Development of eclipsed and staggered forms in some hydrogen bonded complexes

Development of Eclipsed and StaggeredForms in Some Hydrogen BondedComplexes

ALI EBRAHIMI, MOSTAFA HABIBI, NAHID HESABIDepartment of Chemistry, University of Sistan & Balouchestan, P.O. Box 98135-674, Zahedan, Iran

Received 30 April 2008; accepted 12 June 2008Published online 2 October 2008 in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/qua.21850

ABSTRACT: Intermolecular hydrogen bonding in X3CH��NH3 (X � H, F, Cl, and Br)complexes has been studied by B3LYP, B3PW91, MP2, MP3, MP4, and CCSD methodsusing 6-311��G(d,p) and AUG-cc-PVTZ basis sets. These complexes could exist in botheclipsed (EC) and staggered (ST) forms. The differences between binding energies of ECand ST forms are negligible and all EC and ST shapes correspond to minimumstationary states. The order of stabilities of them is in an agreement with the results ofatoms in molecules (AIM) and natural bond orbital (NBO) analyses. On the basis of lowdifferences between binding energies, ST forms are more stable than EC forms in allcomplexes with the exception of Br3CH��NH3, which behaves just opposite. Althoughthe differences between binding energies are negligible, they are consistent with the resultsof AIM analysis. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem 109: 629–638, 2009

Key words: hydrogen bond; eclipsed; staggered; ab initio; AIM; NBO

Introduction

H ydrogen bond is an important intermolecularinteraction in many chemical and biochemi-

cal processes. Many literatures have been devotedto the study of hydrogen bonds [1–5] from a theo-retical stand point. Usually different orientationsare possible for monomers in hydrogen bondedcomplexes [5–10]. Although many studies havebeen performed on conformational analysis of hy-drogen bonded complexes [11 (references therein),

12–19], but eclipsed and staggered conformers,which are possible in some H-bonded complexes,have not yet been considered.

Although conformational analysis is a funda-mental subject in chemistry, not every questionconcerning the conformation analysis is simple toanswer. For example, the preferred staggered con-formation of ethane is widely believed to be causedby the steric repulsion of the hydrogen atoms or ofthe COH bonds [20–22]. However, recently studiesfound that hyperconjugation, not steric repulsion,leads to the staggered structure of ethane [23].

In the present work, hydrogen bonded com-plexes shown in Scheme 1 have been studied by abCorrespondence to: A. Ebrahimi; e-mail: [email protected]

International Journal of Quantum Chemistry, Vol 109, 629–638 (2009)© 2008 Wiley Periodicals, Inc.

initio method. Because of tetrahedral orientation oflone pairs and localized bond orbitals of N and Catoms, the complexes could exist in eclipsed (EC)and staggered (ST) forms.

Although the study of the effect of X atoms onbinding energies is interesting, the relative stabilityof ST and EC forms is also a remarkable consider-ation. Herein, the confronted atoms are far fromeach other. Do the effects of different parameters onthe relative stabilities of EC and ST forms decreasewith increasing distance, so that their stability be-come identical? Do the computational methods dis-tinguish the difference between binding energies ofEC and ST forms, if their stabilities are not equal? IsEC structure a maximum stationary state or a min-imum stationary state? In spite of limitations oncomputational methods, answer to whole questionswas main goal and required purpose of this work.

Computation Methods

Geometry optimization and vibrational fre-quency calculations were fully carried out using theGaussian03 program [24], by the B3LYP three-parameter hybrid functional [25–27], and both6-311��G(d,p) and AUG-cc-PVTZ basis sets [28].

Single point calculations were performed atB3PW91/6-311��G(d,p) [29], MP2/AUG-cc-PVTZ[30] and MP3 [31], MP4 [32], and CCSD/6-311��G(d,p) [33] levels of theory. By comparisonbetween results obtained at these levels of theoryand B3LYP/6-311��G(d,p), the latter could be se-lected as a reliable level for other calculations.

