the spin-resolved nonadiabatic excited state dynamics of Co-doped anatase TiO2 NW by the reduced density operator formalism to elucidate electron-transfer pathways together with energy losses due to lattice induced charge carrier relaxation. Electron−phonon coupling controls nonradiative relaxation dynamics of the photoexcited electron−hole pair in semiconductor nanostructures. We attempt to provide an insight on relaxation rate dependence on excitation energy for models with different charge and spin states. We hypothesize that cobalt should serve as e− donor (n-doping) and try to proof this hypothesis right or wrong for different modes of surface binding.

affect several photoinduced processes and determine suitability of cobalt-doped titania for solar energy applications. The charge transfer between semiconductor and metal cluster is important for efficient separation of electron−hole pairs.48−50 The separated electron or hole reduces or oxidizes the adsorbates such as water molecules to produce hydrogen and oxygen. The relaxation pathways and rates of electron and hole relaxation have significant effects on photocatalytic processes. High charge generation rate and low charge relaxation or recombination rate are beneficial to improve photoelectrochemical yields. Transition metal−TiO2 composites can overcome the lack of visible light response of TiO2 and promote TiO2 photocatalytic activity. Besides using suitable cocatalysts, nanostructured morphology is critical for solving charge transfer difficulties in semiconductors.5,51 When nanostructures of TiO2 are used as photocatalyst, the charge carriers have to migrate relatively short distances on a nm-scale to reach the surface and react with the environment, reducing the probability of charge carrier recombination and trapping.8 The nanowires have many positive aspects, including increased surface area, allowing more interaction with the solvent, better separation of charge carriers and transport of charge carriers along the length, and electronic property tuning by spatial confinement.52−56 Anatase nanowires have been implemented in dye-sensitized solar cells.57 Progress has been made on vertically aligned nanowires to allow for similarity of the thin film concept and even the ability to sputter nanowires onto the other components of the photoelectrochemical cell.58−60 Understanding the charge transfer mechanism and carrier relaxation rates is of critical importance for a wide variety of applications. Experimentally, various types of time-resolved spectroscopy,61 such as time-resolved two-photon photoemission spectroscopy,62 and time-resolved fluorescence spectroscopy,63 have been developed for studying the carrier excitation, relaxation, and charge transfer processes. Typical values of measured charge transfer rates between metal particle and semiconductor are less than 240 fs for Au/TiO2.48 Nonadiabatic dynamics at different levels of implementation have been very helpful in describing photoexcited processes in titania64 and, specifically, for dynamics in titania sensitized by broad variety of dyes.60,65−68 The computational modeling of the hot carrier relaxation rests on partitioning the total energy between the electronic part and nuclear part and allowing for energy flow between them, going beyond the Born− Oppenheimer approximation.50,69 Several successful computational strategies for electronic relaxation are based on the concept of surface hopping between potential energy surfaces.70,71 Numerical implementations of this strategy can be based on various methods ranging from density functional theory (DFT)72 to high-precision nonadiabatic excited state molecular dynamics approach.73,74 It has been proven efficient to use molecular dynamics trajectory for determining the electron-to-lattice coupling in semiconductors.66 A computational procedure integrating relaxation of electrons as an open system with time-dependent density functional theory (TDDFT) treatment of excited states was recently offered.75,76 Historically, in the limit of long time dynamics, low couplings, and multiple electronic states, one considers multilevel Redfield theory as a common approach for electronic relaxation.77−84 Redfield theory of electron relaxation can be combined with onthe-fly coupling of electrons-to-lattice through a molecular dynamics trajectory in the basis of DFT.85 We have used these

II. METHODOLOGY II.a. Theoretical Approaches. It is imperative to use spinunrestricted calculations in order to isolate α and β states for accurate electronic calculations and analysis of relaxation dynamics. The following recently implemented methodology is employed for this purpose.96 The approximation excludes spin flip transitions due to negligible spin−orbit coupling. As an approximation, Kohn−Sham orbitals are used to describe excited states when studying relaxation dynamics.86,88,97−99 In TDDFT approach or in Bethe-Salpeter equation (BSE),100 excited states are composed as superposition of multiple electron−hole pairs and typically have smaller excitation energy due to exciton binding.101 Our approach of independent orbitals approximation (IOA)100 is a first step toward correlated excitation. The electron−hole pairs are elementary contributions, building blocks for correlated excited states, coming out of TDDFT or BSE calculations. In present research the modeling is based on the one electron Kohn−Sham95 equation: 16111


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The Journal of Physical Chemistry C ⎛ −ℏ2 2 ⎞ ⎯ → → ⎯ ∇ + vσ [ r ⃗ , {RI}, ρα , β ( r ⃗)]⎟φiKS ( r ⃗ , {RI}) ⎜ ⎝ 2m ⎠ ,σ ⎯ → ⎯ → = εi , σ {RI}φiKS ( r ⃗ , {RI}) ,σ

