Photorelaxation Pathways of 4-(N,N-Dimethylamino)-4'-nitrostilbene Upon S1 Excitation Revealed by Conical Intersection and Intersystem Crossing Networks.

Multi-state n-electron valence state second order perturbation theory (MS-NEVPT2) was utilized to reveal the photorelaxation pathways of 4-(N,N-dimethylamino)-4'-nitrostilbene (DANS) upon S1 excitation. Within the interwoven networks of five S1/S0 and three T2/T1 conical intersections (CIs), and three S1/T2, one S1/T1 and one S0/T1 intersystem crossings (ISCs), those competing nonadiabatic decay pathways play different roles in trans-to-cis and cis-to-trans processes, respectively. After being excited to the Franck-Condon (FC) region of the S1 state, trans-S1-FC firstly encounters an ultrafast conversion to quinoid form. Subsequently, the relaxation mainly proceeds along the triplet pathway, trans-S1-FC → ISC-S1/T2-trans → CI-T2/T1-trans → ISC-S0/T1-twist → trans- or cis-S0. The singlet relaxation pathway mediated by CI-S1/S0-twist-c is hindered by the prominent energy barrier on S1 surface and by the reason that CI-S1/S0-trans and CI-S1/S0-twist-t are both not energetically accessible upon S1 excitation. On the other hand, the cis-S1-FC lies at the top of steeply decreasing potential energy surfaces (PESs) towards the CI-S1/S0-twist-c and CI-S1/S0-DHP regions; therefore, the initial twisting directions of DN and DAP moieties determine the branching ratio between αC=C twisting (cis-S1-FC → CI-S1/S0-twist-c → trans- or cis-S0) and DHP formation relaxation pathways (cis-S1-FC → CI-S1/S0-DHP → DHP-S0) on the S1 surface. Moreover, the DHP formation could also take place via the triplet relaxation pathway, cis-S1-FC → ISC-S1/T1-cis → DHP-T1 → DHP-S0, however, which may be hindered by insufficient spin-orbit coupling (SOC) strength. The other triplet pathways for cis-S1-FC mediated by ISC-S1/T2-cis are negligible due to the energy or geometry incompatibility of possible consecutive stepwise S1 → T2 → T1 or S1 → T2 → S1 processes. The present study reveals photoisomerization dynamic pathways via conical intersection and intersystem crossing networks and provides nice physical insight into experimental investigation of DANS.

1. Introduction

Molecules with π-conjugated moieties are widely used as photochromic probes and light-driven molecular motors for their peculiar photo-induced isomerization towards the ethylenic bridge [1,2,3,4,5]. As a representative model, stilbene serves as the parent moiety in series of photoswitches [6,7,8,9,10,11]. Upon excitation to the S1 state, both trans- and cis-stilbene evolve along the C=C torsion coordinate and decay via twisted S1/S0 conical intersections (CIs) [12], while for substituted stilbene, the triplet route mediated by intersystem crossing (ISC) may open [13,14], and the formation of stable intramolecular charge transfer (ICT) states evidently affect the fluorescence efficiency [13,14,15,16,17,18,19]. Therefore, the optical properties of stilbenes can be controlled by introducing suitable substitution groups [8]. For example, the nitro, cyano and halogen substitution on the phenyl ring promotes the triplet pathway [20,21,22]; however, the amino group substitution raises the C=C torsion barrier and evidently slow down the isomerization process [23,24].

The 4-(N,N-dimethylamino)-4′-nitrostilbene (DANS) is a typical example of the so called “push–pull” chromophore, which has electron donor (D) and acceptor (A) groups simultaneously. In recent decades, the DANS has attracted great interests for its applications in nonlinear optics (NLO) [25,26] as second-harmonic generators [27] and waveguide electro-optical modulators [28,29] and in organic light-emitting diodes (OLEDs) as emitting color tuners [30]. The ground state trans-DANS possesses a neutral electronic structure with the delocalized π electrons covering the entire molecule. Upon photoexcitation, the electronic structure converts to highly polarized zewitterionic form yielding the planar ICT (PICT) state, which is also known as the locally excited (LE) state [13,14,15,31,32,33,34]. Subsequently, twisting towards central double bond or D/A groups populate the non-fluorescent rotamer or fluorescent twisted ICT (TICT) state, respectively [17]. As a fact of the mixing and interconversion of the conjugated and polarized electronic structures, the complex relaxation dynamics of excited-state DANS are extraordinarily sensitive to the surrounding polarities [35,36,37,38]. The fluorescence quantum yield of DANS increases with solvent changes from non-polar to slightly polar, but then decreases to nearly zero with further increases of solvent polarity. On the other hand, the Stokes shift increases synchronously with the solvent polarity, whereas the photoisomerization quantum yield (Φiso) decreases monotonously. These phenomena were attributed to the interplay of various relaxation pathways [13,14,15,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45]. As proposed on spectroscopy studies in nonpolar solvents [9,10,11], the spin-orbit coupling (SOC) between singlet and triplet states for the transoid intermediate (1t*) is strong enough to populate the transoid triplet conformer (3t*) via ISC. Along the efficient triplet-state C=C bond twisting route, another ISC from the triplet (3P*) to singlet (1P) states takes place at the perpendicular configuration and yields to either trans or cis ground-state isomer with equal probabilities. In slightly polar solvents, fluorescence quantum yields of DANS increase to ~0.5, which is attributed to the formation and radiation decay of the second transoid S1 conformer A* via torsion of dimethylamilino and/or nitrophenyl moieties [14,41]. Meanwhile, the S1 state C=C bond twisting barrier between planar and perpendicular configurations reduces the isomerization yield. In polar solvents, the non-radiative A* becomes more stable for enhanced interactions with solvents; hence both trans ↔ cis isomerization and fluorescence are eliminated [27,28,29]. The A* is proposed to be a TICT state; however, the leading twisting coordinate has been debated for decades. In DANS, the nitro, nitrophenyl, dimethylamino and dimethylaminophenyl groups could twist towards linking bond to perpendicular configuration. Based on the comparative study on DANS and its structural analogues, the formation of the TICT state in polar solvents was attributed to the nitro group torsion [35,36], and the relaxation time constant was suggested to be several picoseconds on time-resolved spectroscopy studies [32,33]. In contrast, studies on torsional hindered aminostilbenes suggest that the twisting of phenylene-amino C–N bond yields to the TICT state [43]. Recently, the combined transient absorption spectroscopy and density functional theory (DFT) calculation studies [37,38] agreed that the nitrophenyl torsion is the dominate relaxation process, as disclosed in previous semiempirical calculation [46].

