# On the Nature of Interplay among Major Flexibility Channels in Molecular Rotors

Authors: M. S. A. Abdel-Mottaleb
Journal: Journal of Chemistry
 (2019)

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## Abstract

As a part of our interest in the excited-state dynamics of flexible materials, we have undertaken a theoretical investigation to the photo-induced reactions of 2-[4-(dimethylamino)benzylidene]malononitrile (BMN) by a combination of the density functional theory, its extended time-dependent (TD-DFT) single reference, and ab initio molecular dynamic (MD) simulations. The results showed that double-bond twisting and the neighbor single-bond twisting togetherness in the excited singlet state is the most important nonradiative deactivation channel to the ground state. Double- and single-bond twisting insert clear intersections among the potential energy surfaces of the singlet states (especially S1/S0) leading to fluorescence quenching. Furthermore, effects of molecular dynamic simulations on molecular properties in the femtosecond to picosecond time domain are studied to validate the results. In agreement with the experimental results, the findings conclude the existence of a flexible geometry-dependent single emission band. Such a study may give information on how the molecule could be externally modified/fixed to yield a desired effect, i.e., more fluorescence or more nonradiative decay.


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## Body

## 1. Introduction

Interest in the photochemistry of twisted ICT molecules, here exemplified by 2-[4-(dimethylamino)benzylidene]malononitrile (BMN) (Figure1), stems in part from their profitable potential applications in molecular optoelectronics, organic light-emitting diodes (OLEDs), and bright sensor materials, NLO material, 3D optical data storage, and advanced biological and molecular imaging [1]. Photo-induced dynamics of simple CT molecules such as p-(N, N-dimethylamino)benzonitrile (DMABN) [2–8], some α, β-enenitriles [9, 10], ethylene and derivatives [11], and many other types of molecules [12–30] have been extensively studied. Flexible chromogens exhibit twisted intramolecular charge transfer (TICT), which is an electron transfer process that occurs upon photoexcitation in molecules that usually consist of a donor and acceptor part linked by single bond(s) and/or double bonds. Such flexible molecules exhibit different possibilities for twisting upon light absorption, which may play together in a synergistic way to act as efficient nonradiative deactivation channels [12–33]. The emission properties are potentially environment-dependent, which makes TICT-based fluorophores ideal sensors for medium or chemical species nature [1–30, 34]. Several TICT-based materials have been reported to become fluorescent upon aggregation or confinement in solid polymer films due to inhibition of twisting [30]. Furthermore, various recent studies in organic optoelectronics, nonlinear optics, and solar energy conversions utilized the concept of twisting to modulate the electronic-state mixing and coupling on charge transfer states.Figure 1
Optimized planar molecular structure of BMN showing the three main rotational pathways. The molecule is also planar in the first excited state.Most fluorescence molecular motors are based on a twisted intramolecular charge transfer (TICT) mechanism [34] in which the nonradiative decay of an excited state can be altered by the surrounding viscosity and have been developed for their rapid responses and high special resolution [35].Some models of nonradiative decay were proposed [31–33] on the basis of experimentally obtained photophysical data of a series of intramolecular charge-transfer complexes of the varied structure (2-[4-(dimethylamino)benzylidene]malononitriles and coumarin dyes). The models specifically describe the relative contributions of the possible internal relaxation channels to nonradiative energy dissipation of the S1,ct states via the free rotor mechanism. The results were supported by simple theoretical predictions based on the semiempirically calculated electron density distributions and the bond-order alternation in the S1,ct state. The photo-induced nonadiabatic decay dynamics of BMN in the gas phase was investigated by Thiele et al. using surface hopping simulations [33]. The semiempirical orthogonalization model 2 (OM2) combined with multireference configuration interaction (MRCI) was employed [31–33]. In the nonadiabatic dynamics of DMN, the twisting around the double bond acts as the driving coordinate toward the lowest-energy S0/S1 conical intersection (CI), which mediates the internal conversion to the electronic ground state. This conical intersection is also characterized by a pronounced pyramidalization at the C10 atom that accompanies the double-bond twisting.The work of Thiele et al. provides the motivation to check the theoretical insights and the proposed dynamics scenario for the gas phase BMN by high-level ab initio calculations.Despite all of the reported experimental and theoretical results and the fact that numerous examples of flexible ICT over a wide range of applications exist, it is reassuring to know that only a relatively small number of design principles are involved. Thus, the future for flexible ICT is promising, and there is still a room for further new research. In a related system, the interplay between the different modes was recently investigated experimentally [36]. Generally, it is concluded that the photophysics of these potentially useful probes and functionally similar malononitriles are still partly comprehended and actively debated.In this investigation, we report on the DFT theoretically obtained results of donor-acceptor flexible ICT 2-[4-(dimethylamino)benzylidene]malononitrile (1) molecule in which three main internal relaxation channels marked in Figure1 (C4-C9 single bond (S1), C1-N1 single bond (S2), and C9-C10 double bond (D)) are most probable. Simulations are carried out in BMN ground (S0) and few excited singlet states. The molecular rotor BMN could be appraised as an α, β-enenitrile derivative with an increase in the complexity and the size. The objectives are to simulate, in a simple and sufficient accurate way, internal dynamics including twisting modes, reflecting the role played by most important deactivation channel(s) and to evaluate the influence of three modes on the molecular and spectroscopic properties. In other words, twisting around different bonds should be echoed in molecular and spectroscopic characteristics, which will be shown in this contribution. Moreover, the energetic requirement for twisting about different possible bonds in BMN will be calculated using different models. Furthermore, to validate the results, we carried out ab initio molecular dynamics (MD) [37, 38], which involve nuclear dynamics to determine the time evolution of the molecular geometry in combination with electronic structure methods. It is capable of computing electronic ground and excited state potential energy surfaces (PESs). A large number of trajectories are usually produced from the MD simulations. Such simulations directly include all nuclear degrees of freedom, which provides a rather rich picture of the time-evolved microscopic processes at a reasonable computing cost. It is well-known that simulations using multireference alternative methods such as the complete active space self-consistent field (CASSCF) method and the various multireference dynamic correlation calculations are very time-consuming [39]. To be concise, however, applying TD-DFT single reference ab initio MD to our system will provide a simplified picture about proximity and intersections that might be occurred among PESs and could help explanation of the nonradiative nature of molecular rotors in a relatively less costly and simplified way. We will discuss the photo-induced dynamics in the nonadiabatic channel of the charge-transfer feature material BMN of the molecular rotor type.The obtained results should not only clarify the general understanding of how photo-induced properties change but also to help evolving useful controllable functional materials photochemically by controlling mode(s) of relaxation.


