NLO and NBOAnalysis of Sarcosine-Maleic Acid by Using HF and B3LYP Calculations

We report a theoretical study onmolecular structure, vibrational spectra, nonlinear optical (NLO), and natural bond orbital (NBO) analysis of sarcosine-maleic acid (C7H11NO6) in the ground state calculated by using the Hartree-Fock (HF) and density functional method (DFT/B3LYP) with 6–31++G(d,p) basis set. We repeat NBO calculations with 6–31G(d,p) basis set so as to see the diffuse function impact on NBO analysis. Stability of the molecule arising from hyper conjugative interactions and charge delocalization has been analyzed using NBO analysis. NBO analysis shows that there is a O–H⋯O and N–H⋯O hydrogen bond in the title compound, which is consistent with the conclusion obtained by the analysis of molecular structure. e calculated HOMO and LUMO energies show that charge transfer occurs within the molecule. Also, these results are supported by the NLO parameters. Finally, the calculated results were applied to simulate infrared and Raman spectra of the title compound which showed good agreement with experimental ones.


Introduction
e development of organic NLO materials for device applications requires a multidisciplinary effort involving both theoretical and experimental studies in the �elds of chemistry, physics, and engineering.Quantum-chemical calculations have made an important contribution to the understanding of the electronic polarization underlying the molecular NLO processes and the establishment of structure-property relationships [1,2].Reliable structure-property relationships, where property here refers to linear polarizability (⟨⟩), and �rst-(⟨⟩) are required for the rational design of optimized materials for photonic devices such as electrooptic modulators and all-optical switches.
Nonlinearity in organic chromophores can be synthetically modulated by varying the composition or length of conjugated -systems, and by evaluating the effects of various electron-donor and -acceptor groups.However, the electron richness or de�ciency of the aromatic rings cannot be predicted reliably on the basis of the calculated ring atom charge densities as these quantities are rather sensitive to the quality of the basis sets employed.Since the NLO properties depend on the extent of charge transfer (CT) interaction across the conjugative paths and the electron transfer ability of an aromatic ring depends primarily on its ionization potential (IP) and electron affinity (EA) which, in the framework of MO theory and Koopman's theorem, are, respectively, equal to the negative of HOMO and LUMO energies, a reliable trend of the electron releasing/withdrawing strengths of the heterocycles may be predicted on the basis of the calculated frontier orbital energies [3,4].
Natural bond orbital (NBO) analysis [5] was originated as a technique for studying hybridization and covalency effects in polyatomic wave functions.e work of Foster and Weinhold was extended by Reed et al., who employed NBO analysis that exhibited particularly H-bonded and other strongly bound van der Waals complexes [6].Ab initio wave functions transformed to NBO form are found to be in good agreement with Lewis structure concepts and with the basic Pauling-Slater-Coulson picture [7,8] of bond hybridization and polarization.e �lled NBOs  of the "natural Lewis structure" are well adapted to describing covalency effects in molecules [6].However, the general transformation to NBOs also leads to orbitals that are unoccupied in the formal Lewis structure and that may be used to describe noncovalent effects.e symbols  and  * are used in a generic sense to refer to �lled and un�lled orbitals of the formal Lewis structure, though the former orbitals may actually be core orbitals (), lone pairs (),  or  bonds ( ), and so forth, and the latter may be  or  antibonds ( * ,  * ), extravalenceshell Rydberg () orbitals, and so forth, according to the speci�c case.
e antibonds represent unused valence-shell capacity, spanning portions of the atomic valence space that are formally unsaturated by covalent bond formation.e noncovalent delocalization effects are associated with    * interactions between �lled (donor) and un�lled (acceptor) orbitals, it is natural to describe them as being of "donoracceptor", charge transfer, or generalized "Lewis base-Lewis acid" type.
Sarcosine, also known as N-methylglycine , is a natural amino acid inhibiting two hydrogen atoms which are located at the nitrogen atom.ere have been several reports investigating qualitatively the crystal structure of sarcosine in pure [9] and made on several crystalline complexes with organic and inorganic acids derivatives [10][11][12][13][14][15][16][17].is amino acid is found naturally in star�sh, sea urchins and in the antibiotic actinomycin [18], and is also used in certain cosmetics [19].It is used in manufacturing biodegradable surfactants and toothpastes as well as in other applications.
