Synthesis, crystal growth and characterization of di-valine maleic – a new nonlinear optical material

Abstract

An amino acid salt di-valine maleic (VM) has been synthesized for the first time and single crystals were grown by the controlled evaporation of the aqueous solution at constant temperature (48 ± 0.03) °C. Crystal and molecular structure of VM was determined by single crystal X-ray diffraction analysis. X-ray crystallography reveals that VM possesses different two-dimensional supramolecular networks through hydrogen bonding interactions. Investigation of intermolecular interactions and crystal packing via Hirshfeld surface analysis clearly quantify the interactions within the crystal structure. The physicochemical properties of the grown crystal were characterized by thermal and optical analysis and measurement of hardness. The second harmonic generation efficiency of VM was investigated by powder method and found to be 0.3 times to KDP. The dipole moment, polarizability, first order hyperpolarizability and the HOMO–LUMO energy gap of VM were calculated using B3LYP functional and 6-31G(d,p) basis set to confirm the suitability of the crystal for nonlinear optical applications. First hyperpolarizability was found to be 5 times of urea.

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Introduction

Among all nonlinear optical (NLO) materials, organic materials are considered to be more versatile for their potentially high nonlinearities and rapid response compared with inorganic compounds. Other advantages of organic compounds involve amenability for synthesis, multifunctional substitutions, higher resistance to optical damage and maneuverability for device applications, etc. In the organic NLO class, amino acids are naturally chiral species and often crystallize in non-centrosymmetric space groups. Those materials have particular features, such as weak van der Waals and hydrogen bonds, wide transparency ranges in the visible regions and zwitterionic nature of the molecules.^1,2

L-Valine is a branched chain amino acid, which has aliphatic nonpolar side chain. It crystallizes in the monoclinic space group P2₁ with lattice constants a = 9.682(2) Å, b = 5.247(1) Å, c = 11.930(2) Å and β = 90.57°.³ Although the structures of several compounds of organic and inorganic acids combined with L-valine have been reported,^3–11 yet to best of our knowledge, very few of them have been reported as NLO materials. Attempts to discover such NLO crystals with relatively large nonlinearity are under progress in our laboratory. Hence, di-valine maleic was successfully synthesized and crystals with relative large size were grown. In the present paper we have discussed the growth of single crystal of di-valine maleic. The cell parameters and crystal structure of di-valine maleic was confirmed by the single-crystal X-ray diffraction analysis and indices of different crystallographic planes of the grown crystals were also determined. This was followed by DTA-TGA analysis, optical transmittance study and second harmonic generation (SHG) efficiency test.

Experimental

Synthesis and crystal growth

To synthesize di-valine maleic (VM), L-valine and maleic acid were added in a stoichiometric ratio of 1 : 1 to a beaker containing double distilled water. All the starting materials were of analytic reagent grade. The resulting mixture is continuously heated and stirred to form a homogeneous solution. At the point when a clear solution is obtained the pH of the solution was measured with a pH meter (Digital μpH METER GOLD 533) and it was found to be 1.02 at temperature 50 °C. The reaction equation is shown below.

2C₅H₁₁NO₂ + C₄H₄O₄ → 2C₅H₁₁NO₂·C₄H₄O₄

The clear solution was stirred with a magnetic stirrer for 5–6 h, filtered and left for crystallization. Crystalline materials of VM were obtained in 6–7 weeks time. The purity of the VM salt was improved by repeated cycles of dissolution and re-crystallization and confirmed by measuring the melting point at each stage.

