Molecular Vibrations Induced Potential Diradical Character in

Article pubs.acs.org/JPCC

Molecular Vibrations Induced Potential Diradical Character in Hexazapentacene Yiwei Feng, Fengying Zhang, Xinyu Song, and Yuxiang Bu* School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, People’s Republic of China S Supporting Information *

ABSTRACT: While the photoelectrochemical behavior of azapentacene has been investigated successfully, insight into the dynamic electronic properties of azapentacene triggered by different energy pulses is very scarce. The present work reports a fascinating phenomenon about potential diradical character governed by structural vibrations in hexazapentacene. In complete contrast to the static equilibrium configuration of hexazapentacene without diradical character, due to the vibration-based structural perturbation, DFT calculations show that some of the transient configurations possess diradical character and thus magnetism, which exhibit different periodic pulse behavior in time evolution. Since each vibrational mode refers to two distortion ways (positive/negative distortions from equilibrium configuration), 7 different possibilities are observed for the vibrationinduced diradical character for all vibrational modes (e.g., a combination of nonradical, singlet diradical, or triplet diradical for positive distortion and those of for negative distortion for each vibrational mode). This intriguing diradical character is rationalized by structural distortions with considerable changes of some energy quantities. The structural distortions cause the HOMO energy raising and LUMO energy lowering and thus an efficient reduction of the HOMO−LUMO energy gap and singlet−triplet gap of the system, which are favorable to the formation of the broken-symmetry open-shell singlet or triplet states. The periodic pulsing behavior is attributed to persistent molecular vibrations and is thus vibrational mode controlled. Compared with pentacene, the remarked effects of nitrogen substitution on the diradical properties and their pulsing behaviors are mainly due to the decreases of both the HOMO and the LUMO energies and considerable narrowing of their gaps in the vibrationsdistorted configurations. This intriguing potential diradical character and its different dynamic behavior suggest hexazapentacene potential applications as promising building blocks in the rational design of novel electromagnetic materials because of its controllable magnetism through energy pulses. This work provides comprehensive understanding of the nature of dynamic variations of the electronic structures and properties of the nitrogen-rich acene derivatives and other materials molecules.

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INTRODUCTION

rarely explored. Actually, when a molecule having a closed-shell (CS) ground state lies in a perturbing environment, it could also present diradical character, which has been exemplified by plentiful theoretical and experimental studies.8−16 Consequently, to further pursue practical applications it is essential to find the functional materials molecules which possess potential diradical character. As it is known, oligoacenes (including N-heteroacenes) could be considered as one of the most significant functional materials molecules because of their unique aggregate proper-

The diradical, the important chemical species in many organic chemical reactions, has attracted intensive attention of theorists and experimentalists in recent years owing to its unique inner structures and attractive electronic and magnetic properties as well as many potential applications in electronic and magnetic materials.1−6 It is defined as a molecule having two weakly interacting unpaired electrons or radical centers which are associated with different regions in a molecule and has an openshell (OS) singlet or triplet (T) ground state depending on their interaction extent.7 Although many more studies have been devoted to the investigation of diradical molecules, the molecules that possess potential diradical character have been © XXXX American Chemical Society

Received: April 23, 2016

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DOI: 10.1021/acs.jpcc.6b03891 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C ties including low fabrication, flexibility, and their intriguing electromagnetic properties and application potential in electronic and magnetic energy systems such as organic lightemitting diodes, conductors, field-effect transistors, memory devices, and photovoltaics.17−29 In general, acenes can be grouped into two categories: electron materials (n-type) and hole materials (p-type). The transporting performance of materials molecules strongly depends upon the nature of their charge transport. Compared with many studies on the p-type molecules, the study on the n-type materials molecules with decent mobility is relatively scarce. Therefore, it has been a formidable task to develop high-performance n-type organic materials. General strategies to obtain n-type acenes are to modify known p-type linear acenes with electron-donating groups or heteroatoms (e.g., N atom) into the p-type linear acenes.30−35 Over the past few years it has been verified that lots of attractive and fascinating electromagnetic properties just come from their extended π delocalization over the entire linear acenes. In fact, an acene diradicaloid consists of two parallel chains of polyacetylene, and their diradical character originates from larger delocalization stabilization of two unpaired electrons on two polyacetylene chains than the cross-linking stabilization between the two chains.36 Among these oligoacenes molecules, pentacene is regarded as a representative of the most active small-molecule semiconductor materials for organic thin-film transistors due to high charge-carrier mobility.37,38 Many electronic systems (e.g., sensor arrays, flexible active-matrix displays, and radiofrequency identification tags) have successfully used pentacene thin-film transistors as fundamental materials.39−41 It is well known that pentacene has a CS singlet ground state, which does not display diradical character. Although pentacene has a closed-shell ground state, our recent ab initio molecular dynamics simulation indicated that appropriate structural perturbations can make it exhibit potential diradical character with irregular pulse behavior in time evolution.42 Thus, this structure-based information might offer an opportunity to enhance its future application. In addition, appropriate structural modification also could exhibit its potential diradical character or other hidden properties, which have been confirmed directly or indirectly in some recent studies.43,44 For example, Julia and co-workers successfully proved that introduction of a heteroatom results in a red-shifted transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) and hence facilitates the appearance of diradical character.44 Another work indicates that introduction of the sp2-hybridized nitrogen atoms considerably lowers the HOMO and LUMO energies and thus improves their stabilities in air and light illumination, decreasing the energy loss of exothermic singlet fission of pentacene derivatives.45 1,4,6,8,11,13-Hexazapentacene (HAP) is a typical kind of representative CS molecule in the family of N-substituted pentacene. Due to successive replacement of the C−H units by nitrogen atoms in pentacene, it presents a number of opportunities to exhibit OS or T broken-symmetry ground state, and thus, it more probably possesses potential diradical character. As known, many experimental and theoretical investigations have proved that substituted pentacene and other oligoacenes not only exhibit diradical character46−48 but also modify the electromagnetic properties of the molecules through twisting them, which exhibits UV absorption red shifted and electrogenerated chemiluminescent, etc.49 HAP has been successfully synthesized and characterized, and photo-

