vibrational Supplementary density of the Beyer-
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1 Supplementary Figure 1 Vibrational ion distributions and density of vibrational states (per cm -1 ). a, picene +, b, pentacene +. Thermal ion fraction distributions of picene and pentacene cations calculated at 20, 80 and 200 C. To calculate the density of vibrational statess ρ we employed the direct counting method based on the Beyer- Swinehart algorithm and the spin-doublet ground-state mode frequencies of picene + and pentacene +. We used a logarithmic scale to plot ρ. 1
2 Supplementary Figure 2 Data sample of dissociation yield β functions retrieved from spectral scans (single FEL-ion-trap measurements) of multiple-photon product ions. The spectral scans A0, A1, A2, A5 and B2 correspond to picene +, and the spectral scanss D1, D3, D5, D6 and D7 correspond to pentacene +. The dotted lines show the final frequency peak positions of measured bands (Fig. 3, Table 1). These typical single measurements exhibit large statistical random fluctuations taking place during experiments but which cancel out upon the averaging procedure (see for instance the partial spectra averages in Supplementary Fig. 3,4). 2
3 Supplementary Figure 3 Normalized partial action spectra (β) of picene + corrected from FEL power variations. (top) IR action spectrum retrieved from a data set sample (B2B3) composed of 2 FEL spectral scans of parent and productt ions. (bottom) IR action spectrum retrieved from a data set sample (A) composed of 5 FEL spectral scans of parent and product ions. Both data sets were measured within a week apart in independent FEL-ion-trap experimental sessions. Apart from the difference in band broadenings and resolution, the spectral deconvolution band fits (Supplementary Tables 3, 4) reveal that spectrum B2B3 reproduces the absorption features seen in spectrum A in the cm -1 range. Data set labels are arbitrary. 3
4 Supplementary Figure 4 Normalized partial action spectra (β) of pentacene corrected from FEL power variations. (top) IR action spectrum retrieved from a data set sample (D1D3D5) composed of 4 FEL spectral scans of parent and product ions. (bottom) IR action spectrum retrieved from a dataa set sample (D6D7) composed of 2 FEL spectral scans of parent and product ions. Both data sets were measured during a FEL-ion-trashown) was recorded within a week apart. Thee spectral deconvolution band fits (Supplementary Tables 5, 6) applied to partial spectra retrieved from all data sets show the absorption features exhibited in the final spectrum. Data set labels are arbitrary. experimental session. An additional data sample set of 6 FEL scans (not e + 4
