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Contents
 1

J. S. Bell.
Speakable and unspeakable in quantum mechanics (Cambridge
University Press, 1987).
 2

T. Kinoshita and W. B. Lindquist.
Eighthorder 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 highprecision comparison of electron and positron 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. 200203
(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 densityfunctional
theory.
Phys. Rev. Lett. 55 (22), 2471 (November 1985).
 12

T. A. Arias, M. C. Payne and J. D. Joannopoulos.
Ab initio moleculardynamics techniques extended to
largelengthscale 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 (Nonrelativistic 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 groundstate energies.
Phys. Stat. Sol. (b) 123, 711 (1984).
 19

H. Englisch and R. Englisch.
Exact density functionals for groundstate energies.
Phys. Stat. Sol. (b) 124, 373 (1984).
 20

M. Levy.
Universal variational functionals of electron densities, firstorder
density matrices, and natural spinorbitals and solution of the
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.
HohenbergKohn 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 ThomasFermi theory.
Rev. Mod. Phys. 34, 627 (1962).
 27

Elliott H. Lieb.
ThomasFermi and related theories of atoms and molecules.
Rev. Mod. Phys. 53 (4), 603 (October 1981).
 28

LinWang Wang and Michael P. Teter.
Kineticenergy 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 orbitalfree density
functional.
J. Phys.: Condens. Matter 5, 3221 (1993).
 30

F. Perrot.
Hydrogenhydrogen interaction in an electron gas.
J. Phys.: Condens. Matter 6, 431 (1994).
 31

Enrico Smargiassi and Paul A. Madden.
Orbitalfree kineticenergy functionals for firstprinciples
molecular dynamics.
Phys. Rev. B 49 (8), 5220 (February 1994).
 32

Michael Foley and Paul A. Madden.
Further orbitalfree kineticenergy functionals for ab initio
molecular dynamics.
Phys. Rev. B 53 (16), 10589 (April 1996).
 33

W. Kohn and L. J. Sham.
Selfconsistent 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 groundstate 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.
Selfinteraction correction to densityfunctional approximations for
manyelectron 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 exchangecorrelation energy of a metallic surface.
Solid State Comm. 17, 1425 (1975).
 40

J. Harris.
Adiabaticconnection approach to KohnSham theory.
Phys. Rev. A 29 (4), 1648 (April 1984).
 41

E. K. U. Gross, E. Runge and O. Heinonen.
ManyParticle 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
spindensityfunctional formalism.
Phys. Rev. B 13 (10), 4274 (May 1976).
 43

David C. Langreth and M. J. Mehl.
Easily implementable nonlocal exchangecorrelation energy functional.
Phys. Rev. Lett. 47 (6), 446 (August 1981).
 44

David C. Langreth and M. J. Mehl.
Beyond the localdensity approximation in calculations of
groundstate 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.
Meanvalue 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 Brillouinzone integrations.
Phys. Rev. B 13 (12), 5188 (June 1976).
 51

D. J. Chadi.
Special points for Brillouinzone 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.
Brillouinzone 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.
point sampling and the method in pseudopotential
total energy calculations.
J. Phys.: Condens. Matter 2, 9837 (1990).
 55

I. J. Robertson and M. C. Payne.
The method in pseudopotential total energy calculations:
error reduction and absolute energies.
J. Phys.: Condens. Matter 3, 8841 (1991).
 56

James C. Phillips.
Energyband 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 solidstate 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. (McGrawHill,
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.
Normconserving pseudopotentials.
Phys. Rev. Lett. 43 (20), 1494 (November 1979).
 67

Alex Zunger and Marvin L. Cohen.
Firstprinciples nonlocalpseudopotential approach in the
densityfunctional formalism. II. Application to electronic and
structural properties of solids.
Phys. Rev. B 20 (10), 4082 (November 1979).
 68

G. P. Kerker.
Nonsingular 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 normconserving 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

MingHsien 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 planewave calculations.
Phys. Rev. B 43 (3), 1993 (January 1991).
 75

