A theoretical exploration of the nonradiative deactivation of hydrogen-bond complexes: isoindole–pyridine and quinoline–pyrrole

Abstract

The second order approximate Moller–Plesset (MP2) and coupled cluster (CC2) methods have been employed to investigate the geometry, electronic transition energies and photophysics of the isoindole–pyridine and quinoline–pyrrole complexes. The most stable geometry of both isoindole–pyridine and quinoline–pyrrole complexes has been predicted to be a perpendicular structure. It has also been found that the first electronic transition in both complexes is responsible for UV absorption owing to its ¹ππ* nature, while a charge transfer ¹ππ* state governs the nonradiative relaxation processes of both complexes. In this regard, excited state intermolecular hydrogen/proton transfer (ESHT/PT) via the charge transfer electronic states plays the most prominent role in non-radiative deactivation. In the HT/PT reaction coordinate, the minimum potential energy profile of the lowest CT-¹ππ* state predissociates the local ¹ππ* state, connecting the latter to a curve crossing with the S₀ state. At the region of this curve crossing, the S₀ and CT state become degenerate, enabling the ¹ππ* state to proceed as the predissociative state and finally direct the excited system to the ground state.

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1. Introduction

During the last two decades, massive attention has been paid to hydrogen bonding in chemistry and biochemistry because of its fundamental implication and importance in many branches of science.^1,2 It has been established that microscopic structures and functions in many molecular systems, such as hydrogen-bonded water or alcohol networks, organic compounds in solution, hydrogen-bond crystal engineering, polymers, proteins, and DNA,^1,3–6 are directly connected to hydrogen bond interactions. In the influential work of Watson and Crick,⁷ it has been proposed that the genetic code is stored in the form of hydrogen-bonds between the canonical nucleic acid bases, which form the main frame of the DNA molecule. They recognized that tautomerization alters the hydrogen-bonding patterns and therefore could lead to mismatches in the canonical base pairs.

The ground-state properties of the hydrogen bonds in molecular systems have been extensively explored by various experimental and theoretical methods.^1,3,4,8–10 Upon photoexcitation of hydrogen-bonded systems, the hydrogen donor and acceptor molecules reorganize due to the significant difference in the charge distribution of the different electronic states.¹ The charge rearrangement in excited systems may trigger the photophysical phenomenon of hydrogen/proton transfer, which is called the “Excited State Hydrogen Transfer (ESHT)”. The ESHT is an important subject in a wide range of sciences, including chemistry and biochemistry.^5,6,11–13

Based on the influential work of Sobolewski and coworkers on the pyrrole–pyridine hydrogen bonded dimer,¹⁴ it has been remarked that the common feature in the photochemistry of hydrogen bonded systems is the electron-driven proton transfer (EDPT) mechanism. Particularly, in these systems, a polar charge transfer state of a ¹ππ* nature forces the proton transfer. The HT/PT process may direct the excited system to a conical intersection of the S₁ and S₀ surfaces.¹⁴ Later, they¹⁵ demonstrated that potential-energy functions of the lowest locally excited ¹ππ* states of the guanine–cytosine complex are crossed along the proton-transfer reaction path by the reactive potential-energy function of the charge transfer (CT) state. The PE curve crossings evolve to the conical intersections (CIs)¹⁶ in the multidimensional pictures. These CIs influence nonadiabatic processes and facilitate upper state to lower state transitions.^16–19 Thus, barrierless access to the charge transfer (CT)-ground state (S₀) conical intersection leads the excited system to the electronic ground state by an ultrafast radiationless decay mechanism. This conclusion indicates the high photostability of the guanine–cytosine base pair against UV radiation as well.¹⁵

Recently, Esboui and Jaidane²⁰ performed a comparative theoretical study on the nonradiative decay mechanisms of the phenol–pyridine complex, a hydrogen bonded cluster. They have predicted that the relaxation mechanism involves internal conversion (IC) and intersystem crossing (ISC) along the O–H bond elongation coordinate. Indeed, the excited state proton transfer reaction, mediated by electron transfer, from phenol to pyridine, governs the photophysics of the phenol–pyridine complex.