5 Supplementary Table 1 Electronic configurations and π states of picene One-electron excitation neutral charged radical cation 4a 2 4b 1 ( ) (*) 4b 1 5a 2 ( ) 4a 2 5b 1 ( ) 3b 1 5a 2 (*) ( ) State (ev) Electronic single configuration 1 A 1 (1a 1 ) 2 (2a 1 ) 2 (1b 1 ) 2 (1a 2 ) 2 (1b 2 ) 2 (2a 2 ) 2 (2b 1 ) 2 (3b 1 ) 2 (3a 2 ) 2 (4a 2 ) 2 (4b 1 ) 2 2 B 1 (0.0) 2 A 2 (0.28) 2 A 2 (2.66) 2 A 2 (3.56) 2 A 2 (4.32) (1a 1 ) 2 (1b 1 ) 1 (2a 1 ) 1 (2a 1 ) 1 (1b 2 ) 1 (1b 2 ) 1 (1b 1 ) 1 (1a 2 ) 2 (2a 2 ) 2 (2b 1 ) 2 (3b 1 ) 2 (3a 2 ) 2 (4a 2 ) 2 (4b 1 ) 1 (4b 1 ) 0 (1a 1 ) 2 (1a 1 ) 2 (2b 1 ) 2 (2a 1 ) 1 (1b 2 ) 1 (1b 2 ) 1 (1a 2 ) 1 (1a 2 ) 2 (2b 1 ) 2 (3b 1 ) 2 (3a 2 ) 2 (4a 2 ) 1 (4b 1 ) 1 (4b 1 ) 1 (4a 2 ) 0 (1a 1 ) 2 (1b 2 ) 2 (1b 1 ) 1 (2a 1 ) 1 (2a 1 ) 1 (1a 2 ) 1 (1a 2 ) 1 (1b 1 ) 1 (2a 2 ) 2 (2b 1 ) 2 (3b 1 ) 2 (3a 2 ) 2 (4a 2 ) 2 (5a 2 ) 1 (4b 1 ) 0 (1a 1 ) 2 (2a 1 ) 2 (1b 1 ) 2 (1a 2 ) 1 (1b 2 ) 1 (1b 2 ) 1 (1a 2 ) 1 (2a 2 ) 2 (2b 1 ) 2 (3b 1 ) 2 (3a 2 ) 2 (4b 1 ) 1 (4a 2 ) 1 (5b 1 ) 1 (4b 1 ) 0 (1a 1 ) 2 (2a 1 ) 2 (1b 2 ) 2 (1a 2 ) 2 (1b 1 ) 2 (2a 2 ) 2 (2b 1 ) 2 (3b 1 ) 1 (3a 2 ) 1 (3a 2 ) 1 (4a 2 ) 1 (4a 2 ) 1 (5a 2 ) 1 (4b 1 ) 1 (3b 1 ) 0 (*) Unbound excited states. Vertical arrows represent α ( ) and β ( ) electrons. Supplementary Table 2 Electronic configurations and π states of pentacene One-electron excitation neutral charged radical cation 3b 2g 2b 3u ( ) 2a u 3b 2g ( ) 2b 1g 2b 3u ( ) 2b 1g 2b 3u ( ) State (ev) Electronic single configuration 1 A g (1b 3g ) 2 (1b 2u ) 2 (1a g ) 2 (1b 1g ) 2 (1b 2g ) 2 (1a u ) 2 (1b 3u ) 2 (2b 2g ) 2 (2b 1g ) 2 (2a u ) 2 (3b 2g ) 2 2 B 2g (0.0) 2 B 3u (1.18) 2 A u (1.27) 2 A u (2.70) 2 A u (3.23) (1b 3g ) 2 (1b 2u ) 2 (1a g ) 2 (1b 1g ) 2 (1b 2g ) 2 (1a u ) 2 (1b 3u ) 2 (2b 2g ) 2 (2b 1g ) 2 (2a u ) 2 (3b 2g ) 1 (3b 2g ) 0 (1b 3g ) 2 (1b 2u ) 2 (1a g ) 2 (1b 1g ) 2 (1b 2g ) 2 (1a u ) 2 (1b 3u ) 2 (2b 2g ) 2 (2b 1g ) 2 (2a u ) 2 (2b 3u ) 1 (3b 2g ) 0 (1b 3g ) 2 (1b 2u ) 2 (1a g ) 2 (1b 1g ) 2 (1b 2g ) 2 (1a u ) 2 (1b 3u ) 2 (2b 2g ) 2 (2b 1g ) 2 (2a u ) 1 (3b 2g ) 1 (3b 2g ) 1 (2a u ) 0 (1b 3g ) 2 (1b 2u ) 2 (1a g ) 2 (1b 2g ) 1 (1b 1g ) 1 (1b 1g ) 1 (1b 2g ) 1 (1a u ) 2 (1b 3u ) 2 (2b 2g ) 1 (2b 1g ) 1 (2a u ) 1 (2b 2g ) 1 (3b 2g ) 1 (2a u ) 1 (2b 3u ) 1 (3b 2g ) 0 (1b 3g ) 2 (1b 2u ) 2 (1a g ) 2 (1a g ) 1 (1b 1g ) 1 (1b 2g ) 2 (1a u ) 2 (1b 3u ) 2 (2b 2g ) 2 (2b 1g ) 1 (2a u ) 1 (2a u ) 1 (2b 3u ) 1 (3b 2g ) 1 (2b 1g ) 0 Vertical arrows represent α ( ) and β ( ) electrons. 5
