Electron Propagator Theory Approach to the Electron Binding

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Electron Propagator Theory Approach to the Electron Binding Energies of a Prototypical Photo-Switch Molecular System: Azobenzene Gabriel Frederico Martins, and Benedito J. Costa Cabral J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b00532 • Publication Date (Web): 19 Feb 2019 Downloaded from http://pubs.acs.org on February 25, 2019

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The Journal of Physical Chemistry

Electron Propagator Theory Approach to the Electron Binding Energies of a Prototypical Photo-Switch Molecular System: Azobenzene Gabriel F. Martins∗,† and Benedito J. C. Cabral∗,†,‡ †Biosystems and Integrative Sciences Institute (BioISI), Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal. ‡Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal E-mail: [email protected]; [email protected] Abstract The electron binding energies for the trans and cis conformers of azobenzene (AB), a prototypical photo-switch, were investigated by electron propagator theory (EPT). The EPT results are compared with data from photoelectron and electron transmission spectroscopies and complemented by the calculation of the differences between vertical and adiabatic ionization energies and electron affinities of the AB conformers. These differences are discussed in terms of the geometry changes associated with the processes of ionization and electron attachment. The results pointed out a major difference between these processes when we compare trans-AB and cis-AB. For trans-AB, electron attachment leads to a small geometry change, whereas for cis-AB, it is the ionised structure that keeps some similarity with the neutral species. We emphasise the interest of the present results for a better understanding of recent experiments on the dark cistrans isomerization in different environments, specifically for azobenzenes in interaction

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with gold nanoparticles, where the proposed cis-trans isomerization mechanism relies on electron transfer induced isomerization.

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INTRODUCTION The structure of azobenzene (AB) species can be represented as Ph-N≡N-Ph structure, where Ph is a phenyl or a substituted phenyl moiety. AB can exist in a trans-[t] or cis-[c] configuration as illustrated in Figures 1 and 2. The trans cis isomerization process is induced by radiation and keeps a close similarity with more complexes conformational changes driven by light such as the reversible shape change in the rhodopsin-retinal protein system. 1–3 The strong interest in AB systems can be explained by their importance as photo-switches with a wide range of applications including biochemical photocontrol, which relies on the coupling of the AB isomerization process to control the functional behaviour of biomolecules. 4,5 AB also plays a fundamental role on photomechanical reversible changes, which are characterized by structural modifications of a host system induced by the conformational changes of a guest photoactive molecule. 1,2,6,7 Other potential application of azobenzenes concerns the storage of solar thermal energy induced by photoisomerization. 8,9 The thermal energy is stored in the molecular framework of a metastable cis conformer generated by photochemical isomerization. The stored energy is then released in the form of heat by subsequent isomerization to the trans conformer. 10 Azobenzene-functionalized carbon nanotubes have been proposed as high-energy density systems for solar thermal storage. 9–12 The nature of photoisomerization processes in different classes of azobenzenes has been extensively discussed by Bandara and Burdette 13 and the potential role of azobenzene-based systems as solar thermal fuels has been recently reviewed. 14 The AB photoisomerization mechanisms have been the subject of several works. 15–24 The electronic properties of azobenzene, specifically the electronic absorption spectrum 25–31 have been investigated by several studies. The vibrational spectra of the AB conformers were discussed by Duarte el al. 32 Density functional theory (DFT) results for vertical and adiabatic electron affinities were also reported. 33 One relevant aspect for a better understanding of the role played by AB as a reversible photo-switch concerns the differences between the electronic properties of trans and cis AB conformers. It is known that for unmodifed AB 3



