CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201402026
Organic Nonlinear Optical Materials: The Mechanism of Intermolecular Covalent Bonding Interactions of Kekul Hydrocarbons with Significant Singlet Biradical Character Jing Liu,[a] Jiarui Xia,[b] Peng Song,*[a] Yong Ding,[a] Yanling Cui,[a] Xuemei Liu,[a] Yumei Dai,[c] and Fengcai Ma*[a] The ground- and excited-state properties of benzene-linked bisphenalenyl (B-LBP), naphthaline-linked bisphenalenyl (N-LBP), and anthracene-linked bisphenalenyl (A-LBP) Kekul molecules and their respective one-dimensional (1D) stacks are investigated using time-dependent density functional theory (TD-DFT) and a range of extensive multidimensional visualization techniques. The results reveal a covalent p–p bonding interaction between overlapping phenalenyl radicals whose bond length
is shorter than the van der Waals distance between carbon atoms. Increasing the linker length and/or number of molecules involved in the 1D stack decreases the HOMO–LUMO energy gap and increases the wavelength of the systems. The charge-transfer mechanism and electron coherence both differ with changes in the linker length and/or number of molecules involved in the 1D stack.
1. Introduction The arrival of the information age has lead to the rapid development of communication technology, IT technology, and optoelectronics, thus leading to an increased demand for nonlinear optical materials.[1–5] Organic non-linear optical materials that possess properties such as high non-linear polarizability, high optical damage thresholds, short response time, and a molecular design that is responsive to non-linear optical stimuli, have great potential for use in high-speed integrated optical devices. Consequently, research on organic non-linear optical materials and their properties has attracted a lot of interest in recent years.[6–11] Photoinduced electron transfer (PET) is a fundamental process that has been shown to play a key role in determining the efficiency of photoelectric materials.[12–14] PET has been widely used in organic photovoltaic cells, fluorescence sensors, and components for high-sensitivity optical analytical techniques.[15–17] Recently, research has focused on the mechanism of PET in organic photoconversion systems with highly efficient charge-transfer and slow charge recombination.[18–20] Charge transfer and charge recombination are the two kinetic process-
[a] J. Liu,+ Prof. P. Song, Prof. Y. Ding, Y. Cui, X. Liu, Prof. F. Ma Department of Physics, Liaoning University Shenyang 110036 (China) E-mail: [email protected] [email protected] [b] J. Xia+ School of Chemistry and Chemical Engineering Shandong University, Jinan 250100 (China) [c] Prof. Y. Dai Normal College, Shenyang University Shenyang 110044 (China) [+] These authors contributed equally.
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es to be considered, and are represented by the electron transfer rate constant (kET) shown in Equation (1).[20] kET ¼ k0 expðbRDA Þ,
ð1Þ
where k0 is a kinetic pre-exponential factor, RDA is the donor– acceptor distance, and b is the attenuation factor.[21] Recently, quinoidal Kekul hydrocarbons have attracted the attention of scientists because of their unusual reactivity and electronic structure.[22] These compounds possess a relatively small energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). This leads to a admixture of the doubly excited configuration 1FH,H!L,L into the ground configuration 1F0 in their ground state description.[23] A consequence of the mixing of electronic configurations is that the electron repulsion is taken into consideration; thereby two electrons with antiparallel spins are permitted to correlate in separate spaces, thus diminishing the covalent bond character and increasing the biradical character of the system.[24] Subsequently, the phenalenyl radical and its derivatives have attracted a lot of attention owing to their interesting properties (e.g. conjugacy, planarity, and high spin delocalizing properties, among others).[11, 25] Kubo and Shimizu et al. have reported the synthesis, isolation, intermolecular interactions, and solid-state properties of a singlet biradical compound utilizing the high spin delocalizing properties of the phenalenyl radical.[11, 26–29] In addition, the properties of the bisphenalenyl molecule were researched through theoretical methods by Huang et al.[30] We now report our investigations into the ground and excited state properties (including singlet biradical character (y), intermolecular covalent bonding p–p distance, HOMO–LUMO ChemPhysChem 2014, 15, 2626 – 2633
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www.chemphyschem.org Table 1. Calculated singlet biradical character (y [%]) of B-LBP, N-LBP, ALBP, and their respective 1D stacks.
Figure 1. Molecular structures of B-LBP, N-LBP, and A-LBP (R = H).
energy gap, absorption spectrum, charge-transfer mechanism and electron–hole coherence) of the benzene-linked bisphenalenyl (B-LBP), naphthaline-linked bisphenalenyl (N-LBP), and anthracene-linked bisphenalenyl (A-LBP) Kekul molecules, and their respective one-dimensional (1D) stacks using density functional theory (DFT) and a range of extensive multidimensional visualization techniques.[31] The molecular structures of the single molecules are shown in Figure 1. The theoretical analysis revealed that there are six charge-transfer mechanisms: 1) intramolecular charge transfer, 2) local excited transition, 3) both local excited transition and intramolecular charge transfer, 4) intermolecular charge transfer, 5) both intra- and intermolecular charge transfer and 6) super-exchange charge transfer. The linker (i.e., benzene, naphthaline, and anthracene) length and the number of molecules (up to three) involved in the 1D stack are important parameters in the ground and excited state properties of these systems.
