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Metallic Bonding cont. Transition metals belong to three series in the periodic table Which correspond to the progressive filling of 3d, 4d, and 5d states. The presence of d electrons changes the picture of bonding in these metals considerably from the simple (free-electron-like) metals (e.g. Al, Na, ..) The cohesive energies are greater than in the simple metals and follow a roughly parabolic variation across the transition metal series. Metallic Bonding cont. 5d Expt. H (eV/atom) Ca-Zn Sr-Cd Ba-Hg 4d 3d Experimental heat of formation for the 3d, 4d, and 5d transition metals. Can see a parabolic variation for the 4d and 5d metals –why? Accompanied by systematic change of stable crystal structure from bcc to hcp to fcc on going from early to late transition metals – why? It has to do with the partly filled d valence shell Metallic Bonding cont. Band structure of Copper – sp-bands in light shaded region – free electron-like d-bands in dark shaded – little dispersion, localized. Free electron band structure The d-band is narrower than the sp-band because the d valence orbitals and thus the overlap between them is significantly smaller than the s and p valence orbitals. Metallic Bonding in transition metals cont. Qualitative picture of two contributions to a transition metal (TM) density of states (DOS) – free electron-like sp-band, and narrow, structured d-band. Due to the large number of d-states, the d-band dominates the DOS and the varying properties over a TM series can be understood as arising from a differing filling of the d-band. “Rigid band model” – the number of valence electrons increase over the TM series Ru 8, Rh 9, Pd 10, Ag 11 – shifts the Fermi energy more and more to the right. At the end of a TM series, the d-band is completely filled and the Fermi level cuts the s-like DOS above the d-band. Metallic Bonding cont. non-bonding bonding anti-bonding Rectangular d-band model Starting with the early TM, fill electrons into the lowest energy d-states. Theses are of bonding type and thus can expect an increase in the cohesive energy. Due to shorter range of d orbitals, bonding will favour smaller lattice constants to maximize wavefunction overlap. Around the middle of the TM series, have strong cohesion and decreasing lattice constants. As filling continues s-electron density becomes higher than the optimum for metallic bonding – called “s-pressure” – competition between contractive tendency from d-orbitals with repulsive tendency from the s electron gas. Metallic Bonding cont. 5d Expt. H (eV/atom) Ca-Zn Sr-Cd Ba-Hg 4d 3d As filling continues non-bonding and anti-bonding are occupied (e.g. middle and late TMs) increasing d-occupancy does not lead to further increase in cohesion energy. The s-pressure leads to an increase in the lattice constants. For the noble metals, d contribution, in this simple view, has cancelled out and cohesive properties comparable to the simple metals is obtained. Why the dip in the middle? – due to particular stability of isolated atoms Metallic Bonding cont. Transition from bcc to hcp to fcc over the TM series can‟t be understood in the simple rectangular d-band model – no structural information. The lattice structure affects the substructure present in actual DOS -characteristic shape for bcc, hcp, fcc -Single particle energies (i.e. energy eigenvalues of the -bandstructure) largely govern the final total energy – thus, preferred crystal structure is that which offers an optimum number of bonding states for a given filling fraction. Hydrogen Bonding Hydrogen Bonding Importance of hydrogen bonds cannot be overstated – most important force determining the 3D structure of proteins, structure of liquid water, and in holding water molecules together in ice Estimated a paper related to H bonding published every 15 minutes Represented as A-H B, where A is an electronegative species, N, O, F, Cl and B must be an electron donor. Example of a typical H bond – Water dimer: H2O-H2O Isosurface of constant electron density for an occupied MO, showing overlap between the wavefunctions of both water molecules Hydrogen Bonding • H bonds are directional, with A-H-B angles close to 180o – the stronger the bond the closer it is to 180o • On H-bond formation, the AH bond is lengthened by 0.01-0.04Å – leads to softening (red-shift) of AH vibrations • H bonds can be „cooperative‟ – strength of H bonds increase as more H-bonds are formed – crucial in biology for providing additional energy to hold certain proteins together under H-bonds ambient conditions Between O(red) and H cooperative behaviour opposite to the more (grey) intuitive behaviour of e.g. covalent bonds, where generally the bond strength decreases as more bonds are formed – e.g. a helix of alanine molecules Hydrogen Bonding:Ice • Everyday ice and snow is hexagonal ice (ice Ih) i.e. the ice in the biosphere, with only a small amount of cubic ice Ic Ice rules: two H atoms