Peculiarities of the Environmental Influence on the Optical Properties

ARTICLE pubs.acs.org/JPCA

Peculiarities of the Environmental Influence on the Optical Properties of PushPull Nonlinear Optical Molecules: A Theoretical Study M. Makowska-Janusik,*,† I. V. Kityk,‡ J. Kulhanek,§ and F. Bures§ †

Institute of Physics, Jan Dlugosz University, Armii Krajowej 13/15, Czestochowa, Poland Electrical Engineering Department, Czestochowa University of Technology, Armii Krajowej 17, Czestochowa, Poland § Institute of Organic Chemistry and Technology, Faculty of Chemical Technology, University of Pardubice, Studentska 573 Pardubice, Czech Republic ‡

ABSTRACT: Gas-phase geometry optimization of NLO-active molecules is one of the standard approaches in the first principle computational methodology, whereas the important role of the environment is usually not considered during the evaluation of structural parameters. With a wide variety of environmentally influenced models in most cases only the high quality single point calculations are prepared. Among different approaches, the most used polarizable continuum model (PCM) seems to be promising. In this study, we have compared the electronic properties of gas-phase optimized geometries of imidazolederived pushpull compounds with those optimized using PCM solvation approach including CH2Cl2 and PMMA as media. We have focused particularly on the linear optical properties of investigated molecules, namely on the UVvis absorption spectra. The analysis of presented results shows the applicability of the different quantum chemical (QC) methods for the UVvis spectra calculations of linear NLO molecules. Herein we also present the need of molecule geometry optimization affected by the environment. Following the performed calculations, the electronic properties of gas-phase optimized molecules give conformable results with respect to those obtained by more time-consuming continuum optimizations. All computational data are supported by experimental investigations.

I. INTRODUCTION Rational design and search for modern optical materials is currently one of the main tasks of materials science research.14 The composites based on polymeric host matrix and NLO-active organic guest molecules (chromophores) play a special role in the area of organic nonlinear optical (NLO) materials. Successful application of such composites requires particular macroscopic optical properties, relevant design of the individual components, and homogeneous distribution of guest molecules. The hostguest interactions affect the physical properties of individual components and, as a consequence, the properties of composite material, namely its electronic structure, cavitations, and dispersion. These effects are more pronounced and complicated in the solid than in the liquidstate phase. Hence, the influence of different components on the optical properties of hostguest materials is a very important task and should not be neglected. The electrostatic interactions of chromophores with the polymer matrix depend largely on the charge distribution and the polarizability of the particular components. In the composite materials, the host and guests relax selfconsistently to the presence of each other. This is particularly important for the bicolor optical treatment,5 where absorption, refractive index, second- and third-order susceptibilities as well as ground and transition dipole moments of the media are changed. The solutesolvent or hostguest interactions occur in many systems, especially in polar media such as NLO materials. r 2011 American Chemical Society

Recently, we developed the method to calculate the effect of a surrounding medium on the electronic properties of a NLO molecules incorporated into polymer matrixes.610 This method involves two stages of computations. The first stage covers the molecular dynamics simulations performed to determine the equilibrium structure of the solvent or polymer around the chromophore in its ground electronic state. The second one is quantum chemical calculations of the molecular electronic properties considering the contribution of the local field effect. However, the formed discrete local field procedure is very timeconsuming and considering the size of the computed system the molecular dynamics simulations may be done using the force field molecular mechanics, the not completely appropriate method for the structural evaluation. Presently, several continuous solvent models are developed, which are procedurally less demanding than the local field discrete approach. Also they may describe environment influences on electronic properties of guest molecules. It was proved in many cases that the effect of the environment on molecular energy, structure, and property can be effectively computed by the continuum solvation models.1113 Received: February 10, 2011 Revised: September 14, 2011 Published: September 27, 2011 12251

dx.doi.org/10.1021/jp2013539 | J. Phys. Chem. A 2011, 115, 12251–12258

The Journal of Physical Chemistry A

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Figure 1. Molecular structures of investigated imidazole-derived pushpull systems IM1IM6.