Moreover, based on previous investigations of the hydrogen-bonded cluster systems, the ¹ππ* excited electronic state has been identified to play the most important photophysical role,^21–24 while for the organic compounds, having intramolecular hydrogen bonding, this process is mostly derived from a repulsive ¹πσ* state.^24,25

In the present study, we focus on the photophysics of two hydrogen-bonded complexes, isoindole–pyridine and quinoline–pyrrole, which are two model-systems, for which the proton donor and acceptor are π-electron conjugated systems. These types of complexes can also be considered as models for fluorescence quenching via intermolecular hydrogen bonding between aromatic chromophores.²⁶ Consequently, this work will be helpful for understanding the quenching mechanism of isoindole and quinoline in the excited state by pyridine and pyrrole.

Isoindole, a benzo-fused pyrrole, is an isomer of indole. Isoindole units are found in phthalocyanines, an important family of dyes. Some alkaloids containing isoindole have been isolated and characterized.²⁷ Also, quinoline is a homologue of naphthalene, in which one of its C–H groups is substituted with nitrogen. These types of compounds are identified as polycyclic aromatic nitrogen heterocycles (PANHs),²⁸ which are interesting from an astrobiological perspective (see ref. 29 and references therein). Thus, we will present ground- and excited-state optimized structures, transition energies and oscillator strengths of isoindole, quinoline, and also their mixed complexes. Then, we will discuss and explain the hydrogen/proton transfer in isoindole–pyridine and quinoline–pyrrole complexes as well.

2. Computational details

The “ab initio” calculations have been performed with the TURBOMOLE program suite,^30,31 making use of the resolution-of-identity (RI) approximation for the evaluation of the electron repulsion integrals. The equilibrium geometry of all systems at the ground state has been determined at the MP2 (Moller–Plesset second order perturbation theory) level.^32,33 Excitation energies and equilibrium geometry of the lowest excited singlet states have been determined at the RI-CC2 (the second-order approximate coupled-cluster method) level.^34,35 The correlation-consistent polarized valence double-zeta (cc-pVDZ) and the aug-cc-pVDZ³⁶ have been employed for most calculations. All of the potential energy curves have been determined with the use of the aug-cc-pVDZ basis function for all atoms.

The abbreviations iIn, Q, Pl and Pn will be used hereafter for isoindole, quinoline, pyrrole and pyridine respectively. In addition, the terms LE and CT will be employed to indicate the local excitation and charge transfer transitions respectively. Moreover, in some cases, we will use the abbreviation “perp.” instead of the word perpendicular. The pyrrole, pyridine, and isoindole monomers and isoindole–pyridine complex have C_2v symmetry, while the quinoline and quinoline–pyrrole complex belong to the C_s symmetry point group. With the exception of a few calculations (we will address them clearly), the symmetry point group of the systems was taken into account for geometry optimization of the ground and excited states.

3. Results and discussion

3.1. Ground state equilibrium structures and excitation energies of monomers

3.1.1. Pyridine and pyrrole. The electronic and geometry structures of pyridine and pyrrole have been well studied experimentally and theoretically.^37–44 Both systems have been identified as planar structures,^26,45 having a C_2v symmetry point group. Excellent summaries of the current state of knowledge on pyridine can be found in the reviews of Ross⁴⁴ and Zewail.⁴³ Pyrrole is also a prototypical heteroatomic aromatic compound,⁴² which has been intensely studied both experimentally and theoretically.^40,46 In particular, the deactivation of the photoexcited pyrrole could serve as a model for photodynamical processes of heteroatomic aromatic systems whose ¹πσ* transition energy is lower than that of the ¹ππ* state. From photophysical aspects, pyrrole and pyridine have been identified as photoacid and photobase systems respectively.²⁶ However, we chose not to present further details on the physical properties of these two well-known compounds and instead we focus on other monomers; (i.e. isoindole and quinoline), for which less information is found in the literature.

3.1.2. Indole, isoindole and quinoline monomers. Indole is the familiar chromophore of the amino acid tryptophan and isoindole is its isomer. Indole has been the subject of several reports (for instance, see ref. 47 and 48 and references therein). In contrast, dedicated reports on either the electronic structure or the physical properties of isoindole are rarely found in the literature. The same is true regarding quinoline. Thus, we briefly attend to the geometry and electronic properties of these two monomers. In the full geometry optimization, the MP2 calculated results show that both structures are planar at the ground state.

The first electronic transition (¹L_b–S₀) of indole has been investigated experimentally and theoretically. The S₁(¹ππ*) band origin of indole has been reported by Mani and Lombardi to be 35 232 cm⁻¹ (4.37 eV).^49,50 We have determined the adiabatic transition energy of indole at the RI-CC2/aug-cc-pVDZ level to be 4.57 eV which is comparable with the experimental value of Mani and Lombardi with an error of +0.2 eV. Based on the comparative theoretical study of Aquino,^51,52 this error is normally related to an overestimation of the CC2 method.

