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Theoretical and computational studies of conformation,natural bond orbital and nonlinear optical properties ofcis-N-phenylbenzohydroxamic acid

Saadullah G. Aziz a, Shabaan A.K. Elroby a,b, Rifaat H. Hilal a,c, Osman I. Osman a,

a Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabiab Chemistry Department, Faculty of Science, Benisuief University, Egyptc Chemistry Department, Faculty of Science, Cairo University, Giza, Egypt

a r t i c l e i n f o

Article history:

Received 20 October 2013Received in revised form 2 December 2013Accepted 2 December 2013Available online 14 December 2013

Keywords:

N-phenylbenzohydroxamic acidTraditional hybridLong-range-correctedNLO propertiesNBO calculations

a b s t r a c t

The gas phase conformational and nonlinear optical properties of cis-N-phenylbenzohydroxamic acid (cis-NPBHA) keto and enol forms were studied applying traditional hybrid and long-range-corrected DensityFunctional Theory (DFT) andtime-dependent densityfunctional(TD-DFT) methods.The calculatedgeomet-ricalparameters for the twoisomersagreed satisfactorily withliteratureones. The ketoform waspredictedto be more stable than the enol counterpart by 10.7012.60 kcal/mol, and the Gibbs free energies for theconversion: enolketo were found to be 11.14 kcal/mol (B3LYP/6-311+G), 12.53 kcal/mol(CAM-B3LYP/6-311+G) and 13.28 kcal/mol (xB97XD/6-311+G). All the selected functionals havecomputed larger total hyperpolarizabilities for the enol tautomer compared to those of the keto rival. Thetraditional hybrid functional yielded higher total hyperpolarizabilities than those of the long-range-corrected ones. The total hyperpolarizabilities were nicely correlated with HOMOLUMO energy gapsand absorption maxima. The support of these molecular properties by natural bond orbital (NBO) calcula-tions was evaluated and discussed.

2013 Elsevier B.V. All rights reserved.

1. Introduction

Hydroxamic acids (R1CONOHR2) are known for their potencytowards combining with metal cations [1]. The most importantbiological use of hydroxamate moieties is their complex formationwith Fe(III) ions[2]. In addition to this vital role, hydroxamic acidsare commonly applied as reagents for colorimetric analysis[3,4], asdrugs for treating bacterial[5] and malaria diseases [6] or as agentsto inhibit urease activity[7]. The properties of hydroxamic acidshave been investigated theoretically[8]; to indicate the preferenceof neutral and anionic Z-amide form of benzohydroxamic acid over

its E counterpart. Ab initio calculations of formohydroxamic andacetohydroxamic acids showed that the E and Z isomers of the ketoform are more stable than those of the enol rival[9].

The conformational behavior of cis and trans isomers ofN-phenylbenzohydroxamic acid (NPBHA) in the gas phase and insolution was investigated by Ciofini[10]using MP2 and DFT meth-ods using the 6-31G(d) basis set. He attributed the relative stabilityof the cis form, over that of the trans one, to the possibility of exis-tence of intramolecular H-bonds in the former. Senthilnithy et al.[11] have complemented this conjecture and predicted the

preference for the Z-isomer of NPBHA derivatives in both gas phaseand water media using Complete Basis Set method (CBS-QB3).

We endeavour in this study, using Density Functional Theory(DFT) methods to probe the electronic and conformational struc-tures of cis-NPBHA keto and enol tautomers, and examine the ori-gin of their stability using mainly natural bond orbital (NBO)theory[12,13] that showed efficient technique to pinpoint theradix of hydrogen bonding[14]and hyperconjugative[15]interac-tions through second order perturbation energy (E(2)) given as:

E2 DEij qiF2

ij

De 1

where qi is the donor orbital occupancy, De is the difference be-tween the energy of an acceptor orbital (j) and a donor orbital (i)andFij is the off-diagonal (NBO) KohnSham Matrix.

The nonlinear optical (NLO) properties of cis-NPBHA isomers areofinterestin datastorage andelectro-optic applications[1618].Formolecules, the NLO properties are related to their hyperpolarizabil-ity(b) through the Einstein summation convention:

liE l0

i aijEj1

2bijkEjEk

1

6cijklEjEkEl 2

wherel0i is the dipole moment in the absence of the electric field(E) and a is the polarizability. It was anticipated that molecules with

2210-271X/$ - see front matter 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.comptc.2013.12.001

Corresponding author. Tel.: +966 2640000x69315; fax: +966 26952709.

E-mail address: oabdelkarim@kau.edu.sa(O.I. Osman).

Computational and Theoretical Chemistry 1028 (2014) 6571

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large hyperpolarizabilities give measurable NLO susceptibilities.Fortunately organic molecules are known to exhibit extremely largehyperpolarizabilities[19,20].