For bulk crystal growth we first determined the solubility of VM in water in the temperature range 35–65 °C. For determination of solubility say at 60 °C, the temperature of the solution was kept above 60 °C accompanied with continuous stirring using a motorized magnetic stirrer to ensure homogeneous temperature and concentration throughout the entire volume of the solution. The saturated solution was allowed to reach equilibrium in 24 h at 60 °C in a temperature-controlled water bath and solubility of VM at 60 °C was determined gravimetrically. The same procedure was repeated for other different temperatures. The solubility curve thus obtained is shown in Fig. 1. From the solubility graph we observed that though the solubility temperature coefficient is positive yet its value is very low, hence slow evaporation of solvent is the best technique for the growth of good quality bulk crystal of VM. Accordingly bulk single crystals of VM of size 10 × 3.5 × 1.2 mm³, were grown from its aqueous solution by solvent evaporation method at constant temperature 48 °C using a microprocessor controlled constant temperature bath stabilized with an accuracy of ±0.03 °C. The photograph of the as-grown single crystals of VM is shown in the Fig. 2.

Fig. 1 Solubility curve of divaline maleic in water.

Fig. 2 As grown crystal of divaline maleic.

Characterization

Chemical composition of VM was determined by CHN analysis using 2400 Series II (PERKIN ELMER) CHN analyzer. The crystal and molecular structure of VM was determined by single crystal X-ray diffraction analysis. The X-ray data was collected at temperature 293(2) K using a Bruker APEX-II CCD diffractometer with graphite monochromatic MoKα radiation (λ = 0.7107 Å). Data reduction was carried out using the program Bruker SAINT.¹² An empirical absorption correction SADABS¹³ was applied. The structure of the title complex was solved by direct method and refined by the full-matrix least-square technique on F² with anisotropic thermal parameters to describe the thermal motions of all non-hydrogen atoms using the programs SHELXS97 and SHELXL97 ¹⁴ respectively. All calculations were carried out using PLATON¹⁵ and WinGX system Ver-1.64.¹⁶ All hydrogen atoms were located from difference Fourier map and refined isotropically. CCDC 947795 contains the supplementary crystallographic data for this paper.† Molecular Hirshfeld surface^17–22 of VM crystal structure has been created based on the electron distribution which has been calculated as the sum of spherical atom electron densities.^23,24 The Hirshfeld surface is unique,²⁵ for a particular crystal structure and set of spherical atomic electron densities. For each point on that isosurface, two distances are defined: d_e, the distance from the point to the nearest nucleus external to the surface, and d_i the distance to the nearest nucleus internal to the surface. The normalized contact distance (d_norm) based on both d_e and d_i, and the van der Waals (vdw) radii of the atom, given by the eqn (1) enables identification of the regions of particular importance to intermolecular interactions.¹⁷ The combination of d_e and d_i in the form of a 2D fingerprint plot^26–29 provides summary of intermolecular contacts in the crystal.¹⁷ The Hirshfeld surfaces are mapped with d_norm, and 2D fingerprint plots were generated using Crystal Explorer 3.0.³⁰

Thermogravimetric (TG) and differential thermal analysis (DTA) were carried out on SDTQ 600 V8.2 instrument with a heating rate of 5 °C min⁻¹ from 27 to 800 °C in a nitrogen atmosphere using VM as sample and alumina as reference. Using a polished crystal sample with the thickness of 1.2 mm, the optical transmission spectrum of the VM single crystal was recorded on the VARIAN, CARY 5000 spectrophotometer in the wavelength range from 200 to 2000 nm. The SHG measurements were performed using a Nd-YAG laser with fundamental radiation of 1064 nm as the optical source. Mechanical property of VM was analyzed by measuring hardness on its prominent growth facet. In our study indentations were made on (200) planes of VM with a Vicker indenter attached to a Leco microhardness tester (LM700). Loads were varied from 1 to 15 g with a regular increment of 5 g. Time of indentation is 10 s in all cases. Microhardness value was calculated using the formula given by eqn (2)

where H_v is the Vicker's hardness number in pascal, P is the applied load in newton and d is the diagonal length of the indented impression in meter. Owing to the observed micro cracks at the corners of the impressions made on the crystals, the maximum load applied was 15 g.

