Vibrational spectra and non linear optical proprieties of l -histidine oxalate: DFT studies

Spectrochimica Acta Part A 79 (2011) 554–561

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Vibrational spectra and non linear optical proprieties of l-histidine oxalate: DFT studies A. Ben Ahmed a,∗ , N. Elleuch a , H. Feki a , Y. Abid a , C. Minot b a b

Laboratoire de Physique Appliquée (LPA), Faculté des Sciences, BP 802, Sfax 3018, Tunisia Laboratoire de Chimie Théorique (LCT), Université Pierre et Marie Curie, Paris VI, France

a r t i c l e

i n f o

Article history: Received 21 December 2010 Received in revised form 28 February 2011 Accepted 11 March 2011 Keywords: Crystal structure Hyperpolarizability DFT TD-DFT IR Raman

a b s t r a c t This paper presents the results of our calculations on the geometric parameters, vibrational spectra and hyperpolarizability of a nonlinear optical material l-histidine oxalate. Due to the lack of sufficiently precise information on geometric structure in literature, theoretical calculations were preceded by redetermination of the crystal X-ray structure. Single crystal of l-histidine oxalate has been growing by slow evaporation of an aqueous solution at room temperature. The compound crystallizes in the non-Centro symmetric space group P21 21 21 of orthorhombic system. The FT-IR and Raman spectra of l-histidine oxalate were recorded and analyzed. The vibrational wave numbers were examined theoretical with the aid of Gaussian98 package of programs using the DFT//B3LYP/6-31G(d) level of theory. The data obtained from vibrational wave number calculations are used to assign vibrational bands obtained in IR and Raman spectroscopy of the studied compound. The geometrical parameters of the title compound are in agreement with the values of similar structures. To investigate microscopic second order nonlinear optical NLO behaviour of the examined complex, the electric dipole tot , the polarizability ˛tot and the hyperpolarizability ˇtot were computed using DFT//B3LYP/6-31G(d) method. According to our calculation, the title compound exhibits non-zero ˇtot value revealing microscopic second order NLO behaviour. Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved.

1. Introduction The role in our modern society of telecommunications makes the field of photonics an extremely important area of technological innovation and research. Materials with high nonlinear optical (NLO) activity are very useful as electro-optic switching elements and for optical information processing. In this context, organic molecules appear as promising candidates since they have several advantages over the inorganic NLO homologues: (i) their dielectric constant and refractive index are much smaller, (ii) their polarizability is purely electronic, and (iii) they are compatible with the polymer matrix for flexible devices, and so forth [1–9,29]. The field of NLO organic molecules is dominated by donor acceptor substituted asymmetric linear molecules which, however, present important drawbacks such as a high tendency toward unfavorable aggregation, difficult non-centrosymmetric crystallization, and small off-diagonal tensor components [1–9]. lHistidine oxalate belongs to the large family of amino acid addition compounds which are known for their non linear optical properties (NLO) [10–15]. Recently, much progress has been made in the

∗ Corresponding author. Tel.: +21696933658. E-mail address: [email protected] (A.B. Ahmed).

development of theses organic materials having non centrosymmetric cell, large polarizability and non linear optical coefficients. Indeed, some l-histidine and l-arginine additions have second harmonic efficiency larger than potassium dihydrogen phosphate (KDP) [16,17]. Then, due to the lack of sufficiently precise information given in the previous work [18] on the geometrical parameters and especially that of hydrogen bond on one hand and due to the lack of a theoretical study on the other hand, the crystal X-ray structure had to be re-determined and theoretical calculations were carried out. This study is extended to the determination of the electric dipole moment tot , the isotropic polarizability ˛tot and the first hyperpolarizability ˇtot of the title compound.

2. Experimental 2.1. Preparation l-Histidine oxalate crystal was produce from aqueous solution with equimolar proportion of l-histidine (purity 99%) and oxalic acid. The synthesized compound was dissolved in doubly distilled water using a magnetic stirrer and filtered twice to remove the suspended impurities in the solution. Two weeks later, transparency crystals were obtained.

