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Abstract
The absorption spectrum of dichloride-bis(5,7-dichloroquinolin-8-olato)tin(IV) of the chemical formula Q2SnCl2 is calculated making use of first-principles methods and is compared with the experimental data. The energy correction terms for the excitation energies are computed by considering the single excited molecular orbitals (SEMO) from ground state to excited states of the molecule. By this approach, the contributions of the Columbic interaction between an excited electron and the remained hole in the absorption spectrum during the process of optical excitation are estimated. The MO energy difference and MO wave functions calculated by the density functional theory (DFT) and SEMO energy contribution are calculated. The results show that the corrections in energies by considering the contributions of the SEMO improve significantly the theoretical optical absorption spectrum. The calculations are based on DFT and necessary parameters and integrals for the computation of SEMO are obtained in DFT scheme. This method proves to be preferred compared to other ab-initio methods for calculating excited states, due to its ability in specifying MOs for any excitation energy, and also its lower computational cost. The method is applied for the first time to the calculation of the energy of transitions and specifies the electronic transition between MOs, especially in the absorption machinery of the OLED. Taking into account the contribution of the electron-hole interaction in the optical mechanism of absorption in the molecule makes the theoretical spectrum closer to that of the experiment. As a result, the crucial role of the electron-hole interaction, i.e. the interaction between the excited electron and the remained hole, in the absorption mechanism cannot be ignored..
© 2017 Optical Society of America
1. Introduction
Since the fabrication of Organic Light Emitting Diode (OLED) as a new source of light (firstly in 1976 from small molecules [1] and then in 1994 from polymers [2]), the optical and the electrical properties of organic molecules have been the focus of theoretical and experimental researches [3, 4]. Understanding Uv-Vis absorption and emission, among other optical mechanisms of OLEDs, are critically relevant for further achieveing the great perspectives seen in the field of lighting sources factory. In these mechanisms, electronic transition between molecular quantum states is of significant importance in order to determine absorption and emission spectra.
Many advanced approaches for describing Uv-Vis absorption spectrum of molecules have been developed in view of analytical quantum chemistry and physics as well as calculational ab-inito methods. Methods such as Frank-Condon diagram [5, 6] focus on molecular potential energy curves, while some other perturbative or ab-initio methods estimate the electron correlation and exchange potentials in linear response theory or configuration interaction methode [7–11]. Also, time-dependent density functional theory (TD-DFT) and GW approximation have become popular in recent decades [12]. Despite of great achievements of these approaches in the calculation of molecular excited states, the role of electronic states in transitions and their contributions in energy remain unclear. Almost all of the light-molecule interaction theories can’t fully specify transition states, especially the initial (occupied) and the final (unoccupied) states of transitions.
On the other side, natural transition orbitals (NTO) were presented to overcome this problem by finding a compact orbital representation for the electronic transition density matrix [13], but this method in many cases is ineffective, too [14]. Excitation of electron from an occupied molecular orbital (MO) in ground state up to an unoccupied MO is the simplest way for constituting excited state of molecule, and can be named as single excited MO (SEMO). In this picture, the main contribution of correlation and exchange energies can be taken into account in excitation energies, when the ground states and excited states of molecule are written in Slater determinant form. Another advantage of SEMO’s resides in low cost of computational time and realizing the effect of physical and geometrical parameters on electronic transitions.
In this work, we aim at calculating the contribution of specified MO’s excitation in the absorption spectrum of the molecule dichloride-bis(5,7-dichloroquinolin-8-olato)tin(IV). The molecule under investigation belongs to the group of tin complexes and has the chemical formula Q2SnCl2. The optimized structure of molecule and its optical spectrum are calculated by DFT and TDDFT, and the contribution of SEMOs in the absorption of the molecule are determined. Our incentive to optical properties of this molecule was the light emitting seen recently in this molecule [15]. In section 2, the material and a brief theoretical introduction to first-principles method for optimization of molecular structure and extracting MOs are provided. Electric dipole moments of molecule and energy of transitions are calculated by TDDFT and the share of SEMO in light emission of molecule is discussed (see section 3). The absorption spectrum of molecule is plotted and the results of SEMO are compared with that of DFT and TDDFT to examine efficiency of new calculating approach. This method is applied for the first time to calculate SEMOs’ contribution in absorption spectrum of a molecular OLED, and shows great advantages on the other ab-initio methods (such as TDDFT) due to its very low computational cost and its ability to take into accounts many states as high as hundreds of states compared to TDDFT, which can include some dozens of states (vide infra).
