Journal of Molecular Structure: THEOCHEM 916 (2009) 119–124

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Journal of Molecular Structure: THEOCHEM

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Substituent effect in n-hexanes and n-hexatrienes based on core-electronbinding energies calculated with density-functional theory

Yuji Takahata a,b,*, Alberto Dos Santos Marques a, Rogério Custodio b

a School of Engineering, Amazonas State University, Av. Darcy Vargas, 1200, Parque 10 – CEP 69065-020, Manaus, Amazonas, Brazilb Departmento of Chemistry, University of Campinas-UNICAMP, CEP 13084-862 Campinas, SP, Brazil

a r t i c l e i n f o

Article history:Received 6 June 2009Received in revised form 8 September 2009Accepted 8 September 2009Available online 12 September 2009

Keywords:Substituent effectCEBEn-Hexanesn-HexatrienesResonance effect

0166-1280/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.theochem.2009.09.015

* Corresponding author. Address: School of Enginversity, Av. Darcy Vargas, 1200, Parque 10 – CEP 690Brazil. Tel.: +55 92 32365573 x 45.

E-mail address: taka@iqm.unicamp.br (Y. Takahata

a b s t r a c t

It was shown that core-electron binding energy (CEBE) is a very convenient quantity to monitor substi-tuent effect at each carbon atom in a substituted n-hexane (1-X–hexane), a chain r-system, and a substi-tuted n-hexatriene (1-X–hexatriene), a chain p-system. The core-electron binding energy was calculatedusing the density-functional theory with a scheme:

DEKSðPW86—PW91Þ=TZPþ Crel==HF=6-31G�

The calculated CEBE(i) of ith orbital is equal to the sum of the ionization energy (�ei) due to the Koopmans’theorem and relaxation energy (R). The variation of the ionization energy (�ei) parallels closely to that ofCEBE(i). The relaxation energy curve does not follow the CEBE curve. The behavior of CEBE in a molecule Mdepends almost exclusively upon the electronic structure of its neutral parent molecule M, and not uponits core-ionized cation M+. The substituent effect in the r-system is considered as inductive effect. Thesubstituent effect in the p-system consists of inductive and resonant/p-electron effects. Assuming thatthe inductive effect of the p-system, 1-X–hexatriene, can be approximated by that of the r-systems, 1-X–hexane, resonant effect of the p-system was estimated.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction cyclohexanes and substituted benzenes and discussed their substi-

A substituent (X) in a molecule can play important role in deter-mining physical, chemical and biological properties of the molecule.Substituent effect is very useful concept in understanding molecularproperties. For instance, Hammett substituent constant [1] is wellknown substituent constant and widely used in chemistry andbiology. Linderberg et al. [2] showed that the core-electron bindingenergy shift of a ring carbon atom correlates linearly to the experi-mental Hammett substituent constant in substituted benzene deriv-atives. This aspect was investigated in a series of previouspublications [3–6]. The magnitude of core-electron binding energyof an atom in a molecule (H-R) depends on the type of the atomand its chemical environment [7]. If the hydrogen atom in H–R issubstituted by a substituent X to form X–R, CEBE of every atom inthe whole molecule shifts because the chemical environment ofeach atom in the molecule varies. Substituent effect can be moni-tored by CEBE which is measurable quantity, and obtained directlyby an experimental technique or it can be calculated with a theoret-ical method. We calculated CEBE of atoms in a series of substituted

ll rights reserved.

eering, Amazonas State Uni-65-020, Manaus, Amazonas,

).

tuent effects in the previous publication [8]. The objective of thepresent work is to study the substituent effect in substituted n-hex-ane (1-X–hexane, Fig. 1A) and substituted n-hexatriene (1-X–hexa-triene, Fig. 1B). 1-X–hexane is a chain r-system with six carbons,while 1-X–hexatriene is a chain p-system with six carbons. In thetwo chain systems, we work only the systems in which the substitu-ent X– is always in C1 position. The use of CEBE to monitor substitu-ent effect is applicable, in principle, to any chemical system.