longer time in comparison to the other states involved in the relaxation. The trap can be due to an increased energy subgap to overcome or the transfer of population between two states with low coupling.104 The mechanism of trapping is hypothetically related to concepts of energy gap law and phonon bottleneck: Electronic transitions are most efficient in case energies of orbitals are offset by a value Δεσ,i = εσ,i+1 − εσ,i matching a normal-mode frequency Δεσ,i ≈ ℏωvib. However, in a case such that energy offset exceeds any of available vibrational frequencies, Δεσ,i > ℏωvib the transition becomes less probable. II.b. Computational Details. The electronic structure, accounting for the Coulomb, correlation, and exchange electron−electron interactions and the interaction of electrons with ions is computed with density functional theory by selfconsistent solving of the Kohn−Sham equations,105 as implemented in the Vienna ab initio simulation package (VASP).106−109 In this work, the Perdew−Burke−Ernzerhof (PBE) exchange-correlation functional under the generalized gradient approximation (GGA)110 was used. The on-site Coulomb correlation of d-electrons was taken into account employing Hubbard corrections in the Dudarev parametrization with U−J value of 3.0 eV for cobalt and 4.2 eV for titanium.111 Calculations were done using PAW formalism, which was developed using the concept of pseudopotentials in the plane-wave basis supplied by VASP.112−114 SI, section 1.2, provides additional details for reproducing the VASP calculations. Bader’s analysis was used for atomic charge analysis115 and results are represented in elementary charge units. The model under study is an anatase nanowire, originally explored in absence of doping and solvent.116,117 The nanowire, with the unit cell shown in Figure 1, is functionalized by a substitutional cobalt dopant replacing a titanium on the surface. The dopant is coordinated with two NH3 ligands and along with four oxygen atoms of the nanowire forms octahedral coordination shown in Figure 2. The constructed model structure is immersed in liquid water represented by 120 water molecules. The unit cell is Co(NH3)2·Ti24O50·(H2O)120, with zero vacuum space along the z-axis to recreate a nanowire via periodic boundary conditions. Three models of cobalt doped anatase nanowires were chosen after initial results testing minimal energy oxidation state and spin configurations. The first is neutral with spin = 1/ 2 doublet state. The second and third models were adjusted by removing two electrons to adjust for a Co2+ oxidation state; one is spin = 1/2 doublet with the other spin = 3/2 quartet, where spin is defined as difference in minority and majority

(1)

⃗ φKS i,σ (r,⃗ {RI})

In eq 1, one finds the set of one-electron orbitals with orbital energy levels εI({R⃗ I}). For the following equations, let σ = α or β to indicate spin. Kohn−Sham (KS) orbitals φKS σ,i , their energies εσ,i({R⃗ I}), occupation numbers for each orbital f i,σ, density for each spin component ρα(r)⃗ ,ρβ(r)⃗ , and total energy ETOT[ρα,ρβ] are all parametrically dependent on the positions of the ions {R⃗ I}. The contribution of each KS orbital to total density is defined either via occupation numbers ρσ(r)⃗ KS = Σi f i,σ|φl,σ (r)⃗ |2 or via density matrix ρσ(r)⃗ = Σlmρσ,lmφKS i,σ (r)⃗ KS φm,σ*(r)⃗ . Time evolution of electronic degrees of freedom is calculated by solving the equation of motion as follows: ρσ̇ , ij = −

i ℏ

⎛ dρσ , ij ⎞ ⎟⎟ ⎝ dt ⎠diss

∑ (Fσ ,ikρσ ,kj − ρσ , jk Fσ ,ki) + ⎜⎜ σ ,k

(2)

Here, the elements of Fock matrix represent adiabatic contribution to energy of electronic subsystem, without perturbation by lattice vibrations Fσ,ik = δikεσ,i(t). Electronic transitions are facilitated by thermal fluctuations of ions taken into account within second order of time dependent perturbation theory.77 Electronic dissipative transitions in eq 2

dρσ , jk

( ) dt

are based on nonadiabatic couplings that are

diss

computed along molecular dynamics trajectory for positions of ions {R⃗ I(t)} with initial conditions for positions {R⃗ I(t = 0)} and ⎯ d→ velocities dt RI(t = 0) representing ambient temperature. Ab

{

}

initio molecular dynamics due to Newton equation of motion MIR̈⃗ = F⃗I[ρα,ρβ] determines trajectory, {R⃗ I(t)}, which results in time dependent changes of electronic structure.102 Specifically, orbitals, φα,i and φβ,i, and their corresponding energies, εα,i({R⃗ I(t)}) and εβ,i({R⃗ I(t)}), experience change and fluctuation with time. On-the-fly nonadiabatic couplings are computed along nuclear trajectory as Vσ , ij(t ) = −

iℏ 2Δt

∫ dr φ⃗ σKS,i *({R⃗I(t )}, r )⃗ φσKS,j ({R⃗I(t + Δt )}, r )⃗ + h. c. (3)

A perturbative correction of second order in the coupling Vσ,ij(t) does enter into eq 2 as parameter.77 The solution of eq 2 for a specific initial excitation allows to find time-dependent orbital population, time-dependent density distributions, expectation values of hot carrier energies, as well as calculated rates of relaxation for electrons and holes as follows:

{∫ = {∫

ke = {τ e}−1 =

kh = {τ h}−1

0

0

N −N

components, S = α 2 β , Nσ = ∫ d3r ρ⃗ σ ( r ⃗). The doublet state corresponds to the low spin case when the Co2+ d-states are split under the effect of crystal field, and the energy difference between the t2g and eg orbital sets is comparatively large. The quartet state corresponds to the high spin case, where the energy difference between the t2g and eg orbital sets is smaller. The labeling of the configuration by declaring oxidation state and spin has some level of vagueness and is less than optimal, as charge may redistribute, providing difference of formal and physical oxidation state. However, this labeling schedule is chosen as a working tool attempted for comparison between the three models to distinguish any differences between the neutral and (2+) models.

