Journal of Nanostructure in Chemistry

, Volume 6, Issue 4, pp 365–372

Theoretical identification of structural heterogeneities of divalent nickel active sites in NiMCM-41 nanoporous catalysts

  • Mahboobeh Balar
  • Zahra Azizi
  • Mohammad Ghashghaee
Open Access
Original Research


This paper deals with the theoretical identification of the digrafted Ni species exchanged into the defect sites of MCM-41 using hybrid density functional theory. The nickel–siloxane clusters included seven 2T–6T rings. The 2MR and 5MR structures were found to be the least and most favorable sites to form thermodynamically. The Ni–O distances ranged from 1.69 to 1.79 Å with the highest asymmetry found in 5MR. The 4MR and 5MR clusters showed also interesting intertwined nickel configurations. Overall, the QTAIM calculations revealed the transient electrostatic nature of the Ni–O bonds.


Nickel MCM-41 DFT Thermodynamics Cluster modeling Silica 


Nickel ions supported on different silica, silica–alumina, natural clay, and zeolite-type porous materials are well-known catalysts for the selective dimerization [1, 2, 3, 4, 5, 6, 7, 8, 9] and oligomerization [1, 5, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19] of olefins in both gas and liquid phases. The application of silica-supported nickel catalysts for the ethylene dimerization dates back to 1980s [20, 21, 22]. Later, the large and well-ordered cavities of the Ni-exchanged MCM-41 proved highly favorable for the oligomerization of olefins [23]. For instance, high productivities of oligomers were obtained over Ni-incorporated MCM-41 catalysts [17] being higher than those reported previously with silica–alumina supports [19]. The strong interactions of Ni2+ cations residing in the mesoporous cavities with the support framework made the reduction of the nickel ions difficult [17]. Further electron spin resonance (ESR) and Fourier transform infrared (FTIR) spectroscopic data [11, 24] served as evidence to support the role of Ni2+ cations as active sites in ethylene dimerization.

The nickel ions incorporated into the ordered mesoporous materials (OMMs) have also been suggested as efficient catalysts for the gas-phase transformation of ethylene to propylene [25, 26, 27, 28, 29, 30, 31, 32, 33, 34]. For instance, the performance and durability of Ni/MCM-41 catalysts prepared from a nickel citrate precursor was ranked as auspicious with a promising potential for closing the gap between the propylene demand and supply [35]. Ikeda et al. [36] proposed that layered nickel-silicate species were the main players in the conversion of ethylene on NiMCM-41 catalysts. In a similar study [4], the threefold coordinated Ni2+ ions situated in the 5-membered rings of the phyllosilicate pore walls of NiMCM-41 were taken as the active sites of the reaction.

Computational studies of Ni2+ binding in FER [37], MFI [38, 39], AFI [40], and silica [4, 41] have been reported earlier. Analogous reports have addressed neutral atoms [42, 43]. The present study aims at a systematic theoretical modeling of the locations of Ni2+ species in a model MCM-41 material at the fundamental level. To our knowledge, the most relevant publication to this target is that by Neiman [41] who considered an O3(SiO)2Ni structure unit cell with a formal charge of +2 for the nickel ion. The author did not investigate all of the defect sites available for the Ni2+ siting. This work is then the first fundamental report on the molecular-level heterogeneities of the NiMCM-41 catalysts.

Computational method

The cluster model approach was employed to simulate the active sites of a nanoporous NiMCM-41 catalyst through exploring the available defect sites of MCM-41 within an extended unit cell. As a common approach [44, 45], the model nanoclusters were terminated by H atoms frozen in agreement with the geometries obtained from the crystallographic data [46, 47, 48, 49, 50, 51]. The divalent nickel cation and the immediate neighbors including the O atoms from two defect-site hydroxyls were allowed to relax during the optimizations. As adopted earlier [52], the remaining part of the cluster was held fixed to mimic the mechanical restrictions of the matrix.

As an approximation, the structure of cristobalite is normally taken as a good representative for the amorphous silica materials in terms of type and density of the surface hydroxyl groups [51, 53, 54, 55, 56]. Many references [42, 43, 57, 58, 59, 60] have then applied this model to ordered silica mesoporous materials such as MCM-41. The optimizations and single-point computations were implemented using hybrid functional M06 [61] and the Def2-TZVP basis set [62, 63, 64]. Moreover, the natural bond orbital (NBO) population [65] as well as the quantum theory of atoms in molecules (QTAIM) [66, 67, 68, 69, 70, 71] analyses were carried out at the same level of theory.