This work focuses on the influence of a solvent and polymeric matrix on the linear optical susceptibility dispersion, namely UVvis absorption spectra, of NLO-active pushpull chromophores. Trisubstituted Y-shaped imidazoles IM1IM6 were chosen as model molecules14 for the present study (Figure 1). It has recently been shown that, in such a class of heterocyclic pushpull compounds end-capped with suitable donors and acceptors, an efficient charge transfer can be achieved.1519 The investigated pushpull IM1IM6 systems possess the acceptor cyano groups appended at the imidazole C4/C5 positions and the N,N,-dimethylamino donors at the imidazole C2 place, whereas the N,N-dimethylamino donor group in IM1 is connected directly to imidazole, the π-conjugated path separating the 4,5-dicyanoimidazole moiety and the donor group in IM2IM6 is successively extended and varied. Thus, the π-conjugated path in IM2 features 1,4-phenylene, (E)-phenylethenyl in IM3, biphenyl in IM4, (E)-phenylethenylphenyl in IM5 and phenylethynylphenyl in (IM6). The linear optical properties of chosen molecules were investigated in dichloromethane (CH2Cl2) as a liquid medium as well as in the solid thin film based on the poly(methyl methacrylate) (PMMA) matrix. Dichloromethane is a widely used organic solvent. The PMMA is a thermoplastic, unpolar material that effectively filters UV light at wavelengths below 300 nm and is very often applied for different optoelectronic applications. Section II presents the used solvation model, and section III describes the principal details concerning quantum chemical methods implemented in the performed calculations. The empirical and theoretical results with the discussion and comparison to the experimental data are described and summarized in the section IV.

II. SOLVATION MODEL There are different models to describe the solventsolute interactions. They may be principally divided into two classes. The first class of models describes the individual solvent molecules explicitly and the second one, more popularly and frequently used, treats solvent as a continuous polarizable medium. It describes the solvent as a continuous medium possessing a fixed macroscopic dielectric constant ε, where the solute molecule is accommodated in a cavity of certain shape and size. Inside the cavity the dielectric constant is set equal to 1, like in a vacuum. Outside the cavity the constant ε usually gets the bulk value of the

considered solvent, but it depends on the model. The solute charge distribution interacts with the medium, polarizes it, and creates an induced charge distribution on the cavity surface. The electric field exerted by the solvent on the solute is called a reaction field. In the term of the reaction potential it is introduced into the solute Hamiltonian, predicting a new electronic structure of the chromophore, which further alters the polarization of the solvent. Presented self-consistence polarizing iteration is the fundamental principle of the self-consistent reaction field (SCRF) method.2022 The reaction field may be represented by an apparent surface charge (ASC)23,24 density distributed on the solvent excluding surface (SES).25 The solute cavity creation, its size and shape definition, and the charge distribution of solute and its classical or quantum mechanical description are very important for the used model. The solvent molecule is called a “probe”, and it is reduced to a sphere equal to the van der Waals (vdW) volume. The solute molecule is the space accumulated by its atoms vdW radius, which naturally generate a surface for the molecule. Typically, the radii of spheres are assumed to be 1.2 times higher than the atomic vdW radius. The SES surface is the boundary of the region inaccessible to a solvent probe sphere as it rolls over the solute molecule. In the computational practice this surface is partitioned into small areas (tesserae), and according to the ASC model, the apparent charge density is discretized into a set of point charges each of them located on own tesserae. The tesserae should be small enough to consider an apparent surface charge constant within each of them. There are many methods to divide the created SES into tesserae. The most used ones in quantum molecular solvation methods is the GEPOL tessellation procedure.26 One of the most frequently used and oldest ASC models is the polarizable continuum model (PCM)20 with its later innovations, implemented into many of quantum-chemical codes. It has recently been developed for nearly all the quantum mechanical methods available for the study of isolated molecules with a very limited increase of computer time for energies, gradients, and second derivatives. It is often used to simulate the solvent effect in molecular HartreeFock (HF) calculations. In the case when the dielectric constant of the medium is changed from the constant, finite value to ε = ∞, as it is for conductors, the implemented model is called conductor-like PCM model (C-PCM).2729 The surface charge distribution discretization gives possibility to use boundary element method (BEM)23 to solve complex differential equation. The convenient form of the BEM equation 12252

dx.doi.org/10.1021/jp2013539 |J. Phys. Chem. A 2011, 115, 12251–12258


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for numerical purposes, applied for C-PCM model is30 Sq ¼