## 2. Experimental and Computational Methods

### 2.1. Electronic and FTIR Spectra of BMN

Measurements of absorption and fluorescence spectra were carried out in acetonitrile solutions (2.0 × 10−5 mole·L−1 of BMN). The FTIR was measured in the solid KBr tablet. The material was supplied by Dr. Rafik O. Loutfy, Toronto, Canada.


### 2.2. Geometry Optimization and Twisting Simulations

Geometry optimization and frequency calculations were carried out using Gaussian16: EM64W-G16 Revision A.03 [40]. DFT (ωB97X-D/6-31G∗∗) and TD-DFT (RCAM-B3LYP/6-31G∗∗) methods for the S0 and S1 states were used, respectively. GaussView 6.0.16 graphical user interface (GUI) was used to visualize Gaussian results.Single point energy computations on optimized structures obtained at different constraints were performed using the cost-effective B3LYP/def2-SV(P) model for unexpansive computing of thermodynamic parameters using Spartan’16 software [41, 42]. The built-in graphics user interface (GUI) of Spartan’16 is used for visualizing the results of Spartan computations.To simulate bond twist, we performed relaxed scans on the S1 state geometry by applying the CIS/6-31G∗ method. The dihedral angles C5-C4-C9-C10 (C4-C9 single bond, S1), C8-N1-C1-C2 (C1-N1 single bond, S2), and C4-C9-C10-C11 (C9-C10 double bond, D) were, in almost all cases, increased from 0° to 90° in 10° increments. In some cases, scans were performed from 0° to 180° in steps. Scanning multiple dihedrals were also performed to obtain the 3D grid graphs. Both program packages were used. The widely used solvation CPCM model was employed in case of the acetonitrile solvent in both the S0 and S1 states.


### 2.3. Ab Initio Molecular Dynamics

Additionally, ab initio molecular dynamics simulations were carried out using Orca 4.0.1.2 package [39], and the generated trajectories were dealt with using Spartan’16 GUI [41, 42].ORCA version 4.0.1.2 [39] allows the combination of the scan feature with CIS or TD-DFT. This can be used to map out the excited state potential energy surfaces as a function of twisting dihedral angle. The output of the trajectory run automatically contains the excited state energies in addition to the ground state energy. Our calculation utilizes the range-separated hybrid DFT basis: def2-TZVPD [43, 44] and the auxiliary basis: def2/JK. The used functional is BP86 with D3 correction and RI approximation [45]. This method speeds up the computation and reasonably estimates the ICT state. Overlap-fitted RIJCOSX approximation was used as a speed-up option that leads to very large speedups [46, 47] at virtually no loss of accuracy [48].Moreover, Orca enabled us to carry out potential energy surface scans along normal coordinates of IR modes obtained from the S0 computations, which should validate scanning dihedrals due to its direct relationship to molecular dynamics. The ground and excited state potential energy surfaces can be mapped as a function of normal coordinates. First, we ran a frequency job using BP86/def2-SV(P) and auxiliary basis def2/J to generate the Hessian matrix. The Hessian matrix was used to construct normal mode displacements [39] (known as motions of the normal mode coordinate). This is followed by using TD-DFT single point scan calculations for a range of the displaced geometries (q). The trajectories were constructed so that corresponding normal coordinates are varied in the chosen displacement range. The DFT-MD simulations were done at the TD-DFT Cam-B3LYP/def2-SVP with RIJCOSX approximation and BP86-D3/def2-SVP levels of theory with RI approximation. Both methods return almost the same results. Moreover, in the trajectory simulation, the temperature is kept constant at 350 K, and the run was submitted for a number of runs aiming at exploring a conformational time domain of 50 fs, 100, 500, and 1000 of 0.5, 1, and 2 fs step, respectively. Because the main emphasis is on the flexible skeleton of the molecule studied, the chosen 2 fs step used for 500 runs is mainly to reduce the computational cost. Orca results are visualized by ChemCraft visualization software.A Broadberry workstation (40 cores) (UK) and a Mac Pro (12 core) workstation were used.


## 2.1. Electronic and FTIR Spectra of BMN

Measurements of absorption and fluorescence spectra were carried out in acetonitrile solutions (2.0 × 10−5 mole·L−1 of BMN). The FTIR was measured in the solid KBr tablet. The material was supplied by Dr. Rafik O. Loutfy, Toronto, Canada.


