Bibliography

1

J. S. Bell.
Speakable and unspeakable in quantum mechanics (Cambridge University Press, 1987).

2

T. Kinoshita and W. B. Lindquist.
Eighth-order anomalous magnetic moment of the electron.
Phys. Rev. Lett. 47 (22), 1573 (November 1981).

3

Robert S. Van Dyck Jr., Paul B. Schwinberg and Hans G. Dehmelt.
New high-precision comparison of electron and positron $g$ factors.
Phys. Rev. Lett. 59 (1), 26 (July 1987).

4

P. A. M. Dirac.
The Principles of Quantum Mechanics, chap. I, p. 15ff. (Clarendon Press, Oxford, 1958), 4th edn.

5

Alastair I. M. Rae.
Quantum Mechanics, chap. 4, p. 63 (Adam Hilger, Bristol, 1986), 2nd edn.

6

M. Born and R. Oppenheimer.
Zur Quantentheorie der Molekeln.
Ann. Phys. (Leipzig) 84 (20), 457 (1927).

7

J. M. Ziman.
Principles of the Theory of Solids, chap. 6, pp. 200-203 (Cambridge University Press, 1972), 2nd edn.

8

Stephen Gasiorowicz.
Quantum Physics, chap. 16, p. 255ff. (John Wiley & Sons, New York, 1974).

9

M. P. Allen and D. J. Tildesley.
Computer Simulation of Liquids, chap. 10, p. 270ff. (Oxford University Press, 1987).

10

M. J. Gillan.
The quantum simulation of hydrogen in metals.
Phil. Mag. A 58 (1), 257 (1988).

11

R. Car and M. Parrinello.
Unified approach for molecular dynamics and density-functional theory.
Phys. Rev. Lett. 55 (22), 2471 (November 1985).

12

T. A. Arias, M. C. Payne and J. D. Joannopoulos.
Ab initio molecular-dynamics techniques extended to large-length-scale systems.
Phys. Rev. B 45 (4), 1538 (January 1992).

13

M. V. Berry and J. M. Robbins.
Indistinguishability for quantum particles: spin, statistics and the geometric phase.
Proc. R. Soc. Lond. A 453, 1771 (1997).

14

L. D. Landau and E. M. Lifshitz.
Quantum Mechanics (Non-relativistic Theory), chap. IX, p. 241ff. (Pergamon Press, Oxford, 1973), 3rd edn.

15

V. B. Berestetskii, E. M. Lifshitz and L. P. Pitaevskii.
Quantum Electrodynamics, chap. II, III, pp. 33ff., 62ff. (Pergamon Press, Oxford, 1979), 2nd edn.

16

P. Hohenberg and W. Kohn.
Inhomogeneous electron gas.
Phys. Rev. 136 (3B), 864 (November 1964).

17

Mel Levy.
Electron densities in search of Hamiltonians.
Phys. Rev. A 26 (3), 1200 (September 1982).

18

H. Englisch and R. Englisch.
Exact density functionals for ground-state energies.
Phys. Stat. Sol. (b) 123, 711 (1984).

19

H. Englisch and R. Englisch.
Exact density functionals for ground-state energies.
Phys. Stat. Sol. (b) 124, 373 (1984).

20

M. Levy.
Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the $v$-representability problem.
Proc. Natl. Acad. Sci. 76, 6062 (1979).

21

Mel Levy and John P. Perdew.
The constrained search formulation of density functional theory.
In Density Functional Methods in Physics (eds. Reiner M. Dreizler and Joao da Providencia), p. 11ff. (Plenum Publishing Corporation, New York, 1985).

22

T. L. Gilbert.
Hohenberg-Kohn theorem for nonlocal external potentials.
Phys. Rev. B 12 (6), 2111 (September 1975).

23

L. H. Thomas.
The calculation of atomic fields.
Proc. Camb. Phil. Soc. 23, 542 (November 1927).

24

E. Fermi.
Un metodo statistico per la determinazione di alcune proprietà dell'atome.
Rend. Accad. Naz. Lincei 6, 602 (1927).