ε1 V ε

ð1Þ

Matrix S includes elements Sii = 1.0694(4π/ai )1/2 and Sij = S j|) where the value ai is the area of the tesserae i. The 1/(|S Bi B numerical factor 1.0694 has been empirically adjusted to reproduce the values given by the exact Born equation for spherical ions. si and sj indicate position variables of the tesserae. q denotes the C-PCM solvent charges. The function f(ε) = (ε 1)/ε was introduced according to the Gauss low to reinstate the finite value of ε. The vector V collects the electrostatic potentials created by the solute at the tesserae surface. In the presented approach, the Hamiltonian for the solute in solvent environment is given by H ¼ H0 þ H 0

ð2Þ

where H0 is the solute Hamiltonian in the gas phase and H0 describes the interaction between the solute and apparent surface charges. The apparent surface charges are obtained by solving eq 1. When light absorption and emission processes are studied, it is necessary to take into account nonequilibrium solute solvent effect. This has been coded in the PCM framework for HF and complete active space (CAS) SCF31,32 methods.

III. COMPUTATIONAL DETAILS Since the computer software and hardware were developed, the most increasing interest is noticed in quantum chemical calculations of optical and electronic properties of materials. From the material engineering point of view, the performed calculations are useful, when the work is done for bulk material and not only for the isolated molecule. The difficulty of calculations, which should be done, consists of the number of parameters necessary to be taken into account. The second problem is the electronelectron interaction, which is not trivial in a real system. The fundamental phenomenon associated with electron correlation is the UVvis absorption. The analysis of electron spectra of the molecular system provides the key knowledge on excited-state dynamics. This problem is exceptionally complex when the intermolecular interactions existing in solvated samples are considered. In presented work the role of quantum chemical (QC) methods on the excited-states calculations will be summarized. Imidazolederived pushpull systems IM1IM6 were investigated in this respect. The environmental effect will also be taken into account concerning the C-PCM model. The CI and time dependent HF (TD-HF) computational levels were used as the wave function based methods. On the contrary, the time dependent DFT (TDDFT) formalism results will be analyzed. The TD-DFT is considered to be the most prominent method to calculate the excited state of medium-sized and large molecules. The analysis of presented results will focus on the applicability of the chosen methods showing their limitations, strengths and weaknesses. These methods and obtained results will be comparatively discussed in relations to the application of the C-PCM model. The electronic and optical properties of investigated molecules were calculated applying HF and DFT methods using GAMESS33 and ADF34 program packages, respectively, in the vacuum, solvent, and polymeric matrix environment. The molecular structural optimization was performed prior to exact quantum chemical calculation. The total energy minimization was carried out at the restricted HF (RHF) level35 with the

standard 6-31G** basis set in C1 symmetry. The geometries of all molecules were specified in Cartesian coordinates. It is wellknown that Z-matrix specification is inappropriate for aromatic molecules.36,37 Eckert and co-workers38 have proofed that the natural internal coordinates show very good performance to optimize the geometry of long organic molecules. The initial Cartesian geometries were taken from the output data obtained by geometry optimization procedure performed by semiempirical PM3 method. The gradient convergence tolerance was equal to 106 Hartree/Bohr using the quadratic approximation (QA) method3941 updating the Hessian matrix during the optimization. The Hessian evaluation was performed to exclude the structures giving the negative modes. The initial geometries of the IM1IM6 compounds have been also calculated at the DFT implementation. The DFT calculations were performed with the standard triple-ζ basis sets extended by one polarized functions (TZP) available in ADF package and described in the references cited there.34 Core electrons of all atoms were kept frozen and any geometry restriction was applied. The exchange correlation (XC) energy in the DFT model was calculated using the generalized gradient approximation (GGA). In this case the BLYP method was applied defined as the Becke gradient correction42 for the exchange part and the LeeYangParr correction43 for the correlation part of functional. The Hessian matrix was updated using the BroydenFletcherGoldfarb Shanno (BFGS)44 method with the criterion for the energy and gradient changes equal to 103 Hartree and 102 Hartree/Å, respectively. It was found that the geometries of the IM1IM6 molecules calculated by BLYP methods are consistent with those computed by HF implementation. As a consequence, the structures obtained by HF calculations were chosen for the later presented computations. After that, the geometries of the molecules optimized at the HF level were validated again by applying the C-PCM solvent model. The C-PCM model implemented in the GAMESS program package33 requires the dielectric constant (ε) values of solvent and the size of its molecular radius. These data for CH2Cl2 were taken as implemented in GAMESS;33 namely, the radius of the solvent molecule is equal to 0.227 nm, and the dielectric constant was specified as 8.93. The radius of PMMA and its dielectric constant were chosen as 1.200 nm and 2.50, respectively.45 The electronic properties of isolated molecules IM1IM6 have been calculated at the self-consisted RHF (SCF RHF) level by applying the standard 6-31++G** basis set as well as using the DFT formalism implemented in the ADF program with its ADFRESPONSE module.46 The excitation energies calculated at the HF level were evaluated using the single configuration interaction (CIS)47,48 and the TD-HF49 method. The SCF convergence criteria were chosen as relative density convergence equal to 1012, which corresponds to no more than 50 iterations. In both methods the Davidson algorithm was used for Hamiltonian diagonalization.5052 CIS and TD-HF are the cheapest excitedstate methods that include electron correlation via wave function methodology and are applicable to large molecules. A conceptually different approach to include electron correlation is represented by TD-DFT formalism.53 It is necessary to emphasize that TD-DFT calculations reproduce well the experimental hyperpolarizabilities for small molecules5457 but give unsatisfactory results for optical properties of long linear chains.58 All parameters for the TD-DFT calculations were applied as for geometry optimization that has been chosen. The standard triple-ζ basis sets extended by two polarized 12253