electrochemical data indicate that HAP is of the n-type semiconductor property.31 Further, its derivatives have also been successfully synthesized and characterized.30−33,35 It is expected that these HAP derivatives with special structures might have practical applications for the construction of organic thin-film transistors and others,22,50−53 and these applications which are based on the modified electronic and magnetic properties are very closely associated with the changes of the energy gaps between the HOMO and the LUMO and also between the CS and the T state. Although HAP has been intensively explored, its magnetic properties are still barely scrutinized and even are unknown. It is particularly well known that HAP has a CS ground state not possessing diradical character, and all known properties can be ascribed to its static structure. Structure-based information due to transient distortion is very lack for HAP, and thus, its further application might be limited. Actually, introduction of nitrogen atoms into pentacene can significantly reduce the energies of both HOMO and LUMO (Figure 1). In comparison with

Figure 1. HOMO and LUMO energies of the CS state for static HAP and pentacene, and the minimum value and maximum value in the structure distortions.

pentacene, the HOMO and LUMO energies of HAP decrease by 1.68 (HOMO) and 1.58 eV (LUMO), and the band gap slightly increases by 0.11 eV. The mild HOMO−LUMO energy gap has implied its propensity toward displaying diradical character. In the case of this observed phenomenon, it is likely that introducing six nitrogen atoms could affect the HOMO− LUMO gaps. As known, the nitrogen atom possesses larger electronegativity than the carbon atom,54 and thus, undoubtedly the substitution of carbon atom(s) by sp2-hybirdized nitrogen atom(s) could make the frontier molecular orbitals stabilize owing to a strong inductive effect caused by nitrogen.55,56 Inspired by these theoretical and experimental data, we chose HAP as our target which originates from the well-known pentacene to analyze whether it possesses potential diradical character or not. We expect that HAP possibly exhibits promising potential diradical character due to the vibration-based structural perturbation. In other words, some of the transient structural distortions of HAP might induce its potential diradical character to appear. Naturally, if the structural perturbation is persistent in a certain periodic way, the diradical character occurs also periodically. Additionally, it is worth mentioning B


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Figure 2. (a) LUNO occupation numbers of the OS singlet states for 20 snapshot configurations in the vibrational process for the 73rd vibrational mode of HAP calculated at the CASSCF(10,10)/6-31G(d) level. Blue line denotes the LUNO occupation number (0.148) of the static HAP in its CS ground state. (b) Linear correlations between the CASSCF and the UB3LYP results for the diradical character indexes of positive distortions of the 73rd vibrational mode, where the blue dots denote the configurations with diradical character, while the black ones denote those without diradical character. ⟨S2⟩ values are calculated at the UB3LYP/6-31++G(d,p) level.

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here that if structural distortion or molecular vibrations are persistent, HAP and any other molecules which lie in their thermal vibrational states have considerable amounts of zeropoint vibrational energies. Clearly, the position fluctuation of atoms in HAP or structural distortion from its planar configuration is associated with the thermal vibrations of the molecule. In short, as one of the molecular inherent properties, structural perturbations of molecules are persistent. It not only modifies a transient configuration, which leads to electronic and magnetic property changes, but also may induce other novel properties and thus exhibits intriguing practical application prospects. Although much more efforts have been made to study the properties of HAP, its potential electronic and magnetic properties are still barely scrutinized, and in particular, no attempt has been made to examine if HAP can exhibit intriguing diradical character which originates from structural perturbation. Density functional theory (DFT), a highly valuable theoretical and computational tool in predicting various physical and chemical properties, has successfully been used in investigating many diradical species owing to its high efficiency and accuracy. Herein, we have chosen DFT as our main research method to investigate possible diradical character in HAP at a single molecular level and use complete active space self-consistent field (CASSCF) as a supplement method to further confirm our conclusions. Surprisingly, we find that HAP, a nitrogen-containing derivative of pentacene, can exhibit different potential diradical characters due to structural vibrations, and such diradical characters present different periodic pulsing behaviors. Clearly, this interesting unexpected behavior implicates potential applications of HAP as a proposing building block of novel electromagnetic materials. This work provides comprehensive understanding of the origin of inherent fluctuations of electronic structure and property in HAP and also provides a valuable strategy to investigate the mechanism of appearance of potential diradical character and other molecular transient properties.