The vertical transition energies for the first two lowest singlet excited states of isoindole have been determined on the basis of ground state optimized geometry. The results have been presented in Table 1.

Table 1 Excited transition energies (vertical and adiabatic), of the considered monomers in this work (pyridine, pyrrole, isoindole and quinoline), computed at the CC2/aug-cc-pVDZ level of theory

	Electronic state	Vertical transition energy/eV	Oscillator strength	Adiabatic transition energy/eV
a The experimental value for S1, 0–0 band of isoindole has been adopted from ref. 53.b The CASPT2 theoretical values for S1 vertical and adiabatic transition energies of pyridine and pyrrole have been taken from ref. 38.c The corresponding experimental values for S1 vertical and adiabatic transition energies of pyridine have been adopted from ref. 54.d The experimental value for S1 0–0 band of pyrrole has been adopted from ref. 55.e The experimental value for S1 0–0 band of quinoline has been adopted from ref. 44.
Isoindole	S1(B1)1 [^1ππ*]	4.15	0.0841	3.91
				3.70^a
	S2(A2)1 [^1πσ*]	4.21	0.0000	—
Pyridine	S1(B2)1 [^1nπ*]	4.98	0.0046	4.54
		4.98^b		4.41^b
		4.74^c		4.31^c
	S2(B1)1 [^1nσ*]	5.21	0.0310	—
Pyrrole	S1(A2)1 [^1πσ*]	5.02	0.0000	4.81
	S5(B1)1 [^1ππ*]	6.22	0.1934	6.00
		5.85^b		5.82^d
Quinoline	S1(A′)1 [^1ππ*]	4.37	0.0247	4.22
				3.99 eV^e
	S2(A′′)1[^1σπ*]	4.44	0.0018

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Based on the C_2v symmetry point group, the first electronic transition of isoindole belongs to the B₁ irreducible representation. The S₁–S₀ transition corresponds to single electron transitions of HOMO–LUMO+8 (61%) and HOMO–LUMO+7 (30%). The frontier molecular orbitals of isoindole are displayed in Fig. 3. As shown, the HOMO, LUMO+7 and LUMO+8 orbitals of isoindole have π and π* natures respectively. Thus its first electronic excited state is of ¹ππ* character. The 1(¹A₂) state corresponds to the second (S₂–S₀) electronic transition of isoindole, arising from a HOMO–LUMO single electron transition (83%). As shown in Fig. 3, the HOMO is a π and LUMO is a σ* orbital which is located over the N–H bond. Hence, the S₂(¹A₂) excited state of isoindole is of ¹πσ* character. More information about excitation energies, oscillator strengths and their relevant configurations is presented in the ESI† file.

The RI-CC2 calculations show that the vertical transition energies of S₁–S₀ and S₂–S₀ of isoindole are around 4.15 and 4.21 eV respectively. At the same level of theory, the adiabatic S₁–S₀ transition of isoindole has been determined to be 3.91 eV. Considering a +0.2 eV overestimation error of the CC2 method, the corrected adiabatic-transition energy of isoindole (3.71 eV) is in excellent agreement with its experimental band origin (3.70 eV), reported by Bonnett and Brown.⁵³ Moreover, the S₁–S₀ transition energy of isoindole is at least 0.35 eV higher than the corresponding transition energy of the indole molecule.

Similar to indole, the S₂–S₀ electronic transition of isoindole has a ¹πσ* character. The vertical transition energy of this state has been determined to be 4.21 eV and 4.84 eV for isoindole and indole respectively. More information regarding the geometry and electronic structure of isoindole can be found in the ESI† file.

We have determined the geometry and electronic properties of quinoline at the MP2 and CC2/aug-cc-pVDZ level of theory. The optimized geometry of quinoline is presented in Fig. 1 and the xyz coordinates have been presented in the ESI† file. The structure is planar, containing a C_s symmetry plane. The CNC bond angle is 117.2° and the CCC angles in the pyridine ring are variable between 119–124°, while they are roughly constant around 120° in the adjacent benzene ring. The C–N bond lengths are 1.376 Å and 1.335 Å, the former is related to the C–N bond which is in the neighbourhood of a benzene ring and the latter is related to the second C–N bond.

Fig. 1 MP2 optimized structure of monomers involved in the structure of complexes considered in this work: (a) isoindole; (b) pyridine (c) quinoline, and (d) pyrrole.