Maleic acid ((Z)-Butenedionic acid) is an organic compound (sometimes named a dicarboxylic acid), a molecule with two carboxyl groups.Maleic acid is the cis isomer of butenedioic acid, whereas fumaric acid is the trans isomer of it [20].It is mainly used as a precursor to fumaric acid, but unlike its parent maleic anhydride, maleic acid enjoys few applications.is acid is naturally present in honey and over the years has been subjected to extensive investigation by several researchers [21].
DFT methods, particularly hybrid functional methods, have evolved to powerful quantum chemical tool for the determination of the electronic structure of molecules [32][33][34].In the framework of DFT approach, different exchange and correlation functionals are routinely used.Among these, the B3LYP combination which is developed by modifying the exchange functional in the hybrid BLYP method is the most used since it proved its ability in reproducing various molecular properties, including vibrational spectra.e combined use of B3LYP functional and standard basis sets provide an excellent agreement between accuracy and computational efficiency of spectroscopic properties for large and medium size molecules.
e FT-IR, FT-Raman, and X-ray crystallography of sarcosine-maleic acid was discussed in detail [18].In spite of its importance, mentioned above, there is not any theoretical calculation on the sarcosine-maleic acid.erefore, we made a deep investigation and studied the structure, vibrational frequencies and frontier molecular orbital energies, NLO, and NBO analysis of the title compound.e evaluations have been performed by means of the HF and DFT/B3LYP level of theory.Also, the chemical hardness () and soness () and electronegativity () parameters have been obtained by using molecular frontier orbital energies.

Computational Details
e molecular structures of the title compound in the ground state are optimized HF and B3LYP with 6-31++G(d p) basis set, then vibrational frequencies for optimized molecular structures have been calculated.e vibrational frequencies for these species are scaled by 0.9131 and 1.0013 for lowfrequency vibrations and 0.8970 and 0.9614 for the rest of vibrations, respectively [35].e RMS (root mean square) force criterion to 3 × 10 −4 and the SCF convergence criteria set to RMSDP = 12 × 10 −4 and MAXDP = 18 × 10 −4 (the maximum absolute value change for individual density matrix elements between two successive SCF cycles).Also, the total static dipole moment (), ⟨⟩, ⟨⟩ values were calculated by using the following equations [28,29,31]: where By using HOMO and LUMO energy values for a molecule, electronegativity, and chemical hardness can be calculated as follows:  = ( + )/2 (electronegativity),  = ( − )/2 (chemical hardness),  = 1/2 (chemical soness) where  and  are ionization potential and electron affinity, and  = − HOMO and  = − LUMO , respectively [36,37].
e natural bonding orbitals (NBO) calculations [38] were performed using NBO 3.1 program [39] as implemented in the Gaussian 09 package [40] at the HF and DFT methods with 6-31++G(d p) and 6-31G(d p) levels.e secondorder Fock matrix was used to evaluate the donor-acceptor interactions in the NBO basis [41].e interactions result in a loss of occupancy from the localized NBO of the idealized Lewis structure into an empty non-Lewis orbital.For each where   is the donor orbital occupancy,   and   are diagonal elements and ( ) is the off-diagonal NBO Fock matrix element.
All the calculations are performed by using Gauss-View molecular visualization program [42] and Gaussian 09 program package [40].
F 1: (a) e experimental structure of the sarcosine-maleic acid crystal and the atoms numbering scheme [18].(b) e calculated geometric structure of the sarcosine-maleic acid.
with 6-31++G(d, p) basis set are listed in Table 1 and are compared with the experimental data of the title compound.Figures 1(a) and 1(b) depict the experimental and theoretical structure of sarcosine-maleic acid.e crystal structure of a complex of sarcosine with maleic acid have already been reported [43].Also, the bond lengths and angles for the sarcosine were taken from the work of Mostad and Natarajan [9] and Krishnakumar et al. [44] and for the maleic acid were taken from Franklin and Balasubramanian [45] and Zhang et al. [46].O-H bond lengths (0.940 and 1.530 Å) in the maleic acid were taken from the work of Zhang et al. [46].For the title molecule, the O-H⋯O bond lengths predicted by HF/6-31++G(d, p) method are 0.966 and 1.627 Å and there are 0.986 and T 3: (a) Selected NBO results showing formation of Lewis and non-Lewis orbitals for sarcosine-maleic acid by using the HF method with 6-31++G(d,p) and 6-31G(d,p) basis sets.(b) Selected NBO results showing formation of Lewis and non-Lewis orbitals for sarcosine-maleic acid by using the B3LYP method with 6-31++G(d,p) and 6-31G(d,p)

Assignments of the Vibration Modes. Ilczyszyn et al.
