J Mol Model (2015) 21:170 DOI 10.1007/s00894-015-2711-4
ORIGINAL PAPER
Structural and electronic properties of an [(Al2O3)4]+ cluster Justyna Jaroszynska-Wolinska 1 & Brady D. Garabato 2 & Jahangir Alam 2 & Asmaul Reza 2 & Pawel M. Kozlowski 2,3
Received: 1 April 2015 / Accepted: 19 May 2015 # Springer-Verlag Berlin Heidelberg 2015
Abstract Density functional theory (DFT) has been applied to investigate the structural and electronic properties of an [(Al2O3)4]+ cluster. Since there is no structural data available from experiment, the geometry of the cluster was obtained based on a model which produced the best agreement with vibrational IR-MPD data. A range of different exchangecorrelation functionals were tested, and it was concluded that the best spectral agreement was produced using the CAMB3LYP and B3LYP functionals, respectively. To further characterize the properties of the cluster, natural bond order analysis was performed, and it was concluded that an appropriate description for the system is [Al8O12]+. The frontier orbitals and spin densities of both cation and neutral systems were considered, and it was concluded that the unrestricted singlet and triplet spin densities of the neutral [Al8O12] system were nearly degenerate, representing a di-radical, with the triplet state being lower in energy.
Keywords Aluminum cluster . DFT . NBO . ESP
Electronic supplementary material The online version of this article (doi:10.1007/s00894-015-2711-4) contains supplementary material, which is available to authorized users. * Pawel M. Kozlowski [email protected] 1
Department of Civil Engineering and Architecture, Lublin University of Technology, 20-618 Lublin, Poland
2
Department of Chemistry, University of Louisville, Louisville, KY 40292, USA
3
Department of Food Sciences, Medical University of Gdańsk, Al. Gen. J. Hallera 107, 80-416 Gdańsk, Poland
Introduction Aluminium oxide molecules have been the subject of many experimental and theoretical investigations [1–5]. They are important materials in high temperature applications, translucent ceramics, corrosion resistance ceramics, electronic packaging, and catalysis. The most important form of aluminium oxide is known as alumina, Al2O3. From a crystalline point of view, Al2O3 may exist in many forms, including α, χ, η, δ, κ, θ, γ, and ρ forms [6]. Among these, the most stable is regarded as α-Al2O3, although differences in surface states exist, most commonly as two forms; a face-centered cubic (fcc), or hexagonal close-packed (hcp) arrangement of oxygen anions, with variations between polymorphs arising from differences between atomic positions within each lattice [7]. Although many metastable forms of alumina exist, including γ-Al2O3, δ-Al2O3, and others, Sierka, Asmis, and coworkers [8] proposed new structural polymorphs of the most stable isomers of [(Al2O3)4]+ and (Al2O3)4 through a combination of experiment and density functional theory (DFT). Specifically, IR multiple-photon dissociation (MPD) spectrum was collected for [(Al2O3)4]+ and the corresponding DFTbased structure was established based on a genetic algorithm applied to an intial geometry derived from the corundum crystal structure. The structure proposed was based on nmemebered rings consisting of six- and four-memebered alternating aluminum and oxygen atoms, and the global minimum was determined to be of an Barrowhead^ shape with Cs symmetry, where the final oxygen atom was coordinated to the top-most alumium vertex of the fragment. This proposed structure was further used to simulate vibrational spectra, and distinguish from other structural analogs. Spin density distribution for this structure corresponding to the energy minimum was also reported, and the density was entirely localized about the arrowhead oxygen.
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Rahane et al. [1] systematically investigated structural and electronic properties of (Al2O3)n clusters with n=1–10 at the pseudopotential DFT level using the generalized gradient approximation for the exchange-correlation energy. They concluded that the lowest energy isomers show preference toward 4- and 6-coordinated Al2O2 and Al3O3 rings respectively, and that these minima have more structural similarity with the γAl2O3 phase than the α-Al2O3 (corundum) phase. In general, they concluded that isomers with cage structures are highest in energy, and in particular for clusters with n=4, the lowest energy (Al2O3)4 isomer was found to be the one without any symmetry (C1). The primary purpose of the present study is to further investigate the structural and electronic properties of [(Al2O3)4]+, employing DFT. This study addresses the following issues, (i) structure based on available vibrational spectra, (ii) natural bond orbital analysis and electrostatic potential surface properties, and (iii) frontier and molecular orbital analysis along with spin density. Finally, conclusions regarding the interpretation of the gas phase [(Al2O3)4]+ are presented.
Computational details All calculations reported in this study were performed using the Gaussian09 suite of programs for electronic structure calculations [9]. The initial structure of the cluster was constructed manually, taking previous investigations into consideration. A number of initial structural guesses were generated, and the corresponding geometries were then optimized using a number of exchange-correlation functionals including B3LYP, CAM-B3LYP, B3PW91, TPSS, TPSSh, BVP86, and BP86. Initially to build the cluster and perform preliminary geometry optimizations, the 6-31G* basis set was used, and final optimizations were then carried out using the larger 6-311G(d,p) basis set. Final optimizations were performed under tight conditions, with no integral symmetry imposed. Force constants were calculated at the first point in each case, and no curvature test was imposed in the Berny optimizations. Frequencies along with their respective IR intensities were then calculated, and the lack of imaginary frequencies confirmed in each case that a true minimum was obtained. The low-spin state corresponding to the doublet was assumed for [(Al2O3)4]+ in its cation form, and confirmed by stability analysis of the wavefunction. Triplet and unrestricted singlet spin states were taken into consideration for the corresponding neutral forms of the C1 [Al8O12] system. The lowest energy spin state was identified as the triplet for C1 [Al8O12], and was confirmed by stability analysis. Natural bond order (NBO) analysis was performed for the optimized C 1 [Al8O12]+ doublet and triplet [Al8O12] structures to determine the nature of bonding within each system. In addition to NBO analysis (NBO 5.9), electrostatic potential (ESP) surfaces
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were calculated and visualized with the Molekel program [10], and frontier molecular orbitals along with spin densities were visualized with Chemcraft [11].
