Carrier Lifetimes and Recombination Pathways in MetalâOrganic

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Carrier Lifetimes and Recombination Pathways in Metal-Organic Frameworks Maria A. Syzgantseva, Nikolay F. Stepanov, and Olga A. Syzgantseva J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b02051 • Publication Date (Web): 14 Aug 2019 Downloaded from pubs.acs.org on August 15, 2019

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The Journal of Physical Chemistry Letters

Carrier Lifetimes and Recombination Pathways in Metal-Organic Frameworks Maria A. Syzgantseva1, Nikolay F. Stepanov1, and Olga A. Syzgantseva2,*

1

Laboratory of Quantum Mechanics and Molecular Structure, Department of Chemistry,

Lomonosov Moscow State University, Moscow 119991, Russia.

2

Laboratory of Molecular Simulation (LSMO), Institut des Sciences et Ingénierie

Chimiques, Valais, Ecole Polytechnique Fédérale de Lausanne (EPFL), Rue de

l’Industrie 17, CH-1951 Sion, Switzerland.

AUTHOR INFORMATION

Corresponding Author

* Olga A. Syzgantseva, Email: [email protected]

ACS Paragon Plus Environment

1

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ABSTRACT

Understanding the excited state charge carrier relaxation in Metal-Organic Frameworks

and revealing the ways to alternate its rate is of primary importance for the development

of novel hybrid photoactive materials with sufficiently long carrier lifetimes. Namely,

shedding light on the main recombination pathways in this class of compounds is needed.

Therefore, in this work the radiative and phonon-assisted non-radiative electron-hole

recombination is investigated theoretically for a model MOF system and the non-radiative

pathway is demonstrated to be dominant even for a pristine defect-free material.

Theoretically predicted electron-hole lifetimes are in line with the available experimental

data, suggesting that the adopted methodology is suitable for prediction of carrier lifetimes

and helpful for the interpretation of experimental data. Based on the obtained conclusions,

the principles for modification of MOF geometrical and chemical structure, enabling the

extension of carrier lifetimes, are formulated.


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The development of materials with optimal characteristics for photovoltaics, sensing

and photocatalysis compels an increasing attention to the novel types of hybrid organicinorganic compounds. Due to an extended structural and chemical tunability1, Metal-

Organic Frameworks (MOF) constitute a promising class of such hybrid materials,

however, their practical implementation in photo-induced applications requires a general understanding of the mechanisms2-4, governing the excited state charge carrier

dynamics. In particular, one of the undesirable processes to be controlled is a fast charge

carrier recombination. In photovoltaics it decreases the carrier lifetime and diffusion length, preventing efficient charge separation and carrier extraction at the electrodes5; in

sensing changing the ratio between radiative and non-radiative recombination rates can serve as a basis of the detectable physico-chemical feature6, while in photocatalysis the

interplay between the time of migration from/toward a substrate or an interface and the recombination rate is essential7.

Therefore, an extension of charge carrier lifetimes demands the knowledge of the

routes to prevent carrier recombination. Meanwhile, even for the most popular MOFs, the


4

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dominant recombination mechanisms, as well as the factors determining the

recombination rate, are still unclear. At the same time, the interpretation of experimental

data on the time-resolved absorption spectroscopy cannot always provide the required

data, as it is sometimes difficult to perform an unambiguous attribution of the observed

decay to the electronic structure levels involving specific chemical moieties. For example,

for the well-known UiO-66-NH2 MOF (Fig. 1) previously reported electron-hole recombination rate and photoluminescence decay rate differ by three orders of magnitude, being equal to 1.5 ps8 and 3.6 ns9, respectively. Precisely, transient absorption spectroscopy measurements8 revealed the relaxation rate to the ground state,

defined as a decay rate of a transient signal at 750 nm, equal to 1.5 ps.