COMPUTATIONAL DETAILS

In view of the successful and a vast number of applications of B3LYP functional in optimizing molecular geometries and examining diradical character,36,42,57−59 herein, we perform a B3LYP functional calculational analysis to obtain a basic understanding of potential diradical character in HAP that appears due to molecular thermal vibrations. Thus, the geometries of CS and T states of static HAP were fully optimized by using the UB3LYP/6-311++G(d, p) method.36,42 The optimized geometries were further verified to be local minima through vibrational analyses, which show no imaginary frequency vibrational mode. Then we examined the diradical character of its 168 distorted configurations since HAP has 84 vibrational modes. Each distorted configuration can be obtained by adding or subtracting the shift vector coordinates (Δx, Δy, Δz) of all atoms in a vibrational mode to their corresponding coordinates in the static configuration (R0). To identify the diradical character of these distorted configurations, single-point calculations on the CS, OS, and T states of the 168 kinds of distorted configurations were carried out at the B3LYP/6-31++G(d,p) level. To examine the gradual variation tendency of the diradical character in a specific vibrational mode, we divide the total shifts of all atoms in the molecule into 10 equivalent subshifts (ΔR), and the relevant snapshot configurations in the vibrational evolution process in the specific mode can be described via their shifted vector coordinates, R = R0 ± nΔR, where ΔR can be viewed as the shift step size in the specific vibrational mode and n denotes the number of steps (n = 1−10). From the above calculated results, the corresponding energies of three states (CS, OS, and T), the HOMO and LUMO energies, and spin contamination ⟨S2⟩ values were obtained. To confirm the B3LYP-calculated results, the CASSCF(10,10) calculations were also performed to determine the orbital occupation numbers for the snapshot configurations possessing diradical character. The CASSCF calculations were performed only with a 6-31G(d) basis set for reducing the calculational cost and also making the CASSCF calculations possible. All of these calculations were carried out using the Gaussian 03 suite of program,60 and some of the additional data and figures are given in the Supporting Information (SI).

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RESULTS AND DISCUSSION It is well known that HAP exhibits a CS ground state and has no diradical character. However, its moderate HOMO−LUMO energy gap in the CS state and the singlet−triplet energy gap offer an opportunity to present diradical character. Clearly, as a C


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Figure 3. Schematic representations for vibration-induced diradicalization of HAP with corresponding orbitals: HOMO and LUMO of the static ground state HAP versus two singly occupied molecular orbitals (SOMO, isovalue = 0.04) and spin density (isovalue = 0.004) of four vibrationdistorted configurations (positive distortions of 17th/OS singlet and 60th/T and negative distortions of 17th/OS singlet and 72nd/T) featuring diradical character for HAP, calculated at the UB3LYP/6-31++G(d,p) level of theory.

many vibration-distorted configurations are significantly different from the standard ⟨S2⟩ value (0) and LUNO occupation numbers (0.148). To verify the agreement between the two methods in describing the diradical character, we examine the correlation between the CASSCF results and the UB3LYP results and find they present a good linear correlation, as shown in Figure 2b for the positive distortions of the 73rd vibrational mode. Clearly, this correlation has verified the accuracy and reasonability of our results. These data have fully indicated that HAP possesses potential diradical character and can present it via structural vibrations. We also analyzed the HOMO and LUMO of the vibration-distorted configurations which do not exhibit diradical character and two singly occupied molecular orbitals (SOMOs) and spin densities of the vibration-distorted configurations which exhibit diradical character and the OS or T ground state (Table S4, SI). Only the results for positive distortions of the 17th (OS state, antiferromagnetism (AFM)) and 60th (T state, ferromagnetism (FM)) vibrational modes and negative distortions of the 17th (AFM) and 72nd (FM) vibration modes are shown in Figure 3. Taking the 17th (AFM) vibrational mode (positive distortion) as an example, qualitatively speaking, the two single electrons reside in two almost degenerate SOMOs and spin densities are spin distinguishable (spin-up versus spin-down) through the entire molecule, indicating a clear diradical character for the 17th vibrational mode-based distorted configuration. Overall, our results again confirm the above conclusion that HAP possesses hidden diradical character to some extent. From a chemical viewpoint, it is important to underline that because of possible singlet−triplet interaction, the diradical character can be obtained. If some of the vibrational modes can lead to large singlet−triplet energy gaps, the triplet state does not affect the singlet state and the molecule possesses a CS ground state and a triplet excited state or conversely a triplet ground state and a singlet excited state. However, if some of the vibrational modes can produce small singlet−triplet energy gaps, the triplet state can interact with the singlet state,

