Supporting Information Optically Triggered Stepwise Double Proton Transfer in an Intramolecular Proton Relay: A Case Study of 1,8-Dihydroxy-2-naphthaldehyde (DHNA) Chia-Yu Peng,, Jiun-Yi Shen,, Yi-Ting Chen, Pei-Jhen Wu, Wen-Yi Hung, Pi-Tai Chou, * Wei-Ping Hu,, * and Department of Chemistry and Biochemistry, National Chung Cheng University, Chia-Yi 62102, Taiwan, R.O.C. Department of Chemistry and Center for Emerging Material and Advanced Devices, National Taiwan University, Taipei 10617, Taiwan, R.O.C. Institute of Optoelectronic Sciences, National Taiwan Ocean University, Keelung 20224, Taiwan, R.O.C. These authors contributed equally to this work. Corresponding Author Email:chop@ntu.edu.tw (P.-T. Chou) Email: chewph@ccu.edu.tw (W.-P. Hu) S1
Contents page Figure S1. Side views of the packing of DHNA in the unit cell... S4 Figure S2. The 1 H NMR spectroscopy of DHNA and HN12... S5 Figure S3. Normalized steady-state absorption spectrum (black lines) and excitation spectra (monitor at 520 nm (red) and 650 nm (blue)) for DHNA in cyclohexane at room temperature... S6 Figure S4 Time-resolved femtosecond fluorescence upconversion of DHNA in cyclohexane monitored at 450 nm (black open square,, an average of five replicas) and instrument response function (red).... S6 Figure S5. Time-resolved relaxation dynamics of DHNA in solid state monitored at 520 nm (black open circles, ), and 650 nm, (blue open square, ). Solid lines depict the corresponding fitting curves (black and blue) and instrument response function (red)... S7 Figure S6. Calculated relative energies (kcal/mol) and wavelengths (nm) of vertical excitation and emission for DHNA in CH 2 Cl 2 at B3LYP/6-31+G(d,p) and TD-B3LYP/6-31+G(d,p) levels... S7 Figure S7. Calculated relative energies (kcal/mol) and wavelengths (nm) of vertical excitation and emission for DHNA in CH 3 CN at B3LYP/6-31+G(d,p) and TD-B3LYP/6-31+G(d,p) levels... S8 Figure S8. Calculated potential energy curves along the TA* TB* reaction path at B3LYP/6-31+G(d,p) (S 0 ) and TD-B3LYP/6-31+G(d,p) (S 1 ) levels... S8 Figure S9. Calculated two-dimensional potential energy (kcal/mol) maps of both ground state (bottom) and 1 st excited state (top) for the proton transfer reactions in the DHNA system in cyclohexane solvent. The minimum energy path (the solid pink circle) obtained by an IRC calculation was also shown. The energies were calculated at the B3LYP/6-31+G(d,p) level using the PCM solvation model... S9 Figure S10. Calculated two-dimensional potential energy (kcal/mol) maps of both ground state (bottom) and 1 st excited state (top) for the proton transfer reactions in the DHNA system in acetonitrile solvent. The minimum energy path (the solid pink circle) obtained by an IRC calculation was also shown. The energies were calculated at the B3LYP/6-31+G(d,p) level using the PCM solvation model...s10 Eqs. S1...S11 Table S1. Crystal data and structure refinement for DHNA... S13 Table S2. Bond lengths for the DHNA crystal structure... S14 Table S3. Hydrogen bond distances and angles for DHNA crystal structure... S14 Table S4. The photophysical properties of DHNA and 3... S14 S2