The Journal of Physical Chemistry A functions (TZ2P) available in ADF were used with core electrons frozen for all atoms. The SCF energy convergence criterion was chosen to be 1012 Hartree. The excitation energies were calculated using the iterative Davidson method59 with an accuracy of 1012 Hartree. All the molecules were rotated to align the ground-state dipole moment along the Z-axis. The UVvis absorption spectra were calculated, for the gasphase geometry optimized molecules and for the molecules with geometry affected by environmental interaction, using the TDHF method combined with the C-PCM model. The solventphase geometry optimization gives the possibility to examine environmental effect on the molecular structures and then on their electronic properties.

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Table 1. RMS Distance Displacement of IM1IM6 Affected by CH2Cl2 and PMMA Environments Obtained for Carbon (C), Nitrogen (N) Atoms, and All Molecules CH2Cl2

PMMA

molecule

C

N

tot

C

N

tot

IM1

0.04876

0.04137

0.08209

0.03841

0.03244

0.06714

IM2

0.03123

0.03139

0.04530

0.05400

0.44200

0.09227

IM3

0.02407

0.03630

0.03225

0.01466

0.02116

0.01756

IM4

0.01604

0.02803

0.02030

0.08253

0.08953

0.14488

IM5 IM6

0.06460 0.03445

0.08358 0.03753

0.11484 0.04694

0.05704 0.03122

0.07823 0.03371

0.10042 0.04232

IV. RESULTS AND DISCUSSION IV.1. Geometry Parameters. Firs of all, the geometries of

studied molecules were optimized in a vacuum, neglecting intermolecular interactions. This optimization will be called the gas-phase geometry optimization procedure. Then, the molecular structures were optimized in CH2Cl2 and PMMA environments, which induces geometry changes important for electronic molecular properties. This procedure will be called the solventphase optimization. The solvation calculations were performed using the C-PCM model. It was found that the geometries of the IM1IM6 gas-phase optimized molecules calculated by BLYP methods are consistent with those obtained by HF method. However, the bond lengths calculated by the HF method are a little bit shorter (up to 0.2 Å) than those obtained by BLYP potential. The DFT method, especially combined with the BLYP potential, has a tendency to overestimate the bond lengths.6062 According to the study of Puzyn63 and Rinnan64 cheaper methods such as HF/6-31G or PM3 may be employed with success for the geometry optimization of big molecules. Often it is better to use the semiempirical methods, for example, PM6,65 instead of the more expensive and time-consuming DFT method. This being the case to use the HF obtained structures for the further examinations. To quantify the geometrical differences for the investigated molecules, the structures optimized in the solvent phase (CH2Cl2 and PMMA) were superimposed on the structure obtained in the gas phase. The root mean square distance (RMSD) displacement was calculated for the superposition between equivalent atoms excluding hydrogen. The hydrogen atoms were excluded because many of them are present in methyl groups having rotational freedom. The RMSD is defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N ðr r Þ2 i, 1 i, 2 ð3Þ RMSD ¼ N i¼1

