Theoretical calculations of the substituent effect on molecular propertiesof the R–CBBN� � �H–F hydrogen-bonded complexes with R = NH2,CH3O, CH3, OH, SH, H, Cl, F, CF3, CN and NO2

Tarsila G. Castro a, Regiane C.M.U. Araujo a,*, Claudia F. Braga a, Liana S. Silva a,Arquimedes M. Pereira a, Kelson C. Lopes a, Antonio B. Carvalho a, Elizete Ventura a,Silmar A. do Monte a, Otavio L. Santana b, Mozart N. Ramos c

a Departamento de Quımica, Universidade Federal da Paraıba, 58036-300 Joao Pessoa, PB, Brazilb Unidade Academica de Educacao, Universidade Federal de Campina Grande, Campus Cuite, PB, Brazilc Departamento de Quımica Fundamental, Universidade Federal de Pernambuco, 50739-901 Recife, PE, Brazil

Vibrational Spectroscopy 49 (2009) 133–141

A R T I C L E I N F O

Article history:

Received 22 November 2007

Received in revised form 19 June 2008

Accepted 19 June 2008

Available online 12 July 2008

Keywords:

Hydrogen bond

Hydrogen fluoride

Nitriles

Theoretical calculations

Vibrational properties

A B S T R A C T

DFT calculations with B3LYP and PBE1PBE functionals and 6–311++G(d,p) basis set have been performed

in order to obtain molecular geometries, binding energies and vibrational properties of the R–CBBN� � �H–F

H-bonded complexes with R = NH2, CH3O, CH3, OH, SH, H, Cl, F, CF3, CN and NO2. As expected, it has been

verified as a red-shift of the H–F stretching frequency (nH–F), in conformity with the elongation of the

bond after complexation. On the other hand, the CBBN stretching frequency (nCBBN) is blue-shifted and

corresponds to a shortening of the bond. The binding energies (DEc), including BSSE and ZPVE corrections,

show a linear correlation with several structural, electronic and vibrational properties. In particular, an

important linear dependence between the binding energy and the calculated dipole moment of the free

R–CBBN molecule (mRCN) has been found. This result suggests that mRCN can be a useful quantity in order to

predict the ability of this fragment to form a hydrogen-bond. The IR intensities of stretching and bending

modes of complexed H–F acid fragment are adequately interpreted through the atomic polar tensor of the

hydrogen atom in H–F using the modified CCFO model for infrared intensities. The new vibrational modes

arising from complexation show several interesting features.

� 2008 Elsevier B.V. All rights reserved.

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1. Introduction

The monoprotic H–F acid has been largely used as a model acidfor the study of hydrogen-bonded complexes [1–8]. Both experi-mental [1–3] and theoretical [4–8] studies have shown that anincrease in the basic character of the proton acceptor fragmentdecreases the HF bond strength, leading to a greater red-shift of theH–F stretching frequency (DnH–F) [1,5]. As a consequence, thesubstitution of hydrogen by a methyl group in acetylene on T-typecomplexation of this molecule with H–F produces more negativevalues for DnH–F [5]. In general, the stronger hydrogen bonds areassociated with greater red-shift of the H–F stretching frequencyand larger intermolecular charge transfers.

Another important relationship that can be used to predict theH-bond strength has been found by Bobadova-Parvanova andGalabov [7–8] through the calculated molecular electrostatic

* Corresponding author. Tel.: +55 83 3216 7590; fax: +55 83 3216 7590.

E-mail address: regiane@quimica.ufpb.br (Regiane C.M.U. Araujo).

0924-2031/$ – see front matter � 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.vibspec.2008.06.005

potential obtained from RHF ab initio calculations with 6–31+G(d,p) basis set. They have shown that this potential can besuccessfully used in predicting the H-bond strength in hydrogen-bonded complexes involving nitrile and carbonyl compounds withhydrogen fluoride. An excellent linear dependence betweenthe energy of hydrogen-bond formation (in R–CBBN� � �H–F andR–CH O� � �H–F complexes) and calculated ab initio molecularelectrostatic potential in the nitrile nitrogen and carbonyl oxygenatoms of the isolated molecules has been found.