In this work, we intended also to estimate the NLO properties ofcis-NPBHA keto and enol forms using Density Functional Theory(DFT) methods. In these calculations, although traditional func-tionals are quite popular, long-range-corrected hybrid functionals[LC-DFT] [21,22] tend to be relatively superior in estimating hyper-polarizabilities [23,24]. In LC-DFT, the electron-electron Coulomboperator (1/r12) is given as a sum of a short-range (SR) and a longrange (LR) component:

1

r121 erfxr12

r12erfxr12

r123

where erf is the error function andx is the range separation param-eter. As a result the contribution to the exchange energy ELC-DFTx isseparated into:

ELC-DFTx ESR-DFT

x x ELR-HF

x x 4

As a result, the HartreeFock part, which constitutes a largerfraction of the exchange energy, is treated exactly as the

electronelectron distances increase. It is this correction that gaveimproved molecular susceptibilities.

These finding necessitated the use of both the traditional(B3LYP) and the long-range corrected functionals (e.g. CAM-B3LYP and xB97XD) in this DFT study. Our objective here is tojudge the advantage of these methods in evaluating the opticalproperties of cis-NPBHA tautomers.

2. Methods of calculations

All calculations were performed using the Gaussian 09Wpackage [25]. The traditional hybrid Becke, three-parameter,LeeYangParr (B3LYP) exchange correlation functions of theDensity Functional Theory (DFT) and the long-range-corrected

CAM-B3LYP andxB97XD functionals were applied using the splitvalence triple zeta [6-311+G] basis set. The geometries of cis-NPBHA keto and enol forms were fully optimized at the aforemen-tioned levels of theory. Frequency analysis calculations were per-formed to characterize the stationary points as minima and toevaluate zero-point energies (ZPE).

The natural bond orbital (NBO) calculations have beenperformed at the B3LYP/6-311+G level using NBO 3.1 [26] asimplemented in the Gaussian 09W software package[25]. Thesecalculations yielded second-order perturbation energies whichhave been utilized in locating hydrogen bonding and hyperconju-gative interactions.

B3LYP, CAM-B3LYP and xB97XD hyperpolarizability calcula-tions were performed for the keto and enol forms of cis-NPBHA

at 6-311+G basis set. They are reported here as total hyperpolar-izabilities (btot) defined as:

btot ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib2x b

2

y b2

z

q 5

where

bi biii

1

3Xi i

bijj bjijbjji 6

We listed hyperpolarizabilities in atomic units (a.u.) which arelinked to electrostatic units (esu) through the conversion factor:1 a.u. = 8.6393 1033 esu.

Calculations of the excited states of the enol and keto isomerswere performed using time dependent Density Functional Theory(TD-DFT) at B3LYP, CAM-B3LYP and xB97XD functionals and6-311+G basis set.

3. Results and discussion

3.1. Structural and thermodynamical features

Fig. 3.1depicts the labeling scheme and the optimized bondlengths of the keto and enol forms of cis-N-phenylbenzohydroxa-mic acid (NPBHA) using B3LYP/6-311+G level of theory. Table3.1lists the optimized bond lengths and dihedral angles of thetwo tautomers which have been obtained using B3LYP, CAM-B3LYP andxB97XD functionals at 6-311+G basis set. Since an iso-lated cis-NPBHA molecule encompasses two separate benzenerings, the initial step, undertaken in this research, was to addressthe coplanarity of the whole NPBHA molecule. With the aim ofcharacterizing the ground state conformation of NPBHA, a relaxedpotential energy surface was calculated with respect to the torsionangle C4C7N9C11(H5). It can be seen that the two benzene ringsdo not have a coplanar configuration as they have H5 of less than20for the keto formand less than 8 for the enol counterpart. This

behavior could be attributed to both steric and repulsion effects.As shown inTable 3.1, the optimized geometry of the keto tau-

tomer agrees satisfactorily with that obtained by Ciofini[10]usingMP2 and DFT/PBE0 methods at 6-31G(d) basis set. The main differ-ences between the geometrical features of the keto and enol formsare: a longer C7N9 bond of the keto form by ca. 0.045 over thatof the enol one. On the one hand, the C7O8 single bond of 1.327 in the enol form is shortened (1.235 ) as it acquired a double bondcharacter in the keto tautomer. On the other hand, the enol formN9O10 double bond of 1.330 is elongated by ca. 0.078 , as atypical single NO bond, in its keto counterpart. The typical O10H22 single bond of 0.983 in the keto form became partiallybonded (1.714 ) in the enol form. A reverse situation occurredfor the O8H22 bond of 1.005 in the enol form and 1.869 in

Fig. 3.1. (a) Labeling of cis N-phenylbenzohydroxamic acid (NPBHA). Some selected bond lengths () of cis N-phenylbenzohydroxamic Acid (NPBHA): (b) keto and (c) enolforms which were computed b using B3LYP/6-311+G level of theory.