25

E. Fermi.
Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente.
Z. Phys. 48, 73 (1928).

26

E. Teller.
On the stability of molecules in the Thomas-Fermi theory.
Rev. Mod. Phys. 34, 627 (1962).

27

Elliott H. Lieb.
Thomas-Fermi and related theories of atoms and molecules.
Rev. Mod. Phys. 53 (4), 603 (October 1981).

28

Lin-Wang Wang and Michael P. Teter.
Kinetic-energy functional of the electron density.
Phys. Rev. B 45 (23), 13196 (June 1992).

29

M. Pearson, E. Smargiassi and P. A. Madden.
Ab initio molecular dynamics with an orbital-free density functional.
J. Phys.: Condens. Matter 5, 3221 (1993).

30

F. Perrot.
Hydrogen-hydrogen interaction in an electron gas.
J. Phys.: Condens. Matter 6, 431 (1994).

31

Enrico Smargiassi and Paul A. Madden.
Orbital-free kinetic-energy functionals for first-principles molecular dynamics.
Phys. Rev. B 49 (8), 5220 (February 1994).

32

Michael Foley and Paul A. Madden.
Further orbital-free kinetic-energy functionals for ab initio molecular dynamics.
Phys. Rev. B 53 (16), 10589 (April 1996).

33

W. Kohn and L. J. Sham.
Self-consistent equations including exchange and correlation effects.
Phys. Rev. 140 (4A), 1133 (November 1965).

34

John P. Perdew and Mel Levy.
Extrema of the density functional for the energy: Excited states from the ground-state theory.
Phys. Rev. B 31 (10), 6264 (May 1985).

35

D. M. Ceperley and B. J. Alder.
Ground state of the electron gas by a stochastic method.
Phys. Rev. Lett. 45 (7), 566 (August 1980).

36

J. P. Perdew and Alex Zunger.
Self-interaction correction to density-functional approximations for many-electron systems.
Phys. Rev. B 23 (10), 5048 (May 1981).

37

R. O. Jones and O. Gunnarsson.
The density functional formalism, its applications and prospects.
Rev. Mod. Phys. 61 (3), 689 (July 1989).

38

J. Harris and R. O. Jones.
The surface energy of a bounded electron gas.
J. Phys. F 4, 1170 (August 1974).

39

D. C. Langreth and J. P. Perdew.
The exchange-correlation energy of a metallic surface.
Solid State Comm. 17, 1425 (1975).

40

J. Harris.
Adiabatic-connection approach to Kohn-Sham theory.
Phys. Rev. A 29 (4), 1648 (April 1984).

41

E. K. U. Gross, E. Runge and O. Heinonen.
Many-Particle Theory, chap. 16, p. 179ff. (Adam Hilger, New York, 1991), English edn.

42

O. Gunnarsson and B. I. Lundqvist.
Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism.
Phys. Rev. B 13 (10), 4274 (May 1976).

43

David C. Langreth and M. J. Mehl.
Easily implementable nonlocal exchange-correlation energy functional.
Phys. Rev. Lett. 47 (6), 446 (August 1981).

44

David C. Langreth and M. J. Mehl.
Beyond the local-density approximation in calculations of ground-state electronic properties.
Phys. Rev. B 28 (4), 1809 (August 1983).

45

Neil W. Ashcroft and N. David Mermin.
Solid State Physics, chap. 8, p. 132ff. (Saunders College, Philadelphia, 1976), International edn.

46

J. L. Lebowitz and Elliott H. Lieb.
Existence of thermodynamics for real matter with Coulomb forces.
Phys. Rev. Lett. 22 (13), 631 (March 1969).

47

L. P. Bouckaert, R. Smoluchowski and E. Wigner.
Theory of Brillouin zones and symmetry properties of wave functions in crystals.
Phys. Rev. 50, 58 (July 1936).

48

A. Baldereschi.
Mean-value point in the Brillouin zone.
Phys. Rev. B 7 (12), 5212 (June 1973).

49

D. J. Chadi and Marvin L. Cohen.
Special points in the Brillouin zone.
Phys. Rev. B 8 (12), 5747 (December 1973).

50

Hendrik J. Monkhorst and James D. Pack.
Special points for Brillouin-zone integrations.
Phys. Rev. B 13 (12), 5188 (June 1976).

