Supporting information for: Second-order Nonlinear Optical Properties of. Stenhouse Photoswitches: Insights from. Density Functional Theory
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1 Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the wner Societies 218 Supporting information for: Second-order Nonlinear ptical Properties of Stenhouse Photoswitches: Insights from Density Functional Theory Claire Tonnelé, Benoît Champagne, Luca Muccioli,, and Frédéric Castet, Institut des Sciences Moléculaires (ISM, UMR CNRS 5255), University of Bordeaux, 351 Cours de la Libération, 3345 Talence, France Unité de Chimie Physique Théorique et Structurale, Chemistry Department, Namur Institute of Structured Matter, University of Namur, Belgium Department of Industrial Chemistry "Toso Montanari", University of Bologna, Viale Risorgimento 4, 4136 Bologna, Italy S1
2 Relative energies Table S1: Relative Gibbs free energies ( G, kcal/mol) between closed and open forms, calculated at the PCM:M6/6-311G(d) level in various solvents, using standard temperature (T = K) and pressure (p = 1 atm) conditions. Positive values indicate that the open form is more stable. Compound Toluene Dichloromethane Water BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S2
3 Molecular geometries R 2 First generation DASAs R 1 N H The geometrical parameters characterizing the strength of electron conjugation in open form pen form () Y DASAs, namely the bond length alternation (BLA) along5: the R 1 conjugated = Me, R 2 = Ph-Me path and the torsional angle within the acyclic- and cyclic-substituted N-methylaniline moieties, are defined in Scheme Second S1. generation For a conjugated DASAs chain containing N carbon atoms, the BLA is calculated as: R H pen form () BLA = 1 N 2 Y NH R 1 R 2 7: R = where d i,j is the interatomic distance between carbons i and j. Y Closed form (C) H N 2 Y R i=1 Closed form (C) MA: =, Y = CMe 2 BA: = NMe, Y = C : R 1 = Me, R 2 = Me 1: R 1 = Et, R 2 = Et 2: R 1 = Me, R 2 = Ph 3: R 1 = Me, R 2 = Ph-F 4: R 1 = Me, R 2 = Ph-Cl 6: R 1 = Me, R 2 = Ph-NMe 2 (d i+1,i+2 d i,i+1 ) ( 1) i+1 (1) 8: R = N N 9: R = Me 1: R = Me 2 N N N N H Y N H Y θ N H Y R 1 R 7 θ N H Y 2: R = H 3: R = F 4: R = Cl 5: R = Me 6: R = NMe 2 θ N H Y 8: R = H 9: R = Me 1: R = NMe 2 Scheme S1: pen form DASAs, with (in red) the conjugated segment considered for the calculation of the bond length alternation, and the torsional angle (θ, defined by the highlighted atoms) between the donor moiety and the conjugated chain. S3
4 Table S2: Bond Length Alternation (BLA, Å) along the conjugated path and torsional angle (θ, degrees) between the donor moiety and the conjugated chain, calculated at the PCM:M6/6-311G(d) level for open form DASAs in various solvents. See Scheme S1 for the definition of the geometrical parameters. Toluene Dichloromethane Water Comp. BLA θ BLA θ BLA θ BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S4
5 Ground state dipole moments Table S3: Ground state dipole moment µ S the PCM:M6-2/6-311+G(d) level. (D) calculated for open and closed DASAs at Toluene Dichloromethane Water Comp. pen Closed pen Closed pen Closed BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S5
6 Electronic absorption properties The variation of the total electron density from the ground (S ) to the excited state (S n ) can be defined as: ρ = ρ Sn ρ S = ρ + + ρ (2) where ρ + and ρ describe the increasing (> ) and decreasing (< ) areas of the electron density, respectively. The corresponding total charge displaced upon excitation is calculated as: q = ρ + (r)dr = ρ (r)dr (3) The charge transfer distance R is evaluated as the distance separating the centroids of the ρ + and ρ functions, while the R vector points from the negative to the positive center by convention. The photo-induced variation of the electric dipole moment is then defined as: µ = q R (4) S6
7 Table S4: Transition energy ( E ge, ev), transition wavelength (λ ge, nm), and oscillator strength (f ge ) for excitations from the ground state towards the low-lying bright (f.1) excited states of closed form DASAs, as well as photoinduced charge displacement ( q, e ), charge transfer distance ( R, Å), and variation of the permanent dipole moment ( µ, D) calculated at the PCM:M6-2/6-311+G(d) level in toluene. state E ge λ ge f ge q R µ BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S7
8 Table S5: Transition energy ( E ge, ev), transition wavelength (λ, nm), and oscillator strength (f ge ) for excitations from the ground state towards the low-lying bright (f ge.1) excited states of open form DASAs, as well as photoinduced charge displacement ( q, e ), charge transfer distance ( R, Å), and variation of the permanent dipole moment ( µ, D) calculated at the PCM:M6-2/6-311+G(d) level in toluene. state E ge λ ge f ge q R µ BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S8
