Molecular Photophysics under Shock Compression: Ab Initio

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Molecular Photophysics Under Shock Compression: Ab Initio Nonadiabatic Molecular Dynamics of Shocked Rhodamine Dye Xin Zhou, Linqiu Li, Dana D. Dlott, and Oleg V. Prezhdo J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12768 • Publication Date (Web): 05 Mar 2018 Downloaded from http://pubs.acs.org on March 7, 2018

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The Journal of Physical Chemistry

Molecular Photophysics Under Shock Compression: Ab Initio Nonadiabatic Molecular Dynamics of Rhodamine Dye

Xin Zhou,1,2 Linqiu Li,2 Dana D. Dlott,3 Oleg V. Prezhdo*2,4

1

College of Environment and Chemical Engineering, Dalian University, Dalian, 116622, P. R. China 2

Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States 3

School of Chemical Sciences and Fredrick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States

4

Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA

*Corresponding author, E-mail: [email protected]

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ABSTRACT: Photo luminescent chromophores can be used as probes for shock-wave propagation, provided that luminescence wavelength and/or lifetime depend on the increased pressure and temperature generated by the propagating shock-wave. Recent experiments have observed such effects with organic dyes and inorganic semiconductor quantum dots. We employ ab initio density functional theory and non-adiabatic molecular dynamics to study the effects of pressure and temperature on fluorescence properties of rhodamine-6G encapsulated in silica. Increase of pressure alone already decreases the luminescence wavelength and lifetime. The combined effect of enhanced pressure and temperature, representing shock conditions, is even stronger, with temperature growth having a particularly strong influence on the non-radiative lifetime. The excitation wavelength is redshifted due to changes in the

HOMO and LUMO energies caused by mechanical distortions

of the π-electron plane of the organic chromophore. The non-radiative relaxation accelerates due to enhancement in the non-adiabatic electron-vibrational coupling, that is particularly sensitive to temperature. The difference in the sensitivity of luminescence wavelength and lifetime to pressure and temperature suggests that it may be possible to determine the thermodynamic properties separately on the basis of the two measured quantities. A broad spectrum of vibrational modes couples to the electronic transition, with lower frequency modes exhibiting stronger coupling. Higher frequency modes become more important under the shock conditions. The simulations show excellent agreement with experiment, characterize how temperature and pressure influence electron-hole recombination in rhodamine-6G encapsulated in a silica matrix, and provide important details on the mechanism of nonequilibrium dynamics in the fluorescent chromophore.


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1. Introduction Insights into the pressure, volume and temperature of materials under shock compression are important, particularly, in deriving the equation of states of materials and predicting materials response under transient extreme conditions of high pressure, high temperature, and high-strain deformation.1-3 Various properties under shock compression have been investigated in recent years, including mechanical properties of shocked materials,4 optical properties of crystals and semiconductor quantum dots,5-7 phase transitions of metal oxides,8 shock-induced changes inside polymers,9-10 and shock dynamics of emissive organic dyes and self-assembled monolayers.3, 11-12 Strain, pressure, temperature and compositions are complex functions of space and time in a shocked micro-structured medium.13-15 Applications of fluorescent materials play an important role in a growing number of disciplines, including biotechnology, medicine, photonics and optoelectronics.16-19 A fluorescent dye can be used to probe shock compression dynamics by measuring shock-induced changes in emission wavelength, linewidth, intensity and lifetime.20-22 Huston et al. found that the crystal-violet lifetime increased from the 100 ps at atmospheric pressure to 200 ps at 2 GPa.11 The effect was attributed to shock-induced increases in glycerol viscosity. Taguchi et al. investigated the emission lifetimes of rhodamine-6G (R6G) in solution at high static pressures up to 0.9 GPa, and attributed the observed changes to chromophore aggregation.23 Dreger et al. studied emission lifetimes of a related dye, rhodamine-B (RhB) in a solid poly-acrylic acid matrix under high static pressures. Their results showed that the RhB lifetime decreased from 6 ns to 3 ns with the increase of pressure from ambient to 7 GPa.24 Because the duration of the shock-wave is in the tens of nanoseconds, which is several times longer than the luminescence lifetime, the chromophore response is faster than the shock duration, and chromophore luminescence can be used as an indicator for shock wave evolution. Fluorescence lifetime imaging has several advantages over measurements of fluorescence intensity and frequency shift. On the one hand, lifetime provides 3 ACS Paragon Plus Environment