David Vanderbilt.
Soft selfconsistent 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 normconserving 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 electronicstructure
calculations.
Phys. Rev. B 41 (8), 5414 (March 1990).
 79

J. Ihm, Alex Zunger and Marvin L. Cohen.
Momentumspace formalism for the total energy of solids.
J. Phys. C 12, 4409 (1979).
 80

P. J. H. Denteneer and W. van Haeringen.
The pseudopotentialdensityfunctional 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 totalenergy
calculations: molecular dynamics and conjugate gradients.
Rev. Mod. Phys. 64 (4), 1045 (October 1992).
 83

G. Kresse and J. Furthmuller.
Efficient iterative schemes for abinitio totalenergy
calculations using a planewave basisset.
Phys. Rev. B 54 (16), 11169 (1996).
 84

X.P. Li, R. W. Nunes and David Vanderbilt.
Densitymatrix electronicstructure method with linear systemsize
scaling.
Phys. Rev. B 47 (16), 10891 (April 1993).
 85

S.Y. Qiu, C. Z. Wang, K. M. Ho and C. T. Chan.
Tightbinding molecular dynamics with linear systemsize scaling.
J. Phys.: Condens. Matter 6, 9153 (1994).
 86

A. Canning, G. Galli, F. Mauri, A. de Vita and R. Car.
O() tightbinding 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.
Bondorder potential and cluster recursion for the description of
chemicalbonds  efficient realspace methods for tightbinding
moleculardynamics.
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 tightbinding methods.
Modelling Simul. Mater. Sci. Eng. 5 (3), 199 (1997).
 89

Weitao Yang.
Direct calculation of electron density in densityfunctional 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 densityfunctional theory.
J. Chem. Phys. 94 (2), 1208 (January 1991).
 91

Qingsheng Zhao and Weitao Yang.
Analytical energy gradients and geometry optimization in the
divideandconquer method for large molecules.
J. Chem. Phys. 102 (24), 9598 (June 1995).
 92

Weitao Yang and TaiSung Lee.
A densitymatrix divideandconquer 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 multipleshell fullerenes.
Phys. Rev. B 49 (16), 11421 (April 1994).
 94

Darrin M. York, TaiSung 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
tightbinding 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 largescale electronicstructure 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

LinWang Wang.
Calculating the density of states and opticalabsorption spectra of
large quantum systems by the planewave 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
electronicstructure 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 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 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 selfconsistent 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 tightbinding molecular
dynamics.
Phys. Rev. Lett. 73 (1), 122 (July 1994).
 106

S. Goedecker and M. Teter.
Tightbinding electronicstructure calculations and tightbinding
molecular dynamics with localized orbitals.
Phys. Rev. B 51 (15), 9455 (April 1995).
 107

Roi Baer and Martin HeadGordon.
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 projection method for firstprinciples 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 electronicstructure calculations.
Phys. Rev. B 48 (23), 17573 (December 1993).
 110

D. M. C. Nicholson and X.G. Zhang.
Approximate occupation functions for densityfunctional calculations.
Phys. Rev. B 56 (20), 12805 (November 1997).
 111

Florian Gagel.
Finitetemperature evaluation of the Fermi density operator.
J. Comp. Phys. 139, 399 (1998).
 112

A. F. Voter, J. D. Kress and R. N. Silver.
Linearscaling 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 electronicstructure calculations with linear
systemsize scaling.
Phys. Rev. B 47 (15), 9973 (April 1993).
 116

Francesco Mauri and Giulia Galli.
Electronicstructure calculations and moleculardynamics simulations
with linear systemsize 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 systemsize scaling methods for electronicstructure
calculations.
Phys. Rev. B 51 (3), 1456 (January 1995).
 119

Jeongnim Kim, Francesco Mauri and Giulia Galli.
Totalenergy 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.
Selfconsistent order densityfunctional 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.
scaling algorithm for densityfunctional calculations of metals
and insulators.
Phys. Rev. B 49 (15), 10088 (April 1994).
 125

