J. Phys. Chem. 1992,96, 4367-4374
4367
Periodic ab Initio Hartree-Fock Calculations of the Low-Symmetry Mineral Kaolinite Anthony C. Has* Molecular Sciences Research Center, Pacific Northwest Laboratory,f Richland, Washington 99352
and Victor R. Saunders SERC Daresbury Laboratory, Daresbury. Warrington, WA4 4AD, UK (Received: October 31, 1991; In Final Form: January 3, 1992)
Periodic ab initio Hartree-Fock LCAO calculationshave been carried out on the P1 symmetry clay mineral kaolinite, Alfii209H4 using STO-3G and modified 6-21G basis sets. The three structural degrees of freedom associated with the inner hydrogen atom of this compound have been optimized using the STO-3G basis. The equilibrium position of the inner hydrogen (described relative to the adjoining 0-H bond) is predicted to be approximately parallel to the (ab) plane (forming an angle of +3.l0) with an (FH bond length of 0.99 A and the two A1-O-H angles of 107.7' and 107.4', respectively. The physical properties of the system were obtained using the 6-21G basis at the geometry deduced from the STO-3G calculations. The total valence density of states has been computed. Projected densities of states have been evaluated for the chemically distinct sets of elements. It is found that the majority of the valence states are composed of oxygen 2s and 2p atomic orbitals with overlap from Si and A1 3s and 3p atomic orbitals. Crystal charge densities and density deformation maps have been computed in the basal plane of the silicate ring system. The calculations have revealed small charge densities in the center of the ditrigonal cavity ( 104-10-5 e/bohr3) and an oblate distortion of the oxygen charge density directed toward the center of the ring system. The formal charges resulting from a Mulliken population analysis of the 6-21G data give the following: Si = +2.5 lei, 0 = -1.7 [el, A1 = +2.1 lei, and H = +OS6 lei. Electrostatic potential maps have been computed in the chemically accessible regions of the structure near the ditrigonal cavities. These maps indicate that the center of the cavity is at a negative potential relative to nearby silicon positions. Analogous calculations have been carried out perpendicular to the layers of the material. The results of these calculations reveal extensive interlayer hydrogen bonding.
Introduction To understand the chemical and physical properties of an im-
TABLE I: Comparison of Experimental and Theoretical Results for Hvdroeen Atom Positions in Kaolinite"
portant class of clay minerals and to demonstrate the applicability of periodic Hartree-Fock theory in treating systems devoid of point symmetry, we have carried out a study on the 1:l dioctahedral clay mineral kaolinite, A12Si209H4. The clay minerals are abundant natural decomposition products of aluminosilicates that have been subject to aqueous environments and, therefore, play an important role in defining the chemical and physical properties of sedimentary systems. Understanding the fundamental nature of these materials will aid in the development of more accurate descriptions of processes such as the subsurface transport of natural and contaminat species. The extremely small particle size of the clays (typically 2-10 pm in the case of kaolinite), combined with the tendency of the natural materials to exhibit both structural and substitutional complicates the elucidation of the properties of "clean" bulk materials. In particular, the small particle size often precludes the use of single-crystal diffraction techniques in the determination of structural parameters, leading to ambiguities in the crystal structure. In addition, the insulating nature of these materials makes the measurement of microscopic properties via standard surface science techniques difficult. In this paper, we will use periodic a b initio quantum chemical methods to predict the position of the inner hydrogen atom in the crystal structure of kaolinite and to describe the properties of several important regions of the crystal lattice. The empirical determination of the crystal structure of kaolinite has been the subject of repeated investigations over the past 60 years. The status of these efforts was recently presented in an excellent review by G e i ~ e . These ~ structural studies seem to have converged on a general description of the heavy-atom (non-hydrogen) positions in the material. The majority of the studies have found the diffraction data to be consistent with a c-centered lattice (space group Cl); however, a recent investigation by Young and Hewatt has indicated that the material may be more accurately described by a primitive triclinic lattice (space group P l ) . The
author surface hydroxyls, deg inner hydroxyls, deg Youne and Hewat4 62. 48.66. 74. 75. 48 12. -22 -36 Ada&' 69; 67; 61' +15 Giese* 70, 72, 61 +3.1 this study 58
Corresponding author. 'Pacific Northwest Laboratory is operated for the US.Department of Energy by Battelle Memorial Institute under Contract DE-AC06-76RLO 1830.
~~~
'All angles reported relative to the ab plane.
P1 symmetry cell proposed by those authors is twice the volume of the more commonly accepted C1 cell. Although the crystal structure proposed by Young and Hewatt4 may be accurate on the average, it possesses several unrealistic Si-0 and A1-0 internuclear distances. The details of that study have been previously di~cussed.~ The most recent structural study has been carried out by Bish and Von Dreele,5 who have preformed a careful X-ray analysis for the non-hydrogen atoms and find no evidence in support of the proposition of Young and Hewatt that the lattice disobeys c centering. The heavy-atom positions resulting from the study by Bish and Von Dreele are illustrated in Figure 1. From Figure 1 it can be seen that the framework structure is composed of a "sheet" of corner-sharing S i 0 4 tetrahedra linked, by common oxygen atoms parallel to the c axis, to a "sheet" of edge-sharing A106 octahedra. The two sheets together form a clay "layer". There are two types of hydrogen atoms found in the structure. The "outer hydrogens" which are bound to oxygens that form a plane of close-packed atoms "above" the plane of the aluminum atoms. This type of hydrogen extends into the interlayer region of the material. The "inner hydrogens" are bound to oxygens "below" the plane of aluminum atoms and extend into ( I ) Chemistry of Soil Constituents; Greenland, D. J., Hayes, M. H. B., Eds.; John Wiley & Sons: New York, 1985. (2) Bailey, S. W. Polytypism of 1:l Layer Silicalites. In Reuiews in Mineralogy: Hydrous Phyllosilicates; Bailey, S . W., Ed.; Minerological Society of America: Washington, DC, 1988; Vol. 19. (3) Giese, R. F. Kaolin minerals: Structures and Stabilities In Reviews in Mineralogy: Hydrous Phyllosilicates; Bailey, S . W., Ed.; Minerological Society of America: Washington, DC, 1988; Vol. 19. (4) Young, R. A.; Hewat, A. W. Clays Clay Miner. 1988, 36, 225. (5) Bish, D. L.; Von Dreele, R. Clays Clay Miner. 1989, 37, 289.