Regarding the electronic transitions on the basis of the CC2 calculation results, the first ¹A′ excited state of quinoline corresponds to the S₁–S₀ electronic transition, and the first ¹A′′ state corresponds to the second (S₂–S₀) electronic transition. All of the 10 singlet electronic transitions are in the UV range (4.37–6.31 eV). S₁–S₀, S₃–S₀ and S₆–S₀ have large oscillator strengths (0.025–0.63), while the rest of the transitions are approximately dark (i.e. having a small oscillator strength; 0.000–0.001).

The frontier molecular orbitals (MOs) of the quinoline monomer are shown in Fig. 3. From the RI-CC2 calculations, the S₁(1-¹A′) state corresponds to the orbital transition from HOMO−1 to LUMO+5 (58%) and HOMO–LUMO+9 (29%). It is obvious that the HOMO has a π character while both the LUMO+5 and LUMO+9 are of π* nature (from Fig. 3). Thus the S₁ state of quinoline has the ¹ππ* feature. In addition, the S₂(1-¹A′′) state of the quinoline corresponds to the orbital transition from HOMO−3 to LUMO+5 (90%), in which the HOMO−3 is of nonbonding character (n) and the LUMO+5 is of π* nature, thus the S₂ state is mostly of ¹nπ* character.

3.2. Ground state equilibrium structures and excitation energies of complexes

We have considered two types of complexes, isoindole–pyridine (iIn–Pn), and quinoline–pyrrole (Q–Pl). Each complex, has been constructed from a photo-acid (i.e. a proton donor) and a photo-base (i.e. a proton acceptor moiety).²⁶ The photo-acid and photo-base systems have been connected by a strong hydrogen bond. In addition to regular hydrogen bond complexes, it is possible that these types of monomers form stack structures, interacting in an approximately parallel arrangement of monomers. Nevertheless, we have found that stack structures are at least 0.30 eV (∼30 kJ mol⁻¹) less stable than those of the regular hydrogen bonded systems. In addition, the H-bonded complexes are more abundant in biological systems than stack structures. Thus we have chosen not to consider stack structures in the present work.

We have considered three hydrogen-bonded configurations for each complex. All of the conformers have been optimized based on the MP2/aug-cc-pVDZ level of calculation. The optimized structures are presented in Fig. 2. As shown, in addition to two symmetric configurations for each complex (perpendicular and planar), there is a full optimized configuration, for which no symmetry constraint has been applied during the S₀ optimization. For the case of iIn–Pn, the minimum unconstrained geometry (Fig. 2c) is almost identical to the perpendicular conformer (Fig. 2a), with the same energy stability. The perpendicular and planar structures belong to the C_2v and C_s symmetry point groups respectively. The planar structure is 0.03 eV less stable than the perpendicular one.

Fig. 2 Complex systems considered in this work. (a) Perpendicular structure of the isoindole–pyridine complex (C_2v symmetry). (b) Planar structure of the isoindole–pyridine complex (C_s symmetry). (c) Optimized structure of the isoindole–pyridine complex without symmetry constraint. (d) Perpendicular structure of the quinoline–pyrrole complex (C_s symmetry). (e) Planar structure of the quinoline–pyrrole complex (C_s symmetry). (f) Optimized structure of the quinoline–pyrrole complex without symmetry constraint.

For quinoline–pyrrole (Q–Pl), both perpendicular and planar structures belong to the C_s symmetry point group. Similar to the case of the iIn–Pn complex, the minimum unconstrained geometry of Q–Pl (Fig. 2f) is almost the same as that of the perpendicular conformer (Fig. 2d), which is 0.06 eV (5.79 kJ mol⁻¹) more stable than planar. Thus, the perpendicular conformer will be representative for the unconstrained geometry of both complexes. In all conformers, there is a strong hydrogen bond between the N–H⋯N moieties. The geometric parameters of the hydrogen bond in the planar and perpendicular conformers of iIn–Pn are approximately identical, the N⋯H hydrogen bonds in perpendicular and planar structures are 1.870 Å and 1.889 Å respectively, indicative of a slight strengthening of the hydrogen-bond in the perpendicular structure. For the case of the Q–Pl complex, the H⋯N, N–H bond lengths and the N–H–N bond angle in planar forms are 1.932 Å, 1.03 Å and 177° respectively and they are 1.849 Å, 1.029 Å and 160.2° for the perpendicular form. This comparison also is consistent with strengthening of the hydrogen bond in the perpendicular conformer. The binding energies of the intermolecular hydrogen H⋯N bond in the perpendicular and planar conformers of iIn–Pn are −0.48 eV and −0.45 eV, respectively, at the RI-MP2 level (the same difference in stability is found when the ZPE is taken into account). The binding energy has been estimated for the two conformers of Q–Pl (perpendicular and planar) to be −0.49 eV and −0.43 eV respectively.