W. Hierse and E. B. Stechel.
Order methods in selfconsistent densityfunctional
calculations.
Phys. Rev. B 50 (24), 17811 (December 1994).
 126

E. Hernández and M. J. Gillan.
Selfconsistent firstprinciples technique with linear scaling.
Phys. Rev. B 51 (15), 10157 (April 1995).
 127

E. Hernández, M. J. Gillan and C. M. Goringe.
Linearscaling densityfunctionaltheory technique: The
densitymatrix 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 densitymatrix 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
in
densityfunctional theory.
Phys. Rev. B 18 (12), 7165 (December 1978).
 132

M. Weinert and J. W. Davenport.
Fractional occupations and densityfunctional energies and forces.
Phys. Rev. B 45 (23), 13709 (June 1992).
 133

M. M. Valiev and G. W. Fernando.
Occupation numbers in densityfunctional 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 dimensional energy bands and Wannier
functions.
Phys. Rev. 135 (3A), 698 (August 1964).
 140

Roi Baer and Martin HeadGordon.
Sparsity of the density matrix in KohnSham density functional
theory and an assessment of linear systemsize scaling methods.
Phys. Rev. Lett. 79 (20), 3962 (November 1997).
 141

P. E. Maslen, C. Ochsenfeld, C. A. White, M. S. Lee and M. HeadGordon.
Locality and sparsity of ab initio oneparticle density matrices and
localized orbitals.
J. Phys. Chem. 102, 2215 (1998).
 142

Sohrab IsmailBeigi 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 tightbinding model for
moleculardynamics 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 linearscaling firstprinciples 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.
Finitedifferencepseudopotential method: Electronic structure
calculations without a basis.
Phys. Rev. Lett. 72 (8), 1240 (February 1994).
 150

P. D. Haynes and M. C. Payne.
Localised sphericalwave basis set for totalenergy
pseudopotential calculations.
Comp. Phys. Comm. 102 (13), 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. KingSmith, M. C. Payne and J. S. Lin.
Realspace implementation of nonlocal pseudopotentials for
firstprinciples totalenergy 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.
Lengthscale ill conditioning in linearscaling DFT.
Comp. Phys. Comm. 112 (23), 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
HeadGordon.
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
HeadGordon.
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. PérezJordá 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 HeadGordon.
The tensor properties of energy gradients within a nonorthogonal
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 densityfunctional theory for ab initio molecular
dynamics of metals and finitetemperature insulators.
Phys. Rev. Lett. 79 (7), 1337 (August 1997).
 166

Daniel SánchezPortal, Emilio Artacho and José M. Soler.
Projection of planewave calculations into atomic orbitals.
Solid State Comm. 95 (10), 685 (1995).
 167

Daniel SánchezPortal, Emilio Artacho and José M. Soler.
Analysis of atomic orbital basis sets from the projection of
planewave 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 localizedorbital transferability using the Harris
functional.
Phys. Rev. B 54 (23), 16515 (December 1996).
 170

Pablo Fernández, Andrea Dal Corso, Alfonso Baldereschi and Francesco Mauri.
Firstprinciples 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 tightbinding 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. 3742
(Cambridge University Press, Cambridge, 1972), 2nd edn.
 179

KaiMing Ho, J. Ihm and J. D. Joannopoulos.
Dielectric matrix scheme for fast convergence in selfconsistent
electronicstructure calculations.
Phys. Rev. B 25 (6), 4260 (March 1982).
 180

P. H. Dederichs and R. Zeller.
Selfconsistency iterations in electronicstructure calculations.
Phys. Rev. B 28 (10), 5462 (November 1983).
 181

G. P. Kerker.
Efficient iteration scheme for selfconsistent 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.
Linearscaling DFTpseudopotential calculations on parallel
computers.
Comp. Phys. Comm. 102 (13), 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).
Peter Haynes