1386-1425/$ – see front matter. Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2011.03.033

A.B. Ahmed et al. / Spectrochimica Acta Part A 79 (2011) 554–561 Table 1 Crystal data and structure refinement of l-histidine oxalate.

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Table 2 The reduced atomic coordinates in the structure of l-histidine oxalate.

Empirical formula

C8 H11 N3 O6

Atom

x/a

y/b

z/c

Formula weight (g/mol) Temperature (K) Wavelength Crystal system Space group Unit cell dimensions (Å)

245.191 293 (2) K␣Ag 0.56087 Orthorhombic P21 21 21 a = 5.530 (2) b = 6.799 (3) c = 26.863 (8) V = 1010.0 (7) 4 1.6124 0.083 512.0 0.45 × 0.3 × 0.2 2.39–25 −8 ≤ h ≤ 8 0 ≤ k ≤ 10 −20 ≤ l ≤ 40 6504 2292 [R(int) = 0.041] 0.033 (5) Full-matrix least-squares on F2 3607/0/200 1.021 R1 = 0.045, wR2 = 0.095 R1 = 0.102, wR2 = 0.111 0.233 and −0.246

O1 O2 O3 O4 O5 O6 N1 N2 N3 C1 C2 C3 C4 C5 C6 C7 C8 H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11

1.45416 (31) 1.79706 (27) 1.22257 (24) 1.36491 (23) 0.91653 (25) 0.77133 (21) 1.10795 (34) 1.12460 (32) 1.22503 (31) 1.31554 (36) 1.30290 (42) 1.00397 (44) 1.48069 (41) 1.47613 (35) 1.58653 (35) 1.19407 (31) 0.93923 (29) 1.40050 (437) 1.05549 (644) 0.87399 (439) 1.08288 (495) 1.43837 (412) 1.65448 (434) 1.16153 (446) 1.13207 (445) 1.23493 (656) 1.56585 (401) 1.51472 (716)

0.54298 (24) 0.37812 (27) 0.21413 (24) 0.24948 (32) 0.23752 (35) 0.24299 (26) −0.06664 (28) −0.10044 (27) 0.39660 (30) 0.01956 (28) 0.04034 (33) −0.15147 (32) 0.10103 (31) 0.32544 (27) 0.42420 (31) 0.23308 (30) 0.23863 (31) 0.10779 (383) −0.07189 (611) −0.23974 (393) −0.14344 (416) 0.04383 (343) 0.06652 (366) 0.32891 (360) 0.38611 (402) 0.53188 (613) 0.36488 (339) 0.25022 (561)

0.43406 (6) 0.42183 (5) 0.17192 (5) 0.24924 (5) 0.28431 (5) 0.20716 (5) 0.47380 (7) 0.39466 (6) 0.35659 (7) 0.40715 (7) 0.45715 (8) 0.43531 (8) 0.36837 (8) 0.36508 (7) 0.41102 (7) 0.21597 (7) 0.23916 (7) 0.47839 (83) 0.51075 (128) 0.43819 (85) 0.36337 (99) 0.33512 (81) 0.37450 (84) 0.33131 (91) 0.38447 (93) 0.34050 (119) 0.33584 (80) 0.23307 (110)

Volume (Å3 ) Z Density calculated (Mg/m−3 ) Absorption coefficient ␮ (mm−1 ) F (000) Crystal size (mm3 ) Theta range for data collection (◦ ) Index ranges

Reflections collected Independent reflections Extinction coefficient Refinement method Data/restraints/parameters Goodness-of-fit on F2 Final R indices [I > 2 sigma(I)] R indices (all data) Largest diff. peak and hole (eÅ−3 )