have recently investigated the Raman and infrared spectra of the title compound, and have assigned bands vibrations [18].e experimental vibrational frequencies of sarcosinemaleic acid have been reported [18], and the experimental values are listed in Table 2, accompanied by the calculated data.e agreement between experimental and calculated frequencies for the monomer is excellent.Although different theoretical level gives different frequencies, seeing frequencies do not change the overall picture.e vibrational frequencies calculated by HF method are always higher than those computed by B3LYP method; no matter what basis sets are used.e HF frequencies are in worse agreement with experimental fundamentals than the other method since electron correlation in the HF calculations is neglected.e performance of local-and gradient-corrected DFT in calculating vibrational frequencies has shown that the computing vibrational frequencies provide good agreement with experimental fundamental ones.e group of bands in the 3150-3000 cm −1 region in the infrared and Raman spectra of both compounds can be assigned to C-H stretching modes.e C-H bands have been calculated at around 3077-2949 cm −1 using HF and 3084-2980 cm −1 using B3LYP method with 6-31++G(d, p) basis set.
e ionised carboxylic group of semimaleate ion has characteristic antisymmetric stretching vibration at approximately 1574 cm −1 and symmetric stretching vibration at approximately 1433 cm −1 [18].ese bands have been calculated at 1589 cm −1 and 1527 cm −1 for HF level.In the infrared spectra of Ilczyszyn et al. with the numerous submaxima at 3189, 2764, 2702, 2652, 2573, and 2420 cm −1 was assigned to the (O-H) (inter) and (N-H) modes.However, we have calculated them at 3369, 3333, and 2292 cm −1 with HF level and at 3361, 3283, and 1899 cm −1 with B3LYP level.
e comparative IR and Raman spectra of experimental and calculated HF and DFT are given in Figures 2 and 3, respectively.As can be seen from Table 2 and Figures 2 and  3 there is good agreement with experimental and theoretical ones.

Natural Bonding Orbital (NBO) Analysis.
e NBO analysis provides an efficient method for studying intraand intermolecular bonding and interaction among bonds, and also enables a convenient basis for investigating charge transfer or conjugative interaction in molecular systems.
NBO analysis provides the most accurate "natural Lewis structure" picture of , because all orbital details are mathematically chosen to include the highest possible percentage of the electron density (ED).NBO calculation was performed at the HF/6-31++G(d, p), HF/6-31G(d, p), DFT/B3LYP/6-31++G(d, p), and DFT/B3LYP/6-31G(d, p) levels.According to Goodman and Sauers, NBO results are more susceptible when using a balanced-basis set [47].e most important interaction between �lled (donor) Lewis-type NBOs and empty (acceptor) non-Lewis NBOs is reported in Table 3. e second-order perturbation theory analysis of Fock matrix in the NBO basis of the molecule has also been performed in Table 4.In NBO analysis [6], the hyperconjugative    * interactions play a highly important role.ese interactions represent the weak departures from a strictly localized natural Lewis structure that constitutes the primary "noncovalent" effects.e results of NBO analysis tabulated in Table 4 indicate that there is a strong hyperconjugative interaction LP2(O2)   * (C 2 -C 1 ) and  (O 6 -C 7 )   * (O 5 -H 11 ) for the title compound is 1.43, 1.10, 27.82, and 19.08 kcal/mol, respectively.e NBO bond polarization and hybridization changes associated with formation of the complex.Herein the percentage changes in the title compound are collected in Table 3.As can be seen in Table 3, the O 5 bond hybrid of the O 5 -H 11 bond gains 30.76% in s character and 68.89% in p character (with hybrid orbital sp 2.24 ).A more conspicuous discrepancy was seen for the H 2 O lone pairs, where the natural hybrids (as well as the numerical maximumoccupancy hybrids) suggest one pure p and one sp 0.57 lone pair [6].e  (O 6 -C 7 ) bond (hybrid orbital shows one pure p character) as donor and  * (C 6 -C 5 ) antibond (hybrid orbital shows one pure p character) as acceptor [ (O 6 -C 7 )   * (C 6 -C 5 )] participates the CT.e CT values are 6.46 and 6.67 kcal/mol (Table 4).e carboxylic group contributes as a better electron-donor.Likewise, the  (C 4 -O 3 )   * (C 6 -C 5 ) interaction supports the CT.