The difference between geometrical parametersand energy data of EC and ST forms are very small.Therefore, employment of “VeryTight” keyword isnecessary for geometry optimization. Furthermore,the geometry optimization has been performedboth with constraint on point group (C3V) and

without it. The frequency calculation was achievedto specify the type of EC and ST forms as minimumor maximum stationary points. In addition, a cor-rected interaction energy excluding the inherentbasis set superposition error (BSSE) was evaluated.The BSSE was calculated using the boys Bernardicounter poise technique [34].

In search for stabilizing factors in EC and STforms, the population analyses were performed bynatural bond orbital (NBO) [35] and atoms in mol-ecules (AIM) [36] methods. The NBO analysis car-ried out on the B3LYP/6-311��G(d,p) geometriesusing the NBO program [37] included in the Gauss-ian 03 package. The topological properties of boththe electronic charge density and the atomiccharges were characterized using the AIM method-ology with the AIM2000 software [38] on the wavefunctions obtained at B3LYP/6-311��G(d,p) levelof theory.

Results and Discussion

GEOMETRICAL PARAMETERS

On the basis of obtained results, the most impor-tant geometrical parameters of complexes andmonomers are reported in Table I. As can beseen, N��H hydrogen bond length ranges in 2.1427–2.7411 Å, and tendency in order of reduction ofhydrogen bond length in both series of complexes(EC or ST) is as follows:

NH3��HCH3 � NH3��HCF3

� NH3��HCCl3 � NH3��HCBr3

N��H bond length depends on the size of X atomand decreases with increasing atomic number of X.In each case N��H bond length in EC is slightlylonger than ST form. Although this is a small dif-ference, but obeys the same order in all cases. Inspite of small differences between structural pa-rameters and energy data of EC and ST forms, theclose similarity of structures shows the importanceof this small difference. The C��N distance ranges in4.2292–4.6761 Å in optimized structures at theaforementioned level. The trend in this structuralparameter is similar to rN��H and increases withN��H bond length. This trend can be expected withrespect to COH and N��H bond lengths. The trendin COH bond length is as N��H and their summa-tion also follow this order.

SCHEME 1. Eclipsed and staggered forms of com-plexes. [Color figure can be viewed in the online issue,which is available at www.interscience.wiley.com.]

EBRAHIMI, HABIBI, AND HESABI

630 INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY DOI 10.1002/qua VOL. 109, NO. 3

The COH bond lengths of monomers are givenin the parentheses in Table I. In each case, the COHbond length of monomer is shorter in comparisonwith corresponding complex (even in NH3��HCH3)and is in a good agreement with red shift in vibra-tional frequency of COH (�COH) calculated at men-tioned level. The red shift is equal to 10.41, 37.05,107.38, and 125.40 cm�1, in H3CH��NH3,F3CH��NH3, Cl3CH��NH3, and Br3CH��NH3 com-plexes, respectively.

Although N��HOC interaction is expected to bean improper hydrogen bond that causes a blue shiftin �COH, but the COH bond length increases in thisseries of complexes and a red shift is observed in�COH. This result is in a good consistent with theresults of AIM and NBO analysis, which will bediscussed in the next section.

The COH bond length elongation multiplied by10�4 is equal to 2, 24, 76, and 88 Å for HCH3, HCF3,HCCl3, and HCBr3 cases, respectively, on complex-ation. The COH bond length increases with esca-lating N��H interaction. Although the difference be-tween COH bond length in EC and ST forms isvery small, but this bond length in each EC form isnot longer than corresponding ST form (with fivedecimal places).