Page Table S5. Calculated bond lengths (Å) of the normal form (N), tautomer A (TA), and TS1 (N TA) on S 0 in various solvents...s15 Table S6. Calculated bond lengths (Å) of the normal form* (N*), tautomer A* (TA*), and TS1* (N* TA*) on S 1 in various solvents... S16 Table S7. Calculated bond lengths (Å) of the tautomer A* (TA*), tautomer B* (TB*), and TS2* (TA* TB*) on S 1 in various solvents... S17 Table S8. Calculated harmonic vibrational frequencies (cm 1 ) of the O H stretching and imaginary frequencies on S 0 in cyclohexane... S18 Table S9. Calculated harmonic vibrational frequencies (cm 1 ) of the O H stretching and imaginary frequencies on S 1 in cyclohexane... S19 Calculated Bond Lengths and Stretching Vibrational Frequencies of the O H Bonds... S21 Table S10. Calculated Transition State Theory (TST) rate constants (s 1 ) and kinetic isotope effects (KIEs) at various temperature (K) in cyclohexane... S22 Table S11. Calculated zero-point energy differences ( ZPEs, ZPE TS ZPE reactant, kcal/mol) in cyclohexane... S22 Calculated the KIEs at Low Temperature... S23 Low Frequency Modes... S23 Table S12. Calculated absorption wavelengths (nm) of the DHNA system in various solvents... S24 Table S13. Calculated emission wavelengths (nm) of the DHNA system in various solvents... S24 S3
Figure S1. Side views of the packing of DHNA in the unit cell. S4
Figure S2. The 1 H NMR spectroscopy of DHNA (up) and HN12(down) in CDCl 3. S5
A. U. 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 300 400 500 600 Wavelength (nm) Figure S3. Normalized steady-state absorption spectrum (black lines) and excitation spectra (monitor at 520 nm (red) and 650 nm (blue)) for DHNA in cyclohexane at room temperature. Note that peaks appearing at ~460 nm and 490-500 nm in the excitation spectrum (monitoring at the 520 nm emission) are the Raman peaks of the solvent. 1.0 0.8 A. U. 0.6 0.4 0.2 0.0-1 0 1 2 3 4 5 Time (ps) Figure S4 Time-resolved femtosecond fluorescence upconversion of DHNA in cyclohexane monitored at 450 nm (black open square,, an average of five replicas) and instrument response function (red). S6
Count. 1.0 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 Time (ns) Figure S5. Time-resolved relaxation dynamics of DHNA in solid state monitored at 520 nm (black open circles, ), and 650 nm, (blue open square, ). Solid lines depict the corresponding fitting curves (black and blue) and instrument response function (red). Figure S6. Calculated relative energies (kcal/mol) and wavelengths (nm) of vertical excitation and emission for DHNA in CH 2 Cl 2 at B3LYP/6-31+G(d,p) and TD-B3LYP/6-31+G(d,p) levels. S7
Figure S7. Calculated relative energies (kcal/mol) and wavelengths (nm) of vertical excitation and emission for DHNA in CH 3 CN at B3LYP/6-31+G(d,p) and TD-B3LYP/6-31+G(d,p) levels. Figure S8. Calculated potential energy curves along the TA* TB* reaction path at B3LYP/6-31+G(d,p) (S 0 ) and TD-B3LYP/6-31+G(d,p) (S 1 ) levels. S8
Figure S9. Calculated two-dimensional potential energy (kcal/mol) maps of both ground state (bottom) and 1 st excited state (top) for the proton transfer reactions in the DHNA system in cyclohexane solvent. The minimum energy path (the solid pink circle) obtained by an IRC calculation was also shown. The energies were calculated at the B3LYP/6-31+G(d,p) level using the PCM solvation model. S9
Figure S10. Calculated two-dimensional potential energy (kcal/mol) maps of both ground state (bottom) and 1 st excited state (top) for the proton transfer reactions in the DHNA system in acetonitrile solvent. The minimum energy path (the solid pink circle) obtained by an IRC calculation was also shown. The energies were calculated at the B3LYP/6-31+G(d,p) level using the PCM solvation model. S10