e second order delocalization energy of  (H 5 -N 1 )   * (C 1 -C 2 ) for the title compound is 0.82 and 0.73 kcal/mol with HF and B3YLP levels.is contributes bond polarization and hybridization changes.e N 1 bond hybrid of the H 5 -N 1 bond gains 25.72% in s character and 74.14% in p character (with hybrid orbital sp 2.88 ).e second  MEP has been used primarily for predicting sites and relative reactivities towards electrophilic and nucleophilic attack, and in studies of biological recognition and hydrogen bonding interactions [48][49][50].e calculated 3D MEP of the title compound was calculated from optimized molecular structure by using B3LYP/6-31++G(d, p) level and also shown in Figure 4.According to the results, the negative region (red) is mainly over the N and O atomic sites, which were caused by the contribution of lone-pair electrons of Mulliken atomic changes (a.u.) nitrogen and oxygen atom while the positive (blue) potential sites are around the hydrogen atoms.A portion of a molecule that has a negative electrostatic potential will be susceptible to electrophilic attack-the more negative is the better.It is not as straightforward to use electrostatic potentials to predict nucleophilic attack [28].Hence, the negative region (red) and positive region (blue) indicate electrophilic and nucleophilic attack symptoms.Also, a negative electrostatic potential region is observed around the O 6 atom.
e charge distribution on the molecule has an important in�uence on the vibrational spectra.e corresponding Mulliken's plot with different HF/6-31++G(d, p) and B3LYP/6-31++G(d, p) methods are shown in Figure 5. Figure 5 reveals the molecular charge distribution of the title compound.Generally, it is noted that the strong negative and positive partial charges on the skeletal atoms (especially for the selected compounds increase with increasing Hammett constant of substituent groups [27,51].ese distributions of partial charges on the skeletal atoms show that the electrostatic repulsion or attraction between atoms can give a signi�cant contribution to the intra-and intermolecular interaction. Table 5 indicates the values of some thermodynamical and molecular parameters (such as zero point energy,  HOMO ,  LUMO , Δ, , etc.) of sarcosine-maleic acid.ermal energy (E) was calculated as the sum of zero point energy and thermal energy corrections for molecular translation, rotation, and vibration at 298.15 K. Enthalpy at 298.15 K and 1 atm was obtained by adding RT to the electronic energy and thermal energy.ese data, as well as the Gibbs free energy, were obtained from the Gaussian output �le in hartrees and converted to kJ/mol (1 hartree = 2625.50kJ/mol).In previously works, the dipole moment and ZPE energies values of some molecules which included 1,2,3/1,2,4-triazole core were obtained to be ∼3.0-6.0D and ∼155.0-476.0kJ mol −1 [50,51].Besides, the   and  values for the maleic acid were found to be 32.409cal/mol K and 3.016 Debye [52].ese results are important to test the reliability of our results.As regard as, the results of the energies, dipole moment, entropy, and ZPE can be used to the new synthesis of some molecules which include sarcosine/maleic acid core.
e average HOMO and LUMO energies for the title compound using HF/6-31++G(d, p) and B3LYP/6-31 ++G(d, p) levels have been obtained to be −10.459eV, −7.592 eV (HOMO) and 0.418 eV, −2.588 eV (LUMO) (Table 5).ese results are consistent with respect to the different molecular structures calculated at semiempirical methods [53,54].Obtained average (for ), parameters from these energies using HF and B3LYP levels have been found to be 5.438, 2.502 eV (for ), 0.099 and 0.199 eV (for ) for the title compound (Table 5).According to these values, the average variation of  displays in�uence of the electron donating/withdrawing power of the title compound.
e polarizabilities and hyperpolarizabilities characterize the response of a system in an applied electric �eld.Electric polarizability is a fundamental characteristic of atomic and molecular systems.e donor and acceptor substituents provide the requisite ground-state charge asymmetry, whereas the -conjugation system provides a pathway for the redistribution of electric charges under the in�uence of electric �elds.Also, the variation of  values is supported by the electrostatic potential.Large  values characterize acids and small  values are found for bases.For any two molecules, electron will be partially transferred from the one of low  to that of high  (electrons �ow from high chemical potential to low chemical potential).
p-Nitroaniline (PNA) is one of the prototypical molecules used in the study of the NLO properties of molecular systems.In this study, the typical NLO material, PNA was chosen as a reference molecule; because there were no experimental values about the title compound in the literature.e relatively NLO compounds compared to PNA indicate their promising applications in NLO materials.erefore it was used frequently as a threshold value for comparative purposes and still continues to be a recognized prototype of organic NLO chromophores.Its hyperpolarizability was studied both experimentally and theoretically in various solvents and at different frequencies [55][56][57][58].