6 Supplementary Table 3 Characterization of dissociation yield (β) action bands of picene + (B2B3 data set) normalized and corrected from FEL power curve IR multiple-photon action Deconvoluted band fit components band ṽ exp β Peak ṽ c ε w ε A ε h a r a b r b b l c d e f Definition of column headings in Table 2. Statistics: Reduced Chi-Sqr 3.97E-03, Residual Sum of Squares 1.65, R-Square (COD) , Adj. R-Square Supplementary Table 4 Characterization of dissociation yield (β) action bands of picene + (A data set) normalized and corrected from FEL power curve IR multiple-photon action Deconvoluted band fit components band ṽ exp β Peak ṽ c ε w ε A ε h a r a b r b b l c Definition of column headings in Table 2. Statistics: Reduced Chi-Sqr , Residual Sum of Squares , R-Square(COD) , Adj. R-Square
7 Supplementary Table 5 Characterization of dissociation yield (β) action bands of pentacene + (D1D3D5 data set) normalized and corrected from FEL power curve IR multiple-photon action Deconvoluted band fit components band ṽ exp β Peak ṽ c ε w ε A ε h a r a b r b c r c c l d e r e e l f Definition of column headings in Table 2. Statistics: Reduced Chi-Sqr 2.56E-03, Residual Sum of Squares 2.11, R-Square (COD) , Adj. R-Square Supplementary Table 6 Characterization of dissociation yield (β) action bands of pentacene + (D6D7 data set) normalized and corrected from FEL power curve IR multiple-photon action Deconvoluted band fit components band ṽ exp β Peak ṽ c ε w ε A ε h a r a b r b c r c c l d e r e e l f Definition of column headings in Table 2. Statistics: Reduced Chi-Sqr 2.61E-03, Residual Sum of Squares 2.04, R-Square (COD) , Adj. R-Square
8 Supplementary Tables 7 16 Calculated harmonic frequencies (freq, cm -1 ) and IR activity (INT, km/mol) of vibrational normal modes (ip = in-plane, oop = out-ofplane) of pentacene and picene in neutral (spin-singlet) and charged (spin-doublet) electronic states: 8
9 Supplementary Table 7 PENTACENE (B3LYP/6-311G**) mode 0.97*freq INT SYM B3U AU B1G B1U B2G B3U B3G AU AG B1G B2G B1U B3U B3G B3U B1G B3U B1G B2U B3G AU B2G B1U AG B2U AG AU B3G B2U B3U B1G B2G AG AU B2G AG B1U B2G B3U AU B2G B2U 9
10 B1G AU B2G B1U B3U B3G B1G B3U AU B2G B2U AG B2U B1U B3G AG B2U B3G AG B1U B3G B2U B1U B3G B3G B1U AG B2U B1U AG B2U B3G B2U AG B2U B1U AG B2U AG AG B2U B3G B3G B1U B3G B1U 10
11 B1U B3G AG B1U B2U B3G B1U AG B2U AG B3G B1U B2U AG TOTAL INT Total INT AU 0 0 % ip Total INT B1U % ip Total INT B2U % oop Total INT B3U % Total INT % INT B3U / (INT B2U + INT B1U) INT B3U / INT B2U INT CHstr /INT CHoop
12 Supplementary Table 8 PENTACENE + (B3LYP/6-311G**) mode 0.97*freq INT SYM B3U AU B1G B1U B2G B3U B3G AU AG B1G B2G B1U B3U B3U B3G B1G B1G B3U B2U B3G AU B2G B1U AG B2U AG AU B3G B2G B2U AG AU B3U B1G B2G AG B1U B2G AU B3U B2U B2G 12
13 B1U B1G AU B3G B2G B3U B1G B3U AU B2G B2U AG B1U B3G B2U AG B3G B2U B1U AG B2U B3G B1U B3G B3G B1U AG B1U B2U AG B2U AG B2U B3G B2U B1U AG B2U AG B3G B2U B3G AG B1U B1U B3G 13