Eqs. S1 In Scheme S1 we also draw a concerted PT pathway (k dpt ) but specify that this process is unlikely to take place according to the kinetic data. This viewpoint is also supported by theoretical arguments based on the PES landscape, concluding that the concerted PT pathway is thermally unfavorable. Based on the experimental data we conclude the rate of first proton transfer k pt1 (N* TA*) to be faster than the system response of (150 fs) -1. Therefore, in a time frame of several ps of interest, it can be assumed that at t ~ 0 (< 150 fs) N* has been depopulated to ~zero and TA* is instantaneously populated (TA* =[TA*] 0 at t ~ 0). Therefore, the time-dependent TA* and TB*, specified as [TA*] and [TB*], respectively, can be expressed as d[ta*] TA* = ( k f + kpt2) [TA*] + k pt2[tb*] dt (1) d[tb*] * = ( k TB f + k ) [TB*] + kpt2[ta*] pt2 dt (2) where k k TA * TB* f and f are the sum of non-esipt decay rate for TA* and TB*, respectively. The differential Eqs. (1) and (2) can be solved by Laplace transformation to obtain Eqs. (3) and (4) [TA*] 0 λ1t λ t TA*] = [( λ2 X ) e + ( X λ1 ) e ] (3) λ λ [ 2 2 1 kpt2 [TA*] 0 λ1t λ2t [ TB*] = [ e e ] (4) λ2 λ1 1 2 Where λ 1,2 = [( X + Y) m ( X Y) + 4 kpt2 k pt2 ] (5) 2 TA* TB* X = k + k, Y = k + (6) pt 2 f pt 2 k f The experimental results also draw the conclusion that the rate of forward TA* TB* (k pt2 ) and * TB* reverse TB* TA* (k -pt2 ) proton transfer is much larger than k k. Under the condition of S11 TA f and f
k >>, it is thus reasonable for us to claim the pseudo equilibrium between TA* and TA* TB* pt2, k-pt2 k f, k f TB* prior to their corresponding emission. As a result, can be written as follows. X k and Y k and λ 1 and λ 2 in Eqs. (5) pt2 pt2 k k + k k k + k K λ (7) TA* TB* TA* TB* 1 f pt 2 f pt 2 f f eq 1 1 = = =, λ2 = = kpt2 + k pt2 τ1 k pt 2 + k pt 2 1+ Keq τ 2 The pre-exponential factors in Eqs. (3) for the [TA*] can be derived further as A A 1 2 [TA*] 0 ( X λ1 ) λ λ k 2 [TA*] 0 ( λ2 X ) λ λ k 2 1 1 pt2 k pt2 pt2 + k k pt2 + k pt2 pt2 (8) (9) The ratio between A 1 and A 2, i.e. A 1 /A 2 is thus derived to be k pt2 /k -pt2, which is equivalent to the equilibrium constant K eq (= k pt2 /k -pt2 ) between TB* and TA* species. We then further convert the time-resolved concentration expression (Eqs. (3) and (4)) to the time-resolved fluorescence intensity of TA* and TB*, denoted as [TA*] f and [TB*] f. This is done by multiplying the instrument factor (I 0 ) and TA* TB* the fluorescence radiative decay rate constant kr and kr for TA* and TB*, respectively, giving Eqs. (10) and (11), which is essentially identical with equation (I) in the text. TA* I 0 kr [TA*] 0 λ1t λ2t [ TA*] f = [( λ2 X ) e + ( X λ1 ) e ] (10) λ λ 2 1 TB* 0 kr kpt2 [TA*] 0 λ t λ t I 1 2 [ TB*] f = [ e e ] (11) λ λ 2 1 S12
Table S1. Crystal data and structure refinement for DHNA Empirical formula C11 H8 O3 Formula weight 188.17 Temperature Wavelength Crystal system Space group 200(2) K 0.71073 Å Monoclinic P2(1)/c Unit cell dimensions a = 8.4818(10) Å α= 90. b = 6.7611(8) Å β= 105.173(2). c = 14.9995(17) Å γ = 90. Volume 830.18(17) Å 3 Z 4 Density (calculated) 1.506 Mg/m 3 Absorption coefficient 0.110 mm -1 F(000) 392 Crystal size 0.42 x 0.30 x 0.10 mm 3 Theta range for data collection 2.49 to 27.50. Index ranges -11<=h<=11, -8<=k<=8, -19<=l<=19 Reflections collected 7218 Independent reflections 1905 [R(int) = 0.0292] Completeness to theta = 27.50 100.0 % Absorption correction Semi-empirical from equivalents Max. and min. transmission 0.9891 and 0.9551 Refinement method Full-matrix least-squares on F 2 Data / restraints / parameters 1905 / 0 / 135 Goodness-of-fit on F 2 1.057 Final R indices [I>2sigma(I)] R1 = 0.0504, wr2 = 0.1429 R indices (all data) R1 = 0.0667, wr2 = 0.1575 Largest diff. peak and hole 0.297 and -0.293 e.å -3 S13