the electronic absorption spectra of t-AB and c-AB are different but overlaping 4 and that it is important to control these differences in substituted azobenzene systems for tuning the trans-cis interconversion dynamics. 4 In comparison with the data for electronic absorption, redox properties of AB, which are related to electron binding energies (ionization energies and electron affinities) were much less studied. Photoelectron spectroscopy (PES) of azobenzene has been reported by Kobayashi et al. 34 Electron transmission spectroscopy (ETS) data on electron attachment energies were discussed by Modelli and Burrow. 35 Proton and electron affinities were also reported. 36,37 Electron attachment to azobenzenes are also of fundamental interest in scanning tunneling microscope (STM)-induced switching, in which the cis-trans isomerization of individual molecules are triggered by tunneling electrons. 38 Some specific issues deserve further attention. The first concerns the comparison between the electron binding energies for the trans and cis AB conformers. The second is related to electron transmission spectroscopy (ETS) 35 and dissociative electron attachment spectroscopy (DEAS), 35 which indicated the formation of temporary anion states of gas-phase trans-AB. 35 These anion states appear as resonances in the electron-molecule scattering cross section and the associated energies correspond to vertical electron attachment processes. 35 In addition, cis-trans isomerization in the dark has been investigated for azobenzene in interaction with gold nanoparticles (AuNps). 39–41 An electron-transfer mechanism has been proposed to explain the increase of the cis-trans isomerization rate for azobenzene in interaction with AuNps. 40,41 More recently, the electrocatalytic cis-trans isomerization of azobenzenes has been investigated and evidence was provided on the significantly faster isomerization rates for radical species relative to the neutral conformers. 42 Therefore, all these recent experiments stress the interest in the AB ionisation and electron attachment processes. Theoretical predictions of virtual orbital energies (VOEs) relying on empirical correlations between measured vertical attachment energies (VAEs) and Hartree-Fock data for parent molecules have been reported by Modelli and Burrow. 35 DFT calculations of vertical and adiabatic ionization energies and electron affinities were also reported. 33,41 However, it

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is important to assess the performance of high level ab initio methods for prediciting electron binding energies (EBEs) of AB as well as to exploit a possible relationship between the EBEs and data from experiments on dark cis-trans isomerization induced by ET. 40,41 In this work, we are presenting a theoretical investigation on the EBEs of the trans and cis AB conformers. The adopted theoretical approach relies on electron propagator theory (EPT). 43,44 Emphasis is placed on the EPT calculation of outer valence and lower virtual orbital energies, which are respectively compared with PES 34 and ETS data. 35 The EPT results are complemented by ∆E calculations of vertical and adiabatic ionization energies and electron affinities, where ∆E represents the energy difference between charged and neutral species. Differences between vertical and adiabatic EBEs are important for discussing the relationship between geometry relaxation, ionization and electron attachment processes. The interest of the present results is illustrated by a discussion on a possible pathway for the electron transfer mechanism driving dark cis-trans isomerization of azobenzenes in interaction with nanoparticles systems playing the role of electron sinks or sources. 40,41

THEORETICAL METHODS Geometry optimisations for the neutral, cationic, and anionic species of trans and cis AB conformers were carried out with second order Möller-Plesset perturbation theory (MP2). 45 For the neutral conformers, geometry optimisations with the hybrid B3LYP exchange-correlation functional 46,47 with the D3 48–50 empirical correction for dispersion interactions (B3LYP-D3) were also carried out. We are not applying the B3LYP-D3 functional to charged species. Apparently, the accuracy of empirical corrections for dispersion interactions is less well established in these cases. 51 Geometry optimisations were carried out with the cc-pVxZ (x=D,T) 52 basis-sets. For the neutral species harmonic frequencies were calculated at the MP2/cc-pVDZ and MP2/ccpVTZ levels. For the charged species, frequencies were calculated only at the MP2/cc-pVDZ

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level. All the frequencies are real thus characterizing the optimized structures as local minima on the potential energy surface. The cc-pVxZ and aug-cc-pVxZ (x=D,T,Q) basis-sets were used in the calculation of the cis-trans isomerization energy. For conciseness the cc-pVxZ and aug-cc-pVxZ basis-sets will be also represented as pVxZ and apVxZ, respectively. Electron binding energies were calculated with EPT 43 by using the outer valence Green’s function (OVGF) 44,53–56 and the partial third order quasi-particle (P3) 55–57 methods. Excellent reviews on EPT were published. 44,57 Here, for completeness only the fundamental equations and concepts are presented

ˆ p )]φp (x) = p φp (x) [Fˆ + Σ(

(1)

ˆ where the self-energy operator Σ(E) depends parametrically on the energy E. Different ˆ approximations to Σ(E) lead by a self-consistent solution of equation 1, to a set of eigenvalues {p } and to the corresponding eigenfunctions {φp (x)}, where x denotes a single-electron coordinate. The eigenfunctions {φp (x)} are associated with ionization or electron attachment processes and are known as Dyson orbitals. Pole strengths are defined as Z Pp =

|φp (x)|2 dx

(2)