2.2. Crystal structure determination The experiment was carried out on a parallelepiped single crystal using Enraf-Nonus C4D4 four circle diffractometer with Mo-K␣ radiation. The crystal structure was solved by direct methods using SHELXS-97. Full-matrix F2 least-squares refinement and subsequent Fourier synthesis procedures were performed by SHELXL-97. Successive refinements based on F2 leads to a reliability factors of R = 0.045. Anisotropy thermal displacement parameter refinement was used for all non-hydrogen atoms. The crystal data and structure solution and refinement details are given in Table 1. 2.3. Spectroscopic measurements Infrared spectroscopy is effectively used to identify the functional groups and to determine the molecular structure of the synthesized compound. In order to analyze qualitatively the presence of functional groups in l-histidine oxalate, FT-IR spectrum (Fig. 1) was recorded using Brukker FT-IR Spectrometer by KBr pellet technique in the range 400–4000 cm−1 . The Raman spectra (Fig. 2(a) and (b)) were performed at room temperature using a Dilor XY set-up. The excitation line was 488 nm. The laser beam was focused on to the sample through a ×50 microscope objective and the laser spot dimensions was around 10 ␮m2 , the laser power was kept less than 5 mW in order to avoid sample heating. As a matter of fact, the Raman spectra showed no evidence for sample degradation (line broadening, intensity losses). 2.4. Computational details The geometries were fully optimized without any constraint with the help of analytical gradient procedure implemented within Gaussian 98 program [19]. All the parameters were allowed to relax and all the calculations converged to an optimized geometry which corresponds to a true energy minimum revealed by the lack of imaginary values in the wave numbers calculations. Vibrational frequencies are calculated with B3LYP/6-31G (d) and then scaled by 0.963 [20]. Vibrational mode assignments were made by visual

inspection of modes animated by using the Molekel program [21] and also with the results reported for similar compounds. 3. Results and discussions 3.1. Structure description l-Histidine Oxalate (Fig. 3) crystallizes in orthorhombic space group P21 21 21 with four formula units in unit cell (Z = 4). The cell ˚ b = 6.799 (3) A, ˚ c = 26.863 (8) A˚ and dimensions are: a = 5.530 (2) A, V = 1010.0 (7) A˚ 3 . These results agree with that found by Dammak et al. The numbering scheme for l-histidine oxalate is shown in Fig. 3a. The reduced atomic coordinates are listed in Table 2. Selected measured bonds lengths and bonds angles together with the calculated ones are grouped in Tables 3 and 4, respectively. The asymmetric unit (Fig. 3a) contains one oxalate anion (C2 HO4 − ) and one l-histidine cation connected with N–H· · ·O and O–H· · ·O hydrogen bonds types. Both oxalate anions are stabilizing the structure Table 3 Comparison between observed and calculated bonds lengths of l-histidine oxalate. Bonds length (Å) Parameters

Observed

Calculated

 (%)

C1–C2 C2–N1 N1–C3 C3–N2 N2–C1 C1–C4 C4–C5 C5–C6 C6–O1 C6–O2 C5–N3 O4–C7 C7–C8 C7–O3 C8–O5 C8–O6

1.352 (3) 1.375 (3) 1.316 (3) 1.326 (3) 1.376 (3) 1.492 (3) 1.528 (3) 1.532 (3) 1.253 (3) 1.241 (3) 1.488 (2) 1.305 (2) 1.542 (2) 1.201 (2) 1.219 (2) 1.266 (2)

1.369 1.381 1.345 1.326 1.384 1.500 1.538 1.557 1.264 1.238 1.508 1.332 1.540 1.204 1.224 1.296

1.24 0.43 2.15 0.00 0.57 0.53 0.65 1.60 0.87 0.24 1.32 2.02 0.13 0.24 0.40 2.31

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Fig. 1. Atom numbering scheme of l-histidine oxalate. (a) The experimental results, (b) the optimized geometry.