molecular inherent property, structural vibrations can certainly induce certain changes in the electronic properties of the molecule in the vibrational process and thus possibly leads to the occurrence of diradical character. From a statistical viewpoint, different atom-motion-based structural vibrations might lead to different geometrical distortions or structural perturbations. Inspired by these we first performed geometry optimizations and then carried out single-point B3LYP/6-31+ +G(d,p) calculations for their CS, OS, and T states, respectively, and get the energies, molecular orbitals, and ⟨S2⟩ values of the OS states. In order to clarify the relevant results, we further calculated the occupation numbers of the lowest unoccupied natural orbital (LUNO) for diradical character of representative vibrational modes at the CASSCF(10,10)/631G(d) level. The calculated results are listed in the SI (Table S1 and Table S2), and the LUNO occupation numbers of the OS state of representative vibration modes are shown in Figure 2a. To our surprise, the calculational results show that some distorted configurations due to molecular vibrations can display considerable diradical character with an OS or T ground state, although the rest still have CS ground states. Additionally, the diradical character displays a progressive increased tendency with the increase of geometrical deformation degree. For example, for the distorted snapshot configuration for the 73rd vibrational mode of negative distortion, when n = 10, its LUNO occupation number being 0.974 indicates that it has a 97.4% diradical character. In contrast, the calculated LUNO occupation number is 0.148 and the ⟨S2⟩ value is 0.0 for static HAP. Apparently, the representative LUNO occupation numbers in the vibration-distorted configurations are considerably larger than that (0.148) of static HAP. In general, HAP is intensively regarded as a CS molecule which has no diradical character and a ⟨S2⟩ value of 0. However, such a LUNO occupation number (0.148) could be roughly viewed as a criterion below which the configuration has no diradical character among all vibration-induced distorted configurations of HAP. Thus, these ⟨S2⟩ and LUNO occupation numbers for D


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Figure 4. Relative singlet−triplet gaps, ΔE1 (ΔE1 = ET − ECS − ΔEstatic, where ΔEstatic is the singlet−triplet energy gap in static structure), for 168 vibration-distorted configurations of HAP, calculated at the UB3LYP/6-31++G(d,p) level. The value −0.13 kcal·mol−1 is the critical value below which the corresponding vibration-distorted configurations exhibit diradical character. The threshold of vibration-distorted configurations featuring triplet diradical is −22.71 kcal·mol−1.

Figure 5. Relative HOMO−LUMO energy gaps, ΔE2 (ΔE2 = ELUMO − EHOMO − ΔEstatic, where ΔEstatic is the HOMO−LUMO energy gap in static structure), of the CS singlet state for 168 vibration-distorted configurations of HAP, calculated at the B3LYP/6-31++G(d,p) level. The value 0.12 eV is the critical value below which the corresponding vibration-distorted configurations exhibit diradical character. The threshold of vibration-distorted configurations featuring triplet diradical is −1.24 eV.

than its T state (ECS < ET), similar to the static HAP without diradical character; (2) the OS singlet (being the ground state) is lower than its T state, even much lower than its CS state (EOS < ECS < ET); (3) the CS singlet state is higher than the T state and OS state (EOS < ET < ECS); (4) the OS triplet ground state is more advantageous in energy than the OS and CS singlet states (ET < EOS < ECS). In the latter three cases, the distorted configurations possess different degrees of diradical character. The detailed results and corresponding energy gaps are listed in Tables S1 and S2 (the SI). The relative values of the singlet− triplet energy gaps ΔE1 (ΔE1 = ET − ECS − ΔEstatic, where ΔEstatic is the CS−T energy gap in static structure) of all 168 vibration-distorted configurations are shown in Figure 4. Clearly, structural fluctuation induced by molecular vibration

resulting in an OS or triplet ground state. Naturally, the potential diradical character in HAP derives from lots of factors. Therefore, it is necessary for us to analyze how the observed diradical character is correlated with the relative stability among three states (CS, OS, and T) and the CS−T energy gaps. A. Energy Gap between Singlet and Triplet States. To reasonably explain the above-mentioned diradical phenomenon, we analyzed relevant energies of all 168 distorted configurations according to the 84 vibrational modes of HAP. After examining the relative energies of all possible states including the CS singlet and OS singlet and triplet states, we unravel that the energetics of all distorted configurations in 84 vibrational modes can be approximately classified into four categories: (1) the CS singlet (being ground state) is still lower E


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Figure 6. Linear correlation between the singlet−triplet and the HOMO−LUMO energy gaps of the CS states of all 168 vibration-distorted configurations, where the red and blue dots denote the configurations with OS singlet diradical (antiferromagnetism, AFM) and T diradical (ferromagnetism, FM) characters, respectively, and the black ones denote those without diradical character (nonmagnetism). Inserted pictures (orbitals and spin density distributions) correspond to positive distortions of three different vibrational modes (45th, 17th (AFM), and 60th (FM)).