## 2.2. Geometry Optimization and Twisting Simulations

Geometry optimization and frequency calculations were carried out using Gaussian16: EM64W-G16 Revision A.03 [40]. DFT (ωB97X-D/6-31G∗∗) and TD-DFT (RCAM-B3LYP/6-31G∗∗) methods for the S0 and S1 states were used, respectively. GaussView 6.0.16 graphical user interface (GUI) was used to visualize Gaussian results.Single point energy computations on optimized structures obtained at different constraints were performed using the cost-effective B3LYP/def2-SV(P) model for unexpansive computing of thermodynamic parameters using Spartan’16 software [41, 42]. The built-in graphics user interface (GUI) of Spartan’16 is used for visualizing the results of Spartan computations.To simulate bond twist, we performed relaxed scans on the S1 state geometry by applying the CIS/6-31G∗ method. The dihedral angles C5-C4-C9-C10 (C4-C9 single bond, S1), C8-N1-C1-C2 (C1-N1 single bond, S2), and C4-C9-C10-C11 (C9-C10 double bond, D) were, in almost all cases, increased from 0° to 90° in 10° increments. In some cases, scans were performed from 0° to 180° in steps. Scanning multiple dihedrals were also performed to obtain the 3D grid graphs. Both program packages were used. The widely used solvation CPCM model was employed in case of the acetonitrile solvent in both the S0 and S1 states.


## 2.3. Ab Initio Molecular Dynamics

Additionally, ab initio molecular dynamics simulations were carried out using Orca 4.0.1.2 package [39], and the generated trajectories were dealt with using Spartan’16 GUI [41, 42].ORCA version 4.0.1.2 [39] allows the combination of the scan feature with CIS or TD-DFT. This can be used to map out the excited state potential energy surfaces as a function of twisting dihedral angle. The output of the trajectory run automatically contains the excited state energies in addition to the ground state energy. Our calculation utilizes the range-separated hybrid DFT basis: def2-TZVPD [43, 44] and the auxiliary basis: def2/JK. The used functional is BP86 with D3 correction and RI approximation [45]. This method speeds up the computation and reasonably estimates the ICT state. Overlap-fitted RIJCOSX approximation was used as a speed-up option that leads to very large speedups [46, 47] at virtually no loss of accuracy [48].Moreover, Orca enabled us to carry out potential energy surface scans along normal coordinates of IR modes obtained from the S0 computations, which should validate scanning dihedrals due to its direct relationship to molecular dynamics. The ground and excited state potential energy surfaces can be mapped as a function of normal coordinates. First, we ran a frequency job using BP86/def2-SV(P) and auxiliary basis def2/J to generate the Hessian matrix. The Hessian matrix was used to construct normal mode displacements [39] (known as motions of the normal mode coordinate). This is followed by using TD-DFT single point scan calculations for a range of the displaced geometries (q). The trajectories were constructed so that corresponding normal coordinates are varied in the chosen displacement range. The DFT-MD simulations were done at the TD-DFT Cam-B3LYP/def2-SVP with RIJCOSX approximation and BP86-D3/def2-SVP levels of theory with RI approximation. Both methods return almost the same results. Moreover, in the trajectory simulation, the temperature is kept constant at 350 K, and the run was submitted for a number of runs aiming at exploring a conformational time domain of 50 fs, 100, 500, and 1000 of 0.5, 1, and 2 fs step, respectively. Because the main emphasis is on the flexible skeleton of the molecule studied, the chosen 2 fs step used for 500 runs is mainly to reduce the computational cost. Orca results are visualized by ChemCraft visualization software.A Broadberry workstation (40 cores) (UK) and a Mac Pro (12 core) workstation were used.


## 3. Results and Discussion

### 3.1. Spectroscopic Characteristics of BMN

Experimentally determined electronic spectra in acetonitrile and FTIR vibrational spectrum are depicted in Figures2 and 3, respectively.Figure 2
Absorption (left) and fluorescence (at 430 nm excitation, right) spectra of BMN in acetonitrile.Figure 3
FTIR in KBr (continuous curve) and Gaussian-shaped IR spectrum of geometrically optimized BMN in the gaseous phase (rectangular stick lines).The noticed differences between experimental IR data in the solid phase (KBr disk) and theoretically computed ones in the gaseous phase is expected in such a flexible molecule suggesting that the geometry in solid is slightly disagreed with that computed in the gas phase. However, it is well-known that the vibrational analysis by Gaussian can only give some rough ideas on normal modes. Vibrational modes (mainly stretching modes) involving the bonds responsible for molecular flexibility are identified and used to carry out PES scans along normal coordinates (normal mode displacements), which will be discussed in Section3.4. Moreover, experimentally obtained fluorescence spectrum in acetonitrile is in excellent agreement with theoretical simulation discussed in Section 3.3.


### 3.2. Relative Energy

Figure4 shows that twisting around the S1-single bond (the C4-C9 (p-N, N-dimethyl aryl group)) induces largest thermal instability relative to twisting around S2-bond or D-bond. It is obvious that twisting around the C9-C10 double bond induces smallest molecular thermal instability. Figure 5 is a sketch of relative potential energy diagram of BMN in the planar S0 and twisted S1,ct states. At 90°, twist angle of the double bond C9-C10 is largest and smallest destabilization energy is noticed in S0 and S1,ct, respectively. Twisting of the anilino moiety (around C4-C9 single bond) induced largest destabilization in the first excited state S1,ct relative to the nontwist state. In conclusion, based on relative potential energy values (refer to Figures 4 and 5), the favorable tendency for radiation-less deactivation process decreases as follows: D-bond > S2-bond > S1-bond. In other words, double-bond twist is the key factor in nonradiative deactivation of the first excited state, most probably, due to the noticed decrease in the calculated energy gap between states (S1–S0) at 90° twist.Figure 4
Bond twisting-induced relative energy change in the S1 state of the BMN molecule.Figure 5
Relative potential energy diagram in the ground and first excited state of the BMN molecule. The arrows represent relative destabilization energy at 90° twist angles around each bond. B3LYP/DEF2-SV(P) was used for computing the thermodynamic data.