2. Material and theoretical methods
Materials verify the most important role in the field of OLED’s research and factory, so lots of groups and people focus on synthesizing new materials to enhance efficiency and quality of OLEDs. Organic molecules used in synthesis of OLED can change the properties of device, like color, intensity, charge and energy transfer, and can improve efficiency of system significantly. Uv-Vis absorption process, which is fundamentally related to electronic structure of molecule, depends on bonding nature and geometrical configuration of molecule [3].
2.1. Molecule
Metal complexes are well-known compounds that experimentally and theoretically have been studied in emitting layer of OLEDs and some of them demonstrate very good efficiency [16].
Recent experimental reports show that tin’s complexes emit good electroluminescent and have photoluminescent property [17]. Tin is a post transition atom with atomic number 50 and its oxidation numbers usually are 2 or 4. The structure of dichloride-bis(5,7-dichloroquinolin-8-olato)tin(IV) has a tin complex with 5,7dichloro quinolin-8-olato group as its two ligands. In 5,7-dichloro quinolin-8olato group two hydrogen sites in oxine group (5 and 7) are substituted for chlorine (Fig. 1).
In this complex, 5,7-dichloroquinolin-8-olato group bond to tin by their oxygen and nitrogen atoms, and the chlorine atom demonstrates dangling bonds. The ligands in tin complexes remain planar with the plane of molecule and the oxygen bonding to tin is shorter and stronger than that of nitrogen.
2.2. Absorption in molecules: first-principle perspective
Molecules have several local minima in energy surface and their global minimum depends on spatial coordinates of nucleus. We should find the global minimum of the molecule to yield the most plausible molecule’s spatial form and its ground state. This is performed by optimizing the geometry of molecule, having selected a close structure as an initial guess. All physical information of optical properties of molecule and its electronic structure are latent in MO, which is a linear combination of atomic orbitals (LCAO).
In the first approximation, during absorption process a photon is absorbed and only one electron transits out to an excited state, so that the coupling between electrons can be ignored in the excitation phenomena. In molecules, an electron in an occupied MO of ground state transits out to an unoccupied MO in excited state. Probability, energy and line-width of transitions are main quantities for plotting Uv-Vis spectrum of molecules. The probability of transitions depends on dipole moments (or oscillator strengths) of transition, and energy of transition can be determined from energy difference between molecular excited and ground state. At last, at room temperature, spectral shape of a transition is generally expressed by a gaussian function.
Since, different transition frequencies co-exist in an optical process, Uv-Vis spectrum of molecule reads as a summation over transitions,
where, νfi shows the frequency of absorbed photon when electron transits from state i to f, and the energy of photon in the transition is expressed by hνfi, where h is Planck constant; Nfi is the normalization factor.2.3. Simulation methods
There exist many routines having different accuracy and computational cost for calculation of molecular optimized ground state structure, such as mechanical equation, semi-empirical calculational methods, Monte-Carlo, density functional theory (DFT). DFT supplemented with its time dependent counterpart for calculation of molecular excited state properties, has become benchmark of ab-initio calculations in last two decades [10].
DFT and TDDFT: we optimize the molecule under question using DFT with local density approximation (LDA). Bonds of Q2SnCl2 are weakly correlated, so B3LYP potential could be used properly to optimize the molecular structure. LanL2DZ basis set is employed for describing all atomic orbitals of molecule containing Sn atom. While the ground-state properties can in principle be obtained by a meaningful degree of accuracy, spectroscopic properties are in general not directly accessible in a DFT calculation. DFT results are used as starting point of many of developed (for excited states) theories such as GW, TDDFT etc.
Transition of electron from ground state to excited state as a time dependent process, can be studied by TDDFT to determine excitation parameters such as dipole moments and energy of transitions. An effective exchange-correlation potential of time dependent density functionallity is the foundation of TDDFT, defined as:
When an electron jumps to a LUMO and leaves a hole behind, the energy of excitation is corrected by the correlation between the excited electron and the remained hole. TDDFT defines correlation and exchange potential to include this energy, but their contributions in the excitation energy can not be distinguished.
Single Excited MO (SEMO): DFT yields reliable occupied MOs. On the other hand, the unoccupied MOs describing the excited states, can be estimated only with a lower approximation level in DFT scheme, so that virtual MOs can be considered as a first order approximation of excited states. Geometries of ground and excited molecule are different, however during optical excitation, molecule’s geometry remains unchanged, thanks to very fast photon absorption process versus nuclear slow motion [18].