B. HOMO−LUMO Energy Gap. On the other hand, the energy gap between the HOMO and the LUMO in the CS states for all 168 vibrational modes was systematically investigated, because they are closely related to the singlet− triplet energy gaps. Naturally, to explain the origin of diradical character in some distorted configurations induced by molecule vibrations, we further check the HOMO−LUMO energy gaps for the CS states of all 168 vibrational structures. Figure 5 indicates that structural perturbation makes ΔE2 (ΔE2 = ELUMO − EHOMO − ΔEstatic, where ΔEstatic is the HOMO−LUMO energy gap in static structure) fall in a large range of −2.19− 1.53 eV, and the criterion for exhibiting diradical character is −0.17 eV, that is, when ΔE2 is less than −0.17 eV, the diradical character appears. On the other hand, the vibration-distorted configurations could display T state diradical character if ΔE2 is smaller than −1.24 eV. In fact, the average ΔE2 is −0.33 eV, meaning that the average HOMO−LUMO energy gap among all vibration-distorted configurations is smaller than that of the static configuration by 0.33 eV. For static HAP and a part of the distorted configurations, they have HOMO−LUMO energy gaps greater than 2.15 eV (the critical value) and thus do not present diradical character. Actually, despite the structural distortion, some of the vibration-distorted configurations still have too large HOMO−LUMO energy gaps, which are unfavorable to the HOMO → LUMO electron transition. In order to obtain a comprehensive understanding of diradical character appearing, we also investigate the relationship between the CS−T energy gaps and the HOMO−LUMO energy gaps in the CS states for all vibration-distorted configurations. As shown in Figure 6, the correlation is highly linear. The correlation line can be divided into two main zones: one is the nonradical region, while the other is the diradical character region displayed by the shaded area, which contains the AFM subregion (OS state) and FM subregion (T state). Furthermore, the inserted pictures in Figure 6 present the distribution characters of HOMO and LUMO of the CS singlet with a comparison of them with those of the α and β singly

could considerably cause the variation of singlet−triplet energy gaps and makes ΔE1 fall across a large range from −48.10 to −46.51 kcal·mol−1. The average ΔE1 is −0.79 kcal·mol−1, meaning that the CS−T energy gaps in the vibration-distorted configurations are on average smaller than that in the static configuration of HAP. More interestingly, for all the vibrational modes which possess diradical character, ΔE1 falls in below −0.13 kcal·mol−1 (viewed as a threshold), that is, only when ΔE1 is smaller than −0.13 kcal·mol−1, the corresponding configuration might present diradical character. On the other hand, the vibrationdistorted configurations could display T state diradical character if ΔE1 is smaller than −22.71 kcal·mol−1. This observation demonstrates that the reason HAP has potential diradical character is due to its capability to possibly attain a relatively small singlet−triplet energy gap. Furthermore, the fact that the static HAP does not display diradical character may be ascribed to the configurable difference between the CS ground state and the T state and thus a Franck−Condon barrier which suppresses reduction of the HOMO−LUMO gap and thus inhibits the HOMO → LUMO electron transition, as mentioned below. Overall, appropriate vibration-based structural change could modify the CS−T energy gap. If the gap is smaller than 19.53 kcal·mol−1, this small ΔE(T‑CS) may yield a sufficient mixing between the CS and the T states, which exhibit potential diradical character. However, similar to static HAP, despite the structural perturbation, we also find that some of the vibrational modes do not induce diradical character. This phenomenon is attributed to the larger CS−T energy differences. When the gap is large, the CS−T state interaction is very small, the T state does not affect the CS ground state, and the diradical character does not occur. In other words, an appropriate energy gap between the T and the CS states could result in an abundant mixing between the CS and the close energy T state, which contributes to the generation of the correct ground state and appearance of diradical character to some extent. F


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Figure 7. (a) Possible variations of the HOMO and LUMO energies of the distorted configurations in the middle-frequency zone (500−1700 cm−1) calculated at the B3LYP/6-31++G(d,p) level. HOMO (−6.29 eV) and LUMO (−3.97 eV) energies of static HAP are also shown for comparison (magenta and violet lines). Blue-line filled areas denote the gaps which refer to the 28 vibration-distorted configurations of OS diradical, while greenline filled areas denote those which refer to 9 vibration-distorted configurations of T diradical. (b) Variation tendency of the HOMO and LUMO energies of three representative vibrational modes. The 17th and 62nd modes are OS singlet and T diradical modes, respectively, while the 45th is nondiradical vibrational modes, calculated at the (U)B3LYP/6-31++G(d,p) level.