Nowadays, the experimental molecular properties of hydrogen-bonded complexes can be predicted with good accuracy throughtheoretical calculations using B3LYP density functional [9] with6–311++G(d,p) basis set [10,11]. From this procedure, thestructural, electronic and vibrational properties of C2H2� � �H–F,C2H(CH3)� � �H–F and C2(CH3)2� � �H–F hydrogen-bonded complexeshave successfully been predicted [5].

The aim of this work is to calculate the structural, electronic andvibrational properties for the R–CBBN chemical series with R = NH2,CH3O, CH3, OH, SH, H, Cl, F, CF3, CN and NO2 acting as electrondonors on complexation with H–F. Another task is to analyze the

T.G. Castro et al. / Vibrational Spectroscopy 49 (2009) 133–141134

effect of modification in CBBN basic character as a function of R onthe H-bond strength in terms of the changes that take place in theevaluated properties on isolated molecules after complexation.

2. Calculations

DFT calculations with B3LYP [9] and PBE1PBE [12] (referred toin this paper as PBE1) functionals and 6–311++G(d,p) basis set [10–11] were performed using the Gaussian 03 W program [13]. In thisprocedure, the molecular geometries of R–CBBN and H–F isolatedmolecules and their R–CBBN� � �H–F hydrogen-bonded complexeswere fully optimized and characterized by a harmonic vibrationalfrequency calculation. The binding energies of R–CBBN� � �H–Fhydrogen complexes have been calculated including the zero-point vibrational energy (ZPVE) and the basis set superpositionerror (BSSE) [14] using the supermolecule approach. For the last,the full counterpoise (CP) method of Boys and Bernardi [15] hasbeen considered, including the fragment deformation energy [14–18]. However, it is important to point out that these problems are,in general, minimized when the CP method is used with a largebasis set, which is flexible enough to provide a good description ofthe electrons in both the atomic core and the long-range region ofthe atoms [19,20].

3. Results and discussion

3.1. Structural properties

Fig. 1 shows the B3LYP optimized structures for theR–CBBN� � �H–F hydrogen-bonded complexes with R = NH2, H and

Fig. 1. Optimized structures of the R–CBBN� � �H–F complexes, with R = NH2, H and NO2,

degrees. PBE1 values are given in parentheses.

NO2. In all cases, both CBBN� � �H and N� � �H–F structures are linear,in contrast with previous results for R–CH O� � �H–F complexes [7].

As expected, the more pronounced structural changesafter complexation are found for CBBN and H–F bond lengths,which are directly involved in the H-bond formation. The bondlengths increments (drCBBN and drH–F), as well as the distancefrom the nitrogen atom in R–CBBN fragment to the fluorine atomin H–F (rN� � �F) are shown in Table 1. The experimental values[21–23] are given in parentheses. As can be observed, the effectof the R substituent is more pronounced for drH–F than for drCBBN.The latter varies only between �0.003 and �0.002 A at bothB3LYP and PBE1 levels. The negative sign indicates that CBBNbond lengths decreased after complexation. The strengtheningof the CBBN bond with hydrogen-bond formation is in agreementwith infrared spectral data [24]. On the other hand, values ofdrH–F vary from 0.007 to 0.019 A with B3LYP functional, and asimilar range has been obtained for PBE1 functional. Thepositive sign indicates that the H–F bond is weakened aftercomplexation, as expected, in contrast with the values for CBBNbond distance. It is interesting to note that the values of drH–F

are larger for electron donor groups, such as R = NH2 and CH3O,and are progressively reduced as the electron withdrawingability of R increases, such that the lower values of drH–F areobtained when R = NO2 and CN. The complexation also increasethe N� � �F bond distance (rN� � �F), but the effect is smaller for moreelectron donating groups. For instance, the B3LYP values forR = NH2 and R = NO2 are 2.719 A and 2.874 A, respectively. It wasobtained a good agreement between B3LYP results and availableexperimental data concerning the N� � �F distance for R = CH3, Hand CN.

obtained with B3LYP and PBE1 functionals. Bond lengths are given in A, angles in

Table 1N� � �F distance and more pronounced structural changes due to complexation, obtained with B3LYP and PBE1 functionals

