J. Phys. Chem. B 2010, 114, 1815–1821
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Linear and Nonlinear Optical Susceptibilities of 3-Phenylamino-4-phenyl-1,2,4-triazole-5-thione A. H. Reshak,*,† D. Stys,† S. Auluck,‡ and I. V. Kityk§ Institute of Physical Biology, South Bohemia UniVersity, NoVe Hrady 37333, Czech Republic; Physics Department, Indian Institute of Technology Kanpur, Kanpur 208016, Uttar Pradesh, India; and Electrical Engineering Department, Technical UniVersity of Czestochowa, Al. Armii Krajowej 17/19, Czestochowa, Poland ReceiVed: September 27, 2009; ReVised Manuscript ReceiVed: December 17, 2009
We report first-principles calculations of the linear and nonlinear optical susceptibilities of 3-phenylamino4-phenyl-1,2,4-triazole-5-thione crystals. The X-ray diffraction structural data of Wang et al. (Molecules 2009, 14, 608.) was used as the starting point of the computational optimization calculation by minimization of the forces acting on the atoms, and the optimized geometry was used to calculate the linear and nonlinear optical susceptibilities. We have employed the full potential linear augmented plane wave (FPLAPW) method within density functional theory (DFT) along with the Engel-Vosko exchange correlation potential. The full potential calculations show that this crystal possesses an indirect energy gap of 3.1 eV. The compound exhibits some uniaxial dielectric anisotropy resulting in a strong birefringence. The 3-phenylamino-4-phenyl-1,2,4-triazole5-thione crystal possesses high second harmonic generation with several nonzeroth components, but only one component, χ(2) 111(ω), is dominant and its second-order optical susceptibility of the total real part and the total absolute value at zero frequency is equal to 0.097 × 10-7 esu. 1. Introduction Nonlinear optics is a domain of both science and technology that has been extensively exploited since the first working laser was built. Among the impressive variety of materials studied in this context, organic and polymer materials have been considered as the most promising for practical applications.2 There are many factors which are required for observation of first-order nonlinear optical susceptibilities. Among them, one can emphasize noncentrosymmetry of particular molecules closely related to ground-state static dipole moments, collinearity between the dipole moments of the chromophore and surrounding background, and relative space alignment of the chromophore. In this work, we will explore the compound 3-phenylamino-4-phenyl-1,2,4-triazole-5-thione (C14H12N4S) which has numerous applications in biology. The compound 3-phenylamino-4-phenyl-1,2,4-triazole-5-thione has been recently synthesized and characterized by Wang et al.1 using elemental analysis and infrared (IR) and X-ray single-crystal diffraction. In general, the compounds containing a 1H-1,2,4-triazole group and its derivatives are very interesting because they exhibit some fungicidal activity and plant growth regulating activity.1,3,4 They also show antibacterial activity against puccinia recondite and root growth regulation for cucumber.1,5 The compound 3-phenylamino-4-phenyl-1,2,4-triazole-5thione can be used as a potential multidentate ligand to coordinate with various metallic ions.1 Wang et al. have synthesized the title compound and studied the crystal structure, second-order molecular hyperpolarizability, βµ, the vector components along the dipole moment direction, and thermodynamic properties. They found that βµ is greater than those for urea, p-nitroaniline (PNA), and for those of similar compounds 4-henyl-3-[(1,2,4-triazol-1-yl)methyl]-triazole-5* Corresponding author. Tel: +420 777729583. Fax: +420-386 361231. E-mail:
[email protected]. † South Bohemia University. ‡ Indian Institute of Technology Kanpur. § Technical University of Czestochowa.