9 Table S6: Transition energy ( E ge, ev), transition wavelength (λ ge, nm), and oscillator strength (f ge ) for excitations from the ground state towards the low-lying bright (f ge.1) excited states of closed form DASAs, as well as photoinduced charge displacement ( q, e ), charge transfer distance ( R, Å), and variation of the permanent dipole moment ( µ, D) calculated at the PCM:M6-2/6-311+G(d) level in dichloromethane. state E ge λ ge f ge q R µ BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S9
10 Table S7: Transition energy ( E ge, ev), transition wavelength (λ ge, nm), and oscillator strength (f ge ) for excitations from the ground state towards the low-lying bright (f ge.1) excited states of open form DASAs, as well as photoinduced charge displacement ( q, e ), charge transfer distance ( R, Å), and variation of the permanent dipole moment ( µ, D) calculated at the PCM:M6-2/6-311+G(d) level in dichloromethane. state E ge λ ge f ge q R µ BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S1
11 Table S8: Transition energy ( E ge, ev), transition wavelength (λ ge, nm), and oscillator strength (f ge ) for excitations from the ground state towards the low-lying bright (f ge.1) excited states of closed form DASAs, as well as photoinduced charge displacement ( q, e ), charge transfer distance ( R, Å), and variation of the permanent dipole moment ( µ, D) calculated at the PCM:M6-2/6-311+G(d) level in water. state E ge λ ge f ge q R µ BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S
12 Table S9: Transition energy ( E ge, ev), transition wavelength (λ ge, nm), and oscillator strength (f ge ) for excitations from the ground state towards the low-lying bright (f ge.1) excited states of open form DASAs, as well as photoinduced charge displacement ( q, e ), charge transfer distance ( R, Å), and variation of the permanent dipole moment ( µ, D) calculated at the PCM:M6-2/6-311+G(d) level in water. state E ge λ ge f ge q R µ BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S12
13 Calculated vertical transition energy (ev) Experimental absorption maximum (ev) Figure S1: Vertical transition energies of open form DASAs calculated at the PCM:M6-2/6-311+G(d) level in dichloromethane plotted against the experimental absorption maxima. The line is a linear fit (correlation coefficient R 2 =.97). S13
14 Second-order nonlinear optical properties Static second-order NL responses Table S1: Static β HRS and β J values (a.u.), as well as ρ and DR, calculated for closed and open form DASAs at the M6-2/6-311+G(d) level in toluene. Closed form pen form Contrast Comp. β HRS DR β J=1 β J=3 ρ β HRS DR β J=1 β J=3 ρ /C BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S14
15 25 2 β TSA (1 3 a.u.) β TDDFT (1 3 a.u.) Figure S2: Static β HRS values of open form DASAs evaluated in toluene using the two-state approximation (TSA), plotted against the values calculated using TDDFT. The line is a linear fit (correlation coefficient R 2 =.98; fit equation: βhrs T SA DDF T = 1.336βT HRS +.122). S15
16 Table S11: Static β HRS and β J values (a.u.), as well as ρ and DR, calculated for closed and open form DASAs at the M6-2/6-311+G(d) level in dichloromethane. Closed form pen form Contrast Comp. β HRS DR β J=1 β J=3 ρ β HRS DR β J=1 β J=3 ρ /C BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S16
17 Table S12: Static β HRS and β J values (a.u.), as well as ρ and DR, calculated for closed and open form DASAs at the M6-2/6-311+G(d) level in water. Closed form pen form Contrast Comp. β HRS DR β J=1 β J=3 ρ β HRS DR β J=1 β J=3 ρ /C BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S17
18 HRS hyperpolarizability (a.u.) BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA1 TL DCM WAT HRS hyperpolarizability (a.u.) MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA1 TL DCM WAT HRS hyperpolarizability (a.u.) BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA1 TL DCM WAT HRS hyperpolarizability (a.u.) MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA1 TL DCM WAT Figure S3: Static β HRS values (a.u.) calculated for closed (top) and open form (bottom) DASAs at the PCM:M6-2/6-311+G(d) level in toluene (TL), dichloromethane (DCM) and water (WAT). S18
19 Hhyperpolarizability contrast BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA1 TL DCM WAT Hhyperpolarizability contrast MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA1 TL DCM WAT Figure S4: Static β HRS contrasts calculated at the PCM:M6-2/6-311+G(d) level in toluene (TL), dichloromethane (DCM) and water (WAT). S19
20 Second-order NL responses Table S13: (λ = 197 nm) β HRS and β J values (a.u.), as well as ρ and DR, calculated for closed and open form DASAs at the M6-2/6-311+G(d) level in toluene. Closed form pen form Contrast Comp. β HRS DR β J=1 β J=3 ρ β HRS DR β J=1 β J=3 ρ /C BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S2
21 Table S14: (λ = 197 nm) β HRS and β J values (a.u.), as well as ρ and DR, calculated for closed and open form DASAs at the M6-2/6-311+G(d) level in dichloromethane. Closed form pen form Contrast Comp. β HRS DR β J=1 β J=3 ρ β HRS DR β J=1 β J=3 ρ /C BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S21