The pole strengths are a measure on the importance of correlation effects included in equation 1 through the self-energy operator. For Hartree-Fock orbitals, the pole strengths are equal to unity and smaller pole strengths are associated with significant correlation effects. Although EPT calculations are computationally demanding it is important to include diffuse functions in the basis-sets, mainly in the case of electron affinities. EPT calculations for AB were carried out with the following basis-sets: cc-pVTZ (H), aug-cc-pVTZ (C), and sp-aug-cc-pVTZ (N). The basis-set for the N atom is a cc-pVTZ basis-set augmented with s and p diffuse functions only. By adopting this basis-set, d and f diffuse functions are

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not included in the N atoms. This choice is a compromise that takes into account the need of diffuse functions for the accurate prediction of electron affinities and also the high computational cost of EPT calculations. Vertical and adiabatic ionization energies and electron affinities were also calculated by the energy (E) difference between neutral and charged species (∆E calculations). ∆E calculations were carried out with energies determined by spin-projected second order MöllerPlesset perturbation theory. 58 The calculations were carried out with the Gaussian09 program. 59

RESULTS AND DISCUSSION Structure and thermal properties Before presenting results for the electronic properties of AB it is important to discuss the reliability of the adopted theoretical methods for predicting the structure and also thermal properties, specifically the enthalpy difference (∆H) between the cis and trans AB conformers, for which experimental data is available. 60–62

Figure 1: t-AB (C2h ); Geometric parameters from MP2/cc-pVTZ optimisations. Bond lengths in Å; angles in degrees: N≡N 1.267 (1.260; 63 1.247 64 ); N-C 1.417 (1.427; 63 1.428 64 ) N≡N-C=113.7 (113.6 63 ); N≡N-C-C= 0.0; C-N≡N-C=180.0.

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Figure 2: c-AB (C2 ); Geometric parameters from MP2/cc-pVTZ optimisations. Bond lengths in Å; angles in degrees: N≡N 1.262 (1.255; 63 1.253 64 ); N-C 1.433 (1.437; 63 1.449 64 ); N≡N-C 120.8 (121.9 64 ); N≡N-C-C 53.9 (53.3 64 ); C-N≡N-C 7.1 (8.2 64 ). Some geometric parameters for the AB conformers are reported in Table 1, where data for the cationic and anionic optimised geometries are also presented (the cartesian coordinates for all the MP2/cc-pVTZ optimised structures are reported as Supporting Information).

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Table 1: Optimised geometries for t-AB and c-AB conformers and respective cationic and anionic species. Optimisations carried out with the cc-pVTZ basisset. Distances in Å, angles in degrees. Experimental values for the neutral species in parentheses. MP2

N≡N N-C N≡N-C N≡N-C-C C-N≡N-C

1

Expt.