The ion exchange energies (ΔEex) were calculated for the following reaction:
$$\left[ {\text{SiO}} \right]{-}\left( {\text{OH}} \right)_{ 2} + {\text{ Ni}}\left( {{\text{NO}}_{ 3} } \right)_{ 2} \to \, \left[ {\text{SiO}} \right]{-}{\text{O}}_{ 2} {\text{Ni}} + 2 {\text{HNO}}_{ 3}$$
Moreover, the binding energies (ΔEb) for the nickel ions at the defect sites of MCM-41 were assessed for the following reaction:
$$\left[ {\text{SiO}} \right]{-}{\text{O}}_{ 2} {\text{Ni }} \to \, \left[ {\text{SiO}} \right]{-}{\text{O}}_{ 2}^{{ 2{-}}} + {\text{ Ni}}^{ 2+ }$$

NWChem 6.5 [72] and Multiwfn 3.3.8 [73] were used for the computations. Finally, the graphical outputs were generated by Mercury 3.3 [74, 75, 76, 77].

Results and discussion

The viable defect sites of MCM-41 for the binding of the divalent nickel ions were determined from exploring the available pairs of vicinal and close non-vicinal silanol groups. Different NiMCM-41 clusters were considered in terms of the number of T-atoms present in the final rings and the interatomic distances between the next-nearest-neighbor Si atoms with respect to the Ni cation. The optimized geometries are shown in Fig. 1. As can be seen, different oxide rings can be formed varying from a simple 2T (a digrafted nickel species stabilized with an interaction with two geminal-type Si–O groups) to tri, tetra, penta, and hexa membered ones. To our knowledge, this heterogeneity and its consequences are discussed theoretically for the first time. As such, the simplest cluster was a 2MR ring followed by a 3MR structure with a nickel cation chemisorbed on two vicinal OH groups located at the two ends of a siloxane bridge. The other clusters represent relatively more complex types of Ni binding with proximate non-vicinal OH groups at two defect sites of the surface linked together via two or more consecutive siloxane bridges (Fig. 1). For the comparisons made here, it will be assumed [78] that the dispersion of the Ni2+ species at the defect sites of MCM-41 is controlled by their thermodynamic stability and not by any kinetic phenomenon in the preparation method.
Fig. 1

The optimized geometries of the NiMCM-41 clusters where the darker atoms refer to the framework oxygen, the plain bigger balls are silicon atoms and the small white balls are terminal hydrogen atoms. The largest atoms represent nickel

Table 1 reports the NBO charges of the selected atoms of the NiMCM-41 clusters. As can be seen, the partial charge of the Ni cation ranged from 0.889 e for 2MR to 1.077 e for 4MR, being almost half the formal charge of +2 for the Ni ions. Except 2MR and 3MR, the bridging O atoms of the O2Ni species did not bear identical charges, falling into the range of −1.157 e to −1.020 e being almost half the formal charge of –2 for the O atoms. Although not linearly correlated, there was a general proportional trend between q(Ni) and –q(O). Such an interconnection was not confirmed on the Mulliken atomic charges (see Table 1). Moreover, the average Mulliken charges of Ni and O atoms were generally 0.60 and 0.46 times those of the NBO calculations and then even more distant from the nominal charges.
Table 1

Calculated charges of selected atoms of NiMCM-41 for different cluster models at M06/Def2-TZVP level of theory







NBO partial charges










































Mulliken atomic charges










































Table 2 contains the enthalpy, entropy, and Gibbs free energy of the exchange reaction for the NiMCM-41clusters and the binding energies of Ni at the investigated sites following Eqs. (1) and (2), respectively. As evident, the grafting reaction considered here is non-spontaneous at 298 K and atmospheric pressure on all of the clusters, connoting the necessity for devising more severe (e.g., hydrothermal) preparation conditions to overcome the exchange non-spontaneity. In any event, the thermodynamic favorability for grafting of the Ni2+ cations onto the available defect sites of MCM-41 followed the sequence of 2MR < 3MR < 4MR < 6MR-3 < 6MR-1 < 6MR-2 < 5MR (53.99–72.72 kcal/mol). This is in accordance with the previous ideas on the favorability of 5MR structures mentioned previously. Moreover, the enthalpy of the exchange reaction followed the order of 5MR < 4MR < 6MR-1 < 6MR-2 < 6MR-3 < 3MR < 2MR, all being endothermic (63.09–84.10 kcal/mol). However, the binding energy for this reaction varied in the order of 4MR < 3MR < 5MR < 6MR-3 < 6MR-2 < 6MR-1 < 2MR (780.6–831.5 kcal/mol). As a result, the 2MR site is more demanding to form despite its largest binding energy.
Table 2