22 Table S15: (λ = 197 nm) β HRS and β J values (a.u.), as well as ρ and DR, calculated for closed and open form DASAs at the M6-2/6-311+G(d) level in water. Closed form pen form Contrast Comp. β HRS DR β J=1 β J=3 ρ β HRS DR β J=1 β J=3 ρ /C BA BA BA BA BA BA BA BA BA BA BA MA MA MA MA MA MA MA MA MA MA MA S22
23 BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA1 Figure S5: Static and dynamic β HRS values (a.u.) calculated for closed (top) and open form (bottom) DASAs at the PCM:M6-2/6-311+G(d) level in toluene. S23
24 BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA1 MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA1 Figure S6: Static and dynamic β HRS contrasts calculated at the PCM:M6-2/6-311+G(d) level in toluene. S24
25 BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA1 MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA1 Figure S7: Static and dynamic β HRS values (a.u.) calculated for closed (top) and open form (bottom) DASAs at the PCM:M6-2/6-311+G(d) level in dichloromethane. S25
26 BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA1 Figure S8: Static and dynamic β HRS contrasts calculated at the PCM:M6-2/6-311+G(d) level in dichloromethane. S26
27 BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA1 MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA1 Figure S9: Static and dynamic β HRS values (a.u.) calculated for closed (top) and open form (bottom) DASAs at the PCM:M6-2/6-311+G(d) level in water. S27
28 BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA MA MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA1 Figure S1: Static and dynamic β HRS contrasts calculated at the PCM:M6-2/6-311+G(d) level in water. S28
29 Unit sphere representation of the second-order NL responses The unit sphere representation (USR) is based on the computation of an effective SHG dipole defined as: µ eff = β : F 2 (θ, φ) (5) where β eff is the first hyperpolarizability tensor and F (θ, φ) is a unit vector of the polarization of the incident electric field with polarization defined for convenience in spherical coordinates (θ, φ). By sampling all possible incident polarizations defined by (θ, φ), a unit sphere is mapped out. Then, at each point (θ, φ) on the unit sphere surface, the corresponding µ eff arrow is plotted. Therefore, the (θ, φ) position on the sphere surface corresponds to the polarization of F 2 (θ, φ), whereas the µ eff arrow at (θ, φ) on the unit sphere provides information about the polarization and magnitude of the generated second harmonic at the particular incident field F 2 (θ, φ). Unit sphere representations reported in the main manuscript have been generated using the DrawMol software (DrawMol, V. Liégeois, UNamur, with the following parameters: for the closed forms: Unit sphere radius = 5, multiplying factor for the β vector =.3, multiplying factor for the USR =.15. for the open forms: MA5: unit sphere radius = 7, multiplying factor for the β vector =.1, multiplying factor for the USR =.35; MA1: unit sphere radius = 7, multiplying factor for the β vector =.6, multiplying factor for the USR =.35. The USR is intrinsically linked to the anisotropy factor ρ, which measures the relative magnitude of the octupolar and dipolar contributions of the first hyperpolarizability. The evolution of the USR with ρ is illustrated in Figure S11 for a set of representative compounds. S29
30 MA5 closed ρ = 4.3 MA3 closed ρ = 2.43 MA2 closed ρ = 1.4 MA7 closed ρ = 1.9 MA1 closed ρ =.91 MA3 open ρ =.865 Figure S11: Evolution of the shape of the hyperpolarizability tensor, represented using the USR, with the anisotropy factor ρ. S3
31 Effect of the DFT exchange-correlation functional (CF) Effect of the CF used in the calculations of the NL properties Table S16: Static β HRS values (a.u.) and β HRS contrasts calculated at the PCM:TDDFT level (in toluene) using different DFT exchange-correlation functionals with the G(d) level basis set. Molecular structures are optimized at the PCM:M6/6-311G(d) level. M6-2 ωb97-d LC-BLYP Comp. closed open Contrast closed open Contrast closed open Contrast BA BA BA BA BA BA BA BA BA BA BA M6-2 wb97d LC-BLYP 4 2 BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA1 Figure S12: Static β HRS contrasts calculated at the PCM:TDDFT level (in toluene) using different DFT exchange-correlation functionals with the G(d) level basis set. Molecular structures are optimized at the PCM:M6/6-311G(d) level. S31
32 Effect of the CF used in the geometry optimizations Table S17: Static β HRS values (a.u.) and β HRS contrasts calculated at the PCM:M6-2/6-311+G(d) level (in toluene), using molecular geometries optimized at the PCM:M6/6-311G(d) and PCM:M6-2/6-311G(d) levels. M6 geometry M6-2 geometry Comp. closed open Contrast closed open Contrast BA BA BA BA BA BA BA BA BA BA BA M6 geometry M6-2 geometry 4 2 BA BA1 BA2 BA3 BA4 BA5 BA6 BA7 BA8 BA9 BA1 Figure S13: Static β HRS contrasts calculated at the PCM:M6-2/6-311+G(d) level (in toluene), using molecular geometries optimized at the PCM:M6/6-311G(d) and PCM:M6-2/6-311G(d) levels.. S32
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