Comparing with sustained experimental interests on DANS, the theoretical studies are limited [36,37,38,46,47,48,49,50,51,52,53,54,55,56]. Early theoretical studies with semiempirical methods [36,47,48,49,50], i.e., AM1, PM3, MNDO and INDO, have suggested the planar ground state trans-DANS. Coupled with the configuration interaction technique, those semiempirical methods were utilized to predict the vertical excitation energies (VEEs), dipole moments and oscillator strengths [41,42,43]. In the semiempirical SAM1 study by Farztdinov and Ernsting [46], the solvent polarity dependence of the twisted intermediates towards the five moieties (C=C, nitro, nitrophenyl, dimethylamino and dimethylaminophenyl) was presented. The variation of energy sequences affect the fluorescence quantum yields, ISC, and trans ↔ cis isomerization of DANS after excitation to S1. Recently, the DFT and time-dependent DFT (TDDFT) calculations were performed for DANS to explore the experimental results of vibrational spectroscopy [52], two photon absorption [53], protonation effects [54] and reduction reaction [55]. Based on the potential energy curves (PECs) along different rotation coordinates, the mechanisms for the formation of TICT states were analyzed [37,38] and the evidences for possible CI and ISC regions were also revealed [37].

Although great efforts have been devoted to uncovering the nature of this unique push–pull chromophore, the discrepancies within the proposed mechanisms clearly indicated that deeper understanding on this molecule is desired, especially from the theoretical point of view. To establish the networks for nonadiabatic decay, the multi-reference computational methods should be employed [57,58], and which are capable of interpreting the interplay of electronic configuration and conformation conversion accompanied with the relaxation process. In this work, we have optimized the stationary geometries, CIs and ISCs within the S0, S1, T1 and T2 states of DANS and presented the possible photorelaxation pathways by multi-state n-electron valence state second order perturbation theory (MS-NEVPT2) method. The rest of the paper is organized as follows. Section 2 briefly describes the computational methods. Section 3 displays all the optimized geometries that participate in the relaxation dynamics and the analyses on the possible relaxation pathways. Concluding remarks and future prospects are given in Section 4.

2. Theoretical Methods and Computational Details

In this work, the lowest three singlet and three triplet states of DANS were considered in the state-average procedure of complete active space self-consistent field (CASSCF) [59,60] with equal weights (SA6-CASSCF). The minima were optimized by the BDF program [61], and the transition states (TS), CIs (S1/S0 and T2/T1) and ISCs (S1/T2, S1/T1 and T1/S0) were optimized by the default procedure within the MOLPRO 2009.1 program [62]. The CASSCF method only considers static correlation energy without dynamic correlation correction and then evidently overestimates the vertical excitation energies, as seen in the results for trans-form DANS shown in Table S2 of the Supplementary Materials. It cannot properly revel the energy evolutions along possible relaxation processes. Therefore, for the SA6-CASSCF optimized geometries, the dynamic correction energies were calculated by the MS-NEVPT2 method implemented in the Xi’an-CI program [63,64] by employing molecular orbital integrals from the BDF program [61]. The 6-31G* basis set [65,66] was used for all atoms in the calculations. The SOC matrices were computed by using the state interaction approach with the Breit–Pauli Hamiltonian (HBP) in MOLPRO 2009.1 program [62]. To qualitatively analyze the photorelaxation pathways within the CI and ISC networks, we calculated the one-dimensional potential energy curves for the six coupled electronic states by linear interpolation of internal coordinates (LIIC) at the MS-NEVPT2 level (CASSCF results are given in the Supplementary Materials).