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the keto tautomer. The significance of the length of the intramolec-ular H-bonds in these two cases will be discussed later. Apart fromH3 and H5, the dihedral angles of the two tautomers do not ex-ceed a deviation of 1.2. H3 measures the coplanarity of one of

the six-membered rings with the intramolecularily cyclized five-membered ring, where the two rings in the keto form deviate fromcoplanarity by 4.4 compared to those of the enol tautomer. h5indicates the coplanarity of the two benzene rings in cis-NPBHAwhich are nearly coplanar in the enol form (4< h5 < 8) and witha considerable deviation from planarity in case of the keto counter-part (12< h5 < 2 0).

To assess the effect of the three functionals (B3LYP, CAM-B3LYPand xB97XD) on the optimized geometrical parameters of cis-NPBHA enol and keto forms, one can cultivate the following obser-vations: (a) the traditional hybrid functional B3LYP gave relativelylonger bond lengths of ca. 0.01 compared to those obtained fromthe long-range corrected functionals (CAM-B3LYP and xB97XD)(b) the two long-range corrected functionals yielded comparable

bond lengths (c) there was no general trend for all dihedral anglesand the differences between them as a result of implementing thefunctionals did not exceed 1for h1,h2 andh4; but h3 opened byca. 3 when using the long-range corrected functionals as com-pared to the traditional one. As for h5,xB97XD gave smaller valuesof ca. 7.28(keto) and 2.63(enol) compared to those due to B3LYPwhich in turn yielded comparable values to those of CAM-B3LYPfunctional.

The B3LYP/6-311+G, CAM-B3LYP/6-311+G andxB97XD/6-311+G values ofDE, DH, DG, DSand Kfor the two isomers arelisted inTable 3.2. Comparing the results from the three DFT func-tionals one can assess their effect on the relative stability of cis-NPBHAketo andenol forms. It is obviousthat allthreefunctionalsfa-voured the keto form at all temperatures. This is indicated by the

negativesvalues ofDG andthe positivevalues ofDS. It is clear alsothat DGis dominated byDHwith little contribution from TDSof5.75% when using B3LYP and CAM-B3LYP and 8.21% forxB97XD

functional. The long-range corrected functionals increaseDE, DHandDG bynot less than 1.5 kcal/molcompared tothoseduethe tra-ditionalhybridfunctional.The valuesoftheequilibriumconstant (K)suggest that the equilibrium concentration of the keto form is over

6.08 108 times that ofthe enol form. In addition,Kis verysensitivetoDGanda changeof 1 kJ/mol at273.15 K,as a resultof implement-ingB3LYP andCAM-B3LYP functionals, increasedthe value of K by afactorof 3; anda factorof 2 whenapplying CAM-B3LYPandxB97XDfunctionals.

3.2. NBO Analysis

Table 3.3lists some of the most influential second order pertur-bation energies of the keto and enol forms of cis-NPBHA usingB3LYP/6-311+G level of theory. All hyperconjugative energiesdue the two phenyl rings yield almost similar values for the twotautomers and were therefore neglected. However, the mostimportant hyperconjugative interactions in determining the stabil-

ity preference of one tautomer over the other have fructified sub-totals of 187.92 and 147.36 kcal/mol for the keto and enol formsrespectively. These findings confirm the total zero-point electronicand free energy predictions which showed that the keto form is byfar more stable than its enol counterpart. A legitimate questionthen arises: what is the origin of the stability of the keto form?

Table 3.1

Selected optimized parameters (bond lengths in and dihedral anglesa in degrees) of N-phenylbenzohydroxamic acid (NPBHA) keto and enol forms together using the electedDFT functionals at 6-311G basis set.

Parameter Enol Keto

B3LYP CAM-B3LYP xB97XD B3LYP CAM-B3LYP xB97XD MP2b PBE0b

R(C7N9) 1.322 1.310 1.311 1.367 1.358 1.357 1.363 1.362R(C7O8) 1.327 1.317 1.318 1.235 1.229 1.229 1.247 1.237R(N9O10) 1.330 1.327 1.319 1.408 1.395 1.389 1.417 1.390R(O10H22) 1.714 1.673 1.717 0.983 0.981 0.977 0.993 0.9883R(H22O8) 1.005 1.009 1.000 1.869 1.864 1.886 1.886 1.816h1 3.33 3.20 3.17 3.32 3.10 3.98 2.0 5.0h2 0.58 0.73 0.62 1.36 1.74 1.92 1.7 0.8h3 31.00 33.63 34.23 35.43 35.86 38.37 39.7 34.8h4 53.59 51.94 54.14 52.43 52.79 51.84 h5 7.55 6.35 4.92 19.59 18.83 12.31

a h1,h2,h3,h4 and h5 are the (O8C7N9O10), (H22O10N9O8), (C5C4C7O8), (C12C11N9O10) and (C4C7N9C11) respectively.b Taken from Ref.[10]at 6-31G(d) basis set.