thione6 and 3-benzyl-4-phenyl-1,2,4-triazile-5-thione.7 As natural extension to this work, we used the X-ray diffraction data of Wang et al. and optimized the structure by minimization of the forces acting on the atoms, keeping the lattice parameters fixed at the experimental values. Using the relaxed geometry, we have calculated the dispersion of linear and nonlinear optical susceptibilities using the full potential linear augmented plane wave (FP-LAPW) method which has proven to be one of the accurate methods8,9 for the computation of the electronic structure of solids within the framework of density functional theory (DFT). This may indicate suggestions of changes in the particular structural fragments of the titled molecular organic crystals to obtain a desirable optical response. For many organic materials there are contributions to the optical susceptibilities originating from the intramolecular and intermolecular interactions representing effective long-range ordering crystalline forces. Simultaneously, the present study is an attempt to understand the functionalization of interesting biological systems possessing both electronic charge transfer as well as chiralities. The search for novel materials with promising structural and optical properties is still a challenge for scientists. The theoretical methods of studying the relationship between structure and the optical susceptibilities of different order may be a better solution before venturing into the physical growth of the crystals. The ab initio DFT calculations were extensively applied for the computations of some essential structural and optical parameters. The extreme structural diversity and flexibility are some major advantages of growing crystals. Further, the efficiency of optical susceptibilities is inherently dependent upon its structural features. As a result, it would be valuable to probe and understand the packing motif of such an overwhelming bias in this class of crystals to choose a useful and general design tool for crystal engineering. We hope that our work will lead to comprehensive experimental studies of these new compounds which have promising linear and nonlinear optical susceptibilities. A detailed description of the optical properties of 3-phenylamino-4-phenyl-1,2,4-triazole-5-thione using a DFT full
10.1021/jp9092755 2010 American Chemical Society Published on Web 01/19/2010
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Figure 1. Crystal structure of 3-phenylamino-4-phenyl-1,2,4-triazole-5-thione.
potential method is very essential and would bring us important insights in understanding the origin of the electronic properties and their relation with dispersion of linear and nonlinear optical constants. In section 2, we present the basic theoretical aspects of the calculation method. The calculated linear and nonlinear optical susceptibilities are given in the section 3, and section 4 is devoted to the discussion of the obtained results. 2. Theoretical Calculation The single-crystal X-ray structural analysis shows that the 3-phenylamino-4-phenyl-1,2,4-triazole-5-thione compound crystallizes in the monoclinic space group Cc with lattice parameters a ) 15.232(3) Å, b ) 11.758(2) Å, c ) 8.6025(17) Å, β ) 121.66(3)°, Z ) 41 (see Figure 1). The Cambridge Crystallographic Data Centre CCDC-649123 contains the supplementary crystallographic data on 3-phenylamino-4-phenyl-1,2,4triazole-5-thione.10 The method used for the crystal growth is described in the ref 1. We have performed calculations using all-electron full potential linearized augmented plane wave (FP-LAPW) method to solve the Kohn-Sham DFT equations within the framework of the WIEN2K code.11 This is an implementation of the DFT12 with different possible approximation for the exchange correlation (XC) screening potentials. Starting from the atomic positions obtained by Wang et al.1 using X-ray diffraction, we have optimized the positions of the atoms in the unit cell structure (see Table 1) by minimization of the forces (1 mRy/au) acting on the atoms, keeping the lattice parameters fixed at the experimental values. Our calculated positions of the atoms are in very good agreement with the XRD data. From the relaxed geometry, the electronic structure and the chemical bonding can be determined and various spectroscopy features can be simulated and compared with experimental data. Once the forces are minimized, one can then find the self-consistent density at these positions by