### 3.3. Fluorescence Properties

Fluorescence deactivation of BMN occurs through twist involving the dicyanomethylene bond (C9-C10 in Figure1), upon which the ground- and the excited-state potential energy surfaces (PESs) come into sufficiently close proximity, or intersect each other, to allow efficient deactivation (Section 3.4). Figure 6 shows that twist-induced fluorescence wavelength and intensity changes are most remarkable at 90° twist. Progressive increase in the twist angle results in fluorescence red shift with quenched emission. Similar behavior is noticed in case of simultaneous twists involving different possible combinations of two bonds (see Figure 7).Figure 6
Twist-induced fluorescence wavelength (red) and intensity (blue) changes. The molecule does not fluoresce at 90° twist. Progressive increase in the twist angle results in fluorescence red shift with quenched emission. Calculated using the CIS/6-31G∗ method of Spartan’16 parallel suite. Plotted using Spartan’16 GUI.Figure 7
3D Relaxed scan grid (of 36 nodes or scan steps “white points on the surface”) plotted by GaussView 6, showing an example of the total molecular electronic energy changes due to D-S1 simultaneous twisting in the S1 state of BMN. Similar plots are obtained in case of D-S2 twisting (Figure 7). The most stable planar molecule is located in the front left corner of the plot, while the least stable is located in back upper red node [9, 10, 34] with twisting angles equal 144 for D-bond and 90 for S1-bond. Calculated using the CIS/6-31G(d, p) method of Gaussian 16 package.The effect of simultaneous twisting of D-S1 and D-S2 bonds on the relative energy (relative to the energy of the nontwisting geometry) of the molecule is depicted in Figure8. The 2D drawing reflect the importance of D-S1 twisting in destabilizing the molecule relative to D-S2, which should be reflected in the simulated fluorescence spectra as indicated in Figure 9.Figure 8
Relative energy due to simultaneous scans (steps represent dihedral angles at each point of coordinates shown in Figure8 and precisely defined in the insets of Figure 10): D-S1 twisting (black line) and D-S2 (blue line).Figure 9
Simulated fluorescence spectra in acetonitrile due to simultaneous two bonds twist angles variation: (a) and (b) represent fluorescence due to relaxed scan steps 1–25 for D-S1 (the insets show the dihedral angles of scan grid points); (c) represents the case of D-S2 scans. Computed using TD-DFT (cam-B3LYP/6-31G∗ model). All spectra are plotted by GaussView 6.
(a)
(b)
(c)Fluorescence spectra in acetonitrile due to simultaneous two bonds twist angles variation are depicted in Figures9(a) and 9(b) for D-S1 and (Figure 9(c)) for D-S2 bonds. All fluorescence bands observed at wavelength 350 nm and higher are of CT nature (HOMO and LUMO orbitals are significantly involved) and stems from the 1st excited state. Below 350 nm, the transitions are from the 2nd excited state with main contribution from HOMO-1, HOMO-2, and LUMO orbitals. The only exception noticed is the fluorescence of the coordinate 23 in case of D-S1, where its fluorescence of the 2nd excited state appears above 400 nm. Red shifted emission bands are characterized by low intensity due to larger progressive nonradiative deactivation with increasing bond twisting angles, which is more pronounced in case of D-S1 relative to D-S2. Figure 6 illustrates the effect of bond twisting at least qualitatively. Furthermore, characters of the low-lying electronic states at equilibrium geometries are given in Table 1. All states have mixed character.Table 1
The most probable contributions of TD-DFT excited states (singlets).
Excited state 1
Excited state 2
50–>53 (0.042613)
50–>53 (0.917816)
51–>53 (0.025393)
51–>53 (0.063071)
52–>53 (0.918180)
The weight of the individual excitations is given if larger than 0.02.We previously reported some experimentally determined fluorescence characteristics of BMN in different solvents [31–33], and the data are in agreement with the theoretically obtained results. Furthermore, experimentally measured fluorescence spectrum given in Figure 2 validates data of Figure 10(b) at twisting coordinates 126 and 90° represented by Step 24.Figure 10
Gaussian’16 results depicts (a) the MO surfaces involved in the electronic transitions from the 1st and 2nd singlet excited states to the ground state and shows clearly (b) the CT nature reflected in HOMO-LUMO involved in electronic transition in a twisted state. Both MO’s shown in (a) and (b) are obtained by Gaussian’16 package. We used different color codes to illustrate the difference between planar and twisted structures. The isovalue for all surfaces is 0.02. All surfaces are plotted by GaussView 6. (a) Planar configuration. (b) Twisted configuration: scan step 18 shown in the inset Figure 9(b).
(a)
(b)The MO involved in the electronic transitions (Figure10(a)) identifies the nature of transitions in case of the planar nontwisted molecule. It is obvious that the more the HOMO-LUMO involvement in a transition is, the more its CT nature is, as shown in Figure 10(b). (HOMO-LUMO in case of twisting).