information on dynamic coupling between the chromophore and the shock environment, not available from time-independent measurements. On the other hand, fluorescence lifetimes are more robust to uncertainties. Fluorescence intensity can change due to many effects occurring during a shock-wave experiments. For instance, the sample can move into or away from the line of focus, or some of the chromophore species can be photo-chemically damaged. A frequency shift is insensitive to intensity changes. However, it is hard to measure since one requires information on the entire spectrum. Unlike emission wavelength, which can be obtained nearly instantaneously, lifetime measurements require a time window of several lifetimes. Recently, Liu et al. explored emission of R6G under shock compression up to 9.1 GPa to understand molecular photophysics in extreme environments.12 The lifetime decreased from 3.25 ns to 1.25 ns as a linear function of shock pressure from 0 to 9 GPa. The observed lifetime decrease was attributed to the shock-induced enhancement of the R6G nonradiative relaxation. R6G was studied as a free dye dissolved in poly(methylmethacrylate) (PMMA), and as a dye encapsulated in silica microparticles suspended in PMMA. It has been shown that fluorescence quantum efficiency and chromophore brightness can be enhanced by encapsulating covalently single or multiple dyes in silica-based materials and making small changes to the internal architecture of the formed particles.25-27 Although many experimental works have focused on the effect of shock compression on the lifetime of fluorescent chromophores, it is unclear what particular pressure and temperature induced changes in the geometric and electronic structure of the chromophore and the matrix, modifications of the chromophore-matrix coupling, and specific vibrational motions are responsible for the inelastic and elastic electron-vibrational scattering that leads to the luminescence decay. It is very challenging to explore experimentally the microscopic properties at extreme conditions. Materials computer simulations are particularly useful and powerful for problems that may be inaccessible to direct experimental studies. Motivated by the experimental work, and particularly ref.,12 we report an ab initio 4 ACS Paragon Plus Environment

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atomistic time-domain investigation of the influence of pressure and temperature used in shock compression on non-radiative relaxation in R6G encapsulated in a silica matrix. We apply the nonadiabatic molecular dynamics (NAMD) approach28 formulated within the framework of real-time time-dependent density functional theory (TDDFT) in the Kohn-Sham (KS) representation.29-32 The next section describes the essential theoretical background and computational details underlying the NAMD simulation. The Results and Discussion section is separated into three parts, focusing on the geometric and electronic structure, electron-vibrational interactions and electron-hole recombination dynamics. We investigate whether the luminescence wavelength changes due to distortion of chromophore geometry under the influence of pressure, or increased thermal fluctuations causing deviations from the optimal geometry, or chromophore physical or chemical interaction with the matrix. The non-radiative channel for luminescence decay can be affected by changes in the electronic excitation energy, the non-adiabatic coupling, and the quantum coherence time. We study how these three characteristics vary due to chromophore deformation under pressure, faster nuclear motions at increased temperature, and interaction with the matrix. The simulation results are compared with the available experimental data. The key findings are summarized in the Conclusions section.