51

D. J. Chadi.
Special points for Brillouin-zone integrations.
Phys. Rev. B 16 (4), 1746 (August 1977).

52

R. A. Evarestov and V. P. Smirnov.
Special points of the Brillouin zone and their use in the solid state theory.
Phys. Stat. Sol. 119, 9 (1983).

53

Sverre Froyen.
Brillouin-zone integration by Fourier quadrature: Special points for superlattice and supercell calculations.
Phys. Rev. B 39 (5), 3168 (February 1989).

54

I. J. Robertson and M. C. Payne.
$k$-point sampling and the $k \cdot p$ method in pseudopotential total energy calculations.
J. Phys.: Condens. Matter 2, 9837 (1990).

55

I. J. Robertson and M. C. Payne.
The $k \cdot p$ method in pseudopotential total energy calculations: error reduction and absolute energies.
J. Phys.: Condens. Matter 3, 8841 (1991).

56

James C. Phillips.
Energy-band interpolation scheme based on a pseudopotential.
Phys. Rev. 112 (3), 685 (November 1958).

57

James C. Phillips and Leonard Kleinman.
New method for calculating wave functions in crystals and molecules.
Phys. Rev. 116 (2), 287 (October 1959).

58

Volker Heine.
The Pseudopotential Concept, vol. 24 of Solid State Physics, p. 1 (Academic Press, New York, 1970).

59

J. Ihm.
Total energy calculations in solid-state physics.
Rep. Prog. Phys. 51 (1), 105 (1988).

60

W. E. Pickett.
Pseudopotential methods in condensed matter applications.
Comp. Phys. Rep. 9 (3), 115 (1989).

61

Conyers Herring.
A new method for calculating wave functions in crystals.
Phys. Rev. 57, 1169 (June 1940).

62

Leonard I. Schiff.
Quantum Mechanics, chap. 5, p. 116ff. (McGraw-Hill, Singapore, 1968), 3rd edn.

63

Michael Teter.
Additional condition for transferability in pseudopotentials.
Phys. Rev. B 48 (8), 5031 (August 1993).

64

A. Filippetti, David Vanderbilt, W. Zhong, Yong Cai and G. B. Bachelet.
Chemical hardness, linear response, and pseudopotential transferability.
Phys. Rev. B 52 (16), 11793 (October 1995).

65

Antonio Redondo, William A. Goddard III and T. C. McGill.
Ab initio effective potentials for silicon.
Phys. Rev. B 15 (10), 5038 (May 1977).

66

D. R. Hamann, M. Schlüter and C. Chiang.
Norm-conserving pseudopotentials.
Phys. Rev. Lett. 43 (20), 1494 (November 1979).

67

Alex Zunger and Marvin L. Cohen.
First-principles nonlocal-pseudopotential approach in the density-functional formalism. II. Application to electronic and structural properties of solids.
Phys. Rev. B 20 (10), 4082 (November 1979).

68

G. P. Kerker.
Non-singular atomic pseudopotentials for solid state applications.
J. Phys. C 13 (9), L189 (March 1980).

69

G. B. Bachelet, D. R. Hamann and M. Schlüter.
Pseudopotentials that work: From H to Pu.
Phys. Rev. B 26 (8), 4199 (October 1982).

70

D. R. Hamann.
Generalized norm-conserving pseudopotentials.
Phys. Rev. B 40 (5), 2980 (August 1989).

71

Andrew M. Rappe, Karin M. Rabe, Efthimios Kaxiras and J. D. Joannopoulos.
Optimized pseudopotentials.
Phys. Rev. B 41 (2), 1227 (January 1990).

72

J. S. Lin, A. Qteish, M. C. Payne and V. Heine.
Optimized and transferable nonlocal separable ab initio pseudopotentials.
Phys. Rev. B 47 (8), 4174 (February 1993).

73

Ming-Hsien Lee.
Advanced Pseudopotentials for Large Scale Electronic Structure Calculations.
Ph.D. thesis, University of Cambridge, Cavendish Laboratory (1994).

74

N. Troullier and José Luís Martins.
Efficient pseudopotentials for plane-wave calculations.
Phys. Rev. B 43 (3), 1993 (January 1991).

75

David Vanderbilt.
Soft self-consistent pseudopotentials in a generalized eigenvalue formalism.
Phys. Rev. B 41 (11), 7892 (April 1990).