R B3LYP PBE1 Exp.

rN� � �F (A) drCBBN (A) drH–F (A) rN� � �F (A) drCBBN (A) drH–F (A) rN� � �F (A)

NH2 2.719 �0.002 0.019 2.683 �0.002 0.020 –

CH3O 2.726 �0.002 0.018 2.690 �0.003 0.019 –

CH3 2.734 �0.002 0.017 2.709 �0.003 0.018 (2.760 � 0.0075)a

OH 2.745 �0.003 0.016 2.718 �0.003 0.017 –

SH 2.758 �0.002 0.015 2.722 �0.002 0.016 –

H 2.783 �0.003 0.013 2.758 �0.003 0.014 (2.795)b

Cl 2.781 �0.002 0.013 2.757 �0.002 0.014 –

F 2.796 �0.003 0.012 2.770 �0.003 0.012 –

CF3 2.839 �0.002 0.009 2.812 �0.002 0.010 –

CN 2.853 �0.002 0.008 2.832 �0.002 0.009 (2.862)c

NO2 2.874 �0.002 0.007 2.851 �0.002 0.008 –

Experimental values are given in parentheses. a,b,cExperimental values from [21–23], respectively.

Table 2BSSE and ZPVE corrected binding energies (DEc), corrections for basis set superposition error (BSSE) and zero-point vibrational energy (ZPVE), complex dipole moments (mc),

polarity enhancements (Dmc) and intermolecular charge transfers from the corrected Mulliken charges (DQc), obtained with B3LYP and PBE1 functionals

R DEc (kJ mol�1) BSSE (kJ mol�1) ZPVE (kJ mol�1) mc (D) Dmc (D) DQc (e)

NH2 33.0 (34.4) 1.7 (1.9) 7.9 (7.9) 8.03 (8.05) 1.40 (1.41) �0.093 (�0.095)

CH3O 31.2 (32.4) 1.8 (2.0) 8.1 (8.1) 7.92 (7.85) 1.21 (1.21) �0.087 (�0.088)

CH3 30.1 (31.4) 1.8 (2.0) 8.2 (8.2) 7.35 (7.37) 1.31 (1.33) �0.084 (�0.086)

OH 28.1 (29.6) 1.7 (1.9) 8.1 (8,0) 7.00 (7.03) 1.04 (1.05) �0.082 (�0.083)

SH 25.8 (26.8) 1.9 (2.1) 7.9 (7.9) 6.92 (6.89) 1.31 (1.31) �0.073 (�0.073)

H 22.5 (23.6) 1.6 (1.7) 8.4 (8.4) 6.06 (6.07) 1.03 (1.04) �0.072 (�0.073)

Cl 22.4 (23.6) 1.9 (2.1) 7.6 (7.6) 6.20 (6.19) 1.27 (1.28) �0.075 (�0.075)

F 20.3 (21.7) 1.8 (2.0) 7.7 (7.7) 5.20 (5.25) 1.04 (1.05) �0.073 (�0.074)

CF3 15.2 (16.5) 1.8 (1.9) 7.1 (7.0) 4.22 (4.32) 1.11 (1.12) �0.065 (�0.066)

CN 13.3 (14.1) 1.9 (2.1) 6.8 (6.8) 3.12 (3.12) 1.14 (1.14) �0.061 (�0.061)

NO2 11.6 (12.5) 1.6 (1.7) 6.5 (6.4) 3.14 (3.18) 1.07 (1.07) �0.060 (�0.061)

PBE1 values are given in parentheses.