−1

∞

} ⟨E ⟩(t )dt}

⟨Ee⟩(t )dt ∞

(4)

−1

h

(5)

where ⟨Ee⟩(t) and ⟨Eh⟩(t) are the energy expectation values of a photoexcited charge carrier defined in eqs S15 and S16 (Supporting Information, SI) and are assuming an exponential fit, which is most applicable in two cases: relaxation between two states and relaxation through states equally spaced in energy.103 The considered model is expected to exhibit what is called a trapping state, when population occupies one state for a 16112


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energy difference indicates that both of the Co2+ ion spin states can be observed experimentally at room temperature. A close up of the octahedral coordinated cobalt dopant is demonstrated in Figure 2. Each ligand is designated and the bond lengths and angles for each considered model are summarized in Table 1. The cobalt-ligand angles for all three Table 1. Bond Lengths and Angles for Each Considered Model between Co Ion and Its Nearest Neighboring Ligands Shown in Figure 2 Co−ligand bond lengths and angles Bond Lengths Co−X (X = Ligand; Å) neutral spin = 1/2

2+ spin = 1/2

N1 1.95 1.94 N2 1.97 2.00 O1 1.91 1.75 O2 1.91 1.88 O3 1.83 1.79 O4 1.95 1.88 Bond Angles X−Co−X (degrees) N1−Co−O4 163.83 166.47 O1−Co−O3 174.58 174.68 O2−Co−N2 167.58 166.47

Δ

2+ spin = 3/2

Δ

−0.01 +0.03 −0.16 −0.03 −0.04 −0.07

1.95 2.00 1.76 1.88 1.79 2.00

0 +0.03 −0.15 −0.03 −0.04 +0.05

+2.64 +0.10 −1.11

166.00 174.94 166.60

+2.17 +0.36 −0.98

models are near exact matches implying the electron count does not affect the angles. The neutral model’s bond lengths differ slightly in that the Co−O bond lengths tend to be a little bit longer. The bond contraction upon charging most likely is due to polaron formation.118 Charge difference distribution between neutral and charged models supports this hypothesis (see Figure S1, SI) Figure 3 illustrates the effect of doping on the electronic properties of the Co-doped TiO2 NW and shows calculated DOS, total and projected on atomic orbitals. It is seen that orbitals in the valence bands are composed as a superposition of 2p orbitals of oxygen, and all orbitals in the CB are composed as superposition of Ti 3d orbitals of titanium and the band gap value of the undoped TiO2 NW immersed in liquid water is equal to 2.8 eV (Figure 4a) that is close to earlier obtained results (2.2 eV without Hubbard on-site correlation corrections).117 All states inside the band gap of bare TiO2 are related to Co 3d states. The neutral model (Figure 4b) shows near matching for α/β electrons in the DOS, while the (2+) spin = 1/2 doublet (Figure 4c) shows the most offset α/β electrons and the (2+) spin = 3/2 quartet (Figure 4d) is slightly offset. The band gap difference in both (2+) models for α/β is also noticeable. The energy band diagrams for each model are shown in Figure 4, which demonstrates the electronic states’ energy around highest occupied (HO) and lowest unoccupied (LU) electronic states. The neutral model shows near matching between α and β states, while LUα and LUβ are slightly off set in energy. For the doublet state model, the α band gap is near zero, while β is about 0.90 eV. For the quartet state model, α has a band gap of 1.3 eV, while β is near zero. Between 0 and 2.8 eV, there are dispersed electronic states for all three models. While unoccupied states have very localized cobalt 3d character, the occupied cobalt states seem to be delocalized throughout the valence band (Figures S2−4, SI). These states are within the original band gap of anatase, and are Co 3d states (Figure 3).

Figure 1. (a) Top and (b) side view of the simulation NW optimized at 0 K.

Figure 2. Close up of the octahedral coordinated cobalt dopant ion with labels to correspond to Table 1.

3. RESULTS 3.a. Electronic Structure. After geometry optimization of both (+2) models, calculations reveal that the quartet state is more energy favorable on the value of 0.013 eV. The small 16113


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Figure 3. Projected density of states for four models and electronic configurations: (a) TiO2−H2O; (b) TiO2−Co−H2O neutral s = 1/2; (c) TiO2− Co−H2O(+2) s = 1/2; (d) TiO2−Co−H2O(+2) s = 3/2. All orbital energies are shifted to make the Fermi level an origin. Fermi level for both charged models lie 0.4 eV lower with respect to the neutral one. Interestingly, s = 1/2 and s = 3/2 models exhibit nearly identical patterns for the bottom of the CB and inside the gap while the top of the VB demonstrates difference in relative energies of spin majority and spin minority components E(CB,α) > E(CB,β) for s = 1/2 and E(CB,α) < E(CB,β) for s = 3/2. Also, for the s = 3/2 one observes an additional feature of α occupied Co 3d orbital near −4.8 eV. For s = 1/2, the β Co 3d feature near +0.8 eV is more pronounced than in the s = 3/2 model.