76

Eric L. Shirley, Douglas C. Allan, Richard M. Martin and J. D. Joannopoulos.
Extended norm-conserving pseudopotentials.
Phys. Rev. B 40 (6), 3652 (August 1989).

77

Leonard Kleinman and D. M. Bylander.
Efficacious form for model pseudopotentials.
Phys. Rev. Lett. 48 (20), 1425 (May 1982).

78

Peter E. Blöchl.
Generalized separable potentials for electronic-structure calculations.
Phys. Rev. B 41 (8), 5414 (March 1990).

79

J. Ihm, Alex Zunger and Marvin L. Cohen.
Momentum-space formalism for the total energy of solids.
J. Phys. C 12, 4409 (1979).

80

P. J. H. Denteneer and W. van Haeringen.
The pseudopotential-density-functional method in momentum space: details and test cases.
J. Phys. C 18, 4127 (1985).

81

Michael P. Teter, Michael C. Payne and Douglas C. Allan.
Solution of Schrödinger's equation for large systems.
Phys. Rev. B 40 (18), 12255 (December 1989).

82

M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias and J. D. Joannopoulos.
Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients.
Rev. Mod. Phys. 64 (4), 1045 (October 1992).

83

G. Kresse and J. Furthmuller.
Efficient iterative schemes for ab-initio total-energy calculations using a plane-wave basis-set.
Phys. Rev. B 54 (16), 11169 (1996).

84

X.-P. Li, R. W. Nunes and David Vanderbilt.
Density-matrix electronic-structure method with linear system-size scaling.
Phys. Rev. B 47 (16), 10891 (April 1993).

85

S.-Y. Qiu, C. Z. Wang, K. M. Ho and C. T. Chan.
Tight-binding molecular dynamics with linear system-size scaling.
J. Phys.: Condens. Matter 6, 9153 (1994).

86

A. Canning, G. Galli, F. Mauri, A. de Vita and R. Car.
O($N$) tight-binding molecular dynamics on massively parallel computers: an orbital decomposition approach.
Comp. Phys. Comm. 94, 89 (1996).

87

A. P. Horsfield, A. M. Bratkovsky, D. G. Pettifor and M. Aoki.
Bond-order potential and cluster recursion for the description of chemical-bonds - efficient real-space methods for tight-binding molecular-dynamics.
Phys. Rev. B 53 (3), 1656 (1996).

88

D. R. Bowler, M. Aoki, C. M. Goringe, A. P. Horsfield and D. G. Pettifor.
A comparison of linear scaling tight-binding methods.
Modelling Simul. Mater. Sci. Eng. 5 (3), 199 (1997).

89

Weitao Yang.
Direct calculation of electron density in density-functional theory.
Phys. Rev. Lett. 66 (11), 1438 (March 1991).

90

Weitao Yang.
A local projection method for the linear combination of atomic orbital implementation of density-functional theory.
J. Chem. Phys. 94 (2), 1208 (January 1991).

91

Qingsheng Zhao and Weitao Yang.
Analytical energy gradients and geometry optimization in the divide-and-conquer method for large molecules.
J. Chem. Phys. 102 (24), 9598 (June 1995).

92

Weitao Yang and Tai-Sung Lee.
A density-matrix divide-and-conquer approach for electronic structure calculations of large molecules.
J. Chem. Phys. 103 (13), 5674 (October 1995).

93

Jian Ping Lu and Weitao Yang.
The shape of large single- and multiple-shell fullerenes.
Phys. Rev. B 49 (16), 11421 (April 1994).

94

Darrin M. York, Tai-Sung Lee and Weitao Yang.
Quantum mechanical study of aqueous polarization effects on biological macromolecules.
J. Am. Chem. Soc. 118, 10940 (1996).

95

R. Haydock, Volker Heine and M. J. Kelly.
Electronic structure based on the local atomic environment for tight-binding bands.
J. Phys. C 5, 2845 (1972).

96

Roger Haydock.
The Recursive Solution of the Schrödinger Equation, vol. 35 of Solid State Physics, p. 215 (Academic Press, New York, 1980).

97

S. Baroni and P. Giannozzi.
Towards very large-scale electronic-structure calculations.
Europhys. Lett. 17 (6), 547 (February 1992).