The Gibbs free energy (kcal/mol), enthalpy (kcal/mol), and entropy (cal/mol/K) of the exchange reaction and the binding energy (kcal/mol) of the digrafted Ni ions in NiMCM-41 at M06/Def2-TZVP level of theory (please see the corresponding reactions in the text)









































In Table 3, the nickel–oxygen bond lengths and the interbond angles of Ni have been listed for comparison. The bridging (Ni–O) bond lengths fell into the range of 1.69–1.79 Å with the highest asymmetry [a difference of 0.03 Å between r(Ni–O1) and r(Ni–O2)] found in the case of 5MR. The O–Ni–O angles changed over a markedly wider range here with the minimum angle (85.6°) on 2MR and the largest one (168.9°) on 4MR. The data reported here indicated that neither the Ni–O distances nor the O1–Ni–O2 angles correlated with the size of the siloxane rings as analogously expressed in our previous study of Cr–silicalite-2 [79].
Table 3

Nickel–oxygen bond length (Å) and interbond angle (in degree) for different optimized cluster models at M06/Def2-TZVP level of theory


Bond lengths

































The characterizing features [71, 80, 81] of QTAIM were employed to determine whether the nickel–oxide solid interactions were of shared or closed-shell nature. The calculated topological properties are shown in Table 4. The tabulated data represent moderate electron densities (ρBCP). Moreover, positive ∇2ρBCP values were obtained as anticipated from a common character of metal–oxygen interactions [80]. The interactions of nickel with the siloxane rings of MCM-41 were all found to be rather polar than purely covalent. More interestingly, however, the 4MR and 5MR structures revealed third Ni–O interactions of electrostatic nature that made the nickel ion interlocked three-coordinated in the plane of the ring. Potential correlations between the properties of the NiMCM-41 active sites were probed. Figure 2 shows an obvious correlation between r(Ni–O) and ρBCP which was also observed in our previous works on MEL structure [79, 82]. No further correlation with an acceptably high coefficient of determination was found between any other two parameters.
Table 4

QTAIM data for different optimized clusters at M06/Def2-TZVP level of theory















































































































Fig. 2

The correlation found between the topological properties and the Ni–O distances in the NiMCM-41 catalysts

The energy levels of electrons and their gaps provide useful data for implications on the reactivity of the active sites [79, 82, 83] according to the frontier molecular orbital (FMO) theory [84]. Table 5 reports the HOMO and LUMO levels and HOMO–LUMO energy gaps for the optimized clusters shown in Fig. 1. The HOMO–LUMO energy gaps increased in the order of 4MR < 5MR < 3MR < 6MR-3 < 6MR-1 < 6MR-2 < 2MR ranging from 3.01 to 4.15 eV. Considering the chemical hardness as η = (ELUMOEHOMO)/2 [85, 86, 87, 88, 89], one can state that the chemical hardness of the digrafted nickel ion was maximized at 2MR and minimized at 4MR and 5MR sites.
Table 5

Calculated HOMO and LUMO and HOMO–LUMO energy gaps (ΔEHOMO−LUMO) for the investigated clusters at M06/Def2-TZVP level of theory


































This paper investigated the diversity of the cluster models of NiMCM-41 in a systematic computational framework. Total of seven active sites (2T–6T rings) were found at the defect sites of an MCM-41 silica model. The NBO partial charge of the nickel cation was less positive on 2MR and largest on 4MR. The thermodynamic favorability of the NiMCM-41 clusters followed the order of 2MR < 3MR < 4MR < 6MR-3 < 6MR-1 < 6MR-2 < 5MR. The optimized structures indicated the Ni–O distances in the range of 1.69–1.79 Å with the highest asymmetry observed in 5MR. The highest reactivity was observed in the case of the digrafted nickel ions at 4MR and 5MR sites and the lowest one at 2MR. The 4MR and 5MR clusters showed also some intertwining features for nickel hosting. The QTAIM calculations revealed intermediate polar Ni–O bonds. Moreover, the electron densities at the BCP correlated with the Ni–O distances.