Figure 8. Vibration-distorted geometries for three representative vibrational modes (positive distortions of 17th, 29th, and 73rd) which have diradical character and the static parent HAP with the indicated bond lengths (Angstroms).

occupied molecular orbitals (SOMOs) of the diradical OS state and the α1 and α2 SOMOs of the diradical T state. Clearly and consequently, molecular vibrations are easy to generate small HOMO−LUMO energy gaps and promote electron transition from the HOMO to the LUMO and further to exhibit diradical character. Nevertheless, when the HOMO−LUMO energy gap and CS−T energy gap decrease to be below critical values (the former is 2.15 eV, and the latter is 19.53 kcal/mol), the diradical character may appear. To find a reasonable reason for the diradical character appearing when going from CS to OS or T, we analyze the HOMO and LUMO energy variations of distorted configurations induced by vibration modes which possess diradical character. The calculated results indicate that structural distortion in combination with the introduction of nitrogen atoms in the pentacene ring can change the HOMO and LUMO energies significantly. The HOMO energy (−6.29 eV) of static HAP is lower by 1.63 eV than that of static pentacene,

while the LUMO energy (−2.39 eV) of static pentacene is higher by 1.36 eV than that of static HAP. As shown in Figure 7a, structural deformation makes the LUMO energy of distorted configurations which display diradical character slightly go down to below that of static HAP and the HOMO energy significantly rise up to above that of static HAP. Figure 7b shows the distorted configurations for the diradicalgenerated representative vibrational modes slightly exhibit the cooperativity of HOMO/LUMO energy variations in narrowing the HOMO−LUMO energy gap, that is, when the HOMO energy goes up, the corresponding LUMO energy goes down. Just owing to the increase of the HOMO energies and the decrease of the LUMO energies, HAP has narrowed HOMO− LUMO energy gaps and further narrowed CS−T gaps in its vibration-distorted configurations, which leads to the appearance of diradical character. Undoubtedly, the above discussions have demonstrated that the narrowed HOMO−LUMO energy gap and CS−T energy G


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makes the HOMO−LUMO energy gaps fall in a range of 0.13− 3.85 eV. Clearly, such energy gaps due to the N-substitution are favorable to the appearance of diradical character compared no matter with static HAP or with static pentacene. In addition, it should be noted that the vibrational modes which induce diradical character are significantly different from those in pentacene not just in the decrease of the number of diradical character vibrational modes. The vibrational mode types inducing diradical character also change. Taking the first diradical vibrational mode as example, as shown in the IR vibrational spectrum (Figure 9), the first distorted configuration

gap are abundant and also essential for the appearance of hidden diradical character at least for HAP. Certainly, this observed regularity could not be suited for all situations because the occurrence of diradical character is related not only to the HOMO−LUMO and CS−T energy gaps but also to the HOMO/LUMO spatial distributions. C. Structural Variation Analyses. Undoubtedly, the HOMO−LUMO energy gaps and singlet−triplet gaps are certainly associated with configuration variations of HAP. Previous theoretical studies have demonstrated that the crosslinking C−C bond length of a distorted configuration in pentacene is an important factor promoting diradical character appearing.36 Therefore, we check the cross-linking C−C distances of all 19 vibration-induced negatively distorted configurations possessing diradical character which are shown in Figures 8 and S7 (SI). To our surprise, for most of the vibrational modes, in their distorted configurations, the crosslinking C−C bond lengths are on average shorter than those of static HAP. In fact, this phenomenon is probably ascribed to the easily accessible HOMO → LUMO electron transition in the distorted configurations exhibiting diradical character. From a chemical structure viewpoint, for any distorted configuration, all cross-linking C−C bonds in the HOMO of its CS state have an antibonding character, whereas those in its LUMO are of bonding property (Figures 3 and 6). Consequently, when a specific energy pulse activates a vibrational mode which contains the reduction of the cross-linking C−C distances, the configuration distortion provides a favorable condition to the HOMO → LUMO electron excitation, and thus, diradical character occurs. Although the vibrational modes can tell us how all atoms in a molecule move and which modes can yield diradical character as mentioned above, it is really difficult to point out what kinds of bond length variations can cause the appearance of diradical character since the bond length variations in all vibrations-distorted configurations do not present any regularities. Thus, we only can roughly conclude that any structural distortions inducing the reduction of the cross-linking C−C distances, waving, as well as varying of the C−C bonds in polyacetylene-like chains could produce a narrowed HOMO−LUMO energy gap and thus a narrowed CS−T energy gap; it favors the interaction of the CS and the T state to generate an OS singlet state, and thus, diradical character could appear. Of course, the detailed structure change inducing diradical character should refer to that according to an actually corresponding vibrational mode. D. Nitrogen Substitution Effect. As the successive substitutive product of the C−H units in pentacene by nitrogen atoms at specific positions, HAP presents different character from pentacene in the HOMO−LUMO energy gaps of the CS state. As shown in Figure 1, the substitution of some C−H units in pentacene by sp2-hybirdized nitrogen atoms effectively decreases the energies of the HOMO and LUMO. In detail, HAP with six doping N atoms has the lower HOMO and LUMO energies compared with pentacene, which are lowered by 1.62 and 1.48 eV, respectively. This observation should be due to the strong electron-withdrawing capability of the nitrogen atom compared with the carbon atom, implying that introducing nitrogen could stabilize the HOMO and LUMO because of the strong inductive effect. However, the HOMO− LUMO energy gap increases slightly from 2.21 to 2.32 eV. As a result of this slightly enlarged gap, the number of diradical vibrational modes in negative distortion reduces from 25 to 19. Meanwhile, Figure 1 also indicates that structural deformation

