ARTICLE pubs.acs.org/JPCA
Structure, Thermodynamics, and Energy Content of AluminumCyclopentadienyl Clusters Kristen S. Williams†,§ and Joseph P. Hooper*,†,‡ †
Research Department, Naval Surface Warfare Center, Indian Head, Maryland 20640, United States Department of Physics, Naval Postgraduate School, Monterey, California 93943, United States § Materials Science and Engineering Program, Texas A&M University, College Station, Texas 77843, United States ‡
ABSTRACT: We present quantum chemistry simulations of aluminum clusters surrounded by a surface layer of cyclopentadiene-type ligands to evaluate the potential of such complexes as novel fuels or energetic materials. Density functional theory simulations are used to examine the aluminum-ligand bonding and its variation as the size of the aluminum cluster increases. The organometallic bond at the surface layer arises mainly from ligand charge donation into the Al p orbitals balanced with repulsive polarization effects. Functionalization of the ligand and changes in Al cluster size are found to alter the relative balance of these effects, but the surface organometallic bond generally remains stronger than AlAl bonds elsewhere in the cluster. In large clusters, such as the experimentally observed Al50Cp12*, this suggests that unimolecular thermal decomposition likely proceeds through loss of surface AlCp* units, exposing the strained interior aluminum core. The calculated heats of combustion per unit volume for these systems are high, approaching 60% that of pure aluminum. We discuss the possibility of using organometallic aluminum clusters as a means of achieving rapid combustion in propellants and fuels.
’ INTRODUCTION Modern solid rocket propellants frequently use aluminum powder as a fuel component due to its high enthalpy of combustion. These powders are generally of micrometer size, but in recent years there has been significant study of nanometer scale Al as a route to increasing the oxidation rates and potentially lowering the ignition threshold.1,2 The outer surface of the aluminum grains consists of an oxidized alumina layer ∼26 nm thick, which can limit rapid reactivity of the internal Al.3 This has led several authors to pursue surface passivation of aluminum nanoparticles with organic functional groups that prevent formation of the oxide.36 However, larger nanoparticles of aluminum will still have oxidation rates limited by the diffusion of fuel to the detached flame front and the agglomeration of condensed aluminum oxide during combustion.7 To this end, we have been pursuing the possibility of molecularscale aluminum clusters with a protective organic layer as novel additives for solid rocket motor propellant formulations. As an example of such a material, H. Schn€ockel and co-workers have previously synthesized a 50-atom Al cluster surrounded by cyclopentadienyl Cp* (C5[CH3]5) ligands.8 The metalligand (M-L) interaction on the exterior of the cluster consists of η5 bonds between the Al and the Cp* rings. Their study of larger aluminum clusters builds on a large body of work on low-valence aluminum coordination complexes.913 A number of these clusters, such as the tetramers Al4Cp4* and Al4(C5Me4H)4, crystallize into lowsymmetry solid state structures and have been observed via X-ray r 2011 American Chemical Society
crystallographic analysis and NMR spectroscopy.14,15 Attempts to isolate similar compounds with unmethylated Cp (C5H5) ligands have generally been unsuccessful due to their tendency to disproportionate to aluminum metal and higher-valence compounds such as AlCp3.11,14 Currently very little is known about the stability or decomposition of the larger aluminumcyclopentadienyl compounds that contain a significant mass fraction of aluminum. Computational studies on these materials are limited and mainly restricted to work on aluminum metallocenes. Early HartreeFock calculations by Ahlrichs and co-workers16 examined basic AlCp as well as Al4Cl4, Al4F4, and Al4Cp4. No correlation effects were included, and with their methodology, Al4Cp4 was found to be unstable with respect to decomposition into monomers. A number of later works considered the simple Al metallocenes in the context of examining trends in a broader range of main-group metallocenes or similar organometallics.1720 In recent years, Huber and Schn€ockel have performed density functional theory calculations in support of their X-ray diffraction and 27Al NMR studies of larger aluminumCp-type clusters.14,21 They proposed that the large clusters, such as Al50Cp12*, may serve as a type of barrier state that prevents the smaller compounds from spontaneously decomposing to metallic aluminum and trivalent aluminum species. Expanded computational studies of these materials are highly Received: July 30, 2011 Revised: October 4, 2011 Published: October 18, 2011 14100
dx.doi.org/10.1021/jp207292t | J. Phys. Chem. A 2011, 115, 14100–14109
The Journal of Physical Chemistry A
ARTICLE
Table 1. Calculated Bond Lengths and Distances of HalfMetallocene Complexesa cluster
CC bond length
AlX distance
slip
(Å)
(Å)
(Å)
hapticity
0.002
η
AlCp ref 16
1.420 1.409
2.064 2.039
ref 17
1.420
2.037
ref 18
1.428
2.059
ref 19
2.06
ref 20
2.05
AlCp*
1.429
2.021
Table 2. Calculated Average Bond Lengths and Distances of Larger AlCp Clusters cluster
5
AlCp3
0.000
η
AlX distance
slip
(Å)
(Å)
(Å)
hapticity
1.083 1.546
η2 η1
1.738
η1
0.958
η2
2.168
η1
2.318
η1
0.003
η5
0.033
η5
1.424
AlCp3*
5
CC bond length
1.439
Al4Cp4
1.420
2.072 2.056
ref 17
1.498
1.989
ref 16
1.408
ref 27b AlC5H4NO2
1.414 1.417
2.063 2.116
1.408
0.003
η5
ref 17 ref 20
AlC5Me4CF3
1.428
2.053
0.058
η5
ref 14
1.429
2.052
AlC5[CF3]5
1.425
2.216
0.031
η5
Al4Cp4*
1.428
2.073
a
2.06
a
Average slip and ligand hapticity are calculated by perpendicular projection of Al atoms onto the Cp-type rings. AlX distances are only calculated for species with η5 bonding. b Experimental data.
