The Dependence of UV â Visible Absorption Characteristics on the

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The Dependence of UV – Visible Absorption Characteristics on the Migration Distance and the Hyperconjugation Effect of Methine Chain Xijiao Mu, Kesu Cai, Wenjing Wei, Yuee Li, Zhong Wang, and Jingang Wang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12596 • Publication Date (Web): 20 Mar 2018 Downloaded from http://pubs.acs.org on March 22, 2018

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The Journal of Physical Chemistry

The Dependence of UV – Visible Absorption Characteristics on the Migration Distance and the Hyperconjugation Effect of Methine Chain Xijiao Mua，Kesu Caia，Wenjing Weia, Yuee Li*a, Zhong Wanga*, Jingang Wangb a

School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China

b

College of Science, Liaoning Shihua University, Fushun,113001, China

* Correspondence to:

Yuee Li and Zhong Wang, Feiyun Building 318, Tianshui South Road 222, Lanzhou

730000, China. E-mail: [email protected], [email protected]

Abstract The coumarin-based dyes containing methine chain have - ∗ conjugation and p- ∗ hyperconjugation effect in electron excitation due to their special conjugated structure. Some of the dye molecules containing methylene group also have the characteristics of long chain length and large charge transfer distance. The excitation energy of the electron conjugated system is related to the degree of electron conjugation, but the quantitative relationship is not clear. In some applications where the molecular absorption spectrum needs to be controlled, it is necessary to know the definite relationship between these parameters. In this work, we analyze the excitation characteristics of coumarin-based dye molecules using the natural transition orbital theory. Then, we apply the method of quantum chemistry and wave function analysis to analyze the dependence of the excitation energy on the electron conjugation/Hyperconjugation intensity, the charge transfer length and the charge transfer direction. In our analyses, the natural bond orbital 2rd-order perturbation energy represents the electron conjugation/Hyperconjugation intensity; the migration distance represents the degree of the charge transfer length; the molecular surface electrostatic potential is calculated to analyze the charge transfer direction. Finally, the exponential decay curve of the excitation energy and the second order perturbation energy dependent on the migration distance are fitted.

Introduction Organic dyes are a class of versatile molecules that are mainly used in dye-sensitized solar cells and organic light-emitting displays (OLED)1-2. They also have widespread application in the field of biochemistry working as fluorescent probes or Raman probes3-4. The position of UV-visible absorption peaks of dye molecules play a key role in these applications. Researchers achieved various dyes with specific absorption spectrum by modifying the molecular. Especially for fluorescent probes and resonant Raman probes, the peak position of the UV-visible spectrum is decisive for choosing the appropriate operating wavelength. Therefore, it is very important to study the relationship between the absorption peak and the molecular structure of the organic dye molecules. In general, with the increase of the molecular system’s conjugation effect, the energy of - ∗ transition decreases and the absorption peak red-shifts. However, there is a hyperconjugation effect between p- ∗ in the Single and double-alternating methine chain, which is much more complex than - ∗ conjugation in conjugated olefins and aromatic systems. Moreover, due to the presence of the conjugate system, the electrons of dye molecules will be delocalized to a larger space. Therefore, there will be a large degree of migration in the process of electronic transition, and this is known as the charge transfer transition (CT). Quantum chemical calculation is a powerful tool for studying the electronic structure and transition behavior of molecules, and the wave function generated in the calculation process contains a lot of information. In recent years,