The vertical transition energies of all considered conformers have been calculated based on the optimized geometry of the ground state. In iIn–Pn (perpendicular conformer, C_2v), the first ¹B₂ excited state corresponds to S₁–S₀, and the first ¹A₂ state corresponds to the second (S₂–S₀) electronic transitions. The S₁ and S₂ electronic transitions have been determined to be 4.04 and 4.17 eV respectively. The frontier molecular orbitals (MOs) of the iIn–Pn complex are shown in Fig. 3. From the RI-CC2 calculations, the S₁(¹B₂) state has the largest oscillator strength among the lowest six electronic transitions of the iIn–Pn complex, corresponding mostly to the single electron transition from HOMO to LUMO+14 (73%). From Fig. 3, it is shown that the HOMO is a π orbital and the LUMO+14 has a π* character, so the S₁ state of the iIn–Pn complex has a ¹ππ* feature. Because both the HOMO and LUMO+14 localize on the isoindole moiety, the S₁(¹ππ*) state is quite a local transition. In addition, the S₂(¹A₂) state of this complex corresponds to the orbital transition from HOMO to LUMO+2 (47%) and HOMO to LUMO (18%), in which the HOMO π orbital is located over the isoindole, and the LUMO+2 and LUMO are located over the pyridine moiety, having a σ* nature. Thus the S₂ state has a CT-¹πσ* character.

Fig. 3 Selected frontier molecular orbitals of: (A) isoindole and quinoline monomers and (B) isoindole–pyridine and quinoline–pyrrole complexes.

Moreover, the first ¹B₁ excited state of iIn–Pn corresponds to the S₃–S₀ electronic transition, which is mostly arising from the HOMO–LUMO+7 single electron transition. Following inspection of Fig. 3, it is shown that the S₃–S₀ electronic transition of iIn–Pn has a charge transfer (CT)-¹ππ* nature. The HOMO π orbital locates over isoindole and LUMO+7, having a π* nature, locates over the pyridine moiety.

In Q–Pl, the perpendicular conformer, the first two excited states (S₁, S₂) belong to the A′ representation, while the first ¹A′′ state corresponds to the third (S₃–S₀) electronic transition.

From the RI-CC2 calculations, the S₁(¹A′) state, has a large oscillator strength, corresponding to the orbital transition from HOMO−3 to LUMO+3 (54%) and HOMO−1 to LUMO+11 (22%). From Fig. 3, it is seen that the HOMO−1 and HOMO−3 have a π character and LUMO+3 and LUMO+11 have a π* nature, thus the S₁ state of the Q–Pl complex can be assigned a ¹ππ* nature. Because all of the MOs, having important contributions in the S₁–S₀ transition of the Q–Pl complex, localized over the quinoline moiety, the S₁(¹ππ*) state is quite a local transition. In addition, the S₂(¹A′2) state of this complex mostly corresponds to the orbital transition from HOMO to LUMO+3, in which the HOMO, π orbital, locates over the pyrrole monomer, and the LUMO+3, π* orbital, locates over the quinoline moiety. Thus the S₂ state, is a ¹ππ* state, having a significant CT character.

3.3. Excited-state minimum geometries and adiabatic excitation energies

The excited-state optimized geometries are required for determination of adiabatic electronic transition energies, which are more appropriate for comparison with corresponding experimental 0–0 bands. In addition, the optimized geometry of the excited state can be a good sign for photophysical exploration, based on the large geometry deformations, hydrogen/proton transfer⁵⁶ processes and ring opening/ring puckering alterations.^57,58 There is a large possibility for each type of deformation to be responsible for an ultrafast non-radiative relaxation pathway of the excited systems to the ground via conical intersections.⁴⁶ Thus we have determined the local and CT-¹ππ* optimized geometry of each complex at the RI-CC2/aug-cc-pVDZ level of theory. The results relevant to the most stable conformers will be briefly discussed.