Later on, a photoluminescence (PL) in UiO-66-NH2 was reported with 3.6+/-0.9 ns decay rate9, determined with time-resolved PL spectroscopy in acetonitrile solution, which

can be assimilated to the electron – hole lifetime, since a PL decay originates from the

transition to the ground state.


5


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Zr C N O H

Figure 1. UiO-66-NH2 crystal structure.

Already this example demonstrates the complexity of the problem and points out the

need to unravel the intrinsic timescale of charge carrier recombination in UiO-66-NH2.

Therefore, in this study we attempt to elucidate the timescale of the electron-hole

recombination processes taking place in a model UiO-66-NH2 system and to figure out the geometrical and electronic structure leverages responsible for the lifetime tuning. For

this purpose, we perform here Density-Functional Theory (DFT) based calculations of the

electron-hole recombination times in UiO-66-NH2 and 25% Ti-doped UiO-66-NH2 systems, considering defect-free materials.


6

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As shown by DFT calculations, in UiO-66-NH2(Zr) the top of the valence band and the bottom of the conduction band are constructed from the ligand-based orbitals (Fig.2a).

a. Zr O C O O C

NH2

O

b. O C O O C

NH2

Zr

O

Ti

Figure 2. Density of states for UiO-66-NH2-Zr and UiO-66-NH2-Zr/Ti, calculated with PBE density functional.


7


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The Zr-oxo-cluster states in the conduction band are situated above the ligand-based

CB edge. As expected, PBE functional underestimates the band gap, providing a value of 2.3 eV against 2.96 eV, reported experimentally8. However, the Density-of-States (DOS) profile obtained with the PBE functional10 is in good agreement with that obtained using HSE0611 and PBE012 functionals (Supporting Information, Fig. S1), the main

difference being the width of the band gap. Hence, the electronic structure itself, namely

the levels constructing the conduction band, are well described by PBE, which therefore

will be retained for this study. Unlike pristine UiO-66-NH2, in the mixed-metal Ti/Zr MOF the bottom of the conduction band comprises the contribution of metal along with the

ligand states (Fig. 2b).

Generally, an electron-hole recombination can proceed either through a radiative or a

non-radiative pathway. Considering an ideal material with no defects, in the case of

radiative electron-hole recombination an emission of a photon with an energy close to the

band gap of a material occurs. In the case of a non-radiative recombination, the excess

energy should be transferred to the lattice vibrations, which is usually referred to as the


8

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phonon-assisted recombination. The energy of phonons (~0.1 eV) is typically smaller than

the band gap (~1 eV) of a material, hence not every phonon can accommodate the energy liberated during the recombination process13. The rate of the phonon-assisted non-

radiative recombination is determined by non-adiabatic coupling coefficients between

ground and excited states. One of the straightforward ways to estimate the rate is to

perform a non-adiabatic ab initio molecular dynamics (AIMD). An efficient MD approach for solid materials, based on Tully’s Fewest Switches Surface Hopping (FSSH)14 method, was developed by Prezhdo and co-workers15-22. In the adopted formalism, the excited states are represented as transitions between one-electron Kohn-Sham orbitals15. In particular, Decoherence Induced Surface Hopping (DISH)16 formulation, accounting for

the loss of coherence occurring in slow relaxation processes, is shown to be suitable for the computation of electron-hole recombination rates19-22.

The practical realization of this approach implies resorting to the Classical Path Approximation17 at a finite temperature, in which it is assumed that thermal vibrations are

dominating in the formation of nuclear trajectory, while the excess excited electron energy


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induces negligible changes to the potential energy surface. Indeed, it is well known that

excited electron dynamics in itself has little to no effect on the ionic dynamics of an extended solid23-25, the last one being defined by the thermal ionic vibrations. This

approximation is in general valid for extended systems, in which total thermal vibrational energy is bigger than the excitation energy, or at high temperatures17,18, that both applies

to the carrier recombination in MOFs.

