Bibliography

1

X.-P.Li,R.W.Nunes and D.Vanderbilt 1993, Phys. Rev. B 47,10891

2

Daw M S 1993, Phys. Rev. B 47,10895

3

Galli G and Parrinello M 1992, Phys. Rev. Lett. 69, 3547

4

Mauri F, Galli G and Car R 1993, Phys. Rev. B 47, 9973

5

Ordejon P, Drabold D, Grunbach M and Martin R 1993, Phys. Rev. B 48, 14646

6

Pettifor D G 1989, Phys. Rev. Lett. 63, 2480

7

Aoki M 1993, Phys. Rev. Lett. 71, 3842

8

Goedecker S and Colombo L 1994, Phys. Rev. Lett. 73, 122

9

Kress J D and Voter A F 1996, Phys. Rev. B 53, 12733

10

Horsfield A P 1996, Mat. Sci. Engin. B 37, 219

11

Stechel E B, Williams A R and Feibelman P J 1994, Phys. Rev. B 49, 10088

12

Horsfield A P, Bratkovsky A M, Fearn M, Pettifor D G and Aoki M 1996, Phys. Rev. B 53, 12964

13

Heine V 1980, Sol. St. Phys. 35, 1

14

Slater J C and Koster G F 1954, Phys. Rev. 94, 1498

15

Sutton A P, Finnis M W, Pettifor D G, and Ohta Y 1988, J. Phys. C 21, 35

16

Pettifor D G 1995, Bonding and Structure of Molecules and Solids, (OUP, Oxford).

17

Sutton A P 1993, Electronic Structure of Materials, (OUP, Oxford).

18

Horsfield A P and Bratkovsky A M 1996, Phys. Rev. B 53, 15381

19

Kohn W 1959, Phys. Rev. 115, 809

20

Nunes R W and Vanderbilt D 1994, Phys. Rev. B 50, 17611

21

Qiu S-Y, Wang C Z, Ho K M, Chen C T 1994, J.Phys.:Condens. Matter 6, 9153

22

Ordejon P, Drabold D A, Martin R M and Grumbach M P 1995, Phys. Rev. B 51, 1456

23

Goringe C M 1995, D.Phil Thesis, Oxford University; Goringe C M 1996, To be submitted to J. Comp. Phys.

24

Goedecker S and Teter M 1995, Phys. Rev. B. 51, 9455

25

Voter A F, Kress J D and Silver R N 1996, Phys. Rev. B. 53, 12733

26

McWeeny R 1960, Rev. Mod. Phys. 32, 335

27

Friedel J 1954, Adv. Phys. 3, 446

28

Ducastelle F and Cyrot-Lackmann F 1970, J.Phys.Chem.Solids 31, 1295

29

Haydock R 1980, Sol. St. Phys. 35, 216

30

Lanczos C 1950, J. Res. Natl. Bur. Stand. 45, 225

31

Beer N and Pettifor D G 1984, Structure and Phase Stability of Alloys, edited by P. Phariseau and W. Temmerman (New York: Plenum Press).

32

Foiles S M 1993, Phys. Rev. B 48, 4287

33

Hellmann H 1937, Einfuhrung in die Quantumchemie (Leipzig: Franz Deutsche).

34

Feynman R P 1939, Phys. Rev. 56, 340

35

Gillan M J 1989, J. Phys.: Condens. Matter 1, 689

36

Xu C H, Wang C Z, Chan C T, and Ho K M 1992, J. Phys.:Condens. Matter 4, 6047

37

Goodwin L, Skinner A J and Pettifor D G 1989, Europhys. Lett. 9, 701

38

A.P.Horsfield, P.D.Godwin, D.G.Pettifor and A.P.Sutton 1996, Phys. Rev. B 54, 15773 (1996).

  

Table 1: The number of atoms included inside a sphere for a given number of hops for a diamond structure and an hcp structure.

Number of Hops	Diamond	hcp
1	5	13
2	17	57
3	41	153
4	83	323
5	147	587
6	239	967
7	363	1483

  

Table 2: The Si(001) surface was relaxed using all the methods. The surface can be characterised by the length of the dimer bond, and the angle it makes with the plane of the surface. A slab was used to perform the relaxations, thus there are two equivalent surfaces. The energy is the excess per surface relative to the bulk. The DMM calculation was carried out with a three hop cutoff. The BOP calculation was carried out using a five hop cutoff, within which 21 moments were taken. Averaged moments and a square root terminator were used. The FOE calculation was carried out with a five hop cutoff, and an electron temperature of 0.1eV, and 61 moments. The GDOS calculation was carried out with a five hop cutoff and 21 moments.

Method	Bond length (Å)	Buckling angle	Surface energy (eV)
k-space	2.43	16.4	4.9
DMM	2.44	16.3	4.5
BOP	2.43	16.0	3.0
FOE	2.43	17.2	6.5
GDOS	2.44	13.9	4.1