  1. 1.
    Andrei, R.D., Popa, M.I., Fajula, F., Hulea, V.: Heterogeneous oligomerization of ethylene over highly active and stable Ni-AlSBA-15 mesoporous catalysts. J. Catal. 323, 76–84 (2015)CrossRefGoogle Scholar
  2. 2.
    Andrei, R.D., Mureseanu, M., Popa, M.I., Cammarano, C., Fajula, F., Hulea, V.: Ni-exchanged AlSBA-15 mesoporous materials as outstanding catalysts for ethylene oligomerization. Eur. Phys. J. Special Topics 224(9), 1831–1841 (2015)CrossRefGoogle Scholar
  3. 3.
    Zhang, H., Li, X., Zhang, Y., Lin, S., Li, G., Chen, L., Fang, Y., Xin, H., Li, X.: Ethylene oligomerization over heterogeneous catalysts. Energy Environ. Focus 3(3), 246–256 (2014)CrossRefGoogle Scholar
  4. 4.
    Tanaka, M., Itadani, A., Kuroda, Y., Iwamoto, M.: Effect of pore size and nickel content of Ni-MCM-41 on catalytic activity for ethene dimerization and local structures of nickel ions. J. Phys. Chem. C 116(9), 5664–5672 (2012)CrossRefGoogle Scholar
  5. 5.
    Iwamoto, M.: One step formation of propene from ethene or ethanol through metathesis on nickel ion-loaded silica. Molecules 16(9), 7844–7863 (2011)CrossRefGoogle Scholar
  6. 6.
    Choo, H., Kevan, L.: Catalytic study of ethylene dimerization on Ni(II)-exchanged clinoptilolite. J. Phys. Chem. B 105(27), 6353–6360 (2001)CrossRefGoogle Scholar
  7. 7.
    Nkosi, B., Ng, F.T.T., Rempel, G.L.: The oligomerization of butenes with partially alkali exchanged NiNaY zeolite catalysts. Appl. Catal. A-Gen. 158(1), 225–241 (1997)CrossRefGoogle Scholar
  8. 8.
    Sohn, J.R., Park, J.H.: Characterization of dealuminated NiY zeolite and effect of dealumination on catalytic activity for ethylene dimerization. Appl. Catal. A-Gen. 218(1–2), 229–234 (2001)CrossRefGoogle Scholar
  9. 9.
    Ng, F.T.T., Creaser, D.C.: Ethylene dimerization over modified nickel exchanged Y-zeolite. Appl. Catal. A-Gen. 119(2), 327–339 (1994)CrossRefGoogle Scholar
  10. 10.
    Moussa, S., Arribas, M.A., Concepción, P., Martínez, A.: Heterogeneous oligomerization of ethylene to liquids on bifunctional Ni-based catalysts: the influence of support properties on nickel speciation and catalytic performance. Catal. Today (2016). doi:10.1016/j.cattod.2015.11.032 Google Scholar
  11. 11.
    Martínez, A., Arribas, M.A., Concepción, P., Moussa, S.: New bifunctional Ni–H-Beta catalysts for the heterogeneous oligomerization of ethylene. Appl. Catal. A-Gen. 467, 509–518 (2013)CrossRefGoogle Scholar
  12. 12.
    Lallemand, M., Finiels, A., Fajula, F., Hulea, V.: Continuous stirred tank reactor for ethylene oligomerization catalyzed by NiMCM-41. Chem. Eng. J. 172(2), 1078–1082 (2011)CrossRefGoogle Scholar
  13. 13.
    Brückner, A., Bentrup, U., Zanthoff, H., Maschmeyer, D.: The role of different Ni sites in supported nickel catalysts for butene dimerization under industry-like conditions. J. Catal. 266(1), 120–128 (2009)CrossRefGoogle Scholar
  14. 14.
    Lallemand, M., Finiels, A., Fajula, F., Hulea, V.: Catalytic oligomerization of ethylene over Ni-containing dealuminated Y zeolites. Appl. Catal. A-Gen. 301(2), 196–201 (2006)CrossRefGoogle Scholar
  15. 15.
    Hulea, V., Lallemand, M., Finiels, A., Fajula, F.: Catalytic oligomerization of ethylene over Ni-containing MCM-22, MCM-41 and USY. In: J. Čejka, N.Ž., Nachtigall, P. (eds.) Studies in Surface Science and Catalysis, Part B, vol. 158. pp. 1621–1628. Elsevier, Amsterdam (2005)Google Scholar
  16. 16.
    Lin, S., Shi, L., Zhang, H., Zhang, N., Yi, X., Zheng, A., Li, X.: Tuning the pore structure of plug-containing Al-SBA-15 by post-treatment and its selectivity for C16 olefin in ethylene oligomerization. Microporus and Mesoporus Mat. 184, 151–161 (2014)CrossRefGoogle Scholar
  17. 17.
    Hulea, V., Fajula, F.: Ni-exchanged AlMCM-41—an efficient bifunctional catalyst for ethylene oligomerization. J. Catal. 225(1), 213–222 (2004)CrossRefGoogle Scholar