Results and discussion Analysis of vibrational data Taking into account that no structural data is available for gas phase [(Al2O3)4]+, the initial focus of this theoretical study was analysis of the vibrational data reported in ref. [8]. Our aim was to understand the elecronic structure and nature of bonding interactions within the [(Al2O3)4]+ geometry that produced the best agreement with experimental spectra. In our calculations, the C1 isomer produced better spectral agreement than the Cs (Fig. S1, SI), and as such was the isomer further considered. Taking the relative energies of C1 and Cs isomer spin states into consideration, the underlying approach was to first build a structural model, optimize its geometry, and compute frequencies to simulate vibrational spectra with no prior assumptions related to the structure of the system. As mentioned in the computational section, initial structures were constructed manually assuming no symmetry, and each geometry was then optimized with no constraints. To recall, xcfunctionals were initially investigated by optimizing geometries using the 6-31G* basis set, and those that produced the best agreement with experiment were then used to optimize the same initial geometries in 6-311g(d,p) basis. The corresponding infrared intensities based on dipole moment derivatives were then computed, and further used to simulate infrared spectrum for direct comparison with expirement. Although a number of different functionals were tested, only BP86, TPSSh, CAM-B3LYP, and B3LYP, produced spectra that were in reasonable agreement with experimental data. Upon closer inspection, it was concluded that only two functionals, B3LYP and CAM-B3LYP produced very good agreement with IR-MPD experimental data. Because computed frequencies are often overestimated by DFT when compared to experimental values due to the insufficient treatment of correlation energy and anharmonicity effects [12], to obtain better agreement with experiment they are typically scaled. The best approach if experimental data permits is the use of multiple scaling factors [12], although a single scaling factor was employed in the present study. Using the most intense experimental band as a reference, a scaling factor was obtained for each functional. Figure 1 shows comparison between experimental spectra and simulated data, based on vibrational frequencies and IR intensities computed at the CAMB3LYP/6-311G(d,p), and B3LYP/6-311G(d,p) levels of theory.
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Fig. 1 Comparison of experimental IR-MPD spectrum (trace a) with simulated spectrum based on B3LYP/6-311G(d,p) (red upper trace), and CAM-B3LYP (blue lower trace). The experimental spectrum was reproduced from ref. [1] with permission
Overall both simulated spectra were in very good agreement with experiment, notably around 1000 cm−1 where the most intense band is present. Each spectra also captures the relative intensities of the experimental bands reasonably well. Because agreement between experimental data was very good for both functionals, a correlation between computed and experimental frequencies was established and around 14 peaks were assigned. Figure 1 shows this correlation in terms of vertical lines, and Table 1 contains the corresponding calculated frequencies. As discussed below, CAM-B3LYP produced the best agreement with experiment, and the eigenvectors for nine of the most significant calculated peaks at the CAM-B3LYP/6-311g(d,p) level are collcted in Fig. 2. While both functionals produced spectra that agreed well with experiment, the differences between the two are presented here for completeness. CAM-B3LYP produces a shoulder (1038 cm−1, 51) within the most intense band (995 cm−1, 53), that correlates to the experimental values of 995 cm−1 and 1011 cm−1. The second most inense experimental peak produced by CAM-B3LYP (1043 cm−1, 54) also correlates better than B3LYP to the 1027 cm−1 experimental value, although the spectra produced B3LYP has an improved resolution of the experimental 1011 cm−1 band. Additionally, CAMB3LYP reproduces the experimental peak at 962 cm −1, (962 cm−1, 50) while B3LYP does not, but improved resolution about the 884 cm−1 and 910 cm−1 experimental values may be attributed to B3LYP. Although both CAM-B3LYP and B3LYP correlate to the experimental spectra comparably about the 771 cm−1, 779 cm−1, and 831 cm−1 wavenumbers, neither functional has significant correlation to the 818 cm−1 or lower 664 cm−1 values. However, CAM-B3LYP does to some extent correlate to the lower energy value (601 cm−1, 34) of the experimental 624 cm−1 transition better than B3LYP. Comparison of the experimental values which correlate most significantly to the scaled eigenvalues produced by the CAMB3LYP and B3LYP functionals are collected in Table 1.
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The eigenvectors associated with the most intense calculated vibrations at the CAM-B3LYP/6-311G(d,p) level mentioned above, are collected in Fig. 2. The most intense peak, 995 cm−1 (51), shows displacement amplitudes of medium strength between all Al and O atoms within the structure, with slightly higher amplitudes associated with Al-O bending about both Al2O3 end-capping moeities. The second most intense peak, 1043 cm−1 (54), on the other hand has significantly large Al-O stretching amplitudes about one of the capping Al2O3 moeities, while the remaining displacement amplitudes were comparatively smaller. The shoulder peak between these two vibrations, 1038 cm−1 (53), has moderately high displacement amplitudes for both Al 2 O 3 capping moeities, with smaller displacements within the central complex. The remaining calculated peaks at 918 cm −1 (49), 904 cm −1 (48), 873 cm −1 (47), 774 cm −1 (41), 748 cm −1 (40), and 710 cm−1 (38) all have moderate displacement amplitudes throughout the entire complex, with the exception that they differ generally in the location of around three high strength amplitudes. The 918 cm−1 (49) eigenvector shows three high amplitude oxygen displacements, while the remaining amplitudes were moderate to small. The eigenvectors corresponding to 904 cm −1 (48) show a high Al-O stretching amplitude, while the 873 cm −1 (47) peak corresponds to a different high amplitude Al-O stretch, and one high O displacement. The eigenvectors of the 774 cm −1 (41) peak are similar to that of 904 cm −1 (48), showing two high amplitude Al-O stretches, but with two additional high amplitude O displacements around one capping moeity. The 748 cm −1 (40) peak is similar to 774 cm −1 (41), with high amplitudes for both oxygen atoms mentioned (although the stretch is asymmetric), and similar small displacement amplitudes throught the remaining geometry. Finally the calculated peak at 710 cm−1 (38), resembles the most intense peak, 995 cm−1 (51), with large overall displacement amplitudes, specifically from some of the oxygens about both capping Al2O3 moeities. Natural bond order analysis and implications for properties of [(Al2O3)4]+ The analysis of vibrational data presented in the previous section, and very good agreement with IR-MPD spectrum (Fig. 1) gives strong confidence that the proposed structural models in the present study are reliable. The coordinates of both geometries used to simulate vibrational spectra shown in Fig. 1 are available in the Supporting information (SI). Although both functionals under consideration produce reliable agreement with experimental data, we ultimately chose the CAM-B3LYP geometry because overall performance of CAM-B3LYP can be considered as slightly better than that of B3LYP. To provide some insight into the nature of bonding within the system in terms of relative bond energies, natural bond