Hence, here we perform a simulation of a Born-Oppenheimer molecular dynamics

trajectory at a finite temperature 300K for a time of approximately 2.7 ps, followed by the excited state dynamics simulation performed within both FSSH14 and DISH16 approaches, as implemented in PYXAID code17,18. Several active space sizes (1x1,2x2,5x5) and

associated initial excitations are considered. Further computational details are given in

the corresponding section.

As depicted in Fig. 3a, the timescale of non-radiative electron – hole recombination rate

obtained with DISH for 1x1 active space, including only HOCO and LUCO orbitals, is 37 ns, i.e. of the order of 101 ns. The overall effect of increasing the active space results in


10

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a slight increase of an electron – hole recombination time (~50 ns), thus HOCO – LUCO

active space (2 KS states) provides the lowest bound of the electron-hole lifetime. Shifting

the band gap by 1.0 eV to attain its experimental value does not change the recombination

timescale.

Interestingly, FSSH approach, which a priori underestimates the recombination rates in the cases, where the decoherence effect plays an important role17, gives the electronhole lifetimes above 101 ps timescale range, that is one order of magnitude larger than the previously experimentally reported time of 1.5 ps8. Meanwhile, as shown by the DISH

approach, hot electron relaxation happens on the 1 ps timescale, after which stationary

excited state populations are observed (Fig. 3b), that is close to the relaxation time of 1.5 ps, revealed in experiment8. Besides, 37 ns non-radiative decay time is closer to the

photoluminescence lifetime of 3.6+/-0.9 ns, reported for UiO-66-NH2 in acetonitrile solution9. Some discrepancies with the PL lifetime9 are expectable, as the real sample

can contain defects, facilitating recombination, therefore the theoretical value should be

considered as an indication of the timescale.


11


Interpreting the results in view of the photoluminescence decay rate, it should be

mentioned that the decay is either due to the radiative emission or the non-radiative

recombination,

while

the

ratio

between

corresponding

lifetimes

defines

the

photoluminescence quantum yield13.

1.00000 0.99999 0.99998

Population P(t)

1.0000

Population P(t)

a.

0.99997

0.9990

FSSH

0.9980

t, fs

0.9970 0.9960

0

1000

2000

0.99996 0.99995

DISH

0.99994

%37ns

0.99993

t, fs 0.99992 0

b.

500

1000

1500

2000

2500

1.00

Ex4

0.90

Ex1

0.80

Population P(t)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.70 0.60 0.50 0.40

Ex3

0.30 0.20

Ex2

0.10

t, fs

0.00 0

500

1000

1500

2000

2500

Figure 3. (a): Decay of the first excited state (HOCO – LUCO) by DISH and FSSH (inset);

(b):Evolution of excited state populations upon HOCO-1–LUCO+1 (Ex4) initial excitation.


12

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To estimate the last one, we compute the rate of radiative recombination in the dipole

approximation by means of Einstein coefficients Amn. The photoemission decay time N the time needed for population of excited state to be decreased in e times due to radiative relaxation into the ground state is defined as an inverse of this coefficient Amn-1:

=

4

3

3

4 3

|

|2

where OP a.u., c=137.036 a.u. , Qnm is energy of the corresponding excited state transition in a.u. (Ha) and |Mnm|2 is a square modulus of transition dipole moment26.

Using the transition dipole elements calculated for the lowest transitions, it is possible

to evaluate the probability of radiative emission. The optical spectrum calculated within

Time-Dependent Density Functional Perturbation Theory (TDDFPT), as implemented in CP2K code27, and PBE density functional depicts the 8 lowest excitations corresponding

to HOCO–i S LUCO transitions, spanning in the 1.83 – 1.95 eV range (Fig.4a). The

HOCO–i orbitals are of the same type centered on the ligand with the contribution of the

NH2 side group and their energy is practically degenerate.