MOs, χi, are written as a linear sum of atomic orbitals, ϕa,
Use will be made of for occupied (unoccupied) up (down) MOs. Ground state wave function is written as a Slater determinant, wherein 2n electrons relax in n occupied MOs (two electrons of opposite spins in each MO, except probably one single electron in 2n + 1-electron systems): When one electron transits to an unoccupied state, the excited state reads:If the optical excitation doesn’t change electrons spins (which is the case in our problem), an occupied MO is replaced by an unoccupied MO with the same spin. Lastly, the energy of excited state can be written by Koopman as:
where, EC is the antisymmetrized two-electron integral given by:When an electron jumps to upper empty MO, we should take into account the difference in electron interactions for two molecular states, so the transition of electron from molecular ground state to excited state produces dipole moment dif for SEMO in a classic homogeneous electromagnetic field,
where, |χi〉 and 〈χf| show initial and final MOs respectively, and the parameters are estimated in atomic units. Probability of electron transition is proportional to |dif|2.3. Results
Uv-Vis spectrum of Q2SnCl2 is an important feature in operation of OLEDs fabricated with this molecule as light emitting layer [15]. This effect is quantum mechanical in nature and we aim at investigation of absorption spectrum and estimation of SEMOs’ contribution in absorption of photons in the molecule under question by quantum mechanical methods.
3.1. Optimization
To optimize the molecular structure, use has been made of Gaussian09 with keywords opt, b3lyp/lanl2dz in DFT calculation, by employing B3LYP potential and LANL2DZ basis set. Fig. 3.1 shows the optimized spatial configuration of Q2SnCl2, and experimental geometry of the molecule is shown in Fig. 3.1 for comparison.
Comparison of optimized configuration with experimental geometry is performed simply referring to Tabs. 1 (Bond legnths between species), 2 (angles between bonds), 3 (dihedral angles). Similarities between theoretical optimized structure and experimental one are clear referring to bond lengths, angles and dihedrals of the molecule in these three parameter tables (1, 2, 3).
Table 1. Bond lengths between species of the molecule Q2SnCl2.
Table 2. Angles between species in the molecule Q2SnCl2.
Table 3. Dihedral parameters of the molecule Q2SnCl2.
DFT is able to optimize molecules such as Q2SnCl2, with lower time and good accuracy, since atomic orbitals of valence electrons that participate in chemical bonds are weakly correlated. Ligands don’t change their shapes and planarity in the molecule, and this can be obviously seen in DFT optimized geometry of Q2SnCl2 in Fig. 2. As expected, oxygen makes shorter bond lengths and stronger bonds to the element tin than to nitrogen. Also, it is seen that the chloride atoms are located around the tin atom in cis configuration. Another difference between the nitrogen and oxygen lies in their spatial configurations in the vicinity of the tin atom; oxygen is included in the trans configuration and nitrogen is included in the cis configuration as seen in Fig. 3.1. Also, it’s seen that chloride atoms locate around tin in cis configuration.
3.2. Electronic structure
LUMO’s (lowest unoccupied molecular orbital) energy of Q2SnCl2 is measured in an electrochemical environment with cyclic voltammetry and is evaluated about −4.05eV as electron affinity of molecule [15]. Energy of HOMO (highest occupied molecular orbital), appraised by subtracting energy gap (determined from Uv-Vis spectrum about 2.5eV) from energy of LUMO, is calculated about −6.55eV [15].
Density of states (DOS) of the molecule under question is shown in Fig. 3. For estimation of DOS, use has been made of a gaussian function with FWHM of 0.3eV. As is seen from Fig. 3, HOMO in DOS stay on −6.79eV, which is in close agreement with experimental value of −6.55eV. A very close occupied MO to HOMO exists at −6.82eV (see inset).
The DOS spectrum (Fig. 3) shows that LUMO energy in DOS is −3.33eV, which unlike HOMO energy has some deviation from experimental value of −4.05eV. In fact, DFT obtains excitation energy of electron from HOMO to LUMO as 3.46eV but experimental measurement of absorption spectrum yields 2.5eV (see below). This difference in LUMO energy may relies in rough approximation of DFT calculations of unoccupied MOs [20].
Spatial form of some of some important MOs participating in Uv-Vis spectrum are plotted in Fig. 4. As the figure shows, localization or delocalization of electrons vary in occupied and unoccupied MOs. This difference in localization characteristics of MOs is important in estimation of dipole moments and their overlap integrals.
3.3. Uv-Vis spectrum
By DFT approximation approach, the transitions of electrons between MOs of energies 2.25eV to 4.6eV is taken into account by calculating dipole moments of transitions. Then, in TDDFT scheme, Uv-Vis spectrum calculation is performed using Gaussian09 with keywords td = (nstates=15) b3lyp/lanl2dz. At the last step, we estimate the correction in energy terms by considering SEMOs (Eq. 8). Uv-Vis absorption spectrum of all methods have been plotted by employing gaussian line-shape (see Eq. 1) with FWHM = 0.1eV for all transitions.