TABLE 1: Calculated Atomic Position in Comparison with the Experimental One1 atom
x(exptl)
x(calcd)
y(exptl)
y(calcd)
z(exptl)
z(calcd)
S(1) N(1) N(2) N(3) N(4) H(1) H(2) H(3) H(4) H(5) H(6) H(7) H(8) H(9) H(10) H(11) H(12) C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) C(10) C(11) C(12) C(13) C(14)
0.15259(6) 0.8109(2) 0.9396(2) 0.96171(19) 0.0304(2) 0.789 0.0726 0.6744 0.5687 0.5818 0.7022 0.8061 0.0215 0.9751 0.8661 0.8081 0.8552 0.6795(3) 0.6168(3) 0.6245(3) 0.6957(3) 0.7586(3) 0.7498(3) 0.9776(3) 0.9502(4) 0.8857(3) 0.8508(3) 0.8782(3) 0.9398(2) 0.0469(2) 0.8989(3)
0.15258 0.8107 0.9397 0.96172 0.0306 0.7889 0.0724 0.6744 0.5686 0.5817 0.7022 0.8061 0.0216 0.9752 0.8660 0.8082 0.8554 0.6795 0.6168 0.6244 0.6957 0.7587 0.7499 0.9775 0.9500 0.8859 0.8508 0.8780 0.9395 0.0470 0.8987
0.11146(8) 0.1901(3) 0.0505(2) 0.1692(2) 0.0311(2) 0.2370 0.9776 0.3253 0.3166 0.1673 0.0284 0.0323 0.3781 0.5288 0.4988 0.3207 0.1689 0.2640(3) 0.2593(4) 0.1708(4) 0.0879(3) 0.0901(3) 0.1792(3) 0.3667(3) 0.4562(3) 0.4379(3) 0.3324(4) 0.2419(3) 0.2612(3) 0.1010(3) 0.8647(3)
0.11140 0.1903 0.0500 0.1602 0.0313 0.2374 0.9780 0.3255 0.3169 0.1670 0.0280 0.0327 0.3785 0.5292 0.4990 0.3200 0.1691 0.2645 0.2590 0.1707 0.0880 0.0904 0.1794 0.3665 0.4560 0.4382 0.3320 0.2417 0.2614 0.1012 0.8646
0.09397(9) 0.5085(3) 0.5852(4) 0.803(3) 0.7497(3) 0.5575 0.7645 0.2841 0.9719 0.8124 0.9675 0.2824 0.8476 0.9620 0.0684 0.0700 0.9577 0.2208(4) 0.034(5) 0.9388(5) 0.0332(5) 0.2207(4) 0.315(4) 0.8908(5) 0.9594(5) 0.0243(5) 0.0582(10) 0.9563(5) 0.8868(4) 0.8814(4) 0.6224(4)
0.09395 0.5084 0.5852 0.805 0.7498 0.5575 0.7644 0.2843 0.9718 0.8124 0.9671 0.2822 0.8477 0.9621 0.0686 0.0705 0.9576 0.2208 0.036 0.9390 0.0333 0.2205 0.313 0.8906 0.9593 0.0245 0.0242 0.9561 0.8866 0.8815 0.6223
turning off the relaxations and driving the system to selfconsistency. The exchange correlation potential was calculated using the generalized gradient approximation (GGA)13 as modified by Engel-Vosko.14 The Engel-Vosko GGA formalism15 optimizes the exchange correlation potential for band structure and gives a better representation of the energy gap. It is well-known in the self-consistent band structure calculation within DFT that both the local density ap-
Optical Susceptibilities of C14H12N4S proximation (LDA) and GGA approaches usually underestimate the energy gap’s values.15 This is mainly due to the fact that they are based on simplified model assumptions which are not sufficiently flexible to accurately reproduce the exchange correlation energy and its charge space derivatives. Engel and Vosko overcame this shortcoming and constructed a new functional form of GGA14 which is able to reproduce better energy gaps at the expense of less agreement in the exchange energy. This approach (EV-GGA) yields better band splitting compared to the GGA. For the electronic and optical properties we have applied the Engel-Vosko (EV-GGA) scheme.14 In order to achieve sufficient energy eigenvalues convergence which is crucial for the optical constant determination, the wave functions in the interstitial regions were expanded in plane waves with a cutoff Kmax ) 9/RMT, where RMT denotes the smallest atomic sphere radius and Kmax gives the magnitude of the largest K vector in the plane wave basis expansion. The muffin-tin radii were assumed to be 1.59 atomic units (au) for S, 1.05 au for N, 0.57 au for H, and 1.13 au for C. The valence wave functions inside the spheres were expanded up to lmax ) 10 while the charge density was Fourier expanded up to Gmax ) 14 au-1. Self-consistency was achieved by use of 300 k-points in the irreducible part of Brillouin zone (IBZ). The density of electronic states and the linear optical properties were calculated using 500 k-points of the IBZ. The nonlinear optical properties are calculated using 1500 k-points of the IBZ. The self-consistent calculations are considered to be converged when the total energy of the system is stable within 10-5 Ry. We would like to mention here that in our previous works16-19 we have calculated the linear and nonlinear optical susceptibilities using FP-LAPW method on several systems whose linear and nonlinear optical susceptibilities are known experimentally. We find very good agreement with the experimental data. Thus, we believe that our calculations reported in this paper would produce very accurate and reliable results. 