The NOH bond length in complexes is longerthan lone NH3 molecule. The trend in NOH bondelongation is as follows:

NH3��HCF3 (2.5) � NH3��HCCl3 (1.33)

� NH3��HCBr3 (1.28) � NH3��HCH3 (0. 57)

The data in the parentheses correspond to NOHbond length elongation in angstroms (multiplied by

103). This elongation seems to be in relationshipwith electronegativity and negative charge densityof X atom. The NOH bond length increases withcharge density of X atom and the elongation isaccompanied with a decrease in HNH bond angle.The trend in decreasing HNH bond angle is thesame as NOH bond elongation

NH3��HCF3 (8.15) � NH3��HCCl3 (6.18)

� NH3��HCBr3 (5.86) � NH3��HCH3 (3.56)

The data in the parentheses correspond to thechange of HNH bond angle in degrees (multipliedby 10�4). The electronic density between N and Hatoms (in NOH bond) decreases with increasingthe electronegativity of X. Thus, NOH bond lengthincreases and subsequently HNH bond angle de-creases on binding (the occupancy of NOH NBOcalculated by NBO analysis and the charges on theH atoms evaluated by NAO and AIM methods willbe considered in the next section).

In all cases, the NOH bond length in the ECform is slightly shorter than the ST form (0 � 10�5

to 3.0 � 10�5 Å). Furthermore, HNH angle in theEC forms is slightly bigger than the ST forms (7 �10�4 to 3.90 � 10�2). In addition, the COX bondlength slightly rises on complexation. This behavioris similar to the NOH bond elongation and theHNH bond angle contraction:

H3N��HCF3 (5.90) � H3N��HCCl3 (4.14)

� NH3��HCBr3 (3.14) � H3N��HCH3 (0.086)

Bond elongation values multiplied by 10�2. Al-though these are small changes but they obey a

TABLE I ______________________________________________________________________________________________The most important geometrical parameters of ST and EC forms at the B3LYP/6-311��G(d,p) levels.

rN � � � H dNC dH � � � X �HN � � � H �HCX � (or r)a rCX �� rNH rCHb

HCH3c 2.7411 3.8325 4.5717 111.342 109.751 109.471 1.0918 107.537 1.0151 1.0914

2.7404 3.8319 4.6761 111.343 109.750 1.0909 1.0918 107.536 1.0151 (1.0909)HCF3 2.2637 3.3558 4.2292 111.771 111.053 110.478 1.3494 107.077 1.0160 1.0921

2.2626 3.3547 4.3666 111.781 111.053 1.3435 1.3494 107.066 1.0161 (1.0897)HCCl3 2.1544 3.2442 4.2357 111.625 107.856 107.484 1.7906 107.274 1.0159 1.0898

2.1537 3.2436 4.4218 111.625 107.861 1.7864 1.7906 107.235 1.0159 (1.0823)HCBr3 2.1452 3.2349 4.2831 111.558 107.067 106.741 1.9554 107.306 1.0158 1.0898

2.1427 3.2324 4.4826 111.582 107.069 1.9523 1.9555 107.280 1.0158 (1.0810)

a In each case, the first and second rows correspond to EC and ST forms, respectively.b Italic data are �HCX and rCX values corresponding to lone HCX3. rNH and �HNH are equal to 1.0145 Å and 107.891° for lone NH3,respectively.c The data in the parentheses are related to HCX3 lone monomers.

ECLIPSED AND STAGGERED FORMS IN SOME HYDROGEN BONDED COMPLEXES

VOL. 109, NO. 3 DOI 10.1002/qua INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 631

logical order, and in any EC shape is not longerthan corresponding ST form. As can be seen inTable I, more reduction in HNH bond angle (withrespect to monomers) is certainly accomplishedwith more increases in HN��H bond angle whicharrange according to

H3N��HCF3 � H3N��HCCl3

� H3N��HCBr3 � H3N��HCH3

This angle in each case of ST shape is bigger thancorresponding EC form (with the exception ofH3N��CHCl3 complex, in which the angles are equalwith five decimal places), and the differences rangein 0.0000–0.02414 degrees. In addition, theHOCOX bond angle increases on complexationthat is according to following order:

H3N��HCBr3 (0.575) � H3N��HCCl3 (0.372)

� H3N��HCF3 (0.326) � H3N��HCH3 (0.280)

This order is in good agreement with N��H bondlength. Hence, HCX bond angle increases with re-duction of N��H bond length (increasing the H-bond strength) on complexation, which in each caseof EC is smaller than corresponding ST (with theexception of H3C��NH3, in which the result is in-versed).