2. Method of calculation

Core-electron binding energy of an atom in a molecule M can becalculated as the difference between total energy of core-ionizedcation, E(M+), and that of the neutral parent molecule, E(M), as gi-ven in Eq. (1),

CEBE ¼ DE ¼ EðMþÞ � EðMÞ ð1Þ

DEs of six carbon atoms, C1–C6, in each of the systems, Fig. 1, werecalculated using density-functional theory with the scheme [9]

DEKSðPW86—PW91Þ=TZPþ Crel==HF=6-31G� ðScheme 2003Þ

DEKS (= CEBE) is the difference in the total Kohn–Sham (KS)energies, Eq. (1), calculated with Amsterdam Density Functional(ADF) package [10], using a triple-zeta polarized (TZP) Slater type

Fig. 1. (A) Substituted n-hexane (1-X–hexane), and (B) substituted n-hexatriene (1-X–hexatriene).

Table 1Calculated CEBEs, in eV, of the six carbon atoms (C1–C6) in 1-X–hexane.

X C1 C2 C3 C4 C5 C6

1 NO2 292.25 291.31 290.99 290.77 290.81 290.782 CN 292.23 291.20 290.91 290.74 290.79 290.773 CF3 291.46 290.95 290.73 290.60 290.68 290.674 CHO 290.98 290.92 290.67 290.58 290.67 290.675 NHCOMe 291.86 290.89 290.75 290.64 290.71 290.716 Cl 292.06 290.85 290.70 290.59 290.67 290.677 COMe 290.72 290.77 290.57 290.52 290.62 290.648 F 292.92 290.78 290.73 290.58 290.65 290.659 SH 291.22 290.71 290.55 290.49 290.59 290.61

10 COOH 291.13 290.63 290.52 290.43 290.55 290.5711 COOMe 290.89 290.49 290.42 290.37 290.50 290.5412 H 290.52 290.47 290.33 290.33 290.47 290.5213 OH 292.03 290.45 290.48 290.40 290.52 290.5514 CH2OH 290.44 290.45 290.35 290.35 290.49 290.5315 OMe 291.82 290.41 290.46 290.39 290.51 290.5516 CONH2 290.81 290.40 290.38 290.33 290.48 290.5117 CH@CH2 290.57 290.37 290.34 290.35 290.49 290.5418 NH2 291.25 290.34 290.36 290.34 290.48 290.5219 Me 290.45 290.30 290.28 290.31 290.45 290.5120 NMe2 290.98 290.25 290.33 290.33 290.47 290.5221 But 290.09 290.16 290.22 290.27 290.44 290.49

Fig. 2. Plot of CEBEs, eV, of selected molecules at each of the six carbon atoms, C1–C6, in 1-X–hexane, where X = NO2, F, H, NH2 and Me.

120 Y. Takahata et al. / Journal of Molecular Structure: THEOCHEM 916 (2009) 119–124

basis set. The TZP basis set consists of two 1s Slater type orbitals(STOs), three 2s and 2p STOs and one 3d STO. STOs are especiallysuited to represent inner core electronic structure. The TZP basisset was found to be the most cost effective resulting average abso-lute deviation (AAD) of 0.16 eV from published experimental CEBEsfor 59 CEBE calculations tested. The maximum absolute deviationfrom experiment was 0.50 eV for the carbon CEBE in CF4. The func-tional combination is the Perdew–Wang 1986 exchange functional[11] and the Perdew–Wang 1991 correlation functional [12]. Therelativistic correction [13] to the CEBEs can be estimated by theempirical equation (2),

Crel ¼ KINnr ð2Þ

where Inr is a non-relativistic CEBE and Crel is the relativistic correc-tion. When both Crel and Inr are in eV, K = 2.198 � 10�7 andN = 2.178. In the case of carbon atom, Crel takes the value 0.05 eV.The geometry of the molecules was optimized by ab initio RHF/6-31G* procedure and atomic charges of the molecules were calcu-lated with GAUSSIAN package [14]. In the geometry optimization,input geometry was prepared such a way that the hexatrienes were‘‘all trans” and the hexanes were ‘‘all staggered” with all carbonatoms in the same plane (Fig. 1). The geometry optimization startedfrom a common conformation for each molecule in the class.