2. Theory and simulation methods The NAMD simulation is carried out using a mixed quantum-semiclassical framework by implementing the decoherence-induced surface hopping (DISH) technique33 in the time-domain KS theory.34 In this approach, the lighter and faster electrons are treated quantum mechanically, while the heavier and slower nuclei are described semiclassically. While fewest switching surface hopping (FSSH) is the most common NAMD methodology,35-36 it requires decoherence corrections37-39 to accurately model slow quantum transitions across large energy gaps, such as the non-radiative relaxation of the R6G chromophore to the ground state. Instead of 5 ACS Paragon Plus Environment


introducing decoherence as a correction, DISH interprets decoherence events as wave-function collapse giving rise to surface hops. The approach employed in the current simulation provides a detailed ab initio picture of the coupled electron-vibrational dynamics on the atomic scale and in the time domain. It has applied successfully to many systems and processes.40-47 The fundamentals of the NAMD methodology are presented in Supporting Information, and a detailed description of the method, as implemented in the PYXAID package, can be found in the original literature.31-32, 48 The current simulation model has been generated as follows. The silica matrix is simulated by a 2×2×2 supercell of β-cristobalite SiO2, subject to periodic boundary conditions in three dimensions. The initial positions of the simulation supercell were taken from the experimentally determined X-ray structure.49-50 The R6G dye contains a xanthene ring substituted with two methyl groups, two ethylamino groups and a carboxyphenyl group. In vacuum, the phenyl ring is found almost perpendicular to the xanthene plane, and therefore, the two fragments are not conjugated. Previous theoretical works showed that the lowest singlet excited state of R6G (S1) is associated with a transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO).51 These two orbitals have little contribution from the carboxyphenyl group. Considering the high cost of the NAMD simulation, the two methyl groups and the carboxyphenyl group in R6G were replaced by hydrogen atoms, and the two ethylamino groups were replaced by amino groups. Then, the simplified R6G molecule was inserted into the SiO2 matrix along the diagonal of SiO2 simulation cell, in order to maximize the separation between the periodic images of the molecule. All atoms of the SiO2 matrix overlapping with the molecule were removed in a stoichiometric way, i.e. in groups of SiO2. Care was taken to minimize the number of dangling bonds of the SiO2 atoms facing the cavity. The cavity was sufficiently large to allow some flexibility in the orientation of the molecule inside the cavity. The final model includes a cubic supercell with the side length of 14.24 Å, containing 42 Si, 85 O, 13 C, 2 N and 10 H atoms. 6 ACS Paragon Plus Environment

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Geometry optimization, adiabatic MD, and NA coupling calculations are carried using Vienna ab initio simulation package (VASP).52 The exchange-correlation interactions are treated using the Pedrew-Burke-Ernzerhof (PBE) functional.53 The interaction between the ionic cores and the valence electrons are described by the projector-augmented wave (PAW) approach.54 The van der Waals interactions are treated by the Grimme DFT-D2 method.55 The kinetic cutoff energy for the plane-wave expansion was set to 400 eV. For the structural optimization, adiabatic MD and density of states (DOS) calculations, a uniform Monkhorst-Pack mesh of 3×3×3 k-points are used, while in the NA coupling and dynamics calculations comprised the Γ-point only. In order to investigate the effect of shock temperature and pressure on the structure and properties of R6G encapsulated in SiO2, we choose the following three sets of conditions: 300 K-0.0001 GPa, 300 K-7 GPa and 525 K-7 GPa. The first set represents ambient conditions. The last set represents a typical shock-wave, which increases both temperature and pressure, according to the Hugoniot plot shown in Figure 2a of ref.12 It important to note that a uniform pressure and temperature increase may not fully represent a shock-wave; for example, a shear stress can be preserved for a long time, especially in solid matrices such as silica. The middle set isolates the effect of increased pressure, while keep temperature low. Because the NA coupling depends on nuclear velocity which depends on temperature, the effect of temperature on non-radiative relaxation is well-known.56-59 Therefore, we focus on the pressure effect. After geometry optimization of the whole model, uniform velocity rescaling was used to bring the temperature of systems to 300 K and 525 K. After that, constant NPT trajectory were generated using Parrinello-Rahman dynamics60 with Langevin thermostat61 for 5000 timesteps at 1 fs per timestep, at pressures of 0.0001 GPa and 7 GPa based on the last configuration of system at 300K, and at a pressure of 7 GPa based on the last configuration of system at 525 K. Figure 1 shows the change in the volume of the SiO2-encapsulated R6G simulation cell along the NPT trajectories. As we can see, the systems equilibrate within 1 ps. The configuration obtained at the end 7 ACS Paragon Plus Environment