ENERGETICS AND POPULATION ANALYSES

The binding energies obtained at different levelsof theory are reported in Table II. The differencebetween results at B3LYP/6-311��G(d,p) and re-

sults at other levels are (E0–Ei, where E0 corre-sponds to B3LYP/6-311��G(d,p) and Ei corre-sponds to each mentioned level, in kJ/mol): �1.75to �10.55 for B3LYP/AUG-cc-PVTZ, �1.04 to�1.80 for B3PW91/6-311��G(d,p), 1.55 to 7.04 forMP2/6-311��G(d,p), �1.72 to 5.64 for MP2/AUG-cc-PVTZ, 0.97 to 4.18 for MP3/6-311��G(d,p), 0.47to 2.79 for MP4/6-311��G(d,p), and 0.73 to 3.18 forCCSD/6-311��G(d,p).

The trend in the calculated binding energies arethe same at B3PW91 and B3LYP/6-311��G(d,p)levels of theory. The absolute values of bindingenergies are close at these levels of theory. In MP2method, as basis set become larger, the results be-come closer to the results obtained at B3LYP/6-311��G(d,p) level.

As the method changes from MP2 to MP3, MP4,and CCSD, the results become closer to the resultsobtained at B3LYP/6-311��G(d,p) level.

With the exception of Cl3CH��NH3 andBr3CH��NH3, with very similar binding energies,the trend in binding energies are identical at alllevels of theory, when the trend in the stability ofeclipsed and staggered forms are also similar.

The values of binding energy calculated atB3LYP/6-311��G(d,p) level of theory, with sym-metry restriction (C3V point group) and without it(C1), with basis set superposition error and withoutit, are given in Table III. E (ST) and E (EC) valuescorrespond to binding energies of ST and EC forms,respectively, without BSSE correction. The E �BSSE values correspond to binding energies cor-

TABLE III _____________________________________Binding energy of ST and EC forms at C3V and C1

point groups, in kJ/mol.

H F Cl Br

C3V point groupE (ST)a �2.323 �20.799 �24.084 �23.036E (EC)a �2.315 �20.784 �24.083 �23.053E � BSSEb �1.210 �18.259 �20.233 �19.991�Ec �7.886 �14.876 �1.392 16.698

C1 point groupE (ST) �2.323 �20.838 �24.090 �23.049E (EC) �2.315 �20.819 �24.071 �23.052E � BSSE �1.210 �18.296 �20.230 �19.996�E �7.886 �18.536 �18.011 2.442

a Binding energy without BSSE correction.b Mean binding energies corrected for BSSE.c The difference between binding energies of EC and STforms [E (ST)-E (EC)] in J/mol.

TABLE II ______________________________________Binding energies calculated at different levels oftheory in kJ/mol.

H F Cl Br

B3LYP(1) �2.32 �20.81 �24.10 �23.06B3LYP(2) �0.57 �15.75 �18.89 �12.51B3PW91(1) �1.28 �19.00 �22.83 �21.87MP2(1) �4.25 �22.36 �29.60 �30.10MP2(2) �3.33 �19.09 �24.44 �28.70MP3(1) �4.13 �21.77 �28.28MP4DQ(1) �3.78 �21.28 �26.89CCSD(1) �3.84 �21.53 �27.28

(1) and (2) correspond to 6-311��G(d,p) and AUG-cc-PVTZbasis sets, respectively.



rected for BSSE, which averaged over the corre-sponding values of EC and ST forms. The differ-ences between binding energies of ST and EC formsare very small and BSSE corrections are approxi-mately identical in both forms. Therefore, the sta-bility of ST and EC forms can be compared withuncorrected values, �E � E (ST) � E (EC), whichare more compatible with the results of AIM anal-ysis.