∑

where the ri,1 and ri,2 are the positions of atom i in structure 1 and 2, respectively, and N is the total number of atoms in the molecule. The RMSD parameters are presented in Table 1. The most flexible molecule in CH2Cl2 is IM5, but the most important changes of atomic position in PMMA environment are observed for IM4. For both molecules, the displacement of nitrogens is more pronounced than the carbon atom movement. This is manifested by the increase of the nitrile group bond length. One may observe that the environment effect twists the 1,4-phenylene groups out of the molecular plane. The twist is more pronounced in PMMA than in CH2Cl2. Generally, the 1,4phenylene groups attached to the imidazole C2 position are

sterically forced out of the imidazole plane. This can be clearly seen for IM5 in CH2Cl2 and IM4 in PMMA (Table 1). The geometry of the smallest molecule IM1 and the longest one, namely IM6 with a rigid CtC bond, respond modestly on the environment. The geometry of molecules IM2 and IM4 is more sensitive for PMMA than for CH2Cl2 environments. Dichloromethane affects molecules IM3 and IM5 most significantly, which may be rationalized by the presence of the isomerizable CdC double bound. The environment geometry reorganization of the remaining molecules is mostly caused by PMMA. The above-described changes concern the twist of the phenyl rings out of the molecule plane but the solvent also affects the molecular length. The solvation distortion of all investigated molecules reduces their length. The CH2Cl2 affects mostly the length of IM2 and IM4 but the PMMA disturbs the remaining molecules. One may conclude that for the molecules more twisted by the solvent their lengths are less contracted. We found that the total energies of molecules obtained in solvent phase using the C-PCM models are smaller than those in the gas phase. It may not clearly define the solvation effect on the stability of investigated molecule. The PCM model provides the free energy of the molecular solute in the liquid environment, as the sum of different energetic contributions related to short- and long-range solutesolvent interactions. The electrostatic contribution deeply affects the solute structure and electronic properties, and it is the most important term in polar solvents. The unpolar systems exhibit vanishing electrostatic contribution. Furthermore, dealing with large size solutes, the cavitation contribution can be larger than the electrostatic one. Finally, the solute total energy changes under the influence of solvent; it is a very interesting subject but is not discussed here. IV.2. Electronic Parameters. The electronic parameters of all investigated molecules IM1IM6 are given in the Table 2. There are summarized data obtained for the gas-phase optimized molecules (columns 1). Columns 2 and 3 show the parameters obtained for IM1IM6 molecules with geometry optimized in the gas phase, but their electronic parameters are affected by CH2Cl2 and PMMA, respectively, implementing the C-PCM model in the QC single point computations. Columns 4 and 5 present the data obtained using the C-PCM model for IM1 IM6 molecules with solvent-phase optimized geometries. The dipole moments of solvent affected molecules, both at the level of structural geometry optimization and the at the level of QC single point calculation, are larger than those in the gas phase. The same relations were found by Cramer and Truhlar12 and by Han and co-workers.66 Han and others proved that the 12254


364

380 597.4

582.8 273.9

284.6

281.0

273.8

290.8

280.7 280.8

290.7 290.1

266.6 2.02

276.0 8.77

8.88 8.82

8.72 8.55

8.70 8.63

8.47 8.68

8.82 14.45

14.54 13.7

14.0 15.0

14.5

15.02 12.78 IM6

14.16 15.01 12.84 IM5

14.11

1.96

285.6 254.0 15.01 14.36 12.67 12.18 IM3 IM4

14.12 13.44

15.16 14.37

14.03 13.09

13.94 13.20

9.07 9.26

8.86 8.91

8.95 9.03

8.99 9.08

9.08 9.31

2.24 2.09

271.5 242.2

286.5 254.6

284.7

381 346 477.5 577.3 281.6 249

293

286.9 254.6

282.9 251.7

455.9

344.8 219.2

236.3 238.9

228.0

243.6

229.5 226.3

242.3

3.18

212.9

9.82

11.25 11.12

9.60 9.60

10.98 10.88

9.41 9.87

11.11 9.20

12.53 12.93

9.98 10.92

14.17 13.14

11.03

14.16

9.12

11.77 IM2

10.22

2.56

230.3

244.5

221.5

316

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IM1

(nm)

exp BLYP

(1) (5) (4) (3)