3. Results and Discussion A. Linear Optical Response. We first consider the linear optical properties. The investigated crystals have monoclinic symmetry, which has several nonzero components of the second-order dielectric tensor. However, from general phenomenology only ε2xx(ω), ε2yy(ω), and ε2zz(ω) are dominant. These are the imaginary parts of the frequency-dependent dielectric function. Figure 2a shows the calculated imaginary part of the anisotropic frequency-dependent dielectric functions ε2xx(ω), ε2yy(ω), and ε2zz(ω). Broadening is assumed to be 0.1 eV which is typical for the broadening originating from the electron-phonon interactions. Following Figure 2a, we notice that there is some anisotropy between ε2xx(ω), ε2yy(ω), and ε2zz(ω). Generally, a compound that shows considerable anisotropy in the linear optical susceptibilities favors an important quantity in second harmonic generation (SHG) and optical parametric oscillator (OPO). From this figure it can be seen that the threshold energy (first critical point) of the yy dielectric function occurs at ∼3.25 eV for εxx 2 (ω), ε2 (ω), and zz ε2 (ω). This point gives the threshold for direct optical transitions between the highest valence and the lowest conduction band. This is known as the fundamental absorption edge. ε2xx(ω) and ε2yy(ω) display two major maxima situated at energies 4.25, 5.25 eV and 4.7, 5.0 eV, respectively, whereas εzz 2 (ω) displays only one major peak at around 5.25 eV. We note an insignificant hump on the left and right
J. Phys. Chem. B, Vol. 114, No. 5, 2010 1817 shoulders of the first peak of ε2xx(ω) and two humps on the xx yy left of the first εyy 2 (ω) peak. The magnitudes of ε2 (ω), ε2 (ω), zz and ε2 (ω) maxima decrease when we move to higher energies. It is known that the spectral peaks in the optical response are caused by the electric-dipole transitions between the valence and conduction bands. These spectral peaks in the linear optical spectra can be identified from the band structure. The calculated band structure along key symmetry directions is given in Figure 2b. The calculated band structure shows that this crystal possesses an indirect band gap. In order to identify the spectral peaks in the linear optical spectra, we need to consider the optical matrix elements. We indicate the transitions, giving the major structure for the three principal components ε2xx(ω), ε2yy(ω), and ε2zz(ω) in the band structure diagram. These transitions are labeled according to the spectral peak positions in Figure 2a. For simplicity, we have labeled the transitions in Figure 2a,b, as A, B, and C. The transitions A are responsible for the structures of ε2xx(ω), ε2yy(ω), and ε2zz(ω) in the energy range 0.0-5.0 eV; the transitions B -5.0 to 10.0 eV, and the transitions C 10.0-14.0 eV. These transitions occur between the occupied C-s/p, H-s, N-s/p, and S-s/p states to the unoccupied C-p, H-s, N-s/p, and S-s states. From the imaginary part of the dispersion of dielectric function ε2xx(ω), ε2yy(ω), and ε2zz(ω), the real part ε1xx(ω), ε1yy(ω), and ε1zz(ω) was calculated using Kramers-Kronig relations.20 yy zz The results of our calculated εxx 1 (ω), ε1 (ω), and ε1 (ω) dispersions are shown in Figure 2c. The calculated ε1xx(0), ε1yy(0), and ε1zz(0) are 2.875, 2.891, and 2.741, respectively. For more details about the spectral features of the optical susceptibilities of the investigated crystal, we have calculated the reflectivity R(ω), absorption coefficient I(ω), optical conductivity σ(ω), and loss function L(ω)spectra. Figure 2d shows the calculated reflectivity spectra. We should emphasize that a reflectivity maximum around 5.5 eV for Rxx(ω), Ryy(ω), and Rzz(ω) arises due to interband transitions in the ultraviolet region. This material can therefore serve as possible shields for ultraviolet radiation. A reflectivity minimum at the energy 6.0 eV for Rxx(ω), Ryy(ω), and Rzz(ω) confirms the occurrence of a collective plasmon resonance. The depth of the plasma minimum is determined by the imaginary part of the dielectric function at the plasmon resonance frequency and is a representative of the degree of overlap between the interband absorption regions. The calculated absorption coefficient