of the 5 ps NPT trajectories were used to run 4 ps adiabatic MD simulations in the microcanonical ensemble with a 1 fs atomic time-step. It is assumed that the electron and hole have relaxed to the LUMO and HOMO, respectively. This process occurs on a picosecond timescale that is much faster than electron-hole recombination. The adiabatic state energies and NA coupling were calculated for each step of the MD runs. The 1000 geometries from the first picosecond of the 4 ps microcanonical trajectories were used as initial conditions for the NAMD simulations using the DISH method implemented within Pyxaid.32 Starting from each initial geometry, 100 random number sequences were generated to obtain 100 DISH simulations. The decoherence time was computed as the pure-dephasing time using the optical response theory in the second cumulant approximation, as done previously for a variety of systems.62-66

3. Results and Discussion 3.1. Geometric and Electronic Structure Figure 2 presents the side views of structural snapshots from the MD simulation at 300 K-0.0001 GPa, 300 K-7 GPa and 525 K-7GPa. As shown in Figure 1, the volume of cell is affected strongly by pressure, and slightly by temperature. The cavity inside the SiO2 matrix shrinks as the pressure increases. A comparison of the three panels in Figure 2 also indicates that thermal fluctuations and pressure have a notable impact on geometry of the R6G chromophore. Considering the molecular plane of the R6G chromophore, we observe significant fluctuations from planarity. During the MD simulation at the ambient conditions, 300 K and 0.0001 GPa, the largest value of the torsion angle of the R6G molecular plane is about 27 degrees. As the pressure is increased to 7 GPa, while the temperature is kept at 300 K, the largest value of the torsion angle recorded during the MD trajectory grows to 77 degrees. When both temperature and pressure are increased to 525 K and 7 GPa, representing shock-wave conditions, Hugoniot plot in Figure 2a of ref,12 the torsion angle fluctuates to as much as 98 degrees. The results show that the R6G chromophore gets more distorted as 8 ACS Paragon Plus Environment

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temperature and pressure are increased, Figure 2. The projected density of states (PDOS) separated into the contributions from SiO2 (blue line) and R6G (red line) is shown in the top panel of Figure 3. The data demonstrate that the valence band maximum is dominated by the R6G dye, and the conduction band minimum is formed mostly from molecular orbitals with a non-negligible contribution of the SiO2 matrix. HOMO and LUMO calculated at the Γ k-point are shown at the bottom of Figure 3. The HOMO and LUMO are localized on the xanthene ring and have π-character, similarly to the electron density localizations in the unmodified R6G chromophore,51 supporting reliability of the simplified structural model of the chromophore. The averaged gap values between HOMO and LUMO are listed in the second column in Table 1. The averaged gap is 2.24 eV at 300 K-0.0001 GPa, which is in good agreement with the experimental value of 2.34 eV.67 The gap decreases with the increase of temperature and pressure, since the noticeable distortion of the molecular plane, Figure 2, breaks conjugation of the π-electron system.

The PDOS show that the LUMO has some contribution from the SiO2

matrix. Such mixing of the R6G and SiO2 orbitals indicated that the excited state energy is sensitive to vibrations of not only the molecule, but also the matrix. Therefore, SiO2 contributes to the NA coupling and the energy gap modulation, having a direct influence on the non-radiative relaxation, in addition to impacting the molecule as a shock-wave transmitting medium.