Theoretical and computational details

Quantum chemical calculations are precious and inexpensive tools for predicting the molecular NLO properties of materials such as dipole moments, polarizability and hyperpolarizabilities. In a medium the nonlinear optical effects arise when the medium interact with the electromagnetic field of intense laser beam. For an isolated molecule this nonlinear response can be represented by a Taylor series expansion of the dipole moment μ_i induced by the electric field³¹where α is the linear polarizability, μ₀ the static dipole moment and β is the first order hyperpolarizability. Here i, j, k denotes either of the x, y, z axes which are orthogonal. The component of the first order hyperpolarizability can be determined using the relation,

In presence on an applied field the first hyperpolarizability is a third rank tensor that can be described by a 3 × 3 × 3 matrix. The 27 components of the 3D matrix can be reduced to 10 components due to Kleinman symmetry.³² Using the x, y, z components the total static dipole moment, μ, the mean dipole polarizability (α), the anisotropy of polarizability (Δα) and the mean first static hyperpolarizability (β_tot) are defined as

α_tot = (α_xx + α_yy + α_zz)/3

We performed the calculations of the dipole moment, polarizability, anisotropy of polarizability and first hyperpolarizability using the Gaussian 09W program package.³³ All the components of Gaussian outputs are reported in atomic units so the calculated values have to be converted into electrostatic units. Molecular geometry optimization was completed by B3LYP functional and 6-31G(d,p) basis set. The optimized molecular geometry represents an isolated molecule with stationary points in the potential surface; no imaginary frequencies were obtained which confirms the convergence. The first hyperpolarizability and the related properties of VM molecule were calculated using the same basis set, based on finite field approach. We obtained a plot of the frontier molecular orbitals of the title compound to analyze the main atomic contributions for these orbitals. The importance of observing these plots was to determine the chemical reactivity of VM. The frontier orbitals (HOMO and LUMO) determine the way in which the molecule interacts with other species. The HOMO is the orbital that primarily acts as an electron donor and the LUMO is the orbital that largely acts as the electron acceptor.³⁴ The energy gap between these orbital are effectively responsible for the chemical and spectroscopic properties of the molecule.³⁵

Results and discussions

Identification

The chemical composition of VM as predicted by the CHN analysis matches well with the theoretically determined percentage composition and hence the formation of the crystal in single phase is confirmed and the molecular formula is henceforth calculated to be C₁₄H₂₆N₂O₈ (2C₅H₁₁NO₂·C₄H₄O₄). Finally the chemical composition and structural formula of VM was determined from the results of single crystal X-ray diffraction analysis. It is observed that the material crystallizes in monoclinic, space group C2, which is recognized as noncentrosymmetric system, thus satisfying one of the most important criteria for a crystal to be second order nonlinear. A summary of crystal data and relevant refinement parameters are given in Table 1.

Table 1 Crystal data and structure refinement for VM

Empirical formula	C7H13N1O4
Formula weight	175.18
Temperature	293(2) K
Wavelength	0.71073 Å
Crystal system, space group	Monoclinic, C2
Unit cell dimensions	a = 22.287(8) Å; α = 90 deg.
	b = 7.310(2) Å; β = 91.683(12) deg.
	c = 5.3371(17) Å; γ = 90 deg.
Volume	869.1(5) Å^3
Z, calculated density	4, 1.339 Mg m^−3
Absorption coefficient	0.110 mm^−1
F(000)	376
Crystal size	0.21 × 0.15 × 0.11 mm
θ range for data collection	1.83 to 24.99°
Limiting indices	−26 ≤ h ≤ 26, −8 ≤ k ≤ 8, −6 ≤ l ≤ 6
Reflections collected/unique	4058/1521 [R(int) = 0.0468]
Completeness to θ	100.0%
Absorption correction	Semi-empirical from equivalents
Max. and min. transmission	0.99 and 0.98
Refinement method	Full-matrix least-squares on F^2
Data/parameters	1521/114
Goodness-of-fit on F^2	1.068
Final R indices [I > 2σ(I)]	R1 = 0.0314, wR2 = 0.0787
R indices (all data)	R1 = 0.0319, wR2 = 0.0792
Extinction coefficient	0.104(6)
Largest diff. peak and hole	0.177 and −0.122 e Å^−3

