Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 1 pp 287-314 | Cite as

# Large Scale Condensed Matter Calculations using the Gaussian and Augmented Plane Waves Method

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## **Abstract**

Density functional theory DFT Kohn-Sham [16] is the method of choice for the calculation of electronic properties of large systems. This is due to the combination of accuracy and efficiency that has been achieved for the Kohn– Sham (KS) method in DFT [19]. DFT based electronic structure calculations are nowadays routinely used by chemists and physicists to support their research. Increasingly complex systems can be treated and the inclusion of environmental effects, through implicit or explicit solvent treatments, as well as the effects of different thermodynamic parameters (temperature, pressure) through first–principles molecular dynamics, opens the door for simulations close to experimental conditions. The accuracy of the method is such that many properties of systems of interest to chemistry, physics, material science, and biology can be predicted in a parameter free way. The success of the KS method makes it also the favorite framework for new developments to improve both, accuracy and efficiency. Better accuracy in this context can be achieved along two lines. On one hand the numerical limit of a given model should be reached and on the other hand more accurate models should be developed (i.e. exchange-correlation functional in DFT). The development of new functionals is an art on its own and will not concern us here. However, it is intimately related to the efficiency problem, as only numerically accurate tests on more and more complex systems can give unambiguous information on the performance of new functionals. The goal of improved algorithms is therefore, to provide methods to accurately and efficiently solve the KS equations.

## Keywords

Plane Wave Root Mean Square Deviation Augmented Plane Wave Maximum Absolute Deviation Auxiliary Basis## Preview