T.G. Castro et al. / Vibrational Spectroscopy 49 (2009) 133–141 135

3.2. Electronic properties

Table 2 shows the corrected binding energies (DEc), correctionsfor basis set superposition error (BSSE) and zero-point vibrationalenergy (ZPVE), complex dipole moments (mc), polarity enhance-ments (Dmc) and intermolecular charge transfers (DQc) for allcomplexes considered in the present work. DEc was calculated bysubtracting the sum of the total energies of the isolated moleculesfrom the total energy of the hydrogen complex, including the BSSEand ZPVE corrections for each fragment. Dmc stands for the dipolemoment difference between the complex and the free molecules.DQc was calculated from the corrected Mulliken charges [25]. BSSEvalues calculated with B3LYP using a basis set that includespolarization and diffuse functions are generally very small [26]. Asexpected, the binding energies are larger when an electron-donorsubstituent is bonded to the CBBN group. For example, thecalculated binding energies at B3LYP and PBE1 levels forR = NH2, an electron-donor substituent, are 33.0 and 34.4 kJ mol�1,1, respectively, while the corresponding values for R = NO2, anelectron-withdrawing substituent, are 11.6 and 12.5 kJ mol�1,respectively. Therefore, the greater the electron-donating ability ofthe substituent R to the CBBN group is, the stronger the H-bond willbe.

From Table 2 it is also possible to note that the change of thebinding energy (DEc) along the R–CBBN� � �H–F series follows thesame behavior that was verified for the intermolecular chargetransfer (DQc). Nevertheless, the change of DQc along the series ismuch small, varying from 0.093 e for R = NH2 to 0.060 e forR = NO2, whereas their binding energies vary from 33.0 to11.6 kJ mol�1, respectively. This change in DQc is very small whencompared to the corresponding values obtained for the complexesacetylene� � �H–X with X = F, Cl, CN, NC and CCH [27], in which case

DQc varies from 0.061 e in acetylene� � �H–F to 0.018 e inacetylene� � �HCCH, while the corresponding binding energies varyfrom 18.5 to 8.4 kJ mol�1.

It is interesting to verify that the changes of corrected bindingenergies (DEc) in R–CBBN� � �H–F can be explained in terms of thedifferent elongations of the H–F bond (drH–F) due to hydrogenbonding formation. Fig. 2 shows that there is a high linearcorrelation between DEc and drH–F, in agreement with the resultsobtained by Galabov and Bobadova-Parvanova from RHF calcula-tions [7,8]. These results confirm that a stronger hydrogen bondcorresponds to a weaker H–F bond.

Galabov and Bobadova-Parvanova [7,8] have also found that theH-bond strength for R–CBBN� � �H–F and R–CH O� � �H–F complexesis adequately explained in terms of the variation of the molecularelectrostatic potential in the nitrogen and oxygen atoms in theisolated molecules, respectively. This represents a very importantcontribution towards an explanation in which the binding energiesof these complexes can be rationalized in terms of a property of theisolated proton-acceptor molecule. However, another importantcorrelation occurs between DEc and the complex dipole moment(mc). Furthermore, since Dmc is relatively constant along the series,varying only from 1.03 to 1.40 D, the dipole moment of the R–CBBNisolated proton-acceptor molecule is capable of explaining thedifferences of the DEc values for the R–CBBN� � �H–F complexes. Infact, Fig. 3 clearly shows that there is a high linear correlationbetween DEc and mRCN, with linear correlation coefficient equal to(r2) equal to 0.969.

The equations below explain 97% of variance between DEc andmRCN:

DEðB3LYPÞc ¼ ð4:24� 0:25ÞmRCN þ ð11:31� 0:82Þ (1a)

Fig. 2. DEc versus H–F bond elongation due to R–CBBN� � �H–F complexation, obtained with B3LYP and PBE1 functionals.

T.G. Castro et al. / Vibrational Spectroscopy 49 (2009) 133–141136

and:

DEðPBE1Þc ¼ ð4:36� 0:26ÞmRCN þ ð12:11� 0:84Þ (1b)

These relations suggest that the dipole moment of R–CBBN can beused as a reactivity index, reflecting the ability of this monomerthrough the studied series to participate in hydrogen bonding. Thisresult is particularly interesting since mRCN can be obtainedexperimentally and, therefore, its value can be useful to predictexperimental binding energies of R–CBBN� � �H–F.

It is important to observe that large enhancements of dipolemoment (Dmc) are found upon complexation, from 1.03 D for R = H

Fig. 3. DEc versus dipole moment of the R–CBBN free mo

to 1.40 for R = NH2. These values are greater than those obtained inCmHn� � �H–F T-type complexes [6], whose values vary from 0.63 Din C2H2� � �H–F to 0.85 D in C3H6� � �H–F. According to Buckinghamet al. [28] these enhancements are mainly due to the distortion ofthe isolated molecule charge densities by induction, dispersion andshort-range forces.