3. Results and discussion

Table 1 lists CEBEs, in eV, of six carbon atoms (C1–C6) in twentyone substituted n-hexanes (1-X–hexane, Fig. 1A). Since 1-X–hex-ane is a r-system, variation of the CEBEs in Table 1 is consideredto be due to inductive effect of the substituent X. The compoundsare listed in descending order of the inductive effect at C2 of thesubstituted n-hexane. Fig. 2 plots CEBE at each of the six carbonsof selected 1-X–hexanes, where X = NO2, F, H, NH2 and Me. n-Hex-ane is considered as a reference molecule because its ‘‘substituent”is X = H. The solid line curve in the figure corresponds to n-hexane.The behavior of the inductive effect of the substituent, X, at C1 issomewhat different from that of the remaining carbon atoms,C2–C6. For instance, the inductive effect of F is the greatest of all

at C1. But it drops sharply at C2, and it diminishes slowly goingfrom C2 to C4. NO2 has the second largest inductive effect at C1. Ithas the greatest inductive effect at the remaining atoms. NO2 iswell known strong electron withdrawing substituent. The effectreaches through the whole chain atoms. NH2 has significant induc-tive effect at C1. The CEBE values of atoms between C2 and C6 in 1-NH2–hexane closely follows to those of 1-H–hexane. NH2 has al-most negligible inductive effect at any carbon between C3 and C6.Me also has almost negligible inductive effect at any carbon be-tween C3 and C6. The inductive effect of electron withdrawing sub-stituents, such as NO2 and F, is far reaching. It reaches the wholeheavy atoms in the molecule. On the other hand, inductive effectof electron donating substituents, such as NH2 and Me, in 1-X–hex-ane is almost negligible except at C1 (and C2). The shape of eachcurve corresponding to each substituent X in Fig. 2 has some sim-ilarity to that of n-hexane, the reference molecule, especially at C4,C5 and C6. The electron withdrawing substituents pull n-hexanecurve (solid line) upward, especially at C1 and C2 in great extent.Electron withdrawing substituents, such as NO2 and F, dominateinductive effect in the r-systems. NH2 is usually known as electrondonating. However, the calculated CEBEs at the site of substitution

Fig. 3. Plot of scaled CEBE (CEBE-289.8 eV), scaled ionization energy (IE-269 eV)due to Koopmans’ theorem, and scaled relaxation energy (R-19.5 eV) at the sixcarbon atoms in 1-NO2–hexane.

Y. Takahata et al. / Journal of Molecular Structure: THEOCHEM 916 (2009) 119–124 121

(C1) suggest it is electron withdrawing. Why it has significantinductive effect at C1? Although CEBEs are sometimes approxi-mated as an initial state property, they do in principle also dependupon the electron distribution in the final, core-ionized state (i.e.,relaxation effect). What is the relaxation effect of the system thatwe are studying? What will be relation between atomic chargeand CEBE? In order to answer all these questions, we must inves-tigate the basic equation, Eq. (1), in details. We rewrite Eq. (1) giv-ing Eq. (3.1) in which CEBE corresponds to ionization of an electronfrom ith core orbital. The total energies of cation, Ei(M+), and parentneutral molecule, E0(M), are calculated independently using SCFprocedures. Because of this, molecular orbitals in M and M+ are dif-ferent from each other. Electron distribution of M+ is reorganizedor relaxed in comparison to M. Let E0,i(M+) represent total energyof M+ calculated using the same molecular orbitals as those of M,the parent neutral molecule. This is the frozen orbital approxima-tion. Eq. (3.2) indicates that, Ei(M+), the SCF optimized total energyof M+ is the sum of E0,i(M+) and its relaxation energy (R). Rearrang-ing Eq. (3.2), one can derive Eq. (3.3). The difference of the two to-tal energies in the brackets is just negative of ith molecular orbitalenergy, �ei, according to the Koopmans’ theorem. Eq. (3.4) showsthat the CEBE of ith core orbital is the sum of ionization energy(IE) of the ith orbital calculated with the Koopmans’ theorem plusthe relaxation energy. Eq. (3.4) has been used extensively byS�thre et al. [15] and Thomas et al. [16] to analyze results of theirobserved 1s photoelectron spectra of alkenes and conjugated chainsystems. Table 2 lists CEBEs, Koopmans’ ionization energies (�ei),and relaxation energies (R) of the 1s orbitals of the six carbonatoms in 1-NO2–hexane. In order to plot the three quantities inone graph, they are scaled. Fig. 3 plots the scaled CEBE (CEBE-289.8 eV), the scaled ionization energy (IE-269 eV) due to theKoopmans’ theorem, and the scaled relaxation energy (R-19.5 eV)at the six carbon atoms in 1-NO2–hexane. The relaxation curve re-mains almost constant. Since 1-NO2–hexane is a r-system, littlerelaxation is expected upon core ionization.