2. Results and Discussion 2.1. Ground-State Properties of the Kekul Hydrocarbons Singlet biradical characters (y) of the B-LBP, N-LBP, and A-LBP molecules, and their respective 1D stacks were estimated by the natural orbital occupation number (NOON) of the LUMO[24] at the DFT/UCAM-B3LYP/6-31G** level,[32] as shown in Table 1. From Table 1, we can see that the y values increase as the length of the linkers (such as benzene, naphthaline and anthracene) increases and/or as the number of molecules (up to three) involved in the 1D stack increases. The larger the y value, the weaker the coupling of two unpaired electrons and the smaller the HOMO–LUMO energy gap in the biradical form.[29] The biradical character of these Kekul molecules im 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Single molecules
B-LBP
N-LBP
A-LBP
y [%] 1D stack of two molecules y [%] 1D stack of three molecules y [%]
58 2B-LBP 67 3B-LBP 71
73 2N-LBP 82 3N-LBP 86
81 2A-LBP 91 3A-LBP 99
plies strong intermolecular interactions in their ground state, a most remarkable feature for singlet biradical compounds.[24] The geometries of the 1D stack containing three B-LBP, N-LBP, and A-LBP molecules (referred to as 3B-LBP, 3N-LBP, and 3A-LBP, respectively) at ground state were fully optimized using DFT with a M06-2X functional and a 6-31G basis set. The results show that the B-LBP, N-LBP, and A-LBP molecules form 1D chains with a slipped stacking arrangement and that the p–p overlap is found only on phenalenyl radicals in the same arrangement (Figure 2). The average p–p distances are 3.158 (experimental: 3.137 ),[24] 3.104 (experimental: 3.170 ),[28] and 3.063 (experimental: 3.122 ),[29] for the 3B-LBP, 3N-LBP, and 3A-LBP 1D stacks, respectively. These p–p distances are substantially shorter than the van der Waals distance between carbon atoms. The overlapping pattern observed in these studies suggests an appreciable intermolecular covalent-bonding interaction, in accordance recent theoretical studies.[33, 34] The intermolecular covalent bonding interaction increases with increasing linker length, which shows that the larger the biradical character, the stronger the intermolecular interactions in their ground state[24] . 2.2. Excited-State Properties of the Kekul Hydrocarbons The energy levels of the LUMO and HOMO, and the corresponding HOMO–LUMO energy gaps for the B-LBP, N-LBP, and A-LBP molecules, and their respective 1D stacks were calculated at the TD-DFT/CAM-B3LYP/6-31G** level (Figure 3). The calculated energy level of the HOMOs for 1B-LBP, 2B-LBP, 3B-LBP, 1N-LBP, 2N-LBP, 3N-LBP, 1A-LBP, 2A-LBP, and 3A-LBP 1D stacks are 5.16, 4.94, 4.83, 4.73, 4.51, 4.41, 4.48, 4.16, and 3.63 eV, respectively. We observed that the HOMO energy level increases as the linker length and/or the number of molecules (up to three) involved in the 1D stack increases. Conversely, the calculated energy level of the LUMO decreases as the linker length and/or the number of molecules (up to three) involved in the 1D stack increases. The calculated energy gaps between the LUMOs and HOMOs are 2.68, 2.35, 2.20, 2.14, 1.82, 1.67, 1.78, 1.29, and 0.30 eV, respectively. Consequently, it is evident that an increase in linker length and/or the number of molecules involved in the 1D stack decreases the energy gap between LUMO and HOMO. This calculated result proves that the larger y value, the smaller the HOMO– LUMO energy gap.[29] To investigate the excited-state properties of these Kekul hydrocarbons, the absorption spectrum of the B-LBP, N-LBP, and A-LBP molecules, and their respective 1D stacks were calChemPhysChem 2014, 15, 2626 – 2633
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Figure 2. Average distance of the p–p interactions in the overlapping phenalenyl rings of the 3B-LBP, 3N-LBP, and 3A-LBP 1D stacks.
culated by using the TD-DFT, CAM-B3LYP functional and 6-31G** basis set, and are shown in Figure 4. The absorption spectrum of B-LBP, 2B-LBP, and 3B-LBP show two distinct absorption peaks at the higher energy band from 290 nm to 350 nm, and the lower energy band from 750 nm to 1050 nm, respectively (Figure 4 a). The absorption peak at the higher energy band is red-shifted from 293.09 nm for B-LBP to 340.98 nm for 3B-LBP, and at the lower energy band from 768.13 nm for B-LBP to 1027.97 nm for 3B-LBP. A weak red-shift for the higher energy band and a drastic red-shift for the lower energy band are observed. However, a significant red-shift is observed for the absorption wavelength of 3B-LBP compared to that of B-LBP and 2B-LBP. The absorption spectra of N-LBP, 2N-LBP, and 3N-LBP also show two distinct absorption peaks at the higher energy band from 300 nm to 400 nm and the lower energy band from 900 nm to 1400 nm (Figure 4 b). Again, the absorption spectra of A-LBP, 2A-LBP, and 3A-LBP show two distinct absorption peaks at the higher energy band from 300 nm to 1100 nm, and the lower energy band from 1000 nm to 4500 nm (Figure 4 c). Figure 4 b and c show that the key characteristics of the systems are similar to Figure 4 a, that is, a weak red-shift for the higher energy band and a drastic red-shift for lower energy band and a significant red-shift observed for the absorption wavelength of 3N-LBP and 3A-LBP, compared to that of N-LBP, or A-LBP and 2N-LBP, or 2A-LBP, respectively. Similar characteristics are also shown in Figure 4 d. It is evident from Figure 4 that the absorption spectra display a significant red-shift for the absorption wavelength, with an increase in linker length and/or the number of molecules (up to three) involved the 1D stack. The red-shift of these systems can significantly decrease the HOMO–LUMO energy gap in these systems,[35] which is consistent with the above HOMO–LUMO energy gap analysis. 2.3. Charge-Transfer Mechanism We have carried out investigations into the change in the static charge distribution upon photoexcitation, the charge dif 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ference densities (CDD), and electron–hole coherence of these electronic transitions for B-LBP, N-LBP, A-LBP and their respective 1D stacks, the results of which are shown in Figures 5–7. 