98

David A. Drabold and Otto F. Sankey.
Maximum entropy approach for linear scaling in the electronic structure problem.
Phys. Rev. Lett. 70 (23), 3631 (June 1993).

99

Lin-Wang Wang.
Calculating the density of states and optical-absorption spectra of large quantum systems by the plane-wave moments method.
Phys. Rev. B 49 (15), 10154 (April 1994).

100

Otto F. Sankey, David A. Drabold and Andrew Gibson.
Projected random vectors and the recursion method in the electronic-structure problem.
Phys. Rev. B 50 (3), 1376 (July 1994).

101

R. N. Silver and H. Röder.
Calculation of the densities of states and spectral functions by Chebyshev recursion and maximum entropy.
Phys. Rev. E 56 (4), 4822 (October 1997).

102

Yang Wang, G. M. Stocks, W. A. Shelton, D. M. C. Nicholson, Z. Szotek and W. M. Temmerman.
Order-${N}$ multiple scattering approach to electronic structure calculations.
Phys. Rev. Lett. 75 (15), 2867 (October 1995).

103

I. A. Abrikosov, A. M. N. Niklasson, S. I. Simak, B. Johansson, A. V. Ruban and H. L. Skriver.
Order-${N}$ Green's function technique for local environment effects in alloys.
Phys. Rev. Lett. 76 (22), 4203 (May 1996).

104

I. A. Abrikosov, S. I. Simak, B. Johansson, A. V. Ruban and H. L. Skriver.
Locally self-consistent Green's function approach to the electronic structure problem.
Phys. Rev. B 56 (15), 9319 (October 1997).

105

S. Goedecker and L. Colombo.
Efficient linear scaling algorithm for tight-binding molecular dynamics.
Phys. Rev. Lett. 73 (1), 122 (July 1994).

106

S. Goedecker and M. Teter.
Tight-binding electronic-structure calculations and tight-binding molecular dynamics with localized orbitals.
Phys. Rev. B 51 (15), 9455 (April 1995).

107

Roi Baer and Martin Head-Gordon.
Chebyshev expansion methods for electronic structure calculations on large molecular systems.
J. Chem. Phys. 107 (23), 10003 (December 1997).

108

Uwe Stephan and David A. Drabold.
Order-${N}$ projection method for first-principles computations of electronic quantities and Wannier functions.
Phys. Rev. B 57 (11), 6391 (March 1998).

109

S. Goedecker.
Integral representation of the Fermi distribution and its applications in electronic-structure calculations.
Phys. Rev. B 48 (23), 17573 (December 1993).

110

D. M. C. Nicholson and X.-G. Zhang.
Approximate occupation functions for density-functional calculations.
Phys. Rev. B 56 (20), 12805 (November 1997).

111

Florian Gagel.
Finite-temperature evaluation of the Fermi density operator.
J. Comp. Phys. 139, 399 (1998).

112

A. F. Voter, J. D. Kress and R. N. Silver.
Linear-scaling tight binding from a truncated approach.
Phys. Rev. B 53 (19), 12733 (May 1996).

113

R. N. Silver, H. Roeder, A. F. Voter and J. D. Kress.
Kernel polynomial approximations for densities of states and spectral functions.
J. Comp. Phys. 124, 115 (1996).

114

Giulia Galli and Michele Parrinello.
Large scale electronic structure calculations.
Phys. Rev. Lett. 69 (24), 3547 (December 1992).

115

Francesco Mauri, Giulia Galli and Roberto Car.
Orbital formulation for electronic-structure calculations with linear system-size scaling.
Phys. Rev. B 47 (15), 9973 (April 1993).

116

Francesco Mauri and Giulia Galli.
Electronic-structure calculations and molecular-dynamics simulations with linear system-size scaling.
Phys. Rev. B 50 (7), 4316 (August 1994).

117

Pablo Ordejón, David A. Drabold, Matthew P. Grumbach and Richard M. Martin.
Unconstrained minimization approach for electronic computations that scales linearly with system size.
Phys. Rev. B 48 (19), 14646 (November 1993).

118

Pablo Ordejón, David A. Drabold, Richard M. Martin and Matthew P. Grumbach.
Linear system-size scaling methods for electronic-structure calculations.
Phys. Rev. B 51 (3), 1456 (January 1995).