The accuracy of CASSCF calculation relies on the active space, and the CASSCF orbitals are the basis for MS-NEVPT2 calculation; therefore, the selection of active space is the most important procedure before performing the calculation study. The CASSCF calculation with full valence active space that consists of all the valence orbitals and electrons for DANS is computationally unaffordable. Therefore, the orbital properties and performance on vertical excitation energy prediction of some common reduced active spaces, such as CAS (10,8), CAS (10,10), CAS (12,12) and CAS (18,12) were investigated, and finally the CAS (18,12) was chosen with consideration of both the computation efficiency and accuracy. Based on the active molecular orbitals of those active spaces for trans-S0 and cis-S0 presented in Supplementary Materials Figure S1, it is evident that the corresponding orbitals of CAS (18,12) were in agreement with CAS (10,8) but different from CAS (10,10) and CAS (12,12). The latter orbitals were more balanced in the treatment of π and π* orbitals; however, CAS (18,12) for trans-S0 had four σ orbitals and more electrons distributed on the electron withdrawing group side than those on the electron donating group side. On the other hand, CAS (18,12) for cis-S0 had only one σ orbital, and the remaining π and π* orbitals were delocalized with electron distributions on both sides. It tended to attribute the different electron distributions of trans-S0 and cis-S0 to the molecular geometry. The planar geometry of trans-S0 led to strong electronic transfer, as shown in Supplementary Materials Figure S1 for active orbitals of CAS (18,12) and CAS (10,8), while the nonplanar geometry of cis-S0 hindered this transfer and maintained a more delocalized distribution. The vertical excitation energies from trans-S0 to S1 calculated by MS-NEVPT2 with reference functions from CAS (10,10) and CAS (12,12) were 4.16 eV and 5.01 eV, respectively, which were remarkably larger than 3.62 eV from CAS (10,8) and 3.53 eV from CAS (18,12) and then 2.97 eV from experiments in cyclohexane [14]. These evidently different S0 → S1 VEEs by respective active space can be explained by the electronic configuration of S1 state. For both CAS(18,12) and CAS(10,8), the main configuration of S1 corresponded to the HOMO → LUMO excitation with the weight of ~0.70, however, which reduces to only 0.51 in CAS(10,10) and gives rise to high excitation energy of 4.16 eV. Conversely, for CAS(12,12), the main configurations of S1 are HOMO → LUMO+2 (0.24), HOMO-3 → LUMO+1 (0.18) and HOMO-2 → LUMO+2 (0.12), respectively. The main configurations of S1 state of trans-S0 do not contain HOMO → LUMO excitation, while this excitation is one of the main configurations of S2 state and the energy gap between S1 and S2 is only 0.17 eV so that they are quasi-degenerate. The strong coupling between these two states may lead to the energy order change of them. Even though the high-lying S2 is assigned as S1, the high vertical excitation energy of 5.18 eV attributes to the small weight of HOMO → LUMO excitation (0.20). Since the initial excitation energy plays an important role in the photochemical reaction, the energy of CAS (18,12) was the closest one to experimental observation so that this active space was feasible for computations in this work.

In order to identify the availability of basis set 6-31G*, we have also performed comparative calculations with larger basis sets of 6-311G* and 6-311+G* for S0 → S1 VEEs at trans-S0 by MS-NEVPT2 with reference wavefunctions from SA6-CASSCF(18,12). The S0 → S1 VEEs by 6-31G*, 6-311G* and 6-311+G* are 3.53 eV, 3.37 eV and 3.14 eV, respectively, which are gradually approaching the experimental value of 2.97 eV with enlarging basis sets. Although the small basis set 6-31G* leads to 0.39 eV overestimation from that of 6-311+G*, which agrees with the convergence trend to experimental value by extending basis set. With the consideration of computations time cost by employing those two larger basis sets, 6-31G* is available basis set in this work.

3. Results and Discussion

The DANS is composed of five basic moieties, namely, olefinic double bond (DB), N,N-dimethylamino (DMA), N,N-dimethylaminophenyl (DAP), nitro (NT) and nitrophenyl (NP). The definition of important internal coordinates correlating with the photorelaxation processes and atomic numbering are given in Scheme 1. The SA6-CASSCF(18,12)/6-31G* optimized internal coordinates for the minimum energy geometries, such as trans-, cis-, twist-DANS, dihydrophenanthrene (DHP) states and ground state TS are listed in Table 1 and those for the CIs and ISCs are given in Table 2. The MS-NEVPT2 calculated potential energies on SA6-CASSCF optimized geometries for six interested states with respect to trans-S0 are presented in the Table 3 and Table 4 for stable geometries and crossings, respectively. The relative potential energies calculated by SA6-CASSCF and Cartesian coordinates for all the optimized geometries were given in Supplementary Materials.

Scheme 1

Important internal coordinates for the photorelaxation of DANS: bond length of the central double bond (rc=c), the bond angles toward inversion motion of the central double bond at amino (θA) or nitro (θN) side, and the dihedral angles corresponding to the torsion towards central double bond (αC=C), benzene ring connecting to the amino (αPh-A) or nitro (αPh-N) group, dimethylamino (αA) or nitro (αN) group and out-of-plane twisting of dimethylamino (αT-A) or nitro (αT-N) group.