2.3.1. Single Molecules The excited-state properties of the single B-LBP, N-LBP, and A-LBP molecules were examined. Through detailed analysis of the CDD for the molecules, we can clearly identify seven models of electrostatic distribution (Figure 5 a). And three charge-transfer mechanisms are in operation, including: 1) intramolecular charge transfer occurring between the main and side chains, 2) local excited transition occurring in the main chain, and 3) a mixture of both intramolecular charge transfer and local excited transition. The first model involves excited electrons and holes delocalized on the main chain of the molecule with charge transfer occurring in the linker, between the phenalenyl radical and linker, and between the two phenalenyl radicals. In addition, photoexcitation, which causes a change in the static-charge distribution is significantly influenced by the linker length: a different unit in the molecule will have a different contribution to the transition when the length of the linker is changed. The excited holes are delocalized on the main chain of B-LBP, and as the linker length increases, the excited holes on the linkers gradually decrease, excited electrons delocalized on the linker of A-LBP indicates that the static charge distribution of the linker is insensitive to photoexcitation. The contour plots of the transition density matrix shown in Figure 5 b show that electron–hole coherence occurs in the linker, between the phenalenyl radical and the linker, and between the two phenalenyl radicals. The second/third model involves excited electrons/ holes delocalized on the main chain, and holes/electrons, mainly delocalized on the two side chains of the molecule, with charge transfer occurring between the main chain and the side chain. The fourth/fifth model involves excited electrons/holes delocalized on the edge of the molecule, and holes/electrons delocalized on the center of the molecule, with ChemPhysChem 2014, 15, 2626 – 2633
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Figure 3. Calculated energy levels of the LUMO and HOMO of B-LBP, N-LBP, A-LBP, and their respective 1D stacks.
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Figure 4. Calculated absorption spectra of B-LBP, N-LBP, A-LBP, and their respective 1D stacks.
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Figure 5. a) The charge difference densities (CDD) of selected excited states for B-LBP, N-LBP, and A-LBP. The dark grey and black regions represent the electron holes and electrons, respectively. b) Contour plots of the transition density matrix of selected electronic excited states for B-LBP, N-LBP, and A-LBP. The color bar shows the absolute values of matrix elements, scaled to a maximum value of 1.0. The electron–hole coherence increases as the absolute values of matrix elements increases. ben = benzene.
charge transfer occurring on the main chain. The sixth model involves excited electrons delocalized on the linker, and holes delocalized on the phenalenyl radicals. Charge transfer occurs on the main chains. The seventh model involves excited electrons and holes delocalized on the sides chains. Charge transfer occurs between the main chain and side chain, and between the two side chains. We can see from the contour plots of the transition density matrix (Figure 5 b) that increasing the linker length significantly decreases the strength of the electron–hole coherence. These findings are in accordance with previous work using CDD, and 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
confirm that the charge-transfer ability of the molecule decreases with increasing linker length. 2.3.2. 1D Stack of Two Molecules The excited state properties of 1D stacks made up of two molecules of B-LBP, N-LBP, and A-LBP were examined. After analysis of the CDD for the molecules, we can clearly identify that there are also seven models of electrostatic distribution (Figure 6 a). Three charge-transfer mechanisms are in operation, including: 1) intramolecular charge transfer, 2) intermolecular ChemPhysChem 2014, 15, 2626 – 2633
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www.chemphyschem.org charge transfer, and 3) a mixture of both intra- and intermolecular charge transfer. The first model involves excited electrons, and holes delocalized on the main chain of the two molecules, with charge transfer occurring between the two molecules. The second/ third model involves excited electrons and holes delocalized on the main chain of the two molecules, with charge transfer occurring both intra- and intermolecularly. The electron–hole coherence between two molecules in the 1D stack is stronger than that of intramolecular charge transfer (Figure 6 b). In addition, intermolecular interactions in the 1D stack are influenced not only by the electron–hole coherence, but also by the electron cloud or hole chain, which overlap between the two molecules in the 1D stack linking the phenalenyl radicals together. The fourth model involves excited electrons and holes delocalized on the main chain of the two molecules, together with the electron cloud and hole-chain overlap between the two molecules in the 1D stack linking the phenalenyl radicals. Charge transfer occurs both intra- and intermolecularly. The fifth/sixth model involves excited electrons/holes delocalized on the main chain of the two molecules, and excited holes/ electrons, which are mainly delocalized on the side chain of the two molecules. Charge transfer occurs in an intramolecular manner between the main chain and side chain, and in an intermolecular manner between the main chains of 1# (the first molecule of the 1D stack)/2# (the second molecule of the 1D stack) and the side chains of 2#/1#. The seventh model involves excited electrons/holes delocalized on the two molecules. In addition, the excited electrons also occur on the side chain of 1#. In the other words, inter- and intramolecular charge transfer occurs between two molecules and in 1#, respectively. From Figure 6 b, we can see that increasing the linker length significantly decreases the strength of the electron–hole coherence and the charge-transfer ability of a 1D stack made up of two molecules. The electron–hole coherence between two molecules in the 1D stack is stronger than that of intramolecular electron–hole coherence. 2.3.3. 1D Stack of Three Molecules
Figure 6. a) The charge difference densities (CDD) of selected excited states for 2B-LBP, 2N-LBP, and 2A-LBP. b) The contour plots of the transition density matrix of selected excited states for 2B-LBP, 2N-LBP and 2A-LBP. 1# and 2# represent the first molecule and the second molecule of the 1D chain stacks, respectively.