14 B1U B3G AG B2U B1U AG B1U B3G B2U AG B3G B1U B2U AG TOTAL INT Total INT AU 0 0 % ip Total INT B1U % ip Total INT B2U % oop Total INT B3U % Total INT % INT B3U / (INT B2U + INT B1U) INT B3U / INT B2U INT CHstr /INT CHoop
15 Supplementary Table 9 PENTACENE + (ROHF/3-611G**) mode 0.97*freq INT SYM B3U AU B1G B1U B2G B3U B3G AU AG B1G B1U B2G B3U B3G B3U B1G B2U B1G B3U B3G AU B2G B1U AG B2U AG AU B3G B2G B2U AG AU B2G B3U B1G AG B1U B2G AU B2U B1U B3U 15
16 B2G B3G AU B1G B2G B3U B2U AG B1G B3U AU B2G B2U B1U B2U B3G AG B3G B1U AG B2U B3G B1U B3G AG B3G B1U B2U B2U B1U AG AG B2U B3G B1U B2U B3G AG B2U AG B1U B3G B2U AG B1U B3G 16
17 B1U B3G AG B2U B1U B3G AG B2U B1U AG B3G B1U B2U AG TOTAL INT Total INT AU 0 0 % ip Total INT B1U % ip Total INT B2U % oop Total INT B3U % Total INT % INT B3U / (INT B2U + INT B1U) INT B3U / INT B2U INT CHstr /INT CHoop
18 Supplementary Table 10 PENTACENE + (B/3-611G**) mode 0.97*freq INT SYM B3U AU B1G B1U B2G B3U AU B3G AG B1G B2G B1U B3U B3U B3G B1G B1G B3U B2U AU B3G B2G B1U AG B2U AG AU B3G B2U B2G AG B3U AU B1G B2G AG B1U B2G AU B3U B2U 18
19 B2G B1G AU B1U B2G B3U B3G B1G B3U AU B2G B2U AG B1U B3G B2U B3G AG B2U AG B1U B3G B2U B3G AG B1U B1U B3G B2U AG B1U B2U AG B2U B3G B1U B2U AG B2U AG B3G B2U AG B3G B1U B1U 19
20 B3G B1U AG B3G B2U B1U B3G AG B1U B2U AG B3G B1U B2U AG Total INT Total INT AU 0 0 % ip Total INT B1U % ip Total INT B2U % oop Total INT B3U % Total INT % INT B3U / (INT B2U + INT B1U) INT B3U / INT B2U INT CHstr /INT CHoop
21 Supplementary Table 11 PENTACENE + (BLYP/3-611G**) mode 0.97*freq INT SYM B3U AU B1G B1U B2G B3U B3G AU AG B1G B2G B1U B3U B3U B3G B1G B1G B3U B2U B3G AU B2G B1U AG B2U AG AU B3G B2G B2U AG B3U B1G AU B2G AG B1U B2G AU B3U B2U 21
22 B2G B1G AU B1U B3G B2G B3U B1G B3U AU B2G B2U AG B1U B3G B2U AG B3G B2U B1U AG B3G B2U B3G B1U B3G B1U AG B1U B2U AG B2U AG B2U B3G B1U B2U AG B2U AG B2U B3G AG B3G B1U B1U 22
23 B3G B1U B3G AG B2U B1U AG B3G B1U B2U AG B3G B1U B2U AG Total INT Total INT AU 0 0 % ip Total INT B1U % ip Total INT B2U % oop Total INT B3U % Total INT % INT B3U / (INT B2U + INT B1U) INT B3U / INT B2U INT CHstr /INT CHoop
24 Supplementary Table 12 PICENE (B3LYP/3-611G**) mode 0.97*freq INT SYM B A B A A A B B A B A A B A A B B B A B B A B A A A B B A A B A B A B B B A B A2 24
25 B A B A A A B A B B A B A B A B A A B B A A B B A B A A B A A B A B B A A B B A A B B A B A1 25
26 A B B A B A B A B A B A B B A A1 Total INT ip Total INT A % Total INT A2 0 0 % oop Total INT B % ip Total INT B % Total INT % INT B1/ (INT B2 + INT A1) INT B1 / INT B INT CHstr /INT CHoop
27 Supplementary Table 13 PICENE + (B3LYP/3-611G**) mode 0.97*freq INT SYM A B B A A A B B A B A A B A A B B B B A A B A B A A B B A A B B A A B B A B B A B2 27
28 A B A A A B A B B A B A B A B A B A B A A B B A A A B B A B A A B B A B A A B B A B A B A B2 28