For the isoindole–pyridine complex, the most stable conformer is a perpendicular structure, which belongs to the C_2v symmetry point group. We have optimized the S₁(¹B₂), S₂(¹A₂) and S₃(¹B₁) states of this conformer, at the RI-CC2/aug-cc-pVDZ level of theory. In Fig. 4, a comparison of the minimum structures between the ground and excited states of the perpendicular conformer are presented. For this conformer, the lowest excited singlet state is of LE-¹ππ* character. Following photoexcitation of this conformer, the H⋯N hydrogen bond decreases by 0.087 Å, while the N–H distance increases by 0.011 Å (Fig. 4a and b). As a consequence, the binding energy of the intermolecular hydrogen bond H⋯N between isoindole and pyridine greatly increases from −0.48 eV to −0.60 eV, which shows a slight increase after excitation. However, the second electronic transition of isoindole–pyridine, is of ¹πσ* character; the π orbital localized on the isoindole part and the σ* orbital mostly locate over the pyridine moiety. Thus the ¹πσ* state has a CT character. The minimum geometry of iIn–Pn (for both conformers), has been determined based on the CC2 geometry optimization. The excited state proton transfer takes place from isoindole to the pyridine moiety.

Fig. 4 Comparison between the optimized structures of the iIn–Pn and Q–Pl complexes at the ground and LE-¹ππ* and CT-¹ππ* excited states. The red circles indicate the transferred proton.

Moreover, the third electronic transition of isoindole–pyridine (S₃–S₀) is of charge transfer ¹ππ* character (i.e. from isoindole to pyridine). The minimum geometry of iIn–Pn has been determined based on the CC2 geometry optimization (Fig. 4c). As shown, at the excited S₃ state, the N–H proton of isoindole transfers to the pyridine N atom. The N–H distance in the pyridine part has been determined to be 1.074 Å, and the H⋯N is 1.687 Å. Also, for the planar conformer of isoindole–pyridine, the lowest three electronic transitions have the same characters as the perpendicular complex.

The optimized geometry of the two first excited states of quinoline–pyrrole for its most stable conformer (perpendicular) can be compared with its ground state structure from Fig. 4d and e. The optimized ground state structure belongs to the C_s symmetry point group. The first and second electronic transitions are LE-¹ππ* and CT-¹ππ* states respectively. The minimum geometry (Fig. 4b) of the lowest excited singlet state, S₁(LE-¹ππ*), does not show significant geometry alteration. Nevertheless the S₂(CT-¹ππ*) geometry optimization has been predicted to accompany a proton transfer from pyrrole to the quinoline moiety.

The adiabatic excitation energies and corresponding oscillator strengths of the two lowest excited singlet states of the two considered conformers of the iIn–Pn and Q–Pl complexes optimized by RICC2/aug-cc-pVDZ calculation are presented in Table 2. The adiabatic transition energy of S₁(¹ππ*)–S₀ for the most stable conformers of isoindole–pyridine and quinoline–pyrrole have been determined to be 3.79 eV and 4.21 eV respectively.

Table 2 Excited transition energies (vertical and adiabatic) of isoindole–pyridine and quinoline–pyrrole complexes, computed at the CC2/aug-cc-pVDZ level of theory. The CC2 geometry optimization at the S₂ and S₃ excited states is accompanied with large deformations, thus, we were unable to report their corresponding adiabatic transition energies

	Electronic state	Vertical transition energy/eV	Oscillator strength	Adiabatic transition energy/eV
iIn–Pn, perp.	S1(B2) [LE-ππ*]	4.04	0.0668	3.79
	S2(A2) [CT-πσ*]	4.17	0.0000	—
	S3(B1) [CT-ππ*]	4.29	0.0000	—
iIn–Pn, planar	S1(B1) [LE-ππ*]	4.04	0.0627	3.79
	S2(A2) [CT-πσ*]	4.18	0.0000	—
	S3(B1) [CT-ππ*]	4.33	0.0017	—
Q–Pl, perp.	S1(A′) [LE-ππ*]	4.35	0.0260	4.20
	S2(A′) [CT-ππ*]	4.49	0.0268	—
	S5(A′′) [CT-πσ*]	5.08	0.0000	—
Q–Pl, planar	S1(A′) [LE-ππ*]	4.36	0.0257	4.21
	S2(A′) [CT-ππ*]	4.47	0.0025	—
	S5(A′′) [CT-πσ*]	5.01	0.0002	—

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Unfortunately, there is no experimental value relevant to electronic transitions of studied complexes to be considered for the evaluation of our theoretical results. However, in previous sections for the S₁–S₀ determination of the individual monomers, we have clarified that our theoretical level of calculations shows an approximately 0.20 eV overestimation error.^52,59 Thus the corrected adiabatic transition energy of iIn–Pn and Q–Pl will amount to 3.59 eV and 4.01 eV respectively.