As can be seen in Table III, with symmetry re-striction and without it, with BSSE correction andwithout it, the trend in binding energy is

NH3��HCCl3 � NH3��HCBr3

� NH3��HCF3 � NH3��HCH3

Remember that binding energy in NH3��HCBr3 isestimated slightly higher than NH3��HCCl3 by MP2method. For H3CH��NH3, the complexation energycorrected with BSSE is equal to approximately �1.2kJ/mol, which can be categorized as weak hydro-gen bonds. In other cases, the complaxation energyrange in �18 to �20 kJ/mol, which may begrouped in medium hydrogen bonds. By consider-ing N��H bond length, the binding energy ofBr3CH��NH3 is expected to be higher than

Cl3CH��NH3, whereas the reverse is true with re-spect to the results that have been reported in TableIII. In addition to hydrogen bonding, other factorsalso affect the stability of complexes.

To compare the interactions within differentcomplexes in more detail, the population analyseshave been achieved by AIM and NBO methods onthe wave functions obtained at B3LYP/6-311��G(d,p) level of theory. Two sample molecular graphsof EC and ST forms are shown in Figure 1. Thetopological properties of electronic charge densitycalculated at N��H BCP are reported in Table IV.

The trend in the average values of electron den-sity � and also 2�BCP (for EC and ST forms) are asfollows

NH3��HCBr3 (0.0218, 0.0618)

� NH3��HCCl3 (0.0216, 0.0607)

� NH3��HCF3 (0.0173, 0.0489)

� NH3��HCH3 (0.0072, 0.0180)

The first and second data in the parenthesescorrespond to average values of �BCP and 2�BCP,respectively. In addition, energy density values,HBCP, calculated at N��H BCP are reported in TableIV. In all cases, 2�BCP � 0 and HBCP 0. Thus, theinteractions could be considered as medium hydro-gen bonds according to findings of Rozas et al. [39].The � and 2� values calculated at N��H BCP arecompatible with N��H bond length. There is a linearrelationship between � (or 2�), and N��H bondlength, with R2 � 0.99 in both cases.

Some results of natural population analysis(NPA) are recorded in Table V. The results of ECforms are as same as ST forms. The calculated nat-

TABLE IV _____________________________________Electron density (�BCP), Laplacian of electrondensity (�2�BCP), Lagrangian kinetic energy (GBCP),and energy density values (HBCP) in atomic units.

102�BCP 1022�BCP 103GBCP 104HBCP

CH4 ST 0.72 1.80 0.40 �5.30EC 0.72 1.80 0.40 �5.29

CHF3 ST 1.73 4.89 1.07 �15.63EC 1.73 4.89 1.06 �15.60

CHCl3 ST 2.19 6.08 1.37 �15.02EC 2.14 6.06 1.36 �14.97

CHBr3 ST 2.19 6.20 1.40 �15.20EC 2.18 6.18 1.39 �15.22

FIGURE 1. Sample molecular graphs obtained fromAIM analysis for eclipsed (EC) and staggered (ST)forms. Small red spheres and lines correspond to bondcritical points (BCPs) and bond paths, respectively.[Color figure can be viewed in the online issue, which isavailable at www.interscience.wiley.com.]



ural charge on N atom is negative and approxi-mately equal to �1.06 e in all cases. As was ex-pected, the calculated natural charge on the H atomof N��H bond is positive. The lowest natural chargecorresponds to F3CH��NH3, which is not consistentwith high electronegativity of F atom. In addition,the natural charges (on F atoms) are not in agree-ment with the charges calculated by AIM method,which are given in the parentheses in Table V.These are in accord with the chemical behavior of Hand F atoms. The natural charge on H atoms of NH3monomer is approximately equal to 0.36 e in allcases, which are in harmony with the charges cal-culated by AIM method.

