I. Background and Fundamentals. III.Other Simple Environments IV. Complex Environments, Biological and Otherwise

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1 Solvation Dynamics: Fundamentals and A Survey of Results in Simple and Complex Environments I. Background and Fundamentals II. Polar Solvation Dynamics III.ther Simple Environments IV. Complex Environments, Biological and therwise 1

2 II. Polar Solvation Dynamics Experimental Results with C153 Probe Dielectric Continuum Models Insights from Computer Simulation (Molecular Theories) 11/1/25 II-Dipolar Solvation 2

3 Solvation Dynamics Probes H R R R R H H R X R R X R R C + + H H S I S S I 11/1/25 II-Dipolar Solvation 3 S H S I

4 Polar Solvation Dynamics change in u-v interaction due to change in solute permanent charge distribution interacting with solvent permanent charge distribution non-specific part (i.e. not H-bonding dynamics) in dipolar solvents well understood + CF 3 11/1/25 II-Dipolar Solvation 4

5 Coumarin 153 Electrical Potentials from Ψ well characterized dipolar solvation probe CF 3 μ(obs.) μ(calc.) S 6.5 D 6.8 D S D 15 D Δ(S1-S) 8-9 D 8. D 7.1±.4D* *Kanya & shima, CPL 37, 211 (23) 11/1/25 II-Dipolar Solvation 5

6 C153 Spectral Dynamics C153/DMS Spectra 1λ upconversion 12 fs IRF t ν(t) peak ss em abs obs t= est t= 1st mom. Horng, Maroncelli, J. Phys. Chem. 99, (1995) 11/1/25 II-Dipolar Solvation 6

7 Is It Just Solvation? Potential Complications: multiple electronic states? vibronic effects? joulolidine ring conformations? C153/cyclohexane obs. dyn. calc. vibronic dyn. vibronic relax. <2fs conf. not important (S 1 well isolated) 11/1/25 II-Dipolar Solvation 7

8 Subtle Aspects of Spectra C153/DMS (1λ) Width C153/CH 3 C (FLUPS) Width (norm. & expanded) Asym. Asym. Horng, Maroncelli, J. Phys. Chem. 99, (1995) Zhao, Ernsting, Phys. Chem. Chem. Phys. 7, 1716 (25) 11/1/25 II-Dipolar Solvation 8

9 e S ν (t) Spe ectral Respons The Spectral/Solvation Response S ν ( t) { ν ( t) ν } { ν ν } C153/RT Solvents 1. 1e t /ps C 5 H.1.8 C 5 H.7 C H 6 HMPA CH 3 C THF C 1 H Time / ps CH 3 C Time / ps 11/1/25 II-Dipolar Solvation 9

10 S ν (t) Characteristics 1. MeH 1. Decay Time Distributions S ν ( t) = A( τ )exp( t / τ ) dτ Spe ectral Re esponse e S ν (t) CH 3 C DMF.4 DMS φ-c 1 exp HMPA Time / ps 11/1/25 II-Dipolar Solvation 1

11 Dielectric Continuum Models ε,n 2a Predicted d Stokes Shift: 2 2( Δμ) Δν = F( ε, n) 3 a 2 ε 1 n 1 F( ε, n) = 2 ε + 2 n + 2 m -1 Stokes Shift Δν / 1 3 cm C153 Stokes Shifts nondipolar alcohols, amides dipolar aprotics =25; r 2 = Dielectric Factor F(ε, n) Reynolds, Maroncelli, J. Phys. Chem. 1, 1337 (1996) 11/1/25 II-Dipolar Solvation 11

12 Benzene is a Polar Solvent C153 Stokes Shifts in on-dipolar Solvents p-dioxane benzene Reynolds, Maroncelli, J. Phys. Chem. 1, 1337 (1996). 11/1/25 II-Dipolar Solvation 12

13 Dielectric Response ε(ω) ε P r ε (ω) (t) r E( t) D r ( t) rotation r r r r = E cosωt 4πP( t) = D( t) E( t) = E r { ε ( ω)cosωt + ε ( ω)sinωt} libration & vibration electronic E r (t) ε (ω) Bottcher, Theory of Dielectrics (Elsevier, 1973) 11/1/25 II-Dipolar Solvation 13

14 S ν (t) and ε(ω) when the static electrical u-v interaction can be written: U el = Φ 2 m χ m solute q,μ,q, ( ε ) solvent susceptibility the solvation response to a change in Φ m is approximately: 1 S ( t) = L ~ ε () ε~ ( p) p ~ ε ( p ) = ˆ( ε i ω ) ˆ ε ( ω) = ε ( ω) + iε ( ω) {[ ] } m p / inverse Laplace transform for example: χ = 1 ( (ε ) q ε aε for Debye type ε(ω) 2 ε 1 ε ε χ ( ε ˆ ε ω = ε + ) = ( ) μ 3 a 2ε iωτ D S m ( t) = exp( t / τ m) ε τ D "ττ L" ε τ = = q 2 ε +1 τ μ = τ 2ε + 1 τ D longitudinal relaxation time 11/1/25 II-Dipolar Solvation 14

15 on-debye ε(ω) ε =78 real solvents are show more complex ε(ω) than Debye form Water ε(ω) ε (ω) Debye ε =7ε inclusion of highfrequency (mainly librational) part of ε(ω) essential ε (ω) if Debye ε =78, ε ~7, τ D =8 ps, so τ μ ~.8 ps ω / ps -1 Trokhymchuk et al., J. Phys. Chem. 1996, 1, 1411(1996). 11/1/25 II-Dipolar Solvation 15