The behavior of the CEBE curve and the Koopmans’ curve arevery similar. This indicates that the behavior of the CEBE in themolecule M depends exclusively upon the electronic structure ofits neutral parent molecule M, and not upon the core-ionized cat-ion M+. Exactly the same conclusion as this was obtained for al-kenes [15] and conjugated dienes [16]. Eq. (3.5) shows thedefinition of negative of ith orbital energy. The right hand side ofEq. (3.5) consists of three terms; kinetic (ti), nuclear–electronattraction (vne), and electron–electron interaction (vee) energy,respectively. Consider the case in which a 1sA electron of an atomA is removed. The 1sA atomic orbital can be considered as approx-imate representation of ith orbital, wi (the first part of Eq. (3.6)). wj

Table 2CEBE due to DEKS, and due to Koopmans’ theorem (�ei), and relaxation (R) energy for1-NO2–hexane and 1-NH2–hexatriene. All in unit of eV.

CEBE Koopmans Relaxation (R)

1-NO2–hexaneC1 292.25 271.18 21.07C2 291.31 270.22 21.09C3 290.99 269.95 21.05C4 290.77 269.71 21.07C5 290.81 269.66 21.15C6 290.78 269.39 21.39

1-NH2–hexatrieneC1 290.87 270.59 20.28C2 289.87 269.28 20.59C3 289.95 269.55 20.40C4 289.57 269.37 20.20C5 290.05 269.49 20.56C6 289.14 269.05 20.09

is approximated as a linear combination of atomic orbitals /l (thesecond part of Eq. (3.6)). Eq. (3.7) defines density matrix elementPlm. Substitution of Eqs. (3.6) and (3.7) into Eq. (3.5) results Eq.(3.8) which consists of five terms, (I)–(V). Since we concern CEBEof carbon atom only, 1sA remains the same for all the six carbonatoms, C1–C6, in the molecule (Fig. 1). The first two terms, (I) and(II), in Eq. (3.8), remains the same for the six carbons. The valuesof the remaining three terms, (III)–(V), in the equation depend onthe position of a carbon atom in the molecule. Term (III) is attrac-tion energy between the electron in the 1sA orbital and all nuclei inthe molecule except the atomic nucleus A. Term (IV) is electron–electron interaction energy between the electron in the 1sA orbitaland all the electrons that belongs to atom A. Term (V) is electron–electron interaction energy between the electron in the 1sA orbitaland all the electrons that belong to the remaining atoms in themolecule. If the value of term (III) increases, CEBE increases. Ifthe value of terms (IV) and (V) decreases, CEBE increases. CEBE de-creases when the contrary occurs.

CEBEðiÞ ¼ EiðMþÞ � E0ðMÞ ð3:1Þ¼ ½E0;iðMþÞ þ R� � E0ðMÞ ð3:2Þ¼ ½E0;iðMþÞ � E0ðMÞ� þ R ð3:3Þ¼ �ei þ R ð3:4Þ

� ei ¼ i12r2

��������i

� �þ i

Xa

Za

ra

����������i

* +�X

j

hijjjiji ð3:5Þ

wi � 1sA; wj ¼Xl

Cjl/l ð3:6Þ

Plm ¼X

j

CjlCjm ð3:7Þ

� e1sA ¼ 1sA12r2

��������1sA

� �þ 1sA

ZA

rA

��������1sA

� �þ 1sA

Xa–A

Za

ra

����������1sA

* +" #Vne

ðIÞ ðIIÞ ðIIIÞ

�XA

l;mPA

lm 1sAlAjj1sAmA� �

þXB–A

l;mPB

lm 1sAlBjj1sAmB� �" #

Vee

ð3:8Þ

ðIVÞ ðVÞ

Using Eq. (3.8), we can obtain qualitative answers to all the ques-tions raised above in relation to Fig. 2.