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Table 1 Frequencies of the most intense experimental IR-MPD bands of [(Al2O3)+]4 correlated with computed frequencies, with the most intense noted in bold, subjected to single-parameter scaling assuming vibration # 51 as a reference EXP (IR-MPD)/cm−1
B3LYP/cm−1 (eigenvalues)
CAM-B3LYP/cm−1 (eigenvalues)
1027
1050 (54)
1043 (54)
1011 995 962 938 929 910 884 831 818 799 771 654 624
1027 (53) 995 (51) 905 (49) 881 (48) 880 (47) 839 (45) 768 (42) 754(40) 703 (38) 603 (35) 582 (34)
1038 (53) 995 (51) 962 (50) 918 (49) 904 (48) 873 (47) 850 (45) 803 (43) 774 (41) 748 (40) 710 (38) 634 (35) 601 (34)
order (NBO) analysis was performed for [(Al2O3)4]+ and the corresponding neutral species. It should be noted that although full populations were calculated, NBOs are orthonormal sets of localized Bmaximum occupancy^ orbitals, and the delocalization in NBO basis provides a qualitative energetic description of bonding based on a linear combination of all natural hybrid orbitals, and those considered within a certain energetic threshold, in this case 4.0 kcal mol-1. As previously outlined, geometries were optimized in the gas phase at the CAMB3LYP/BP86 level of theory, and their wavefunctions were confirmed to be stable. The addition of a single electron to [(Al2O3)4]+ produced a triplet state rather than a singlet, with the energies of both states very close to each other, as will be discussed along with frontier orbitals in further sections. To represent the results of the NBO analysis, a graphical scheme was adopted shown in Fig. 3, as three realtive bond strength ranges of 4.5-10.0, 10.5-20.0, and >20.5 kcal mol-1, represented as dashed, solid-thin, and solid-thick lines between corresponding atoms, respectively. Relative bond strengths represented in this way were determined by summation of significant NBO donating or withdrawing contributions from natural bonding orbitals within each system, with a threshold for inclusion of 4.0 kcal mol-1. Occupancies of Rydberg states were below the threshold for inclusion. It should be noted that the graphical representation in Fig. 3 does not include the directionality of interactions between NBO fragments explicitly, but the total relative strengths of all natural bonds between fragments.
Although most interactions within each cluster were determined to be bonding in nature, those between Al atoms (Al-Al bonds), were determined to be primarily anti-bonding. Within the neutral cluster having triplet multiplicity, three additional Al-Al anti-bonding interactions were found. On the other hand, most of the Al-O bonds were found to be moderately strong. Based on NBO analysis, it is difficult to distinguish individual Al2O3 monomers within clusters regardless of cationic or neutral character. Although Al2 moieties may be distinguished within each structure under consideration, it is apparent from NBO analysis that the most appropriate description of the [(Al2O3)4]+ cluster, is consistent with the forumula [Al8O12]+, implying that the complex should be viewed as a molecule. Likewise, for neutral [(Al2O3)4], the same observation holds based on NBO analysis, and it should also be viewed as [Al8O12]. In sum, individual Al2O3 monomers cannot be identified clearly within the obtained geometries, and a molecular rather than a cluster interpretation describing overall bonding should be adopted. One of the most significant differences in geometry between the [Al8O12]+ doublet, and [Al8O12] triplet is the distortion of an Al away from the molecule upon addition of an electron, as shown in Fig. 3. Although this Al-03 moiety remains bound to the system with relatively high bond strengths, this distortion produces one O-Al bond that is significantly weaker. This oxygen is weakly bound to an Al-Al bond, which is also notably more weakly bound to outer oxygens in the O-Al-Al-O moiety in the triplet neutral geometry. Furthermore, within the geometry having neutral charge, significant Al-Al antibonding may be seen as occuring within the core of the neutral system, while this is not observed for the cation. The Al-O3 moeity capping the core of the molecule from the other side, is similar in both cation and neutral geometries, with one slightly stronger Al-O bond attributed to the triplet. The outer oxygens that are generally weakly associated with Al-Al bonds also remain essentially the same between both complexes, with some differences. Notably the triplet species contains the most weakly bound outer oxygen atom, with two ~5 kcal mol-1 bonds to the most strongly antibonding Al-Al pair. This oxygen in the triplet geometry is then associated with the strongest bonding and antibonding Al-O-Al moiety of both geometries. Electrostatic properties The electrostatic potential energy (ESP) surfaces of both molecules mapped to their respective electron densities (using an isovalue of 0.02), are shown in Fig. 4. The distorted Al atom observed in the optimized neutral geometry, remains attractive for both species, and as may be expected, is attractive to a greater degree in the cation, corresponding to electrostatic potential energies of around 0.05 and 0.25, V respectively. It may be noted that the remaining Al atoms within both
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Fig. 2 Selected eigenvectors of [Al8O12]+ corresponding to computed frequencies employing CAM-B3LYP
1043 cm -1 (54)
1038 cm -1 (53)
995 cm -1 (51)
918 cm -1 (49)
904 cm -1 (48)
873 cm -1 (47)
774 cm -1 (41)
748 cm -1 (40)
710 cm -1 (38)
molecules, with the exception of the Al atom bound to the distorted Al-O3 moiety, are also attractive, and the extent of predicted electrostatic attraction in these regions of electron density also occurs to a greater degree in the cation. Furthermore, the region of repulsive electron density about the Al atom bound to the distorted Al-O3 moiety is similarly more repulsive for the neutral triplet, than for the cation, corresponding to electrostatic potential energies of around −1.16, and −0.99 V, respectively. This may be interpreted as an area of relatively greater positive attraction within the cation, that upon addition of an electron is stabilized within the triplet by distortion of the Al-O 3 moiety, through antibonding interactions
within the inner part of the complex. This stabilization is also reflected in the spin density of both molecules, as will be discussed. Frontier molecular orbital and spin-density analysis To provide more insight into the electronic structure of the aluminium oxide molecules under consideration, frontier orbitals of the [Al8O12]+ cation and the [Al8O12] neutral geometries were obtained from DFT calculations. The frontier molecular orbitals of these systems are shown in Fig. 6 along with corresponding molecular orbital energy level diagrams for α and β sub-spaces respectively. Similarities were observed