t-AB

[t-AB]+

[t-AB]−

t-AB

t-AB

1.267 1.417 113.7 0.0 180.0

1.207 1.390 130.9 0.0 180.0

1.340 1.370 111.6 0.0 180.0

1.248 1.416 115.6 0.0 180.0

1.260;11.2472 1.427;11.4282 113.61 0.0 180.0

c-AB

[c-AB]+

[c-AB]−

c-AB

c-AB

1.238 1.421 121.8 31.6 10.9

1.354 1.362 117.1 16.6 65.2

1.239 1.433 123.6 52.3 8.6

1.255;11.2532 1.437;11.4492 121.92 53.32 8.22

N≡N 1.262 N-C 1.433 N≡N-C 120.8 N≡N-C-C 53.9 (53.6)3 C-N≡N-C 7.1 (7.3)3 3

B3LYP-D3

2 From Tsuji et al; 63 From Bouwstra et al; 64 RI-MP2/cc-pVTZ calculations. 26

The experimental structure of t-AB was investigated by gas electron diffraction (GED) 63 and X-ray diffraction(XRD). 64 Comparison between some geometric parameters from MP2 and B3LYP-D3 optimisations for the neutral species and experimental data shows, in general, a good agreement. For the t-AB conformer the N≡N bond length from MP2 (1.267 Å) is in very good agreement with GED (1.260 Å). 63 The N≡N-C angle (113.7 degrees) is also in very good agreement with GED(113.6). 63 For the cis conformer the N≡N-C-C (53.9 degrees) and C-N≡N-C (7.1 degrees) dihedral angles are in very good agreement with XRD data (53.3 and 8.0 degrees, respectively). It should be expected that the cis conformer is energetically stabilised by dispersion interactions between the phenyl rings. Therefore, the observed agreement between the predicted geometry of the cis conformer and experimental data can be seen as an indication of an adequate representation of dispersion interactions by MP2 and B3LYP-D3. We notice that for the neutral conformers, geometry optimisations

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with a variant of the MP2 method, RI-MP2 (RI stands for resolution of the identity) were reported by Fliegl et al. 26 Their results for trans-AB coincide with the present ones and only very small differences in the geometry of cis-AB are observed (see Table 1). In the following discussion the ionised species, which are radical cations or radical anions, will be represented as [t-AB]+ and [t-AB]− (with a similar notation for the cis conformer). In the [t-AB]+ ionised conformer, the N≡N bond length is shortened by 0.06 Å relative to the neutral species, whereas the N≡N-C angle increases from 113.7 to 130.9 degrees, which is the more significant change when we compare the relaxed structure of [t-AB]+ with the neutral species. In [t-AB]− , N≡N is increased by 0.073 Å relative to t-AB, which is explained by the presence of an additional electron in the LUMO of the neutral species. 33 A very small decrease of the N≡N-C angle (2.1 degrees) is observed in [t-AB]− relative to t-AB. In the case t-AB the results indicate that relaxation effects are more important for the ionised than for the anionic structure. For the c-AB conformer, comparison of the ionised and anionic structures with the neutral species shows that for the N≡N and N-C bond lengths the changes are qualitatively the same observed in t-AB. However, for c-AB the N≡N-C angles (values in degrees) are not very different in c-AB (120.8), [c-AB]+ (121.8), and [c-AB]− (117.1). The two major changes are observed for the N≡N-C-C and C-N≡N-C dihedral angles. The first changes from 53.9 degrees (c-AB) to 16.6 degrees ([c-AB]− ). The second one changes from 7.1 (c-AB) to 65.2 ([c-AB]− ). In the case of c-AB it seems reasonable to assume that relaxation effects are more important upon electron attachment than ionization, which is the inverse trend observed in t-AB. Thermal data for the trans-cis isomerization are gathered in Table 2, which also reports data from experiment.

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Table 2: Energy differences (in kJ/mol) between the cis and trans AB conformers. ∆X ≡ X[cis] − X[trans] for X = H, G, which are, respectively the enthalpy and Gibbs free energy. B3LYP calculations rely on B3LYP-D3/cc-pVxZ (x=D,T) optimisations and thermal corrections with the cc-pVTZ basis-set. MP21 apVDZ apVTZ apVQZ CBS(D,T,Q)

1 2

B3LYP-D3 apVDZ apVTZ

∆H

37.4

42.9

44.6

45.3

55.4

52.6

∆G

40.3

45.9

47.5

48.2

57.3

54.4

Expt. 48.2 ± 0.3;2 49.1;347.0 ± 1.34

MP2/cc-pVTZ optimisation and thermal corrections at the same level; 3 4 From Wolf and Cammenga 60 From Dias et al.; 61 From Zhu and Yu. 62

