ARTICLE pubs.acs.org/JPCA
Mechanism of Linear and Nonlinear Optical Properties of the Urea Crystal Family Shi Jun Luo, Jun Tao Yang,* Wen Feng Du, and Amel Laref School of Science, Hubei Automotive Industries Institute, Hubei 442002, China ABSTRACT: First-principles calculations of the second-order optical response functions and the dielectric functions of urea [CO(NH2)2] and some of its derivatives such as monomethylurea (H2NCONHCH3, MMU), and N,N0 -dimethylurea (H3CHNCONHCH3, DMU) crystals are performed. On the basis of the density functional theory (DFT) in the local-density approximation (LDA), the highly accurate full-potential projected augmented wave (FP-PAW) method was used to obtain the electronic structure. Over a wide frequency range (0.010.0 eV), the dielectric constants and second-harmonic generation (SHG) susceptibilities of the urea crystal family have been obtained, and the results are in good agreement with the experimental values. The origin of the linear and nonlinear optical (NLO) properties of the urea crystal family has been analyzed by coupling the calculated electronic structure and optical spectrum. The prominent spectra of χ(2) are successfully correlated with the dielectric function ε(ω) in terms of single-photon and double-photon resonances. The virtual electron (VE) and virtual hole (VH) processes have also been performed for the urea crystal family. From the research into the electron deformation density, crystal configuration, substitutional group, and so forth, it is found that the origin of the SHG of the urea crystal family is the charge transfer due to the strong “pushpull” effect along the hydrogen bond, which favors a head-to-tail arrangement of the molecules and enhances the SHG response. The electron-donating substitutional group supplies more electrons to the electron-accepting group, and helps to form large dipoles in molecules. The influence on the NLO properties of the local symmetry of the substitutional group is also discussed in detail.
1. INTRODUCTION Crystalline urea [CO(NH2)2] is among the first organic materials found to have an application in nonlinear optics, specifically, in phase-matched second-harmonic generation (SHG) in the ultraviolet, as discussed in the review by Halbout and Tang.1 The electronic and optical properties of urea have been the focus of experimental and theoretical investigations211 over the past three decades. The theoretical researchers often adopted urea as a model to study nonlinear optical (NLO) properties due to its simple structure. The unit cell of the urea crystal with P421m space group symmetry is shown in Figure 1a. In addition to urea, some compounds belonging to the urea crystal family, such as monomethylurea (H2NCONHCH3) (MMU), N,N0 -dimethylurea (H3CHNCONHCH3) (DMU), and so forth, also exhibit SHG nonlinearity.1214 The unit cell of MMU crystal with P212121 space group symmetry is shown in Figure 1b. The orthorhombic DMU crystal can crystallize into the two crystal phases with space group Fdd2 (DMU-Fdd2)15 (as shown in Figure 1c), and space group P21212116 (DMU-P212121) (as shown in Figure 1e), respectively. Another monoclinic crystal phase of the DMU with space group Cc (DMU-Cc)17 (as shown in Figure 1d) was reinterpreted by Marsh,15 and we also calculated the linear and NLO properties of DMU-Cc crystal in order to study the influence of the crystal configuration on the NLO properties. r 2011 American Chemical Society
Zha and his co-workers performed the crystallization tests of MMU and DMU-Fdd2.18,19 The MMU crystal was grown by the mechanical direction limitation method and top seeding method. The growth habit of MMU is similar to that of urea, but the growth of MMU appears to be much more stable, and the MMU crystal has high structural and optical quality. The DMU-Fdd2 crystal was grown by the normal freezing method, and displays good mechanical and optical properties. The DMU-P212121 was obtained by slow evaporation from a concentrated solution of DMU in aqueous phosphoric acid.16 The geometry parameters of the five members of the urea crystal family (urea, MMU, and the DMUs) are given in Table 1, and their molecular sketches are shown in Figure 2. The urea crystal has been extensively studied since the 1970s for its outstanding optical properties by using different theoretical methods.20 Morrell and his co-workers4 performed a complete neglect of differential overlap/spectroscopic (CNDO/S) calculation on urea crystal. They obtained the electro-optic coefficient γ63 value, which is only a few percent of that of potassium dihydrogen phosphate (KDP). Svendens et al.5 calculated the Received: January 6, 2011 Revised: April 12, 2011 Published: April 28, 2011 5192
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Figure 1. The molecular packing of (a) urea, (b) MMU, (c) DMU-Fdd2, (d) DMU-Cc and (e) DMU-P212121 . The dashed lines indicate the calculated intermolecular hydrogen bonds, and the dotted lines indicate the calculated distances between C atoms of the methyl group and O atoms of the carbonyl group (Units: Å).