3.3. Vibrational properties

The vibrational spectrum of a hydrogen-bonded complexcontains bands due to acid (H–F) and base (R–CBBN) fragments,

lecules, obtained with B3LYP and PBE1 functionals.

Table 3Harmonic frequencies (nc

i ; cm�1), frequency shifts (Dni; cm�1), infrared intensities (Ai, km mol�1) and intensity ratios (Aci =Ai) of the CBBN and H-F stretching modes due to

complexation, obtained with B3LYP and PBE1 functionals

R ncC�N DnC�N Ac

C�N AcC�N=AC�N nc

H�F DnH�F AcH�F Ac

H�F=AH�F

NH2a 2382 (2419) +30 (+32) [+42] 211 (218) 1.7 (1.7) 3678 (3707) [3500] �419 (�462) [�461] 1403 (1491) 10.8 (10.8)

CH3O 2386 (2428) +33 (+35) 314 (325) 1.5 (1.5) 3697 (3726) �400 (�443) 1404 (1488) 10.8 (10.8)

CH3b 2387 (2418) +25 (+26) [+32] 38 (42) 3.1 (3.0) 3706 (3746) [3525] �392 (�423) [�436] 1380 (1445) 10.6 (10.5)

OH 2412 (2451) +34 (+35) 213 (224) 1.5 (1.5) 3736 (3777) �361 (�392) 1313 (1361) 10.1 (9.9)

SH 2303 (2337) +23 (+24) 66 (71) 2.7 (2.7) 3755 (3788) �343 (�380) 1405 (1500) 10.8 (10.9)

Hc 2224 (2248) +28 (+29)

[+26] 12 (13) 6.3 (6.2) 3797 (3843) [3668] �301 (�326) [�293] 1011 (1056) 7.8 (7.7)

Cld 2335 (2371) +26 (+26) [+37] 100 (107) 1.9 (1.9) 3798 (3846) [3639] �300 (�323) [�322] 1226 (1275) 9.4 (9.3)

Fd 2448 (2489) +35 (+36) [+37] 176 (186) 1.4 (1.4) 3829 (3875) [3704] �268 (�294) [�257] 965 (1011) 7.4 (7.3)

CF3 2407 (2438) +21 (+22) 13 (13) 0.5 (0.5) 3878 (3927) �219 (�242) 946 (991) 7.3 (7.2)

CNd 2277 (2306) +14 (+14)

[+11] 1 (1) 8.9 (19.0 3897 (3953) [3799] �200 (�215) [�162] 1030 (1065) 7.9 (7.7)

NO2 2357 (2393) +22 (+22) 5 (5) 0.3 (0.3) 3918 (3974) �179 (�195) 899 (932) 6.9 (6.8)

PBE1 and experimental values are given in parentheses and in brackets, respectively.a,b,c,dExperimental values from [29–32], respectively.

T.G. Castro et al. / Vibrational Spectroscopy 49 (2009) 133–141 137

which differ from free acid and base molecules depending on thestrength and orientation of the hydrogen-bonding interaction.Table 3 shows the results of the harmonic frequencies, frequencyshifts, infrared intensities and intensity ratios after complexationof CBBN and H–F stretching modes. The experimental values aregiven when available [29–32].

Analogously to the results obtained for C2H2–m(CH3)m� � �H–F(m = 0, 1 or 2) [5], a more pronounced effect on normal modes offree molecules due to complexation occurs for H–F stretchingmode, which is strongly red-shifted upon H-bond formation. Thisresult is in conformity with the elongation of rH–F uponcomplexation and reflects the weakening of the bond, as it wasalso verified through RHF calculations [7,8]. However, the lattershows a poor reasonable agreement with the experimental values,varying from �251 cm�1 for R = NH2 to �175 cm�1 for R = H,whereas the corresponding experimental values are �461 and�293 cm�1, respectively. On the other hand, the present B3LYP andPBE1 results show a good agreement with all available experi-mental values. As expected, a linear relation between DEc and DnH–

F is found (Badger-Bauer rule) [33,34], as it can be seen from the

Fig. 4. DEc versus H–F frequency shift in R–CBBN� � �H–F co

B3LYP results shown in Fig. 4. A greater frequency shift DnH–F isfound for R = NH2, which corresponds to the strongest boundcomplex, whereas the lower shift is found for R = NO2, thatrepresents the weakest bound complex.