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The excited-state properties of 1D stacks made up of three molecules of B-LBP, N-LBP, and A-LBP were examined. Five models of electrostatic distribution can be summarized by analyzing the CDD of the molecules, as shown in Figure 7 a. In addition, four charge-transfer mechanisms are in operation, including: 1) intramolecular charge transfer, 2) intermolecular charge transfer between 1# and 2#, or 2# and 3#, 3) a superexchange mechanism occurring between 1# and 3#, and 4) a mixture of both intra- and intermolecular charge transfer. The first/second model involves excited electrons and holes delocalized on the main chain of the three molecules, as well as the phenalenyl radical overlap of the three molecules in the 1D stack linked by the electron cloud/hole chain. Charge transfer occurs both in an intramolecular manner and in an intermolecular manner between 1# and 2#. Furthermore, charge super-exchange can also be observed between 1# and 3#. The ChemPhysChem 2014, 15, 2626 – 2633
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www.chemphyschem.org third model involves excited electrons, and holes delocalized on 1# and 3#. Charge transfer occurs in both an intra- and intermolecular manner. The fourth model involves excited electrons/holes delocalized on the three molecules. Charge transfer occurs both intra- and intermolecularly. The fifth model involves excited electrons delocalized on the main chains of the three molecules and the excited holes delocalized on the side chains of three molecules. Separate intramolecular charge transfer occurs in 1# or 3# and intermolecular charge super-exchange between 1# and 3#. As can be clearly seen from Figure 7 b, increasing the linker length significantly decreases the strength of the electron– hole coherence and the chargetransfer ability. The charge super-exchange mechanism occurs in the 1D stacks, which are made up of three molecules. The intermolecular interaction of the 1D stack is stronger than the intramolecular interaction, which is in accordance with the experimental results.[29] Overall, increasing the length of the linker and/or the number of molecules (up to three) making up the 1D stack decreases the charge-transfer ability, which shows that the larger the biradical character, the weaker the coupling of two unpaired electrons.[29] Instead of intramolecular interaction, the intermolecular interaction of the 1D stack becomes more and more dominant. In addition, intermolecular charge super-exchange apparently occurs in the 1D stack made up of three molecules.
3. Conclusions Figure 7. a) The charge difference densities (CDD) of the selected excited states for 3B-LBP, 3N-LBP and 3 A-LBP. Note: the resolution of the first CDD for 3A-LBP is one hundred times that of the other systems. b) The contour plots of the transition density matrix of the selected excited states for 3B-LBP, 3N-LBP and 3A-LBP. 1#, 2#, and 3# represent the first, second, and third molecules of the 1D stack, respectively.
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We have reported our theoretical investigations on the ground- and excited-state properties of B-LBP, N-LBP, A-LBP mol-
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CHEMPHYSCHEM ARTICLES ecules, and their respective 1D stacks using density functional theory calculations and visualized real-space analytical methods. We conclude that the singlet biradical character, intermolecular covalent bonding interaction, and charge-transfer mechanism differ with changes in linker length and/or the number of molecules (up to three) involved in the 1D stack. These Kekul hydrocarbons with significant singlet biradical character may potentially be NIR molecular functional materials. Consequently, our results can be used for the rational design and synthesis of organic non-linear optical materials with differing properties, by adjusting the linker length and the number of molecules (up to three) present in the 1D stack of these systems.
Computational Methods All of the quantum chemical calculations were carried out using the Gaussian 09 software.[35] The geometries of B-LBP, N-LBP, and A-LBP molecules, and their respective 1D stacks at ground state were fully optimized using DFT with the UCAM-B3LYP/CAM-B3LYP functional and the 6-31G**/6-31G basis set.[32, 36] TD-DFT with the CAM-B3LYP/6-31G** basis set were used in the excited-state properties calculations.[37] In this paper, the charge-transfer mechanisms were investigated with the three-dimensional cube representation of charge difference density, which indicates the result of intraand intermolecular charge-transfer during electronic transition. In addition, the electron–hole coherences are analyzed using two-dimensional contour plots of the transition density matrix.[38, 39]
Acknowledgements This work was financially supported by the Program of Shenyang Key Laboratory of Optoelectronic Materials and Technology (F12254-1-00), the National Natural Science Foundation of China (11374353, 11304135, and 11274149), the Natural Science Foundation of Liaoning Province of China (2013020100), the Program for Liaoning Excellent Talents in University, China (LR2012001), and the Shenyang Natural Science Foundation of China (F12-265-4-00). Keywords: Charge transfer · covalent bonding interactions · electron-hole coherence · organic optical materials · singlet biradical character [1] B. J. Coe, J. A. Harris, K. Clays, A. Persoons, K. Wostyn, B. S. Brunschwig, Chem. Commun. 2001, 10, 1548 – 1549. [2] B. J. Coe, J. A. Harris, L. A. Jones, B. S. Brunschwig, K. Song, K. Clays, J. Garn, J. Orduna, S. J. Coles, M. B. Hursthouse, J. Am. Chem. Soc. 2005, 127, 4845 – 4859. [3] B. J. Coe, J. A. Harris, B. S. Brunschwig, I. Asselberghs, K. Clays, J. Garn, J. Orduna, J. Am. Chem. Soc. 2005, 127, 13399 – 13410. [4] S. Di Bella, L. Fragal, Synth. Met. 2000, 115, 191 – 196. [5] P. G. Lacroix, Eur. J. Inorg. Chem. 2001, 339 – 348. [6] S. L. Gilat, S. H. Kawai, J. M. Lehn, Chem. Eur. J. 1995, 1, 275 – 284. [7] L. T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, S. R. Marder, J. Phys. Chem. 1991, 95, 10631 – 10643.