Table 1. Experimental and Calculated Lattice Parameters of the Urea Crystal Family (Units: Å) lattice parameters
a
expt.
calc. a
urea
a = b = 5.572, c = 4.86
a = b = 5.6960, c = 4.7585
MMU
a = 8.477, b = 6.981, c = 6.923b
a = 9.2396, b = 7.6092, c = 7.5457
DMU-Fdd2
a = 10.3483, b = 6.1408, c = 11.5913c
a = 10.1413, b = 6.0180, c = 11.3595
DMU-Cc
a = b = 6.1408, c = 10.3480d
a = b = 6.2536, c = 10.5550
DMU-P212121
a = 4.9790, b = 10.7750, c = 4.5764e
a = 5.3490, b = 11.7005, c = 5.0803
Reference 25. b Reference 26. c Reference 15. d Reference 17. e Reference 16.
Figure 2. The molecular sketches of (a) urea, (b) MMU, and (c) DMU. 5193
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The Journal of Physical Chemistry A dynamic second-order susceptibilities and electro-optic coefficients of urea with CNDO including an extended basic set. In 1993, Levine and Allan6 reported a first-principles calculation based on the local-density approximation (LDA) to calculate the linear and nonlinear optical parameters of urea, and pointed out that nonlinear local-field corrections are important for predicting the SHG susceptibility. In 2003, Lin et al.7 studied the linear and nonlinear optical properties of urea and gave the explanation of the origin of nonlinear effects through real-space atomcutting analysis. This method isolates the contribution of individual atoms or groups to the linear and nonlinear optical properties by removing spatial localized wave functions from the evaluation. They obtained the SHG coefficients at the static limit d14 = 1.04 pm/V. The investigation of density of states (DOS) shows that the framework OCN2 is an entity, and the contributions from the virtual electron (VE) process to NLO response are dominant in urea. Urea remains a subject of current research interest for frequency doubling of NLO properties in recent years. In 2008, Champagne and his co-workers9 calculated the linear and second-order nonlinear susceptibilities of urea by using a supermolecule approach on a large cluster by combining semiempirical calculations (i.e., TDHF/AMI) with density functional theory (DFT) and coupled-cluster methods through a multiplicative scheme. Their results of the second-order nonlinear susceptibilities, especially the linear properties, are evidently smaller than the experimental values. In 2009, Hermet10 and Ferrero11 also took on the theoretical investigation of the linear and nonlinear properties of urea crystal with different methods. They still obtained underestimated values, especially for the SHG response. The previous studies on the optical properties of urea crystal using different methods have been restricted to a determination of the response function at zero frequency. In this work, we studied the dielectric functions and the SHG response coefficients over a wide frequency range (0.010.0 eV) by using the full-potential projected augmented wave (FP-PAW)21 method, which is based on the DFT with the LDA. By using this method, we have studied the dielectric functions and the SHG response coefficients of 4-nitro-40 -methylbenzylidene aniline (NMBA) crystal in our previous work,22 and the calculated results of SHG response of NMBA are in good agreement with the experimental data. Moreover, it is found that the charge transfer (CT) due to the strong “pushpull” effect is the origin of the large NLO susceptibility, and the relationship between the electronic structure and linear and nonlinear optical properties is well explained. What is the influence of molecular structure, substitutional group, and crystal configuration on the nonlinear properties? The urea crystal and its derivatives;MMU, DMUFdd2, DMU-Cc, and DMU-P212121;have the same backbone of carboxide and amino N2CO, and different substitutional styles, molecular arrangements, and crystal configuration. Thus, the urea crystal and its four derivatives are the perfect objects for our researching interest. This paper is organized in the following way. In section 2, we give the details of our calculations. The dielectric functions and SHG coefficients of urea, MMU, and the DMUs are presented and discussed in part A of section 3. In part B of section 3, we investigate the influence of VE and virtual hole (VH) processes on the NLO response. In part C of section 3, we carry on research into the microscopic mechanism of NLO of the urea crystal family. Finally, a summary is given in section 4.