Table S2. Bond lengths for the DHNA crystal structure Bond Lengths (Å) O(1)-C(11) 1.2303(18) C(5)-C(10) 1.424(2) O(2)-C(7) 1.3503(16) C(5)-C(6) 1.4271(19) O(3)-C(1) 1.3560(18) C(6)-C(7) 1.4269(19) C(1)-C(2) 1.380(2) C(7)-C(8) 1.386(2) C(1)-C(6) 1.4221(19) C(8)-C(9) 1.4155(19) C(2)-C(3) 1.391(2) C(8)-C(11) 1.4409(19) C(3)-C(4) 1.367(2) C(9)-C(10) 1.355(2) C(4)-C(5) 1.4098(19) Table S3. Hydrogen bond distances and angles for DHNA crystal structure D-H A d(d-h)/å d(h A)/Å d(d A)/ Å <(DHA)/ O(2)-H(2)...O(1) 0.92(2) 1.73(2) 2.5603(14) 148(2) O(3)-H(3)...O(2) 0.87(2) 1.90(2) 2.6433(15) 143(2) Table S4. The photophysical properties of DHNA and 3 Compounds observed λ abs/nm (ε/m 1 cm 1 ) λ monitor /nm Q. Y (%) τ obs (pre-exp. factor) DHNA 400 (1.1 10 4 ) 520 650 0.24 1.1 ± 0.2 ps a (0.68); 53 ± 3.6 ps a,b (0.32) 1.1 ± 0.3ps a (-0.43); 54 ± 3.2 ps a,b (0.57) 3 365 (5.5 10 3 ) 450 0.26 1.75 ns c DHNA (solid) 520 650 5.0 228 ± 20 ps b 223 ± 22 ps b a. The lifetime was measured using an ultrafast fluorescence upconversion technique. b. Lifetime was measured by a TCSPC system with femtosecond excitation pulses. c. Lifetime was measured by a TCSPC system with a pulsed hydrogen-filled lamp as the excitation source. S14
Table S5. Calculated bond lengths (Å) of the normal form (N), tautomer A (TA), and TS1 (N TA) on S 0 in various solvents normal form (N) TS1 (N TA) tautomer A (TA) cyclohexane CH 2 Cl 2 CH 3 CN cyclohexane CH 2 Cl 2 CH 3 CN cyclohexane CH 2 Cl 2 CH 3 CN O(3) H(3) 0.975 0.976 0.976 0.983 0.983 0.984 0.990 0.991 0.992 O(2) H(3) 1.786 1.783 1.781 1.748 1.742 1.740 1.693 1.683 1.680 O(2) H(2) 1.009 1.008 1.008 1.236 1.234 1.234 1.547 1.550 1.551 O(1) H(2) 1.604 1.609 1.610 1.179 1.179 1.179 1.023 1.022 1.022 C(1) O(3) 1.356 1.358 1.359 1.351 1.354 1.355 1.347 1.350 1.352 C(7) O(2) 1.348 1.349 1.349 1.313 1.314 1.315 1.287 1.289 1.289 C(11) O(1) 1.248 1.249 1.250 1.284 1.285 1.286 1.311 1.312 1.312 S15
Table S6. Calculated bond lengths (Å) of the normal form* (N*), tautomer A* (TA*), and TS1* (N* TA*) on S 1 in various solvents normal form* (N*) TS1* (N* TA*) tautomer A* (TA*) cyclohexane CH 2 Cl 2 CH 3 CN cyclohexane CH 2 Cl 2 CH 3 CN cyclohexane CH 2 Cl 2 CH 3 CN O(3) H(3) 0.990 0.987 0.987 0.996 0.994 0.993 1.021 1.020 1.020 O(2) H(3) 1.718 1.732 1.736 1.687 1.698 1.700 1.565 1.565 1.565 O(2) H(2) 1.053 1.048 1.047 1.158 1.154 1.154 1.608 1.614 1.615 O(1) H(2) 1.477 1.487 1.489 1.282 1.285 1.284 1.017 1.014 1.014 C(1) O(3) 1.338 1.340 1.340 1.337 1.340 1.341 1.334 1.337 1.338 C(7) O(2) 1.359 1.359 1.359 1.346 1.347 1.347 1.317 1.318 1.319 C(11) O(1) 1.286 1.292 1.294 1.299 1.306 1.307 1.330 1.335 1.337 S16
Table S7. Calculated bond lengths (Å) of the tautomer A* (TA*), tautomer B* (TB*), and TS2* (TA* TB*) on S 1 in various solvents tautomer A* (TA*) TS2* (TA* TB*) tautomer B* (TB*) cyclohexane CH 2 Cl 2 CH 3 CN cyclohexane CH 2 Cl 2 CH 3 CN cyclohexane CH 2 Cl 2 CH 3 CN O(3) H(3) 1.021 1.020 1.020 1.269 1.228 1.221 1.450 1.512 1.526 O(2) H(3) 1.565 1.565 1.565 1.168 1.200 1.205 1.062 1.037 1.032 O(2) H(2) 1.608 1.614 1.615 1.729 1.730 1.730 1.766 1.786 1.791 O(1) H(2) 1.017 1.014 1.014 0.995 0.995 0.995 0.990 0.986 0.986 C(1) O(3) 1.334 1.337 1.338 1.307 1.312 1.314 1.295 1.295 1.295 C(7) O(2) 1.317 1.318 1.319 1.343 1.343 1.343 1.354 1.359 1.360 C(11) O(1) 1.330 1.335 1.337 1.330 1.336 1.338 1.329 1.333 1.335 S17