3.2. Electron-Vibrational Interactions Electron-vibrational interactions result in elastic and inelastic electron-vibrational scattering. Both types of scattering events influence the excited-state lifetime. The electronic energy lost during the electronic transition from LUMO to HOMO is transferred to vibrations by inelastic scattering. Elastic scattering of electrons with the vibrational bath destroys electronic coherence, which is formed between HOMO and LUMO as they become coupled during the nonradiative relaxation by the NA interaction. Elastic electron-vibrational scattering is responsible for homogeneous 9 ACS Paragon Plus Environment


optical linewidth, and is known in optical measurements as pure-dephasing.68 Figure 4 presents Fourier transforms (FTs) of the fluctuations of the HOMO-LUMO energy gaps in the R6G-SiO2 system under the three sets of P-T conditions. The FT characterizes the vibrational modes that couple to the electronic subsystem during the non-radiative relaxation, induce decoherence, and accommodate the excess electronic energy. The FT is known as the influence spectrum or spectral density. The intensity of the peaks in the influence spectra characterizes the strength of the electron-vibration coupling for the vibration at a particular frequency. The data demonstrate that vibrations over a broad range of frequencies contribute to the nonradiative relaxation, with lower frequency modes showing stronger contributions. The low frequency modes below 1200 cm-1 correspond to collective motions of SiO2 matrix.69 Torsional and bending motions of the R6G chromophore also fall within this range. Higher frequency modes in the 1600-1900 cm-1 range can be attributed to intramolecular C-C and C-O bond stretching of the R6G chromophore. As the temperature and pressure are increased, higher frequency modes become more prominent in the influence spectra. Figure 5 depicts the optical pure-dephasing functions, computed using the second-order cumulant approximation.70 The functions characterize the time-scale of elastic electron-vibrational scattering. The pure-dephasing times, τ, summarized in Table 1, were obtained by fitting the functions to a Gaussian, exp[-0.5(t/τ)2]. The pure-dephasing time is more sensitive to temperature than pressure. As the pressure is increased from 0.0001 GPa to 7 GPa, while the temperature is kept at 300 K, the pure-dephasing time grows from 9.8 fs to 10.6 fs. As the temperature is increased from 300 K to 525 K, while the pressure is kept constant, the pure-dephasing time decreases from 10.6 fs to 6.1 fs. The unnormalized autocorrelation functions (un-ACF) of the fluctuations of the HOMO-LUMO energy gaps are shown in the inset of Figure 5. Under the cumulant approximation, the pure-dephasing function is computed by double time-integrating un-ACF. In the present case the three un-ACF decay on similar timescale, and the 10 ACS Paragon Plus Environment

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main difference is in their initial values. The ACF decay fast because many vibrational modes couple to the electronic subsystem, Figure 4. Simple analysis shows that a greater initial value of un-ACF favors faster dephasing.70 The initial value equals to the energy gap fluctuation squared. As pressure is increased while temperature is kept constant, the gap fluctuation decreases slightly, because the SiO2 cavity occupied by the R6G molecule shrinks, Figure 1, and the molecular motions become more restricted. This is why the pure-dephasing time grows from 9.8 fs to 10.6 fs. As the temperature is increased while the pressure is kept constant, the energy gap fluctuation grows significantly, blue line in insert in Figure 5, and the pure-dephasing time decreases from 10.6 fs to 6.1 fs. The elastic electron-vibrational scattering time for non-radiative relaxation across a large energy gap is much shorter than the relaxation time.71-72 Generally, shorter coherence leads to slower dynamics, as exemplified by the quantum Zeno effect in which the dynamics ceases in the limit of infinitely fast decoherence.73-75

3.3. Non-radiative Luminescence Quenching The temperature and pressure dependence of the non-radiative electron-vibrational relaxation from the excited to the ground electronic state, Figure 6, can be used to detect shock-waves. Since the electronic energy gap (emission wavelength) shows different dependence on pressure and temperature than the relaxation time, Table 1, it may be possible to use the emission wavelength and relaxation time together in order to determine pressure and temperature separately. The data shown in Figure 6 and Table 1 show that, at the fixed temperature, the higher pressure slightly accelerates the relaxation.