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2. THEORY AND COMPUTATIONAL METHOD In the present work, we calculated the band and electronic structure, the dielectric functions, and the SHG of the urea crystal family, using the DFT with LDA. The first-principles calculations for the urea crystal family were performed using the FP-PAW21 method, as implemented in the Vienna Ab-initio Simulation Package (VASP).23,24 In each primitive unit cell, there are two molecules for urea, four for MMU, and two for DMU-Fdd2, DMU-Cc, and DMU-P212121, respectively. In the self-consistent band and electronic structure calculations, the Γ-centered Monkhorst-pack scheme was used to generate the k-points in the Brillouin zone. Table 1 lists out the experimental and optimized lattice parameters of the urea crystal family. In the present calculations, the force convergence criterion is taken to be 10 3 eV/Å. The experimental lattice parameters of urea, DMU-Fdd2, and DMU-Cc are from the neutron diffraction, and that of MMU and DMU-P212121 are from X-ray diffraction. In general, the neutron diffraction and X-ray diffraction experiments result in the rather different lattice parameters, and the accuracy of the experimental lattice parameters for neutron diffraction is very low compared with X-ray diffraction. This is the reason why the theoretical corrections for experimental values are so different, as apparent in Table 1. The convergence criterion of the total energy 10 6 eV was adopted in the calculations, and a cutoff energy of 300 eV for plane wave expansion is used to ensure the numerical accuracy. The k-mesh of 11 11 11 was used for the urea crystal family, in addition to the kmesh of 11 11 7 used for DMU-Cc. Furthermore, the band and electronic structure were also applied to the calculations of the linear and nonlinear optical properties. The optical properties were calculated based on the independent-particle approximation, i.e., the excitonic effects and the local-field corrections were neglected. In our calculation, the imaginary part of the dielectric function ε(ω) due to direct interband transitions is given by the Fermi golden rule,27 (atomic units are used in the rest of this paper), i.e., 00
εaa ðωÞ ¼
X X 4π2 wk jpaij j2 δðεkj εki ωÞ ð1Þ 2 Ωω i ∈ VB, j ∈ CB k
where Ω is the unit cell volume, and ω is the photon energy. Also, VB and CB denote the valence and conduction bands, respectively. The dipole transition matrix elements Paij = Ækj|^pa| kiæ were obtained from the self-consistent band structures within the PAW formalism.28 Here the Ækiæ is the ith Bloch state wave function with crystal momentum k, and a denotes the Cartesian components. The real part of the dielectric function is obtained from ε00 (ω) by a KramerKronig transformation 2 ε ðωÞ ¼ 1 þ P π 0
Z
¥ 0
dω0
ω0 ε00 ðω0 Þ ω0 2 ω2
ð2Þ
Here P denotes the principal value of the integral. Given the complex dielectric function (ε0 þ iε00 ), all other linear optical properties such as refractive index, reflectivity, and absorption spectrum can be calculated. Following previous NLO calculations, the imaginary part of the second-order optical susceptibility due to direct interband 5194
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transitions is given by2931 00
00
ð2Þ
00
ð2Þ
ð2Þ
χabc ð 2ω, ω, ωÞ ¼ χabc, VE ð 2ω, ω, ωÞ þ χabc, VH ð 2ω, ω, ωÞ
ð3Þ where the contribution due to the so-called VE process (i represents the VB states, and j and l represent the CB states) is 00
ð2Þ
χabc, VE ð 2ω, ω, ωÞ ¼ ( Im½pajl Æpbli pcij æ π X X X wk δðεli ωÞ ε3li ðεli þ εji Þ 2Ω i ∈ VB j, l ∈ CB k
Im½paij Æpbjl pcli æ ε3li ð2εli εji Þ
δðεli ωÞ þ
16Im½paij Æpbjl pcli æ ε3ji ð2ε3li ε3ji Þ
)
δðεji 2ωÞ ð4Þ
and that due to the VH process (i and l represent the VB states, and j represents the CB states) is 00
ð2Þ
χabc, VH ð 2ω, ω, ωÞ ( Im½pali Æpbij pcjl æ π X X X δðεjl ωÞ wk ¼ ε3jl ðεjl þ εji Þ 2Ω i, l ∈ VB j ∈ CB k
Im½paij Æpbjl pcli æ ε3jl ð2εjl ε3ji Þ
Figure 3. (a) Band structure and (b) DOS and PDOS of urea.