quartet state are deeper in the valence band. Because of this, the cobalt dopant does not act as an electron donor in this system, but as an acceptor with empty states near the conduction band edge. Therefore, the additional unpaired electrons in the (2+) quartet model do not significantly alter the electronic or optical properties when comparing it to the (2+) doublet model. The Fermi energy of the 2+ models are both shifted downward by 0.4 eV with respect to the same value for neutral model. The doublet and quartet 2+ models have very similar electronic state patterns, but differ in occupation, highlighted in Figure 3. Without a clear electron count, it is difficult to definitively define the oxidation state of cobalt. Table 2 shows the numerical summation of each electron density type as well as a summation of occupied and unoccupied electron density. All three models follow the same trend and henceforth will be summarized in a single analysis. Bader charge analysis confirms that the charge state for Co ion for all three models (Table 2). Figure 5 shows the energy fluctuations of the electronic states energies after heating to room temperature. The empty cobalt states in the original band gap of TiO2 are very noticeable and have much higher amplitude of fluctuations in energy compared to the densely packed Ti states in the conduction band and O states in the valence band. This is likely due to the isolation of the cobalt unoccupied states; they are unable to share the electron density with numerous states as in the valence and conduction bands, so the influence of heating causes more drastic changes in energy with the vibrations of the dopant ion. We postulate that, as the system is brought to room temperature and henceforth more energy is available, the

Figure 4. Energy band diagrams for all considered models. Energy band diagrams of (A) the neutral model, (B) 2+ and spin = 1/2, and (C) 2+ and spin = 3/2 are shown above. Without consideration of occupied and unoccupied states, the dispersion of states of the neutral model differs from that of both 2+ models.

Table 2 shows all three models have the same electronic configuration for the cobalt ion: near zero s electrons, 6p electrons (α + β), very localized unoccupied 3d states, and highly delocalized occupied 3d states. The electronic states are clearly altered when looking at the (2+) doublet and quartet models to the neutral. The general makeup of the electronic states is similar when comparing spin = 1/2 doublet and 3/2 quartet; however, the α/β band gaps seem to switch with spin configuration. Figure S5 shows the additional electrons of the 16114


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The Journal of Physical Chemistry C Table 2. Projected Density of States of Each Type of Cobalt State (s,p,d)a 4s model neutral 2+ spin = 1/2 2+ spin = 3/2

3p

3d

orbital

occ.

unocc.

occ.

unocc.

occ.

unocc.

charge state

charge state (Bader)

α β α β α β

0.191 0.188 0.212 0.205 0.211 0.213

0.037 0.031 0.010 0.010 0.008 0.009

3.287 3.277 3.342 3.330 3.323 3.322

0.048 0.040 0.016 0.019 0.015 0.018

3.964 3.168 4.167 2.973 4.179 2.972

1.049 1.832 0.902 2.071 0.903 2.062

0.925

1.470

0.771

1.514

0.78

1.515

Each model shows total α + β electron density for occupied orbitals of valence electrons (in elementary charge units) is less than 0.5 for 4s, ∼6.5 for 3p, and ∼7 for 3d states. The electronic configuration for each model is then 3p63d74s0, an indication that each cobalt ion is taking on 2+ oxidation state. The charge state was calculated as a difference between number of valence electrons on Co that is equal to 15 and sum of charges for all occupied orbitals. Bader charge states were evaluated by the similar way. a

Figure 5. Molecular dynamics. Energy fluctuations of electronic states with time upon heating to 300 K are illustrated for three configurations: (a) neutral, (b) Co2+, spin = 1/2, (c) Co2+, spin = 3/2. For each configuration, energies of both spin components are illustrated. The Ti 3d state in the conduction band and O 2p states in the valence band have lower amplitudes of oscillations and are densely packed. The Co 3d states in the gap have higher amplitudes due to the more localized nature of the states.

The ground state optical properties are calculated using eqs S10−12 (SI). Figure 6 shows the optical absorption spectrum and Table 3 identifies the highest oscillator strength transition for each labeled peak in Figure 6. All models show very interesting properties. While the neutral model does have both α and β absorption from 400 to 650 nm, past 650 nm only β absorbs. For both (2+) models, when α absorbs, β does not and

oxygen 2p, although unoccupied, relaxes at an energy more suitable for a 2p state such that it is essentially in the valence band. Figure 5 shows the sub gaps between these cobalt states that seem to vary quite a bit when comparing α/β between each individual model. It is an indication that relaxation dynamics between α and β could vary in rates due to the need for the electron to overcome a larger energy gap. 16115