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Considering only the lowest transition (HOCO – LUCO), the photoluminescence decay

time in UiO-66-NH2 equals to ~2500 ns, about two orders of magnitude larger than the non-radiative recombination rate estimated in our calculations (ca. 37 ns). Summing up

the transition rates of 8 closely lying lowest transitions between the same kind of ligand-

centered orbitals gives the lifetime value of ~450 ns. This is in line with the experimental data9. Indeed, the prevalence of non-radiative recombination channel (37 ns vs 2500 ns) is supported by the small value9 of experimental photoluminescence quantum yield typical

for non-radiative quenching. Moreover, T calculated from the theoretical lifetimes, by its value is close to the experimental one. By definition13, it equals to the actual

recombination time N which is a superposition of radiative and non-radiative lifetimes,

divided by radiative lifetime Nr.

1

=

1

+

1

=


14

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a.

b.

Figure 4. Absorption spectrum of (a) UiO-66-NH2(Zr) and (b) UiO-66-NH2(Zr/Ti).

For N = 37 ns and Nr = 2500 ns T is close to 0.01, observed in experiment9. Interestingly, if the 1.5 ps decay, obtained in time-resolved transient absorption experiment8 would

result mainly from the non-radiative recombination, then the timescale of the radiative one


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with 0.01 quantum efficiency would equal to 0.1 ns, that is four orders of magnitude lower

than the estimate of radiative recombination rate given by TDDFPT. We simulate the

absorption spectrum also for one of the Ti-doped compositions (25%) and observe the

decrease of the oscillator strength (Fig. 4b) of the first transition by approximately two orders of magnitude +Nr ~105 ns), that is expectable as the bottom of the conduction band in UiO-66-NH2(Zr,Ti) is centered on the metal states, while the top of the valence band is still formed by the ligand ones, thus corresponding orbitals are spatially separated and

transition dipole moment between them is decreased. The increase of the radiative

lifetime of Ti-sample is in line with the experimentally observed decrease of quantum efficiency9. Performing a DISH computation on the 25% Ti-doped structure and setting the band gap parameter to the experimental value (~2.3 eV)9, we observe the nonradiative recombination time of the order of 102 ns, in fair agreement with 24.5 ± 1.7 ns lifetime and PL quantum efficiency of the order of 0.001, reported experimentally9.

Finally, the prevalence of the non-radiative recombination implies that the routes for

extension of carrier lifetimes should damp the phonon assisted non-radiative pathways.


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To analyze the vibrations, contributing to the electron-hole recombination we calculate

the spectral density for the transition between the first excited and ground state. It reveals the major contribution of the soft modes around 60 cm-1 and 200 cm-1, as well as modes at approximately 660 cm-1 and 880 cm-1, to the non-radiative decay (Fig. 5).

1

Spectral function

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

2

3

4

4 3 2

0

1000

2000

3000

4000

0, cm-1 Figure 5. Spectral density for the transition between ground and first excited state.

The modes around 60 cm-1 are mainly benzene-ring hindered rotations, with some contribution of ligand – cluster rotations. Modes at approximately 200 cm-1 and 660 cm-1


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comprise displacements both within ligand and metal cluster, the first one being to a great

extent an out-of-plane ligand motion, while the second one is primarily due to the oxygen atom vibrations within Zr oxide cluster of UiO-66-NH2. The mode around 880 cm-1 is mainly related to the change of H-C-C-H or H-C-C-N dihedral angle of the ligand benzene

ring. Therefore, an optimization of electron-hole lifetimes can be achieved by damping

the major energy transfer modes, that can be done by means of ligand replacement, as

well as the metal substitution within the metal node. Practically, it implies that electron-

hole recombination rate in MOFs can be efficiently tuned by engineering of frontier orbitals

in a way to optimize electron-phonon coupling resonant with the ground state – excited

state transition.