δðεjl ωÞ þ
16Im½paij Æpbjl pcli æ ε3ji ð2εjl εji Þ
)
δðεji 2ωÞ ð5Þ
Here Æpbjlpcliæ = (1/2)(pbjlpcli þ pblipcjl) and εji = εkj εki. The real part of0 0 the second-order optical susceptibility is then obtained from (2) by the KramerKronig transformation χabc Z ¥ 2 ω0 χ00 ð2Þ ð 2ω0 , ω0 , ω0 Þ ð2Þ dω0 ð6Þ χ0 ð 2ω, ω, ωÞ ¼ P π 0 ω0 2 ω2 In the present calculations, the δ function in eqs 1, 4, and 52 is2 approximated by a Gaussian function δ(x) ≈ 1/[(πΓ)1/2]ex /Γ with Γ = 0.2 eV, and the same k-point grid as in the self-consistent calculation is used.
3. RESULTS AND DISCUSSION A. Dielectric Functions and SHG Coefficients. The total DOS and the partial DOS (PDOS) are plotted in Figure 3 and Figure . 4 for the urea crystal family. For simplicity, only the band structure of urea was plotted in Figure 3a, and it is found that it can be divided into three subregions. The lowest subregion below 15.0 eV is composed of C, N, and O 2s states, which are core states; the middle subregion is the VB from 11.0 eV to 0.5 eV, and the top of VB is mostly composed of N and O 2p states. The top-region is the CB, and the bottom of CB is mostly composed of C 2p states. The DOS indicates that the SHG effect of urea mostly comes from the group N2CO. The electron structures of MMU, DMU-Fdd2, and DMU-P212121 look similar to that of urea, and the top of VB and bottom of CB are also from the states of the group N2CO. Especially, the region from 7.0 to 4.5 eV of the VB is mainly composed from the states of the CH3 group for the derivatives of urea. Both the top of the valence bands (VBs) and the bottom of the conductive bands (CBs) for the urea crystal family are at the point G, and the energy bands are all nearly flat and not seriously
Figure 4. The DOS and PDOS of (a) MMU, (b) DMU-Fdd2, (c) DMU-Cc, and (d) DMU-P212121.
dispersive, and typical of the electronic structure of a molecular crystal. The calculated direct band gaps are 4.85, 4.62, 4.20, 3.93, and 4.43 eV for urea, MMU, DMU-Fdd2, DMU-Cc, and DMUP212121, respectively. As is well-known, the band gap calculated by the LDA of the DFT is usually smaller than the experiment data. To overcome this shortcoming, we take the so-called “scissors approximation” in the form proposed by Hughes and Sipe.32 The experimental values of the direct bandgap of urea, MMU, and DMU-Fdd26,18,13 are 6.18, 5.75, and 5.82 eV, respectively. To our knowledge, there are no report about the 5195
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Figure 5. Real and imaginary parts of dielectric functions ε(ω) of urea.
experimental values of the direct band gap of DMU-Cc and DMU-P212121. In the present calculations, we take the direct band gap of DMU-Cc and DMU-P212121 to be the same as that of DMU-Fdd2, 5.82 eV. Consequently, in the subsequent calculations of linear and nonlinear optical properties, the scissors energies 1.33, 1.13, 1.62, 1.89, and 1.39 eV were used for urea, MMU, DMU-Fdd2, DMU-Cc, and DMU-P212121, respectively. The calculated dielectric functions of urea are shown in Figure 5. We can find numerically that εxx = εyy, and this conclusion is consistent with the symmetry consideration. The calculated dielectric function εzz is different from εxx (εyy). The results show that urea crystals have two main crystallographic axes (a = b, c): the c-axis with the CdO bond is oriented along the z-axis, the a-axis and b-axis are oriented at 45 with respect to x and y, respectively.11 The spectrum εxx can be roughly divided into two regions: the low energy range from 6.18 to 10.0 eV and the high energy range from 10.0 to 30.0 eV. Below about 6.18 eV, the absorptive (imaginary) part of the dielectric function ε00xx is zero, and ε0xx tends to a constant as the photon energy approaches zero. The ε00xx becomes nonzero only above the 6.18 eV band gap and exhibits its highest peak at 7.3 eV, which is due to the transitions from the top of VB to the bottom of CB. In the high energy region, the ε00xx exhibits two prominent peaks at 12.7 and 16.4 eV, respectively. The ε00zz is very similar to ε00xx in the low energy region, while in the high energy region, it is roughly made up a broad hump starting from 10.0 eV. The theoretical calculated values of dielectric constants at zero frequency of urea are ε0xx(0) = 2.15 and ε0zz(0) = 2.50, which are in perfect agreement with the exprimental values,33 and it shows a moderate optical anisotropy. It is well-known that the refractive indices are obtained theoretically from the imaginary part of the dielectric function through the KramerKroning transformation. We also calculated refractive indices of urea by the relation √ of n(ω) = (1/ 2)[(ε0 (ω)2 þ ε00 (ω)2)1/2 þ ε0 (ω)]1/2. At the static states, our caluctulations of the refractive indexes nx = ny and nz are 1.465 and 1.580, respectively, and in good agreement with the experimental data nx = ny = 1.472 and nz = 1.579.33 The real and imaginary parts of calculated dielectric functions of MMU, DMU-Fdd2, DMU-Cc, and DMU-P212121 are showed in Figure 6ad, respectively. As seen in Figure 6, the peaks at 9.5 eV for ε00xx of MMU, 10.4 eV for ε00xx of DMU-Fdd2, 11.4 eV for ε00xx of DMU-Cc, and 9.4 eV for ε00yy of DMU-P212121 are notable, and we found that these peaks are all due to the main transition from the part of VBs from 7.0 eV to 4.5 eV to the bottom of CBs. From the DOS and PDOS of the urea crystal family, we noticed that
Figure 6. Imaginary and real parts of the dielectric functions ε(ω) of (a) MMU, (b) DMU-Fdd2, (c) DMU-Cc, and (d) DMU-P212121.