ref 14
1.437
ref 9a
2.059 2.015
Al8Cp4
1.421
2.000
0.006
η5
Al8Cp4*
1.432
1.956
0.005
η5
Al50Cp12
1.442 1.437
1.992
1.231 0.00
η1 η5
Al50Cp12*
1.429
2.064
0.209
η5
QM/MM
1.429
2.121
ref 8a
1.421
1.981
desirable to elucidate their reactivity, stability, and potential combustion properties. In this work we present first-principles calculations of the structure, thermodynamics, and energy content of these aluminum cluster materials, with a particular focus on their possible role as rapidly combusting fuels or propellants. We examine their structure and chemical bonding, steric hindrance, thermodynamics, and likely initial decomposition steps. Using calculated thermodynamic data, we examine the proposed mechanism for the stability of these clusters discussed above and show that our calculations are in disagreement with this mechanism. We also estimate the energy release potential of these clusters, comparing heats of combustion and specific impulses to other common propellant ingredients to examine their possible utility as rapidly burning fuels.
’ RESULTS AND DISCUSSION
’ COMPUTATIONAL METHODOLOGY Calculations on aluminum organometallic clusters are performed using density functional theory with the B3LYP functional22 and a 6-31G(d,p) basis set. For comparison and assurance of accurate thermodynamic values, we also calculate heats of formation using the G2 method23 for a number of the smaller clusters. B3LYP/6-31G(d,p) gives accurate thermodynamics while still being efficient enough to calculate structures and vibrational properties of the large clusters (350 atoms). All calculations are performed with the Gaussian 09 program24 at the AFRL supercomputing center. For geometry optimization of the largest cluster, Al50Cp12*, a multilayer QM/MM method25 is used in which the methyl groups on each Cp* ligand are modeled with Rappe’s Universal Force Field (UFF)26 and remaining atoms are treated with DFT. Layer neutrality is automatically imposed such that the dangling bonds in each layer are passivated with hydrogen. This hybrid approach is only used in finding optimized geometries of Al50Cp12*; thermodynamic calculations are then performed with a full DFT calculation at the B3LYP/ UFF geometry. The small structural differences between the QM/MM and full DFT approach have a minimal effect on calculated energy difference or enthalpies of formation. As discussed below, the energy barrier for rotation of the outer
Structure and Bonding. We first present results on the theoretical structure of aluminum complexes bound to cyclopentadienyl type ligands. In Table 1 we list the calculated B3LYP/6-31G(d,p) bond lengths for half-metallocene configurations of Al with Cp and related derivatives. In addition to providing insight into the individual Al-L bonding, these structures also form the protective outer layer on the larger aluminum clusters discussed below. The distance from the Al to the center of the Cp ring (Al-X) is given, along with the CC bond length in the ring. The CC bond lengths presented are averaged over all intraring carbons. The Al-ring center distances are obtained via perpendicular projection of Al onto the plane of the C5 ring. The absolute difference between this projection and the ring center is defined as the ring slip. Our calculated slip values are then used to assign hapticities in accordance with the study of main-group half metallocenes by Budzelaar and co-workers:19 η5, 0 Å; η3, 0.8 Å; η2, 1.0 Å; η1, g1.2 Å. Our calculated geometries for AlCp are in good agreement with other recent studies of main-group metallocenes, such as that by Rayon and Frenking.18 In addition, we consider three substituted Cp derivatives; nitroCp (C5H4NO2), trifluoromethyl-Cp* (C5Me4CF3), and pentatrifluoromethyl-Cp* (C5[CF3]5). The substituted Cp ligands allow us to examine the M-L bond strength with various electron withdrawing groups that may also serve as oxidizers for the
b
a
Experimental data. b QM/MM refers to geometry optimization of the largest cluster (Al50Cp12*) with the multilayer method B3LYP/631 g(d,p):UFF.
methyl groups is extremely small and the contribution of the methyl vibrations to the thermodynamic partition function is negligible.
14101
dx.doi.org/10.1021/jp207292t |J. Phys. Chem. A 2011, 115, 14100–14109
The Journal of Physical Chemistry A
Figure 1. Calculated structures of (a) Al4Cp4* and (b) Al8Cp4*.
ARTICLE
Figure 3. Calculated structures of Al50Cp12 (left) and Al50Cp12* (right). Surface aluminum atoms directly involved in organometallic bonding are shown in teal.
Table 3. Average Distances between Al Atoms Located in the Interior Cages of the Clustersa cluster Al4
Al4
2.795
Al4
2.764
Al4Cp4* Al8Cp4
Al4 Al4 shell
2.869 (2.767)b 2.788
Al50Cp12
aluminum complexes during thermal decomposition. All substituted Cp ligands result in only slight shifts of the Al (