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Structural description

The molecular view³⁶ of the asymmetric unit of VM is shown in Fig. 3. Structural study of VM reveals that the C7 atom of the maleic acid molecule is located in an inversion centre (−x + 2, y, −z + 1), however the valine conformer consists of one independent molecule in the asymmetric unit. The bond-lengths and angles are in normal range and are given in Table 2.

Fig. 3 ORTEP view and atom numbering scheme of VM with displacement ellipsoids at 30% probability level. Hydrogen atoms are shown as small spheres of arbitrary radii. Symmetry transformations used to generate equivalent atoms: −x + 2, y, −z + 1.

Table 2 Bond lengths [Å] and angles [°] for VM^a

Bond lengths [Å]		Bond angles [°]
a Symmetry transformations used to generate equivalent atoms: #1 (−x + 2, y, −z + 1).
O(2)–C(1)	1.259(2)	O(4)–C(6)–O(3)	124.48(16)
O(1)–C(1)	1.245(2)	O(4)–C(6)–C(7)	119.97(15)
O(3)–C(6)	1.299(2)	O(3)–C(6)–C(7)	115.52(14)
O(4)–C(6)	1.217(2)	C(7)#1–C(7)–C(6)	123.02(19)
C(6)–C(7)	1.481(2)	N(1)–C(2)–C(1)	109.27(12)
C(7)–C(7)#1	1.319(3)	N(1)–C(2)–C(3)	113.46(13)
N(1)–C(2)	1.500(2)	C(1)–C(2)–C(3)	111.28(14)
C(2)–C(1)	1.526(2)	O(1)–C(1)–O(2)	126.75(15)
C(2)–C(3)	1.540(2)	O(1)–C(1)–C(2)	116.10(13)
C(3)–C(4)	1.512(3)	O(2)–C(1)–C(2)	117.13(13)
C(3)–C(5)	1.516(3)	C(4)–C(3)–C(5)	111.66(19)
		C(4)–C(3)–C(2)	113.68(14)
		C(5)–C(3)–C(2)	112.03(17)

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The solid-state structure of VM is stabilized through N–H⋯O, O–H⋯O and weak C–H⋯O hydrogen bonding interactions (Table 3). Since the classical hydrogen bonds dominate the crystal packing, the VM structure allows us to distinguish between the effects of each type of interactions by which we can generate the individual substructures. In the first substructure, the C7 atom of the maleic acid in the molecule at (x, y, z) acts as donor to the carboxylate carbonyl oxygen atom O4 in the molecule at (2 − x, y, 2 − z) to generate a centrosymmetric R₂²(8) dimeric ring motif (homo synthon) centered at (1, 0, 1) (Fig. 4).

Table 3 Hydrogen bonding geometry of VM (Å, °)

D–H⋯A	d(D–H)	d(H⋯A)	d(D⋯A)	D–H⋯A	Symmetry
N(1)–H(1A)⋯O(1)	0.89	2.14	3.022(2)	168	x, y, −1 + z
N(1)–H(1B)⋯O(4)	0.89	1.98	2.853(2)	167	−1 + x, −1 + y, −1 + z
N(1)–H(1C)⋯O(1)	0.89	1.95	2.814(2)	163	1/2 − x, −1/2 + y, 1 − z
O(3)–H(3)⋯O(2)	0.82	1.71	2.522(2)	172	3/2 − x, 1/2 + y, 1 − z
C(5)–H(5C)⋯O(4)	0.96	2.56	3.456(4)	155	−1 + x, −1 + y, −1 + z
C(7)–H(7)⋯O(4)	0.93	2.57	3.448(2)	158	2 − x, y, 2 − z

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Fig. 4 Formation 2D assembly through weak C–H⋯O hydrogen bonds in VM.