29 A B A B A B A B A B A B B A A1 Total INT ip Total INT A % Total INT A2 0 0 % oop Total INT B % ip Total INT B % Total INT % INT B1/ (INT B2 + INT A1) INT B1 / INT B INT CHstr /INT CHoop
30 Supplementary Table 14 PICENE + (ROHF/6-311G**) mode 0.97*freq INT SYM A B B A A A B B B A A B A B A A B B B B A A B A A A B B A A B B A B A B A B B A B1 30
31 A A B B A A B A B A B A B B A B A A B A B A B A B A A B A B A B A A B A B B A B A B A B A B2 31
32 A B A B A B A B A B A B B A A1 Total INT ip Total INT A % Total INT A2 0 0 % oop Total INT B % ip Total INT B % Total INT % INT B1/ (INT B2 + INT A1) INT B1 / INT B INT CHstr /INT CHoop
33 Supplementary Table 15 PICENE + (B/3-611G**) mode 0.97*freq INT SYM A B B A A A B B A B A A B A A B B B B A A B A B A A B B A A B B A A B B A B B A A2 33
34 B B A A A B A B B A B A B A B A B B A A A B B A A A B A B B A A B B A B A B A B A A B B A B2 34
35 A B A B A B A B A B A B B A A1 Total INT ip Total INT A % Total INT A2 0 0 % oop Total INT B % ip Total INT B % Total INT % INT B1/ (INT B2 + INT A1) INT B1 / INT B INT CHstr /INT CHoop
36 Supplementary Table 16 PICENE + (BLYP/3-611G**) mode 0.97*freq INT SYM A B B A A A B B A B A A B A A B B B B A A B A B A A B B A A B B A A B B A B B A A B1 36
37 B A A A B A B B A B A B A B A B A B A A B B A A A B B A B A A B B A B A B A B A A B B A B A1 37
38 B A B A B A B A B A B B A A1 Total INT ip Total INT A % Total INT A2 0 0 % oop Total INT B % ip Total INT B % Total INT % INT B1/ (INT B2 + INT A1) INT B1 / INT B INT CHstr /INT CHoop
39 Supplementary Table 17 All-in mode contributions (%) to IR activity Picene + ROHF B BLYP B3LYP Modes 35A (27) ν 1, ν 2 ν 35 16B (39) ν 53, ν 54 ν 68 34B (34) ν 69, ν 70 ν 102 Pentacene + 17B 1u (32) ν 60, ν 61 ν 76 17B 2u (27) ν 77, ν 78 ν 93 9B 3u (41) ν 94, ν 95 ν 102 IR-active modes grouped by symmetry of picene + (C 2v ) and pentacene + (D 2h ) according to ROHF, B, BLYP and B3LYP quantum-chemical methods. The contributions in parenthesis belong to neutral state. The basis set used is 6-311G**. Supplementary Table 18 C 2 H 2 (1) and C 4 H 4 (2) loss ion signals of picene + action bands recorded without FEL power-level attenuation (0 db; B0B1) (1) m/z db (2) m/z db band ṽ exp (cm -1 ) S ion (arb. u.) ṽ exp (cm -1 ) S ion (arb. u.) Δṽ exp (1)-(2) Δṽ exp (1)-(2) a r a b r b b l c d e f avg 0.30 sdev
40 Supplementary Table 19 C 2 H 2 (1) and C 4 H 4 (2) loss ion signals of picene + action bands recorded with FEL power-level attenuation (3 db; B2B3) (1) m/z db (2) m/z db band ṽ exp (cm -1 ) S ion (arb. u.) ṽ exp (cm -1 ) S ion (arb. u.) Δṽ exp (1)-(2) Δṽ exp (1)-(2) a r a b r b b l c d e f avg 0.22 sdev 0.13 band Δṽ exp3db-0db (1) Supplementary Table 20 Percentage differences between band frequencies and product ion signals, and channel ion signal ratios at 0 and 3 db FEL power levels. Signals increments are positive (+) and decrements are negative (-). (1) m/z 252 (2) m/z 226 (1) m/z 252 (2) m/z 226 m/z 252 : m/z 226 Δṽ exp3db-0db (1) Δṽ exp3db-0db (2) Δṽ exp3db-0db (2) ΔS 0dB-3dB (1) ΔS 0dB-3dB (2) 0 db 3 db a r a b r b b l c d e f avg 0.81 avg 0.95 avg sdev 0.66 sdev 0.74 sdev