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Fig. 3 Structural models of the [Al8O12]+ doublet (left) and the [Al8O12] triplet (right), along with corresponding interactions based on NBO analysis. Dotted lines: 4.5-10.0 kcal mol-1; thin-solid lines: 10.5-20.0 kcal mol-1; thick-solid lines: > 20.5 kcal mol-1
between the highest occupied molecular orbitals (HOMOs), and lowest unoccupied molecular orbitals (LUMOs) of both systems, specifically the α LUMO and β LUMOs of the [Al8O12]+ cation were similar to the α singly occupied molecular orbital (SOMO) and β LUMO of the neutral [Al8O12] system. The energy gap of the [Al8O12]+ doublet was determined to be 4.5108 eV, and corresponds to the energy difference between the highest β occupied molecular orbital (HOMO), and lowest β occupied molecular orbital (LUMO). The corresponding HOMO and LUMO molecular orbitals of this gap were characterized as four oxygen p-type orbitals about the weakly bound Al03 moiety, and two oxygen p-type orbitals about the strongly bound AlO3, respectively. The difference in energy between the α HOMO and α LUMO was 8.0219 eV, and these molecular orbitals were characterized as four oxygen p-type orbitals, and two Al orbitals (with some electron density
from adjacent oxygens) about the stronger bound AlO3, respectively. The α and β HOMO orbitals of the cation were furthermore very close in energy with a difference of 0.00347 eV, as can be seen in the molecular orbitals of both energy levels being oxygen p-type and almost identical. The energy gap of the [Al8O12] triplet was determined to be 2.5698 eV, and was between the α SOMO and the β LUMO. These molecular orbitals were characterized as an Al orbital about the strongly bound AlO3, and two oxygen p-orbitals about the same AlO3, respectively. As mentioned, the α LUMO of [Al8O12]+ is similar to the α SOMO of [Al8O12], with electron density in the triplet about the distorted Al only. This may be interpreted as electron density localized about the distorted Al, upon addition of an electron to the cation, effectively lowering the energy of the α LUMO by occupancy. The difference in energy between the α SOMO and α LUMO was determined to be 4.6855 eV. The SOMO as mentioned was
Fig. 4 Electrostatic potential surfaces of [Al8O12]+doublet (left), and [Al8O12] triplet (right)
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α LUMO
β LUMO
α LUMO
β LUMO
α HOMO
β HOMO
α SOMO
β HOMO
+
Fig. 5 Orbital energies (upper) and corresponding frontier orbitals (lower) for the [Al8O12] doublet (upper left and lower left four panels) and the [Al8O12] triplet (upper right and lower right four panels)
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Fig. 6 Spin density the [Al8O12]+ doublet (left) and the [Al8O12] triplet (right)
characterized as an Al orbital, and the α LUMO as three oxygen p-orbitals about the weakly bound AlO3 moiety. The difference in energy between the β HOMO and β LUMO of the [Al8O12] neutral triplet was found to be 6.11475, and their molecular orbitals were characterized as seven oxygen p-type orbitals of varying electron density for β HOMO, and similar to [Al8O12]+, two oxygen p-type orbitals about the strongly bound AlO3 moiety for β LUMO. The total spin-densities of both molecules were also determined, and are shown in Fig. 5. While the spin density for [Al8O12]+ was located only about the two oxygens of the strongly bound Al2O3, additional spindensity is observed in the [Al8O12] triplet on the Al atom of the analagous distorted Al 2 O 3 . This may be interpreted as a shift in location of total spin density in [Al8O12]+, away from the core of the molecule upon addition of an electron. The spin-density we have calculated looks noticably different from that of Sierka, Amis, and co-workers. While we have determined density located on oxygen for the energy minimum corresponding to the C1 [Al8O12]+, this density is located on two oxygen atoms adjacent to a distorted Al, in contrast to density about a single extruding oxygen of the minimum Cs
Barrowhead^ geometry of Sierka et al. Notably the [Al8O12] triplet has additional spin density located about the vicinal Al, corresponding to the SOMO as shown in Figs. 5 and 6. Furthermore, the triplet [Al 8 O 1 2 ] wavefunction was used as an initial guess to break singlet symmetry, and total spin density of the the unrestricted Hartree-Fock (UHF) singlet was determined to be stable under the perturbations considered. As shown in Fig. 7, the spin densities of the unrestricted singlet [Al8O12], and the triplet [Al8O12] systems shown in Fig. 6, and are indistinguishable at this level of theory. This pseudo-degeneracy between unrestricted singlet and triplet [Al8O12] states may be interpreted as a di-radical molecule. Although we also found the energy of the Barrowhead^ cation to be slightly lower than for the corresponding C1 geometry, the difference in energy between the unrestricted singlet, and the triplet was much greater for the Barrowhead^ structure. Additionally, the lowest energy restricted singlet may be attributed to the C1 geometry in agreement with Rahane et al. A low-energy singlet in the C1 geometry in addition to pseudo-degeneracy of the C1 triplet and unrestricted singlet states, may contribute to the observed improved IR spectral agreement between experiment and the C1 cation.
Conclusions
Fig. 7 Spin density of the UHF singlet with broken symmetry. The triplet [Al8O12] wavefunction was used as the initial guess for the unrestricted CAM-B3LYP singlet wavefunction (S**2=.998), that was determined to be stable under the perturbations considered (S**2=0.00 for stability matrix). The unrestricted singlet and the triplet are thus indistinguishable (at this level of theory) representing a diradical
The purpose of this study was to investigate the structural and electronic properties of [Al8O12] +, and its neutral analog, [Al8O12]. Because no structural data was available, a model was used that produced the best agreement with experimental spectra. It was demonstrated that some ambiguity exists regarding the exact structure of the gas phase cluster, and on the basis of NBO analysis, it was concluded that both cation [Al8O12]+ and neutral [Al8O12] systems are most appropriately described as molecules, rather than [(Al2O3)4]+, and [(Al2O3)4] clusters respectively. Frontier orbital and spin density analysis revealed that the C1 neutral system, [Al8O12], has a di-radical nature arising from a near degeneracy of the triplet and unrestricted singlet states.
J Mol Model (2015) 21:170 Acknowledgments We would like to acknowledge support from the Polish Ministry of Science and Higher Education within the statutory research number S-12/2015. Visiting professorship of Pawel M. Kozlowski at the Medical University of Gdansk was partially supported by the KNOW program. In addition, we would like to acknowledge the Cardinal Research Cluster (CRC) at the University of Louisville for ensuring computational resources.