these peaks are due to the CH3 groups for the four urea derivatives. The calculated dielectric constants of the five crystals at zero frequency are presented in Table 2. The values show that the four urea derivatives are all optical anisotropy. The differences of the dielectric constant among the five crystals are not large, and the static dielectric constants of urea are the biggest among them. Urea crystal belongs to the point group 42m, and there are three possible independent components of the SHG tensor: (2) (2) χ(2) 123 = χ231 and χ312 . The calculated real and imaginary parts of the SHG coefficient χ(2) 123 are shown in Figure 7a. The SHG coefficient χ(2) 123 is significant in the entire range of the photon energy as seen in Figure 7a. Furthermore, for the photon energy smaller0 0 than 3.1 eV, the χ(2) 123 is purely dispersive. The absorptive (2) is 0nonzero only above about 3.1 eV, half of the band part χ123 0 (2) spectrum exhibits one prominent peak at about gap.34 The χ123 3.6 eV, and shows oscillations around zero in the energy range from 6.0 to 10.0 eV. The real part of χ(2) 123 remains nearly constant at low photon energies from 0.0 eV to about 1.5 eV, then increases steadily with the photon energy, and finally peaks at about 3.4 eV. The real part of χ(2) 123 begins to become negative at 3.6 eV and also oscillate between 6.0 and 10.0 eV. It can be seen from eqs 4 and 5 that the calculated χ(2) 123 spectra may have pronounced features due to both single- and double-frequency resonant terms. To analyze the feature in the calculated0 0 χ(2) 123 spectra, (2) with the it is helpful to compare the absolute value of χ123 absorptive part of the corresponding dielectric function ε00xx. Thereof both ω fore, the calculated ε00xx are shown in Figure 7c as a function 00 (2) is due to and ω/2. Clearly, the first sharp peak at 3.6 eV of χ123 double-photon resonance, and the peaks in the energy region above 6.2 eV come from both the single- and double-photon resonance. Considering the symmetry, there are three independent components of the SHG tensor for MMU and DMU-P212121 5196
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Table 2. Calculated Static Dielectric Constants and the Typical Components of SHG Susceptibilities (Units: pm/V) of the Urea Crystal Family ε(0) xx
yy
λ zz
din =
0
1/2χijk(2) 0
urea
2.15
2.15
2.50
(2) d14 = 1/2χ123
MMU
1.92
1.73
2.03
(2) d14 = 1/2χ123
DMU-Fdd2 DMU-Cc
2.19 2.22
2.06 2.09
2.35 1.97
(2) d15 = 1/2χ131 0 (2) d12 = 1/2χ122
DMU-P212121
1.96
1.96
2.16
(2) d36 = 1/2χ321
0 0
0
¥
1064 (nm)
597 (nm)
1.00
1.15
1.75
0.22
0.27
0.47
0.017 0.48
0.019 0.57
0.029 0.84
0.67
0.82
1.35
Figure 7. For urea, (a) real and imaginary parts of χ(2) 123(2ω,ω,ω), (b) the absolute value of the imaginary part of χ(2) 123(2ω,ω,ω), and (c) ε00xx(ω) and ε00xx(ω/2) (imaginary part of the dielectric function).