Table 3

Structure: THEOCHEM 916 (2009) 119–124

Question 1 (Q1): Why is the CEBE at C1 greatest when X = F?

Calculated CEBEs, in eV. of six atomic carbons (C1–C6) in 1-X–hexatriene.

X C1 C2 C3 C4 C5 C6

1 NO2 291.29 291.39 291.01 291.03 291.17 290.402 CN 291.20 291.25 290.86 290.83 291.03 290.233 CF3 290.52 291.10 290.70 290.71 290.92 290.134 CHO 290.25 291.04 290.74 290.76 290.98 290.195 NHCOMe 291.25 290.28 290.28 289.93 290.36 289.456 Cl 291.28 290.71 290.50 290.33 290.64 289.807 COMe 290.04 290.84 290.60 290.60 290.86 290.068 F 292.23 290.74 290.54 290.32 290.62 289.779 SH 290.52 290.47 290.32 290.17 290.51 289.67

10 COOH 290.28 290.89 290.62 290.63 290.87 290.0811 COOMe 290.12 290.71 290.51 290.49 290.78 289.9712 H 289.80 290.61 290.32 290.32 290.61 289.8013 OH 291.55 290.15 290.18 289.85 290.27 289.3814 CH2OH 289.84 290.38 290.22 290.16 290.50 289.6715 OMe 291.32 290.01 290.10 289.75 290.20 289.3016 CONH2 290.12 290.81 290.54 290.52 290.79 289.9817 CH@CH2 290.00 290.17 290.17 290.00 290.40 289.5418 NH2 290.87 289.87 289.95 289.57 290.05 289.1419 Me 289.88 290.22 290.14 290.03 290.41 289.5720 NMe2 290.29 290.19 290.18 290.09 290.51 289.6221 But 289.58 290.04 290.06 289.94 290.36 289.50

Answer 1 (A1): The nuclear charges of F (ZF) and N (ZN) are 9 and7, respectively. The nuclear–electron attraction energy ZF/r interm (III) in Eq. (3.8) is greater than ZN/r. The nuclear chargeof F is the greatest of all substituents in study. Apparently, term(III) predominates in determining the value of CEBE at C1.Q2: Why does it decrease in the order NO2 > NH2 in Fig. 2?A2: CEBE at C1 is greater when X = NO2 than when X = NH2. Thisis because term (III) corresponding to X = NO2 is greater thanthat corresponding to X = NH2.Q3: Why do the CEBEs of carbons C2–C6 for X = F and NO2

remain larger than any other substituents in Fig. 2?A3: Term (III) in Eq. (3.8) remains larger for X = F and NO2 thanany other substituents for the carbons C2–C6. Term (III) seemsto predominate in determining the value of the CEBEs for thewhole molecule. Terms (IV) and (V) in Eq. (3.8) remains nearlyconstant because electrons in the r-bonds tends to remain intheir original places.Q4: Why are the CEBE curves corresponding to C4 to C6 regionare similar to each other?A4: Terms (III)–(V) in Eq. (3.8) of the systems have similar val-ues because the distance between the substituent X and C4 (andC5, C6) is long.Atomic charge at each atom in a molecule also depends on itschemical environment. It is of interest to compare changes ofCEBEs and atomic charges. Fig. 4 shows three curves corre-sponding to three different atomic charges at the six carbonatoms in 1-NO2–hexane calculated by three different methods;(1) Atoms-In-Molecule (AIM) [17], (2) Electrostatic Potential(ESP) [18], (3) Mulliken population analysis [19]. A scaled valueof CEBE, (CEBE-291.3 eV), of the molecule, is plotted in the fig-ure also for the sake of comparison. AIM and Mulliken curvesroughly parallel the CEBE curve, while ESP does not. Atomiccharge (dA) of an atom A in a molecule is defined as the differ-ence between nuclear charge (ZA) and electron density (qA) ofthe atom; dA = ZA � qA. The electron density (qA) of the atom Acontributes to term (IV) in Eq. (3.8). The variation of CEBEdepends not only term (IV) but also terms (III) and (V) in Eq.(3.8). The electron density of the atom A (qA) is not the sole fac-tor that determine the value of the CEBE. That is the reason whythe CEBE curve and some of the charge curves parallel only par-tially (Fig. 4).