MP2 calculations for ∆H of isomerization shows a significant basis-set dependence. By using the apVDZ basis-set, it is 37.4 kJ/mol, which is ∼ 10 kJ/mol below the more recent experimental value (47.0 ± 1.3 kJ/mol). 62 Calculations with the apVTZ and apVQZ basisset lead to 42.9 and 44.6 kJ/mol, respectively. By applying a CBS(D,T,Q) extrapolation procedure relying on the exponential ansatz of Halkier et al 65 to the total energy, 66 our best estimate for ∆H is 45.3 kJ/mol, which underestimates experiment by only ∼ 2 kJ/mol. The CBS(D,T,Q) result is also in very good agreement with a recent G3MP3 calculation (45.8 kJ/mol). 62 B3LYP-D3 results overestimate the more recent experimental value, although they are in better agreement with the data from Dias et al (49.1 kJ/mol). 61 Overall, the results indicate that both MP2 and B3LYP-D3 are adequate for investigating the structure of the trans and cis AB conformers as well as the ∆H of isomerization. Moreover, it should be observed that ∆H (apVTZ) is 2.4 kJ/mol (∼ 0.02 eV) below the CBS(D,T,Q) value, which leads credence to the reliability of this basis-set for predicting electron binding energies. It is interesting to compare the cis-trans isomerization energy for charged species with that one for the neutral AB conformers. For the anions this energy at the MP2/apVTZ level is 67.6 kJ/mol, whereas for the cations it is 108.0 kJ/mol (the uncorrected ZPVE value for the neutral species is 43.9 kJ/mol). 11



Electron propagator theory calculations for the AB conformers Figure 3 illustrates the two highest occupied and the two lowest unoccupied Kohn-Sham (KS) molecular orbitals for the AB conformers. It is assumed that KS orbitals are connected to Dyson orbitals and that they provide an acceptable representation of correlation effects on the electronic density. 67,68 A qualitative assessment on the nature of the ionisation and electron attachment processes can be inferred from these orbital representations. For the t-AB conformer, it appears that the ag (H) orbital is mainly localized on the N≡N bond with minor contributions from the phenyl rings. Electron attachment to the bg (L) orbital involves mainly the phenyl rings. For the c-AB conformer, both b(H) and a(L) orbitals are delocalized over the AB moiety, thus indicating that ionization and electron attachment are non-localized processes. Similar conclusions on the nature of ionization and electron attachment processes are obtained by using canonical Hartree-Fock orbitals. Here, the choice of KS orbitals stresses the interest in their connection with Dyson orbitals. 67,68

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Figure 3: Kohn-Sham frontier molecular orbitals and respective symmetries for trans (left) and cis (right) AB conformers. t-AB [C2h ] bg (L+1)

cis-AB [C2 ] a (L+1)

bg (L)

a (L)

ag (H)

b (H)

au (H-1)

b (H-1)

For comparison with experimental data, 34,35 we are reporting in Table 3 EPT results for the orbital energies. We are not aware of PES data for the c-AB conformer. Pole strengths (PS), represented in parentheses in Table 3, are a measure of correlation effects for a given orbital. 44 Lower PS values reflect larger correlation effects. For OVGF 13



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Table 3: Orbital energies (in eV) from electron propagator theory for the optimised structures of the trans [C2h ] and cis [C2 ] conformers of azobenzene (AB). For EPT calculations the following basis-set was adopted: cc-pVTZ for H; aug-cc-pVTZ for C; sp-aug-cc-pVTZ for N. Pole strengths in parentheses.

Geometry

t-AB virtual bg bg (L) t-AB occupied ag (H) au au bg c-AB virtual a a (L) c-AB occupied b (H) b a b

MP2

B3LYP-D3

HF

OVGF

P3

OVGF

P3

Expt./Others

1.24 1.04

0.92 (0.98) −0.39(0.89)

0.88(0.98) −0.50(0.88)

0.92(0.98) −0.32(0.89)

0.88(0.98) −0.43(0.89)

0.881 [−0.83]2

−8.26 −8.34(0.88) −8.58 (0.86) −8.39 (0.88) −9.35 −9.31 (0.88) −9.44 (0.86) −9.33 (0.88) −9.37 −9.32 (0.88) −9.45 (0.83) −9.34 (0.88) −9.89 −9.77(0.87) −9.93(0.86) −9.78 (0.88) 1.28 1.10

0.97 (0.98) 0.74(0.98)

0.93 (0.98) 0.60 (0.98)

0.97 (0.98) 0.74 (0.98)

−8.48 −8.39(0.88) −8.65(0.87) −8.16 −9.41 −9.34(0.88) −9.51 (0.87) −9.34 −9.43 −9.33 (0.88) −9.51 (0.87) −9.35 −9.85 −9.68(0.88) −9.87 (0.87) −9.66

(0.88) (0.88) (0.88) (0.88)