41 Supplementary Table 21 Characterization of absolute dissociation yield (β * ) action bands of picene + (B0B1 data set) recorded without FEL power-level attenuation IR multiple-photon action Deconvoluted band fit components band ṽ exp β * Peak ṽ c ε w ε A ε h a r a b r b b l c d e f Definition of column headings in Table 2. Statistics: Reduced Chi-Sqr 8.85E-07, Residual Sum of Squares 1.76E-04, R-Square(COD) , Adj. R-Square Supplementary Table 22 Characterization of absolute dissociation yield (β * ) action bands of picene + (B2B3 data set) recorded with FEL power-level attenuation (3 db) IR multiple-photon action Deconvoluted band fit components band ṽ exp β * Peak ṽ c ε w ε A ε h a r a b r b b l c d e f Definition of column headings in Table 2. Statistics: Reduced Chi-Sqr 9.40E-07, Residual Sum of Squares 3.91E-04, R-Square (COD) , Adj. R-Square
42 Supplementary Table 23 Characterization of absolute dissociation yield (β * ) action bands of pentacene + (D6D7 data set) recorded at power values between B0B1 and B2B3 power values IR multiple-photon action Deconvoluted band fit components band ṽ exp β * Peak ṽ c ε w ε A ε h a r a b r b c r c c l d e r e e l f Definition of column headings in Table 2. Statistics: Reduced Chi-Sqr 8.68E-07, Residual Sum of Squares 6.81E-04, R-Square (COD) , Adj. R-Square
43 Supplementary Note 1 First-order mode perturbation expansion of Ψ g The molecular electronic ground-state wavefunction Ψ g at the equilibrium geometry written as a first-order expansion 1 of adiabatic one-electron state wavefunctions Ψ ξ with respect to the nuclear displacement normal coordinate Q: Ψ ;, 0, 0, 0, 0 (1) where the derivatives are evaluated at the equilibrium position (Q 0 ) represented by the subscript 0. The wavefunctions Ψ ξ (ξ=o: ground state; ξ=i: low-lying excited state) are anti-symmetric electronic configurations written as single Slater determinants of molecular orbital (MO) functions. The MOs are constructed from linear combinations of atomic orbitals (LCAOs). In this work the LCAOs are based on John Pople s splitvalence triple-ζ basis set 6-311G with polarization functions p and d (see Methods). Supplementary Reference 1. Marconi, G., Orlandi, G. & Malpezzi, L. Vibronic coupling and IR intensities. Chem. Phys. Lett. 61, (1979). 43
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