near each O atom, one H atom on each O …O bond, H-O-H angle little less than the tetrahedral angle (109.47°), at about 107°. Cohesive energy 0.58eV; lattice constant 2.75Å Hydrogen Bonding:Ice Oxygen is electronegative it draws the electrons in the bonds it shares with the hydrogen atoms towards it. The hydrogen atoms are left with a net positive charge and the oxygen is negative. This results in the water molecule having a large dipole moment. Two water molecules can therefore form a strong electrostatic interaction Relatively easy to make and reform hydrogen bonds without any need for energy inputs or catalysis. Hydrogen Bonding:Ice Ice IV Snowflakes by Wilson Bentley, 1902 Hydrogen Bonding:Ice Snowflakes by Wilson Bentley, 1902 Morphology depends sensitively on temperature and humidity OH-vibrational frequency (cm-1) Hydrogen Bonding: OH vibrational frequencies OH vibrational frequency versus A-B distance, for a host of H bonded complexes; Can see as separation of A-B decreases, the vibrational frequency decreases – red shift O-H….O A A-B distance (Å) B Hydrogen Bonding: DFT Calculations • Electronic character of H-bond not clear and matter of debate • Unique role H plays due to negligible ion core size, and high ionization energy of the one electron it has – contrast to the alkali metals which can readily donate their electron • Generally thought H-bonds are mediated by electrostatic forces – Coulomb interaction (partial positive charge on H and partial negative charge on atom B) • Not purely electrostatic, e.g. overlap of orbitals as seen in the water molecule – more characteristic of covalent bonding. Gas phase H-bonded complexes Surfaces Surfaces Surface energy: energy required to create a surface Experimental values for simple, transition, and noble Metals – vary as the cohesive energy Total energy of slab with N atoms Total energy of atom in bulk material Can calculate from DFT: Surfaces cont. • Knowledge of the atomic arrangement in the surface region is a prerequisite to understanding the properties of surfaces. • Because atoms at surfaces have fewer neighbours than they do in solids, unlikely they will remain at their precise “bulk truncated” positions. • Surface relaxations – small displacements e.g to few layers move inwards or outwards but retain their periodicity parallel to the surface • Surface reconstructions – more pronounced lateral displacements which alter the translation symmetry parallel to the surface and/or change the surface layer atomic density. Surfaces cont. Examples – surface relaxations at metal surfaces % change DFT/ Expt Al(111) Ti(0001) Cu(111) Pd(111) Pt(111) d12 LDA +1.35 -6.44 -1.58 -0.22 +0.88 GGA +1.35 -6.84 -1.19 -0.01 +1.14 LEED +1.3 -4.9 -0.7 +1.3 +0.87 LDA +0.54 +2.64 -0.73 -0.53 -0.22 GGA +0.54 +2.82 -0.65 -0.41 -0.29 LEED +0.5 +1.4 LDA +1.04 +0.37 -0.43 -0.33 -0.17 GGA +1.06 -0.51 -0.24 -0.22 -0.21 d23 d34 LEED -1.1 +0.7 +0.7 For Al and Pt, excellent agreement; Cu very good. For Pd there is not good agreement and there is still open questions (e.g. H contamination?) Example of surface reconstruction Au{111} 23 x 3 112 A uniaxial contraction along one of the [-110] directions in the top layer leads to a layer with a higher density of atoms in it than the unreconstructed (111) surface 110 Au(111) Surface 6 K Scanning Tunnelling Microscopy images Run 5_2 X = 12.5 nm Y = 12.5 nm Z = 46.13 pm Atomic Resolution Herringbones Au(111) Surface – corrugation of the surface due to different relative positions of atoms in the top layer 3- fold symmetry Strain in the one direction is relaxed over whole surface in 2 dimensions Au{111} 23 x 3 120 degree turns give uniform contraction! What about the elbows? fcc fcc fcc Screw Dislocation: STMA 1004, Vtip = 0.05 V/ 200pA 170 Å x 170 Å The famous (7x7) reconstruction of the Si (111) surface Surfaces cont. From IBM's "STM Image Gallery": 48 iron atoms are positioned into a circular ring on Cu(111 in order to "corral" some surface state electrons and force them into "quantum" states of the circular structure. The ripples in the ring of atoms are the density distribution of a particular set of quantum states of the corral. Adsorption on a surface Surfaces: adsorption cont. Interaction of the electronic states of a H atom with a transition metal surface The interaction between the H 1s-level and the substrate s- and d-bands gives rise to a broadening and the formation of an anti-bonding level (above the d-band) and a bonding level (below the d-band). For the H 2s-level, the bonding state is at about the lower edge of the d-band. Surfaces: adsorption cont. Na on Al (simple metal, no d-states) O on Ru (transition metal) Side view of the surface, and the adsorbate-induced change in the density of states as a function of distance. [Energy levels for the atoms are the mean values of the ionization energy and electron affinity (Na: 2.8 eV, O, 7.5 eV)] Surfaces: Adsorption cont. Surfaces: Adsorption Difference of electron density: