By Robin Chapman

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**Example text**

3. It is narrower than the total density of states, peaked around 4 eV, with weaker and broader structures around 3 and 5 eV. 0 ... ~ til 0 .... J (eV) B 10 12 Fig. 3. JDOS of Si(lll) lxI-As projected on the first layer, as calculated in the present approach. 3 ~ 3' J. l (eV) B 10 Fig. 4. Polarisability of a Si(lll) slab of 10 Si and 2 As planes [37]. The Linear Optical Response 25 surface states to occur mainly at these energies. The imaginary part of the slab polarisability in dimension of length is shown in Fig.

Circles and stars: measured values for light polarised along [110] (x) and [001] (y) respectively [14]. Solid and dashed lines: calculated (Rclean - R H )/RH for H atoms aligned along the missing bonds [27]. 4 The Bond Approach to the Linear Optical Response Models for the lattice dynamics and optical properties of solids which treat a solid as an ordered array of polarisable atoms, ions or bonds have existed for some time. Early work by Born and Huang [46] and Maradudin et at [47] included electronic degrees of freedom, but focused on lattice dynamics.

CI Fig. 12. (a) Schematic diagram of the Si3H9 cluster and contour plots of (b) As lone pair GVB orbitals and (c) the Si-As bond GVB orbitals. 02 atomic units. Crosses indicate atomic positions in the plane while triangles and X symbols indicate atomic positions in front of and behind the plane, respectively [33, 61]. 34 R. Del Sole, A. I. -P. Jiang, and C. R. 2 Bond Dipole Moments Expanded in the Local Field Bond polarisabilities are calculated in one of two ways. Either all bonds in a cluster are permitted to relax from their zero-field orbital shapes in an electrostatic field [61], or bonds are allowed to relax individually or in pairs in an electrostatic field [62, 63].

### A Guide to Arithmetic [Lecture notes] by Robin Chapman

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