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3.b. Electronic Dynamics. The numerical relaxation rates are presented in Table 3 for holes (Kh) and electrons (Ke) in ps−1, computed according to eq 4 and eq 5. In order to compare and contrast the relaxation dynamics, a transition between 3.65 and 3.69 eV (335−340 nm) was chosen for each model and each spin (α and β); the comparative transition is labeled i in each respective section in Table 3. For the independent transitions ii−iv/v, except the neutral α, holes relax much more quickly compared to electrons; whereas the neutral α relaxation rates are more similar for electrons and holes. All photoexcited transitions have the cobalt atom as the electron acceptor. Even though electron relaxation is occurring almost exclusively within the cobalt dopant ion, the relaxation is still slower than that of holes. Additionally, for the (2+) spin = 1/2 doublet α and (2+) spin = 3/2 quartet β, who have LU as an O 2p state, the rate does not seem affected by the necessity to transition from Co 3d to O 2p electronic states. While the band gap law119,120 could explain why the neutral α model has faster relaxation rates due to the evenly dispersed unoccupied Co 3d states, it cannot necessarily explain why the (2+) spin = 1/2 doublet β electron relaxes more quickly when excited to a higher energy state (LU+2) opposed to being excited to LU+1. To further help explain the relaxation dynamics, we first compare/contrast transition i for each model and spin, then explore each model in depth by looking at relaxation rates in relation to the band gap law as well as pathways of relaxation. All the type i transitions are labeled in the optical absorption spectrum in Figure 6 and occur around 340 nm. The relaxation rates all followed the general trend that the holes relax much more quickly than the electrons. Three particular transitions stick out: the neutral, α hole relaxation rate, the neutral, β electron relaxation rate, and the (2+), spin = 3/2 quartet β electron relaxation rate. The neutral, α hole relaxation is overall one of the slowest hole relaxation rates but consistent with the α, neutral hole relaxation rates. The slow relaxation rate (in comparison to the other hole relaxations) is due mostly to the HO-1 trap state. So even though the hole only needs to relax through four states, the trap significantly decreases the relaxation rate. The electron in the type i neutral, α relaxes very quickly despite being excited deep into the conduction band. While analysis of the dynamics is not possible due to the extensive noise (Figure 5), the longer relaxation rates of transitions ii and iii indicate LU+1 serves as a trap state. It is worth noting the neutral, α transition originates very close to the valence band edge and goes quite deeply into the conduction band. For the neutral β transition, both hole and electron relaxation rates of i are comparable to the ii−v transitions. The hole relaxes quickly through the O 2p valence band while the electron experiences a slight trap at LU+2 and LU+1. The only other excitation where the acceptor state is not LU is a type ii transition; therefore, the rates are similar as both type i and ii transitions are trapped on LU+1. For the (2+) doublet model, the α relaxation for both electron and hole are consistent with the other transitions. The electron relaxation is faster than that of the LU+1 transitions due to the LU+2 state being a dominant trap (Figure 8) and having a near direct charge transfer from LU+2 to the LU state. The β transition originates very close to the valence band edge causing a very quick hole relax and ends deep into the conduction band, slowing down the electron relaxation. For the (2+) quartet model, both α and β relaxation rates for the holes are consistent and expected, but the α and β electron rates are slower when comparing to the ii-iv transitions for each

Figure 6. Optical absorption spectra are shown for each model above. (a) CoNW neutral spin = 1/2; (b) CoNW (2+) spin = 1/2; (c) CoNW (2+) spin = 3/2. Each peak is labeled with a lower case roman numeral number. The peaks are characterized by the transition most likely to occur (highest oscillator strength), and described in Table 3. As α/β for each model do not have a peak in common, a transition for each spin and each model is presented in Figures 8−10. The spectra simply give a more visual and experimentally expected depiction of the independent orbital transitions.

vice versa (past 400 nm). This is noteworthy in that one could theoretically control the dynamics based on wavelength of photoexcitation, but further exploration into the relaxation dynamics is needed to fully understand if drastic differences in rates and pathways exist between each model as well as between the α/β relaxation dynamics. For simplicity purposes, each peak is represented by the most likely transition to occur, based on oscillator strength. Figure 7 is a graphical representation of the relaxation dynamics coefficients for each model and spin indication. A higher bar indicates a faster relaxation between a pair of orbitals, a lower bar slower relaxation, and no bar indicates very slow or no relaxation between two adjacent states. In general, for all models, the holes will relax through the valence band much quicker than the electrons through the conduction band; also, relaxation drops off drastically when close to HO/LU. Additionally, the (2+) models have a larger number of paired orbitals with zero or very low bars compared to that of the neutral model. 16116


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The Journal of Physical Chemistry C Table 3. Transition Corresponding to Peaks and Relaxation Ratesa model

spin

peak

transition

OS

eV

nm

Kh (ps−1)

Ke (ps−1)

neutral spin = 1/2

α HO = 694

i ii iii iv v i ii iii iv v i ii iii iv i ii iii iv v i ii iii iv i ii iii iv

HO-3 → LU+30 HO-12 → LU+1 HO-1 → LU+1 HO-6 → LU HO → LU HO-13 → LU+13 HO-6 → LU+1 HO-39 → LU HO-5 → LU HO → LU HO-20 → LU+8 HO-28 → LU+2 HO-27 → LU+1 HO-7 → LU+1 HO-2 → LU+27 HO-30 → LU+2 HO-12 → LU+2 HO-31 → LU HO-12 → LU+1 HO-21 → LU+8 HO-29 → LU+1 HO-29 → LU HO-12 → LU HO-21 → LU+11 HO-30 → LU+3 HO-5 → LU+4 HO-30 → LU+1

0.95 0.72 0.91 1.33 1.34 1.04 0.98 0.76 1.72 4.85 1.00 0.29 0.74 1.39 0.84 0.41 0.46 1.24 1.35 0.83 0.41 1.10 0.77 0.99 0.42 0.36 2.03

3.65 2.53 2.22 2.02 1.71 3.65 2.52 2.19 1.47 1.15 3.65 2.36 1.99 1.61 3.62 2.80 2.53 1.48 1.23 3.69 2.35 1.97 1.70 3.65 2.78 2.56 1.44

340 489 558 613 724 339 492 566 841 1082 339 526 623 770 343 442 490 835 1006 336 529 628 726 339 446 485 862