Since the C7 atom is located in the inversion centre, on either side of the conformer generates dimeric ring motif propagating along (0 0 1) direction (Fig. 4). Interestingly, valine molecule plays an important role in binding the parallel layers of the dimeric ring motifs of maleic acid conformer. The methyl carbon C5 of the valine conformer in the molecule at (x, y, z) acts as donor to the carbonyl oxygen O4 of maleic acid in the molecule at (−1 + x, −1 + y, −1 + z) possess a weak hydrogen bonding interaction. In another end of the valine molecule, the carboxylate oxygen atom O2 of valine molecule acts as an acceptor to the carboxylate oxygen O3 of maleic acid at (3/2 − x, 1/2 + y, 1 − z), thus connecting the parallel layers of dimeric maleic acid conformers. Hence at each junction of the layers, valine molecules connect them by forming R₆⁵(28) ring motifs and propagates in (1 0 1) plane (Fig. 4).

In another substructure, the amino nitrogen atom N1 at (x, y, z) acts as donor to the carboxylate oxygen atom O1 in the molecule at (x, y, −1 + z) and this oxygen atom acts as acceptor to the N1 atom of the partner molecule through symmetry operation (1/2 − x, −1/2 + y, 1 − z), thus a tetrameric R₄⁴(14) ring motif is generated among the valine conformers of the structure. Repetition of this tetrameric ring motif builds a supramolecular network structure in (0 1 1) plane which is generated only through N–H⋯O hydrogen bonding interactions (Fig. 5).

Fig. 5 2D supramolecular network structure in (0 1 1) plane generated through N–H⋯O hydrogen bonding interactions.

In another substructure (Fig. 6), the amine N1 atom of valine molecule interacts with its carboxylate oxygen atom O1 along with the carbonyl oxygen atom O4 of the partner conformer. The amine nitrogen N1 at (x, y, z) acts as donor both to the carboxylate oxygen at (1/2 − x, −1/2 + y, 1 − z) and also to the carbonyl oxygen O4 of partner conformer at (−1 + x, −1 + y, −1 + z) through dual N–H⋯O hydrogen bonds. Thus a R₈⁸(38) ring motif is generated and repetition of this ring motif lead the molecules to propagate along (1 1 0) plane (Fig. 6).

Fig. 6 Another 2D supramolecular network structure in (1 1 0) plane generated through N–H⋯O hydrogen bonding interactions.

Hirshfeld surface

The X-ray crystallographic analysis reveals that the asymmetric unit of VM comprised of valine and maleic acid conformers. The Hirshfeld surfaces^17–22 of the VM structure was analyzed to clarify the nature of the intermolecular interactions and is illustrated in Fig. 7 showing the surfaces that have been mapped over a d_norm. During Hirshfeld surface calculation, the valine and maleic acid conformers have been analyzed individually to discern different types of intermolecular interactions and to obtain quantitative insight into the intermolecular interactions in molecular solids.

Fig. 7 Hirshfeld surface mapped with d_norm for VM.