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ORIGINAL PAPER
Structural and electronic properties of an [(Al2O3)4]+ cluster Justyna Jaroszynska-Wolinska 1 & Brady D. Garabato 2 & Jahangir Alam 2 & Asmaul Reza 2 & Pawel M. Kozlowski 2,3
Received: 1 April 2015 / Accepted: 19 May 2015 # Springer-Verlag Berlin Heidelberg 2015
Abstract Density functional theory (DFT) has been applied to investigate the structural and electronic properties of an [(Al2O3)4]+ cluster. Since there is no structural data available from experiment, the geometry of the cluster was obtained based on a model which produced the best agreement with vibrational IR-MPD data. A range of different exchangecorrelation functionals were tested, and it was concluded that the best spectral agreement was produced using the CAMB3LYP and B3LYP functionals, respectively. To further characterize the properties of the cluster, natural bond order analysis was performed, and it was concluded that an appropriate description for the system is [Al8O12]+. The frontier orbitals and spin densities of both cation and neutral systems were considered, and it was concluded that the unrestricted singlet and triplet spin densities of the neutral [Al8O12] system were nearly degenerate, representing a di-radical, with the triplet state being lower in energy.
Keywords Aluminum cluster . DFT . NBO . ESP
Electronic supplementary material The online version of this article (doi:10.1007/s00894-015-2711-4) contains supplementary material, which is available to authorized users. * Pawel M. Kozlowski [email protected] 1
Department of Civil Engineering and Architecture, Lublin University of Technology, 20-618 Lublin, Poland
2
Department of Chemistry, University of Louisville, Louisville, KY 40292, USA
3
Department of Food Sciences, Medical University of Gdańsk, Al. Gen. J. Hallera 107, 80-416 Gdańsk, Poland
Introduction Aluminium oxide molecules have been the subject of many experimental and theoretical investigations [1–5]. They are important materials in high temperature applications, translucent ceramics, corrosion resistance ceramics, electronic packaging, and catalysis. The most important form of aluminium oxide is known as alumina, Al2O3. From a crystalline point of view, Al2O3 may exist in many forms, including α, χ, η, δ, κ, θ, γ, and ρ forms [6]. Among these, the most stable is regarded as α-Al2O3, although differences in surface states exist, most commonly as two forms; a face-centered cubic (fcc), or hexagonal close-packed (hcp) arrangement of oxygen anions, with variations between polymorphs arising from differences between atomic positions within each lattice [7]. Although many metastable forms of alumina exist, including γ-Al2O3, δ-Al2O3, and others, Sierka, Asmis, and coworkers [8] proposed new structural polymorphs of the most stable isomers of [(Al2O3)4]+ and (Al2O3)4 through a combination of experiment and density functional theory (DFT). Specifically, IR multiple-photon dissociation (MPD) spectrum was collected for [(Al2O3)4]+ and the corresponding DFTbased structure was established based on a genetic algorithm applied to an intial geometry derived from the corundum crystal structure. The structure proposed was based on nmemebered rings consisting of six- and four-memebered alternating aluminum and oxygen atoms, and the global minimum was determined to be of an Barrowhead^ shape with Cs symmetry, where the final oxygen atom was coordinated to the top-most alumium vertex of the fragment. This proposed structure was further used to simulate vibrational spectra, and distinguish from other structural analogs. Spin density distribution for this structure corresponding to the energy minimum was also reported, and the density was entirely localized about the arrowhead oxygen.
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Rahane et al. [1] systematically investigated structural and electronic properties of (Al2O3)n clusters with n=1–10 at the pseudopotential DFT level using the generalized gradient approximation for the exchange-correlation energy. They concluded that the lowest energy isomers show preference toward 4- and 6-coordinated Al2O2 and Al3O3 rings respectively, and that these minima have more structural similarity with the γAl2O3 phase than the α-Al2O3 (corundum) phase. In general, they concluded that isomers with cage structures are highest in energy, and in particular for clusters with n=4, the lowest energy (Al2O3)4 isomer was found to be the one without any symmetry (C1). The primary purpose of the present study is to further investigate the structural and electronic properties of [(Al2O3)4]+, employing DFT. This study addresses the following issues, (i) structure based on available vibrational spectra, (ii) natural bond orbital analysis and electrostatic potential surface properties, and (iii) frontier and molecular orbital analysis along with spin density. Finally, conclusions regarding the interpretation of the gas phase [(Al2O3)4]+ are presented.
Computational details All calculations reported in this study were performed using the Gaussian09 suite of programs for electronic structure calculations [9]. The initial structure of the cluster was constructed manually, taking previous investigations into consideration. A number of initial structural guesses were generated, and the corresponding geometries were then optimized using a number of exchange-correlation functionals including B3LYP, CAM-B3LYP, B3PW91, TPSS, TPSSh, BVP86, and BP86. Initially to build the cluster and perform preliminary geometry optimizations, the 6-31G* basis set was used, and final optimizations were then carried out using the larger 6-311G(d,p) basis set. Final optimizations were performed under tight conditions, with no integral symmetry imposed. Force constants were calculated at the first point in each case, and no curvature test was imposed in the Berny optimizations. Frequencies along with their respective IR intensities were then calculated, and the lack of imaginary frequencies confirmed in each case that a true minimum was obtained. The low-spin state corresponding to the doublet was assumed for [(Al2O3)4]+ in its cation form, and confirmed by stability analysis of the wavefunction. Triplet and unrestricted singlet spin states were taken into consideration for the corresponding neutral forms of the C1 [Al8O12] system. The lowest energy spin state was identified as the triplet for C1 [Al8O12], and was confirmed by stability analysis. Natural bond order (NBO) analysis was performed for the optimized C 1 [Al8O12]+ doublet and triplet [Al8O12] structures to determine the nature of bonding within each system. In addition to NBO analysis (NBO 5.9), electrostatic potential (ESP) surfaces
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were calculated and visualized with the Molekel program [10], and frontier molecular orbitals along with spin densities were visualized with Chemcraft [11].