Table 3.2

Zero-point electronic energy changes (DE/kcal/mol), enthalpy changes (DH/kcal/mol), free energy changes (DG/kcal/mol) and entropy changes (DS/cal/mol K) forcis-NPBHA enolM keto isomerization which have been computed by using differentDFT functionals at 6-311+G basis set.

Parameter B3LYP CAM-B3LYP xB97XD

DE 10.73 12.05 12.52DH 10.50 11.81 12.19DG 11.14 12.53 13.28DS 2.34 2.64 3.28

K 6.08108 1.061 1010 6.706 1010

Table 3.3

Selected second order perturbation energies of the keto and enol forms which werecalculated using B3LYP/6-311+G chemistry level.

No Interaction Keto Enol

1 rC1C4 ! rC7C8 14.46 5.05

2 rO10H22 !rN9C11 3.37 6.00

3 rC11C15!

r

N9O10 4.50 1.614 rC15C16 !rN9C11 4.16 4.47

5 n2O8 !rC4C7 16.62

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the enol form. Yet, the traditional functional (B3LYP) gave a lowervalue compared to those approximated by the LC-DFT functionals.Fig. 3.2shows that the electronic distribution of the HOMO of theenol or the keto form is delocalized mainly over C@Np-bonding,nitrogen and oxygen lone pairs and the benzene rings; whereasthe LUMO of either isomer is mainly constituted by the C@Np-anti-bonding and C@Cp-bonding of the two benzene rings. Itcan be seen fromFig. 3.3that the LUMO is progressively destabi-lized in the sequence: xB97XD > CAM-B3LYP > B3LYP; while theHOMO is gradually stabilized in the same order. The net effect ofthese changes produced energy gaps in the order:xB97XD > CAM-B3LYP > B3LYP. All these molecular propertiesare in complete agreement with previous studies[2931].

The total hyperpolarizabilities of the two isomers computed byB3LYP are larger than those from CAM-B3LYP and xB97XD. This isexpected since traditional functionals are known to yield overesti-mated hyperpolarizabilities[3033]. The btotvalues estimated byCAM-B3LYPare, inturn,largerthan thoseapproximatedbyxB97XD.This is in good agreement with Garza et als [29] findings.

It is worth mentioningthat theconversion of cis-NPBHA ketointoenol form is accompanied by a drastic increase ofbtot. The three DFTfunctionals computed total hyperpolarizabilities of the enol formofca. three times that of the keto counterpart. These results indicatethat the enol tautomer could be considered for NLO applications[29]. The two phenyl rings are nearly co-planar (less than 8) in theenol tautomer as compared with their mutual positions (less than20) in the keto counterpart. This near co-planarity favours a largercharge transfer between the enolic carbon and the oxo nitrogenatomsin theenol form. This situationmay account for thelargerbtotof644 a.u. for the enolform compared to243 a.u.for the keto tauto-mer using CAM-B3LYP/6-311+G level of theory. Furthermore, theCN bond that acquired a partial p-bonding character (shorter byca. 0.045 ) in the enol form may facilitate charge transfer betweenthese moieties, compared to its partialr-bondingnature in theketocounterpart.

It is of interest to note, however, that the large values of btotcomputed for the enol tautomer may also be explained in termsof specific large second-order perturbation hyperconjugative ener-gies in this isomer compared to the keto form. These hyperconju-gations are exemplified by the charge transfer due to then2O8 !rC7N9 andr

2C7N9 !r

2C4C5 interactions which contrib-uted 49.49 and 22.82 and 36.03 and < 0.5 kcal/mol for the enoland keto forms respectively. The stronger H-bonding delocaliza-tion of 19.0 kcal/mol in the enol form compared to 7.62 kcal/molfor the keto tautomer further favours the extremely largerbtotval-ues of the former.

InTable 3.4is also shown the inverse relationship between thebtot and E.G. values. A number of theoretical [34,35]and experi-

Fig. 3.2. The molecular orbital surfaces of the HOMO and LUMO of (a) Enol form and (b) keto form which have been constructed by using CAM-B3LYP/6-311+G

level oftheory.

Fig. 3.3. Schematic molecular orbital energy level diagram of cis-NPBHA enol andketo forms which have been calculated using B3LYP, CAM-B3LYP andxB97XDfunctionals at 6-311+G basis set.

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