0022-3654/92/2096-4367%03.00/0 0 1992 American Chemical Society
4368 The Journal of Physical Chemistry, Vol. 96, No. I I, I992
+--
I
ll
charge density elestrostatic map
@
-
@
-HYDROGEN
(@
SILICON OXYGEN
Figure 1. Kaolinite structure, non-hydrogen atoms placed at the experimental positions of Bish and Von Dreele,s inner hydrogen positions shown at the optimized positions found in this study. Arrows depict the region of the structure where the charge density (Figure 8) and the electrostatic potentials (Figure 9) were sampled. Crystal is projected into the bc plane with the ab plane parallel to the clay layers.
the intralayer cavity of the clay. There have been several diffraction s t ~ d i e s ~ 9(both ~ 9 ~ X-ray and neutron) designed to locate the exact positions of both types of hydrogen atoms in the structure. The results of these studies (summarized in Table I) indicate that the “outer” hydrogens are oriented over a range of values (48-69’) relative to the ab (001) plane and form long “hydrogen bonds” to the adjacent layer. There is, however, no general consensus in the literature conceming the atomic positions of the inner hydrogen atoms. In the P1 Rietveld refinement of Young and Hewatt, for example, one finds two inequivalent positions, one +12O from the ab plane and the other -22O, whereas the Reitveld refinement of Adams7 find a single positions located -36” from the ab plane. The previous model electrostatic calculations of Geise8predict a value of +l 5 O . To date, experimental values for the inner hydrogen atom position range over nearly 4 8 O . Since the lattice basis is sensitive to the number of independent hydrogen atoms in the structure the Bravais lattice of this material remains a matter of debate.3 Kaolinite possesses two distinct interior “surfaces” with which an intercalated specie could interact (see Figure 1 ) : a pseudohexagonal silicate ring system and an aluminum hydroxide network. The individual layers of the material (Figure 2) are charge neutral, and the centers of the silicates rings (Figure 3) have been proposed to be chemically reative sites in the mineral? The central regions of these silicate rings are known as ditrigonal cavities and are thought to behave, chemically, as weak Lewis bases. The basic nature of the ditrigonal cavities is generally attributed to the presence of nonbonding p orbitals centered on the oxygen atoms in the ring. Sposito9 has proposed that the presence of these nonbonding electrons could contribute electron density to the center of the silicate ring, making it an active site for the uptake of charge neutral polar species, such as H 2 0 . The behavior of this region of the crystal structure is evident from the electrostatic potentials and charge density difference maps and projected density of states (PDOS). It will be shown that the total crystal charge density in the ditrigonal cavity is, in fact, quite small (approximately 104-10-5 e/bohr3) and that the electrostatic potential in the center of the cavity is only slightly negative when compared to the nearby silicon sites. In contrast, regions closer to the silicate ring are found to form a mote of negative potential relative to the central region of the cavity. We (6) Suitch, P. R.; Young, R. A. Clays Clay Miner. 1983, 31, 357. (7) Adams, J. M. Clays Clay Miner. 1983, 31, 352. (8) Giese, R. F., Jr.; Datta, P. Am. Mineral. 1973, 58, 471. (9) Sposito, G. The Surface Chemistry of Soils; Oxford University Press: New York, 1984.
Hess and Saunders also note the presence of strong electric fields in the cavity associated with regions of space near oxygen positions in the silicate framework. These results are qualitatively insensitive to the two basis sets employed. In general, the calculations indicate that charge has been transferred to the ring oxygen atoms from the neighboring silicon atoms, which results in a strongly negative electrostatic potential in that region of the structure. From these data, it can be concluded that the center of the ditrigonal cavity is energetically favorable to a cation. This does not result from large charge densities in that region, but rather it maximizes the cation’s interactions with the negative potential associated with regions of space near the ring oxygens while simultaneously minimizing short-range repulsive interactions with the silicate framework. The end result is qualitatively similar to the intuitive arguments advanced by S p o ~ i t o . ~ We begin with a brief review of the theoretical method and a discussion of the computational details and the optimization of the inner hydrogen position. This review is followed by a general discussion of the density of states, charge density distributions, and the electrostatics and concluding remarks.
Method The calculations reported have been carried out using the self-consistent-field linear combinations of atomic orbitals HartreeFock (LCAO-HF) program for periodic systems CRYSTAL.lo Many researchers have contributed to the development of these methods,11-14 and we present here only a brief overview of the approach adopted. In general, the method seeks to obtain solutions to the Hartree-Fock-Roothaan equations subject to periodic boundary conditions. This is accomplished by CRYSTAL,in “direct” space and begins by evaluating all one- and two-electron integrals in an atomic orbital basis necessary to construct the direct space Fock matrix. In the following, we define the local atomic basis as
a r ) = x,(r - R - 7 3 = IaR)
(1)
where p = {n,l,m)denotes the set of principal quantum numbers defining an atomic orbital in the unit cell referenced by the direct lattice vector R located at position 7,. The Bloch functions are then given by