### 3.4. PES in Different Electronic States

In order to identify, at least qualitatively in a simple way, conical intersections (CIs) [49] between electronic potential energy surfaces and the roles played in molecular relaxation processes, we carried out several scans of the dynamics of the BMN material with the help of the molecular mechanical and ab initio trajectories methods. It is well-known that simulations using alternative methods such as the complete active space self-consistent field (CASSCF) method and the various multireference dynamic correlation calculations, which are proper methods, are very time-consuming. One should also be aware that, with multireference methods, it is very easy to let a large computer run for a long time and still not to produce a meaningful result [37, 38, 41, 42]. Thus, we tried to obtain at least a qualitative picture by carrying out several scans of the dynamics of the BMN material with the help of the molecular mechanical and ab initio trajectories methods.Potential energy surface scans of different ground and excited states were performed by two techniques: (1) scanning dihedrals and (2) scanning along normal coordinates of IR modes, which should validate scanning dihedrals due to its direct relationship to molecular dynamics. The ground and excited state potential energy surfaces can be also mapped as a function of normal coordinates. The results PES obtained by scanning dihedrals revealed the presence of apparent intersection points between the singlet state and the ground state, corresponding to C9-C10 double-bond twisting (Figure11). Apparent intersection in case of single-bond twisting is also noticed (Figure 11(a)). Passage through these apparent intersections on the PES leads to nonradiative energy dissipation due to bond twisting. Recalling, it is well-understood that our single reference computational methodology cannot describe the CI topology. This is why we clearly see that the S1 state becomes lower than the S0 state near 90°. This feature was discussed before [50–53]. As pointed out before [50], one should not expect good agreement in cases where charge transfer is important, since ionic states are often strongly stabilized by dynamical electron correlation.Figure 11
2D PES due to single (S1-bond) twisting (a) and double (C9-C19 bond) twisting angles (b). ORCA: BP86 D3 RIJCOSX DEF2-SVP DEF2/JK TIGHTSCF. Orca computation results are graphically represented using Spartan’16 GUI.
(a)
(b)However, our simplified approach clearly shows the existence of points of intersections in certain geometries, which could be helpful in describing photochemical-induced dynamics. More accurate and quantitative examinations of CI would require a CASSCF computation with large active spaces [50–53]. It should be pointed out here that applying the CASSCF method would result in accurate description of the double cone topology of the CI. It is clear that single reference TD-DFT would provide a much more economical alternative, with a possible application to large molecules.It could be safely concluded that simulation of molecular dynamics of the complex BMN molecule in case of S1-bond and D-bond twisting reveals that double-bond twisting and the neighbor single-bond twisting togetherness in the excited singlet state is the most important nonradiative deactivation channel to the ground state. The noticed PES intersections between different excited and ground states strongly suggest that only one radiative transition (one fluorescence band) is most probable. This is consistent with the theoretically and experimentally obtained fluorescence spectra in acetonitrile.Furthermore, PESs obtained from scanning along normal coordinates of some relevant IR modes (Figure11) were obtained and analyzed. Although no clear PES intersection is noticed between S1 and S0 states, different state trajectories become closer to each other due to vibrational modes mostly related to dynamical motions involving the flexible coordinates, i.e., the S1-, S2-, and D-bonds. This should result in radiation-less relaxation of the excited BMN molecule.


### 3.5. Ab Initio Molecular Dynamics

In order to further identify intersection points between electronic potential energy surfaces and the roles played in molecular relaxation processes, ab initio molecular dynamics are investigated. MD trajectories were computed at the geometry of singlet/singlet crossing points depicted in Figure11, i.e., starting from 90° and 176°, as shown in Figure 11, for single- and double-bond twisting, respectively. Then, the physical quantities (energies, bond lengths, dihedrals, and angles) that are needed in the time evolutions, have been calculated at the CIS/6-31G∗ level of theory and visualized using the Spartan’16 software packages. Our data graphically visualized in Figures 12 and 13 confirm that the propensity for a radiation-less transition is large in the vicinity of nuclear configurations where potential energy surfaces intersect.Figure 12
PESs scanned along some IR normal coordinate modes in the ground state (a) shows PESs of ground and the first two excited singlet states scanned along the displacement coordinate (q) due to different IR modes (from the left to right): mode 63 (at 1597 cm−1 mainly due to D-, S1-, and S2-bond vibration), mode 64 (at 1633 cm−1 due to D- and S2-bonds), and mode 65 (at 1682.8 cm−1 mainly due to D-bond vibration), respectively. (b) An example of most important mode 65 visualizing the displacement vibrational vectors (shown as arrows) involved in the dynamical motions due to the molecular flexibility.
(a)
(b)Figure 13
Time evolution of (a) the relative potential energy and bond lengths of the C9-C10, C4-C9, and C1-N1 bonds. (a) the trajectory starts from 90° twisting angle for S1-bond while (b) the trajectory start from (d) the intersection point of the seam at 176° twisting angle for D-bond. (b) Bond twisting (dihedral angles) and pyramidalization of C10 ((a) at 90° twisting angle for S1-bond and (b) at 176° twisting angle for D-bond). (c) Changes in properties during 1000 femtoseconds (1.0 picosecond).
(a)
(b)
(c)It is clear from Figure13(c) that as the time evolves, the molecule becomes more relaxed (relative energy becomes more negative) due to radiation-less deactivation.Ultrafast internal conversion (IC) (femto-to-picosecond time domain) from the first excited electronic state (S1) to the ground electronic state (S0) via a conical intersection (CI) can play an essential role in the initial steps of the decomposition of energetic materials. Such nonradiative relaxations following electronic excitation quench emission dissipate the excitation energy in the vibrational modes of the ground electronic state.Figure13 summaries the results of the trajectory dynamic simulation in 50 and 1000 fs time domains. Inspection of Figures 13(a) and 13(b) reveals rapid change in dynamics parameters/energies which are noticed even during the first 50 fs time period. Regarding changes in bond length by time evolution, Figure 13(a) indicates that D-bond, S1-bond, and S2- single bond lengths remarkably changed during first 30 fs. S1 single bond length shows small changes while both other two bond lengths as the time evolves change periodically at the points of intersections.Time evolution graphs (Figures13(a) and 13(c)) show a significant potential energy increase, which amounts to over 100 kJ/mol and is attained in around 15 fs. The structure then exhibits irregular periodic energy stabilization-destabilization amounts to 100–25 kJ/mol during the first 50 fs (with a major geometry change due to involvement of bonds twisting, in-plane and out-of-plane bending, as well as H-atoms stretching and bending (rocking and wagging) beside ring deformation and ring C-C stretching). Then, in about 200–250 fs further, the molecule enjoys stabilization. In about 800 fs, further stabilization mounts to −40 kJ/mol is achieved. Pyramidalization of C10 (Figure 13(b) is obviously attained in about 12 fs confirming the twisting around the C10-C9 double bond. Figure 13(b) indicates also that double bond and S1-single-bond twisting tends to change almost periodically out of phase with respect to each other, whereas C1-N1 single-bond twisting starts to increase after 30 fs. This suggests that, at points of intersections (176° and 90° for D and S1-bonds, respectively), both D-bond and S1-bond behave similarly as time evolves and most probably simultaneously play major role in the radiation-less deactivation process of the excited states.