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many wave function analysis methods have been developed to extract a lot of evidence from the wave function information to analyze the physical essence of macroscopic phenomena. Here, we use the wave function analysis method called natural bond orbital (NBO) theory to quantitatively analyze the π-π∗ conjugate effect. The charge transfer and the UV absorption spectrum are analyzed quantitatively by calculating the distance between the electrons and the hole δR before and after the charge excitation (Figure 1.). In this paper, we select six derivatives of coumarin as our research objects (Figure 2.). Coumarin, as a natural product dye, has been used in a variety of applications5. The main peaks of the absorption spectra of these six derivatives gradually move to the long wavelength with the increase of the methine chain length (Figure 3(a).). The differences in the molecular structure of the six derivatives mainly originate from the length of the methine chain, and the second difference comes from the introduction of the chromophore-cyano group. It is the best research object for studying the conjugation effect and charge transfer migration distance in the base chain. Here, the density functional theory (DFT)6 is used to calculate the electronic structure and the excited state of the molecule. Electrons of coumarin derivatives show high delocalization, therefore, we use the long-range transfer optimized range-separation functional to accurately express the charge transfer and delocalization characteristics of the molecular system. A variety of wave function analysis methods, such as electron hole analysis, NBO analysis and molecular surface electrostatic potential quantitative analysis are handled to study the physical nature contained in spectrum red-shift phenomenon.

Figure 1 Schematic diagram of charge transfer process in electron excited state


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Figure 2 Molecule structures of coumarin derivatives

Figure 3 (a) Normalized absorption spectra of all coumarin derivates and (b) Comparison of calculated molar absorption coefficients of NKX2388, NKX2311 and NKX2384 Computational detail In this paper, all results of quantum chemistry were calculated by ORCA 4.0.12 program7. The NBO analyses were carried out by GENNBO6. The electron-hole analysis, migration distance and



natural transition orbital (NTO) wavefunction cubes were done using Multiwfn.3.4.18 program. Molecule structure were optimized by wB97X functional9 and def2TZVP10 basis set. The RI auxiliary basis set is Def2/J11, and the excited energy and wavefunction information were calculated by the ORCA and the “tprint” command needs to be used for controlling the output threshold of the configuration coefficients. Five excited states are considered for all of our TD-DFT calculations with the Solvation Model based on Density (SMD) of water. The NTOs and the electrostatic potential (ESP) are visually demonstrated by using VMD12 software. Transition characteristics analysis Transition of electronic state is often not predominated by only one pair of Molecular orbitals (MOs) transition, in most cases many different MOs transitions simultaneously have non-negligible contributions, which can be evaluated by squaring the corresponding configuration coefficient. This fact brings a great hindrance for analyzing transition character by means of visualizing related MOs. The NTO method 13 aims to relieve this difficulty, it separately performs unitary transformation for occupied MOs and virtual MOs, so that only one or very few number of orbital pairs have dominant contributions, which makes orbital inspection much easier. The eigenvalue of the NTO wave function, which is no longer the orbital energy, gives the configuration component of the excited state. Therefore, the eigenvalue of the orbital wave function must be smaller than 1. Figure 4 and Figure 5 show the NTO isosurface and transition density matrices of NKX-2311 and NKX-2384 molecules, respectively. For NKX2311 molecules, the highest energy occupied orbit is No. 111 orbit, whose NTO orbital eigenvalue is 0.951154, indicating that the properties of the entire excited state can be described by No. 111 orbit. The vacant orbit with lowest energy is No. 112 orbit. Figure 4 also shows that the natural transition orbit of NKX-2311 is conjugately arranged on a single and double alternating methine chain, which is a typical π-π transition. It also presents a p-π hyperconjugation effect because the methine is mono alternating, there is. For NKX2384 molecule, the highest energy occupied orbit and the lowest energy vacant orbit is the 87th, 88th orbit respectively (Figure 5). The eigenvalue of the 87th orbital wave function is 0.96745, so the whole excitation feature can also be represented by this NTO orbit. Notably, the π-π transition is dominant for the NTO of NKX2384.