Raising the temperature at the same pressure, accelerates the

relaxation much more significantly, the last column of Table 1. In comparison, the HOMO-LUMO gap decreases by about the same amount due to pressure and temperature increases, the third column of Table 1. The calculated times for non-radiative luminescence quenching are in good agreement with the experimental results.12 Because of the necessarily small size of the simulation cells and the fact that 11 ACS Paragon Plus Environment


electron-vibrational coupling is usually stronger in smaller systems, consider molecules vs. bulk materials, one may expect that the coupling strengths and the charge recombination rates are slightly overestimated. The frontier orbitals are localized primarily on the chromophore, with LUMO having a small contribution from SiO2. Therefore, the size of the matrix surrounding the chromophore should have a small effect on the excited state decay. The observed dependence of the non-radiative recombination rate on temperature and pressure can be by considering the values of the energy gap, NA coupling, and pure-dephasing time, Table 1. Because the energy gap is large, the system is in the inverted Marcus regime,76 and the relaxation accelerates when the gap decreases. The relaxation also accelerates for larger NA coupling and longer pure-dephasing time. The pressure growth leads to decrease of the energy gap, increase in the NA coupling and increase in the pure-dephasing times. All factors favor faster relaxation. Because the changes in the gap, NA coupling and pure-dephasing are small, the relaxation time changes little.

The growth in temperature decreases the energy gap by a larger

amount. It increases the NA coupling significantly, because the NA coupling is directly proportion to nuclear velocity, which grows with temperature. The pure-dephasing time becomes shorter. The increase in the NA coupling is key to the reduced relaxation time.

4. Conclusions We have used NAMD in combination with real-time TDDFT to simulate non-radiative electron-vibrational relaxation responsible for luminescence quenching of the R6G chromophore encapsulated in a silica matrix under shock-wave conditions. Showing good agreement with the experimental data, the reported study characterizes the effects of temperature and pressure on luminescence wavelength and lifetime, and generates an atomistic understanding of the observed effects. The excited state energy and lifetime exhibit different dependencies on pressure and temperature, and therefore, together, they may be used to determine independently the pressure and temperature 12 ACS Paragon Plus Environment

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in a propagating shock-wave. The simulations indicate that increases in pressure and temperature have similar effects on the luminescence wavelength, while non-radiative quenching of luminescence depends much stronger on temperature than pressure. The energy gap is influenced by geometric distortions to the π-electron plane of the conjugated R6G chromophore. Both increased pressure and temperature perturb the chromophore structure and reduce the gap. The non-radiative relaxation depends much

more

strongly

on

temperature

than

pressure,

because

the

NA

electron-vibrational coupling is proportional to nuclear velocity. A broad range of vibrational modes couple to the electronic subsystem, with lower frequency modes having a larger contribution. The weak NA electron-vibrational coupling combined with a fast loss of coherence in the electronic subsystem result in nanosecond luminescence lifetimes, which are sufficiently long to facilitate experimental detection, and sufficiently short compared to shock-wave duration, allowing one to track shock-wave propagation. The research presented in this paper advances our understanding of the key factors influencing and controlling luminescence properties of organic chromophores under shock compression. Acknowledgments X. Z. acknowledges support of the National Natural Science Foundation of China, grant No. 21473183. L. L., D. D. D and O. V. P. acknowledge funding from the US Department of Defense, Multidisciplinary University Research Initiative, grant No. W911NF-16-1-0406.