Table 1

The SA6-CASSCF(18,12)/6-31G* optimized internal coordinates for the trans-, cis-, twist-, TS-DANS and DHP. a.

	r c=c	θ A	θ N	α C=C	αPh-A	αPh-N	α A	α N	α T-A	α T-N
trans-S0	1.351	127.36	126.31	180.00	−180.00	−180.00	0.00	0.00	−180.00	180.00
cis-S0	1.326	129.03	128.70	−4.21	135.64	138.83	66.01	−0.32	136.84	−179.92
DHP-S0	1.451	121.42	120.93	−11.00	178.88	−4.21	65.43	0.40	135.67	179.89
TS-S0	1.476	124.65	124.90	−92.20	−177.51	−177.89	−22.22	−0.11	−147.07	179.99
trans-S1	1.348	127.11	126.69	179.99	179.56	179.41	0.02	0.02	179.98	−179.98
twist-S1	1.443	125.27	123.77	−89.47	−179.51	−175.91	−0.13	−0.13	−179.44	179.86
DHP-S1	1.380	121.96	121.65	−8.40	162.46	169.35	61.04	1.45	137.58	−179.97
trans-T1	1.329	127.57	126.83	−180.00	−180.00	−180.00	0.00	0.00	−180.00	180.00
twist-T1	1.473	124.82	124.95	−90.88	−177.87	−177.31	63.80	−0.11	137.68	180.00
DHP-T1	1.366	121.74	121.34	−3.92	164.82	165.89	63.79	2.26	136.46	−179.95
trans-T2	1.330	127.51	126.93	−180.00	−180.00	−180.00	0.00	0.00	−180.00	180.00
cis-T2	1.337	131.08	128.80	−5.02	158.66	127.58	56.55	0.15	142.23	179.93
DHP-T2	1.447	120.30	121.56	−13.06	172.61	−179.46	64.66	0.87	135.99	179.95

a Bond lengths are in angstroms (Å); bond and dihedral angles are in degrees (°).

Table 2

The SA6−CASSCF(18,12)/6-31G* optimized internal coordinates for the conical intersections (CI) and intersystem crossings (ISC). a.

	r c=c	θ A	θ N	α C=C	αPh-A	αPh-N	α A	α N	α T-A	α T-N
CI-S1/S0-trans	1.400	127.88	124.39	−154.63	−137.36	−170.91	−67.28	−0.51	131.95	179.96
CI-S1/S0-cis	1.401	134.04	130.64	−31.98	129.04	−176.86	67.94	−0.31	135.67	−179.97
CI-S1/S0-twist-c	1.441	126.13	114.22	−109.14	178.61	−158.95	−6.14	0.39	−179.37	−179.97
CI-S1/S0-twist−t	1.454	126.22	97.28	−96.74	−175.11	140.11	−1.53	−2.26	−177.69	179.12
CI-S1/S0-DHP	1.401	122.81	121.21	−18.97	160.98	165.98	19.86	2.33	160.41	−179.92
CI-T2/T1-trans	1.329	126.56	126.13	−179.72	−161.99	−160.59	−14.81	0.03	137.51	−179.96
CI-T2/T1-cis	1.341	132.07	129.00	0.94	−178.69	87.75	14.37	0.05	−141.70	−179.95
CI-T2/T1-tict	1.383	126.91	122.80	179.79	179.18	−89.13	1.67	0.05	−177.34	−179.99
ISC-S0/T1-twist	1.474	124.93	125.05	−86.76	−178.90	−177.23	64.23	−0.08	137.69	180.00
ISC-S1/T1-cis	1.466	121.59	120.94	−36.99	165.78	172.89	10.83	0.35	176.12	179.68
ISC-S1/T2-trans	1.331	127.50	126.94	180.00	179.98	179.98	−0.01	−0.01	−179.98	179.99
ISC-S1/T2-cis	1.442	127.36	126.85	−49.66	173.40	176.60	1.06	0.23	179.55	179.80
ISC-S1/T2-twist	1.470	124.43	124.95	−98.65	−175.31	−176.93	−0.05	−0.01	−179.87	−179.94

a Bond lengths are in angstroms (Å); bond and dihedral angles are in degrees (°).

Table 3

The relative potential energies (in eV) calculated by MS-NEVPT2 method for the trans-, cis-, twist-, TS-DANS and DHP optimized by SA6-CASSCF (18,12).

Geometry	S0	S1	S2	T1	T2	T3
trans-S0	0.00	3.53	4.91	2.97	4.62	4.7
cis-S0	0.04	4.24	5.23	3.82	4.21	4.75
DHP-S0	1.38	4.48	5.59	3.48	4.89	5.36
TS-S0	2.12	2.87	5.30	2.15	5.25	5.27
trans-S1	0.75	3.23	5.02	3.03	3.28	4.97
twist-S1	2.22	2.45	5.37	2.38	5.30	5.34
DHP-S1	1.71	3.09	3.32	2.13	3.73	4.41
trans-T1	0.50	3.56	4.76	3.35	3.37	4.66
twist-T1	2.18	3.17	5.37	2.21	5.31	5.39
DHP-T1	1.75	3.49	3.74	2.15	4.43	5.30
trans-T2	1.46	3.94	5.84	3.72	4.11	5.78
cis-T2	0.30	3.83	5.40	3.43	3.94	4.94
DHP-T2	1.39	3.63	4.26	2.74	3.61	4.88

Table 4

The relative potential energies (in eV) calculated by MS-NEVPT2 method for the conical intersections and intersystem crossings optimized by SA6-CASSCF (18,12).