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Received: February 11, 2014 Revised: April 7, 2014 Published online on May 30, 2014
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Organic Nonlinear Optical Materials: The Mechanism of Intermolecular Covalent Bonding Interactions of Kekul Hydrocarbons with Significant Singlet Biradical Character Jing Liu,[a] Jiarui Xia,[b] Peng Song,*[a] Yong Ding,[a] Yanling Cui,[a] Xuemei Liu,[a] Yumei Dai,[c] and Fengcai Ma*[a] The ground- and excited-state properties of benzene-linked bisphenalenyl (B-LBP), naphthaline-linked bisphenalenyl (N-LBP), and anthracene-linked bisphenalenyl (A-LBP) Kekul molecules and their respective one-dimensional (1D) stacks are investigated using time-dependent density functional theory (TD-DFT) and a range of extensive multidimensional visualization techniques. The results reveal a covalent p–p bonding interaction between overlapping phenalenyl radicals whose bond length
is shorter than the van der Waals distance between carbon atoms. Increasing the linker length and/or number of molecules involved in the 1D stack decreases the HOMO–LUMO energy gap and increases the wavelength of the systems. The charge-transfer mechanism and electron coherence both differ with changes in the linker length and/or number of molecules involved in the 1D stack.
1. Introduction The arrival of the information age has lead to the rapid development of communication technology, IT technology, and optoelectronics, thus leading to an increased demand for nonlinear optical materials.[1–5] Organic non-linear optical materials that possess properties such as high non-linear polarizability, high optical damage thresholds, short response time, and a molecular design that is responsive to non-linear optical stimuli, have great potential for use in high-speed integrated optical devices. Consequently, research on organic non-linear optical materials and their properties has attracted a lot of interest in recent years.[6–11] Photoinduced electron transfer (PET) is a fundamental process that has been shown to play a key role in determining the efficiency of photoelectric materials.[12–14] PET has been widely used in organic photovoltaic cells, fluorescence sensors, and components for high-sensitivity optical analytical techniques.[15–17] Recently, research has focused on the mechanism of PET in organic photoconversion systems with highly efficient charge-transfer and slow charge recombination.[18–20] Charge transfer and charge recombination are the two kinetic process-
[a] J. Liu,+ Prof. P. Song, Prof. Y. Ding, Y. Cui, X. Liu, Prof. F. Ma Department of Physics, Liaoning University Shenyang 110036 (China) E-mail: [email protected] [email protected] [b] J. Xia+ School of Chemistry and Chemical Engineering Shandong University, Jinan 250100 (China) [c] Prof. Y. Dai Normal College, Shenyang University Shenyang 110044 (China) [+] These authors contributed equally.
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es to be considered, and are represented by the electron transfer rate constant (kET) shown in Equation (1).[20] kET ¼ k0 expðbRDA Þ,
ð1Þ
where k0 is a kinetic pre-exponential factor, RDA is the donor– acceptor distance, and b is the attenuation factor.[21] Recently, quinoidal Kekul hydrocarbons have attracted the attention of scientists because of their unusual reactivity and electronic structure.[22] These compounds possess a relatively small energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). This leads to a admixture of the doubly excited configuration 1FH,H!L,L into the ground configuration 1F0 in their ground state description.[23] A consequence of the mixing of electronic configurations is that the electron repulsion is taken into consideration; thereby two electrons with antiparallel spins are permitted to correlate in separate spaces, thus diminishing the covalent bond character and increasing the biradical character of the system.[24] Subsequently, the phenalenyl radical and its derivatives have attracted a lot of attention owing to their interesting properties (e.g. conjugacy, planarity, and high spin delocalizing properties, among others).[11, 25] Kubo and Shimizu et al. have reported the synthesis, isolation, intermolecular interactions, and solid-state properties of a singlet biradical compound utilizing the high spin delocalizing properties of the phenalenyl radical.[11, 26–29] In addition, the properties of the bisphenalenyl molecule were researched through theoretical methods by Huang et al.[30] We now report our investigations into the ground and excited state properties (including singlet biradical character (y), intermolecular covalent bonding p–p distance, HOMO–LUMO ChemPhysChem 2014, 15, 2626 – 2633
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www.chemphyschem.org Table 1. Calculated singlet biradical character (y [%]) of B-LBP, N-LBP, ALBP, and their respective 1D stacks.
Figure 1. Molecular structures of B-LBP, N-LBP, and A-LBP (R = H).
energy gap, absorption spectrum, charge-transfer mechanism and electron–hole coherence) of the benzene-linked bisphenalenyl (B-LBP), naphthaline-linked bisphenalenyl (N-LBP), and anthracene-linked bisphenalenyl (A-LBP) Kekul molecules, and their respective one-dimensional (1D) stacks using density functional theory (DFT) and a range of extensive multidimensional visualization techniques.[31] The molecular structures of the single molecules are shown in Figure 1. The theoretical analysis revealed that there are six charge-transfer mechanisms: 1) intramolecular charge transfer, 2) local excited transition, 3) both local excited transition and intramolecular charge transfer, 4) intermolecular charge transfer, 5) both intra- and intermolecular charge transfer and 6) super-exchange charge transfer. The linker (i.e., benzene, naphthaline, and anthracene) length and the number of molecules (up to three) involved in the 1D stack are important parameters in the ground and excited state properties of these systems.