119

Jeongnim Kim, Francesco Mauri and Giulia Galli.
Total-energy global optimizations using nonorthogonal localized orbitals.
Phys. Rev. B 52 (3), 1640 (July 1995).

120

K. C. Pandey, A. R. Williams and J. F. Janak.
Localized orbital theory of electronic structure: A simple application.
Phys. Rev. B 52 (20), 14415 (November 1995).

121

Pablo Ordejón, Emilio Artacho and José M. Soler.
Self-consistent order-$N$ density-functional calculations for very large systems.
Phys. Rev. B 53 (16), 10441 (April 1996).

122

Jeongnim Kim, John W. Wilkins, Furrukh S. Khan and Andrew Canning.
Extended Si {311} defects.
Phys. Rev. B 55 (24), 16186 (June 1997).

123

Giulia Galli.
Linear scaling methods for electronic structure calculations and quantum molecular dynamics simulations.
Current Opinion in Solid State and Materials Science 1 (6), 864 (1996).

124

E. B. Stechel, A. R. Williams and Peter J. Feibelman.
$N$-scaling algorithm for density-functional calculations of metals and insulators.
Phys. Rev. B 49 (15), 10088 (April 1994).

125

W. Hierse and E. B. Stechel.
Order-$N$ methods in self-consistent density-functional calculations.
Phys. Rev. B 50 (24), 17811 (December 1994).

126

E. Hernández and M. J. Gillan.
Self-consistent first-principles technique with linear scaling.
Phys. Rev. B 51 (15), 10157 (April 1995).

127

E. Hernández, M. J. Gillan and C. M. Goringe.
Linear-scaling density-functional-theory technique: The density-matrix approach.
Phys. Rev. B 53 (11), 7147 (March 1996).

128

John M. Millam and Gustavo E. Scuseria.
Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations.
J. Chem. Phys. 106 (13), 5569 (April 1997).

129

Andrew D. Daniels, John M. Millam and Gustavo E. Scuseria.
Semiempirical methods with conjugate gradient density-matrix search to replace diagonalization for molecular systems containing thousands of atoms.
J. Chem. Phys. 107 (2), 425 (July 1997).

130

Karl Blum.
Density Matrix Theory and Applications, chap. 2, p. 37ff. (Plenum Press, New York, 1981).

131

J. F. Janak.
Proof that $\partial E / \partial n_i = \epsilon_i$ in density-functional theory.
Phys. Rev. B 18 (12), 7165 (December 1978).

132

M. Weinert and J. W. Davenport.
Fractional occupations and density-functional energies and forces.
Phys. Rev. B 45 (23), 13709 (June 1992).

133

M. M. Valiev and G. W. Fernando.
Occupation numbers in density-functional calculations.
Phys. Rev. B 52 (15), 10697 (October 1995).

134

R. McWeeny.
Some recent advances in density matrix theory.
Rev. Mod. Phys. 32 (2), 335 (April 1960).

135

W. Kohn.
Density functional and density matrix method scaling linearly with the number of atoms.
Phys. Rev. Lett. 76 (17), 3168 (April 1996).

136

W. Kohn.
Analytic properties of Bloch waves and Wannier functions.
Phys. Rev. 115 (4), 809 (August 1959).

137

E. I. Blount.
Formalisms of Band Theory, vol. 13 of Solid State Physics, p. 305 (Academic Press, New York, 1962).

138

Jacques des Cloizeaux.
Energy bands and projection operators in a crystal: Analytic and asymptotic properties.
Phys. Rev. 135 (3A), 685 (August 1964).

139

Jacques des Cloizeaux.
Analytical properties of $n$-dimensional energy bands and Wannier functions.
Phys. Rev. 135 (3A), 698 (August 1964).

140

Roi Baer and Martin Head-Gordon.
Sparsity of the density matrix in Kohn-Sham density functional theory and an assessment of linear system-size scaling methods.
Phys. Rev. Lett. 79 (20), 3962 (November 1997).

141

P. E. Maslen, C. Ochsenfeld, C. A. White, M. S. Lee and M. Head-Gordon.
Locality and sparsity of ab initio one-particle density matrices and localized orbitals.
J. Phys. Chem. 102, 2215 (1998).