  18. 18.
    Nicolaides, C.P., Scurrell, M.S., Semano, P.M.: Nickel silica-alumina catalysts for ethene oligomerization—control of the selectivity to 1-alkene products. Appl. Catal. A-Gen. 245(1), 43–53 (2003)CrossRefGoogle Scholar
  19. 19.
    Heydenrych, M.D., Nicolaides, C.P., Scurrell, M.S.: Oligomerization of ethene in a slurry reactor using a nickel(II)-exchanged silica–alumina catalyst. J. Catal. 197(1), 49–57 (2001)CrossRefGoogle Scholar
  20. 20.
    Kimura, K., Hideo, A.-I., Ozaki, A.: Tracer study of ethylene dimerization over nickel oxide-silica catalyst. J. Catal. 18(3), 271–280 (1970)CrossRefGoogle Scholar
  21. 21.
    Sohn, J.R., Ozaki, A.: Structure of NiO-SiO2 catalyst for ethylene dimerization as observed by infrared absorption. J. Catal. 59(2), 303–310 (1979)CrossRefGoogle Scholar
  22. 22.
    Sohn, J.R., Ozaki, A.: Acidity of nickel silicate and its bearing on the catalytic activity for ethylene dimerization and butene isomerization. J. Catal. 61(1), 29–38 (1980)CrossRefGoogle Scholar
  23. 23.
    Finiels, A., Fajula, F., Hulea, V.: Nickel-based solid catalysts for ethylene oligomerization—a review. Catal. Sci. Technol. 4(8), 2412–2426 (2014)CrossRefGoogle Scholar
  24. 24.
    Martínez, A., Arribas, M.A., Moussa, S.: Development of bifunctional Ni-based catalysts for the heterogeneous oligomerization of ethylene to liquids. In: Kanellopoulos, N. (ed.) Small-Scale Gas to Liquid Fuel Synthesis. pp. 377–400. CRC Press, Boca Raton (2015)Google Scholar
  25. 25.
    Frey, A.S., Hinrichsen, O.: Comparison of differently synthesized Ni(Al)MCM-48 catalysts in the ethene to propene reaction. Microporus and Mesoporus Mat. 164, 164–171 (2012)CrossRefGoogle Scholar
  26. 26.
    Alvarado Perea, L., Wolff, T., Veit, P., Hilfert, L., Edelmann, F.T., Hamel, C., Seidel-Morgenstern, A.: Alumino-mesostructured Ni catalysts for the direct conversion of ethene to propene. J. Catal. 305, 154–168 (2013)CrossRefGoogle Scholar
  27. 27.
    Alvarado Perea, L., Wolff, T., Hamel, C., Seidel-Morgenstern, A.: Direct conversion of ethene to propene on Ni/AlMCM-41–study of the reaction mechanism. In: Jahrestreffen Deutscher Katalytiker, Weimar, Germany (2014)Google Scholar
  28. 28.
    Alvarado Perea, L.: Direct conversion of ethene to propene on Ni-alumino-mesostructured catalysts: synthesis, characterization and catalytic testing. PhD dissertation, Otto-von-Guericke Universität (2014)Google Scholar
  29. 29.
    Iwamoto, M., Kosugi, Y.: Highly selective conversion of ethene to propene and butenes on nickel ion-loaded mesoporous silica catalysts. J. Phys. Chem. C 111(1), 13–15 (2007)CrossRefGoogle Scholar
  30. 30.
    Iwamoto, M.: One step formation of propene from ethene or ethanol through metathesis on nickel ion-loaded silica. Molecules 16, 7844–7863 (2011)CrossRefGoogle Scholar
  31. 31.
    Taoufik, M., Le Roux, E., Thivolle-Cazat, J., Basset, J.-M.: Direct transformation of ethylene into propylene catalyzed by a tungsten hydride supported on alumina: trifunctional single-site catalysis. Angew. Chem. 119, 7340–7343 (2007)CrossRefGoogle Scholar
  32. 32.
    Taoufik, M., Le Roux, E., Thivolle-Cazat, J., Basset, J.-M.: Direct transformation of ethylene into propylene catalyzed by a tungsten hydride supported on alumina: trifunctional single-site catalysis. Angew. Chem. Int. Ed. 46, 7202–7205 (2007)CrossRefGoogle Scholar
  33. 33.
    Iwamoto, M.: Conversion of ethene to propene on nickel ion-loaded mesoporous silica prepared by the template ion exchange method. Catal. Surv. Asia 12(1), 28–37 (2008)CrossRefGoogle Scholar
  34. 34.
