ORIGINAL PAPER

Benchmarking of ONIOM method for the study of NH3

dissociation at open ends of BNNTs

Ali Ahmadi & Javad Beheshtian &

Mohammad Kamfiroozi

Received: 8 May 2011 /Accepted: 26 July 2011 /Published online: 12 August 2011# Springer-Verlag 2011

Abstract The reliability of ONIOM approach have beenexamined in calculations of adsorption energies, transitionstructures, change of HOMO-LUMO energy gaps andequilibrium geometries of the interaction between NH3

and N-enriched (A) or B-enriched (B) open ended boronnitride nanotubes. To these ends, four models of the A or B,with different inner and outer layers have been studied. Inaddition, various low-levels including, AM1, PM3, MNDOand UFF have been examined, applying B3LYP/6-31 G* inall high-levels. It was shown, that in the case of A,(choosing two atom layers of the tube open-end as innerlayer) the results of ONIOM approach are in best agreementwith those of the pure density functional theory (DFT)calculations, while their results significantly differ fromthose of DFT in the case of B in same conditions. All aboveand population analysis demonstrate that the ONIOM maybe a reliable scheme in the study of weak interactions whileit is a controversial approach and should be appliedcautiously in the case of strong interactions. We also probedthe effect of tube length and diameter on the consistency

between ONIOM and DFT results, showing that thisconsistency is independent of the mentioned parameters.

Keywords Adsorption . B3LYP. Boron nitride nanotubes .

DFT. NH3. ONIOM

Introduction

The applications of computational chemistry span predict-ing the structure, spectra, transition states and reactivity ofcomplicated molecules. To serve as a predictive tool,however, the methods should be applicable to a largeenough portion of the system, reflecting the features of thereal system. Among the all quantum mechanical methods, afew of them can be easily applied to the study ofthermodynamics and reaction mechanisms in large systemssuch as proteins, nanotubes, etc. In fact, the calculation timein accurate ab initio methods grows much faster than thenumber of atoms. This growth is roughly relative to thethird power of the number of atomic basis functions used tosolve the Schrödinger equation, at least within the densityfunctional theory (DFT) context.

Developed by Morokuma et al., ONIOM is a method tostudy the large molecules by dividing them into two orthree layers, where a high-level calculation is performed onthe smallest layer (inner layer) and the rest layer (outerlayer) effects are included at a low-level of theory [1, 2].

In spite of several theoretical studies on single-walledcarbon nanotubes, applying ONIOM method, [3, 4] onlyfew works have been published on the case of boron nitridenanotubes (BNNTs) [5]. BNNTs as inorganic nanomaterials,have received considerable research interests [6, 7] becauseof their remarkable electronic, mechanical, and thermalproperties.

A. AhmadiYoung Researchers Club, Islamic Azad University,Islamshahr branch,Islamshahr, Iran

J. Beheshtian (*)Department of Chemistry,Shahid Rajaee Teacher Training University,P.O. Box: 16875–163, Tehran, Irane-mail: J.Beheshtian@srttu.edu

M. KamfirooziDepartment of Chemistry, Islamic Azad University,Shiraz branch,Shiraz, Iran

J Mol Model (2012) 18:1729–1734DOI 10.1007/s00894-011-1202-5

The ONIOM method is still a controversial method, ithas been recently reported that the often-used ONIOM(B3LYP:AM1) approach is not appropriate for somenanotube systems [8, 9]. In the present work, we areinterested in ONIOM study of the N-H bond cleavage ofNH3 at the open ends of BNNTs, evaluating its reliabilityby comparing its results with our previous reported fullDFT ones [10]. To this aim, several combinations ofdifferent levels of theory as well as different partitions ofthe inner and outer layers were considered.

The N-H bond cleavage is a challenging problem notonly toward the transformation of NH3 into a useful aminocompound but also toward the starting of many catalyticreactions [11–13]. Since only methodological aspects of theONIOM method have been studied in the present work, nodiscussion was addressed with respect to either experimen-tal data or absolute accuracy of the chosen levels ofcalculations.

Computational details

All calculations were carried out with the Gaussian 98 suiteof programs [14]. A zigzag (4, 0) BNNT, B20N20H4 waschosen with open ends, in which only one end wassaturated with four H atoms. Existing two differentterminals for zigzag BNNTs, two forms of open-endedtypes were used in order to model the NH3 dissociation atthe tube ends, including N-enriched (A) and B-enriched (B)types (Fig. 1).