142

Sohrab Ismail-Beigi and Tomás Arias.
On the locality of physics in metals, semiconductors, and insulators.
Phys. Rev. Lett. submitted.

143

Gregory H. Wannier.
The structure of electronic excitation levels in insulating crystals.
Phys. Rev. 52, 191 (August 1937).

144

S. F. Boys.
A general method of calculation for the stationary states of any molecular system.
Proc. R. Soc. Lond. A 200, 542 (1950).

145

S. Obara and A. Saika.
Efficient recursive computation of molecular integrals over Cartesian Gaussian functions.
J. Chem. Phys. 84 (7), 3963 (April 1986).

146

Otto F. Sankey and David J. Niklewski.
Ab initio multicenter tight-binding model for molecular-dynamics simulations and other applications in covalent systems.
Phys. Rev. B 40 (6), 3979 (August 1989).

147

E. Hernández, M. J. Gillan and C. M. Goringe.
Basis functions for linear-scaling first-principles calculations.
Phys. Rev. B 55 (20), 13485 (May 1997).

148

Ross A. Lippert, T. A. Arias and Alan Edelman.
Multiscale computation with interpolating wavelets.
J. Comp. Phys. 140, 278 (1998).

149

James R. Chelikowsky, N. Troullier and Y. Saad.
Finite-difference-pseudopotential method: Electronic structure calculations without a basis.
Phys. Rev. Lett. 72 (8), 1240 (February 1994).

150

P. D. Haynes and M. C. Payne.
Localised spherical-wave basis set for $O(N)$ total-energy pseudopotential calculations.
Comp. Phys. Comm. 102 (1-3), 17 (June 1997).

151

R. Courant and D. Hilbert.
Methods of Mathematical Physics, vol. 1, p. 535ff. (Interscience Publishers, New York, 1953), 1st edn.

152

R. D. King-Smith, M. C. Payne and J. S. Lin.
Real-space implementation of nonlocal pseudopotentials for first-principles total-energy calculations.
Phys. Rev. B 44 (23), 13063 (December 1991).

153

S. Goedecker.
Electronic structure methods exhibiting linear scaling of the computational effort with respect to the size of the system.
Rev. Mod. Phys. submitted.

154

Y. Saad.
Iterative methods for sparse linear systems (PWS Publishing Co., Boston, 1996).

155

D. R. Bowler and M. J. Gillan.
Length-scale ill conditioning in linear-scaling DFT.
Comp. Phys. Comm. 112 (2-3), 103 (1998).

156

Leslie Greengard.
Fast algorithms for classical physics.
Science 265, 909 (August 1994).

157

Christopher A. White, Benny G. Johnson, Peter M. W. Gill and Martin Head-Gordon.
The continuous fast multipole method.
Chem. Phys. Lett. 230, 8 (November 1994).

158

Matthew C. Strain, Gustavo E. Scuseria and Michael J. Frisch.
Achieving linear scaling for the electronic quantum Coulomb problem.
Science 271, 51 (January 1996).

159

Christopher A. White, Benny G. Johnson, Peter M. W. Gill and Martin Head-Gordon.
Linear scaling density functional calculations via the continuous fast multipole method.
Chem. Phys. Lett. 253, 268 (May 1996).

160

Ross D. Adamson, Jeremy P. Dombroski and Peter M. W. Gill.
Chemistry without Coulomb tails.
Chem. Phys. Lett. 254, 329 (May 1996).

161

José M. Pérez-Jordá and Weitao Yang.
Fast evaluation of the Coulomb energy for electron densities.
J. Chem. Phys. 107 (4), 1218 (July 1997).

162

S. Goedecker and O. V. Ivanov.
Linear scaling solution of the Coulomb problem using wavelets.
Solid State Comm. 105 (11), 665 (1998).

163

Christopher A. White, Paul Maslen, Michael S. Lee and Martin Head-Gordon.
The tensor properties of energy gradients within a non-orthogonal basis.
Chem. Phys. Lett. 276, 133 (September 1997).

164

Nicola Marzari.
Ab initio Molecular Dynamics for Metallic Systems.
Ph.D. thesis, University of Cambridge, Cavendish Laboratory (1996).