Figure 9. IR vibrational spectrum and the corresponding IR diradical character (⟨S2⟩) spectrum of HAP in the middle-frequency zone ranging from 400 to 1750 cm−1, which contains 37 vibration modes inducing diradical character. All results are calculated at the UB3LYP/ 6-31++G(d,p) level.

with diradical character corresponds to a vibrational mode at 501.1 cm−1 and refers to the waving of the entire molecule. However, the first diradical-generating vibrational mode of pentacene is a symmetrical in-plane molecular swing at 263.3 cm−1. This difference can be ascribed to the unique N-doping position and internal electronic structure of HAP. In short, introduction of six nitrogen atoms into pentacene can significantly modify the molecular electronic configuration and consequently change some energy quantities such as the HOMO/LUMO energies and their gap and relative stabilities of the electronic states (CS singlet, OS singlet and triplet), etc., which favor the appearance of diradical character. E. Frequency-Dependent Analyses and Periodic Pulsing Behavior. To further understand the structural nature of the diradical character appearing, we performed single-point calculations for the CS, T, and BS states of all vibration-distorted configurations and examined their potential diradical character (Table S4 in the SI) and relationships with the singlet−triplet and HOMO−LUMO energy gaps (Figures 6). Additionally, infrared spectra of the optimized structure in combination with the spin-squared values ⟨S2⟩ were used to analyze the effects of various normal vibrations. As shown in Figure S2, HAP possesses 84 normal vibrational modes which distribute in the region of 38.33−3208.66 cm−1. Furthermore, we find that it is very scarce for static HAP for the normal molecular vibrations in displaying diradical character, that is, only appropriate molecular vibrations can induce the appearance of diradical character in HAP. H


Article


The next intriguing phenomenon is the periodic pulsing property of the observed diradical character. As shown in Figure 10, the vibration-induced structural perturbation in HAP

In fact, our DFT calculations indicate that only 24 vibrational modes can induce the appearance of diradical character, and all of these modes exhibit the reduction of all or a part of the cross-linking C−C distances, including waving of the entire molecule and possible distortions due to hydrogen swings. Some other vibrational modes including stretching, bending, twisting, and in-plane ring swing of the entire molecule and inplane and out-of-plane swings of hydrogen atoms do not directly induce diradical character. In detail, all distortions in low- (e.g., 3000 cm−1) frequency zones do not induce diradical character. Main contributors to inducing diradical character appearing are the middle-frequency zone, the fingerprint zone (500−1700 cm−1). For a frequency less than 500 cm−1, the vibrations exhibit 16 vibrational modes including molecular bending, twisting, inplane swing, stretching, and out-of-plane swing of hydrogen atoms, while for a frequency higher than 3000 cm−1, the vibrations contain 8 vibrational modes originating from various C−H stretching vibrations. The distorted configurations induced by these vibrational modes do not result in the appearance of diradical character. However, in the range from 500 to 1300 cm−1, there exist 40 vibrational modes which are related to various distortions induced by swings, deforming, waving, and stretching. Only those causing the C−C bond changes and waving of the entire molecule can induce diradical character. In the range from 1300 to 1700 cm−1, the vibrations are mainly due to various C−C bond stretching. It has been mentioned above that the ring deformations in these modes are the main contributors to the appearance of diradical character. Only a small part of the vibrations correspond to the in-plane hydrogen swing and ring deformation and basically do not induce diradical character. In the 500−1100 cm−1 zone, 9 vibrational modes are assigned to stretching, swing, and inplane deformation of rings and various swings of hydrogen atoms and at the same time left 15 vibrational modes corresponding to the C−C stretching distribute in from 1300 to 1700 cm−1. For all vibrations, each vibrational mode includes two distortion ways (positive/negative distortions from equilibrium configuration). As shown in Table 1, 7 different

Figure 10. Time evolutions of ⟨S2⟩ of HAP for three representative vibrational modes in which the corresponding diradical characters present periodic pulsing behavior with different pulse periods. ⟨S2⟩ values are calculated at the UB3LYP/6-31++G(d,p) level. Oscillating periods are 126.2 (17th), 101.1 (25th), and 41.8 fs (68th) for the three modes, respectively, and a period includes two peaks (one for positive distortion and one for negative distortion) for each mode.