I(ω) is shown in Figure 2e; again it shows a considerable anisotropy between the three components. One can see that at high energies the absorption coefficient rapidly increases to achieve its maximum value at around 13.5 eV. In Figure 2f, we present the electron energy loss L(ω) spectra. The loss function is given by Im[-1/ε(ω)] where ε(ω) is the complex dielectric function and it is defined as ε(ω) ) ε1(ω) + Iε2(ω). The imaginary part ε2(ω) of dielectric functions was calculated from the momentum matrix elements between the occupied and unoccupied wave functions.21 The real part ε1(ω) was evaluated from the ε2(ω) by the Kramers-Kronig transformation. The main peaks in the energy loss function, which defines the screened plasmon frequency ωp,22 are located at 6.0 eV for Lxx(ω), and about 6.5 eV for both of Lyy(ω) and Lzz(ω). These main peaks correspond to the abrupt reduction of the reflectivity spectrum R(ω) and to the zero crossing of ε1(ω). As there are no experimental results for the spectral
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yy zz Figure 2. (a) Calculated εxx 2 (ω) (dark solid curve), ε2 (ω) (light dashed curve), and ε2 (ω) (light solid curve) spectra. (b) The optical transitions yy (ω) (dark solid curve), ε (ω) (light dashed curve), and εzz depicted on a generic band structure. (c) Calculated εxx 1 1 1 (ω) (light solid curve) spectra. (d) Calculated Rxx(ω) (dark solid curve), Ryy(ω) (light dashed curve), and Rzz(ω) (light solid curve) spectra. (e) Calculated absorption coefficient Ixx(ω) (dark solid curve), Iyy(ω) (light dashed curve), and Izz(ω) (light solid curve) spectra. (f) Calculated loss function of Lxx(ω) (dark solid curve), Lyy(ω)(light dashed curve), and Lzz(ω) (light solid curve) spectra. (g) Calculated refractive indices nxx(ω) (dark solid curve), nyy(ω)(light dashed curve), and nzz(ω) (light solid curve) spectra. (h) Calculated birefringence ∆n(ω).
features of the optical susceptibilities available for these compounds, we hope that our work will stimulate more works. B. Refractive Indices and Birefringence. The single crystal of 3-phenylamino-4-phenyl-1,2,4-triazole-5-thione possesses anisotropy of refractive indices determining the birefringence. This factor determines phase matching conditions for the second harmonic generation (SHG) and optical parametric oscillators (OPO). The birefringence can be calculated from the linear response function’s dispersion from which the anisotropy of the index of refraction is obtained by using the expression given in ref 20
n(ω) ) (1/ √2)[√ε1(ω)2 + ε2(ω)2 + ε1(ω)]1/2 We determined the value of the extraordinary and ordinary refraction indices dispersion. Following the definition the
birefringence as the difference between the extraordinary and ordinary refraction indices, ∆n(ω) ) n|(ω) - n⊥ (ω), where n|(ω) is the index of refraction for an electric field oriented along the c-axis and n⊥ (ω) is the index of refraction for an electric field perpendicular to the c-axis. Figure 2g,h shows the refractive indices and the birefringence ∆n(ω) for this single crystal. The birefringence is important only in the nonabsorbing region, which is below the energy gap. In the absorption region, the absorption will make it difficult to evaluate for these compounds and to be used as nonlinear crystals in optic parametric oscillators or laser frequency doublers and triples. We note that the shape of the ∆n(ω)curve shows strong oscillations around zero which could be broadened out by choosing a larger broadening. We find that the birefringence at zero energy is negative and equal to -0.05. C. Nonlinear Optical Response. The complex second-order (2) nonlinear optical susceptibility tensor χabc (-2ω;ω;ω) can be
Optical Susceptibilities of C14H12N4S
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(2) (2) (2) (2) (2) Figure 3. (a) Calculated Im χ(2) 111(ω), Im χ 112(ω), and Im χ 122(ω) spectra. (b) Calculated Im χ 133(ω), Im χ 211(ω), and χ 212(ω) spectra. (c) (2) (2) (2) Calculated Im χ(2) (ω) and Im χ (ω) spectra. (d) Calculated Im χ (ω) and Im χ (ω) spectra. (e) Calculated total Im χ(2) 222 233 323 331 111(ω) spectrum (2) along with the intra (2ω)/(1ω)- and inter (2ω)/(1ω)-band contributions. (f) Calculated Re χ111(ω) spectrum. (g) Calculated absolute value of -7 (2) χ(2) 111(ω) spectrum. The |χ 111(ω)| is multiplied by 10 , in esu units.