1.65 2.16 1.39 1.88

0.14 1.39 1.39

3.87 4.72 2.14 5.41

0.27 0.21

4.60 4.58 4.56 5.85 9.28 5.22 6.31 5.15 6.31 6.04 5.98 5.98 6.62 5.46 5.38 7.11 5.38

0.13 0.15 0.10 0.10 0.11 0.30 0.30

β HO = 693

2+ spin = 1/2

α HO = 693

β HO = 692

2+ spin = 3/2

α HO = 694

β HO = 691

1.09 0.13 0.37

0.30 0.64 1.45 1.09

a

Table characterizing each transition (labeled in Figure 6) with the calculated relaxation rates for the electron and hole. Each peak is described by the most likely transition, dependent upon oscillator strength, although more transitions may contribute to the intensity for the peak. The single orbital transitions were identified via the optical absorption spectra, as it was calculated using oscillator strength values assigned to singe orbital transitions, via independent orbital approximation.100.

respective spin. Both α and β transitions end deeper in the conduction band which explains the slower electron relaxation rates. 3.c. Relaxation in Neutral, S = 1/2 Doublet Model. The α relaxation dynamics follow the general trend that holes relax more quickly than electrons. However, in comparison of the different models and spins, the holes have the slowest relaxation dynamics of all holes and the electrons, in general, have the fastest relaxation rates. Interestingly, the transition at 489 nm has the quickest hole relaxation despite having the largest energy gap to overcome. The closest transition in energy gap is the 613 nm transition but it is about 15% slower in relaxation. When analyzing the hole relaxation pathway in Figure 8, the 489 nm transition uses mainly two states to transition to the HO. The hole is first on HO-12 (yellow), but then spends a considerable amount of time on HO-11 (magenta) with barely any occupation on the HO-10 to HO-2 states. Like the 613 nm transition, HO-1 (green) is a slight trap due to the O 2p (Co 3d) occupation before final relaxation to the HO, O 2p state (blue). For the 613 nm transition, the HO-6 is the original hole occupied state, then the hole spends almost equal time and occupation on HO-5 to HO-2, with a slight trap on HO-1, and then relaxes to HO. So, the 413 nm hole relaxation rate can be explained by the use of the HO-11 state as a way to bypass the relaxation pathway, which slows down the other hole relaxation rates in the neutral, α transitions. The electrons are easily explainable as the excitation occurs to either LU or LU+1. The

1/3 eV energy gap between LU and LU+1 as well as both being Co 3d state allows for quick electron relaxation. The β relaxation dynamics show the β holes are quicker than that of α which is likely due to most of the holes being located closer to the valence band edge compared to α. The slowest hole relaxation is at 566 nm and is slower due to a larger energy gap to overcome in relaxation as opposed to that of the transitions at 492 and 841 nm. Due to a considerable amount of noise in the hole relaxation images (Figure 8), analysis of trapping states is not possible. Only one transition involves a non-LU state, the transition at 489 nm to LU+1. The relaxation for the electron is much slower than that of the α electrons. While the β electron must relax almost a full eV, the α ΔE for LU+1 and LU is only 1/3 of an eV. The large sub gap slows down the β electron relaxation. This energy gap is evident in Figure 5 and Figure 8 when looking at the R images comparing α/β electron relaxation (red line). For the pathway of relaxation throughout the crystal (Figure 8, Z), the HO/LU states for α and β are very similar, but not exact. Both α/β HO are O 2p ligand states, and both α/β LU are Co states with LU β also having some charge density on the O 2p ligands (Figures S2−4). Because the electrons are all excited to Co 3d states, little change in location of the negative charge is noted for any of the neutral model’s relaxation dynamics. The 489 nm beta transition shows the electron isolated on the Co ion, but after relaxation to the LU, the electron density is partially on the O ligands. For the holes, especially those deeper in the valence band, the positive charge 16117


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Figure 7. Population relaxation rates between neighboring states. Rates of population transfer from states i to j (Riijj) for states around the band gap, calculated according to eq 5c. A large peak indicates a very fast relaxation, while no peak indicates a trapping state or the possibility of the transfer from state i to state j being skipped altogether for a more efficient pathway.

H, the relaxation pathway of α has a slight trap at the HO-1 state before full relaxation to HO, likely the cause of the slower α hole relaxation in comparison to β. In general, the hole relaxation rate is dependent on the energy gap between the original hole and HO with a larger gap indicative of longer relaxation. Despite the electrons being excited very close to the conduction band edge, the relaxation is extremely slow in comparison to that of the holes for both α and β. Focusing first on the α electron relaxation, we notice in Figure S3 that α LU is an O 2p state in the energy range of the valence band. Since LU +1 and LU+2 are Co states, it is likely one or both will act as an

is dispersed ligands of the dopant ion. With the deeper valence band transitions, the negative charge on the cobalt dopant is isolated for slightly less than 1 ps for both α and β transitions. The separation is ideal, but 1 ps duration ideally needs to be extended in order to provide more time for the negative charge to induce the photoelectrochemical reaction on the surrounding water atoms. 3.d. Relaxation in Cationic (2+), S = 1/2 Doublet Model. The rates of hole relaxation for the (2+) spin = 1/2 doublet, for both α and β, are quicker than that of the neutral hole relaxation (Table 3). The α hole relaxation rates are slightly slower than that of β. When analyzing Figure 9, column 16118