PMMA CH2Cl2 PMMA

(2) (1) (1)

CH2Cl2 vacuum CIS

(1)

BLYP PMMA

(5) (4)

CH2Cl2 PMMA

(3) (2)

CH2Cl2 vacuum

(1) (1)

BLYP PMMA

(5) (4)

CH2Cl2 PMMA

(3) (2)

optimization

CH2Cl2 vacuum

solvent-phase HF

gas-phase

(1)

optimization optimization

solvent-phase gas-phase

optimization

HF

ΔEHOMOLUMO (eV) μ (D)

optimization

molecule

solvent-phase gas-phase

optimization

TD-HF

HF

λmax (nm)

Table 2. Electronic Parameters Calculated Using HF and DFT Theory for the Isolated Molecules IM1IM6 in a Vacuum (1) and for the Molecules with Gas-Phase Optimized Geometries [(2) and (3)] as Well as for the Molecules with Solvent-Phase Optimized Geometries [(4) and (5)] for Which the Data Were Calculated Using the C-PCM Model


Figure 2. Variation of the molecular dipole moment changes calculated by HF method affected by CH2Cl2 and PMMA solvent. Δμ was obtained as the difference between the molecular dipole moment computed in vacuum and in solvent (the solid curves were obtained for the gas-phase optimized geometry; the dashed lines, for the solvent-phase optimized geometry).

dipole moment of solute increases with solvent polarity. The dipole moment of long, polar molecules as nucleic acid based aqueous solvation increases by more than 40% for the gas-phase optimized geometries.67 The dipole moment changes of small molecules affected by aqueous solvation may vary from 8% to 31%.68 It was also shown that the dipole moments of the nucleic acid increase by up to 10% more upon relaxation of their geometries in the solvent phase.67 In our case, the dipole moment of gas-phase optimized molecules affected by CH2Cl2 increases from almost 17% for long molecules like IM6, IM5, and IM4 to 21% for the smallest ones, IM1 (Table 2). These changes are less pronounced for the gas-phase optimized molecules affected by the PMMA environment (10% to 12%). For the solvent-phase geometry optimized molecules, the dipole moment changes are from 13% to 20% and from 7% to 11%, in CH2Cl2 and PMMA, respectively. In Figure 2 the molecules IM1IM6 are ordered according to their increasing dipole moment calculated by the HF methodology (axis X). The presented changes of the dipole moment (Δμ) are calculated as the difference from the molecular dipole moments in a vacuum (Table 2). The smallest changes of the dipole moment are noticed for IM6 and IM1 solvent-phase optimized geometries affected by PMMA. Also the CH2Cl2 solvent reacts on IM1 and IM6 in the least intensity. The charge distribution of these molecules seems to be the most stable according to the environmental interaction even if their length changes are important. It means that the shortening of the molecular length compensates the charge transfer magnifying the dipole moment. The most pronounced changes of dipole moment are observed for gasphase geometry optimized molecule IM2 and IM3 when their Hamiltonians are affected by the CH2Cl2 and PMMA environments, respectively. The absorption bands of all investigated molecules measured in CH2Cl2 lie in the spectral region of visible light.14 The experimental λmax position (Table 2) depends on the character of π-conjugated space between the donor and acceptor groups. The less transparent is the IM3 molecule with a styryl linker possessing λmax= 381 nm. Very similar results were observed for IM5 featuring the E-phenylethenylphenyl linker (λmax = 380 nm). The same role of π-conjugated path may be reproduced by the 12255



Figure 3. Variation of the first absorption peak position calculated by the HF method affected by CH2Cl2 and PMMA solvent. λmax was obtained as the difference between the first absorption peak position computed in a vacuum and in a solvent (the solid curves were obtained for the gas-phase optimized geometry; the dashed lines, for the solventphase optimized geometry).