Table 3 lists calculated CEBEs (eV) of six carbon atoms of twentyone 1-X–hexatrienes (Fig. 1B). The compounds are listed in the

122 Y. Takahata et al. / Journal of Molecular

Fig. 4. Plot of scaled CEBE (CEBE-291.3 eV), atomic charges calculated by (1) AIM,(2) ESP, and (3) Mulliken methods at the six carbon atoms in 1-NO2–hexane.

descending order of the CEBE at C2 of 1-X–hexatriene. Fig. 5 plotsthe substituent effect of the CEBE of some typical substituents asfunction of the six carbon atoms, C1–C6, in 1-X–hexatriene. Hexa-triene in which X = H is the reference molecule (solid line in thefigure). The pattern of change of the CEBE curves of the p-systemsin Fig. 5 is substantially different from that observed in Fig. 2 forthe r-systems. The CEBE curves for the region of C4, C5 and C6

atoms, in Fig. 5, are very similar to each other. All the curves havemaxima at C5 and minima at C6. The basic pattern of change at C4,C5 and C6 in hexatriene remains the same even after substitution ofH atom by a substituent X at C1. The impact of the substituent, X, atC1 decreases in the order C1 > C2 > C3. Substituent effect at C1 is pe-culiar in comparison to the remaining atoms, C2–C6. In the case X =NO2, the CEBEs increase at all atoms in the molecule in comparisonto hexatriene, the reference molecule. On the other hand, in thecases X = NH2, Me, the CEBEs decrease at atoms, C2–C6, in compar-ison to hexatriene.

Since 1-X–hexatriene (Fig. 1B) is a conjugate p-system, wemight expect some relaxation (R) effect for core-ionized cation.Numerical values corresponding to CEBE, Koopmans’ energy(�ei), and R that appears in Eq. (3.4) for 1-NH2–hexatriene arelisted in Table 2. Fig. 6 plots scaled CEBE (CEBE-289 eV), scaled

Fig. 5. Plot of CEBE, eV, of selected molecules at each of the six carbon atoms, C1–C6,in 1-X–hexatriene, where X = NO2, F, H, NH2 and Me.

Fig. 6. Plot of scaled CEBE (CEBE-289 eV), scaled ionization potential (IP-269 eV)due to Koopmans’ theorem, and scaled relaxation energy (R-19 eV) for the sixcarbon atoms in 1-NH2–hexatriene.

Fig. 7. Plot of scaled CEBE (CEBE-289.9 eV), atomic charges calculated (1) AIM, (2)ESP, and (3) Mulliken methods for six carbons in 1-NH2–hexatriene.

Y. Takahata et al. / Journal of Molecular Structure: THEOCHEM 916 (2009) 119–124 123

ionization energy (IE-269 eV) due to the Koopmans’ theorem, andscaled relaxation energy (R-19 eV) at the six carbon atoms in 1-NH2-hexatriene. The behavior of the relaxation curve at C1, C2

and C3 is entirely different from that of the CEBE curve at the cor-responding atoms. The behavior of the relaxation curve at C4, C5

and C6 is similar to the CEBE curve. On the other hand, the behaviorof the CEBE curve and the Koopmans’ curve are very similar. Thisindicates that the behavior of CEBE in a conjugated p-system suchas 1-NH2–hexatriene depends mainly upon the electronic structureof its neutral parent molecule, and not electronic structure of its re-laxed cation. Analysis of �ei provides information as to under-standing the behavior of CEBE curve in the molecule through theuse of Eq. (3.8). Using Eq. (3.8), one can explain those observationsmade on the behavior of the CEBE curves in Fig. 5 in a manner sim-ilar to the cases of the CEBE curves in Fig. 2. Most of the answers(A1–A4) given previously for the questions concerning to 1-NO2–hexane, apply to 1-NH2–hexatriene. One can add more questions:

Q5: NH2 is usually known as electron donating. However, thecalculated CEBEs at the site of substitution (C1) suggest it iselectron withdrawing. Why?A5: Nuclear charges of N (ZN) is 7. Nuclear–electron attractionenergy ZN/r in term (III) in Eq. (3.8) is larger than any othersexcept F. Apparently, term (III) predominates in determiningthe value of CEBE at C1. The large contribution of ZN/r meanslarge electron drawing.Q6: Why the CEBE curve of, for instance, 1-NH2–hexatriene, p-system, oscillate?A6: The CEBE curve of 1-NH2–hexane, r-system, in Fig. 2 doesnot oscillate. The oscillating nature of the CEBE curve of 1-NH2–hexatriene is due to the presence of the p-electrons. Theoscillation is caused by the electron–electron interaction terms,(IV) and (V) terms, in Eq. (3.8), not by the nuclear–electronattraction term, (III). The non bonding orbital in NH2– has p-character. It occupies a large space. The pair of electron in thenon bonding orbital repel the pair of electrons in the p-orbitallocalized in C1@C2 of 1-NH2–hexatriene. This causes a decreaseof electron density on C1 and an increase of electron density onC2. The redistribution of the electron density in C1@C2 causessimilar redistribution of electron density in C3@C4 and C5@C6.The electron density decreases on C1, C3, and C5, whereas itincreases on C2, C4 and C6 upon substitution of H with NH2 atC1 in n-hexatriene. The redistribution of the electron densityin the molecule causes the oscillation of the CEBE curve

(Fig. 5). The well known concept of ‘‘resonance structures” ofa p-system can be applied to 1-NH2–hexatriene and the sameconclusion can be drawn. In order to discuss the matter inquantitative terms, we can use atomic charges that can be cal-culated with some methods. Fig. 7 plots atomic charges calcu-lated (1) AIM, (2) ESP, and (3) Mulliken methods, scaled CEBE(CEBE-289.9 eV), for the six carbons in 1-NH2–hexatriene. Mul-liken charge (and ESP) curve oscillates almost parallel to CEBEcurve indicating term (IV) in Eq. (3.8) predominates the trendof CEBE variation among the six carbon atoms in the molecule.The Mulliken charge curves parallel to the CEBE curves both inthe r-system (Fig. 4) and p-system (Fig. 7).

Eq. (4) calculates DCEBE(X, Ci), which is a difference betweenCEBE values of Cith atom in 1-X–hexatriene and 1-X–hexane:

DCEBEðX;CiÞ ¼ CEBEðCi in 1-X—hexatrieneÞ� CEBEðCi in 1-X—hexaneÞ ð4Þ

DCEBE(X, Ci) in Eq. (4) represents contribution of p-electrons to theCEBE at Cith atom in 1-X–hexatriene. The contribution of p-elec-trons is known as resonance effect. There exist both resonanceand inductive effect in 1-X–hexatriene, whereas only inductive ef-fect exists in 1-X–hexane. DCEBE(X, Ci)’s were calculated accordingto Eq. (4) for the twenty one different X’s, and listed in Table 4. Fig. 8plots resonant/p-electron effect in 1-X–hexatriene for the five rep-resentative X’s. In the case of hexatriene, the reference moleculewith X = H, the shape of resonance plot (solid line in Fig. 8) is verymuch similar to the plot of CEBE (solid line in Fig. 5) of correspond-ing system. This means that p-electron predominate electron distri-bution in the molecule. The characteristic oscillating feature of theresonance plot corresponding to 1-NH2–hexatriene in Fig. 8 is par-alleled in that of CEBE plot in Fig. 5, implying also predominance ofp-electron in electron distribution in the molecule.