Supporting Information Available: Basics of the time-dependent density functional theory and non-adiabatic molecular dynamics, snapshots of the R6G chromophore encapsulated in an amorphous SiO2 matrix, representative system coordinates and densities of states along the MD trajectories, and NAMD convergence tests. The material is available free of charge via the Internet at http://pubs.acs.org. 13 ACS Paragon Plus Environment



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2.0

The volume of supercell (nm3)

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


1.9

300K-0.0001GPa 300K-7GPa 525K-7GPa

1.8

1.7

1.6

1.5

0

1

2

3

4

5

Time (ps)

Figure 1. Change in the volume of the simulation cell containing the R6G dye encapsulated in silica along the molecular dynamics trajectories performed at constant temperature and pressure. The systems equilibrate within 1 ps.



Figure 2. Structural snapshots of the R6G chromophore encapsulated in amorphous SiO2, taken from the molecular dynamics trajectories at (a) ambient 300 K and 0.0001 GPa, (b) 300 K and pressure increased to 7 GPa, and (c) shock-wave conditions of 525 K and 7 GPa, Figure 2a of ref.12 The chromophore gets more distorted as temperature and pressure are increased.


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Figure 3. (a) Projected density of states of the R6G molecule and SiO2 matrix. (b) HOMO and LUMO charge densities. The isosurface value is set to 0.002 e/A3. The HOMO and LUMO localize on the molecule and have a small admixture from nearby atoms of the matrix.



(a) 300K-0.0001GPa

Spectral Density (arbitrary units)

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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(b) 300K-7GPa

(c) 525K-7GPa

0

500

1000

1500

2000

-1

Frequency (cm )

Figure 4. Fourier transforms of autocorrelation functions for the HOMO−LUMO gap fluctuation at (a) ambient 300 K-0.0001 GPa, (b) 300 K and pressure increased to 7 GPa and (c) shock-wave conditions of 525 K-7 GPa, Figure 2a of ref.12 These so-called influence spectra characterize the phonon modes that couple to the electronic transition. Vibrations of all frequencies contribute to the nonradiative relaxation, with lower frequency modes showing strongest contributions.


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un-normalized ACF (eV 2 )

1.0

0.8

Dephasing 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


0.6

300K-0.0001GPa 300K-7GPa 525K-7GPa

0.02

0.00

0.4 0

200

400

600

Time (fs)

0.2

0.0 0

10

20

30

Time (fs)

Figure 5. Pure-dephasing functions for the HOMO − LUMO transition in the R6G/SiO2 system under the three sets of conditions. The data are fitted by Gaussians, and the pure-dephasing times are given in Table 1. The inset shows the unnormalized autocorrelation functions. Their initial values represents the HOMO-LUMO gap fluctuation squared. Pure-dephasing characterizes elastic electron-phonon scattering. Temperature has a much stronger effect on the pure-dephasing time than pressure.



0.0025

300K-0.0001GPa 300K-7GPa 525K-7GPa

0.0020

Population

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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1.15 ns

0.0015

0.0010

4.12 ns 0.0005

5.65 ns 0.0000 0

500

1000

1500

2000

2500

3000

Time (fs)

Figure 6. Ground state population growth due to nonradiative electron-hole recombination in the R6G/SiO2 system under the three sets of conditions. The pressure increase already accelerates the nonradiative relaxation, while the temperature increase has a more significant effect.


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Table 1. Maximum observed torsion angle in the R6G molecular plane, and statistically averaged HOMO-LUMO energy gap, corresponding wavelength, absolute value of non-adiabatic coupling, pure-dephasing time and nonradiative electron-hole recombination time for the R6G-SiO2 system at different conditions. The simulations are performed in the isothermal-isobaric ensemble. Torsion angle (degrees)

HOMOLUMO gap (eV)

Wavelength (nm)

Non-adiabatic coupling (meV)

Puredephasing (fs)

Recombi nation (ns)

300K-0.0001 GPa

∼27

2.24

554

1.34

9.8

5.65

300K-7GPa

∼77

2.04

608

1.38

10.6

4.12

525K-7GPa

∼98

1.75

708

1.69

6.1

1.15



TOC Graphic


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Molecular Photophysics under Shock Compression: Ab Initio

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