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Figure 8. Visualization of relaxation dynamics for neutral model. The transition labeled in Figure 6 and characterized in Table 3 are visualized. H shows the occupation of states by holes during relaxation wth time, ρij,σ(t). E shows population of states during electron relaxation with time. R shows the change in population of states with energy vs time. Due to a considerable amount of noise in some relaxation images, analysis of trapping states is not possible. Z shows the change in population along the Z axis with time. For R, Z, the color legend in reference to occupation by an electron/hole (n) is as follows: green, Δn = 0, no change in occupation; red, Δn < 0, negative, gaining an electron; blue, Δn > 0, positive, gaining a hole.

transitions involving LU+2 have the negative charge on the Co atom, and once relaxation occurs it is a mixed state of cobalt and oxygen ligands. Both LU and LU+1 are cobalt/ligand states so the charge evolution remains constant throughout the relaxation process. The model is of particular interest due to the difference in relaxation rates for the holes and the electron. The cobalt acts as a p-type dopant for every transition and the negative charge is isolated on the cobalt ion for an extended period of time. The hole, for the entirety of relaxation, is delocalized on oxygen 2p ions in the anatase nanowire. Additionally, because the absorption spectrum allows for explicit excitation of an α or β electron, the α-electron can be targeted due to the prolonged negative charge on the cobalt ion. 3.e. Relaxation in Cationic (2+), S = 3/2 Quartet. The relaxation of various photoexcitations for the model with charge (2+) in quartet multiplicity is illustrated in Figure 10. The rates

electron trap slowing down the relaxation process. When analyzing the electron relaxation shown in Figure 9, column E, HO-1 is an extremely efficient trap, slowing down electron relaxation to HO to about 100 fs. The trap is most noticeable in the HO-28 → LU+2 transition shown in Figure 9, column R. Because the other two transitions are to the LU+1 state, they are slightly quicker. The extended negative charge on cobalt is observed (Z) until full relaxation to LU occurs, where both positive and negative charge is dispersed throughout the O 2p ions. β-Electron relaxation is also slow, but not quite as slow as α due to the LU β state being that of Co 3d in character. The LU +2 to LU+1 sub gap significantly slows down electron relaxation as compared to the almost zero gap between LU+1 and LU. The two transitions involving LU+2 relaxation rates are 1/3 that of the LU+1 relaxation rate. The charge evolution along the z-axis, shown in Figure 9, column Z, shows the two 16119


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Figure 9. Visualization of relaxation dynamics for the model of oxidation = (2+), spin = 1/2. The transition labeled in Figure 6 and characterized in Table 3 are visualized. H shows the occupation of states by holes during relaxation wth time, ρij,σ(t). E shows population of states during electron relaxation with time. R shows the change in population of states with energy vs time. Due to a considerable amount of noise in some relaxation images, analysis of trapping states is not possible. Z shows the change in population along the Z axis with time. For R, Z, the color legend in reference to occupation by an electron/hole (n) is as follows: green, Δn = 0, no change in occupation; red, Δn < 0, negative, gaining an electron; blue, Δn > 0, positive, gaining a hole.

of hole relaxation are again very quick and no trapping states are noted, much like (2+), spin = 1/2 doublet β hole relaxation. A significant difference is found in α/β electron relaxation. Even though β HO is an O 2p state and has larger sub gaps to overcome, the β electron relaxes more quickly than that of α, excluding the transitions to LU. Two factors are contributing to this phenomenon. The first is the decoupling between the α LU and LU+1 states. Despite both being Co 3d states, Figure 5 shows some decoherence in the vibrational energies, which possibly slows the relaxation of the α electron. Second, β uses a transition state which allows for quick relaxation. Although the β LU state is O 2p, the LU+1 state is a mixed state involving Co and ligand oxygen atoms (Figure S4). All β transitions occur to a Co 3d unoccupied state; the electron then relaxes through the cobalt states where the LU+1 state of mixed Co 3d/O 2p

character has quicker than normal relaxation despite the O 2p LU.

4. CONCLUSIONS An in-depth analysis was performed on three structurally equal, but electronically different models of cobalt-doped, solvated anatase nanowires. The main purpose of the simulations is to look for properties that indicate the material would be a good candidate for use in a photoelectrochemical cell. The most indicative properties are (i) absorption in the visible light range, (ii) spatial charge separation of electrons and holes upon photoexcitation, and (iii) prolonged electron/hole separation after photoexcitation. Electronic structure calculations are used to describe ground state properties such as density of states, projected density of states, optical absorption, and partial charge density spatial distributions, while density matrix 16120


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Figure 10. Visualization of relaxation dynamics for the model of oxidation = (2+), spin = 3/2. The transition labeled in Figure 6 and characterized in Table 3 are visualized. H shows the occupation of states by holes during relaxation wth time, ρij,σ(t). E shows population of states during electron relaxation with time. R shows the change in population of states with energy vs time. Due to a considerable amount of noise in some relaxation images, analysis of trapping states is not possible. Z shows the change in population along the Z axis with time. For R, Z, the color legend in reference to occupation by an electron/hole (n) is as follows: green, Δn = 0, no change in occupatoin; red, Δn < 0, negative, gaining an electron; blue: Δn > 0, positive, gaining a hole.