2. Results and Discussion 2.1. Ground-State Properties of the Kekul Hydrocarbons Singlet biradical characters (y) of the B-LBP, N-LBP, and A-LBP molecules, and their respective 1D stacks were estimated by the natural orbital occupation number (NOON) of the LUMO[24] at the DFT/UCAM-B3LYP/6-31G** level,[32] as shown in Table 1. From Table 1, we can see that the y values increase as the length of the linkers (such as benzene, naphthaline and anthracene) increases and/or as the number of molecules (up to three) involved in the 1D stack increases. The larger the y value, the weaker the coupling of two unpaired electrons and the smaller the HOMO–LUMO energy gap in the biradical form.[29] The biradical character of these Kekul molecules im 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Single molecules
B-LBP
N-LBP
A-LBP
y [%] 1D stack of two molecules y [%] 1D stack of three molecules y [%]
58 2B-LBP 67 3B-LBP 71
73 2N-LBP 82 3N-LBP 86
81 2A-LBP 91 3A-LBP 99
plies strong intermolecular interactions in their ground state, a most remarkable feature for singlet biradical compounds.[24] The geometries of the 1D stack containing three B-LBP, N-LBP, and A-LBP molecules (referred to as 3B-LBP, 3N-LBP, and 3A-LBP, respectively) at ground state were fully optimized using DFT with a M06-2X functional and a 6-31G basis set. The results show that the B-LBP, N-LBP, and A-LBP molecules form 1D chains with a slipped stacking arrangement and that the p–p overlap is found only on phenalenyl radicals in the same arrangement (Figure 2). The average p–p distances are 3.158 (experimental: 3.137 ),[24] 3.104 (experimental: 3.170 ),[28] and 3.063 (experimental: 3.122 ),[29] for the 3B-LBP, 3N-LBP, and 3A-LBP 1D stacks, respectively. These p–p distances are substantially shorter than the van der Waals distance between carbon atoms. The overlapping pattern observed in these studies suggests an appreciable intermolecular covalent-bonding interaction, in accordance recent theoretical studies.[33, 34] The intermolecular covalent bonding interaction increases with increasing linker length, which shows that the larger the biradical character, the stronger the intermolecular interactions in their ground state[24] . 2.2. Excited-State Properties of the Kekul Hydrocarbons The energy levels of the LUMO and HOMO, and the corresponding HOMO–LUMO energy gaps for the B-LBP, N-LBP, and A-LBP molecules, and their respective 1D stacks were calculated at the TD-DFT/CAM-B3LYP/6-31G** level (Figure 3). The calculated energy level of the HOMOs for 1B-LBP, 2B-LBP, 3B-LBP, 1N-LBP, 2N-LBP, 3N-LBP, 1A-LBP, 2A-LBP, and 3A-LBP 1D stacks are 5.16, 4.94, 4.83, 4.73, 4.51, 4.41, 4.48, 4.16, and 3.63 eV, respectively. We observed that the HOMO energy level increases as the linker length and/or the number of molecules (up to three) involved in the 1D stack increases. Conversely, the calculated energy level of the LUMO decreases as the linker length and/or the number of molecules (up to three) involved in the 1D stack increases. The calculated energy gaps between the LUMOs and HOMOs are 2.68, 2.35, 2.20, 2.14, 1.82, 1.67, 1.78, 1.29, and 0.30 eV, respectively. Consequently, it is evident that an increase in linker length and/or the number of molecules involved in the 1D stack decreases the energy gap between LUMO and HOMO. This calculated result proves that the larger y value, the smaller the HOMO– LUMO energy gap.[29] To investigate the excited-state properties of these Kekul hydrocarbons, the absorption spectrum of the B-LBP, N-LBP, and A-LBP molecules, and their respective 1D stacks were calChemPhysChem 2014, 15, 2626 – 2633
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Figure 2. Average distance of the p–p interactions in the overlapping phenalenyl rings of the 3B-LBP, 3N-LBP, and 3A-LBP 1D stacks.
culated by using the TD-DFT, CAM-B3LYP functional and 6-31G** basis set, and are shown in Figure 4. The absorption spectrum of B-LBP, 2B-LBP, and 3B-LBP show two distinct absorption peaks at the higher energy band from 290 nm to 350 nm, and the lower energy band from 750 nm to 1050 nm, respectively (Figure 4 a). The absorption peak at the higher energy band is red-shifted from 293.09 nm for B-LBP to 340.98 nm for 3B-LBP, and at the lower energy band from 768.13 nm for B-LBP to 1027.97 nm for 3B-LBP. A weak red-shift for the higher energy band and a drastic red-shift for the lower energy band are observed. However, a significant red-shift is observed for the absorption wavelength of 3B-LBP compared to that of B-LBP and 2B-LBP. The absorption spectra of N-LBP, 2N-LBP, and 3N-LBP also show two distinct absorption peaks at the higher energy band from 300 nm to 400 nm and the lower energy band from 900 nm to 1400 nm (Figure 4 b). Again, the absorption spectra of A-LBP, 2A-LBP, and 3A-LBP show two distinct absorption peaks at the higher energy band from 300 nm to 1100 nm, and the lower energy band from 1000 nm to 4500 nm (Figure 4 c). Figure 4 b and c show that the key characteristics of the systems are similar to Figure 4 a, that is, a weak red-shift for the higher energy band and a drastic red-shift for lower energy band and a significant red-shift observed for the absorption wavelength of 3N-LBP and 3A-LBP, compared to that of N-LBP, or A-LBP and 2N-LBP, or 2A-LBP, respectively. Similar characteristics are also shown in Figure 4 d. It is evident from Figure 4 that the absorption spectra display a significant red-shift for the absorption wavelength, with an increase in linker length and/or the number of molecules (up to three) involved the 1D stack. The red-shift of these systems can significantly decrease the HOMO–LUMO energy gap in these systems,[35] which is consistent with the above HOMO–LUMO energy gap analysis. 2.3. Charge-Transfer Mechanism We have carried out investigations into the change in the static charge distribution upon photoexcitation, the charge dif 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ference densities (CDD), and electron–hole coherence of these electronic transitions for B-LBP, N-LBP, A-LBP and their respective 1D stacks, the results of which are shown in Figures 5–7. 