In summary, obtained results are helpful for the interpretation of experimental data on

time-resolved spectroscopic experiments, providing an indication on the time-scale of charge carrier dynamics in MOFs. Indeed, the non-radiative decay timescale of 101 ns is

in good agreement with experimentally observed photoluminescence decay in UiO-66-

NH2, i.e. the recombination occurs in the nanoseconds timescale. Some discrepancies


18

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with the time observed in experiment can be due to the presence of defects in a real

sample or the impact of the solvent. The recombination is shown to be dominated by non-

radiative decay channels mainly due to the phonon soft modes, rather than high

frequency modes. Therefore, damping these low frequency modes is a route for the

extension of electron-hole lifetime in UiO-66 class. The same considerations on reducing

non-radiative recombination apply to any MOF and can be systematically employed for a

targeted engineering of electron-hole recombination rates in MOFs via substitution of its

constituents.

Computational Methods. Initial structure of UiO-66 was taken from ref.28 to which aminogroups (NH2-) were added resulting in a unit cell containing 504 with a stoichiometry [C8H5NO4]24 [Zr6O4(OH)4]4, comprising 4 Zr-oxo-clusters and 24 2-aminoterephtalate (BDC-NH2) ligands. The whole structure including cell parameters (preserving orthorhombic symmetry) was relaxed using PBE functional14 of Density Functional Theory, MOLOPT DZPV basis sets29, GTH pseudopotentials30 for the description of core electron region, 800 Ry cutoff for auxiliary plane wave basis using CP2K program27. The


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ab initio molecular dynamics trajectory of 2.7 ps was obtained after equilibrating the system for about 60 ps in the NVT ensemble at 300K using Nose-Hoover chains31 as

implemented in CP2K. The DFT wavefunctions were then calculated with Quantum Espresso package32-33 with PBE functional, ultrasoft pseudopotentials34, 80 Ry and 800

Ry wavefunction and charge density cutoffs, respectively, using Y6

centered mesh.

The computation of non-adiabatic Hamiltonian and the non-adiabatic molecular dynamics (NAMD) runs were performed using PYXAID libraries17,18. The production trajectory

length was approximately 2.7 ps, the initial conditions included averaging over 10 different

starting points and using at least 100000 stochastic realizations for each of them. Both FSSH14 and DISH16 schemes were considered. The size of the active space was varied

from 2 (1 occupied and 1 empty) to 10 (2x5) KS states. The calculation of transition dipole

moments was performed within Time-Dependent Density Functional Perturbation Theory (TDDFPT), implemented in CP2K, for 400 empty states, 200 Ry cutoff and 10-3 eV

convergence threshold. The calculation of vibrational frequencies was done by the finitedisplacement method using a Phonopy code35, performing a single-point calculations of


20

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forces on the structures with finite displacements by VASP code36-39. The images of the structures are created with VESTA code40.

ASSOCIATED CONTENT

Supporting Information: Density-of-states computed with PBE, HSE06 and PBE0

functionals for UiO-66-NH2 structure. Relationship between Einstein coefficients and transition dipole moments.

AUTHOR INFORMATION

Notes

The authors declare no competing financial interests.

ACKNOWLEDGMENTS

The research is carried out using the equipment of the shared research facilities of HPC

computing resources at Lomonosov Moscow State University. This work was supported


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by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID

s888.

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Figure 1. UiO-66-NH2 crystal structure. 256x112mm (300 x 300 DPI)



Figure 2. Density of states for UiO-66-NH2-Zr and UiO-66-NH2-Zr/Ti, calculated with PBE density functional. 133x184mm (300 x 300 DPI)


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Figure 3. (a): Decay of the first excited state (HOCO – LUCO) by DISH and FSSH (inset); (b):Evolution of the excited state populations upon HOCO-1 – LUCO+1 (Ex4) initial excitation. 157x214mm (300 x 300 DPI)



Figure 4. Absorption spectrum of (a) UiO-66-NH2(Zr) and (b) UiO-66-NH2(Zr/Ti). 187x249mm (300 x 300 DPI)


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Figure 5. Spectral density for the transition between ground and first excited state. 246x174mm (300 x 300 DPI)



TOC 250x180mm (300 x 300 DPI)


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