Table S8. Calculated harmonic vibrational frequencies (cm 1 ) of the O H stretching and imaginary frequencies on S 0 in cyclohexane normal form (N) TS1 (N TA) tautomer A (TA) 2977 3022 (O(2) H(2) and C(11) H(11) asymmetric stretching) (O(2) H(2) and C(11) H(11) symmetric stretching) 1015 i (Imaginary frequency) 2774 (O(2) H(2) stretching) 3125 (C(11) H(11) stretching) 3183 (C(11) H(11) stretching) 3645 (O(3) H(3) stretching) 3493 (O(3) H(3) stretching) 3345 (O(3) H(3) stretching) H(2) and H(3) substituted by deuterium 2977 (O(2) D(2) stretching) 756 i (Imaginary frequency) 2037 (O(2) D(2) stretching) 2654 (O(3) D(3) stretching) 2545 (O(3) D(3) stretching) 2439 (O(3) D(3) stretching) S18
Table S9. Calculated harmonic vibrational frequencies (cm 1 ) of the O H stretching and imaginary frequencies on S 1 in cyclohexane normal form* (N*) TS1* (N* TA*) tautomer A* (TA*) 2309 (O(2) H(2) stretching) 766 i (Imaginary frequency) 2756 3370 (O(3) H(3) stretching) 3247 (O(3) H(3) stretching) 2889 (O(1) H(2) and O(3) H(3) asymmetric stretching) (O(1) H(2) and O(3) H(3) symmetric stretching) H(2) and H(3) substituted by deuterium 1720 (O(2) D(2) stretching) 574 i (Imaginary frequency) 2018 2457 (O(3) D(3) stretching) 2369 (O(3) D(3) stretching) 2116 (O(1) D(2) and O(3) D(3) asymmetric stretching) (O(1) D(2) and O(3) D(3) symmetric stretching) S19
Table S9. Continued tautomer A* (TA*) TS2* (TA* TB*) tautomer B* (TB*) 2756 2889 2018 2116 (O(1) H(2) and O(3) H(3) stretching) (O(1) H(2) and O(3) H(3) stretching) (O(1) D(2) and O(3) D(3) asymmetric stretching) (O(1) D(2) and O(3) D(3) symmetric stretching) 751 i (Imaginary frequency) 2237 (O(2) H(3) stretching) 3284 (O(1) H(2) stretching) 3398 (O(1) H(2) stretching) H(2) and H(3) substituted by deuterium 558 i (Imaginary frequency) 1670 (O(2) D(3) stretching) 2391 (O(1) D(2) stretching) 2474 (O(1) D(2) stretching) S20
Calculated Bond Lengths and Stretching Vibrational Frequencies of the O H Bonds As shown in Table S5, the O(3) H(3) bond lengths of the N, TS1, and TA on the ground state (S 0 ) in cyclohexane were calculated to be 0.975, 0.983, and 0.990 Å, respectively. On the other hand, the calculated O(3) H(3) stretching vibrational frequencies of these conformations on S 0 were 3645, 3493, and 3345 cm 1, respectively (see Table S8). The O H bond strengths were significantly affected by the corresponding H(3) Ο(2) hydrogen bond strengths. The hydrogen bond strength increases from N, TS1, to TA, so the O(3) H(3) bond length increases and the O(3) H(3) stretching frequency decreases from N to TA. On the 1 st singlet excited state (S 1 ), the N*, TS1*, and TA* in cyclohexane were predicted to have stronger O(2) H(3) hydrogen bond than those on S 0. The O(3) H(3) bond lengths were calculated to be 0.990, 0.996, and 1.021 Å (Table S6), respectively. The calculated O(3) H(3) stretching vibrational frequencies of these conformations on S 1 were 3370, 3247, and 2889 cm 1 (Table S9) which are significantly lower than those on S 0. We noticed that the bond length of the O(3) H(3) in TA* was nearly the same as that of O(1) H(2) (1.017 Å), but they are quite different in TA. The O(2) H(2) bond length (1.053 Å) in N* is very long because of the very strong O(1) H(2) hydrogen bond. The corresponding OH stretching frequency is only 2309 cm 1 which is even lower than the O(3) D(3) frequency in TA*. The O(2) H(3) in TB* was predicted to be the longest O H bond (1.062 Å) and with the lowest vibrational frequency (2237 cm 1 ). It suggested that O(3) H(3) in TB* is the strongest hydrogen bond in the current system. The O(2) D(3) frequency in TB* was predicted to be as low as 1670 cm 1. S21