−8.62 −9.46 −9.47 −9.95

(0.86) −8.46;3[−8.77]4 (0.87) −9.303 (0.87) −9.303 (0.86) −9.773

0.93 (0.98) 0.69 (0.98) −8.59 −9.51 −9.53 −9.84

(0.87) (0.87) (0.87) (0.87)

1

Experimental result from Modelli and Burrow; 35 2 3 Theoretical estimate from Modelli and Burrow; 35 From Kobayashi et al; 34 4 34 Value reported by Kobayashi et al estimated from a broad PES band.

the PS values are above or equal to 0.87 (bg occupied orbital of t-AB). Smaller PS values are observed for the P3 approximation. First, we will discuss the results for the energy of occupied orbitals from EPT with MP2 geometry optimisations. For t-AB, the experimental values from PES 34 are also reported in Table 3. Comparison between the present results and experimental data shows a good agreement. Specifically, the energies of the HOMO orbital from OVGF and P3 (−8.34 and −8.58 eV, respectively) are in good agreement with the PES value (−8.46 eV). 34 A very good agreement between EPT and experimental values is also observed for the other valence orbitals. Moreover, OVGF results are in better agreement

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with experiment than P3. For c-AB the HOMO energies from OVGF and P3 are −8.39 eV and −8.65 eV, respectively. Thus, the first vertical ionization energies of c-AB and t-AB are predicted to be quite similar, which is also verified when other valence orbital energies are compared. The energy of virtual orbitals correspond to the minus signed vertical electron affinities. For t-AB the energies of the LUMO predicted by OVGF and P3 are (in eV) −0.39 and −0.50, respectively. By using a scaled of virtual orbital energies relying on empirical equations, Modelli and Burrows predicted that the LUMO (L) energy of t-AB is −0.83 eV, 35 which is significantly lower than our EPT predictions. These authors also reported virtual orbital energies measured by ETS. 35 The energies (in eV) of L+1 (bg ) virtual orbital are 0.92 and 0.88 from OVGF and P3, respectively and the P3 energy coincides with the experimental value of 0.88 eV. 35 In contrast with t-AB, the LUMO energy of c-AB is positive thus indicating that vertical electron attachment to the cis AB conformer is not energetically favourable. Comparison between EPT results based on MP2 and B3LYP-D3 geometry optimisations show that, in general, they are similar. This reflects the overall good agreement between MP2 and B3LYP-D3 geometries.

Vertical and adiabatic ionization energies and electron affinities of azobenzene conformers from ∆E calculations. Results for vertical and adiabatic ionization energies and electron affinities of azobenzene conformers from ∆E calculations are reported in Table 4, where data from experiment and other theoretical calculations are gathered. The vertical ionization energy (VIE) of t-AB at the MP2/apVTZ//MP2/pVTZ level is 8.37 eV, in very good agreement with the EPT value of 8.34 eV (OVGF). From MP2 ∆E calculations the adiabatic ionization energy (AIE) is ∼ 0.7 eV lower than the vertical one. This difference is in keeping with the geometry relaxation of t-AB upon ionization previously discussed and that pointed out a significant increase of the N≡N-C angle from

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Table 4: Vertical and adiabatic ionization energies and electron affinities (in eV) for the trans and cis AB conformers from ∆E calculations. Geometries optimised at the MP2/pVTZ level. Values in brackets are adiabatic properties corrected for ZPVE calculated at the MP2/pVDZ level. t-AB VIE AIE VEA AEA

pVTZ

apVTZ

Expt./Others

8.28 7.61 [7.71] 0.53 0.56 [0.39]

8.37 7.71 [7.81] 0.72 0.74 [0.58]

8.461

pVTZ

apVTZ

8.27 8.31 [8.42] −0.06 0.29 [0.07]

8.38 8.38 [8.49] 0.16 0.49 [0.27]

1.01;20.833 1.05;21.378;40.575

c-AB VIE AIE VEA AEA 1

6.966 0.432 1.01;20.726

Experimental (PES) value from Kobayashi et al. 34 2 Theoretical calculations from Fuechsel et al. 33 3 Theoretical estimate from Modelli and Burrow 35 4 Experimental value from Chen et al. 37 5 Experimental value from Ingemann et al. 36 6 Theoretical calculations from Titov et al. 41