with point group D2222, five for DMU-Fdd2 with point group C2vmm2, and ten for DMU-Cc with point group Cvm. We calculated all the independent susceptibilities of the SHG of the four urea derivatives. The typical spectra of the SHG (2) (2) susceptibility χ(2) 123 of MMU, χ131 of DMU-Fdd2, χ122 of DMU(2) Cc, and χ321 of DMU-P212121 are plotted in Figure 8ad, respectively. The imaginary part of the SHG of MMU, DMUCc, and DMU-P212121 exhibits new prominent negative peaks compared with urea at ∼4.7, ∼5.7, and ∼4.7 eV, respectively. Correspondingly, the real part of the SHG of MMU, DMU-Cc, and DMU-P212121 shows a pair of positive and negative peaks at about the same positions. Surprisingly, the DMU-Fdd2 shows some unique features: the spectra oscillate around zero in the low-energy region, and the peaks are mostly in the high-energy region. The values of calculated dielectric constants at zero frequency and the typical SHG susceptibilities are presented in Table 2. The urea crystal family has a large different SHG, as apparent in Table 2. The SHG effect of the urea crystal family is closely related to their respective structures, and it will be further discussed in part C of section 3. B. The Influence of VE and VH Processes and Single- and Double-Photon Resonances on the NLO Response. To investigate the reason why urea’s derivative crystals exhibit such different second-order optical properties compared with that of urea, the contributions of the VE and the VH transitions to SHG
(2) Figure 8. Imaginary and real parts of (a) χ(2) 123 of MMU, (b) χ131 of (2) (2) DMU-Fdd2, (c) χ122 of DMU-Cc, and (d) χ321 of DMU-P212121.
effect were calculated in order to investigate the respective influence of the various transitions on the SHG effect, and the results are given in Figure 9. From eqs 4 and 5, we can identify the contributions of the VE and VH processes29,30 to the SHG response. Figure 9a shows that the contribution of the VE process to SHG for urea is dominant in the region from 3.1 to 4.3 eV, where the spectrum exhibits one prominent peak. In the high-energy region, the contribution of the VE process is also much lager than that of the VH process. Much the same as urea, the contribution of the VE process is dominant for all of the other four urea derivative crystals in the high energy region; however, in the low energy region, not only the VE process, but also the VH process has contributions to the first prominent peaks of the χ00 (2) spectra for MMU, DMU-Cc, and DMU-P212121. Furthermore, the second peaks of the χ00 (2) spectra of MMU, DMU-Cc, and DMU-P212121 are dominated by the VH process. For DMU5197
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Figure 10. The absolute value of the imaginary parts of SHG, ε00xx(ω) and ε00xx(ω/2) (imaginary part of the dielectric function) of (a) MMU, (b) DMU-Fdd2, and (c) DMU-Cc, and (d) ε00yy(ω) and ε00yy(ω/2) of DMU-P212121.
00
00
(2) (2) Figure 9. The VE0 0 and VH processes 0of (a) urea χ123 , (b) MMU χ123 , 0 00 (2) (2) (2) (c) DMU-Fdd2 χ131 , (d) DMU-Cc χ122 , and (e) DMU-P212121 χ321 .