Energy and dipole moment of transitions, calculated by TDDFT, DFT and SEMO, are reported in Tab. 4. In this table, ΔED, ΔES and ΔET indicate the transition energy estimated by DFT, SEMO and TDDFT, respectively. In the lowest excitation energy, SEMO corrects the transition energy from 3.46eV to 2.97eV corresponding to transition of electron from H-1 to L (see second line of Tab. 4 and electronic transition between MOs from Fig. 3.2 to Fig. 3.2); this value is different from the most probable MOs at TDDFT scheme corresponding to transition of electron from H to L (first line of Tab. 4). For each dipole moment, TDDFT indicates two or more transitions between MOs together with their contribution’s percent. This analysis of optical transitions may deviate from the electron-photon interaction pictures considering transition of one electron from an occupied state to an unoccupied one.
Table 4. Energy (eV) and dipole moment ( ) of electronic transitions between states and their contribution percents, calculated by different approximation schemes (DFT=D, SEMO=S, TDDFT=T).
In Fig. 5, the experimental data for the absorption spectrum of Q2SnCl2 are provided; as the figure shows, two distinguished peaks are situated around 324nm and 402nm wavelengths, alongside with some small peaks in between.
In experimental absorption spectrum, the lowest energy edge lies on 2.75eV that is much less than the lowest energy over-estimated by DFT method. The results of calculations by DFT method, compared with experiment, are shown in Fig. 6. DFT estimates peaks of spectrum at 348nm and 261nm with some shift through UV from two experimental measured peaks about 54nm and 63nm, respectively (the UV side is not shown in the picture). These shifts are attributed to error of DFT in calculating energy of virtual states, since both peaks are shifted to wavelength with higher energies where electron-hole correlation can’t be considered by Kohn-Sham potentials.
Fig. 6 Theoretical absorption spectrum of Q2SnCl2 by the method of DFT compared with experiment; as the figure shows, DFT can estimate some overall features especially in small wave-lengths region.
Figure 7 shows the results of TDDFT calculations and compares them with experiment. TDDFT estimates the location of lowest peak better than DFT close to experiment measurement about 2.90eV (ΔET in Tab. 4). TDDFT also shows two peaks in absorption spectrum at 422nm and 309nm, one of them shifted to longer and the other to smaller wavelengths. As expected, TDDFT determine wavelength of absorption peaks more accurate than DFT.
Fig. 7 Calculational absorption spectrum of Q2SnCl2 by the method of TDDFT compared with experiment; as seen from the figure, TDDFT can estimate peaks of absorption better than DFT and predicts an extra peak in larger wave-lengths region.
A considerable difference between two methods (DFT and TDDFT) relies in orbitals participating in dipole moments. In DFT, occupied orbitals of lower energies and in TDDFT, virtual orbitals are more conveniently used in calculation of transition probabilities. Also, DFT and TDDFT have some pitfalls in calculating the intensity of absorption peaks and justifying small intermediate peaks in absorption spectrum, as is obvious in Figs. 6 and 7.
At last, we calculate part of the energies lost in DFT calculations and ignored in TDDFT calculations, by considering SEMOs to rebuild energy of transitions.
Figure 8 shows the absorption spectrum calculated by considering energies and dipole moments estimated by SEMO approach. The first peak from left is located at 393nm that is very close to 402nm of experimental calculation. It is noteworthy that the second peak 300nm in experiment, have been split into two peaks at 341nm and 311nm with mean of 326nm (very close to 324nm in experiment). Therefore, as can be seen from Fig. 8, SEMO can improve Uv-Vis spectrum significantly, meaning that part of energy of transition is lost in the excitation process, and can be recovered when expressing in two specified MOs.
Fig. 8 Absorption spectrum of Q2SnCl2, corrected by estimating SEMOs in calculation of energy of Coulombic interaction between the excited electron and the remaining hole.
4. Conclusion
We calculate Uv-Vis absorption spectrum of a metal complex of chemical formula Q2SnCl2 with a straightforward picture in which, an electron absorbs a photon by appropriate energy and transits from an HOMO to an LUMO. Energy difference between ground and excited states of molecule isn’t only the difference between initial and final MO energies, but the correlations and exchange energy in excited molecule is latent in the excitation process by the Coulombic interaction between the excited electron and the remained hole. Comparison of experimental spectrum with SEMO-corrected terms emphasizes on MO importance in optical behavior of the molecule. The corrected energy extracted from electron repulsion integral (ERI) could be obtained using common ab-initio codes (as Gaussian 09) with no additional computations. The main issue used firstly in this work is the specification of initial and final MOs corresponding to any optical transition and calculating SEMO’s contribution in absorption spectrum of OLED.
As an open problem, the calculation of SEMO’s contribution in emission spectrum of the mentioned molecule can be performed by the same method described here.
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