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113.7 degrees (t-AB) to 130.9 degrees ([t-AB]+ ). Our best estimate for the vertical electron affinity (VEA) of t-AB is 0.72 eV, which is ∼ 0.2 eV above the P3 value reported in Table 3. Other theoretical value is 1.01 eV from B3LYP calculations. 33 The adiabatic electron affinity (AEA) of t-AB (0.74 eV) is quite similar to the vertical value, and it is ∼ 0.3 eV below the result reported by Fuechsel et al. (1.05 eV). 33 Similar values for the VEA and AEA of t-AB reflects the relatively small geometry relaxation of t-AB upon electron attachment, the only significant change being the N≡N stretching (see Table 1). Experimental values for the AEA of t-AB range from 0.57 eV 36 to 1.38 eV. 37 The VIE of c-AB is 8.38 eV, which is in agreement with the EPT results of Table 3. Our ∆E predictions indicate that the AIE of c-AB is quite similar to the vertical one. This seems to reflect small changes of the geometric parameters relevant to the ionization process, that should be particularly sensitive to the N≡N and N-C bond lengths, and to the N≡N-C angle. We are not aware of experimental values for the AIE of c-AB and our best estimate (8.38 eV) is ∼ 1.4 eV above a recent theoretical value relying on B3LYP/6-31G* calculations. 41 From ∆E calculations, quite small VEAs are predicted by MP2/apVTZ calculations, which is in keeping with EPT predictions indicating that vertical electron attachment to c-AB is not energetically favourable. The predicted AEA’s of c-AB are, however, significantly increased relative to VEA’s, which can be explained by the differences between the geometries of cAB and relaxed [c-AB]− . Other predictions for the VEA and AEA of c-AB are 0.43 and 1.01 eV, 33 respectively. Although the difference between them (∼ 0.6 eV) is 0.2 eV above the present MP2 results, they are in keeping with a significant geometry relaxation of c-AB upon electron attachment. VEAs from the energy difference calculations (Table 4) are significantly smaller than those predicted by the OVGF and P3 approximations (Table 3), mainly in the case of the c-AB conformer. Recently, a systematic analysis on the accuracy of EPT for predicting EBEs was reported. 69 From this analysis it appears that EAs based on EPT approximations that neglect the off-diagonal elements of the self-energy matrix in the canonical Hartree-

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Fock orbitals representation, such as OVGF and P3, can exhibit significant deviations from reference values. This limitation, together with the strong dependence on the basis-sets and their localized/nonlocalized nature are possible explanations for the presently observed discrepancies. ZPVE corrections to adiabatic ionisation energies (bracketed values in Table 4) amount to ∼ +0.1 eV. These corrections rely on unscaled harmonic MP2/cc-pVDZ frequencies. It is not clear that empirical scaling factors for MP2 frequency calculations, that in principle take into account anharmonic effects, should be the same for the neutral and charged species. When the vertical and adiabatic ionisation energies are quite similar, which is the case of t-AB, introduction of harmonic ZPVE corrections should be taken with care. ZPVE corrections to electron affinities also introduce some small changes, which are below ∼ |0.15| eV. Therefore, it seems reasonable to assume that ZPVE corrections to adiabatic EBEs do not change our conclusions based on the uncorrected values. Our results can be useful for a better understanding of dark cis-trans isomerization mechanism of azobenzenes in interaction with gold nanoparticles. 39–41 AuNPs can play the role of electron sources or sinks, which can be controlled by applied potentials. 70 Recently, it has been proposed that the dark cis-trans isomerization rate of AB is fostered by the interaction with gold nanoparticles (AuNps) through an electron-transfer (ET) mechanism. 40,41 Hallett-Tapley et al 40 proposed that the pathway for the ET mechanism relies firstly on the ionization of c-AB species (ET from c-AB to AuNPs) leading to the formation of the [c-AB]+ radical cation that isomerizes to an intermediate structure and then relaxes to t-AB after ET to AuNPs. 40 Titov et al 41 reported a DFT investigation on the gas-phase cis-trans isomerization energy barriers defined by the transition state structures for both the neutral, anionic, and cationic azobenzene species, and concluded that the barriers for charged species are significantly lowered relative to the neutral ones. These authors also analysed the possible pathway for the ET mechanism and pointed out that the formation of charged species near a planar metallic surface should take into account the work function of the surface and