Fig. 2. Molecular arrangement of l-histidine oxalate. The hydrogen bonds are shown as the dashed lines. (View along a direction.)

by forming hydrogen bonds with the l-histidinium cations. In the crystal packing (Fig. 4), two type of molecular arrangement forming a wave design across a axis are observed. The crystal data confirm the zwitterions form adopted by the l-histidine cation, with additional protonation of the N(1) and N(2) ring atoms. The oxalate anions are related to each other through two O–H· · ·O hydrogen bonds (Fig. 5) and form infinite chains. The l-histidine cations are joined together through three N–H· · ·O hydrogen bonds (Fig. 6). The

various hydrogen bond parameters are summarized in Table 5. The optimized parameters are in well agreement with the experimental data and the largest discrepancies do not exceed 2.4%. This discrepancies can be explained by the fact that the calculation relates to the isolated molecule where the intermolecular Coulombic interaction with the neighboring molecules are absent, whereas the experimental result corresponds to interacting molecules in the crystal lattice. The largest discrepancies between the calculated

Fig. 3. Chains of oxalate anions running along the crystallographic b direction.

A.B. Ahmed et al. / Spectrochimica Acta Part A 79 (2011) 554–561

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Fig. 4. Chains of l-histidinium cations running along the crystallographic b direction.

4000

3600

3200

2800

2400

2000

1600

1200

800

400

Fig. 5. FT-IR spectrum of l-histidine oxalate.

and experimental geometrical parameters are observed for X–H (X = N, O). Since large deviation from experimental X–H bonds may arises from the low scattering factors of hydrogen atoms in the Xray diffraction experiment we did not discuss N–H and O–H bonds lengths.

3.2. Vibrational study To the best of our knowledge, any theoretical vibrational study made on the title compound was found in the literature. Then, we have calculated the vibrational spectra (Figs. 7 and 8) of l-

Fig. 6. Calculated IR spectrum of l-histidine oxalate in the region 400–4000 cm−1 .

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Fig. 7. Raman spectra of l-histidine oxalate measured at room temperature in the two regions (a) 300–1800 cm−1 and (b) 2800–3400 cm−1 .

Fig. 8. Calculated Raman spectra of l-histidine oxalate in the region 300–3800 cm−1 .

A.B. Ahmed et al. / Spectrochimica Acta Part A 79 (2011) 554–561 Table 4 Comparison between observed and calculated bonds angles of l-histidine oxalate. Bonds angles (◦ )

559

Table 6 Observed and calculated frequencies (cm−1 ) of l-histidine oxalate. Calculated

Observed

Assignment

Parameters

Observed

Calculated

(%) (%)

Raman

IR

FT-IR

FT-Raman

C1–C2–N1 C1–N2–C3 C1–C4–C5 C2–N1–C3 C2–C1–C4 C2–C1–N2 C4–C5–C6 C4–C5–N3 C7–C8–O5 C7–C8–O6 N1–C3–N2 N2–C1–C4 N3–C5–C6 O1–C6–C5 O2–C6–O1 O2–C6–C5 O3–C7–C8 O4–C7–O3 O4–C7–C8 O6–C8–O5

107.97 (19) 109.91 (17) 113.61 (17) 108.58 (18) 133.35 (19) 105.33 (17) 112.61 (16) 110.43 (16) 119.73 (16) 113.38 (14) 108.21 (19) 121.30 (18) 110.65 (15) 116.60 (17) 126.53 (21) 116.87 (17) 121.39 (16) 126.09 (17) 112.52 (14) 126.88 (18)

106.42 109.43 114.11 109.25 134.29 106.86 111.16 112.96 118.42 113.66 108.02 122.82 109.76 115.68 128.90 115.38 123.46 125.20 111.31 127.90

1.42 0.43 0.43 0.61 0.70 1.43 1.28 2.40 1.09 0.24 0.17 1.23 0.80 0.79 1.83 1.27 1.67 0.70 1.07 0.80