quantum chemical calculations applying HF methodology supplemented by CI as well as by TD-HF procedure (Table 2, column 1), but the TD-HF formalism gives better results. Among the many HF formalisms treating the molecule and light interaction, the TD-HF method is most widely used for investigations of laser-induced ionization69,70 computations of nonlinear susceptibilities71,72 and locating excited electronic states73,74 with respect to experimental data. An application of the TD-DFT methodology with BLYP potential does not consider the charge-transfer (CT) mechanism occurring in studied pushpull molecules. The CT mechanism is the most important feature of the UVvis absorption process existing in the investigated molecules. The BLYP obtained λmax values are very far from the experimental results and the character of their changes does not correspond to the measured data. In our previous work it has been shown that for the long pushpull molecules the BLYP methodology is not suitable to reproduce their λmax values.75 The CT-type excitation energies are often significantly underestimated by TD-DFT calculations employing conventional exchangecorrelation functionals. To partially correct the shortcomings, the range-separated exchange correlation functionals, such as Coulomb-attenuated B3LYP (CAM-B3LYP)76 or long-rangecorrected BLYP (LC-BLYP)77 have been designed for accurately describing CT excitations in TD-DFT calculations. In our case the λmax values for all investigated gas-phase optimized molecules were also calculated using CAM-B3LYP and LC-BLYP functionals. These functionals overestimate the λmax values not so drastically as was obtained for BLYP, but they do not improve the tendency of the UVvis absorption changes for the individual molecules. An alternate way will be to use so-called asymptotically correct functionals. Unfortunately, they are rarely implemented in any available quantum chemistry packages and, therefore, are not well tested. Analyzing the obtained results, one may conclude that, for the investigated molecules, the best tendency of λmax changes are computed using TD-HF formalism. Therefore, only the TD-HF obtained data were taken for the “solvent” calculations. Both equilibrium and nonequilibrium effects can be treated within the frame of the C-PCM model. The solvent reaction field in the nonequilibrium regime depends on the dielectric constant at optical frequency. Generally, the

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Figure 4. Absorption spectra calculated for IM1: (a) in a vacuum; (b) and (c) molecules with gas-phase optimized geometry affected by CH2Cl2 and PMMA environments, respectively; (d) and (e) molecules with solvent-phase optimized geometry affected by CH2Cl2 and PMMA environments, respectively.

solvent effects do not tune the UVvis spectra so drastically but should be accounted for. The best accuracy of absorption spectra is obtained with the nonequilibrium PCM solutions.78 In presented work the nonequilibrium C-PCM calculations were performed for the UVvis absorption spectra. The dielectric constant taken into account for the solvent molecules was related to the square of the solvent refractive index. Figure 3 shows that the most important changes in UVvis absorption energies are obtained for the smallest molecule IM1. Analysis of the HOMO and LUMO energies shows that only for IM1 do both solvents change the atomic orbitals contribution to the HOMO energy level. The atomic orbitals of carbons in imidazole ring contribute to the HOMO energy level obtained for the isolated molecule. When the molecule is affected by solvent, the molecular orbitals representing HOMO level are shifted to the nitrogen atom in N, N-dimethylamino group. The solvent-phase optimized geometries affect the absorption level of IM4 and IM5 through the electron excitation from the HOMO f LUMO to the HOMO f LUMO+1 energy level. This may be caused by the pronounced change of IM4 and IM5 geometries obtained in the solvent phase, but it does not change drastically the absorption shift (Figure 3). Figure 3 clearly shows that the C-PCM effect for the gas-phase optimized molecules shifts the first UVvis absorption band bathochromatically. The molecules with solvent-phase optimized geometries give the opposite spectral shift. This holds true for all of the investigated molecules (Figures 4 and 5). On the other hand, a blue shift occurs as a rule when the ground-state dipole moment of a solute is larger than that in the excited state and it is noticed for all solvent-phase optimized molecules. Similar results were obtained for the S-TBS merocyanine.66 For the solvent-phase optimized molecules the changes of dipole moments correlate to the variation of Δλmax (compare Figures 2 and 3). The environment affects the electronic structure of the investigated molecules by changing the spectral position of λmax as well as the positions of other electron excitation bands. The aforementioned changes for molecules IM1 and IM6 are presented 12256



Figure 5. Absorption spectra calculated for IM6: (a) in a vacuum; (b) and (c) molecules with gas-phase optimized geometry affected by CH2Cl2 and PMMA environments, respectively; (d) and (e) molecules with solvent-phase optimized geometry affected by CH2Cl2 and PMMA environments, respectively.