Geometry	S0	S1	S2	T1	T2	T3
CI-S1/S0-trans	4.28	4.77	7.72	4.58	7.67	7.91
CI-S1/S0-cis	4.91	5.20	8.10	4.96	8.04	8.65
CI-S1/S0-twist-c	2.99	3.20	6.01	3.19	5.54	5.99
CI-S1/S0-twist-t	3.77	4.20	6.82	4.21	6.33	6.41
CI-S1/S0-DHP	2.12	2.61	3.41	2.49	4.47	4.88
CI-T2/T1-trans	1.23	3.27	5.59	3.06	3.70	4.59
CI-T2/T1-cis	0.39	4.17	5.61	3.71	4.14	5.08
CI-T2/T1-tict	0.67	4.01	5.89	4.15	4.38	5.38
ISC-S0/T1-twist	2.17	3.21	5.38	2.24	5.37	5.38
ISC-S1/T1-cis	2.60	3.24	4.71	3.03	5.46	5.89
ISC-S1/T2-trans	1.60	3.39	5.62	3.20	3.76	5.56
ISC-S1/T2-cis	0.61	2.87	4.79	1.82	4.08	4.10
ISC-S1/T2- twist	2.47	4.87	5.07	2.56	5.04	5.43

3.1. Minimum Geometries in trans-, cis- and twist-DANS and DHP Form

By employing the CASSCF (18,12) calculation, the trans-form DANS minima were optimized in S0, S1, T1 and T2 states; however, only in S0 and T2 states could the cis-form minima be observed, and alternatively, the twist-form minima were obtained in S1 and T1 states. Furthermore, the ring-closing products of cis-DANS, 4a,4b-DHP conformers were optimized in all involved states. All the trans-minima were planar due to the conjugated π orbitals that covering the entire molecule. In agreement with previous semiempirical and DFT calculations [37,38,46], the C7–C8 was a double bond with length of 1.351 Å in optimized trans-S0; the NP and DAP moieties were in benzoid form. The geometries of trans form minima in S1, T1 and T2 states were quite similar to trans-S0. For trans-S0, the vertical excitation energy (VEE) to the S1 state (3.53 eV) was quite close to trans-S1 (3.23 eV) and trans-T1 (3.35 eV), and considering their similar geometry, there are competing relaxation pathways in S1 and T1 states.

In cis-S0, the DB moiety was very flat with C7=C8 of 1.326 Å and the benzene rings in NP and DAP twisted ~45° to eliminate the repulsion between them. Similar to trans-T2, the C7-C8 in cis-T2 was a double bond and as a fact of the localized electronic excitation in NP, the twisting of the DAP and NP moieties were nonsymmetrical, with αPh-A = 158.66° and αPh-N = 127.58°, respectively. In S0, S1, T1 and T2 states, we also obtained the DHP form minima, which were the ring-closing product of cis conformers on the respective state. For these DHP isomers, the π-conjugation system broke down due to the redundant H15 and H26 atoms, which resulted in a distorted phenanthrene plane. The phenanthrene ring in DHP-S0 occupied a polyene configuration with alternating single and double bonds. The aromaticity of DHP-S1, DHP-T1 and DHP-T2 was stronger, and the C-C bond lengths in the phenanthrene ring were more averaged in comparison with DHP-S0.

For the S1 and T1 states, the DANS molecule could twist towards the evidently weakened C7–C8 bond and thus the twist-S1 and twist-T1 achieved stable minima with similar αC=C. Moreover, the DMA moiety was planar in twist-S1, but pyramidal in twist-T1. In twist-S1, there were independent conjugated systems within quinoid DAP and NP, respectively, leading to the planar DMA moiety. However, in twist-T1, both NP and DAP were in typically benzoid form, and the DMA was pyramidalized. These midway minima along the αC=C torsional path overlapped with the twisted form CIs and ISCs, and played important roles in nonadiabatic relaxation dynamics. The TS-S0 lay in the middle of the αC=C torsional path with αC=C = −92.20°, αPh-A = −177.51° and αPh-N = −177.89°, respectively. Moreover, the two methyl groups in DMA bent in the same direction without twisting around C12–N24. The ground state cis ↔ trans isomerization process could be divided into two parts, from trans-S0 to TS-S0, basically evolving along αC=C torsion with slight pyramidalization of DMA, and from TS-S0 to cis-S0, there were synchronous twistings towards αC=C, αPh-A and αPh-N.

3.2. Conical Intersections and Intersystem Crossings

The investigation on CIs and ISCs within low-lying electronic states of DANS is of crucial importance in unveiling the nature of nonadiabatic decay accompanied with trans ↔ cis isomerization and ring-closing reactions [67,68]. In previous studies, crossing regions were avoided and singlet–triplet quasi-degenerations were disclosed in one-dimensional PECs towards αC=C [37]; however, the geometries and properties for possible CIs and ISCs involved in the photoisomerization and ring-closing of DANS are still unknown. In this work, we observed five S1/S0 and three T2/T1 CIs and three S1/T2, one S1/T1 and one S0/T1 ISCs at the SA6-CASSCF(18,12)/6-31G* level and the optimized geometries are depicted in Figure 1.

