Abstract
We discuss algorithms that can be used to calculate electron densities using computer resources – memory and processor time – that increase only linearly with system size. We focus on the Hartree-Fock and density functional theories and calculations using Gaussian basis sets. However, many of the approaches discussed here are applicable also for other methods and for any local basis. Particular attention is directed towards error control and how to avoid the use of the ad-hoc selected parameters and threshold values often associated with computational approximations employed to reach linear scaling. The discussed aspects include multipole methods, linear scaling computation of the Hartree-Fock exchange and density functional theory exchange-correlation matrices, hierarchic representation of sparse matrices, and density matrix purification. The article also describes how these different parts are put together to achieve linear scaling for the entire Hartree-Fock or density functional theory calculation, controlling errors in the self-consistent field procedure by considering rotations of the occupied subspace.
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References
Goedecker S (1999) Rev Mod Phys 71:1085
Bowler DR, Miyazaki T, Gillan MJ (2002) J Phys Condens Matter 14:2781
Wu SY, Jayanthi CS (2002) Phys Rep 358:1
Rudberg E, Rubensson EH, Sałek P Ergo (2009) Version 2.0: a quantum chemistry program for large scale self-consistent field calculations. http://www.ergoscf.org
Rudberg E, Rubensson EH, Sałek P (2008) J Chem Phys 128:184106
Rubensson EH (2008) Matrix algebra for quantum chemistry. PhD thesis, Department of Theoretical Chemistry, Royal Institute of Technology, Stockholm
Rudberg E (2007) Quantum chemistry for large systems. PhD thesis, Department of Theoretical Chemistry, Royal Institute of Technology, Stockholm
Rubensson EH, Rudberg E, Sałek P (2008) J Math Phys 49:032103
Helgaker T, Jørgensen P, Olsen J (2000) Molecular electronic-structure theory Wiley, Chichester
Pulay P (1980) Chem Phys Lett 73:393
Pulay P (1982) J Comput Chem 3:556
Benzi M, Kouhia R, Tuma M (2001) Comput Meth Appl Mech Eng 190:6533
Rubensson EH, Rudberg E, Sałek P (2007) J Comput Chem 28:2531
Rubensson EH, Bock N, Holmström E, Niklasson AMN (2008) J Chem Phys 128:104105
Lea Thøgersen (2005) Optimization of densities in Hartree-Fock and density-functional theory, Atomic orbital based response Theory, and Benchmarking for radicals. PhD thesis, Department of Chemistry, University of Aarhus, Aarhus
Kudin KN, Scuseria GE (2007) Math Model Num Anal 41:281
Zerner MC, Hehenberger M (1979) Chem Phys Lett 62:550
Cancès E, Le Bris C (2000) Int J Quantum Chem 79:82
Häser M, Ahlrichs R (1989) J Comput Chem 10:104
Rudberg E, Sałek P (2006) J Chem Phys 125:084106
Greengard L, Rokhlin V (1987) J Comput Phys 73:325
Schmidt KE, Lee MA (1991) J Stat Phys 63:1223
Panas I, Almlöf, J, Feyereisen, MW (1991) Int J Quantum Chem 40:797
Panas I, Almlöf J (1992) Int J Quantum Chem 42:1073
White CA, Johnson BG, Gill PMW, Head-Gordon M (1994) Chem Phys Lett 230:8
White CA, Head-Gordon M (1994) J Chem Phys 101:6593
Challacombe M, Schwegler E, Almlöf J (1995) J Chem Phys 104:4685
Challacombe M, Schwegler E (1997) J Chem Phys 106:5526
White CA, Johnson BG, Gill PMW, Head-Gordon M (1996) Chem Phys Lett 253:268
Strain MC, Scuseria GE, Frisch MJ (1996) Science 271:51
Choi CH, Ruedenberg K, Gordon MS (2001) J Comput Chem 22:1484
Sierka M, Hogekamp A, Ahlrichs R (2003) J Chem Phys 118:9136
Watson MA, Sałek P, Macak P, Helgaker T (2004) J Chem Phys 121:2915
Gan CK, Tymczak C, Challacombe M (2004) J Chem Phys 121:6608
Schwegler E, Challacombe M (1996) J Chem Phys 105:2726
Burant JC, Scuseria GE (1996) J Chem Phys 105:8969
Schwegler E, Challacombe M, Head-Gordon M (1997) J Chem Phys 106:9708
Ochsenfeld C, White CA, Head-Gordon M (1998) J Chem Phys 109:1663