Results and discussion Analysis of vibrational data Taking into account that no structural data is available for gas phase [(Al2O3)4]+, the initial focus of this theoretical study was analysis of the vibrational data reported in ref. [8]. Our aim was to understand the elecronic structure and nature of bonding interactions within the [(Al2O3)4]+ geometry that produced the best agreement with experimental spectra. In our calculations, the C1 isomer produced better spectral agreement than the Cs (Fig. S1, SI), and as such was the isomer further considered. Taking the relative energies of C1 and Cs isomer spin states into consideration, the underlying approach was to first build a structural model, optimize its geometry, and compute frequencies to simulate vibrational spectra with no prior assumptions related to the structure of the system. As mentioned in the computational section, initial structures were constructed manually assuming no symmetry, and each geometry was then optimized with no constraints. To recall, xcfunctionals were initially investigated by optimizing geometries using the 6-31G* basis set, and those that produced the best agreement with experiment were then used to optimize the same initial geometries in 6-311g(d,p) basis. The corresponding infrared intensities based on dipole moment derivatives were then computed, and further used to simulate infrared spectrum for direct comparison with expirement. Although a number of different functionals were tested, only BP86, TPSSh, CAM-B3LYP, and B3LYP, produced spectra that were in reasonable agreement with experimental data. Upon closer inspection, it was concluded that only two functionals, B3LYP and CAM-B3LYP produced very good agreement with IR-MPD experimental data. Because computed frequencies are often overestimated by DFT when compared to experimental values due to the insufficient treatment of correlation energy and anharmonicity effects [12], to obtain better agreement with experiment they are typically scaled. The best approach if experimental data permits is the use of multiple scaling factors [12], although a single scaling factor was employed in the present study. Using the most intense experimental band as a reference, a scaling factor was obtained for each functional. Figure 1 shows comparison between experimental spectra and simulated data, based on vibrational frequencies and IR intensities computed at the CAMB3LYP/6-311G(d,p), and B3LYP/6-311G(d,p) levels of theory.
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Fig. 1 Comparison of experimental IR-MPD spectrum (trace a) with simulated spectrum based on B3LYP/6-311G(d,p) (red upper trace), and CAM-B3LYP (blue lower trace). The experimental spectrum was reproduced from ref. [1] with permission
Overall both simulated spectra were in very good agreement with experiment, notably around 1000 cm−1 where the most intense band is present. Each spectra also captures the relative intensities of the experimental bands reasonably well. Because agreement between experimental data was very good for both functionals, a correlation between computed and experimental frequencies was established and around 14 peaks were assigned. Figure 1 shows this correlation in terms of vertical lines, and Table 1 contains the corresponding calculated frequencies. As discussed below, CAM-B3LYP produced the best agreement with experiment, and the eigenvectors for nine of the most significant calculated peaks at the CAM-B3LYP/6-311g(d,p) level are collcted in Fig. 2. While both functionals produced spectra that agreed well with experiment, the differences between the two are presented here for completeness. CAM-B3LYP produces a shoulder (1038 cm−1, 51) within the most intense band (995 cm−1, 53), that correlates to the experimental values of 995 cm−1 and 1011 cm−1. The second most inense experimental peak produced by CAM-B3LYP (1043 cm−1, 54) also correlates better than B3LYP to the 1027 cm−1 experimental value, although the spectra produced B3LYP has an improved resolution of the experimental 1011 cm−1 band. Additionally, CAMB3LYP reproduces the experimental peak at 962 cm −1, (962 cm−1, 50) while B3LYP does not, but improved resolution about the 884 cm−1 and 910 cm−1 experimental values may be attributed to B3LYP. Although both CAM-B3LYP and B3LYP correlate to the experimental spectra comparably about the 771 cm−1, 779 cm−1, and 831 cm−1 wavenumbers, neither functional has significant correlation to the 818 cm−1 or lower 664 cm−1 values. However, CAM-B3LYP does to some extent correlate to the lower energy value (601 cm−1, 34) of the experimental 624 cm−1 transition better than B3LYP. Comparison of the experimental values which correlate most significantly to the scaled eigenvalues produced by the CAMB3LYP and B3LYP functionals are collected in Table 1.
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The eigenvectors associated with the most intense calculated vibrations at the CAM-B3LYP/6-311G(d,p) level mentioned above, are collected in Fig. 2. The most intense peak, 995 cm−1 (51), shows displacement amplitudes of medium strength between all Al and O atoms within the structure, with slightly higher amplitudes associated with Al-O bending about both Al2O3 end-capping moeities. The second most intense peak, 1043 cm−1 (54), on the other hand has significantly large Al-O stretching amplitudes about one of the capping Al2O3 moeities, while the remaining displacement amplitudes were comparatively smaller. The shoulder peak between these two vibrations, 1038 cm−1 (53), has moderately high displacement amplitudes for both Al 2 O 3 capping moeities, with smaller displacements within the central complex. The remaining calculated peaks at 918 cm −1 (49), 904 cm −1 (48), 873 cm −1 (47), 774 cm −1 (41), 748 cm −1 (40), and 710 cm−1 (38) all have moderate displacement amplitudes throughout the entire complex, with the exception that they differ generally in the location of around three high strength amplitudes. The 918 cm−1 (49) eigenvector shows three high amplitude oxygen displacements, while the remaining amplitudes were moderate to small. The eigenvectors corresponding to 904 cm −1 (48) show a high Al-O stretching amplitude, while the 873 cm −1 (47) peak corresponds to a different high amplitude Al-O stretch, and one high O displacement. The eigenvectors of the 774 cm −1 (41) peak are similar to that of 904 cm −1 (48), showing two high amplitude Al-O stretches, but with two additional high amplitude O displacements around one capping moeity. The 748 cm −1 (40) peak is similar to 774 cm −1 (41), with high amplitudes for both oxygen atoms mentioned (although the stretch is asymmetric), and similar small displacement amplitudes throught the remaining geometry. Finally the calculated peak at 710 cm−1 (38), resembles the most intense peak, 995 cm−1 (51), with large overall displacement amplitudes, specifically from some of the oxygens about both capping Al2O3 moeities. Natural bond order analysis and implications for properties of [(Al2O3)4]+ The analysis of vibrational data presented in the previous section, and very good agreement with IR-MPD spectrum (Fig. 1) gives strong confidence that the proposed structural models in the present study are reliable. The coordinates of both geometries used to simulate vibrational spectra shown in Fig. 1 are available in the Supporting information (SI). Although both functionals under consideration produce reliable agreement with experimental data, we ultimately chose the CAM-B3LYP geometry because overall performance of CAM-B3LYP can be considered as slightly better than that of B3LYP. To provide some insight into the nature of bonding within the system in terms of relative bond energies, natural bond