## 3.1. Spectroscopic Characteristics of BMN

Experimentally determined electronic spectra in acetonitrile and FTIR vibrational spectrum are depicted in Figures2 and 3, respectively.Figure 2
Absorption (left) and fluorescence (at 430 nm excitation, right) spectra of BMN in acetonitrile.Figure 3
FTIR in KBr (continuous curve) and Gaussian-shaped IR spectrum of geometrically optimized BMN in the gaseous phase (rectangular stick lines).The noticed differences between experimental IR data in the solid phase (KBr disk) and theoretically computed ones in the gaseous phase is expected in such a flexible molecule suggesting that the geometry in solid is slightly disagreed with that computed in the gas phase. However, it is well-known that the vibrational analysis by Gaussian can only give some rough ideas on normal modes. Vibrational modes (mainly stretching modes) involving the bonds responsible for molecular flexibility are identified and used to carry out PES scans along normal coordinates (normal mode displacements), which will be discussed in Section3.4. Moreover, experimentally obtained fluorescence spectrum in acetonitrile is in excellent agreement with theoretical simulation discussed in Section 3.3.


## 3.2. Relative Energy

Figure4 shows that twisting around the S1-single bond (the C4-C9 (p-N, N-dimethyl aryl group)) induces largest thermal instability relative to twisting around S2-bond or D-bond. It is obvious that twisting around the C9-C10 double bond induces smallest molecular thermal instability. Figure 5 is a sketch of relative potential energy diagram of BMN in the planar S0 and twisted S1,ct states. At 90°, twist angle of the double bond C9-C10 is largest and smallest destabilization energy is noticed in S0 and S1,ct, respectively. Twisting of the anilino moiety (around C4-C9 single bond) induced largest destabilization in the first excited state S1,ct relative to the nontwist state. In conclusion, based on relative potential energy values (refer to Figures 4 and 5), the favorable tendency for radiation-less deactivation process decreases as follows: D-bond > S2-bond > S1-bond. In other words, double-bond twist is the key factor in nonradiative deactivation of the first excited state, most probably, due to the noticed decrease in the calculated energy gap between states (S1–S0) at 90° twist.Figure 4
Bond twisting-induced relative energy change in the S1 state of the BMN molecule.Figure 5
Relative potential energy diagram in the ground and first excited state of the BMN molecule. The arrows represent relative destabilization energy at 90° twist angles around each bond. B3LYP/DEF2-SV(P) was used for computing the thermodynamic data.


## 3.3. Fluorescence Properties

Fluorescence deactivation of BMN occurs through twist involving the dicyanomethylene bond (C9-C10 in Figure1), upon which the ground- and the excited-state potential energy surfaces (PESs) come into sufficiently close proximity, or intersect each other, to allow efficient deactivation (Section 3.4). Figure 6 shows that twist-induced fluorescence wavelength and intensity changes are most remarkable at 90° twist. Progressive increase in the twist angle results in fluorescence red shift with quenched emission. Similar behavior is noticed in case of simultaneous twists involving different possible combinations of two bonds (see Figure 7).Figure 6
Twist-induced fluorescence wavelength (red) and intensity (blue) changes. The molecule does not fluoresce at 90° twist. Progressive increase in the twist angle results in fluorescence red shift with quenched emission. Calculated using the CIS/6-31G∗ method of Spartan’16 parallel suite. Plotted using Spartan’16 GUI.Figure 7
3D Relaxed scan grid (of 36 nodes or scan steps “white points on the surface”) plotted by GaussView 6, showing an example of the total molecular electronic energy changes due to D-S1 simultaneous twisting in the S1 state of BMN. Similar plots are obtained in case of D-S2 twisting (Figure 7). The most stable planar molecule is located in the front left corner of the plot, while the least stable is located in back upper red node [9, 10, 34] with twisting angles equal 144 for D-bond and 90 for S1-bond. Calculated using the CIS/6-31G(d, p) method of Gaussian 16 package.The effect of simultaneous twisting of D-S1 and D-S2 bonds on the relative energy (relative to the energy of the nontwisting geometry) of the molecule is depicted in Figure8. The 2D drawing reflect the importance of D-S1 twisting in destabilizing the molecule relative to D-S2, which should be reflected in the simulated fluorescence spectra as indicated in Figure 9.Figure 8
Relative energy due to simultaneous scans (steps represent dihedral angles at each point of coordinates shown in Figure8 and precisely defined in the insets of Figure 10): D-S1 twisting (black line) and D-S2 (blue line).Figure 9
Simulated fluorescence spectra in acetonitrile due to simultaneous two bonds twist angles variation: (a) and (b) represent fluorescence due to relaxed scan steps 1–25 for D-S1 (the insets show the dihedral angles of scan grid points); (c) represents the case of D-S2 scans. Computed using TD-DFT (cam-B3LYP/6-31G∗ model). All spectra are plotted by GaussView 6.
(a)
(b)
(c)Fluorescence spectra in acetonitrile due to simultaneous two bonds twist angles variation are depicted in Figures9(a) and 9(b) for D-S1 and (Figure 9(c)) for D-S2 bonds. All fluorescence bands observed at wavelength 350 nm and higher are of CT nature (HOMO and LUMO orbitals are significantly involved) and stems from the 1st excited state. Below 350 nm, the transitions are from the 2nd excited state with main contribution from HOMO-1, HOMO-2, and LUMO orbitals. The only exception noticed is the fluorescence of the coordinate 23 in case of D-S1, where its fluorescence of the 2nd excited state appears above 400 nm. Red shifted emission bands are characterized by low intensity due to larger progressive nonradiative deactivation with increasing bond twisting angles, which is more pronounced in case of D-S1 relative to D-S2. Figure 6 illustrates the effect of bond twisting at least qualitatively. Furthermore, characters of the low-lying electronic states at equilibrium geometries are given in Table 1. All states have mixed character.Table 1
The most probable contributions of TD-DFT excited states (singlets).
Excited state 1
Excited state 2
50–>53 (0.042613)
50–>53 (0.917816)
51–>53 (0.025393)
51–>53 (0.063071)
52–>53 (0.918180)
The weight of the individual excitations is given if larger than 0.02.We previously reported some experimentally determined fluorescence characteristics of BMN in different solvents [31–33], and the data are in agreement with the theoretically obtained results. Furthermore, experimentally measured fluorescence spectrum given in Figure 2 validates data of Figure 10(b) at twisting coordinates 126 and 90° represented by Step 24.Figure 10
Gaussian’16 results depicts (a) the MO surfaces involved in the electronic transitions from the 1st and 2nd singlet excited states to the ground state and shows clearly (b) the CT nature reflected in HOMO-LUMO involved in electronic transition in a twisted state. Both MO’s shown in (a) and (b) are obtained by Gaussian’16 package. We used different color codes to illustrate the difference between planar and twisted structures. The isovalue for all surfaces is 0.02. All surfaces are plotted by GaussView 6. (a) Planar configuration. (b) Twisted configuration: scan step 18 shown in the inset Figure 9(b).
(a)
(b)The MO involved in the electronic transitions (Figure10(a)) identifies the nature of transitions in case of the planar nontwisted molecule. It is obvious that the more the HOMO-LUMO involvement in a transition is, the more its CT nature is, as shown in Figure 10(b). (HOMO-LUMO in case of twisting).