Table S10. Calculated Transition State Theory (TST) rate constants (s 1 ) and kinetic isotope effects (KIEs) at various temperature (K) in cyclohexane Temperature N TA N* TA* TA* TB* Rate constant Rate constant KIE 200 K 1.12 10 12 1.59 10 14 2.61 10 12 250 K 1.55 10 12 8.48 10 13 3.30 10 12 303 K 1.96 10 12 5.53 10 13 3.95 10 12 H(2) and H(3) replaced by deuterium 200 K 1.63 10 11 3.70 10 13 5.00 10 11 250 K 3.24 10 11 2.60 10 13 8.72 10 11 303 K 5.24 10 11 2.05 10 13 1.31 10 12 200 K 6.89 4.31 5.23 250 K 4.79 3.26 3.78 303 K 3.74 2.69 3.02 Table S11. Calculated zero-point energy differences ( ZPEs, ZPE TS ZPE reactant, kcal/mol) in cyclohexane N TA N* TA* TA* TB* ZPE H 2.19 1.82 1.97 a ZPE D 1.45 1.24 1.31 a ZPE D represents the calculated ZPEs for the H(2) and H(3) replaced by deuterium S22
Calculated the KIEs at Low Temperature The absence of measured KIEs on S 1 suggested that the reaction bottleneck might not be located at the TS where the transferred hydrogen atom moves from the donor to the acceptor. Instead, we suspect that the bottleneck might be mainly related to the entropic effects due to the excited large-amplitude bending or twisting vibrations of the TA* which may easily disrupt the hydrogen boding along which the proton transfer occur. At lower temperature, the entropic effects are supposed to be less important and the TS might become the reaction bottleneck if the low-frequency large-amplitude motions can be quenched more effectively. The calculated KIEs by TST theory at 250 and 200 K were 3.8 and 5.2, respectively, which are significantly larger than the value at 303 K. There is a chance that the deuterium KIEs can be observed at lower temperature. Low Frequency Modes Using an ultrashort pulse of e.g. <10 fs pulse, the oscillation of time-resolved signal at early time has been occasionally resolved for several ESIPT system via fluorescence upconversion or transient absorption. For these cases, the time-domain signal can be Fourier transformed to frequency-domain to obtain the corresponding low frequency motions that modulate the hydrogen bond and hence induce ESIPT. Experimentally we have been trying very hard in attempts to resolve the possible early time oscillation but unfortunately in vain. This may be due to a much longer pulse excitation (~120 fs) used in the current experimental setup, together with relatively low signal to noise ratio. On the other hand, from the computational approaches, it is hard to pin down which modes exactly cause the slower rate constants and the absence of the KIEs. It is reasonable to assume that upon excitation, some of the low frequency modes such as the various low-frequency ring bending and twisting modes are in highly excited states and exhibit large amplitude motions. These motions may easily modulate/disrupt the hydrogen bonding along which the proton transfer occurs. In the current case, all the modes below 200 cm -1 (3 in total: 76, 113, and 168 cm -1 ) of TA* are susceptible. In the language of thermodynamics, TA* may have a much lower free energy (larger entropy) than expected and thus the TS is harder to reach and the rate constants are lower than those as expected based on the equilibrium distribution. Since these large amplitude motions are not sensitive to the mass of the hydrogen being transferred, so no KIEs were observed. S23
Table S12. Calculated absorption wavelengths (nm) of the DHNA system in various solvents cyclohexane CH 2 Cl 2 CH 3 CN TD-B3LYP/6-31+G(d,p) TD-B3LYP/6-311+G(2df,2pd)// B3LYP/6-31+G(d,p) N 407 407 405 TA 427 427 425 N 409 410 409 TA 429 431 429 Table S13. Calculated emission wavelengths (nm) of the DHNA system in various solvents cyclohexane CH 2 Cl 2 CH 3 CN TD-B3LYP/6-31+G(d,p) TD-B3LYP/6-311+G(2df,2pd)// TD-B3LYP/6-31+G(d,p) N* 459 466 469 TA* 498 506 509 TB* 599 618 622 N* 464 460 458 TA* 503 496 493 TB* 605 597 590 S24