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Table 1 Frequencies of the most intense experimental IR-MPD bands of [(Al2O3)+]4 correlated with computed frequencies, with the most intense noted in bold, subjected to single-parameter scaling assuming vibration # 51 as a reference EXP (IR-MPD)/cm−1
B3LYP/cm−1 (eigenvalues)
CAM-B3LYP/cm−1 (eigenvalues)
1027
1050 (54)
1043 (54)
1011 995 962 938 929 910 884 831 818 799 771 654 624
1027 (53) 995 (51) 905 (49) 881 (48) 880 (47) 839 (45) 768 (42) 754(40) 703 (38) 603 (35) 582 (34)
1038 (53) 995 (51) 962 (50) 918 (49) 904 (48) 873 (47) 850 (45) 803 (43) 774 (41) 748 (40) 710 (38) 634 (35) 601 (34)
order (NBO) analysis was performed for [(Al2O3)4]+ and the corresponding neutral species. It should be noted that although full populations were calculated, NBOs are orthonormal sets of localized Bmaximum occupancy^ orbitals, and the delocalization in NBO basis provides a qualitative energetic description of bonding based on a linear combination of all natural hybrid orbitals, and those considered within a certain energetic threshold, in this case 4.0 kcal mol-1. As previously outlined, geometries were optimized in the gas phase at the CAMB3LYP/BP86 level of theory, and their wavefunctions were confirmed to be stable. The addition of a single electron to [(Al2O3)4]+ produced a triplet state rather than a singlet, with the energies of both states very close to each other, as will be discussed along with frontier orbitals in further sections. To represent the results of the NBO analysis, a graphical scheme was adopted shown in Fig. 3, as three realtive bond strength ranges of 4.5-10.0, 10.5-20.0, and >20.5 kcal mol-1, represented as dashed, solid-thin, and solid-thick lines between corresponding atoms, respectively. Relative bond strengths represented in this way were determined by summation of significant NBO donating or withdrawing contributions from natural bonding orbitals within each system, with a threshold for inclusion of 4.0 kcal mol-1. Occupancies of Rydberg states were below the threshold for inclusion. It should be noted that the graphical representation in Fig. 3 does not include the directionality of interactions between NBO fragments explicitly, but the total relative strengths of all natural bonds between fragments.
Although most interactions within each cluster were determined to be bonding in nature, those between Al atoms (Al-Al bonds), were determined to be primarily anti-bonding. Within the neutral cluster having triplet multiplicity, three additional Al-Al anti-bonding interactions were found. On the other hand, most of the Al-O bonds were found to be moderately strong. Based on NBO analysis, it is difficult to distinguish individual Al2O3 monomers within clusters regardless of cationic or neutral character. Although Al2 moieties may be distinguished within each structure under consideration, it is apparent from NBO analysis that the most appropriate description of the [(Al2O3)4]+ cluster, is consistent with the forumula [Al8O12]+, implying that the complex should be viewed as a molecule. Likewise, for neutral [(Al2O3)4], the same observation holds based on NBO analysis, and it should also be viewed as [Al8O12]. In sum, individual Al2O3 monomers cannot be identified clearly within the obtained geometries, and a molecular rather than a cluster interpretation describing overall bonding should be adopted. One of the most significant differences in geometry between the [Al8O12]+ doublet, and [Al8O12] triplet is the distortion of an Al away from the molecule upon addition of an electron, as shown in Fig. 3. Although this Al-03 moiety remains bound to the system with relatively high bond strengths, this distortion produces one O-Al bond that is significantly weaker. This oxygen is weakly bound to an Al-Al bond, which is also notably more weakly bound to outer oxygens in the O-Al-Al-O moiety in the triplet neutral geometry. Furthermore, within the geometry having neutral charge, significant Al-Al antibonding may be seen as occuring within the core of the neutral system, while this is not observed for the cation. The Al-O3 moeity capping the core of the molecule from the other side, is similar in both cation and neutral geometries, with one slightly stronger Al-O bond attributed to the triplet. The outer oxygens that are generally weakly associated with Al-Al bonds also remain essentially the same between both complexes, with some differences. Notably the triplet species contains the most weakly bound outer oxygen atom, with two ~5 kcal mol-1 bonds to the most strongly antibonding Al-Al pair. This oxygen in the triplet geometry is then associated with the strongest bonding and antibonding Al-O-Al moiety of both geometries. Electrostatic properties The electrostatic potential energy (ESP) surfaces of both molecules mapped to their respective electron densities (using an isovalue of 0.02), are shown in Fig. 4. The distorted Al atom observed in the optimized neutral geometry, remains attractive for both species, and as may be expected, is attractive to a greater degree in the cation, corresponding to electrostatic potential energies of around 0.05 and 0.25, V respectively. It may be noted that the remaining Al atoms within both
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Fig. 2 Selected eigenvectors of [Al8O12]+ corresponding to computed frequencies employing CAM-B3LYP
1043 cm -1 (54)
1038 cm -1 (53)
995 cm -1 (51)
918 cm -1 (49)
904 cm -1 (48)
873 cm -1 (47)
774 cm -1 (41)
748 cm -1 (40)
710 cm -1 (38)
molecules, with the exception of the Al atom bound to the distorted Al-O3 moiety, are also attractive, and the extent of predicted electrostatic attraction in these regions of electron density also occurs to a greater degree in the cation. Furthermore, the region of repulsive electron density about the Al atom bound to the distorted Al-O3 moiety is similarly more repulsive for the neutral triplet, than for the cation, corresponding to electrostatic potential energies of around −1.16, and −0.99 V, respectively. This may be interpreted as an area of relatively greater positive attraction within the cation, that upon addition of an electron is stabilized within the triplet by distortion of the Al-O 3 moiety, through antibonding interactions
within the inner part of the complex. This stabilization is also reflected in the spin density of both molecules, as will be discussed. Frontier molecular orbital and spin-density analysis To provide more insight into the electronic structure of the aluminium oxide molecules under consideration, frontier orbitals of the [Al8O12]+ cation and the [Al8O12] neutral geometries were obtained from DFT calculations. The frontier molecular orbitals of these systems are shown in Fig. 6 along with corresponding molecular orbital energy level diagrams for α and β sub-spaces respectively. Similarities were observed