The H–F stretching intensity is greatly enhanced upon H-bondformation, as can be seen by the Ac

H�F=AH�F ratio, from Table 3.However, there is not a linear relation between the stretchingintensity ratio and the H-bond strength, in contrast to what wasverified with DnH–F. Unfortunately, the experimental value for theH–F stretching intensity after complexation is unknown. On theother hand, it is well known that the increase in the H–F stretchingintensity, or in other H–X oscillators, can be correlated to thecharge-flux term [5,6].

The modified charge–charge flux-overlap (CCFO) model[25,35,36] for infrared intensities has shown the importance ofthe charge-flux term in the H–X stretching intensity enhancement.It is possible to confirm this behavior by the atomic polar tensor PH

X

for the hydrogen atom through comparison between PHXX and PH

ZZ

elements before and after complexation. According to the modifiedCCFO model, the PH

XX element is a measure of the hydrogen atomic

mplexes, obtained with B3LYP and PBE1 functionals.

Table 4Atomic polar tensors of the hydrogen atom in H–F before and after R–CBBN� � �H–F complex formation, with R = NH2, H and NO2, obtained with B3LYP and PBE1 functionals

PBE1 values are given in parentheses. Values are given in units of electrons (e).

T.G. Castro et al. / Vibrational Spectroscopy 49 (2009) 133–141138

charge in the equilibrium position:

PHXX ¼ q0

H (2a)

whereas the PHZZ element measures the sum of the hydrogen atomic

charge and a charge-flux term associated to the H–F stretching:

PHZZ ¼ q0

H þ@qH

@zH

� �r0

H�F (2b)

Moreover, the H–F stretching intensity is given by:

AstrH�F ¼ KðPH

ZZÞ2

(2c)

where K = 975 km mol�1 e�2 for values of IR intensity in km mol�1.

Fig. 5. Normal coordinates for the CBBN stretching mode in R–CBBN� � �H–F

The interpretation of the results obtained from Eqs. (2a)–(2c)leads to a better understanding of the H–F stretching intensityafter complexation. The enlargement in the H–F stretchingintensity can been associated to the effect of the charge-fluxterm. In general, the charge-flux term is strongly affected bycomplexation, in contrast to what happens with the hydrogencharge. The latter is always positive, whereas the charge-flux isslightly negative in the free-molecule and becomes quite positiveafter complexation. Therefore, in the complex the hydrogencharge and the charge-flux term have the same algebraic sign.Since the H–F stretching intensity is proportional to the squares ofthe sum of these terms, it is enormously increased upon H-bondformation.

complexes, with R = CH3O and CN, obtained with B3LYP functional.

T.G. Castro et al. / Vibrational Spectroscopy 49 (2009) 133–141 139

Table 4 gives the results of the atomic polar tensors of thehydrogen atom in H–F before and after R–CBBN� � �H–F complexformation, for R NH2, H and NO2.

According to Table 4, the PHXX element, associated with the

hydrogen atomic charge, is only slightly decreased after com-plexation. On the other hand, the PH

ZZ element, associated withcharge-flux due to the H–F stretching, is highly increased. UsingEqs. (2a) and (2b), it is possible to calculate the charge-flux term. AtB3LYP level, it varies from �0.090 e in free H–F to +0.779 e forR = NH2, +0.620 e for R = H and +0.569 e for R = NO2. A similarbehavior is also found for the PBE1 calculation. Thus, it isinteresting to verify that the charge-flux term is negative in thefree molecule and becomes quite positive after complexation.Furthermore, it is also interesting to notice that the charge-fluxterm seems to increase with the H-bond strength.