3.4. Potential energy profiles and internal conversions

3.4.1. Isoindole–pyridine. The CC2 geometry optimization of the isoindole–pyridine complex at the S₃(¹B₁-¹ππ*) state leads to a proton transfer from isoindole chromophore to pyridine. Thus we have been motivated to investigate the PE profiles of this complex along the PT reaction coordinate. In Fig. 5, the CC2 PE profiles calculated along the minimum-energy path for proton transfer from the isoindole N–H group to the N atom of pyridine are presented. For clarity, only the lowest three excited singlet states (LE-¹ππ*, CT-¹πσ* and CT-¹ππ* states) along with the electronic ground state are displayed. The geometries of all solid curves have been optimized along the reaction path, while the dashed line (i.e. ground-state PE profile) is computed at the CT-¹ππ* optimized geometries as a complementary potential energy curve. Thus, the S₁^S1 denotes the energy of the S₁ state calculated along the reaction path, optimized in the S₁ state (without symmetry constraint), while the S₁^S1(ππ*-LE) denotes the energy of the S₁ state calculated along the reaction path optimized in the S₁(ππ*-LE) state, under the C_s symmetry constraint. Also, the S₀^S0 notation denotes the energy of the S₀ state calculated along the reaction path optimized in the S₀ state, etc.

Fig. 5 CC2 PE profiles of the isoindole–pyridine complex at the electronic ground state and few excited states, as a function of the N–H stretching coordinate. Full lines represent the minimum energy profiles of the reaction paths determined in the same electronic state (S₀^(S0), S₁^(S1), …), while the dashed line (S₀^(ππ*)) stands for the energy profile of the ground state based on the optimized complementary electronic S₃ (CT-ππ*) state. The red coloured curve shows the minimum S₁ potential energy profile of isoindole–pyridine based on the CC2 geometry optimization of the S₁ state without symmetry considerations.

Following an inspection of the results presented in Fig. 5, it is seen that the PE profiles of the ground state and the lowest valence LE-¹ππ* excited states increase with increasing N–H distance, while the PE profile of the CT-¹ππ* state is essentially repulsive. The increasing trend of the S₀ PE profile indicates that the ground state hydrogen/proton transfer process in isoindole–pyridine is extremely unlikely due to its endoenergetic nature (ΔE > 1.0 eV). The repulsive CT-¹ππ* PE profile crosses with the LE-¹ππ* and CT-¹πσ* MPE profiles at the beginning of the reaction coordinate and then intersects with the S₀ potential energy profile at the end of the reaction path, where the proton is entirely transferred to the pyridine moiety. In a multidimensional picture, the CT-(¹ππ*)-S₀ curve crossing in Fig. 5 develops into a conical intersection (CI).^16,17,19,60 Although there are two CIs (LE-¹ππ*/CT-¹πσ* and CT-¹ππ*/LE-¹ππ*) at the beginning of the reaction coordinate, the latest CI (CT-¹ππ*-S₀) is real because its relevant PE profiles (i.e. CT-¹ππ* and the S₀ state) have been determined based on the same optimized geometries. This conical intersection can be responsible for ultrafast nonradiative relaxation of the isoindole–pyridine complex, after photoexcitation to the S₁ LE-(¹ππ*) excited state.

One may be concerned with the barrier existing at the beginning of the reaction coordinate, in the region where LE-(¹ππ*) intersects with the CT-(¹ππ*) excited state. We have determined the adiabatic PE profile of the coupled LE-(¹ππ*)-CT-(¹ππ*). This PE sheet has been determined based on S₁ geometry optimization, without any symmetry constraint. In this manner, the vibronic coupling between LE-¹ππ* and CT-¹ππ* will be allowed. However, the adiabatic PE profile exhibits no barrier in the vicinity of the conical intersection. The barrier-less S₁ potential energy curve indicates ultrafast dynamics of the ESHT/PT process from isoindole to the pyridine moiety.