in Figures 4 and 5, respectively. All of the calculated absorption bands are shifted bathochromatically for all molecules with solvent-phase optimized geometries (Figures 4 and 5). For the molecule IM2 with the gas-phase optimized geometry peak C stays at the same position but peaks A and B are shifted in the red wavelength direction. For the molecule IM1 with the gas-phase optimized geometry peak B has a small shoulder at the higher wavelength side. Whereas this spectral peak has a stable position for these geometries, the shoulder is shifted bathochromatically. Peaks A and C also move to the red wavelength side. For the molecule IM1 with the geometry optimized in the solvent, the shoulder at peak B disappears and all peaks (A, B, C) move hypsochromically, as is noticed for all investigated molecules. Peaks B of molecules IM5 and IM6 with the geometry optimized in the gas phase are also spread into two peaks with stable spectral position. For both molecules, peak C does not change the spectral position. For molecule IM5 peak A shows a small red shift but it does not move for IM6. The solvent effect does not change the absorption peak’s positions for the molecule IM4 with the geometry optimized in the gas phase. For molecule IM3 with the geometry optimized in the gas phase peak B does not change its position but peaks A and C are red-shifted.

V. CONCLUSIONS In this work we present the theoretical investigations of the UVvis absorption spectra of the imidazole-derived pushpull molecules. The performed computations may be divided into two stages. At the first stage, the geometries of all molecules were optimized in the gas phase (in a vacuum) and then the electronic properties were affected by solvents. The second stage of calculations presents the results for molecules with solvent-phase optimized geometries and electronic properties computed by C-PCM solvent model approach. The molecules were dissolved in CH2Cl2 and PMMA media.

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Both solvents affect the geometries of investigated molecules in different ways. Whereas PMMA twists the molecules possessing the single bond between phenyl rings, CH2Cl2 affects the planarity of IM3 and IM5 bearing a double bond. The presence of solvent shortens the length of all molecules. When the molecule is more twisted by the solvent, its length is less contracted but it is not yet explained. The geometry of the smallest molecule IM1 and the longest one, namely IM6 with a rigid CtC bond, act the most poorly on the influence of environment. The geometry of the molecules IM2 and IM4 is more sensitive for the PMMA environment than for CH2Cl2. The CH2Cl2 acts more on the IM3 and IM5 molecules than on the remaining ones. Probably it is connected with the origin of the chemical bond between the phenylene groups. The atomic orbitals of carbons in the imidazole group contribute to the HOMO energy level obtained for the isolated molecule. When the molecule is affected by solvent, the molecular orbitals representing the HOMO level are shifted to the nitrogen atom in the N,N-dimethylamino group. The environment affects the electronic structure of the investigated molecules by changing not only the position of λmax but also the positions of other electron excitation bands. All of the calculated absorption bands for all investigated molecules with solvent-phase optimized geometries are red-shifted. It may be concluded that the C-PCM single point calculations for the gas-phase equilibrated molecules shift the absorption band bathochromically, whereas the environment included by the PCM model at the level of geometry optimization and single point calculations causes the hypsochromic shift when compared to the vacuum calculations. The comparison of the experimental and computed data showed that the C-PCM implementation only at the single point calculations gives better results. This conclusion may be approximated for all rodlike NLO active molecules characterized by charge-transfer effects. From the other side maybe the timedependent solvation effects require proper dynamic models. Finally, it is worthy of mention that in several systems bulk solvent effects are not sufficient for an accurate treatment of the static and dynamic contributions to excited-state properties.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Calculations have been carried out at the Wroclaw Centre for Networking and Supercomputing (http://www.wcss.wroc.pl), grant No. 171. J.K. and F.B. thank the Ministry of Education, Youth, and Sport of the Czech Republic (MSM 0021627501). ’ REFERENCES (1) Balakina, M. Y. ChemPhysChem 2006, 7, 2115. (2) Hu, X.; Jiang, P.; Ding, C.; Yang, H.; Gong, Q. Nat. Photonics 2008, 2, 185. (3) Kolev, T.; Koleva, B.; Kasperczyk, J.; Kityk, I. V.; Tkaczyk, S.; Spiteler, M.; Reshak, A. H.; Kuznik, W. J. Mater. Science: Mater. Electron. 2009, 20, 1073. (4) Abbotto, A.; Beverina, L.; Manfredi, N.; Pagani, G. A.; Archetti, G.; Kuball, H.-G.; Wittenburg, C.; Heck, J.; Holtmann, J. Chem.—Eur. J. 2009, 15, 6175. 12257


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Peculiarities of the Environmental Influence on the Optical Properties

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