Fdd2, the VE and VH process are all small in the low energy region, and the contributions to the SHG effect are almost due to the VE process in the high-energy region, while the little contribution of the VH process to the SHG effect is possibly due to the fact that the influence of the methyl groups is inhibited. The comparison of the absolute value of χ00 (2) of the urea derivatives with the absorptive part of the corresponding dielectric functions of both ε00 (ω) and ε00 (ω/2) is showed in Figure 10. Obviously for MMU, DMU-Cc, and DMU-P212121, the peaks of χ00 (2) in the low-enegy region are mostly from the 2ω (doublephoton) resonance, and the single-photon resonance has little contribution to SHG in the region. The second peak of the imaginary part of SHG, which does not exist for urea, corresponds to the peak of ε00 (ω/2) at ∼4.7 eV for MMU, ∼ 5.7 eV for DMU-Cc, and ∼4.7 eV for DMU-P212121. These second peaks of ε00 (ω/2) mostly come from the transitions from the energy region between 7.5 eV and 4.5 eV of VBs to the bottom of CBs. From a detailed analysis of the DOS and PDOS of MMU, DMU-Cc, and DMU-P212121, we find that the C2 (C3) 2p states and H 1s states of the CH3 group make the major contributions in this energy region from 7.5 eV to 4.5 eV. Consequently, these new peaks come from the contributions of the methyl groups. The result indicates that the influences of CH3 groups on the NLO properties of MMU, DMU-Cc, and DMU-P212121 are mainly from the VH process. The methyl groups play an important role in the NLO properties for MMU, DMU-Cc, and DMU-P212121. However, for the DMU-Fdd2 crystal, the absorptive part of χ(2) 131 shows small oscillations
around zero below the energy of 6.5 eV, only from doublephoton resonance, and the typical peaks are mostly found within the energy region between 6.5 and 8.0 eV. Figure 10b shows that 00 (2) are due to both the single- and double-photon resonance χ131 contributions above about 6.5 eV. C. Microscopic Mechanism of NLO of Urea Crystal Family. We have so far focused on the NLO properties of the urea crystal family. Now we turn our attention to study the microscopic mechanism of NLO properties from the viewpoint of the molecular structure and crystal configuration. Here, the electron deformation density is adopted to study the nature and extent of the polarization ensuing in the molecule. The electron deformation density of the molecule is the difference between the density of the molecule and that of the independent atom model (IAM), F FIAM,35 as shown in Figure 11. The molecules of the urea crystal family are linked by hydrogen bonds NH 3 3 3 O, and the calculated lengths of hydrogen bonds are labeled in Figure 1. The O atom of carbonyl group is involved in four hydrogen bonds for urea, three for MMU, and two for DMU-Fdd2, DMU-Cc, and DMU-P212121, respectively. The hydrogen bonds of urea and DMU crystals are symmetric; however, MMU crystal does not show this feature. Furthermore, the electron deformation maps show that the urea crystal family possesses intermolecular hydrogen bonds NH 3 3 3 O. Due to the intermolecular hydrogen bond, the valence electrons of the O atom are polarized toward the two H atoms of the nearest neighbor amino groups. The electron deformation maps suggest that the covalent groups are CO, NH, and/or CH3 for the urea crystal family. Furthermore, the CO group with the two adjoining N atoms constitute a big covalent group N2CO. The electron distributions of N2CO shift toward H atoms along the hydrogen bond direction through the CdO bond, and the electron distributions of amino and methyl groups are approximately along the same direction as that of N2CO. The critical points of the bonds OC, CN, and NH are displaced from the midpoint of the bond 5198
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Figure 11. Deformation density maps of (a) urea, (b)MMU, (c) DMU-Fdd2, and (d) DMU-P212121 with contour levels of 0.1e Å 3 (green lines are positive, red lines are negative, black lines are zero).
Table 3. Calculated Distance between the C Atom (Methyl) and the Neighboring O Atom of DMU-Fdd2 and DMU-Cc (Units: Å) DMU-Fdd2
DMU-Cc
C2 3 3 3 O1
C2 3 3 3 O1
C3 3 3 3 O1
C3 3 3 3 O1
C2 3 3 3 O1
C2 3 3 3 O1
C3 3 3 3 O1
C3 3 3 3 O1
molecule 1
4.154
4.070
4.154
4.070
5.523
4.532
5.517
4.510
molecule 2
5.310
4.343
5.310
4.343
5.517
4.532
5.523
4.510
molecule 3 molecule 4
5.310 4.343
4.343 4.070
5.310 4.343
4.343 4.070
4.510 4.510
4.261 4.261
4.333 4.333
4.241 4.241
approximately toward the O atom. The electron deformation maps show that the charge density is polarized along the CdO bond. The electron-withdrawing group carbonyl “CO” with high electron affinity gains electrons from the electron-donating group amino “NH2” and/or methyl “CH3” . Thus, the CT in intermolecules and intramolecules through the hydrogen bond will generally favor a head-to-tail (noncentrosymmetrical) arrangement of molecules, and thereby enhance the SHG response. Here, we discuss the influence of the molecular arrangement to the SHG effect. As seen in Figure 1, due to the effects of intermolecular hydrogen bonds in the direction of c axis, the molecules of urea and DMU-P212121 crystal pack into two parallel sequences, and the CdO bond orientations of the two parallel sequences are opposite. The molecular structures of urea and DMU-P212121 have bilateral groups, which are symmetric with respect to the backbone CdO group. Such parallel stacking of molecules favors a head-to-tail arrangement of molecules in one plane. For urea, one O atom is connected with the four hydrogen atoms of the neighboring molecules by the hydrogen bonds. The coplanar hydrogen bond helps the electron-withdrawing group carbonyl “CO” to gain more electrons from the electron-donating group amino “NH2”. The system forms a superdipole due to the CT, and it has a prominent second-order