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generally written as the sum of physically different contributions in the form (see refs 23 and 24)
abc χinter (-2ω;ω;ω) )
(
∑
∑
]
[
ie3 2 a b c fVc (rVc;c + rcV;b )+ rVc 2 ω (ω 2p Ω cV,k cV cV - 2ω) 1 a c rcV )+ (ra rb + rVc;b ωcV(ωcV - ω) Vc;c cV 1 4 c b ra (rb ∆c + rcV ∆cV )ωcV - ω ωcV - 2ω Vc cV cV
abc χintra (-2ω;ω;ω) )
1 2 ωcV
[
a c rVc {rbcnrnV } 2fVc e3 + 2 p Ω cVn,k (ωnV - ωcn) ωcV - 2ω fVn fnc + ωnc - ω ωVn - ω
)
1 c b rcV ) (rb rc + rVc;a 2ωcV(ωcV - ω) Vc;a cV
]
b c b c c b rVc} ) (1/2)(rnV rVc + rnV rVc) is a symmetrized in which {rnV a a ) δcnPcn /Im ωcn, combination of the dipole matrix elements rcn which are in turn obtained from the dipole momentum matrix a , where δcn is a factor restricting the correction to elements Pcn pairs of bands involving one conduction and one intermediate band state. Superscripts a, b, and c refer to the Cartesian coordinates; V(c) indicates a valence (conduction) bands and n the intermediate band, which is either a valence or a conduction band. It was established by Aspnes25 that only one virtualelectron transitions (transitions between one valence band state and two conduction band states) give a significant contribution to the second-order tensor. Here we have ignored the virtualhole contribution (transitions between two valence band states and one conduction band state) because it was shown to be negative and more than an order of magnitude smaller than the virtual-electron contribution for these compounds. For simplic(2) (2) (-2ω;ω;ω) as χabc (ω). Since the investigated ity, we call χabc crystal belong to the point group Cc, there are 10 independent components of the SHG third-rank tensor, namely, the 111, 112, 122, 133, 211, 212, 222, 233, 323, and 331 components (1, 2, and 3 refer to the x, y, and z axes, respectively).26 These are (2) (2) (2) (2) (2) (2) (2) χ(2) 111(ω), χ112(ω), χ122(ω), χ133(ω), χ211(ω), χ212(ω), χ222(ω), χ233(ω), (2) (2) χ323(ω), and χ331(ω). The second-order nonlinear optical susceptibility is very sensitive to the value of the energy gap as shown in the above formulas. There is no experimental value for the energy gap of title compound. Since we have used the EV-GGA, we hope that our calculated energy would be close to the experimental one (whenever it is measured). Allowing for an underestimate in the energy band gap of around 5%,27,28 we had applied very small shift to the energy gap (scissor’s correction)17,23-26 of about 0.15 eV (5% of the calculated band gap) in order to compensate the underestimation of the band gap by EV-GGA. Generally, the nonlinear optical susceptibilities are more sensitive to small changes in the band structure than the linear optical properties. Hence any anisotropy in the linear optical properties is enhanced in the nonlinear spectra. This is attributed (2) (ω) involves to the fact that the second harmonic response χabc 2ω resonance in addition to the usual ω resonance. Both the ω and 2ω resonances can be further separated into interband and intraband contributions. The calculated imaginary parts of the second harmonic generation susceptibility are shown in Figure 3a-e. A definite enhancement in the anisotropy on going from linear optical properties to the nonlinear optical properties is
(2) TABLE 2: Calculated Total |χ111 (ω)| and the Total Re (2) (2) χ111 (ω) at λ ) 1064 nm, the Total |χ111 (0)|, the Total Re (2) χ111(0) and Intraband, Interband of the Real Part of the Dominant Component at the Zero Frequency
total |χ(2) 111(ω)| at λ ) 1064 nm Re χ(2) 111(ω) total at λ ) 1064 nm total |χ(2) 111(0)| Re χ(2) 111(0) total Re χ(2) 111(0) inter (2ω) Re χ(2) 111(0) inter 1ω) Re χ(2) 111(0) intra (2ω) Re χ(2) 111(0) intra (1ω)
0.191 × 10-7 esu ) 8.0pm/V 0.191 × 10-7 esu ) 8.0pm/V 0.097 × 10-7 esu ) 4.1pm/V 0.097 × 10-7 esu ) 4.1pm/V -0.012 × 10-7 esu 0.035 × 10-7 esu 0.046 × 10-7 esu 0.030 × 10-7 esu