Figure 4 NTO isosurface and transition density matrix of NKX 2311


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Figure 5 NTO isosurface and transition density matrix of NKX 2384 In Figure 4 and Figure 5, the color-fill surface represents the transition density matrix, the x-axis and the y-axis represent the atomic number, and the z-axis is the transition density. The peak on the diagonal is the local excitation of each atom and the non-diagonal one is indicative of the charge transfer of dissimilar atoms. We can see that non-diagonal elements dominate the excitation of this kind of molecule, which means the charge transfer excitation plays a major role. Hyperconjugative effect Modern quantum chemistry calculations are basically based on the MO theory, but the molecular orbital usually shows a strong delocalization, which cannot map the classical chemical conception of the chemical bond, lone pair of electrons etc. It is difficult to analyze the bond and other issues. And almost all quantitative computations today apply extended basis-sets and it is hard to find a one-to-one corresponding relation with atomic orbits (even no relation, e.g. planar wave functions). The eigenvectors of natural orbits are obtained after the diagonalization of the density matrix in the process of quantification. The corresponding eigenvalues are the occupancy numbers of natural orbits. The eigenvector is transformed into a natural atomic orbit (NAO) after the occupancy-weighted symmetric orthogonalization. NBO can be grabbled by searching the density matrix of NAO-based vector. NBO is divided into Lewis and non-Lewis orbitals. Hyperconjugation (such as electron delocalization or orbital mixing) between a Lewis-type orbit i (electron donor) and a non-Lewis-type orbit j (electron acceptor) results in a reduction of the system energy by 2-order Perturbation Theory. , ∆ where is the donor orbital occupancy, and are diagonal elements (orbital energies) and , is the off-diagonal NBO Fock, also called Kohn–Sham matrix element. Only the hyperconjugation orbitals on the methine chain are analyzed here, as shown in Figure 6 and Figure 7. The hyperconjugation effect between Lewis and non-Lewis orbitals of the methine chain of NKX-2311 and NKX-2586 molecules is presented by the orbital overlap. A hyperconjugation effect between p- ∗ in the Single and double-alternating methine chain presents a link for two parts of the dye molecule (chromophore and auxochrome). The hyperconjugation effect of methine chain plays a "bridge" role, which connect the maximum and minimum point of ESP.



Figure 6

Side View Top View The Hyperconjugative NBOs isosurface of NKX-2311

Figure 7

Side View Top View The Hyperconjugative NBOs isosurface of NKX-2586


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The second-order perturbation theory analysis of Fock matrix in NBO confirms strong intramolecular hyperconjugative interactions, which are presented in Table 1. This interactions are formed by the orbital overtype between two orbitals (p or σ with π orbital) which results in intramolecular charge transfer (ICT) and the increase of the system’s stabilization energy. This intramolecular hyperconjugative interaction dominates the contributions of all delocalization for the stabilization energies and charge transfers (2rd-perturbation energy in Table 1). Table 1 Excited state characteristics of coumarin derivative Molecule

Transition Dipole

Oscillator

moment

strength

δR

Excited Energy

2rd-Perturbation Energy [Kcal/mol]

C343

3.729598

1.101558

4.003225

3.2324

--

NKX-2398

4.537533

1.5412241

4.8446848

3.0554

25.56

NKX-2388

4.811711

1.5885768

5.235356

2.8006

32.59

NKX-2384

4.332365

1.1948532

6.05849

2.5984

42.16

NKX-2311

5.728938

2.0664386

6.730151

2.5699

93.85

NKX-2586

6.537029

2.487199

8.155215

2.3757

121.5

The degree of electrons delocalization increases with the increase of the length of the base chain, the total 2rd-perturbation stabilization energy equals to the sum of all the NBO conjugate orbits energy of methine. Since the molecular C343 does not have a methine group, there is no second-order perturbation energy of the methine chain. It can be seen from Table 1 that, with the increase of the methane chain length, the second order perturbation increases and the excitation energy of those molecules decreases, along with the red-shift of the absorption spectrum. 3.4

Excitation Energy [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


NBO 2rd-perturbation Energy Fitting curve Confidence zones

3.2 3.0 2.8 2.6 2.4 2.2 50

100

NBO 2rd-Perturbatuion Energy [Kcal/mol]

Figure 8 Fitting curve of NBO 2rd-Perturbation Energy and excitation energy We use the exponential asymptotic model to give the fitting curve of NBO 2rd-Perturbation Energy and excitation energy. The equation of model is ∙

The coefficients of this equation is a=2.46886 ± 0.06931, b= -5.22968 ± 5.3599, c= 0.91809 ± 0.03579. The residual square ! is 0.96945 and the confidence coefficient P=0.03579

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