    Lehmann, T., Wolff, T., Zahn, V.M., Veit, P., Hamel, C., Seidel-Morgenstern, A.: Preparation of Ni-MCM-41 by equilibrium adsorption—Catalytic evaluation for the direct conversion of ethene to propene. Catal. Commun. 12(5), 368–374 (2011)CrossRefGoogle Scholar
  35. 35.
    Zahn, V.M., Wolff, T., Lehmann, T., Hamel, C., Seidel-Morgenstern, A.: Direct synthesis of propene using supported bifunctional nickel catalysts: preparation and potential. In: ISCRE 21-21st International Symposium on Chemical Reaction Engineering (2010)Google Scholar
  36. 36.
    Ikeda, K., Kawamura, Y., Yamamoto, T., Iwamoto, M.: Effectiveness of the template-ion exchange method for appearance of catalytic activity of Ni–MCM-41 for the ethene to propene reaction. Catal. Commun. 9(1), 106–110 (2008)CrossRefGoogle Scholar
  37. 37.
    Šponer, J.E., Sobalík, Z., Leszczynski, J., Wichterlová, B.: Effect of metal coordination on the charge distribution over the cation binding sites of zeolites. A combined experimental and theoretical study. J. Phys. Chem. B 105(35), 8285–8290 (2001)CrossRefGoogle Scholar
  38. 38.
    Rice, M.J., Chakraborty, A.K., Bell, A.T.: Site availability and competitive siting of divalent metal cations in ZSM-5. J. Catal. 194(2), 278–285 (2000)CrossRefGoogle Scholar
  39. 39.
    Rice, M.J., Chakraborty, A.K., Bell, A.T.: Theoretical studies of the coordination and stability of divalent cations in ZSM-5. J. Phys. Chem. B 104(43), 9987–9992 (2000)CrossRefGoogle Scholar
  40. 40.
    Brogaard, R.Y., Olsbye, U.: Ethene oligomerization in Ni-containing zeolites: theoretical discrimination of reaction mechanisms. ACS Catal. 6(2), 1205–1214 (2016)CrossRefGoogle Scholar
  41. 41.
    Neiman, M.L.: Interaction of cobalt and nickel with the hydroxylated silanol silica surface: a theoretical study. MSc thesis, Lehigh University (2002)Google Scholar
  42. 42.
    Ma, Q., Klier, K., Cheng, H., Mitchell, J.W., Hayes, K.S.: Interaction between catalyst and support. 1. Low coverage of Co and Ni at the silica surface. J. Phys. Chem. B 104(45), 10618–10626 (2000)CrossRefGoogle Scholar
  43. 43.
    Ma, Q., Klier, K., Cheng, H., Mitchell, J.W., Hayes, K.S.: Interaction between catalyst and support. 3. Metal agglomeration on the silica surface. J. Phys. Chem. B 105(38), 9230–9238 (2001)CrossRefGoogle Scholar
  44. 44.
    Pietrzyk, P.: Spectroscopy and computations of supported metal adducts. 1. DFT study of CO and NO adsorption and coadsorption on Cu/SiO2. J. Phys. Chem. B 109(20), 10291–10303 (2005)CrossRefGoogle Scholar
  45. 45.
    Ferullo, R.M., Garda, G.R., Belelli, P.G., Branda, M.M., Castellani, N.J.: Deposition of small Cu, Ag and Au particles on reduced SiO2. J. Mol. Struct. 769(1–3), 217–223 (2006)CrossRefGoogle Scholar
  46. 46.
    Downs, R.T., Palmer, D.C.: The pressure behavior of α cristobalite. Am. Mineral. 79(1–2), 9–14 (1994)Google Scholar
  47. 47.
    Wright, A.F., Leadbetter, A.J.: The structures of the β-cristobalite phases of SiO2 and AlPO4. Philos. Mag. 31(6), 1391–1401 (1975)CrossRefGoogle Scholar
  48. 48.
    Hatch, D.M., Ghose, S.: The α-β phase transition in cristobalite, SiO2. Phys. Chem. Miner. 17(6), 554–562 (1991)CrossRefGoogle Scholar
  49. 49.
    Leadbetter, A.J., Smith, T.W., Wright, A.F.: Structure of high cristobalite. Nature 244, 125–126 (1973)Google Scholar
  50. 50.
    Peacor, D.R.: High-temperature single-crystal study of the cristobalite inversion. zkri 138(1–4), 274–298 (1973)Google Scholar
  51. 51.
    Pophal, C., Fuess, H.: Investigation of the medium range order of polyhedra forming the walls of MCM-41—An X-ray diffraction study. Microporus and Mesoporus Mat. 33(1–3), 241–247 (1999)CrossRefGoogle Scholar
  52. 52.
    Lopez, N., Illas, F., Pacchioni, G.: Adsorption of Cu, Pd, and Cs atoms on regular and defect sites of the SiO2 surface. J. Am. Chem. Soc. 121(4), 813–821 (1999)CrossRefGoogle Scholar
  53. 53.