Schwegler E, Challacombe M (1999) J Chem Phys 111:6223
Ochsenfeld C (2000) Chem Phys Lett 327:216
Lambrecht DS, Ochsenfeld C (2005) J Chem Phys 123:184101
Aquilante F, Pedersen TB, Lindh R (2007) J Chem Phys 126:194106
Murray CW, Handy NC, Laming GJ (1993) Mol Phys 78:997
Challacombe M (2000) J Chem Phys 113:10037
Treutler O, Ahlrichs R (1995) J Chem Phys 102:346
Lebedev VI, vychisl, Zh (1975) Mat mat Fiz 45:48
Lindh R, Malmqvist PA, Gagliardi L (2001) Theor Chem Acc 106:178
Becke AD (1988) J Chem Phys 88:2547
Stratmann RE, Scuseria GE, Frisch MJ (1996) Chem Phys Lett 257:213
Rudberg E, Rubensson EH, Sałek P (2009) J Chem Theory Comput 5:80
Sankey OF, Drabold DA, Gibson A (1994) Phys Rev B 50:1376
Bekas C, Kokiopoulou E, Saad Y, SIAM J (2008) Matrix Anal Appl 30:397
Drabold DA, Sankey OF (1993) Phys Rev Lett 70:3631
Wang LW, Zunger A (1994) J Chem Phys 100:2394
Gao B, Jiang J, Liu K, Wu Z, Lu W, Luo Y (2007) J Comput Chem 29:434
McWeeny R (1956) Proc R Soc London Ser A 235:496
Heath MT (1997) Scientific computing: an introductory survey. McGraw-Hill, Singapore
Li XP, Nunes RW, Vanderbilt D (1993) Phys Rev B 47:10891
Millam JM, Scuseria GE (1997) J Chem Phys 106:5569
Daw MS (1993) Phys Rev B 47:10895
Challacombe M (1999) J Chem Phys 110:2332
Helgaker T, Larsen H, Olsen J, Jørgensen P (2000) Chem Phys Lett 327:397
Dyan A, Dubot P, Cenedese P (2005) Phys Rev B 72:125104
Larsen H, Olsen J, Jørgensen P, Helgaker T (2001) J Chem Phys 115:9685
Shao Y, Saravanan C, Head-Gordon M, White CA (2003) J Chem Phys 118:6144
Goedecker S, Colombo L (1994) Phys Rev Lett 73:122
Goedecker S, Teter M (1995) Phys Rev B 51:9455
Baer R, Head-Gordon M (1997) J Chem Phys 107:10003
Bates KR, Daniels AD, Scuseria GE (1998) J Chem Phys 109:3308
Liang W, Saravanan C, Shao Y, Baer R, Bell AT, Head-Gordon M (2003) J Chem Phys 119:4117
Silver RN, Roeder H, Voter AF, Kress JD (1996) J Comput Phys 124:115
Palser AHR, Manolopoulos DE (1998) Phys Rev B 58:12704
Niklasson AMN (2002) Phys Rev B 66:155115
Niklasson AMN, Tymczak CJ, Challacombe M (2003) J Chem Phys 118:8611
Holas A (2001) Chem Phys Lett 340:552
Mazziotti DA (2003) Phys Rev E 68:066701
Xiang HJ, Liang WZ, Yang J, Hou JG, Zhu Q (2005) J Chem Phys 123:124105
Pino R, Scuseria GE (2002) Chem Phys Lett 360:117
Rubensson EH, Rudberg E, Sałek P (2008) J Chem Phys 128:074106
Paterson MS, Stockmeyer L, SIAM (1973) J Comput 2:60
Saravanan C, Shao Y, Baer R, Ross PN, Head-Gordon M (2003) J Comput Chem 24:618
Maslen PE, Ochsenfeld C, White CA, Lee MS, Head-Gordon M (1998) J Phys Chem A 102:2215
Rubensson EH, Rudberg E, Sałek P (2009) J Comput Chem 30:974
Rubensson EH, Rudberg E, Sałek P (2007) Proceedings of PARA’06, Springer LNCS 4699:90
Gotoblas. http://www.tacc.utexas.edu/resources/software/#blas
Automatically tuned linear algebra software (ATLAS). http://mathatlas.sourceforge.net/
Intel math kernel library (Intel MKL). http://www.intel.com/cd/software/products/asmo-na/eng/307757.htm
AMD core math library (ACML). http://developer.amd.com/cpu/libraries/acml/Pages/default.aspx
Elmroth E, Gustavson F, Jonsson I, Kågström B (2004) SIAM Rev 46:3
Becke AD (1993) J Chem Phys 98:1372
Spartan’02 (2002) Molecular modeling package by Wavefunction, Inc.
Challacombe M (2000) Comp Phys Commun 128:93
Bowler DR, Miyazaki T, Gillan MJ (2001) Comp Phys Commun 137:255
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Rubensson, E.H., Rudberg, E., Salek, P. (2011). Methods for Hartree-Fock and Density Functional Theory Electronic Structure Calculations with Linearly Scaling Processor Time and Memory Usage. In: Zalesny, R., Papadopoulos, M., Mezey, P., Leszczynski, J. (eds) Linear-Scaling Techniques in Computational Chemistry and Physics. Challenges and Advances in Computational Chemistry and Physics, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2853-2_12
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