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## References

- 1.EMSL Gaussian Basis Set Order Form. http://www.emsl.pnl.gov/forms/basisform.htmlGoogle Scholar
- 2.A. D. Becke (1988) Density-functional exchange-energy approximation with correct asymptotic-behavior.
*Phys. Rev. A***38**(6), pp. 3098–3100CrossRefADSGoogle Scholar - 3.A. D. Becke (1988) A multicenter numerical integration scheme for polyatomic molecules.
*J. Chem. Phys.***88**(4), pp. 2547–2553CrossRefADSGoogle Scholar - 4.H. M. Berman, W. K. Olson, D. L. Beveridge, J. Westbrook, A. Gelbin, T. Demeny, S.-H. Hsieh, A. R. Srinivasan, and B. Schneider (1992) The nucleic acid database: A comprehensive relational database of three-dimensional structures of nucleic acids.
*Biophys. J.***63**, pp. 751–759CrossRefADSGoogle Scholar - 5.P. Blöchl (1994) Projector augmented-wave method.
*Phys. Rev. B***50**(24), pp. 17953–17979CrossRefADSGoogle Scholar - 6.CPMD, Version 3.9. copyright IBM Corp. 1990–2004, copyright MPI für Festkörperforschung Stuttgart 1997-2001; http://www.cpmd.org/Google Scholar
- 7.R. M. Dickson and A. D. Becke (1993) Basis-set-free local density-functional calculations of geometries of polyatomic-molecules.
*J. Chem. Phys.***99**(5), pp. 3898–3905CrossRefADSGoogle Scholar - 8.B. I. Dunlap, J. W. D. Connolly, and J. R. Sabin (1979) On first-row diatomic molecules and local density models.
*J. Chem. Phys.***71**(12), pp. 4993–4999CrossRefADSGoogle Scholar - 9.T. H. Dunning (1989) Gaussian-basis sets for use in correlated molecular calculations .1. the atoms boron through neon and hydrogen.
*J. Chem. Phys.***90**(2), pp. 1007–1023CrossRefADSGoogle Scholar - 10.K. Eichorn, O. Treutler, H. Öhm, M. Häser, and R. Ahlrichs (1995) Auxiliary basis sets to approximate coulomb potentials.
*Chem. Phys. Lett.***240**, pp. 283–290CrossRefADSGoogle Scholar - 11.S. Goedecker (1999) Linear scaling electronic structure methods.
*Rev. Mod. Phys.***71**(4), pp. 1085–1123CrossRefADSGoogle Scholar - 12.S. Goedecker, M. Teter, and J. Hutter (1996) Separable dual-space Gaussian pseudopotentials.
*Phys. Rev. B***54**(3), pp. 1703–1710CrossRefADSGoogle Scholar - 13.C. Hartwigsen, S. Goedecker, and J. Hutter (1998) Relativistic separable dualspace Gaussian pseudopotentials from H to rn.
*Phys. Rev. B***58**(7), pp. 3641–3662CrossRefADSGoogle Scholar - 14.T. Helgaker, P. Jørgensen, and J. Olsen (2000)
*Molecular Electronic-Structure Theory*. John Wiley & Sons, Ltd, ChichesterGoogle Scholar - 15.T. Helgaker and P. R. Taylor (1995)
*Modern Electronic Structure Theory, Part II*. World Scientific, SingaporeGoogle Scholar - 16.P. Hohenberg and W. Kohn (1964) Inhomogeneous electron gas.
*Phys. Rev. B***136**(3B), pp. B864–B871CrossRefADSMathSciNetGoogle Scholar - 17.G. Hura, D. Russo, R. M. Glaeser, T. Head-Gordon, M. Krack, and M. Parrinello (2003) Water structure as a function of temperature from x-ray scattering experiments and ab initio molecular dynamics.
*Phys. Chem. Chem. Phys.***5**, pp. 1981–1991CrossRefGoogle Scholar - 18.M. Iannuzzi, T. Chassaing, T. Wallman, and J. Hutter (2005) Ground and excited state density functional calculations with Gaussian and augmented method.
*Chimia*,**59**, pp. 499–503CrossRefGoogle Scholar - 19.W. Kohn and L. J. Sham (1965) Self-consistent equations including exchange and correlation effects.
*Phys. Rev.***140**(4A), pp. A1133–A1139CrossRefADSMathSciNetGoogle Scholar - 20.M. Krack and A. M. Köster (1998) An adaptive numerical integrator for molecular integrals.
*J. Chem. Phys.***8**(108), pp. 3226–3234CrossRefADSGoogle Scholar - 21.M. Krack and M. Parrinello (2000) All-electron ab-initio molecular dynamics.
*Phys. Chem. Chem. Phys.***2**(10), pp. 2105–2112CrossRefGoogle Scholar - 22.I.-F. W. Kuo and C. J. Mundy (2004) An ab initio molecular dynamics study of the aqueous liquid-vapor interface.
*Science***303**, pp. 658–660CrossRefADSGoogle Scholar - 23.I.-F. W. Kuo, C. J. Mundy, M. J. McGrath, J. I. Siepmann, J. VandeVondele, M. Sprik, J. Hutter, B. Chen, M. L. Klein, F. Mohamed, M. Krack, and M. Parrinello (2004) Liquid water from first principles: Investigation of different sampling approaches.
*J. Phys. Chem. B***108**(34), pp. 12990–12998CrossRefGoogle Scholar - 24.V. I. Lebedev (1977) Spherical quadrature formulas exact to order-25-order-29.
*Siberian Mathematical Journal***18**(1), pp. 99–107zbMATHCrossRefGoogle Scholar - 25.C. T. Lee, W. T. Yang, and R. G. Parr (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron-density.
*Phys. Rev.**B***37**(2), pp. 785–789CrossRefADSGoogle Scholar - 26.G. Lippert, J. Hutter, and M. Parrinello (1997) A hybrid Gaussian and plane wave density functional scheme.
*Mol. Phys.***92**(3), pp. 477–487CrossRefADSGoogle Scholar - 27.G. Lippert, J. Hutter, and M. Parrinello (1999) The Gaussian and augmentedplane- wave density functional method for ab initio molecular dynamics simulations.
*Theor. Chem. Acc.***103**(2), pp. 124–140Google Scholar - 28.D. Marx and J. Hutter.
*ab-initio*Molecular Dynamics: Theory and Implementation. In J. Grotendorst, editor,*Modern Methods and Algorithms of Quantum Chemistry*, volume 1 of*NIC Series*, pages 329–477. FZ Jülich, Germany, 2000. see also http://www.fz-juelich.de/nic-series/Volume1/Google Scholar - 29.B. Miehlich, A. Savin, H. Stoll, and H. Preuss (1989) Results obtained with the correlation-energy density functionals of Becke and Lee, Yang and Parr.
*Chem. Phys. Lett.***157**(3), pp. 200–206CrossRefADSGoogle Scholar - 30.S. Obara and A. Saika (1986) Efficient recursive computation of molecular integrals over cartesian gaussian functions.
*J. Chem. Phys.***84**(7), pp. 3963–3974CrossRefADSGoogle Scholar - 31.R. Parthasarathy, M. Malik, and S. M. Fridey (1982) X–ray structure of a dinucleoside monophosphate a2’p5’c that contains a 2’–5’ link found in (2’- 5’)oligo(a)s induced by interferons: Single-stranded helical conformation of 2’–5’–linked oligonucleotides.
*Proc. Natl. Acad. Sci. USA***79**, pp. 7292–7296CrossRefADSGoogle Scholar - 32.The CP2K developers group. http://cp2k.berlios.de/, 2004Google Scholar
- 33.J. VandeVondele and J. Hutter (2003) An Efficient orbital transformation method for electronic structure calculations.
*J. Chem. Phys.***118**(10), pp. 4365–4369CrossRefADSGoogle Scholar - 34.J. VandeVondele, M. Krack, F. Mohamed, M. Parrinello, T. Chassaing, and J. Hutter (2005) Quickstep: Fast and accurate density functional calculations using a mixed gaussian and plane waves approach.
*Comp. Phys. Comm.***167**, pp. 103–128CrossRefADSGoogle Scholar - 35.J. VandeVondele, F. Mohamed, M. Krack, J. Hutter, M. Sprik, and M. Parrinello (2005) The influence of temperature and density functional models in ab initio molecular dynamics simulation of liquid water.
*J. Chem. Phys.***122**, p. 014515CrossRefADSGoogle Scholar - 36.E. T. Whittaker and G. N. Watson (1990)
*A Course in Modern Analysis, 4th ed.*Cambridge University PressGoogle Scholar - 37.J. L. Whitten (1973) Coulombic potential energy integrals and approximations.
*J. Chem. Phys.***58**(10), pp. 4496–4501CrossRefADSGoogle Scholar - 38.D. E. Woon and T. H. Dunning (1993) Gaussian-basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon.
*J. Chem. Phys.***98**(2), pp. 1358–1371CrossRefADSGoogle Scholar