could lead to the appearance of hidden diradical character in a periodic oscillating way which exhibits a sustained diradical pulse behavior. Clearly, this periodic pulsing phenomenon should be contributed by regular molecular vibration. In detail, molecular vibration may afford energy for the molecule, leading to the motions of some atoms according to the corresponding modes. When a molecule lies in a special vibrational mode which possibly leads to diradical character, the thermal fluctuation or external energy may make the energy of the system increase, and thus, the molecule becomes a metastable state. Such a process keeps on along with the progress of deformation. After reaching the maximum shift, the molecule relaxes back to the low-energy state along the corresponding vibrational mode. Clearly, in this vibrational period, if the distorted configuration appears with reduction of the crosslinking C−C distances or waving of a whole molecule or variations of the polyacetylene chain C−C bonds, the diradical character could be observed, that is, the diradical character appears and then disappears, exhibiting a pulse in this time period. Thus, the continuous molecular vibration makes periodic motions of relevant atoms according to this special vibrational mode. On the other hand, when the distorted structure occurs in time evolution, the diradical character does not appear in some time scale until the next distorted structure, leading to the occurrence of diradical character. Similarly, the observed diradical characters and pulsing behavior present a close dependence on CS−T and HOMO−LUMO energy gaps of HAP in its distorted configurations. Clearly, these results unravel an inherent periodic pulsing diradical character through vibrational mode analyses and accurate DFT calculations. In addition, it should be noted that for the diradical modes to achieve such vibration-shift amplitudes where the diradical character appears, the required energies are different and even have large differences among them. In most of the 19 diradical modes, the required energies for diradical character appearing

Table 1. Seven Different Possibilities for the VibrationInduced Diradical Charactera positive distortion (ground state)

negative distortion (ground state)

BS

BS

T BS CS T BS T

BS CS BS CS T T

modes 17, 19, 27, 34, 58, 64, 68, 73, 75 25 29, 48, 66 33, 51 60, 65 71, 72 74, 62

a

Each refers to a combination of nonradical, singlet diradical, or triplet diradical for the positive distortion and those of for negative distortion for each vibrational mode.

possibilities refer to a combination of nonradical, singlet diradical, or triplet diradical for positive distortion and those for negative distortion for each vibrational mode. In summary, the above mode analyses further testify the conclusion that the occurrence of diradical character originates from the reduction of the cross-linking C−C distances. I


Article

The Journal of Physical Chemistry C are in the 0.6−6.0 eV range and only some of the diradical modes have large energy requirements (>6.0 eV, e.g., the modes 25, 64, 65, 73 and 75). For example, for the diradical mode 60, the diradical character appearing requires only ∼0.6 eV, while those require 3.15, 2.67, 3.46, and 2.19 eV for the diradical modes 17, 48, 62, and 66, respectively. Of course, this is only a qualitative analysis, indicating the possibility of diradical character appearing through vibrational activation. A practical application certainly requires detailed analyses of the vibrational energetics of a single molecule and its assemblies and crystals and relevant intra- and intermolecular electronic couplings.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +86-531-88365740. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by NSFC (21573128, 21373123, and 20973101) and NSF (ZR2013BM027) of Shandong Province. Part of the calculations were carried out at National Supercomputer Center in Jinan, Shanghai Supercomputer Center, and High-Performance Supercomputer Center at SDU-Chem.

CONCLUSIONS We used the B3LYP and CASSCF approaches to characterize potential diradical character in HAP. The calculated results suggest that HAP possesses the vibration-induced potential diradical character. In general, static HAP possesses a CS ground state. However, it is interesting to note that HAP in some of its vibration-distorted configurations exhibits the OS singlet or T ground state and thus diradical character, and they present different regular pulse behavior depending on the vibrational modes and frequencies. Since each vibrational mode has two distortion configurations (R = R0 ± ΔR), 7 different possibilities are observed for the vibration-induced diradical phenomena for all vibrational modes (e.g., a combination of CS, OS, or T for R = R0 − ΔR and CS, OS, or T for R = R0 + ΔR for each vibrational mode). The appearance of diradical character is attributed to the variations of the carbon−carbon distances as well as wave vibrations of the molecule. These structural variations modify the energy gaps between the HOMO and the LUMO and between the CS and the T states, thus making the diradical character appear. As a general tendency, when geometrical vibration leads to narrowed HOMO−LUMO and CS−T energy gaps, the diradical character could occur, whereas when geometrical vibration leads to enlarged HOMO−LUMO and CS−T energy gaps, the vibration-distorted configuration does not present diradical character. Clearly, with this intriguing vibration-induced pulsing diradical character, HAP can be viewed as a promising building block in the design of novel magnetic materials, that is, we can use a specific energy pulse to activate a vibrational mode of the target molecule with hidden diradical character and to make diradical character appearing for magnetism-targeted applications. In this work, we provide new insights into the inherent electronic property in HAP and a comprehensive understanding of the dynamic electronic and magnetic properties in the magnetism-targeted molecules.

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densities of the OS states for all 84 vibration-distorted configurations of HAP (PDF)

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b03891. All data and figures calculated at the (U)B3LYP/6-31+ +G (d,p) level including the energies for the CS singlet, broken-symmetry OS singlet and triplet state, corresponding energy orders, ⟨S2⟩ values, intramolecular magnetic exchange coupling constants, corresponding geometrical characters, HOMO−LUMO gaps (H−L gap, eV) of the closed-shell singlet states, singlet−triplet energy gaps, HOMO/LUMO/SOMO (α,β), spin J


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Molecular Vibrations Induced Potential Diradical Character in

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