4. Conclusion

It was shown that core-electron binding energy is a very conve-nient quantity to monitor substituent effect (Figs. 2 and 5) at eachcarbon atom in substituted n-hexane (1-X–hexane, Fig. 1A), a chainr-system, and substituted n-hexatriene (1-X–hexatriene, Fig. 1B),a chain p-system. CEBE(i) of ith orbital is equal to the sum of ion-ization energy (�ei) due to Koopmans’ theorem and relaxation en-ergy (R) according to Eq. (3.4). Variation of ionization energy (�ei)due to the Koopmans’ theorem parallel closely to that of CEBE(i)

Table 4Resonance/p-electron effect, in eV, at six carbon atoms (C1–C6) of 1-X–hexatriene,calculated as difference between CEBE of 1-X–hexatriene and CEBE of 1-X–hexane.

X C1 C2 C3 C4 C5 C6

1 NO2 �0.96 0.08 0.03 0.25 0.36 �0.382 CN �1.03 0.05 �0.05 0.08 0.24 �0.543 CF3 �0.93 0.15 �0.03 0.11 0.24 �0.554 CHO �0.74 0.13 0.07 0.18 0.31 �0.495 NHCOMe �0.61 �0.61 �0.47 �0.71 �0.36 �1.266 Cl �0.78 �0.14 �0.20 �0.26 �0.03 �0.877 COMe �0.68 0.07 0.03 0.08 0.24 �0.588 F �0.69 �0.04 �0.18 �0.25 �0.03 �0.889 SH �0.70 �0.24 �0.24 �0.32 �0.08 �0.94

10 COOH �0.85 0.26 0.10 0.20 0.32 �0.4911 COOMe �0.77 0.22 0.08 0.13 0.27 �0.5612 H �0.72 0.14 �0.01 �0.01 0.14 �0.7213 OH �0.48 �0.30 �0.30 �0.55 �0.25 �1.1714 CH2OH �0.60 �0.07 �0.13 �0.20 0.01 �0.8615 OMe �0.50 �0.40 �0.36 �0.64 �0.32 �1.2516 CONH2 �0.70 0.41 0.15 0.20 0.30 �0.5317 CH@CH2 �0.57 �0.20 �0.17 �0.35 �0.09 �0.9918 NH2 �0.38 �0.47 �0.41 �0.77 �0.43 �1.3819 Me �0.57 �0.09 �0.14 �0.27 �0.04 �0.9420 NMe2 �0.70 �0.06 �0.15 �0.24 0.03 �0.9021 But �0.51 �0.13 �0.17 �0.33 �0.08 �0.99

Fig. 8. Resonance or p-electron effect in 1-X–hexatriene for selected substituents.

124 Y. Takahata et al. / Journal of Molecular Structure: THEOCHEM 916 (2009) 119–124

(Figs. 3 and 6). The relaxation energy curve does not follow theCEBE curve. These facts indicate that the behavior of CEBE in a mol-ecule M depends exclusively upon the electronic structure of itsneutral parent molecule M, and not upon core-ionized cation M+.

Qualitative interpretation of the CEBE curves in Figs. 2 and 5 canbe obtained with the aid of the mathematical expression of �ei,i.e., Eq. (3.8). The plots of Mulliken atomic charges reproduce thetrend of the CEBE plots for both 1-NO2–hexane and 1-NH2–hexatri-ene. The substituent effect in the r-system is considered as induc-tive effect. The substituent effect in the p-system consists ofinductive and resonant/p-electron effect. Assuming that inductiveeffect of the p-system, 1-X–hexatriene, can be approximated bythat of the r-systems, 1-X–hexane, resonant effect of the p-systemwas estimated. The resonant/p-electron effect predominates elec-tron distribution in the p-system (Fig. 8).

Acknowledgements

We thank José Luis de Souza Pio of Amazonas State University.Y.T. expresses his gratitude to Delano P. Chong for his encourage-ment, stimulus discussion and long lasting collaboration. Theauthors acknowledge Conselho Nacional de DesenvolvimentoCientífico e Tecnológico (CNPq) of Brazil for research fellowshipes,304751/2006-5 for Y.T. and 302440/2005-4 for A.D.S.M. A.D.S.M.also thanks Ministério da Ciência e Tecnologia, Conselho Nacionalde Desenvolvimento Científico e Tecnológico (MCT/CNPq) forfinancial support from (553292/2005-6, CT/AMAZÔNIA/MCT/CNPq). We thank FAPESP for financial aids.

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