165

Nicola Marzari, David Vanderbilt and M. C. Payne.
Ensemble density-functional theory for ab initio molecular dynamics of metals and finite-temperature insulators.
Phys. Rev. Lett. 79 (7), 1337 (August 1997).

166

Daniel Sánchez-Portal, Emilio Artacho and José M. Soler.
Projection of plane-wave calculations into atomic orbitals.
Solid State Comm. 95 (10), 685 (1995).

167

Daniel Sánchez-Portal, Emilio Artacho and José M. Soler.
Analysis of atomic orbital basis sets from the projection of plane-wave results.
J. Phys.: Condens. Matter 8, 3859 (1996).

168

M. D. Segall, C. J. Pickard, R. Shah and M. C. Payne.
Population analysis in plane wave electronic structure calculations.
Mol. Phys. 89 (2), 571 (1996).

169

W. Hierse and E. B. Stechel.
Robust localized-orbital transferability using the Harris functional.
Phys. Rev. B 54 (23), 16515 (December 1996).

170

Pablo Fernández, Andrea Dal Corso, Alfonso Baldereschi and Francesco Mauri.
First-principles wannier functions of silicon and gallium arsenide.
Phys. Rev. B 55 (4), 1909 (January 1997).

171

Nicola Marzari and David Vanderbilt.
Maximally localized generalized Wannier functions for composite energy bands.
Phys. Rev. B 56 (20), 12847 (November 1997).

172

Walter Kohn.
Density functional/Wannier function theory for systems of very many atoms.
Chem. Phys. Lett. 208 (3,4), 167 (June 1993).

173

A. P. Sutton, M. W. Finnis, D. G. Pettifor and Y. Ohta.
The tight-binding bond model.
J. Phys. C 21, 35 (1988).

174

Jim Asher, Owen C. Jones, John G. Noyes and Geoffrey F. Phillips, eds.
Kaye & Laby's Tables of Physical and Chemical Constants, pp. 45, 214 (Longman, Harlow, Essex, 1995), 16th edn.

175

P. P. Ewald.
Zur Begründung der Kristalloptik.
Ann. Phys. (Leipzig) 54 (23), 519 (1917).

176

P. P. Ewald.
Zur Begründung der Kristalloptik.
Ann. Phys. (Leipzig) 54 (24), 557 (1917).

177

P. P. Ewald.
Die Berechnung optischer und elektrostatischer Gitterpotentiale.
Ann. Phys. (Leipzig) 64, 253 (1921).

178

J. M. Ziman.
Principles of the Theory of Solids, chap. 2, pp. 37-42 (Cambridge University Press, Cambridge, 1972), 2nd edn.

179

Kai-Ming Ho, J. Ihm and J. D. Joannopoulos.
Dielectric matrix scheme for fast convergence in self-consistent electronic-structure calculations.
Phys. Rev. B 25 (6), 4260 (March 1982).

180

P. H. Dederichs and R. Zeller.
Self-consistency iterations in electronic-structure calculations.
Phys. Rev. B 28 (10), 5462 (November 1983).

181

G. P. Kerker.
Efficient iteration scheme for self-consistent pseudopotential calculations.
Phys. Rev. B 23 (6), 3082 (March 1981).

182

H. Hellmann.
Einfuhrung in die Quantumchemie (Deuticke, Leipzig, 1937).

183

R. P. Feynman.
Forces in molecules.
Phys. Rev. 56, 340 (August 1939).

184

P. Pulay.
Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. i. theory.
Mol. Phys. 17 (2), 197 (1969).

185

C. M. Goringe, E. Hernández, M. J. Gillan and I. J. Bush.
Linear-scaling DFT-pseudopotential calculations on parallel computers.
Comp. Phys. Comm. 102 (1-3), 1 (1997).

186

M. Abramowitz and I. Stegun.
Handbook of Mathematical Functions, chap. 10, p. 435 (Dover, New York, 1965).

187

R. Fletcher and C. M. Reeves.
Function minimisation by conjugate gradients.
Comp. J. 7, 149 (1964).

188

D. M. Greig.
Optimisation, chap. 2, p. 41ff. (Longman, London, 1980).

189

E. Polak.
Computational Methods in Optimisation (Academic Press, 1971).