optical susceptibility. Furthermore, the neighboring parallel sequences of urea are vertical to each other, and the neighboring molecules sit directly above the CO group. For DMU-P212121, due to the influence of CH3 groups, there are only two intermolecular hydrogen bonds, the angles between the neighboring parallel sequences is about 89.6,16 and the neighboring molecules no longer sit directly above the CO group. Consequently, urea has the strongest SHG effect due to the CT, and DMU-P212121 has the second strongest SHG effect within the urea crystal family. The MMU crystal has three noncoplanar asymmetry intermolecular hydrogen bonds; this feature does not favor the head-to-tail arrangement of molecules, and reduces the SHG effect. We find that the VH processes are enhanced for MMU, DMU-P212121, and DMU-Cc, but it is inhibited for DMUFdd2. Obviously, the DMU-Fdd2 and DMU-Cc crystals have the same molecules, and very similar electronic structure and molecular arrangement. The molecules of DMU-Fdd2 and DMU-Cc pack into two parallel sequences with the same direction of the CdO bond. Why is the SHG effect of DMU-Fdd2 so different from that of DMU-Cc, especially, in the low-energy region? Sarma and Cole36,37 have pointed out that the relative orientation and proximity of one molecule with respect to another one is also important to the polarization of a molecule in a crystal. This polarization anisotropy is 5199
dx.doi.org/10.1021/jp200164s |J. Phys. Chem. A 2011, 115, 5192–5200
The Journal of Physical Chemistry A therefore three-dimensional and thus (beyond the molecule) dependent upon supermolecular symmetry. Let us pay attention to the environment of the methyl groups of DMU-Fdd2 and DMU-Cc. In order to reveal the local symmetry of molecules for DMU-Fdd2 and DMU-Cc, the calculated distances between the C atom of methyl group and the O atom of the carbonyl of the two nearest neighbor molecules are listed in Table 3, and also presented in Figure 1c,d. We will give an example to help readers to understand. For the DMU-Fdd2, the distance 4.154 Å between the C2 atom and the O1 atom is equal to that between the C3 atom and the O1 atom, and the distance 4.070 Å between the C2 atom and the O1 atom is also equal to that between the C3 atom and the O1 atom. Similarly, the distances between the C2 atom of the methyl group and its neighboring C atoms of the other methyl groups are equal to the corresponding distances between the C3 atom and the neighboring C atoms of the other methyl groups. However, the DMU-Cc dos not possess the character; for example, the distance between the C2 atom and the O1 atom is 4.510 Å, and the distance between the C3 atom and the O1 atom is 4.532 Å. Thus, the methyl group of the DMU-Fdd2 has a more symmetrical environment than that of DMU-Cc. Previously we pointed out that the VH process for MMU, DMU-Cc, and DMUP212121 in the low energy region is mainly from the contribution of the methyl group. So, the VH process from the methyl for the DMU-Fdd2 is inhibited by its local symmetry. This may be the reason why the SHG of the DMU-Fdd2 is small compared with that of other members of the urea crystal family.
4. CONCLUSIONS We have studied the linear and nonlinear optical properties of the urea crystal family using the FP-PAW method based on the DFT in LDA. The calculated results show that the urea crystal family consists of typical insulators. The dielectric constants and SHG susceptibilities of the urea crystal family have been obtained from the wave functions and band energies, and the calculated results are in good agreement with the experimental values. From the research of the influence of the molecular structure, substitutional group, and crystal configuration on the NLO properties, we reach the following conclusions, which are useful for designing second-order NLO materials. (1) The origin of the SHG property is the CT due to the strong pushpull effect along the hydrogen bond direction through CdO π bond bridge. (2) The parallel and layer-like stacking of molecules favors a head-to-tail arrangement of the hydrogen bonds in one plane, and helps the system to form a superdipole. (3) The suitable substitutional group (methyl) plays an important role in the NLO materials. The local symmetry of the substitutional group evidently reduces the secondorder NLO effect, which should be noted in designing second-order NLO materials.
’ ACKNOWLEDGMENT The authors thank Dr. L. M. Kettle for a through reading of the manuscript. This work was supported by the China National Natural Science Foundation under Grant No. 10974048, and the excellent middle age and youth people creative team of the Science and Technology Foundation of the Educational Department of the Hubei Province No. T200805.
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