Using Eq. (2c) one can make a self-check of the calculated H–Fstretching intensities. In free H–F, the intensities obtained fromthis equation are 124 and 132 km mol�1, respectively, using B3LYPand PBE1 values for PH

ZZ from Table 4, whereas the correspondingvalues obtained directly from a normal mode analysis are 130 and138 km mol�1, from Table 3. For R–CBBN� � �H–F complexes withR = NH2, H and NO2, the H–F stretching intensities obtained fromEq. (2c) using the PH

ZZ element at B3LYP level are 1310, 1008 and904 km mol�1, respectively, whereas their B3LYP calculated valuesusing the normal mode analysis are 1403, 1011 and 899 km mol�1,respectively. The agreement of the values coming from Eq. (2c) andfrom a normal mode analysis indicate that this vibration isdominated by the movement of the hydrogen atom along the axisof the H–F bond, which is here represented by the z cartesian axis.

In contrast with the results obtained for the H–F stretching mode,the intensities of the normal modes of R–CBBN fragment are onlyslightly modified after complexation. A more pronounced effect isobtained to the CBBN stretching intensity, which is slightly shiftedupward (blue-shifted) upon H-bond formation. It is interesting tonotice that the C�N stretching intensity varies substantially alongthe series, depending directly on the electronic nature of the Rsubstituent. The stretching intensity ratio Ac

C�N=AC�N indicates thatits value is increased after complexation, except for R = CF3 and NO2.This behavior reflects the high degree of mixture of this normalmode. Fig. 5 shows the relative lengths of the vectors representing

Fig. 6. New intermolecular vibrational modes for the R–CBBN� � �H

the atomic displacements for this normal mode with R = CH3O andCN. There is a reasonable degree of mixturein considering the changeof the magnitude of the normal vectors in each complex, as well as itsdependence on the R substituent. In this case, there is not a linearrelation between the H-bond strength and the vibrational char-acteristics of this oscillator, in terms of IR frequency and intensity.

The formation of the R–CBBN� � �H–F complexes gives rise to newvibrational modes. Fig. 6 shows the schematic representations ofthe new vibrational modes for R NH2 complex.

The new vibrational modes for R–CBBN� � �H–F series are shownin Table 5.

Several interesting features come out from the new vibrationalmodes. First, the lowest-frequency modes of each complex consist ofin-plane and out-of-plane intermolecular bending vibrations, wherethe atoms, in each molecule of the complex, move in a perpendiculardirection with respect to the molecular axis. Their IR intensities arevery weak and these normal modes are not localized. They aredegenerated for R = CH3, H, Cl, F, CF3 and CN. Second, in contrast towhat was observed in C2H2�m(CH3)m� � �H–F [5], a linear dependencebetween the H-stretch frequency and the H-bond strength was notfound. Its IR intensity is also very weak and thus its assignment in theexperimental vibrational spectrum is not easy. Additionally, the twoH–F bending modes, which are associated with the in-plane (b2) andout-of-plane (b1) motions, where the proton of the H–F moleculemoves along a line which is perpendicular to the H–F chemical bondaxis and which are pure rotations in the H–F isolated molecule,become infrared-active after complexation. Analogously to thecomplex bending modes, these H–F bending modes are degeneratedfor R= CH3, H, Cl, F, CF3 and CN. On the other hand, a good linearcorrelation between this vibrational frequencies and the H-bondstrengths was found, which are shown in Fig. 7.

It is interesting to notice that the H–F out-of-plane bendingintensity is practically determined by the hydrogen equilibriumcharge, obtained from the PH

XX element of the atomic polar tensor,according to the equation:

Aout-of-planeH�F ¼ KðPH

XXÞ2

(2d)

From Table 4 and Eqs. (2a) and (2d), the B3LYP calculated values forR = NH2, H and NO2 are 141, 154 and 151 km mol�1, respectively,

–F complex, with R = NH2, obtained with B3LYP functional.

Fig. 7. DEc versus H–F in-plane bending frequency in R–CBBN� � �H–F complexes, obtained with B3LYP and PBE1 functionals.