In all cases, as was expected, the most importantdonor-acceptor interaction is nN 3 �*CH (see TableV). The lowest and highest interactions correspondto H (1.28 kcal/mol) and Cl (8.58 kcal/mol), respec-tively. There is a very good liner correlation be-tween interaction energies (E(2)) and the complex-ation energies calculated at B3LYP/6-311��G(d,p)level of theory (R2 � 0.996). It is clear that changesin the occupancies of nN and �*CH orbitals increasewith E(2). No negative frequency appears in calcu-lations. Thus, all EC and ST forms correspond tominimum stationary points. The lowest vibrationalfrequency is given in Table VI. This vibrationalfrequency corresponds to torsion around N��Cbond. The values given in the parentheses corre-spond to EC form and range in 4–26 cm�1. With theexception of HCH3��NH3 complex, vibrational fre-quency of EC is higher than ST form. The differencebetween lowest frequencies of EC and ST forms (�� EC � �ST) is equal to �10.23, 0.45, 1.45, and 7.40in H3CH��NH3, Cl3CH��NH3, Cl3CH��NH3, andBr3CH��NH3, respectively. There is a good linear re-

lationship between �� and m1/2 (m is atomic mass ofX) with R2 � 0.96.

The corrections of zero point energy (ZPE) andthermal energy (THE) have also been performed onbinding energies (see Table VI). The binding energyis low for H3N��HCH3 complex. With ZPE and THEcorrection, �E, �H, and �G become positive. Thus,as was expected with respect to the obtained resultsat mentioned levels, the H3CH��NH3 complex couldnot be formed, even at low temperatures. For othercomplexes, the binding energy also decreases withZPE and THE corrections. Despite this, the �Hvalue is still negative and ranges in �14 3 �18kJ/mol. With refer to the negative values of �S, thecomplexes could not be formed at temperatureshigher than 200 K. The values of �G at 100 K aregiven in Table VI.

TABLE V ______________________________________________________________________________________________The results of natural atomic orbital (NAO) and natural bonding orbital (NBO) analyses.

H F Cl Br

Na �1.05 (�0.99) �1.06 (�1.01) �1.06 (�1.005) �1.06 (�1.004)Ha 0.23 (0.046) 0.16 (0.19) 0.26 (0.21) 0.27 (0.22)H (N)a 0.35 (0.33) 0.36 (0.34) 0.36 (0.35) 0.36 (0.35)n 3 �*(CH)b 1.28 7.17 8.58 8.47nc 1.9927 1.9802 1.9738 1.9715�*(CH)d 0.0037 0.0558 0.0538 0.0465

The data in the parentheses calculated by AIM analysis at mentioned level.a Natural charge on N and H atoms in a.u., calculated at B3LYP/6-311��G(d,p) level.b Donor-acceptor interaction energy in kcal/mol.c The occupation number of a lone pair orbital of N atom.d The occupation number of �*(CH).

TABLE VI _____________________________________Energetics (in kJ/mol) and the lowest vibrationalfrequency in cm�1.

H F Cl Br

a�E � ZPE 1.071 �16.164 �18.996 �18.004b�E � therm 5.372 �12.444 �15.388 �14.317c�H 2.891 �14.922 �17.867 �16.795d�G 12.562 �7.309 �9.378 �8.283� 14.27 18.89 22.26 18.69

e(4.04) (19.34) (23.72) (26.09)

a The binding energies corrected for zero point energy.b The binding energies corrected for thermal energies.c The binding enthalpies.d The binding Gibbs free energies at 100 K.e The data in the parentheses correspond to EC forms.



Although the geometry optimization has beenperformed by using “VeryTight” keyword and fre-quency calculation specified EC and ST forms asminimums stationary points, because of very smalldifferences between binding energies of EC and STforms, the energy surface has been scanned aroundHNCX dihedral angle from zero (EC form) to 60degrees (ST form) and in a reverse process, to rec-ognize the structures of stationary points and effec-tive factors in stability of EC and ST forms in moredetail.

The relative energies versus HNCX dihedral an-gle are shown in Figure 2. To show periodic changeof energy, the curves have been extrapolated to120°. Although the changes and the differences be-tween binding energies of EC and ST forms arenegligible, but they are important from computa-tional stand point on geometry optimization espe-cially in using “VeryTight” keyword.