Firstly, four models of the A tube were selected in whichthe inner layers consist of N4B4 (A1), N8B4 (A2), N8B8(A3) and N5B5 (A4), Fig. 2. In models of A1, A2 and A3,two, three and four rows of atoms were placed respectivelyin the inner layer, and in the A4 two hexagonal rings wereselected as inner layer. All of models with and without NH3

were optimized using ONIOM (B3LYP/6-31 G*:AM1) andadsorption energy (Ead ) were computed (Table 1). The Ead

is defined here as follows:

Ead ¼ Etot NH3 þ open� ended BNNTð Þ� Etot open� ended BNNTð Þ � Etot NH3ð Þ;

where Etot is the total energy of a given system.In addition, the other low-levels were applied in the

ONIOM study of A3 model including the semiempiricalMNDO and PM3 methods and also the molecular mechan-ics universal force field (UFF). All calculations performedon A model were repeated for B model, as well. Finally, toexplore the effect of tube length and diameter on theconsistency of ONIOM and DFT, the A3 model of threeother BNNTs were studied, including: (5,0), (6,0) and (7,0)zigzag types.

Results and discussion

At first, we probed reliability of the ONIOM(B3LYP/6-31 G*:AM1) level of theory in calculation of geometricalparameters and Ead of NH3 dissociation at open ends of A1,A2, A3, and A4 models. B3LYP, has the most generalityand predictive capacity providing a sufficiently accuratedescription of finite-size nanotubes [15–19]. As we haverecently showed, during the NH3 adsorption process, asingle NH3 molecule dissociates into an -H atom and an-NH2 group at the open ends of BNNTs [10].

In the present work, we compare the results of ONIOMmethod with those of full DFT in ref. [10]. The calculatedEad amounts for A1, A2, A3 and A4 models are −80.8,-70.5, -64.8 and −74.7 kcal mol-1, respectively (Table 1).The results indicate that only the Ead of NH3 on A3 modelpartly agrees with B3LYP/6-31 G* result (−63.1 kcal mol-1)and the energy difference is about 1.7 kcal mol-1 (with 3%error). As shown in Table 1, the other models showsignificant errors. The calculated values for three represen-tative bond lengths including, N1-NH2, N2-H and N1-N2(Table 1, Fig. 3), indicate that geometrical parameters haveno dependency upon the type of tube models.

However, adopting the A3 as the appropriate model, wesubsequently compared the reliability of four different low-levels (AM1, PM3, UFF and MNDO) in Ead, activationenergy (Eact), HOMO-LUMO energy gap (Eg), chargetransfer (QT), dipole moment (μ) and structure geometry

Fig. 1 (a) The model of A (N-enriched open-ended BNNTs), (b) Themodel of B (B-enriched open ended BNNTs)

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calculations. The Eg, μ and QT were computed using fullB3LYP/6-31 G* level of theory (performing a single point(SP) calculation on the optimized structures of ONIOM), dueto inability of the ONIOM method in their calculations.Frequency calculations verified the obtained transition struc-tures (with one imaginary frequency). Ugliengo et al. showedthat the results of frequency calculations using ONIOMmethod are comparable with full DFT ones [20–22].

All calculated parameters are shown in Table 2, indicat-ing that the results of Ead are near to that of ref. [10], exceptthose of UFF, showing an error of 7.4%. However, amongall low-levels, Ead of MNDO is the nearest to that ofB3LYP. We once more performed a SP energy calculationson the A3 and H-A3-NH2 complexes, using B3LYP/6-31 G*. It is observed that the difference of Ead betweenONIOM and full DFT is relatively reduced in the all cases(Table 2). It seems that performing a high-level SPcalculation on the ONIOM-based optimized structuresimprove the initial results of Ead.

The UFF has the most deviation in Eg calculations.Either PM3 or MNDO overestimates Eg about 0.11 eV,

while AM1 underestimates it about 0.13 eV. Generally, allmethods give eligible results, except the UFF. In Eact

calculations, we observe a good consistency betweenONIOM and DFT as the result of PM3 is in the bestagreement with that of full DFT.

In the cases of structure geometry and QT calculations,the results of the different ONIOM methods show nosignificant difference in comparison to those of DFT,indicating that these properties are not dependent uponlow-levels. Finally, the largest and lowest deviations belongto the UFF and PM3, respectively, in the case of μcalculation.