    Chuang, I.S., Maciel, G.E.: A detailed model of local structure and silanol hydrogen bonding of silica gel surfaces. J. Phys. Chem. B 101(16), 3052–3064 (1997)CrossRefGoogle Scholar
  54. 54.
    Maciel, G.E.: Probing hydrogen bonding and the local environment of silanols on silica surfaces via nuclear spin cross polarization dynamics. J. Am. Chem. Soc. 118(2), 401–406 (1996)CrossRefGoogle Scholar
  55. 55.
    Chuang, I.S., Kinney, D.R., Bronnimann, C.E., Zeigler, R.C., Maciel, G.E.: Effects of proton-proton spin exchange in the silicon-29 CP-MAS NMR spectra of the silica surface. J. Phys. Chem. 96(10), 4027–4034 (1992)CrossRefGoogle Scholar
  56. 56.
    Sindorf, D.W., Maciel, G.E.: Silicon-29 NMR study of dehydrated/rehydrated silica gel using cross polarization and magic-angle spinning. J. Am. Chem. Soc. 105(6), 1487–1493 (1983)CrossRefGoogle Scholar
  57. 57.
    Lillehaug, S.: A theoretical study of Cr/oxide catalysts for dehydrogenation of short alkanes. PhD dissertation, University of Bergen (2006)Google Scholar
  58. 58.
    Handzlik, J., Kurleto, K.: Assessment of density functional methods for thermochemistry of chromium oxo compounds and their application in a study of chromia–silica system. Chem. Phys. Lett. 561–562, 87–91 (2013)CrossRefGoogle Scholar
  59. 59.
    Lillehaug, S., Jensen, V.R., Børve, K.J.: Catalytic dehydrogenation of ethane over mononuclear Cr(III)–silica surface sites. Part 2: C—H activation by oxidative addition. J. Phys. Org. Chem. 19, 25–33 (2006)CrossRefGoogle Scholar
  60. 60.
    Chempath, S., Zhang, Y., Bell, A.T.: DFT studies of the structure and vibrational spectra of isolated molybdena species supported on silica. J. Phys. Chem. C 111(3), 1291–1298 (2006)CrossRefGoogle Scholar
  61. 61.
    Zhao, Y., Truhlar, D.: The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Account 120(1–3), 215–241 (2008)CrossRefGoogle Scholar
  62. 62.
    Weigend, F.: Accurate Coulomb-fitting basis sets for H to Rn. Phys. Chem. Chem. Phys. 8(9), 1057–1065 (2006)CrossRefGoogle Scholar
  63. 63.
    Weigend, F., Ahlrichs, R.: Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Phys. Chem. Chem. Phys. 7(18), 3297–3305 (2005)CrossRefGoogle Scholar
  64. 64.
    Feller, D.: The role of databases in support of computational chemistry calculations. J. Comput. Chem. 17(13), 1571–1586 (1996)CrossRefGoogle Scholar
  65. 65.
    Glendening, E., Badenhoop, J., Reed, A., Carpenter, J., Weinhold, F.: NBO 3.1. Theoretical Chemistry Institute, University of Wisconsin, Madison (1996)Google Scholar
  66. 66.
    Rodríguez, J.I., Bader, R.F.W., Ayers, P.W., Michel, C., Götz, A.W., Bo, C.: A high performance grid-based algorithm for computing QTAIM properties. Chem. Phys. Lett. 472(1–3), 149–152 (2009)CrossRefGoogle Scholar
  67. 67.
    Bader, R.F.W.: A quantum theory of molecular structure and its applications. Chem. Rev. 91(5), 893–928 (1991)CrossRefGoogle Scholar
  68. 68.
    Bader, R.F.W.: The quantum mechanical basis of conceptual chemistry. Monatsh. Chem. 136(6), 819–854 (2005)CrossRefGoogle Scholar
  69. 69.
    Bader, R.F.W.: Molecular fragments or chemical bonds. Accounts Chem. Res. 8(1), 34–40 (1975)CrossRefGoogle Scholar
  70. 70.
    Bader, R.F.W.: Atoms in Molecules: A Quantum Theory, vol. 22. International series of monographs on chemistry. Oxford University Press, USA (1994)Google Scholar
  71. 71.
    Matta, C.F., Boyd, R.J.: The quantum theory of atoms in molecules: from solid state to DNA and drug design. Wiley, New York (2007)CrossRefGoogle Scholar
  72. 72.
    Valiev, M., Bylaska, E.J., Govind, N., Kowalski, K., Straatsma, T.P., Van Dam, H.J.J., Wang, D., Nieplocha, J., Apra, E., Windus, T.L., de Jong, W.A.: NWChem: a comprehensive and scalable open-source solution for large scale molecular simulations. Comput. Phys. Commun. 181(9), 1477–1489 (2010)CrossRefGoogle Scholar