e variations of ⟨⟩, Δ, and ⟨⟩ for the title compound are tabulated in Table 6.ese variations are caused from the electron donating/withdrawing atom/group and ab initio calculations for the title compound.According to ab initio calculations, the variation of ⟨⟩ and ⟨⟩ values for the title compound is different (Table 6).e results of these variations with HF/6-31++G(d, p) level is larger than ones with the B3LYP/6-31++G(d, p) level.Also, the variation of ⟨⟩ values for the title compound explicitly decreases from the largest molecular structures to the smallest molecular structures.Calculated ⟨⟩ and ⟨⟩ values for the title compound are similar to the different theoretical and experimental studies for different molecular structures [25,28,29,31,[59][60][61][62][63][64].

Conclusion
Investigation throughout the work proves that the NLO and NBO analysis of sarcosine-maleic acid can be successfully predicted by ab-initio HF and B3LYP methods with 6-31++G(d, p) basis set.To investigate nonlinear optical properties, the compound which have sarcosine and maleic acid substituted by various electron donating/withdrawing atom/group have been used.Also, how NBO analysis change with different two methods and the consistency of these methods have also been investigated.e best �ttings between calculated and measured vibrational frequencies were achieved by B3LYP/6-31++G(d, p) level.With this level, the deviations between calculated and experimental values are ignorable for a given type of vibration.ese results are accurate enough with the deviations in the same order as anharmonicity corrections and effect from matrix or crystal.erefore, this study con�rms that the theoretical calculation of vibrational frequencies is quite useful for the vibrational assignment and for predicting new vibrational frequencies.e variation of ⟨⟩ and ⟨⟩ values with different two methods is different due to the different electron donating/withdrawing atom/group.e , , and  parameters of the compound are directly related to the HOMO and LUMO calculations.e ESP and MEP plots for compound show the distribution of charge of compounds with respect to the difference between positive and negative charge.e small  values display the  HOMO statement (i.e., Lewis base or nucleophile) and the larger values display  LUMO statement (i.e., Lewis acid or electrophile).To sum up, the negative region (red) is mainly over the N and O atomic sites, which were caused by the contribution of lone-pair electrons of nitrogen and oxygen atom while the positive (blue) potential sites are around the hydrogen atoms.e compound exhibits strong effective intra-and intermolecular charge transfer and shows large second-order nonlinearity.e sarcosine and maleic acid systems can be used as an effective -bridge in the design of new organic and inorganic acids molecules.

3. 4 .
Other Molecular Properties.e 3D plots of highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), electrostatic potential (ESP), electron density (ED), and the molecular electrostatic potential map (MEP) �gures for the title molecule at the B3LYP method with 6-31++G(d, p) level are shown in Figure4.e ED plot for molecule shows a uniform distribution.While the negative ESP is localized more over the oxygen atoms, the positive ESP is localized on the rest of the molecule.

F 4 :
Molecular surfaces of the sarcosine-maleic acid (obtained from B3LYP method).
T 1: Selected experimental and theoretical bond lengths and angles for sarcosine-maleic acid.
basis sets.T 4: (a) Second-order perturbation theory analysis of Fock matrix on NBO basis for sarcosine-maleic acid by using the HF and B3LYP methods with 6-31++G(d,p) basis set.(b) Second-order perturbation theory analysis of Fock matrix on NBO basis for sarcosine-maleic acid by using the HF and B3LYP methods with 6-31G(d,p) basis set.T 5: e calculated thermodynamic and molecular parameters of sarcosine-maleic acid.6: Total static dipol moment (), the mean polarizability (⟨⟩), the anisotropy of the polarizability (Δ), and the mean �rst-order hyperpolarizability (⟨⟩) for Sarcosine-maleic acid molecule.
a E(2) means energy of hyperconjugative interactions (stabilization energy).bEnergydifference between donor and acceptor i and j NBO orbitals.cF(i,j) is the Fock matrix element between i and j NBO orbital.LP(n)A is a valence lone pair orbital (n) on A atom.1.652ÅforB3LYP/6-31++G(d, p) method and it shows good agreement with the experimental data of 0.940 and 1.530 Å.In the study the N-H⋯O bond is calculated at 2.588 Å and 2.578 Å with HF and B3LYP method, respectively.But, this bond between sarcosine and maleic acid was not observed experimentally.According to the results in Table1, the bond lenghts and angles calculated by HF and B3LYP methods are in good agreement with the experimental values.Moreover, the result suggests that all the calculated bond lengths for this complex are overestimated to some extent.T