16 ε(ω) Predictions characteristic times predicted to within a factor of 2 for wide range of solvents near room T no distinction with H-bonding bserve ed Time / ps C153 in 22 solvents (298 K) 1 3 t 2 1 <τ> 1 2 t 1e polar aprotic H-bonding Calculated Time / ps 11/1/25 II-Dipolar Solvation 16

17 Temperature Dependence connection to ε(ω) persists over wide T range but few examples Solvation Time <τ> / s T dependence in m-thf Ru(byp) 2 (C) H H 1-5 ε(ω) 1-7 T g 1-9 H Richert, Maroncelli, Chem. Phys. Lett. 229, 32 (1994) K / T 11/1/25 II-Dipolar Solvation 17

18 More Sophisticated ε(ω) Calcs. Song & Chandler, J. Chem. Phys. 18, 2594 (1998) τ L CH 3 H spherical approx. expt spherical full CH 3 C H 2 11/1/25 II-Dipolar Solvation 18

19 Key Points solvation in many solvents is remarkably rapid >1 ps but >1 3 variation in t 1e at room T biphasic, with many solvents showing a pronounced fast component highly non-exponential, esp. in alcohols essential features captured by dielectric continuum models 11/1/25 II-Dipolar Solvation 19

20 Computer Simulations (usually) classical dynamics, pairwise additive potentials (LJ+q), 1 solute and 25-1 solvent molecules equilibrium and non-equilibrium dynamics Ando, Benjamin, Berkowitz, Brown, Callis, Fonseca, Ladanyi, Hynes, Kim, itzan, Patey, Rossky, Schwartz, Stratt, 11/1/25 II-Dipolar Solvation 2

21 Simulation & Experiment CF 3 standard solvent models solute q, q Δq from Ψ S ν (t) S ν (t) 1..8 CH 3 H.6 exp.4.2 sim ε(ω) ( ) Time / ps sim exp CH 3 C AF H Time / ps Kumar&Maroncelli, JCP 13, 338 (1995); Jimenez et al., ature 369, 471 (1994). 11/1/25 II-Dipolar Solvation 21 2

22 MD of Simple Solutes studies of simple solutes afforded many insights 1 (m= ) + C CH 3 1 CH 3 Cl often linear response S ν (t) (C153) 1 CH 3 C prominent inertial or Gaussian decay mainly solvent rotation speed tied to solvent polarity H /1/25 II-Dipolar Solvation Time / ps 22

23 Linear Response? Atomic Solute in CH 3 C except for large Δq or specific interactions response is linear S ν (t) S ν (t) CH 3 C.8 CH 3 H e Time / ps Maroncelli, JCP 94, 284 (1991); Kumar & Maroncelli, JCP 13, 338 (1995) 11/1/25 II-Dipolar Solvation 23

24 The Initial Gaussian + + C CH 3 S(t) normal )normal no trans. rigid cage no solvent-solvent interactions (or trans) Time / ps Perera & Berkowitz, J. Chem. Phys. 97, 5253 (1992); Maroncelli, JCP 94, 284 (1991); initial gaussian decay is free-streaming rotational motion 11/1/25 II-Dipolar Solvation 24

25 Little time, little motion Δν 3 cm -1 in ~2 fs 3-Methyindole / water Superimposed trajectories t 1 ps Δν 75% from =25, θ< cm -1 θ 25 Muiño & Callis, J. Chem. Phys. 1, 493 (1994) 11/1/25 II-Dipolar Solvation 25

26 A Simple Interpretation + 1 S solv C rot ( t) { C ( t)} rot ( t) = μ ˆ ˆ( μ t) α 2 4 πμ ρ 1 α = (1 1/ ε ) 3k B T Polar solvation is solvent rotation. Greater coupling (α) means less motion is required & thus greater speed. C rot (t) α C rot (t), S(t), 1 {C rot } α S solv C rot μ=2 D (α=8) CH 3 H (α=8) H 2 (α=19) CH 3 C (α=2) Maroncelli et al., J. Phys. Chem. 97, 13 (1993); also JCP 19, 324 (1998); and Raineri et al. JCP 11, 6111 (1994) Time / ps Time / ps 11/1/25 II-Dipolar Solvation 26

27 Character of Δq Matters S(t t) m = CH 3 C As solute multipole m increases: spatial range response 3 CH 3H collectivity α α translation effect of solute motion m Time (ps) m Time (ps) Kumar & Maroncelli, JCP 13, 338 (1995) Ladanyi & Maroncelli, JCP 19, 324 (1998). 11/1/25 II-Dipolar Solvation 27

28 Molecular Theories extend ε(ω) to ε(k,ω) site-site formulation for realistic systems ab initio treatment of Stockmayer model F.. Raineri and H. L. Friedman, "Solvent Control of Electron Transfer Reactions," Adv. Chem. Phys. 17, (1999). B. Bagchi and R. Biswas, "Polar and onpolar Solvation Dynamics, Ion Diffusion, and Vibrational Relaxation: the Role of Biphasic Solvent Response in Chemical Dynamics," Adv. Chem. Phys. 19, (1999). V. Kapko and S. A. Egorov, "Polar solvation dynamics in supercritical fluids: A mode-coupling treatment," J. Chem. Phys. 121, (24). 11/1/25 II-Dipolar Solvation 28

29 Key Points computer simulations show that: initial Gaussian decay is free streaming motion (rotation) extreme speed is result of collective nature of solvation - small-amplitude motion has large effect in presence of high polarity α multipole character of Δq matters molecular theories can now reproduce simulation & experiment 11/1/25 II-Dipolar Solvation 29