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Fig. 3 Structural models of the [Al8O12]+ doublet (left) and the [Al8O12] triplet (right), along with corresponding interactions based on NBO analysis. Dotted lines: 4.5-10.0 kcal mol-1; thin-solid lines: 10.5-20.0 kcal mol-1; thick-solid lines: > 20.5 kcal mol-1
between the highest occupied molecular orbitals (HOMOs), and lowest unoccupied molecular orbitals (LUMOs) of both systems, specifically the α LUMO and β LUMOs of the [Al8O12]+ cation were similar to the α singly occupied molecular orbital (SOMO) and β LUMO of the neutral [Al8O12] system. The energy gap of the [Al8O12]+ doublet was determined to be 4.5108 eV, and corresponds to the energy difference between the highest β occupied molecular orbital (HOMO), and lowest β occupied molecular orbital (LUMO). The corresponding HOMO and LUMO molecular orbitals of this gap were characterized as four oxygen p-type orbitals about the weakly bound Al03 moiety, and two oxygen p-type orbitals about the strongly bound AlO3, respectively. The difference in energy between the α HOMO and α LUMO was 8.0219 eV, and these molecular orbitals were characterized as four oxygen p-type orbitals, and two Al orbitals (with some electron density
from adjacent oxygens) about the stronger bound AlO3, respectively. The α and β HOMO orbitals of the cation were furthermore very close in energy with a difference of 0.00347 eV, as can be seen in the molecular orbitals of both energy levels being oxygen p-type and almost identical. The energy gap of the [Al8O12] triplet was determined to be 2.5698 eV, and was between the α SOMO and the β LUMO. These molecular orbitals were characterized as an Al orbital about the strongly bound AlO3, and two oxygen p-orbitals about the same AlO3, respectively. As mentioned, the α LUMO of [Al8O12]+ is similar to the α SOMO of [Al8O12], with electron density in the triplet about the distorted Al only. This may be interpreted as electron density localized about the distorted Al, upon addition of an electron to the cation, effectively lowering the energy of the α LUMO by occupancy. The difference in energy between the α SOMO and α LUMO was determined to be 4.6855 eV. The SOMO as mentioned was
Fig. 4 Electrostatic potential surfaces of [Al8O12]+doublet (left), and [Al8O12] triplet (right)
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α LUMO
β LUMO
α LUMO
β LUMO
α HOMO
β HOMO
α SOMO
β HOMO
+
Fig. 5 Orbital energies (upper) and corresponding frontier orbitals (lower) for the [Al8O12] doublet (upper left and lower left four panels) and the [Al8O12] triplet (upper right and lower right four panels)
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Fig. 6 Spin density the [Al8O12]+ doublet (left) and the [Al8O12] triplet (right)
characterized as an Al orbital, and the α LUMO as three oxygen p-orbitals about the weakly bound AlO3 moiety. The difference in energy between the β HOMO and β LUMO of the [Al8O12] neutral triplet was found to be 6.11475, and their molecular orbitals were characterized as seven oxygen p-type orbitals of varying electron density for β HOMO, and similar to [Al8O12]+, two oxygen p-type orbitals about the strongly bound AlO3 moiety for β LUMO. The total spin-densities of both molecules were also determined, and are shown in Fig. 5. While the spin density for [Al8O12]+ was located only about the two oxygens of the strongly bound Al2O3, additional spindensity is observed in the [Al8O12] triplet on the Al atom of the analagous distorted Al 2 O 3 . This may be interpreted as a shift in location of total spin density in [Al8O12]+, away from the core of the molecule upon addition of an electron. The spin-density we have calculated looks noticably different from that of Sierka, Amis, and co-workers. While we have determined density located on oxygen for the energy minimum corresponding to the C1 [Al8O12]+, this density is located on two oxygen atoms adjacent to a distorted Al, in contrast to density about a single extruding oxygen of the minimum Cs
Barrowhead^ geometry of Sierka et al. Notably the [Al8O12] triplet has additional spin density located about the vicinal Al, corresponding to the SOMO as shown in Figs. 5 and 6. Furthermore, the triplet [Al 8 O 1 2 ] wavefunction was used as an initial guess to break singlet symmetry, and total spin density of the the unrestricted Hartree-Fock (UHF) singlet was determined to be stable under the perturbations considered. As shown in Fig. 7, the spin densities of the unrestricted singlet [Al8O12], and the triplet [Al8O12] systems shown in Fig. 6, and are indistinguishable at this level of theory. This pseudo-degeneracy between unrestricted singlet and triplet [Al8O12] states may be interpreted as a di-radical molecule. Although we also found the energy of the Barrowhead^ cation to be slightly lower than for the corresponding C1 geometry, the difference in energy between the unrestricted singlet, and the triplet was much greater for the Barrowhead^ structure. Additionally, the lowest energy restricted singlet may be attributed to the C1 geometry in agreement with Rahane et al. A low-energy singlet in the C1 geometry in addition to pseudo-degeneracy of the C1 triplet and unrestricted singlet states, may contribute to the observed improved IR spectral agreement between experiment and the C1 cation.
Conclusions
Fig. 7 Spin density of the UHF singlet with broken symmetry. The triplet [Al8O12] wavefunction was used as the initial guess for the unrestricted CAM-B3LYP singlet wavefunction (S**2=.998), that was determined to be stable under the perturbations considered (S**2=0.00 for stability matrix). The unrestricted singlet and the triplet are thus indistinguishable (at this level of theory) representing a diradical
The purpose of this study was to investigate the structural and electronic properties of [Al8O12] +, and its neutral analog, [Al8O12]. Because no structural data was available, a model was used that produced the best agreement with experimental spectra. It was demonstrated that some ambiguity exists regarding the exact structure of the gas phase cluster, and on the basis of NBO analysis, it was concluded that both cation [Al8O12]+ and neutral [Al8O12] systems are most appropriately described as molecules, rather than [(Al2O3)4]+, and [(Al2O3)4] clusters respectively. Frontier orbital and spin density analysis revealed that the C1 neutral system, [Al8O12], has a di-radical nature arising from a near degeneracy of the triplet and unrestricted singlet states.
J Mol Model (2015) 21:170 Acknowledgments We would like to acknowledge support from the Polish Ministry of Science and Higher Education within the statutory research number S-12/2015. Visiting professorship of Pawel M. Kozlowski at the Medical University of Gdansk was partially supported by the KNOW program. In addition, we would like to acknowledge the Cardinal Research Cluster (CRC) at the University of Louisville for ensuring computational resources.
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