There are two transition states (maximumstationary points) and one ground state forH3CH��NH3 between 0 and 60 (at a dihedral angle�HNCX � 30°, which is more stable than EC andST forms). In HCF3��NH3 complex, three transitionstates are observed at dihedral angles �HNCX � 6,22, 52. Thus, two ground state structures can beseen in this region at both dihedral angles HNCX �18 and 46°. These are not lower than ST form andhigher than EC form from energetic standpoint.

The behavior of Cl3CH��NH3 complex is verysimilar to H3CH��NH3. However, the energy of

minimum stationary structure is higher than bothEC and ST forms.

Only one maximum structure is observed be-tween 0 and 60 degrees in Br3CH��NH3 complex. Byscanning HNCX angle from 0 to 60 (and also scan-ning in the reverse direction) the EC was located ina little bit lower than ST form. Because of very smalldifference between EC and ST forms, it was ex-pected that the NBO method cannot explore theeffective factors over the relative stabilities of ECand ST forms. However, the NBO analyses werecarried out on the structures obtained from scan-ning HNCX dihedral angle. The results did notclear these tiny differences.

To investigate more about the stability of bothforms, the kinetic energy (KE), electron–electronrepulsion energy (EE), nuclear–nuclear repulsionenergy (NN), and nuclear–electron attraction en-ergy (NE) calculated at B3LYP/6-311��G(d,p)level are plotted versus HNCX dihedral angle inFigures 3.

In HCH3��NH3 complex, KE is approximatelyconstant in the range of 0–60°. So, the changes instability are influenced by other energetic terms. Abig change is seen around 40°. The attractive poten-tial energy (NE) is dominated for ST, on the con-trary while the repulsive potential energy (EE andNN) is dominated for EC form. The results showthat the influence of increasing NE (negative val-ues) in the stability of ST is more than the influenceof decreasing EE, NN in the stability of EC form.Thus, ST is more stable than EC form.

The changes of PE and KE versus dihedral angleHNCX are also illustrated for F3CH��NH3 complexin Figure 3. In comparison with H3CH��NH3 com-plex, similar behaviors were observed for EE, NE,and NN terms. Herein, the change of KE versusHNCX dihedral angle is not negligible. The role ofKE in the relative stability of EC and ST forms issimilar to NE. The relative stability of these formsshow that the influence of decreasing KE and NE(become more negative) overcome to increasing EEand NN so that ST form becomes more stable thanEC form. The changes of KE, NE, EE, and NN areslightly different for Cl3CH��NH3 (see Fig. 3). First,both EE and NN decrease versus HNCX dihedralangle (on the contrary to previous case), next EEoscillates slowly after an abrupt jump between 20and 30°, subsequently NN decreases with a highslope. With respect to neglecting sudden change inthe range of 20–30°, the NE value increases (theabsolute value decreases) whereas KE value slowlydecreases from 0 to 60.

FIGURE 2. The relative energy (cal/mol) versus HNCXdihedral for H3N��HCH3 (�), H3N��HCF3 (F),H3N��HCCl3 (Œ), H3N��HCBr3 (�). The data forH3N��HCH3 multiplied by 1000 in order to be within theemployed range. [Color figure can be viewed in the on-line issue, which is available at www.interscience.wiley.com.]



Lower KE and NN values cause more stability ofST form. On the contrary, NE and EE behave onopposite side. Herein, the effect of KE and NN ispredominant, so that the ST is still more stableform.

Although the sudden changes in EE, NN, andNE are too small in Br3CH��NH3 complex, but KE isaccompanied with several changes. In this case, theKE and NE values cause more stability of ST shape,but the EE and NE values behave completely dif-ferent. The results show that the lower values of EEand NN in EC form dominate higher values of NE

FIGURE 3. The kinetic energy (�), electron–electronrepulsion energy (f), nuclear-nuclear repulsion energy(Œ), and nuclear–electron attraction energy (�) changescalculated at B3LYP/6-311��G(d,p) level versus HNCXdihedral angle. All data multiplied by 103 with the ex-ception of KE in CH4 and all quantities in CHBr3, whichmultiplied by 105 and 102, respectively. [Color figurecan be viewed in the online issue, which is available atwww.interscience.wiley.com.]