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the distance from the AB species to the surface (it should be noticed, however, that the work function of metallic species is very dependent on the surface curvature 71 ). The theoretical calculations by Titov et al 41 indicated that the formation of cations is energetically favoured relative to anionic species thus supporting the pathway proposed by Hallett-Tapley et al. 40 However, they also observed that their experiments were carried out for gold nanoparticles in solution and azobenzene species interacting with them, whereas their calculations were carried out for gas phase azobenzene. 41 Other relevant experimental work for understanding the ET mechanism for AB in interaction with AuNps aggregates was reported by Yoon and Yoon. 39 Based on surface-enhanced Raman scattering (SERS) they pointed out the presence of significantly weakened N≡N bonds for cis-AB when it is in interaction with AuNP aggregates. 39 The present results show that upon electron attachment the N≡N bond length of [c-AB]− is increased by 0.09 Å relative to the neutral AB (see Table 1). In addition, upon ionization the N≡N bond length is shortened (stronger bond energy) relative to the c-AB neutral species what would make difficult a conformational change involving, for example, a rotation mechanism about the N≡N bond. Based on the present findings, other possible pathway for the ET cis-trans isomerization mechanism could be defined by the following steps: (1) electron attachment to c-AB generating the [c-AB]− radical anion; (2) isomerization of [cAB]− to [t-AB]− ; (3) electron transfer from [t-AB]− to the AuNPs that is playing the role of electron sink; (4) relaxation to the t-AB conformer. We notice that [t-AB]− and t-AB have similar structures (see Table 1). A possible pathway for dark cis-trans isomerization induced by electron transfer is illustrated in Fig. 4. It should be observed that the proposed pathway is not taking into account the interactions with AuNPs. Although this limitation and the absence of any experimental evidence confirming this specific pathway, it is in keeping with the present data on the structural changes of gas phase AB conformers upon ionization and electron attachment. Interestingly, a similar pathway has been considered as a possibility in the graphical abstract of a recent work by Saalfrank and collaborators. 41

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Figure 4. Possible pathway for dark cis-trans isomerization of azobenzene in interaction with gold nanoparticles (AuNPs) that can play the role of electron sources or sinks. 70

CONCLUSIONS Electron propagator theory (EPT) calculations of the electron binding energies for the trans and cis conformers of azobenzene, a prototypical photo-switch, are reported. The outer valence ionization energies of t-AB are in very good agreement with data from PES. 34 Moreover, we are reporting results for the outer valence ionization energies of the c-AB conformer. It has been verified that they are quite similar to those of the t-AB conformer. EPT calculations show that in contrast with t-AB, the LUMO energy of c-AB is positive, indicating that vertical binding of an excess electron to this conformer is not energetically favourable. The EPT calculations are complemented with ∆E calculations for the vertical and adiabatic ionization energies, and electrons affinities. The ∆E calculations for the vertical properties support the main conclusions of the EPT predictions for the VIEs. However, some discrepancies between EPT and ∆E (MP2) results for the VEAs are observed, mainly in the case of c-AB. ∆E (MP2) calculations predict that the VEA of the c-AB conformer

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is only 0.16 eV, which is ∼ 0.6 eV below the value for t-AB. The main conclusion from ∆E calculations concerns the differences between vertical and adiabatic processes and their relationship with geometry relaxation effects. The results pointed out a major difference between these processes when we compare t-AB and c-AB conformers. For the first one, electron attachment leads to small geometry changes. For the second one, it is the ionised structure that keeps some similarity with the neutral species. The interest of the present results for a better understanding of dark cis-trans conformational changes of AB in different environments, particularly in electron-transfer induced isomerization 40,41 should be stressed.

Acknowledgement This work was supported by Fundação para a Ciência e a Tecnologia (FCT, Portugal) through the funding project PTDC/QUI-QFI/29174/2017.

Supporting Information Available Azobenzene-Coord.docx contains the cartesian coordinates for the MP2/cc-pVTZ optimised structures of the trans and cis AB conformers and respective anionic and cationic species. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Graphic Toc

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Electron Propagator Theory Approach to the Electron Binding

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