Figure 1

Geometries for SA6-CASSCF (18,12) optimized CIs and ISCs of DANS.

Four S1/S0 CIs were distributed along the S1 trans ↔ cis isomerization pathway with αC=C of −31.98°, −109.14°, −96.74° and −154.63°, and labelled as CI-S1/S0-cis, CI-S1/S0-twist-c, CI-S1/S0-twist-t and CI-S1/S0-trans, respectively. In CI-S1/S0-cis, the C7–C8 bond became polarized and increased to 1.401 Å. The C7 atom was still in sp2 hybridization, and both C7 and H20 atoms stayed coplanar with an NP moiety. In contrast, the C8 converted to sp3 hybridization with H21 distortion to the rear side of C7–C8, similar as a hydrogen migration TS. Moreover, the DAP moiety also twisted towards C7–C8 with a αPh-A decrease to 129.04°. The DB moiety in CI-S1/S0-trans was similar to that in CI-S1/S0-cis, except that the pyramidalization of C8 atom was in the opposite direction. Accompanied with the DAP twisting towards the DANS molecule plane for 42.64°, the DMA turned perpendicular to the neighboring benzene plane. As a fact of the highly distorted geometry, the potential energies of CI-S1/S0-cis and CI-S1/S0-trans were ~1.00 eV higher than S1-S0 VEE of the respective ground state minima. Hence, these two CIs were not energetically accessible on gas phase dynamics upon S1 excitation. The highly distorted CI-S1/S0-twist-c and CI-S1/S0-twist-t were ~0.43 eV lower and ~0.45 eV higher than trans-S1-FC, respectively, but both were lower than cis-S1-FC with ~1.14 eV and ~0.25 eV. The polarization of C7 and C8 atoms also existed in CI-S1/S0-twist-c or CI-S1/S0-twist-t; however, pyramidalization took place at the C7 atom in the opposite direction and exhibited –65.98° and –132.53° of dihedral angle H20–C7–C8–H21, respectively. In both of them, the DAP moiety stayed coplanar with C7–C8, while the NP moieties twisted 22.75° and –30.42° towards C7–C8, respectively.

In vicinity of trans-S1, we optimized ISC-S1/T2-trans, which was only ~0.05 eV and ~0.35 eV higher than trans-S1-FC and trans-S1, respectively, and their representative internal coordinates were very similar. Moreover, the SOC at ISC-S1/T2-trans was 41.6 cm−1 and thus was an efficient relaxation channel. With αPh-A and αPh-N twisting for 18.01° and 19.41° and pyralmidalization of DMA, the CI-T2/T1-trans was observed at ~0.20 eV lower than ISC-S1/T2-trans and could serve as the intermediate for the S1 → T1 decay process. Twisting of the NP moiety alone created CI-T2/T1-tict, in which both NP and DAP moieties were planar and perpendicular to each other. However, the energy of CI-T2/T1-tict was ~1.03 eV higher than trans-S1, therefore, which was hardly achieved by trans-DANS upon S1 excitation.

Along the DB twisting coordinate started from the cis-S1-FC region, we optimized the CI-S1/S0-DHP, ISC-S1/T1-cis and ISC-S1/T2-cis with αC=C values of −18.97°, −36.99° and −49.66°, respectively. Additionally, the SOC at ISC-S1/T1-cis and ISC-S1/T2-cis were both less than 1.0 cm−1, respectively. The peculiar CI-S1/S0-DHP and ISC-S1/T1-cis lay in the ring-closing pathway that led to the formation of DHP on S0 and T1 states, respectively. Similar reaction pathways have been reported for tetraphenylethylene [69]. The potential energies of CI-S1/S0-DHP and ISC-S1/T1-cis were ~1.87 and ~1.10 eV lower than cis-S1-FC, respectively. Within CI-S1/S0-DHP (ISC-S1/T1-cis), both of the two benzene rings twisted clockwise to approach each other with C1–C14 distance at only 1.984 (2.174) Å. Simultaneously, the C1 and C14 atoms showed evident an pyramidal structure with the C1–H15 and C14–H26 bonds bending out of the respective benzene ring plane for ~40 (~29)°. The ISC-S1/T2-cis lay at ~0.77 eV lower than cis-S1-FC with both NP and DAP moieties in planar form. The CI-T2/T1-cis lay in the vicinity of the cis-S1-FC region with αC=C of −1.1°, in which the planar NP moiety stayed perpendicular to the coplanar DB and DAP moieties and the energy was ~0.32 eV lower than cis-S1-FC. The steep αC=C twisting pathway with the reverse motion from low energy ISC-S1/T2-cis to high energy CI-T2/T1-cis along the reverse direction was unlikely to take place, and thus ISC-S1/T2-cis and CI-T2/T1-cis were not suitable partners to accomplish the S1 → T1 relay decay process within cisoid conformation. The alternative decay channel for T2 DANS after passing ISC-S1/T2-cis involved ISC-S1/T2-twist that lay in the middle of the αC=C twisting pathway. However, the energy was ~0.72 eV higher than cis-S1-FC, and the SOC had an extremely weak strength of 0.2 cm−1; therefore, the ISC-S1/T2-twist was located beyond the accessible region of cis-DANS upon S1 excitation. Moreover, the high energy ISC-S1/T2-twist prevented further forward αC=C twisting on the T2 surface and thus excluded the possibility of decay via transoid form CI-T2/T1-tict or CI-T2/T1-trans. For molecules in the T1 state, the decay channel to the S0 state passed through ISC-S0/T1-twist, which overlapped with the trans-T1 potential well and lay above the TS-S0.