For maleic acid conformer, the symmetrically generated counterpart has not been considered in the d_norm surface calculation. The Hirshfeld surfaces have been mapped over d_norm (−0.83 to 1.38 Å) and (−1.22 to 1.33 Å) for valine and maleic acid conformers respectively (Fig. 7). The surfaces are shown as transparent to allow visualization of the molecular moiety around which they were calculated. The d_norm surfaces reveal the close contacts of hydrogen bond donors and acceptors, but other close contacts are also evident. In d_norm surfaces, the large circular depressions (deep red) are the indicators of hydrogen bonding contacts whereas other visible spots are due to H⋯H contacts. The dominant O–H⋯O intermolecular interactions appear as distinct spikes in the 2D fingerprint plots^26–29 (Fig. 8) of the valine conformer in the region 1.53 Å < (d_e + d_i) < 1.62 Å whereas the spikes appearing in the region 1.53 Å < (d_e + d_i) < 1.86 Å belong to maleic acid conformer. The O⋯H contributions have the larger variety (21.1% in valine and 41.9% in maleic acid) than its H⋯O counterparts (28.0% in valine and 14.0% in maleic acid) for each molecule of the conformers. The proportions of O⋯H/H⋯O interactions comprising 49.1%, and 55.8% of the total Hirshfeld surface area for each molecule of valine and maleic acid conformer respectively (Fig. 8).

Fig. 8 Fingerprint plots of VM: full (left) and resolved into various contacts showing the percentages of contacts contributed to the total Hirshfeld surface of molecules.

In the title structure, no significant C–H interaction has been observed with C–H close contacts varying from 4.9% (valine) to 13.8% (maleic acid). Since the C7 atom of the maleic acid conformer is located in an inversion centre, the C⋯C close contact comprise 7.1% of the total Hirshfeld surface area of the molecule whereas the valine molecule comprises only 0.4% of the total Hirshfeld surface area. A significant difference between the molecular interactions in valine and maleic acid conformer in terms of H⋯H interactions is reflected in the distribution of scattered points in the fingerprint plots, which comprises 45.0% and 23.1% in valine and maleic acid conformers respectively.

Thermal properties

The TGA thermogram of the grown crystal is shown in Fig. 9. From TGA graph we see that the initial decomposition of the compound starts at 137.53 °C. Since this temperature is beyond 100 °C, the chance of existence of water of crystallization or physically absorbed water in VM crystal is ruled out. The endothermic peak around 231.41 °C corresponds to the melting point of VM. Sharpness of the peak indicates the good crystallinity of the material.³⁷ The sharp slope of the TG curve up to melting point indicates that the compound decomposes completely on melting. The DTA-TGA analysis does not show any kind of phase transition of VM crystal.

Fig. 9 TGA-DTA thermogram of divaline maleic.

Optical properties

Transmittance studies. The observed UV-vis-NIR spectrum obtained from a transparent and colorless crystal of thickness 1.2 mm of di-valine maleic (VM) is shown in Fig. 10. The transmittance lies in the range of 55–65% over the entire range of transmission (320–1860 nm). Thus both the fundamental and the second harmonic wavelength of the Nd-YAG laser can easily transmit through the crystal. The lower cut-off wavelength for the crystal is 279.9 nm.

Fig. 10 Transmittance spectrum of divaline maleic crystal. Inset: Tauc's plot.

To obtain information about the optical band gap (E_g) of our grown crystal, the absorption coefficient (α) is first obtained from the transmission spectrum as described by the following equation

where t is the thickness and T the transmittance of the sample. These absorption coefficient values were used to determine the optical energy gap (E_g) near the absorption edge using the Tauc's equation³⁸

αhν = A(hν − E_g)^m (6)

where A is a constant, E_g is the optical band gap, h is the Planck constant, ν the frequency of the incident photon and m is a constant which characterizes the nature of band transition. m can have values of 1/2, 3/2, 2 and 3 depending on the nature of the electronic transition responsible for the absorption. m = 1/2 for allowed direct transition, m = 3/2 for forbidden direct transition and m = 3 for forbidden indirect transition, while m = 2 refer to indirect allowed transitions.³⁹ Among all possible transitions, m = 1/2 is found to be more suitable for VM crystal since it gives the best linear curve in the band edge and hence the transition is direct transition. The variation of (αhν)² with hν (Tauc plot) for VM crystal is shown in the inset of Fig. 10. The value of E_g for the sample is calculated by extrapolating the linear region of the curve to meet the energy axis at (αhν)² = 0. The value of E_g thus obtained is found to be 3.82 eV.