Fig. 2 Four optimized modelsof the A tube at ONIOM(B3LYP/6-31 G*:AM1)

Fig. 3 The structural geometryof A3/NH3 complex withdifferent ONIOM methods

Table 1 Ead (kcal mol-1) and representative bond lengths (Å) ofdifferent models of A tube, which are compared with the results of fullDFT of ref. [10]

Model Ead Error N1-NH2 N2-H aN1, N2

A1 −80.8 28% 1.449 1.023 2.562

A2 −70.5 12% 1.434 1.025 2.541

A3 −64.8 3% 1.454 1.023 2.497

A4 −74.7 18% 1.459 1.025 2.553

A −63.1 - 1.455 1.022 2.495

a N1, N2 is the distance between N1 and N2

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However, PM3 is the most reliable among all low-levelmethods and the results of UFF are the most misleading,especially in the calculations of Ead, Eact and μ. The resultsof MNDO are somewhat similar to those of PM3 byexperience, the PM3 usage is difficult in comparison to thatof MNDO, due to many convergence failures in theGaussian program.

Subsequently, we assessed the reliability of the ONIOMmethod in Ead calculation of NH3 dissociation at the openend of B model, using the same three semiempirical low-levels. The data of Table 3 show that the results of ONIOMmethod for all B models are not in agreement with DFT.The best agreement belongs to the B3 model with 25%error. It is noteworthy to mention that the designation of Bmodels is similar to those of the A models. In the B3 case,the calculated Ead values for AM1, PM3, and MNDO are−156.5, -202.5 and −182.6 kcal mol-1 while that of fullDFT is −131.1 kcal mol-1 [10].

In contrast to the case of A, the results of ONIOMmethod significantly differ with that of DFT in all modelsof B. For example in B3 model, the calculated errors are26%, 63% and 47% for AM1, PM3, and MNDO,respectively. This induces very cautiously usage of ONIOMmethod in computational studies.

Here, we interpret in detail why the ONIOM method isappropriate for A3 model, while it is not for B3 (with thesame atoms in low-level). To this end, we performedMulliken population analysis on the A3 and B3 tubes andtheir NH3 adsorbed complexes. It is noteworthy to say thatour main objective is a comparative study and, the exactvalues of Mulliken charges (MCs) is not the purpose of thepresent manuscript. However, during the NH3 adsorptionprocess, the MCs of atoms change within the tubes,whereas the amounts of changes reduce going away fromtheir ends.

The percentage of MC changes were computed duringthe adsorption process for five layers at the open end ofboth A3 and B3. We have designated the name of “layer”for a row of N atoms with a row of B atoms. The results aredepicted in Fig. 4 and collected in Table 4. In the case ofA3, the changes are 34.7% and 10.1% for layers 1 and 2(region 1) while those are only 2.6%, 0.3% and 0.1% forlayers 3, 4 and 5 (region 2), respectively. It demonstratesthat the MCs of atoms of region 1 significantly changeduring the adsorption process, while their changes in region2 are not significant.

In other words, region 1 is a chemically active site and itis necessary to locate in high-level of ONIOM scheme

Fig. 4 The percentage change of Mulliken charges in layers 3, 4 and5 of both A3 and B3 models

Table 2 The Ead and Eact ( in kcal mol-1) and QT for NH3 adsorption at open ends of A3 model and the μ (debye), Eg and representative bondlengths (Å) of A3 model, calculated at various low levels. These date are compared with those of full DFT of ref. [10]

Method Ead Ead(SP) Eact QT (e) Eg (eV) μ N1-NH2 N2-H bN1, N2

AM1 −64.8 −63.5 11.3 0.39 2.64 2.60 1.454 1.022 2.496

PM3 −62.2 −63.4 13.9 0.39 2.88 1.96 1.455 1.022 2.495

MNDO −63.0 −63.4 15.1 0.39 2.88 2.60 1.455 1.022 2.498

UFF −67.8 −65.9 a- 0.40 3.33 3.12 1.452 1.022 2.495

Ref. [10] −63.1 −63.1 13.7 0.39 2.77 1.74 1.455 1.022 2.494

a Using this low level of theory, the TS structure was not found. b N1, N2 is the distance between N1 and N2

Table 3 Ead values (kcal mol-1) and representative bond lengths (Å)of different models of B tube, which compared with the results of fullDFT of ref. [10]

Model Ead Error(%) B1-NH2 B2-H aB1,B2

B1 −491.6 275 1.385 1.192 2.419

B2 −866.2 561 1.383 1.191 2.346

B3 −163.6 25 1.386 1.190 2.481

B4 −863.8 559 1.382 1.196 2.427

B −131.1 - 1.386 1.191 2.424

a B1, B2 is the distance between B1 and B2

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while region 2 is not a sufficiently active area and can beplaced in low-level. As discussed above, this strategy hasbeen applied in our ONIOM calculations for the case of A3,justifying the reliable results. In the models of A1, A2 andA4 some atoms of region 1 are located in low-level oftheory, justifying the large errors in the Ead results.