3514 3338 3200 3002 2973 1798 1695 1616 1448 1350 1260 1172 1117 1024 930 884 809 650 590 496 412

3514 3387 3201 3005 2973 1793 1693 1616 1453 1389 1258 – – 1081 – 885 813 713 645 586 500 441

– – 3196s 2924s – 1715s 1603vs 1503vs 1404s 1342s 1217s – – 1079s – 863s 813s 709w 627s 518s 500s –

– – 3136s 3008vs 2976 1715vw 1620vw 1528s 1432vs 1342vs 1224s 1150m 1100m 1050w 900m 852m 816m 710w 618w 523w 495m 378vw

histidine oxalate by using DFT method with 6-31G(d) basis set. The frequencies of the calculated and observed bands are provided in Table 6. The vibration of l-histidine cation and oxalate anion appear in the 400–4000 cm−1 frequency range. As it can be seen from Table 6 a noticeable difference between the experimental and the calculated frequencies associated to the N–H, C–H, C O and C–N stretching were found. Such discrepancies were reported in the literature [2,7,8,15]. In fact, the bands calculated at 3514 cm−1 are assigned to the O–H stretching of oxalate anion. The band observed at 3196 cm−1 in the IR spectrum and at 3136 cm−1 in the Raman spectrum, calculated at 3201 and 3200 cm−1 , is assigned to the asymmetric NH3 + stretching. Two peaks observed at 3008 (2924 cm−1 in IR) and 2976 cm−1 in the Raman spectrum are usual range of appearance for asymmetric and symmetric stretching modes of –(CH2 )– groups, respectively. As it can be seen from Table 6 the calculated values of these modes (as (CH2 ) and s (CH2 )) are not sensitive to the environment. The bands observed at 1715 and 1432 cm−1 in the Raman spectrum, are assigned respectively to the asymmetric and symmetric stretching modes of COO− . In IR spectra, these modes appear at 1715 and 1404 cm−1 , respectively. The corresponding calculated values are 1798 and 1448 cm−1 with the Raman, 1793 and 1493 cm−1 with IR, respectively. The amino group of the l-histidine cation is protonated. The asymmetric and symmetric bending vibrations of NH3 + groups give the bands at 1620 cm−1 (1603 cm−1 in IR) and 1528 cm−1 (1503 cm−1 in IR), respectively. Inspection of Table 6 reveals that these modes are well reproduced by calculations. According to the X-ray data (Table 5) there are two hydrogen bonds types in the crystal. The hydrogen Table 5 Hydrogen-bonding geometries for l-histidine oxalate.

s, strong; w, weak; v, very; m, medium; asym, asymmetric; sym, symmetric; bend, bending; stretch, stretching; rock, rocking (asymmetric in plane bending); wag, wagging (symmetric out of plane bending); twisting (asymmetric out of plane bending); def: deformation.

˚ while bonds length of O–H· · ·O type range from 2.516 to 3.194 A, ˚ The weak Raman the N–H· · ·O types extends from 2.622 to 3.255 A. band located at 1100 cm−1 (calculated at 1117 cm−1 ) is assigned to the set of weak interactions including both N–H· · ·O. The weak Raman band located at 3338 cm−1 (3387 in IR) is assigned to the set of weak interactions including both N–H· · ·O, but the weak Raman located in 3514 cm−1 (3514 cm−1 in IR) is assigned to the set of weak interactions including O–H· · ·O. 3.3. Hyperpolarizability calculation As mentioned above, this study is extended to the determination of the electric dipole moment tot , the isotropic polarizability ˛tot and the first hyperpolarizability ˇtot of the title compound. It is well known that the non linear optical response of an isolated molecule in an electric field Ei (ω) can be presented as a Taylor series expansion of the total dipole moment, tot , induced by the field: tot = 0 + ˛ij Ej + ˇijk Ej Ek + · · · where 0 the permanent dipole moment, ˛ij is the linear polarizability, and ˇijk is the first hyperpolarizability tensor components. The isotropic (or average) linear polarizability is defined as [22]: ˛tot =