Table 5Harmonic frequencies (ni, cm�1) and infrared intensities (Ai, km mol�1) of the new vibrational modes, obtained with B3LYP and PBE1 functionals

R Complex-H bend in plane Complex-H bend out of plane H-bond stretch H–F bend in plane H–F bend out of plane

n A n A n A n A n A

NH2 41 (39) 4 (4) 51 (50) 1 (2) 187 (196) 8 (9) 713 (735) 154 (151) 736 (755) 144 (142)

CH3O 37 (37) 2 (2) 42 (42) 0 (0) 176 (183) 5 (5) 716 (734) 144 (143) 710 (728) 146 (144)

CH3 48 (49) 1 (1) 48 (49) 1 (1) 183 (186) 6 (7) 716 (728) 145 (144) 716 (728) 145 (144)

OH 48 (49) 3 (4) 46 (47) 7 (7) 177 (180) 7 (7) 691 (704) 149 (148) 683 (695) 155 (154)

SH 43 (43) 1 (1) 39 (39) 0 (0) 163 (170) 6 (6) 682 (698) 146 (144) 672 (689) 147 (146)

H 82 (83) 11 (11) 82 (83) 11 (11) 181 (183) 5 (5) 662 (622) 159 (158) 662 (622) 159 (158)

Cl 40 (41) 0 (0) 40 (41) 0 (0) 155 (157) 5 (6) 637 (644) 150 (149) 637 (644) 150 (149)

F 46 (46) 0 (0) 46 (46) 0 (0) 158 (160) 4 (5) 614 (625) 155 (155) 614 (625) 155 (155)

CF3 33 (33) 3 (3) 33 (33) 3 (3) 142 (133) 4 (4) 571 (580) 148 (148) 571 (580) 148 (148)

CN 36 (37) 5 (5) 36 (37) 5 (5) 138 (138) 5 (5) 547 (550) 132 (142) 547 (559) 132 (142)

NO2 32 (32) 4 (4) 37 (37) 5 (5) 126 (127) 4 (4) 520 (525) 148 (147) 528 (532) 159 (158)

PBE1 values are given in parentheses.

T.G. Castro et al. / Vibrational Spectroscopy 49 (2009) 133–141140

whereas the values obtained from a frequency calculation are 144,159 and 159 km mol�1, which are in good agreement with thecalculated ones.

In contrast to what was found in C2H2�m(CH3)m� � �H–F (m = 0,1 or 2) complexes, for which the H–F in-plane bending intensityis practically half of that relative to the H–F out-of-plane mode,both the intensity values are practically equal. This means thatthe contribution from the in-plane charge flux term for its in-plane IR intensity is negligible. Thus, both vibrational modes arehighly localized on the proton of H–F, as it can be seen in Fig. 6.This similarity is also verified in relation to their frequencyvalues.

4. Conclusions

In this work DFT calculations with B3LYP and PBE1 functionalsand 6–311++G(d,p) basis set were performed for R–CBBN� � �H–Fcomplexes (with R = NH2, CH3O, CH3, OH, SH, H, Cl, F, CF3, CN andNO2). The obtained results revealed a linear dependence betweenthe H-bond strength and several structural, electronic andvibrational properties. In particular, an important linear depen-

dence between the BSSE and ZPVE corrected binding energies andthe calculated dipole moment of the R–CBBN free molecule wasfound. This result suggests that mRCN can be useful to predict theability of R–CBBN molecules to form hydrogen-bonds, similarly towhat was found by Galabov and Bobadova-Parvanova from theanalysis of calculated molecular electrostatic potential in thenitrile nitrogen in isolated nitrile molecules. As expected, the H–Fstretching frequency, in conformity with the rH–F elongation, isred-shifted upon complexation. On the other hand, CBBN stretchingfrequency is blue-shifted and corresponds to a shortening of theCBBN bond. The IR intensities of the H–F stretching and bendingmodes in the complex are adequately interpreted through theatomic polar tensor of the hydrogen atom in H–F, using themodified CCFO model for infrared intensities. The new vibrationalmodes arising from complexation have shown several interestingfeatures.

Acknowledgements

The authors thank the Brazilian funding agencies CNPq, CAPES,FAPESQ/PB and FINEP for the partly financial support.

T.G. Castro et al. / Vibrational Spectroscopy 49 (2009) 133–141 141

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