2.3.1. Single Molecules The excited-state properties of the single B-LBP, N-LBP, and A-LBP molecules were examined. Through detailed analysis of the CDD for the molecules, we can clearly identify seven models of electrostatic distribution (Figure 5 a). And three charge-transfer mechanisms are in operation, including: 1) intramolecular charge transfer occurring between the main and side chains, 2) local excited transition occurring in the main chain, and 3) a mixture of both intramolecular charge transfer and local excited transition. The first model involves excited electrons and holes delocalized on the main chain of the molecule with charge transfer occurring in the linker, between the phenalenyl radical and linker, and between the two phenalenyl radicals. In addition, photoexcitation, which causes a change in the static-charge distribution is significantly influenced by the linker length: a different unit in the molecule will have a different contribution to the transition when the length of the linker is changed. The excited holes are delocalized on the main chain of B-LBP, and as the linker length increases, the excited holes on the linkers gradually decrease, excited electrons delocalized on the linker of A-LBP indicates that the static charge distribution of the linker is insensitive to photoexcitation. The contour plots of the transition density matrix shown in Figure 5 b show that electron–hole coherence occurs in the linker, between the phenalenyl radical and the linker, and between the two phenalenyl radicals. The second/third model involves excited electrons/ holes delocalized on the main chain, and holes/electrons, mainly delocalized on the two side chains of the molecule, with charge transfer occurring between the main chain and the side chain. The fourth/fifth model involves excited electrons/holes delocalized on the edge of the molecule, and holes/electrons delocalized on the center of the molecule, with ChemPhysChem 2014, 15, 2626 – 2633
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Figure 3. Calculated energy levels of the LUMO and HOMO of B-LBP, N-LBP, A-LBP, and their respective 1D stacks.
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Figure 4. Calculated absorption spectra of B-LBP, N-LBP, A-LBP, and their respective 1D stacks.
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Figure 5. a) The charge difference densities (CDD) of selected excited states for B-LBP, N-LBP, and A-LBP. The dark grey and black regions represent the electron holes and electrons, respectively. b) Contour plots of the transition density matrix of selected electronic excited states for B-LBP, N-LBP, and A-LBP. The color bar shows the absolute values of matrix elements, scaled to a maximum value of 1.0. The electron–hole coherence increases as the absolute values of matrix elements increases. ben = benzene.
charge transfer occurring on the main chain. The sixth model involves excited electrons delocalized on the linker, and holes delocalized on the phenalenyl radicals. Charge transfer occurs on the main chains. The seventh model involves excited electrons and holes delocalized on the sides chains. Charge transfer occurs between the main chain and side chain, and between the two side chains. We can see from the contour plots of the transition density matrix (Figure 5 b) that increasing the linker length significantly decreases the strength of the electron–hole coherence. These findings are in accordance with previous work using CDD, and 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
confirm that the charge-transfer ability of the molecule decreases with increasing linker length. 2.3.2. 1D Stack of Two Molecules The excited state properties of 1D stacks made up of two molecules of B-LBP, N-LBP, and A-LBP were examined. After analysis of the CDD for the molecules, we can clearly identify that there are also seven models of electrostatic distribution (Figure 6 a). Three charge-transfer mechanisms are in operation, including: 1) intramolecular charge transfer, 2) intermolecular ChemPhysChem 2014, 15, 2626 – 2633
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www.chemphyschem.org charge transfer, and 3) a mixture of both intra- and intermolecular charge transfer. The first model involves excited electrons, and holes delocalized on the main chain of the two molecules, with charge transfer occurring between the two molecules. The second/ third model involves excited electrons and holes delocalized on the main chain of the two molecules, with charge transfer occurring both intra- and intermolecularly. The electron–hole coherence between two molecules in the 1D stack is stronger than that of intramolecular charge transfer (Figure 6 b). In addition, intermolecular interactions in the 1D stack are influenced not only by the electron–hole coherence, but also by the electron cloud or hole chain, which overlap between the two molecules in the 1D stack linking the phenalenyl radicals together. The fourth model involves excited electrons and holes delocalized on the main chain of the two molecules, together with the electron cloud and hole-chain overlap between the two molecules in the 1D stack linking the phenalenyl radicals. Charge transfer occurs both intra- and intermolecularly. The fifth/sixth model involves excited electrons/holes delocalized on the main chain of the two molecules, and excited holes/ electrons, which are mainly delocalized on the side chain of the two molecules. Charge transfer occurs in an intramolecular manner between the main chain and side chain, and in an intermolecular manner between the main chains of 1# (the first molecule of the 1D stack)/2# (the second molecule of the 1D stack) and the side chains of 2#/1#. The seventh model involves excited electrons/holes delocalized on the two molecules. In addition, the excited electrons also occur on the side chain of 1#. In the other words, inter- and intramolecular charge transfer occurs between two molecules and in 1#, respectively. From Figure 6 b, we can see that increasing the linker length significantly decreases the strength of the electron–hole coherence and the charge-transfer ability of a 1D stack made up of two molecules. The electron–hole coherence between two molecules in the 1D stack is stronger than that of intramolecular electron–hole coherence. 2.3.3. 1D Stack of Three Molecules
Figure 6. a) The charge difference densities (CDD) of selected excited states for 2B-LBP, 2N-LBP, and 2A-LBP. b) The contour plots of the transition density matrix of selected excited states for 2B-LBP, 2N-LBP and 2A-LBP. 1# and 2# represent the first molecule and the second molecule of the 1D chain stacks, respectively.