D–H· · ·A

D–H (Å)

H· · ·A (Å)

D· · ·A (Å)

D–H· · ·A (◦ )

N1–H2· · ·O1 N1–H2· · ·O2 N2–H4· · ·O3 N2–H4· · ·O6 N3–H8· · ·O2 N3–H7· · ·O5 N3–H7· · ·O4 N3–H9· · ·O6 O4–H11· · ·O6 O4–H11· · ·O5

1.035 1.035 0.919 0.919 0.911 0.892 0.892 1.018 0.935 0.935

1.597 2.608 2.166 2.199 2.108 1.953 2.533 1.924 1.581 2.615

2.622 3.255 2.911 2.991 2.947 2.802 3.149 2.912 2.516 3.194

169.93 120.34 137.58 143.84 152.79 158.26 126.70 162.94 177.40 120.52

[−x + 2, y − 1/2, −z + 1/2]; [−x + 2, y − 1/2, −z + 1/2]; [x − 1, y, z]; [x − 1/2, −y + 1/2, −z + 1]; [x − 1/2, −y + 1/2, −z + 1]; [x + 1, y, z]; [x + 1, y, z]; [−x + 2, y + 1/2, −z + 1/2].

O–H stretch N–H stretch NH3 + asym stretch CH2 asym stretch and C–H stretch CH2 sym stretch COO− asym stretch NH3 + asym bend and C–C stretch NH3 + sym bend COO− sym stretch CH2 twist and C–N bend C–C stretch and C–O stretch C–H in plane bend N–H in plane bend C–N stretch Ring sym stretch Ring sym stretch C–C def and C O def C–C def O–C O def C–N and C–C–O def O–H bend NH3 + rock

˛xx + ˛yy + ˛zz 3

First hyperpolarizability is a third rank tensor that can be described by 3 × 3 × 3 matrix. The 27 components of 3D matrix can be reduced to 10 components due to the Kleinman symmetry [23] (ˇxyy , ˇyxy , ˇyyx , ˇyyz , ˇyzy , ˇzyy ,. . . likewise other permutations also take same value). The output from Gaussian 98 provides 10 components of this matrix as ˇxxx , ˇxxy , ˇxyy , ˇyyy , ˇxxz , ˇxyz , ˇyyz , ˇxzz , ˇyzz , ˇzzz , respectively. The components of the first hyperpolarizability can be calculated using the following equation [24]: ˇi = ˇiii +

1 (ˇijj + ˇjij + ˇjji ) 3 i= / j

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Table 7 The electric dipole moment  (D) the average polarizability ˛tot (×10−24 esu) and first hyperpolarizability ˇtot (×10−31 esu) for l-histidine oxalate. x y z  ˛xx ˛yy ˛zz ˛xy ˛xz ˛yz ˛tot

ˇxxx ˇyyy ˇzzz ˇxyy ˇxxy ˇxxz ˇxzz ˇyzz ˇyyz ˇxyz ˇtot

2.7714 4.0260 −1.4988 5.1123 −17.0560 −12.3224 −14.6232 6.9149 0.3777 −1.7622 14.6672

5.2353 3.2065 −0.3525 −0.8647 4.4823 −2.0677 −0.3028 0.5066 −2.1579 −1.4825 10.2308

Table 8 Comparison of static first hyperpolarizability, polarizability, dipole moment, and HOMO-LUMO energy gap for the constituents of the title compound calculated with DFT//B3LYP/6-31G(d). Compound

 (D)

˛tot (×10−24 esu)

ˇtot (×10−31 esu)

EH–L (eV)

C2 HO4 C8 H12 N3 O6

5.12 5.11

3.66 14.66

3.79 10.23

0.23 0.17

Using the x, y and z components of ˇ, the magnitude of the first hyperpolarizability tensor can be calculated by:

 (ˇx2 + ˇy2 + ˇz2 )

ˇtot =

The complete equation for calculating the magnitude of ˇ from Gaussian 98 output is given as follows:

indicates that intermolecular hydrogen bonds have a substantial influence on the first hyperpolarizability. 4. Summary In this work, geometric parameters, vibrational frequencies and non linear optical properties of l-histidine oxalate have been investigated by DFT (B3LYP) method. The theoretical calculations were preceded by re-determination of the crystal X-ray structure. Single crystal of l-histidine oxalate has been growing by slow evaporation of an aqueous solution at room temperature. The title compound crystallizes in the non-Centro symmetric space group P21 21 21 of orthorhombic system. FT-IR and Raman spectra have been recorded in the range [400–4000] and [300–3400]. All the experimental vibrational bands have been discussed and assigned to normal mode or to combinations on the basis of our calculations. Non linear optical NLO behaviour of the examined complex was investigated by the determination of the electric dipole moment tot , the polarizability ˛tot and the hyperpolarizability ˇtot using the DFT//B3LYP/6-31G(d) method. The value of ˛tot for the title compound is predicted about 4 times larger than for the oxalate anion while the increment of ˇtot is about 2.7 times than for the corresponding one of oxalate. This clearly indicates that in acid–base hybrid crystals, hydrogen bonds play an important role not only in the creation of crystal structure and its stability, but also in the enhancement of the polarizability ˛ and the hyperpolarizability ˇ of the crystal due to the perturbation of the electronic structure of l-histidine and also due to the strong electron–phonon coupling.

 ˇtot =

2

2

(ˇxxx + ˇxyy + ˇxzz ) + (ˇyyy + ˇyzz + ˇyxx ) + (ˇzzz + ˇzxx + ˇzyy )

Since the values of the polarizability ˛tot and the first hyperpolarizability ˇtot of Gaussian 98 output are reported in atomic units (a.u.), the calculated values have been converted into electrostatic units (esu) (˛: 1 a.u. = 0.1482 × 10−24 esu; ␤: 1 a.u. = 8.6393 × 10−33 esu. Table 7 listed the B3LYP/6-31G(d) results of the electronic dipole moment i (i = x, y, z), polarizability ˛ij and the first hyperpolarizability ˇijk for l-histidine oxalate. The calculated dipole moment is equal to 5.1123 D (Debay). The highest value of dipole moment is observed for component y . In this direction, this value is equal to 4.0260 D. For direction x and z, these values are equal to 2.7714 D and −1.4988 D, respectively. The calculated polarizability ˛tot , is equal to 14.6672 × 10−24 esu. As we can see in Table 7, the calculated polarizability ˛ij have non zero values and was dominated by the diagonal components. The first hyperpolarizability value ˇtot of the title compound is equal to 10.2308 × 10−31 esu, which is 7.87 times that of urea (1.3 × 10−31 esu) [25]. The hyperpolarizability ˇ dominated by the longitudinal components of ˇxxx , ˇyyy , ˇxxy , ˇxxz and ˇyyz . Domination of particular components indicates on a substantial delocalization of charges in these directions. In directions of ˇzzz , ˇxzz , ˇxyy , ˇxyz , and ˇyzz the values of components are relatively medium. In other directions, the particular components are practically equal to 0. In order to investigate the effect of the hydrogen bonds we have calculated tot , ˛tot and ˇtot of the oxalate anion. As shown in Table 8, the value of ˛tot for the title compound is predicted to be about 4 times than for the corresponding one of oxalate anion while the increase of ˇtot is about 2.7 times that of oxalate. Similar results have been reported in our previous works [26–28]. To understand this phenomenon in the context of molecular orbital picture, we examined the molecular HOMOs and molecular LUMOs generated via Gaussian 98. The calculated energies gaps are listed in Table 8. As it can be seen, the compound having the higher ˇtot value, correspond to the low HOMO-LUMO energy gap. This result

2

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