evident (Figure 3a-e). We can identify the origin of the peaks in these figures as being 2ω/ω resonance of the peaks in the linear dielectric function. We have calculated the total complex susceptibility. We notice that χ(2) 111(ω) is the dominant component. (2) (ω) is shown in The real part of the dominant component χ111 (2) Figure 3f. The zero-frequency limit of Re χ111(0) and the total (2) (2) (0)| are listed in Table 2 along with the total |χ111 (ω)| at |χ111 different wavelengths. In Figure 3e, we show the 2ω and ω inter- and intraband contributions to the dominant component χ(2) 111(ω). One can see the opposite signs of the two contributions throughout the frequency range. This fact may be useful for molecular engineering of the crystals in the desirable directions. In particular, appropriate regulating by the contribution of the different signs allows to enhance the NLO effects. The valence band maximum (VBM) and the conduction band minimum (CBM) seem to be parallel. This gives an additional amplifying factor when one takes the integrals over the Brillouin zone, making the oscillator strength of the entire peak larger. As can be seen, the total second harmonic generation susceptibility is zero below half the energy band gap. The 2ω terms start contributing at energies ∼1/2Eg and the ω terms for energy values above Eg. In the low-energy regime (e1.63 eV) the SHG optical spectra are dominated by the 2ω contributions. Beyond 3.25 eV (values of the fundamental energy gaps) the major contribution comes from the ω term. (2) (ω) could be One would expect that the structures in Im χ111 understood from the structures in ε2(ω). Unlike the linear optical spectra, the features in the SHG susceptibility are very difficult to identify from the band structure because of the presence of 2ω and ω terms. But we can make use of the linear optical spectra to identify the different resonance leading to various (2) (ω) features in the SHG spectra. The first structure in Im χ111 between 1.63 and 3.5 eV is mainly from 2ω resonance and arises from the first structure in ε2(ω). The second structure between 3.5 and 4.5 eV is associated with interference between a ω resonance and 2ω resonance and associated with high structure in ε2(ω). The higher energy structure from 4.5 to 5.5 is mainly originated from ω resonance and is associated with the tail in ε2(ω). The lack of experimental data prevents any conclusive comparison with experiment over a large energy range. From an experimental viewpoint, one of the quantities of interest is the magnitude of SHG (proportional to the second-order susceptibility). We present the total absolute value of the SHG (2) (ω)| in Figure 3g. The tensor for the dominant component |χ111 first peak for this component is located at 2ω ) 2.5 eV with the peak values of 2.3 × 10-7 esu. Our calculations demonstrate the large anisotropy of some tensor components. 4. Conclusions We have performed first-principles FPLAPW calculations on the spectral features of the linear and nonlinear optical suscep-
Optical Susceptibilities of C14H12N4S tibilities of 3-phenylamino-4-phenyl-1,2,4-triazole-5-thione. We have reported optimized positions of the atoms in the unit cell by minimizing the forces on each atom. Our calculations based on the Engel-Vosko exchange correlation potential indicate that this compound is a semiconductior with an indirect gap of 3.1 eV. This compound shows some anisotropy in the linear optical properties leading to a strong birefringence which suggests its use as optic parametric oscillator or frequency doubler and tripler. Anisotropy in the linear optical properties leads to enhancement of the second harmonic generation. This compound has a high second harmonic generation with 10 nonzeroth (2) (ω) component is the dominant one with components. The χ111 second-order optical susceptibility of the total real part and the total absolute value at zero frequency of about 0.097 × 10-7 esu. We hope that our results will be verified by experimental studies. Acknowledgment. This work was supported from the institutional research concept of the Institute of Physical Biology, UFB (No. MSM6007665808). References and Notes (1) Wang, H.-Y.; Zhao, P.-S.; Li, R.-Q.; Zhou, S.-M. Molecules 2009, 14, 608. (2) Lee, K.-S., Ed.; Polymers for Photonic Applications; Springer: Berlin, 2002; Vol. 2. (3) Xu, L. Z.; Jian, F. F.; Qin, Y. Q.; Jiao, K. Chem. Res. Chin. UniV. 2004, 20, 305–307. (4) Genin, M. J.; Allwine, D. A.; Anderson, D. J.; Barbachyn, M. R.; Emmert, D. E.; Garmon, S. A.; Graber, D. R.; Grega, K. C.; Hester, J. B.; Hutchinson, D. K.; Morris, J.; Reischer, R. J.; Ford, C. W.; Zurenko, G. E.; Hamel, J. C.; Schaadt, R. D.; Stapert, D.; Yagi, B. H. J. Med. Chem. 2000, 43, 953–970. (5) Banting, L.; Nicholls, P. J.; Shaw, M. A.; Smith, H. J. Progress in Medicinal Chemistry; Elsevier Science: Amsterdam, 1989.
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