FIGURE 4. The contour maps of electron density forEC and ST forms in a plane containing three atoms of aHN��C part calculated at B3LYP/6-311��G** level. Theoutermost contour is �(r) � 0.001 au, and the remainingcontours increase in the order 2 � 10n, 4 � 10n, and8 � 10n, with n � �3, �2, �1, and 0. The bold con-tour is �(r) � 0.02 a.u. [Color figure can be viewed inthe online issue, which is available at www.interscience.wiley.com.]



(more negative) in ST form, so that it become morestable than ST.

To follow more investigation, electron densitycontour maps and electron density correspondingto each countor are shown in Figure 4. The countorsthat are illustrated by bold lines correspond to � �0.008 au. It is obvious that the electronic overlap(continuity in countor) is observed for H3N��HCH3at an electron-density equal to 0.004 au, whereas forH3N��HCF3 and H3N��HCCl3 is occurred at 0.008and 0.002 au, respectively. The electronic overlapfor EC and ST is similar and has been illustrated atidentical densities, in three cases. On the basis ofelectron-density countor maps, obtained results arein a good agreement with energy data. The bindingenergy increases with the electronic overlap. Inthree cases, ST is more stable than EC form. On thecontrary, in Br3CH��NH3 complex that EC is morestable than ST form, different countors are observedfor two forms. The electronic overlap occurs at 0.02au (similar to Cl3CH��NH3) for EC form, whereas itoccurs at 0.008 au in ST form. Thus, lower bindingenergy in Br3CH��NH3 in comparison withCl3CH��NH3 and also more stability of EC inBr3CH��NH3 complex could be discussed by thesemaps.

To recognize effective factors over relative stabil-ity of EC and ST forms, AIM analysis has beenundertaken on all structures obtained from scan-ning HNCX dihedral angle (from 0 to 60). On thebasis of our observation (see Fig. 5), electron den-sity �BCP, Laplacian of electron density 2�BCP andLagrangian kinetic energy GBCP increase from 0 to60° in all complexes. These changes are accompa-nied with increasing energy density HBCP in H, Fand Cl cases. Hence, ST is expected to be morestable than EC form in these complexes. On thecontrary, increasing �BCP, 2�BCP, and GBCP is ac-companied with decreasing HBCP. The results indi-cate that the effect of decreasing HBCP is predomi-nant factor over three other properties and ECshould be more stable form in Br3CH��NH3 com-plex.

Conclusions

The most important results of theoretical in-vestigation of hydrogen bonded complexesX3CH��NH3, with both EC and ST forms could bementioned as follows. The trend in binding ener-gies is in a good agreement with both geometricalparameters and the results of AIM and NBO anal-

ysis. The higher binding energy is relevant toBr3CH��NH3 complex with a few individual char-acters such as lower N��H hydrogen bond length,higher � value at HBCP, and higher donor-acceptorinteraction energy (nN 3 �*CH).

The difference between binding energies of ECand ST forms are negligible. In all cases, ST is morestable than EC with the exception of Br3CH��NH3complex, which behaves just opposite. Whole EC

FIGURE 5. The changes of topological properties ofelectron charge density versus HNCX dihedral angle.The plots illustrated by �, F, Œ, and � correspond toH3CH��NH3, F3CH��NH3, Cl3CH��NH3, and Br3CH��NH3,respectively. [Color figure can be viewed in the onlineissue, which is available at www.interscience.wiley.com.]



and ST shapes correspond to minimum stationarystates. Energy versus XCNH dihedral angle indi-cates different minimum and maximum stationarypoints between EC and ST forms. Although thedifferences between stabilization energies of thesepoints are negligible, but some of them are lower inenergy than EC and ST forms. The relative stabilityof EC and ST forms are in a good agreement withthe results of AIM analysis.

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Development of eclipsed and staggered forms in some hydrogen bonded complexes

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