  73. 73.
    Lu, T., Chen, F.: Multiwfn: a multifunctional wavefunction analyzer. J. Comput. Chem. 33(5), 580–592 (2012)CrossRefGoogle Scholar
  74. 74.
    Bruno, I.J., Cole, J.C., Edgington, P.R., Kessler, M., Macrae, C.F., McCabe, P., Pearson, J., Taylor, R.: New software for searching the Cambridge structural database and visualizing crystal structures. Acta Crystallogr. B 58(3 Part 1), 389–397 (2002)Google Scholar
  75. 75.
    Macrae, C.F., Bruno, I.J., Chisholm, J.A., Edgington, P.R., McCabe, P., Pidcock, E., Rodriguez-Monge, L., Taylor, R., van de Streek, J., Wood, P.A.: Mercury CSD 2.0—new features for the visualization and investigation of crystal structures. J. Appl. Crystallogr. 41(2), 466–470 (2008)CrossRefGoogle Scholar
  76. 76.
    Macrae, C.F., Edgington, P.R., McCabe, P., Pidcock, E., Shields, G.P., Taylor, R., Towler, M., van de Streek, J.: Mercury: visualization and analysis of crystal structures. J. Appl. Crystallogr. 39(3), 453–457 (2006)CrossRefGoogle Scholar
  77. 77.
    Taylor, R., Macrae, C.F.: Rules governing the crystal packing of mono- and dialcohols. Acta Crystallogr. B 57(6), 815–827 (2001)CrossRefGoogle Scholar
  78. 78.
    Handzlik, J., Grybos, R., Tielens, F.: Structure of monomeric chromium(VI) oxide species supported on silica: periodic and cluster DFT studies. J. Phys. Chem. C 117(16), 8138–8149 (2013)CrossRefGoogle Scholar
  79. 79.
    Ghambarian, M., Azizi, Z., Ghashghaee, M.: Diversity of monomeric dioxo chromium species in Cr/silicalite-2 catalysts: a hybrid density functional study. Comp. Mater. Sci. 118, 147–154 (2016)CrossRefGoogle Scholar
  80. 80.
    Sierraalta, A., Añez, R., Brussin, M.-R.: Theoretical study of NO2 adsorption on a transition-metal zeolite model. J. Catal. 205(1), 107–114 (2002)CrossRefGoogle Scholar
  81. 81.
    Gatti, C.: Chemical bonding in crystals: new directions. zkri 220, 399–457 (2005)Google Scholar
  82. 82.
    Ghashghaee, M., Ghambarian, M., Azizi, Z.: Characterization of extraframework Zn2+ cationic sites in silicalite-2: a computational study. Struct. Chem. 27(2), 467–475 (2016)CrossRefGoogle Scholar
  83. 83.
    Ghambarian, M., Ghashghaee, M., Azizi, Z., Balar, M.: Effect of cluster size in computational modeling of Cu+/ZSM-11 catalysts. In: 3rd International Congress of Chemistry and Chemical Engineering, pp. 292–299 (2016)Google Scholar
  84. 84.
    Fukui, K., Yonezawa, T., Shingu, H.: A molecular orbital theory of reactivity in aromatic hydrocarbons. J. Chem. Phys. 20(4), 722–725 (1952)CrossRefGoogle Scholar
  85. 85.
    Parthasarathi, R., Subramanian, V., Chattaraj, P.K.: Effect of electric field on the global and local reactivity indices. Chem. Phys. Lett. 382(1–2), 48–56 (2003)CrossRefGoogle Scholar
  86. 86.
    Parr, R.G., Szentpály, Lv, Liu, S.: Electrophilicity Index. J. Am. Chem. Soc. 121(9), 1922–1924 (1999)CrossRefGoogle Scholar
  87. 87.
    Parr, R.G., Pearson, R.G.: Absolute hardness: companion parameter to absolute electronegativity. J. Am. Chem. Soc. 105(26), 7512–7516 (1983)CrossRefGoogle Scholar
  88. 88.
    Datta, D.: On Pearson’s HSAB Principle. Inorg. Chem. 31(13), 2797–2800 (1992)CrossRefGoogle Scholar
  89. 89.
    Parr, R.G., Weitao, Y.: Density-functional theory of atoms and molecules. International Series of Monographs on Chemistry. Oxford University Press, New York (1989)Google Scholar

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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Mahboobeh Balar
    • 1
  • Zahra Azizi
    • 1
  • Mohammad Ghashghaee
    • 2
  1. 1.Department of Chemistry, Karaj BranchIslamic Azad UniversityKarajIran
  2. 2.Faculty of PetrochemicalsIran Polymer and Petrochemical InstituteTehranIran

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