## 3.4. PES in Different Electronic States

In order to identify, at least qualitatively in a simple way, conical intersections (CIs) [49] between electronic potential energy surfaces and the roles played in molecular relaxation processes, we carried out several scans of the dynamics of the BMN material with the help of the molecular mechanical and ab initio trajectories methods. It is well-known that simulations using alternative methods such as the complete active space self-consistent field (CASSCF) method and the various multireference dynamic correlation calculations, which are proper methods, are very time-consuming. One should also be aware that, with multireference methods, it is very easy to let a large computer run for a long time and still not to produce a meaningful result [37, 38, 41, 42]. Thus, we tried to obtain at least a qualitative picture by carrying out several scans of the dynamics of the BMN material with the help of the molecular mechanical and ab initio trajectories methods.Potential energy surface scans of different ground and excited states were performed by two techniques: (1) scanning dihedrals and (2) scanning along normal coordinates of IR modes, which should validate scanning dihedrals due to its direct relationship to molecular dynamics. The ground and excited state potential energy surfaces can be also mapped as a function of normal coordinates. The results PES obtained by scanning dihedrals revealed the presence of apparent intersection points between the singlet state and the ground state, corresponding to C9-C10 double-bond twisting (Figure11). Apparent intersection in case of single-bond twisting is also noticed (Figure 11(a)). Passage through these apparent intersections on the PES leads to nonradiative energy dissipation due to bond twisting. Recalling, it is well-understood that our single reference computational methodology cannot describe the CI topology. This is why we clearly see that the S1 state becomes lower than the S0 state near 90°. This feature was discussed before [50–53]. As pointed out before [50], one should not expect good agreement in cases where charge transfer is important, since ionic states are often strongly stabilized by dynamical electron correlation.Figure 11
2D PES due to single (S1-bond) twisting (a) and double (C9-C19 bond) twisting angles (b). ORCA: BP86 D3 RIJCOSX DEF2-SVP DEF2/JK TIGHTSCF. Orca computation results are graphically represented using Spartan’16 GUI.
(a)
(b)However, our simplified approach clearly shows the existence of points of intersections in certain geometries, which could be helpful in describing photochemical-induced dynamics. More accurate and quantitative examinations of CI would require a CASSCF computation with large active spaces [50–53]. It should be pointed out here that applying the CASSCF method would result in accurate description of the double cone topology of the CI. It is clear that single reference TD-DFT would provide a much more economical alternative, with a possible application to large molecules.It could be safely concluded that simulation of molecular dynamics of the complex BMN molecule in case of S1-bond and D-bond twisting reveals that double-bond twisting and the neighbor single-bond twisting togetherness in the excited singlet state is the most important nonradiative deactivation channel to the ground state. The noticed PES intersections between different excited and ground states strongly suggest that only one radiative transition (one fluorescence band) is most probable. This is consistent with the theoretically and experimentally obtained fluorescence spectra in acetonitrile.Furthermore, PESs obtained from scanning along normal coordinates of some relevant IR modes (Figure11) were obtained and analyzed. Although no clear PES intersection is noticed between S1 and S0 states, different state trajectories become closer to each other due to vibrational modes mostly related to dynamical motions involving the flexible coordinates, i.e., the S1-, S2-, and D-bonds. This should result in radiation-less relaxation of the excited BMN molecule.