3.3. The Relaxation Pathways for DANS Upon S1 Excitation

It is well accepted that the interplay of minima, CIs and ISCs determines the fate of excited-state molecule; therefore, the LIIC curves that connect those critical geometries present the intuitive view for the possible relaxation pathways. The MS-NEVPT2 calculated LIIC curves for CI-S1/S0-twist-c, CI-S1/S0-DHP and ISC-S1/T1-cis with the corresponding reactant and product are depicted in Figure 2a, Figure 2b and Figure 2c, respectively. The LIIC for multistep triplet relaxation pathway that involves ISC-S1/T2-trans, CI-T2/T1-trans and ISC-S0/T1-twist is presented in Figure 2d. Based on these LIIC curves, the qualitative analysis on the photoisomerization mechanisms of trans- and cis-DANS upon S1 excitation is presented.

Figure 2

The linear interpolations of internal coordinates (LIICs) for (a) trans-S1-FC ↔ CI-S1/S0-twist-c ↔ cis-S1-FC, (b) cis-S1-FC ↔ CI-S1/S0-DHP ↔ DHP-S0, (c) cis-S1-FC ↔ ISC-S1/T1-cis ↔ DHP-T1 ↔ DHP-S0 and (d) trans-S1-FC ↔ ISC-S1/T2-trans ↔ CI-T2/T1-trans ↔ ISC-S0/T1-twist ↔ cis-S1-FC calculated by MS-NEVPT2 method.

After photoexcitation to trans-S1-FC, in-plane geometrical and electronical rearrangement took place and the molecule converted to the quinoid form. The subsequent relaxation may have been proceeding via intramolecular vibrational energy redistribution within trans-S1 potential well to populate enough energy to out-of-plane torsion modes and start the relaxation along αC=C twisting coordinate. Another choice was stepwise decay to the T1 state via ISC-S1/T2-trans that overlapped with the trans-S1 potential well region and CI-T2/T1-trans and was followed by DB torsional relaxation in T1 state. A similar triplet relaxation channel was suggested by previous spectroscopy studies [13,14,18]. The relaxation started from cis-S1-FC was faster than those from trans-S1-FC because of disappearance of bound potential well around cis-S1-FC and the much steeper PES towards crossing regions. The simultaneous twisting of DAP and NP in the same or opposite direction gave rise to the competing DHP formation and αC=C twisting relaxation pathways. Along ring closing, there was bifurcation into singlet or triplet pathway via CI-S1/S0-DHP and ISC-S1/T1-cis, respectively. Additionally, the αC=C twisting pathway via ISC-S1/T2-cis was excluded because all the possible consecutive decays, via CI-T2/T1-cis, CI-T2/T1-tict, CI-T2/T1-trans or ISC-S1/T2-twist, were not favored under S1 excitation. DANS trapped in twist-S1 or twist-T1 potential well could return to the ground state and yield to either cis- or trans-S0 via CI-S1/S0-twist-c and ISC-S0/T1-twist, respectively.

The detailed information for relaxation dynamics is given as follows. Except for CI-S1/S0-twist-c, the other three CIs along S1 αC=C twisting pathway of DANS, CI-S1/S0-cis, CI-S1/S0-twist-t and CI-S1/S0-trans lay beyond the capability of S0 → S1 vertical excitation of the adjacent cis-S0 or trans-S0 and thus prevented nonadibatic decay channels on gas phase. As shown in Figure 2a, although the energy of CI-S1/S0-twist-c was lower than trans-S1-FC, there was a considerable barrier between them, and such a topology of PEC agreed with previous DFT results [37]. With consideration of the constraint of planar conformation and more than 1.03 eV of barrier in the out-of-plane αC=C twisting pathway, the singlet pathway for trans-S1-FC played a minor role. For the counterpart cis-S1-FC, there was a wide low barrier for accessing the CI-S1/S0-twist-c region. Nevertheless, due to the high initial potential energy, the cis-S1-FC → CI-S1/S0-twist-c relaxation could be achieved efficiently and serve as dominant isomerization pathway as in parent stilbene [70,71,72,73]. Additionally, the potential energy of CI-S1/S0-twist-c was ~0.65 eV higher than twist-S1, and the repeated oscillation toward the deep well before successful decay may result in evidently extended S1 lifetime. It should be noted that the T1 state stayed close to the S1 state at CI-S1/S0-twist-c, indicating that the competition between singlet and triplet pathways existed not only in the FC region. Another feasible singlet relaxation pathway for cis-S1-FC is given in Figure 2b, which corresponded to the ring-closing process on the S1 surface via CI-S1/S0-DHP. As a fact of the monotonous decreasing of PEC towards the crossing region, this decay channel was efficient, and after successful hopping to S0, the DANS molecule could persist the ring-closing process or back to cis-S0 as the CI-S1/S0-DHP was basically a barrier on S0 state.