Second harmonic generation efficiency measurement. The non-linear optical property was confirmed by the second harmonic generation (SHG) efficiency test of the grown crystals by the Kurtz powder technique.⁴⁰ The grown crystal was finely powdered to a uniform particle size of 120–150 μm and filled in the capillary tube. The capillary is subjected to a fundamental Q-switched Nd:YAG laser beam of wavelength 1064 nm, 8 ns pulse width and energy 6.3 mJ per pulse. Potassium dihydrogen phosphate (KDP) was taken as a reference material. Emission of green light confirms the second harmonic generation by VM crystal and this light of wavelength 532 nm was finally detected by a photomultiplier tube (PMT) and displayed on the oscilloscope (CRO). It observed that the measured SHG efficiency of VM was 0.3 times of potassium di-hydrogen phosphate (KDP).

Mechanical properties

The variation of Vickers hardness number (H_v) with load (P) for the plane (200) of di-valine maleic (VM) crystal of thickness 0.99 mm is shown in Fig. 11. The figure shows that the hardness value increases with increasing load. Thus the plane considered for study exhibit reverse indentation size effect (ISE).⁴¹

Fig. 11 Variation of microhardness with load of divaline maleic crystal. Inset: Meyer's plot.

In the case of the reverse ISE a specimen does not offer resistance or undergo elastic recovery, but undergoes relaxation involving a release of the indentation stress away from the indentation site. This leads to a larger indentation size which gives rise to a lower hardness at low loads.⁴¹ When the indenter just touches the surface of the crystal, dislocations are generated in the indenter region, so microhardness increases initially. Above a particular load, the microhardness attains a constant value due to the rearrangement of dislocations and mutual interactions of dislocations.⁴² The hardness and strength critically depend on the ease with which dislocations move. To understand the existence of ISE, we used the classical power law (7) known as Meyer's law,

P = Adⁿ (7)

log P = log A + n log d (8)

where A is a power fit constant, and the exponent n is the work hardening coefficient or the Meyer's index. The plot of log P vs. log d is shown in inset of Fig. 11. This curve is linear fitted and its slope gives the Meyer's index number ‘n’ of the sample. Combining eqn (2) and (7) we have

H_v = Bdⁿ⁻² (9)

From relation (9) it is clear that for normal ISE the value of ‘n’ should be less than 2. In the present study, the value of n is 2.958 which being greater than 2 confirms the reverse ISE. From careful observations on various materials, Onitsch⁴³ and Hanneman pointed out that n lie between 1 and 1.6 for hard materials, and it is more than 1.6 for soft materials. In the present study, n being greater than 2 confirms the prediction of Onitsch⁴³ that the material is soft and follows reverse ISE. From the hardness value, the yield strength (σ_v) can be calculated using the relation for Meyer's index n > 2,⁴⁴

where σ_v is the yield strength in MPa, H_v is the Vicker's hardness number in kg mm⁻². Also the elastic stiffness constant (C₁₁) calculated using Wooster's⁴⁵ empirical formula [C₁₁ = H_v^7/4] for different load is tabulated in Table 4. This gives an idea about stiffness of bonding between neighbouring atoms.

Table 4 The values of elastic stiffness constant (C₁₁) and the yield strength (σ_v) at different loads

Load (g)	Yield strength (σv) × 10^9 (Pa)	Stiffness constant (C11) × 10^16 (Pa)
1	15.34	8.47
5	24.74	19.55
10	33.49	33.23
15	36.19	38.04