Due to the noticeable hybridization of occupied cobalt states with oxygen, the oxidation state of cobalt was not clear in any of the models. As such, the projected density of states for cobalt was calculated. The cobalt electrons in the neutral model were spread among many states, but within a short energy range. Upon summation, it was found that all three models had a ground state d7 electronic configuration; even the neutral model had a cobalt 2+ oxidation state. The additional two electrons were spread among the many oxygen 2p states in the valence band. The optical absorption spectra show a rather unique pattern post 400 nm, where the α and β absorptions happen independently and isolated from each other. Essentially, the relaxation dynamics can be controlled as when an α electron is excited, there is near zero probability a β-electron is allowed to excite and vice versa. The isolated exemption is between 400 and 650 nm in the neutral model.

approach is used to describe nonradiative relaxation after photoexcitation. While one model had no change to electron count and spin count (neutral model), the other two models were assigned a charge of 2+, one in a doublet and the other a quartet spin configuration. The idea behind the 2+ charge was to force the cobalt dopant into the 2+ oxidation state. All the dopants took on octahedral coordination and only slight differences in bond length and angles were noted between the neutral and the 2+ models, with the electronic configuration also varying. Because of the subtraction of two electrons for the 2+ models, each had one spin configuration with a LU that was an O 2p state and within the energy range of the valence band. For these particular spin states, the LU+1 states act as a trap, allowing prolonged charge separation upon photoexcitation. 16121



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All of the models show promise for use in a photoelectrochemical cell as all absorb in the visible range, the electrons and holes have drastic differences in relaxation rates, and the spatial separation occurs upon excitation and subsequent trapping. Because the valence band does not have any localized Co states, the hole quickly relaxes through the dominant oxygen states in the valence band very quickly. The electron, however, relaxes through the Ti 3d states (when excited deep enough) and, in general, spends a considerable amount of time on the cobalt states near the conduction band edge. The most significant traps occur on the spin states where an oxygen 2p state is LU as the energy transfer from Co to O takes time. Even more so, these specific spin states can be targeted due to the aforementioned absorption spectra which indicate when α absorbs, β does not and vice versa. In this model, cobalt acts purely as an electron acceptor. Therefore, the following redox half and full reactions are proposed upon photoexcitation for the doped nanowire:

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Dmitri S. Kilin: 0000-0001-7847-5549 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research has been supported by NSF CHE-1413614 for methods development and CHE-1460872 for support of undergraduate researchers who helped in atomistic model building. Authors thank DOE BES NERSC facility for computational resources, Allocation Award #91202, “Computational Modeling of Photo-catalysis and Photo-induced Charge Transfer Dynamics on Surfaces” supported by the Office of Science of the DOE under Contract No. DE-AC0205CH11231. The authors would like to thank Douglas Jennewein for support and maintaining the High-Performance Computing system at the University of South Dakota. Thanks are also extended to Aaron Forde, Dane Hogoboom, Wendi Sapp, Adam Erck, Yulun Han, Brendon Disrud, and Bakhtyor Rasulev for collective discussion and editing. D.S.K. thanks Svetlana Kilina (NDSU), Sergei Tretiak, Amanda Neukirch (LANL), and James Hoefelmeyer for stimulating discussions. D.S.K. acknowledges support of Center for Nonlinear Studies (CNLS) and Center for Integrated Nanotechnology (CINT), a U.S. Department of Energy and Office of Basic Energy Sciences user facility, at Los Alamos National Laboratory (LANL). This research used resources provided by the LANL Institutional Computing Program. T.M.I. thanks the Center for Computational Materials Science, Institute for Materials Research, Tohoku University (Sendai, Japan) for their continuous support of the SR16000 M1 supercomputing system. T.M.I. gratefully acknowledges financial support of the Ministry of Education and Science of the Russian Federation in the framework of the Increase Competitiveness Program of NUST MISIS (No. K3-2016-021). The calculations were partially performed at supercomputer cluster “Cherry” provided by the Materials Modeling and Development Laboratory at NUST “MISIS” (supported via the Grant from the Ministry of Education and Science of the Russian Federation No. 14.Y26.31.0005). This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan within the program of funding research activities through grants for 2015−2017 “Development of Hydrogen Energy and Technology in the Republic of Kazakhstan”.

Co2 + + hv → Co+ + h+ O2 − + hv → O− + e− hv

Co2 + + O2 − → Co+ + O−

Based on these proposed reactions, one hypothesizes d8 excited state cobalt configuration. Our results show the 2+ oxidation state is more probable as even the neutral model cobalt took on a 2+ oxidation state. Additionally, the doublet and quartet spin states did not alter the stability of the models so both are likely to occur. The charged models also contain a larger wavelength range of the controllable absorption to explicitly excite either an α- or β-electron. However, in experiment, it is likely there will be a mixture of all models present. As we neglect spin orbit coupling in this study, high angular momentum properties, like spin flip, are not allowed. It is possible that upon temperature changes, strain, or photoabsorption, electrons flip from α to β (or vice versa) which is not possible to calculate with spin unrestricted DFT. Future research on this model should include the implementation of spin orbit coupling DFT analysis along with noncollinear spin density matrix theory,121 removing the NH3 functional on the cobalt dopant to allow direct binding of water, replacing the cobalt dopant with other transition metals, and possibly adding a p-type codopant. In conclusion, all three models show properties suited for photoelectrochemical applications, but the (2+) models trap states slow down electron relaxation, making the charged models slightly better options than the neutral.

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ASSOCIATED CONTENT

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