## 3.5. Ab Initio Molecular Dynamics

In order to further identify intersection points between electronic potential energy surfaces and the roles played in molecular relaxation processes, ab initio molecular dynamics are investigated. MD trajectories were computed at the geometry of singlet/singlet crossing points depicted in Figure11, i.e., starting from 90° and 176°, as shown in Figure 11, for single- and double-bond twisting, respectively. Then, the physical quantities (energies, bond lengths, dihedrals, and angles) that are needed in the time evolutions, have been calculated at the CIS/6-31G∗ level of theory and visualized using the Spartan’16 software packages. Our data graphically visualized in Figures 12 and 13 confirm that the propensity for a radiation-less transition is large in the vicinity of nuclear configurations where potential energy surfaces intersect.Figure 12
PESs scanned along some IR normal coordinate modes in the ground state (a) shows PESs of ground and the first two excited singlet states scanned along the displacement coordinate (q) due to different IR modes (from the left to right): mode 63 (at 1597 cm−1 mainly due to D-, S1-, and S2-bond vibration), mode 64 (at 1633 cm−1 due to D- and S2-bonds), and mode 65 (at 1682.8 cm−1 mainly due to D-bond vibration), respectively. (b) An example of most important mode 65 visualizing the displacement vibrational vectors (shown as arrows) involved in the dynamical motions due to the molecular flexibility.
(a)
(b)Figure 13
Time evolution of (a) the relative potential energy and bond lengths of the C9-C10, C4-C9, and C1-N1 bonds. (a) the trajectory starts from 90° twisting angle for S1-bond while (b) the trajectory start from (d) the intersection point of the seam at 176° twisting angle for D-bond. (b) Bond twisting (dihedral angles) and pyramidalization of C10 ((a) at 90° twisting angle for S1-bond and (b) at 176° twisting angle for D-bond). (c) Changes in properties during 1000 femtoseconds (1.0 picosecond).
(a)
(b)
(c)It is clear from Figure13(c) that as the time evolves, the molecule becomes more relaxed (relative energy becomes more negative) due to radiation-less deactivation.Ultrafast internal conversion (IC) (femto-to-picosecond time domain) from the first excited electronic state (S1) to the ground electronic state (S0) via a conical intersection (CI) can play an essential role in the initial steps of the decomposition of energetic materials. Such nonradiative relaxations following electronic excitation quench emission dissipate the excitation energy in the vibrational modes of the ground electronic state.Figure13 summaries the results of the trajectory dynamic simulation in 50 and 1000 fs time domains. Inspection of Figures 13(a) and 13(b) reveals rapid change in dynamics parameters/energies which are noticed even during the first 50 fs time period. Regarding changes in bond length by time evolution, Figure 13(a) indicates that D-bond, S1-bond, and S2- single bond lengths remarkably changed during first 30 fs. S1 single bond length shows small changes while both other two bond lengths as the time evolves change periodically at the points of intersections.Time evolution graphs (Figures13(a) and 13(c)) show a significant potential energy increase, which amounts to over 100 kJ/mol and is attained in around 15 fs. The structure then exhibits irregular periodic energy stabilization-destabilization amounts to 100–25 kJ/mol during the first 50 fs (with a major geometry change due to involvement of bonds twisting, in-plane and out-of-plane bending, as well as H-atoms stretching and bending (rocking and wagging) beside ring deformation and ring C-C stretching). Then, in about 200–250 fs further, the molecule enjoys stabilization. In about 800 fs, further stabilization mounts to −40 kJ/mol is achieved. Pyramidalization of C10 (Figure 13(b) is obviously attained in about 12 fs confirming the twisting around the C10-C9 double bond. Figure 13(b) indicates also that double bond and S1-single-bond twisting tends to change almost periodically out of phase with respect to each other, whereas C1-N1 single-bond twisting starts to increase after 30 fs. This suggests that, at points of intersections (176° and 90° for D and S1-bonds, respectively), both D-bond and S1-bond behave similarly as time evolves and most probably simultaneously play major role in the radiation-less deactivation process of the excited states.


## 4. Conclusion

We discussed the photo-induced dynamics in the nonadiabatic channel of the charge-transfer feature material of the molecular rotor type. And we tried to clarify the relaxation channels on the excited state of BMN by using electronic structure calculations on-the-fly dynamics. We report on the DFT, TD-DFT, and ab initio MD theoretically obtained results of stimuli-responsive molecular and spectroscopic properties induced by controlled twisting pathways of the charge transfer molecule, 2-[4-(dimethylamino)benzylidene]malononitrile (BMN) as a model compound of donor-acceptor material. Simulations are carried out in BMN ground (S0) and first few excited states in vacuum and in acetonitrile. It is verified that following dynamical displacements of vibrational vectors and intramolecular twisting, the excited states of this flexible molecule return to the ground state either through red-shifted emission or by nonradiative relaxation via conical intersections. The present simulation study shed lights on simultaneous all possible two bond twists in an ICT molecule BMN. Induced changes of molecular properties such as bond length, relative energy, and electronic spectroscopic characteristics (UV-Vis and fluorescence) by simultaneous two bonds twist should deepen our view to the TICT states in flexible molecules of potential applications by identifying, and probably controlling, the roles played by specific bonds twisting. The results are validated by carrying out several scans of the dynamics of the BMN material with the help of the molecular mechanical and ab initio trajectories methods. Simulation of molecular dynamics of the complex BMN molecule showed that double-bond twisting and the neighbor single-bond twisting togetherness in the excited singlet state is the most important nonradiative deactivation channel to the ground state.Points of intersections between electronic potential energy surfaces are identified by a single reference TDDFT computation and play a crucial role in arguing molecular relaxation pathways. Our data confirms that the propensity for a radiation-less transition is large in the vicinity of nuclear configurations where potential energy surfaces intersect. More sophisticated multireference methods brought about the same conclusions.Hopefully, this study may provide the foundation for more future investigations on the fluorescence quenching mechanism in D-A materials, which may be reflected in the photochemical molecular design of new efficient materials for a wide range of profitable and new applications. Additionally, it will be interesting to check the theoretical insights and the proposed dynamics scenario for BMN from the current single reference molecular dynamics simulations by high-level ab initio calculations.



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*Source: 8359527-2019-01-02.xml*