The triplet relaxation pathways for cis-S1-FC and trans-S1-FC were rather different. At trans-S1-FC, it was a T2 mediated S1 → T1 process with relaxation along twisting coordinate on T1 surface, followed by the decay to ground state via ISC-S0/T1-twist. However, in the vicinity of the cis-S1-FC region, the only conformation and energy allowed triplet decay channel was the DHP formation via ISC-S1/T1-cis. As show in Figure 2c, the S1 PEC from cis-S1-FC to ISC-S1/T1-cis decreased mildly and thus favored a relaxation pathway with NP and DAP twisting in opposite directions. After a decay to the T1 state, the widespread degeneration between T1 and S0 states existed along the ring-closing procedure, which offered a possible T1 → S0 decay channel, as has been revealed in o-nitrophenol [74]. Moreover, this triplet pathway was still limited by insufficient SOC strength. In case the large amplitude αC=C twisting on T2 surface was feasible, the CI-T2/T1-trans and CI-T2/T1-tict were both energetically accessible after the cis-S1-FC → ISC-S1/T2-cis process; unfortunately, as evidenced in Figure 2a, the twisting conformation on T2 surface was a barrier between cis- and twist-regions. The stepwise triplet isomerization pathway, trans-S1-FC ↔ ISC-S1/T2-trans ↔ CI-T2/T1-trans ↔ ISC-S0/T1-twist ↔ cis-S1-FC is presented in Figure 2d. Starting from trans-S1-FC, the potential energy decreased mildly until the arrival of CI-T2/T1-trans and then became steep towards ISC-S0/T1-twist. As the internal conversion was usually more efficient than ISC, the ISC-S0/T1-twist (1.9 cm−1) with much smaller SOC value in comparison with ISC-S1/T2-trans (41.6 cm−1) was the rate-controlling step. Although the SOC at ISC-S0/T1-twist was weak, the decay event could still take place in case that there were enough times of repeated attempts and suitable coupling between crossing states.

4. Conclusions

We investigated the photorelaxation mechanisms of DANS upon S1 excitation by constructing the interwoven conical intersection and intersystem crossing networks at the SA6-CASSCF//MS-NEVPT2/6-31G* level. A schematic plot for the possible relaxation routes is displayed in Figure 3 and competitions within them are presented as follows.

Figure 3

Photorelaxation pathways for DANS upon S1 excitation.

After excitation to the trans-S1-FC, with in-plane electronic and geometry rearrangement, the DANS quickly convert to quinoid conformation. Subsequently, the relaxation mainly takes place along the triplet pathway ISC-S1/T2-trans → CI-T2/T1-trans → ISC-S0/T1-twist → trans- or cis-S0. Another competitive triplet pathway via CI-T2/T1-tict is unlikely taking place for its high energy. Nevertheless, the singlet pathway, trans-S1-FC → CI-S1/S0-twist-c → trans- or cis-S0, contribute a little as it is hindered by a rather high barrier on the S1 surface between trans-S1-FC and CI-S1/S0-twist-c. The other conical regions on the S1 surface, CI-S1/S0-trans, CI-S1/S0-twist-t and CI-S1/S0-cis, stay away from the accessible region of DANS started from trans-S1-FC. The mechanisms for trans-DANS presented in this work are consistent with the experimentally observed ~0.1 singlet-triplet branching ratio in nonpolar solvents [68]. For DANS excited to cis-S1-FC, two singlet pathways, cis-S1-FC → CI-S1/S0-twist-c → trans- or cis-S0 and cis-S1-FC → CI-S1/S0-DHP → DHP-S0, decay along the steeply descending S1 surface and thus are the dominate pathways. The fate of the cis-form DANS on the S1 surface is determined by the coupling of the initial twisting direction of DN and DAP. A similar ring-closing pathway observed on the T1 surface is cis-S1-FC → ISC-S1/T1-cis → DHP-T1 → DHP-S0, which is less important compared with the singlet counterpart due to the weak SOC strength. The other two possible triplet pathways mediated by ISC-S1/T2-cis are cis-S1-FC → ISC-S1/T2-cis → CI-T2/T1-cis → ISC-S0/T1-twist → trans- or cis-S0 and cis-S1-FC → ISC-S1/T2-cis → ISC-S1/T2-twist → CI-S1/S0-twist-c → trans- or cis-S0, which are basically impossible due to geometry and energy incompatibility. To quantitatively reveal the lifetimes of involved excited state intermediates, quantum yields for photoisomerization, interplay and branch ratios between different relaxation channels, we are continuing with full-dimensional nonadiabatic trajectory surface hopping molecular dynamics simulations with potential energies and gradients calculated by SA6-CASSCF, and the results will be presented in our forthcoming work.