Furthermore, the credibility of the RI-CC2, as a single reference method, for determination of the excited state potential energy profiles, is a subject of question. However, this matter has been investigated previously⁵¹ by comparing the CC2 PE results with accurate CASPT2 and MR-AQCC data. It has been established that RI-CC2 predicts qualitatively reliable energy profiles and its results are reliable for the qualitative determination of PE profiles.^2,15,61–64

3.4.2. Quinoline–pyrrole. In Fig. 6, the CC2 PE profiles calculated along the minimum-energy path for proton transfer between pyrrole and quinoline are presented. Only the lowest LE-¹ππ*, CT-¹ππ* and the electronic ground state are displayed. However, for determination of the potential energy curves, the geometries of the ground and excited states have been optimized along the reaction path, while a complementary ground state PE profile has been determined on the basis of the CT-¹ππ* optimized geometries. The reaction coordinate is defined as the N–H bond distance of the pyrrole monomer and describes the position of the proton relative to the nitrogen atom of pyrrole. It is shown that the PE profiles of the ground state and the lowest ¹ππ* excited state slightly increase with an increase in the reaction coordinate, while the CT-¹ππ* profile has a decreasing pattern.

Fig. 6 CC2 PE profiles of the quinoline–pyrrole complex at the electronic ground state and a few excited states, as a function of the N–H stretching coordinate.

From the increasing trend of the S₀ PE profile in Fig. 6, it is seen that the ground state hydrogen/proton transfer (GSHT/PT) process from pyrrole to quinoline is quite unlikely due to its endoenergetic nature (needing at least 1.0 eV energy). Nevertheless, the minimum potential energy curve of the CT-¹ππ* state shows a decreasing trend following a flat structure at the beginning of the reaction coordinate. Thus, it crosses with the local ¹ππ* PE profile and later, at the end of the reaction coordinate, it approaches the ground state PE sheet. Although our results do not exactly show the curve crossing between the CT-¹ππ* state of the quinoline–pyrrole complex with that of the S₀ state, at the end of reaction coordinate, the difference between these two levels is only 0.10 eV. This small energetic-gap significantly increases the electronic-coupling possibilities between the two states, which can play the role of a curve crossing at the end of the reaction coordinate.

It is noteworthy that the RI-CC2 method, owing to its single reference nature, is not appropriate for treatment of the regions which have strong multi-reference characters such as conical intersections and bond breaking regions. Instead, it is trustworthy for the qualitative determination of the PE profiles in these regions.^61–65

The resulting lower adiabatic PE sheet of the coupled LE-¹ππ*/CT-¹ππ* states exhibits a small barrier roughly in the middle of the reaction coordinate, corresponding to the position where a proton is located between two monomers. We have evaluated this barrier by breaking the C_s symmetry of the system. The barrier has been estimated to be 0.30 eV. In the gas phase, a wave packet prepared in the LE-¹ππ* state of the quinoline–pyrrole complex by optical excitation with sufficient excess energy (≃0.3 eV) will bypass this barrier and then evolve on the CT-¹ππ* surface. The low-energy part of the ¹ππ* surface is separated from the region of the strong non-adiabatic interactions with the ground state by this barrier on the PE surface of the lowest excited singlet state.

4. Conclusion

Ab initio electronic-structure and reaction-path calculations have been performed to characterize the intra-cluster proton-transfer processes in isoindole–pyridine and quinoline–pyrrole complexes. It has been predicted that a nonradiative deactivation mechanism in the titled complexes is mostly governed by the N–H bond stretching and the S₁/S₀ conical intersections. The PE profile of the CT-¹ππ* state is dissociative along the N–H reaction path. The N–H bond elongation, mediated by coupled electron/proton transfer, leads to deactivation via CT-¹ππ*/S₀ conical intersection. In this respect, two readily accessible conical intersections of LE-ππ*/CT-¹ππ* and CT-¹ππ*/S₀ in the gas phase, which are encountered along the reaction path, are responsible for nonradiative relaxation of these types of complexes. However, for the isoindole–pyridine complex, this relaxation pathway has been predicted to be quite barrier-free, while in the quinoline–pyrrole case, a barrier of 0.30 eV in the middle of reaction coordinate, prohibits the excited wave-packet from the FC region of LE-¹ππ* to proceed quickly along the N–H reaction coordinate. Nevertheless, the tunneling effect of the hydrogen atom through this barrier increases the possibility of its access to the dissociative part of the S₁ PE profile. The conical intersection arisen from the coupled electron/proton transfer process in the quinoline–pyrrole complex can be responsible for ultrafast nonradiative deactivation of the S₁ excited system to the ground via internal conversions.

Acknowledgements

The research council of Isfahan University is acknowledged for financial support. We kindly appreciate the use of computing facility cluster GMPCS of the LUMAT federation (FR LUMAT2764).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra18950k

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