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The excited-state properties of 1D stacks made up of three molecules of B-LBP, N-LBP, and A-LBP were examined. Five models of electrostatic distribution can be summarized by analyzing the CDD of the molecules, as shown in Figure 7 a. In addition, four charge-transfer mechanisms are in operation, including: 1) intramolecular charge transfer, 2) intermolecular charge transfer between 1# and 2#, or 2# and 3#, 3) a superexchange mechanism occurring between 1# and 3#, and 4) a mixture of both intra- and intermolecular charge transfer. The first/second model involves excited electrons and holes delocalized on the main chain of the three molecules, as well as the phenalenyl radical overlap of the three molecules in the 1D stack linked by the electron cloud/hole chain. Charge transfer occurs both in an intramolecular manner and in an intermolecular manner between 1# and 2#. Furthermore, charge super-exchange can also be observed between 1# and 3#. The ChemPhysChem 2014, 15, 2626 – 2633
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www.chemphyschem.org third model involves excited electrons, and holes delocalized on 1# and 3#. Charge transfer occurs in both an intra- and intermolecular manner. The fourth model involves excited electrons/holes delocalized on the three molecules. Charge transfer occurs both intra- and intermolecularly. The fifth model involves excited electrons delocalized on the main chains of the three molecules and the excited holes delocalized on the side chains of three molecules. Separate intramolecular charge transfer occurs in 1# or 3# and intermolecular charge super-exchange between 1# and 3#. As can be clearly seen from Figure 7 b, increasing the linker length significantly decreases the strength of the electron– hole coherence and the chargetransfer ability. The charge super-exchange mechanism occurs in the 1D stacks, which are made up of three molecules. The intermolecular interaction of the 1D stack is stronger than the intramolecular interaction, which is in accordance with the experimental results.[29] Overall, increasing the length of the linker and/or the number of molecules (up to three) making up the 1D stack decreases the charge-transfer ability, which shows that the larger the biradical character, the weaker the coupling of two unpaired electrons.[29] Instead of intramolecular interaction, the intermolecular interaction of the 1D stack becomes more and more dominant. In addition, intermolecular charge super-exchange apparently occurs in the 1D stack made up of three molecules.
3. Conclusions Figure 7. a) The charge difference densities (CDD) of the selected excited states for 3B-LBP, 3N-LBP and 3 A-LBP. Note: the resolution of the first CDD for 3A-LBP is one hundred times that of the other systems. b) The contour plots of the transition density matrix of the selected excited states for 3B-LBP, 3N-LBP and 3A-LBP. 1#, 2#, and 3# represent the first, second, and third molecules of the 1D stack, respectively.
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We have reported our theoretical investigations on the ground- and excited-state properties of B-LBP, N-LBP, A-LBP mol-
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CHEMPHYSCHEM ARTICLES ecules, and their respective 1D stacks using density functional theory calculations and visualized real-space analytical methods. We conclude that the singlet biradical character, intermolecular covalent bonding interaction, and charge-transfer mechanism differ with changes in linker length and/or the number of molecules (up to three) involved in the 1D stack. These Kekul hydrocarbons with significant singlet biradical character may potentially be NIR molecular functional materials. Consequently, our results can be used for the rational design and synthesis of organic non-linear optical materials with differing properties, by adjusting the linker length and the number of molecules (up to three) present in the 1D stack of these systems.
Computational Methods All of the quantum chemical calculations were carried out using the Gaussian 09 software.[35] The geometries of B-LBP, N-LBP, and A-LBP molecules, and their respective 1D stacks at ground state were fully optimized using DFT with the UCAM-B3LYP/CAM-B3LYP functional and the 6-31G**/6-31G basis set.[32, 36] TD-DFT with the CAM-B3LYP/6-31G** basis set were used in the excited-state properties calculations.[37] In this paper, the charge-transfer mechanisms were investigated with the three-dimensional cube representation of charge difference density, which indicates the result of intraand intermolecular charge-transfer during electronic transition. In addition, the electron–hole coherences are analyzed using two-dimensional contour plots of the transition density matrix.[38, 39]
Acknowledgements This work was financially supported by the Program of Shenyang Key Laboratory of Optoelectronic Materials and Technology (F12254-1-00), the National Natural Science Foundation of China (11374353, 11304135, and 11274149), the Natural Science Foundation of Liaoning Province of China (2013020100), the Program for Liaoning Excellent Talents in University, China (LR2012001), and the Shenyang Natural Science Foundation of China (F12-265-4-00). Keywords: Charge transfer · covalent bonding interactions · electron-hole coherence · organic optical materials · singlet biradical character [1] B. J. Coe, J. A. Harris, K. Clays, A. Persoons, K. Wostyn, B. S. Brunschwig, Chem. Commun. 2001, 10, 1548 – 1549. [2] B. J. Coe, J. A. Harris, L. A. Jones, B. S. Brunschwig, K. Song, K. Clays, J. Garn, J. Orduna, S. J. Coles, M. B. Hursthouse, J. Am. Chem. Soc. 2005, 127, 4845 – 4859. [3] B. J. Coe, J. A. Harris, B. S. Brunschwig, I. Asselberghs, K. Clays, J. Garn, J. Orduna, J. Am. Chem. Soc. 2005, 127, 13399 – 13410. [4] S. Di Bella, L. Fragal, Synth. Met. 2000, 115, 191 – 196. [5] P. G. Lacroix, Eur. J. Inorg. Chem. 2001, 339 – 348. [6] S. L. Gilat, S. H. Kawai, J. M. Lehn, Chem. Eur. J. 1995, 1, 275 – 284. [7] L. T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, S. R. Marder, J. Phys. Chem. 1991, 95, 10631 – 10643.
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Received: February 11, 2014 Revised: April 7, 2014 Published online on May 30, 2014
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