In the case B3, we observed different results so as thechanges of MCs in region 2 are not negligible. Thesechanges are 31.3%, 27.3% and 6.2% in layers 3, 4 and 5,respectively. This suggests that region 2 may be a part ofchemically active site that should be studied in high-level oftheory. As shown before, this region has been placed inlow-level of theory and it may be the origin of the largeerrors in Ead of B3 model. As a result, we conclude that theONIOM may be a reliable scheme in the study of weakinteractions, while in the case of strong interactions it is acontroversial approach and should be applied cautiously. Inother words, in the case of ONIOM-based strong interactionstudies, more atoms should be located in high-level incomparison to that of weak interaction studies.

Subsequently, we probed the effect of tube length anddiameter on reliability of ONIOM results. Here we onlyconsidered case A, because the ONIOM results of B modelsare very different from those of DFT. To this end, wecalculated Ead values of NH3 dissociation at open ends ofA3 models of (5,0), (6,0) and (7,0) tubes with ONIOM(B3LYP/6-31 G*:AM1) and full B3LYP/6-31 G*. The dataof Table 5 indicate that the results of ONIOM and full DFTare in best agreement for different diameter tubes. Inaddition, to investigate the effect of length, we consideredthe (5,0)-A3 model with various length including: 9, 8, 7, 6and 5 layers. The results (Table 6) show that Ead values for

all tubes with various lengths do not differ significantly forboth ONIOM and DFT and there is good consistencybetween these approaches. Generally, we conclude that theagreement between the results of ONIOM and DFTapproaches are independent of tube length and diameter.

We mention that the absolute values of Ead are increasedas the tube diameter is elongated. This phenomenon isjustified as the weakening of tube edge bonds resultingfrom the bond length elongation because of diameterenlargement.

Conclusions

We used the ONIOM method to calculate the adsorptionenergies (Ead), transition structures, the change of HOMO-LUMO energy gaps (Eg) and structure geometries of theNH3 adsorption on the A (N-enriched) and B (B-enriched)models of open ended BNNTs. Different low-levelsincluding, AM1, PM3, MNDO and UFF have beeninvestigated, applying B3LYP/6-31 G* in all high-levelsof ONIOM calculations. PM3 method is the most reliableamong all low-levels used here especially in calculation ofEad, Eact and dipole moment and UFF is the mostmisleading. Either PM3 or MNDO overestimates theEg, while AM1 underestimates it. We showed that in thecase of A, by selecting two atom layers of the open end ofthe tube as inner layer, the results of ONIOM approach isin best agreement with those of the pure DFT calculationswhile in the case of B with the same condition, the resultsof ONIOM significantly differ with those of DFT. Finally,the results demonstrated that the ONIOM might be areliable method in the study of weak interactions while inthe case of strong interactions it is a controversialapproach and should be applied cautiously. In addition,we showed that the agreement between the results ofONIOM and DFT approaches are independent of tubelength and diameter.

Table 6 The calculated Ead for NH3 dissociation at open ends of(5,0)-A3 models with different models. The unit of energy is kcal mol-1. The first column shows the number of tube layers

(5,0)-A3 Ead(DFT) Ead(ONIOM)

5 −73.7 −73.36 −73.6 −73.37 −74.2 −73.38 −74.3 −73.39 −75.6 −73.2

Table 5 The Ead values of NH3 dissociation at the open ends of A3model achieved from ONIOM and DFT. The energy unit is kcal mol-1

BNNT Ead(DFT) Ead(ONIOM)

(4,0) −63.1 −64.8(5,0) −73.7 −73.4(6,0) 80.1 −82.4(7,0) −86.5 −87.2

Layer A3 B3

3 2.6% 31.3%

4 0.3% 27.3%

5 0.1% 6.2%

Table 4 The percentageMulliken charges changes inlayers 3, 4 and 5 of both A3 andB3 models

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