If a crystal structure is composed of discrete units of ligand and metal only (and units are mediated through solvent molecules using hydrogen bonding), what is its dimensionality (Zero dimensional or one dimensional)?
I think if you take discrete units held together by any interaction weaker than H-bonds (i.e. pi stacking) then it's zero dimensional.
I would like to add some more information to the above comment. If molecules are connected with each other through bonding like H-bond, covalent bond in only any of a, b or c axis; then it can be called as one dimensional. If these molecules are co-ordinated or connected in 2 or 3 axis then they can be said as 2D or 3D. Please go through the structures using .cif file of the paper by Srinivasan Natarajan et.al. (DOI: 10.1039/b708060c), where you will find the different structures aquired from same metal and ligand, but with different dimensionality.
If its a crystal then it is, by definition, a three-dimensional object and will have interactions in all three dimensions. The concept of dimensionality reflects the strongest of the intermolecular interactions and the direction(s) they propagate in. Whilst we use a hydrogen bond as our typical benchmark for what we consider to be a structure-directing interaction there are other interactions such as dipole-dipole etc too, evidenced by the fact that the majority of compounds crystallise at some finite temperature even in the absence of hydrogen bonds! If there were no interactions in the second and third directions then the sample wouldn't be a crystal! If you have hydrogen-bonds - as you suggest - then the dimensionality depends upon how many hydrogen-bond donors and acceptors there are. Though this should also be treated with caution: in the simple case of two donors and 2 acceptors they can generate a 2-D square grid or a 3-D diamond-like lattice...!
If the crystal is composed of discrete units of ligand and metal, the dimensionalilty of the crystal is 3D since it extends in all the three axis x, y and z..
A lattice, whatever it is, is defined in terms of translational symmetry relations. Therefore, the dimensionality of the lattice simply coincides with the number of independent elementary translations that are needed to fully define the translational symmetry you are interested in. Note that the dimensionality of the lattice may or not be the same of the dimensionality of the vectorial space you are dealing with. For example, a crystal is a three-dimensional object that must be described by a three-dimensional vector space, and its lattice has dimensionality 3 as it is periodic in all the independent directions of this space. On the other hand, a surface may be described by a two-dimensional lattice spanning a two-dimensional space. Eventually, if you have a three-dimensional object that is periodic only in one or two directions (for example, a metal slab), you should use a three-dimensional space that is periodic just in one or two independent directions, i.e. you should use a subperiodic symmetry group to take into account all of its symmetries. For more information, you may take a look at the Volume E of the International Tables for Crystallography.
In any case, within high-dimensionality lattices it is always possible to single out sublattices with lower dimensionality. Actually, this is extremely useful to highlight specific structural, thermal, electronic or magnetic properties, that may not share the whole periodicity of the crystal lattice. For instance, graphite shows anisotropic electrical conductivity due to its layered structure. In other words, the whole graphite lattice is three-dimensional, but it is convenient to define a two-dimensional sublattice to describe the 2D periodicity characterizing each hydrocarbon layer. At the same time, within a molecular crystal several hydrogen-bonded rods, or layers, can be identified, whose constituents are regularly repeated and translationally invariant. In turn, these latter can be described by a sublattice of the proper dimensionality, as in turn they may determine specific anisotropies in the intensive physical properties of the material (such as, for instance, its thermal expansion coefficient).
whate do mean by zero dimintion?
I think for crystal structure there are 3D.If you mean crystal growth dimintions :if it is a uniform growth it can be in 1D for layer by layer or 2D for different types of surface uniform growth and 3D for island growth.
I would like to say, A crystal is always a three dimensional system, But if one of its dimension is very large as compered to other two dimensions (e.g along x-axis the crystal is translated by ~10 e6 approx. unit cells and along y and z direction by few unit cell say ~10- 100approx.) Then the crystal will be called as 1D crystal. In short If along one axis its lengths is very large as compared to other two axis then we call the Crystal as 1D Crystal. Similarly if along x-axis and y-axis translation or reparation of unit cell is about 10 e6 or more while along z-axis transition of crystal is ~1-100approx. unit cell , we call the crystal as 2D crystal and if along all axis the translation is of only few unit cells then we call Crystal as 1D and finally if the translation of unit cell along every axis is ~1000 or more unit cells then we call the crystal 3D.
Read Crystal Engineering A Textbook Chapter 1 page 3
http://www.worldscientific.com/doi/suppl/10.1142/8060/suppl_file/8060_chap01.pdf
I think Nagapradeep is asking about the dimensionality of network created by H-bondings. If it is so, then the dimension is one if the H-bonding network is only in one direction, 2D if the network is in two directions and 3D if the network is in 3 directions. If you have the XRD structure, sent me the .cif file and I'll let you know which dimension your compound is.
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