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Computational studies

The optimization of the geometry of VM molecule was completed by using B3LYP functional and 6-31G(d,p) basis set. The dipole moment, polarizability and hyperpolarizability of the optimized structure were then calculated with the same functional and basis set and listed in Table 5. The value of dipole moment is maximum (3.3606 D approx.) along x-direction. Table 5 shows the calculated polarizability of VM molecule, α_ij, have non zero values and are dominated by the diagonal components. The theoretical calculation seems to be more helpful in the determination of particular components of β tensor than in establishing the real values of β. The biggest value of hyperpolarizability is noted along β_xxx direction and subsequently delocalization of electron cloud is more in this particular direction. The calculated first-order hyperpolarizability (β_tot) of VM is 4.4456 × 10⁻³⁰ esu, which is nearly 5 times that of urea [0.8103 × 10⁻³⁰ esu]. This high value of β and the non-zero value of μ are responsible for the second order nonlinear optical properties such as SHG.

Table 5 The dipole moment (μ), polarizability (α) and first hyperpolarizability (β) of VM derived from computational calculations

Dipole moment (μ) debye
μx	3.3606	μy	1.7952	μz	2.5396	μtot	4.5788
Polarizability (α) × 10^−23 esu
αxx	1.0334	αxy	−0.0641	αyy	0.9855	αtot	1.5958
αxz	−0.0108	αyz	−0.0073	αzz	0.8483	Δα	0.1675
Hyperpolarizability (β) × 10^−30 esu
βxxx	1.9985	βxxy	0.6042	βxyy	0.8027
βyyy	0.7489	βxxz	0.5543	βxyz	0.4933	βtot	4.4456
βyyz	0.6769	βxzz	0.7513	βyzz	0.5685
βzzz	0.6260

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The plot of the frontier molecular orbitals, HOMO and LUMO are shown in Fig. 12. The charge transfer character of the HOMO–LUMO transition is demonstrated by the topology of these orbitals.

Fig. 12 HOMO–LUMO plot of VM molecule.

It is found that the HOMO is localized mainly over the carboxyl group of the valine molecule while the LUMO are mostly delocalized over the C–C bonds of the maleic acid molecule. The energy eigenvalues and the energy gap for the HOMO and the LUMO as calculated at B3LYP/6-31G(d,p) level is shown in Fig. 12. The value of the energy gap is 2.9657 eV. This low HOMO–LUMO energy gap explains the probable intermolecular charge transfer (ICT) taking place inside the molecule enhancing the molecular hyperpolarizability. This asserts the suitability of the grown crystal for NLO application.

Conclusions

An organic nonlinear optical material, di-valine maleic (VM) has been synthesized and grown by slow evaporation of solvent method at room temperature and structurally characterized by single crystal X-ray diffraction. VM displays two-dimensional supramolecular frameworks in the solid-state and Hirshfeld surface analysis was successfully deployed for quantification of intermolecular interactions. Crystal of size 10 × 3.5 × 1.2 mm³ was obtained. The VM crystal has a wide transparency range in the entire visible and NIR range. The second harmonic generation efficiency of VHM is 0.3 times of KDP. The thermal behaviour of the grown crystals proved the absence of water of crystallization. From the mechanical measurements, it was observed that the hardness of VM follows reverse indentation size effect. The value of work hardening coefficient is 2.958. Calculated first order hyperpolarizability (β_tot) of VM is 4.4456 × 10⁻³⁰ esu, which is nearly 5 times that of urea [0.8103 × 10⁻³⁰ esu]. The low value of HOMO–LUMO gap might have enhanced the molecular hyperpolarizability too. Moreover the decrease in HOMO–LUMO gap explains charge transfer from electron donor to electron acceptor groups. Due to such specific properties we can consider VM crystal as a potential NLO material.

Acknowledgements

Authors are grateful to the DST-funded National Single Crystal X-ray Diffraction facility at the Department of Inorganic Chemistry, Indian Association for the Cultivation of Science, India, for data collection. S. K. Seth acknowledges University Grants Commission (New Delhi) India for Major Research Project [42-830/2013 (SR)].

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Footnote

† CCDC 947795. For crystallographic data in CIF or other electronic format see DOI: 10.1039/c6ra21466e

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