Highly accurate O(N) method for delocalized systems

Theoretical Chemistry Accounts

Volumn 130, Issue 4-6, 2011, Pages 595-608

  Aoki, Yuriko ^a,b   Loboda, Oleksandr ^a   Liu, Kai ^a   Makowski, Marcin A ^a,c   Gu, Feng Long ^b,d  

^a KYUSHU UNIVERSITY   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^c JAGIELLONIAN UNIVERSITY   (Poland)

^d SOUTH CHINA NORMAL UNIVERSITY   (China)

Author keywords

carotene; Ab initio method; Elongation method; Fullerene; Lycopene; Nanotube; Nanowire; Porphyrin

Indexed keywords

EID: 81855207309     PISSN: 1432881X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00214-011-1011-z     Document Type: Article

References (62)

1. Imamura A, Aoki Y, Maekawa K (1991) A theoretical synthesis of polymers by using uniform localization of molecular orbitals: Proposal of an elongation method. J Chem Phys 95: 5419-5431.
2. Aoki Y, Imamura A (1992) Local density of states of aperiodic polymers using the localized orbitals from an ab initio elongation method. J Chem Phys 97: 8432-8440.
3. Aoki Y, Suhai S, Imamura A (1994) An efficient cluster elongation method in density functional theory and its application to poly-hydrogen-bonding molecules. J Chem Phys 101: 10808-10823.
4. Makowski M, Korchowiec J, Gu FL, Aoki Y (2010) Describing electron correlation effects in the framework of the elongation method-Elongation-MP2: formalism, implementation and efficiency. J Comput Chem 31: 1733-1740.
5. Gu FL, Imamura A, Aoki Y (2006) Elongation method for polymers and its application to nonlinear optics, in atoms, molecules and clusters in electric fields: theoretical approaches to the calculation of electric polarizabilities. In: Maroulis G (ed) Computational numerical and mathematical methods in sciences and engineering, Imperial College Press, London, 1: 97-177. http://www. icpress. co. uk/chemistry/p464. html.
6. Goedecker S (1999) Linear scaling electronic structure methods. Rev Mod Phys 71: 1085-1123.
7. Salek P, Hoest S, Thoegersen L, Joergensen P, Manninen P, Olsen J, Jansik B, Reine S, Pawlowski F, Tellgren E, Helgaker T, Coriani S (2007) Linear-scaling implementation of molecular electronic self-consistent field theory. J Chem Phys 126: 114110.
8. Goedecker S, Teter M (1995) Tight-binding electronic-structure calculations and tight-binding molecular dynamics with localized orbitals. Phys Rev B 51: 9455-9464.
9. Stephan U, Drabold D (1998) Order-N projection method for first-principles computations of electronic quantities and Wannier functions. Phys Rev B 57: 6391-6407.
10. Li X-P, Nunes W, Vanderbilt D (1993) Density-matrix electronic-structure method with linear system-size scaling. Phys Rev B 47: 10891-10894.
11. Zhao Q, Yang W (1995) Analytical energy gradients and geometry optimization in the divide-and-conquer method for large molecules. J Chem Phys 102: 9598-9603.
12. Kim J, Mauri F, Galli G (1995) Total-energy global optimizations using nonorthogonal localized orbitals. Phys Rev B 52: 1640-1648.
13. Hernandez E, Gillan M (1995) Self-consistent first-principles technique with linear scaling. Phys Rev B 51: 10157-10160.
14. Yang W (1991) Direct calculation of electron density in density-functional theory. Phys Rev Lett 66: 1438-1441.
15. Yang W, Lee T-S (1995) A density-matrix divide-and-conquer approach for electronic structure calculations of large molecules. J Chem Phys 103: 5674-5678.
16. Akama T, Kobayashi M, Nakai H (2007) Implementation of divide-and-conquer method including Hartree-Fock exchange interaction. J Comput Chem 28: 2003-2012.
17. Kobayashi M, Imamura Y, Nakai H (2007) Alternative linear-scaling methodology for the second-order Møller-Plesset perturbation calculation based on the divide-and-conquer method. J Chem Phys 127: 074103.
18. Kitaura K, Ikeo E, Asada T, Nakano T, Uebayasi M (1999) Fragment molecular orbital method: an approximate computational method for large molecules. Chem Phys Lett 313: 701-706.
19. Fedorov DG, Kitaura K (2004) The importance of three-body terms in the fragment molecular orbital method. J Chem Phys 120: 6832-6840.
20. Fedorov DG, Kitaura K (2004) On the accuracy of the 3-body fragment molecular orbital method (FMO) applied to density functional theory. Chem Phys Lett 389: 129-134.
21. Fedorov DG, Kitaura K (2007) Extending the power of quantum chemistry to large systems with the fragment molecular orbital method. J Phys Chem A 111: 6904-6914.
22. Mochizuki Y, Koikegami S, Nakano T, Amari S, Kitaura K (2004) Large scale MP2 calculations with fragment molecular orbital scheme. Chem Phys Lett 396: 473-479.
23. Mochizuki Y, Fukuzawa K, Kato A, Tanaka S, Kitaura K, Nakano T (2005) A configuration analysis for fragment interaction. Chem Phys Lett 410: 247-253.
24. Mochizuki Y, Ishikawa T, Tanaka K, Tokiwa H, Nakano T, Tanaka S (2006) Dynamic polarizability calculation with fragment molecular orbital scheme. Chem Phys Lett 418: 418-422.
25. Mochizuki Y, Yamashita K, Murase T, Nakano T, Fukuzawa K, Takematsu K, Watanabe H, Tanaka S (2008) Large scale FMO-MP2 calculations on a massively parallel-vector computer. Chem Phys Lett 457: 396-403.
26. White SR (1992) Density matrix formulation for quantum renormalization groups. Phys Rev Lett 69: 2863-2866.
27. Kurashige Y, Yanai T (2009) High-performance ab initio density matrix renormalization group method: applicability to large-scale multireference problems for metal compounds. J Chem Phys 130: 234114.
28. Mizukami W, Kurashige Y, Yanai T (2010) Communication: novel quantum states of electron spins in polycarbenes from ab initio density matrix renormalization group calculations. J Chem Phys 133: 091101.
29. Gu FL, Aoki Y, Korchowiec J, Imamura A, Kirtman B (2004) A new localization scheme for the elongation method. J Chem Phys 121: 10385-10391.
30. Aoki Y, Gu FL (2009) Generalized elongation method: from one-dimension to three-dimension. In Champagne B, Gu FL, Luis JM, Springborg M (org) International conference of computational methods in sciences and engineering 2009 (ICCMSE 2009) 46-49. http://www. uni-saarland. de/fak8/springborg/ICCMSE2009/boax. pdf.
31. Makowski M, Gu FL, Aoki Y (2010) Elongation-CIS method: describing excited states of large molecular systems in regionally localized molecular orbital basis. J Comput Method Sci Eng 10: 473-481. doi: 10. 3233/JCM-2010-0312. http://iospress. metapress. com/content/7t71004j74717106/fulltext. pdf.
32. Korchowiec J, Gu FL, Imamura A, Kirtman B, Aoki Y (2005) Elongation method with cutoff technique for linear SCF scaling. Int J Quantum Chem 102: 785-794.
33. Makowski M, Korchowiec J, Gu FL, Aoki Y (2006) Efficiency and accuracy of the elongation method as applied to the electronic structures of large systems. J Comp Chem 27: 1603-1619.
34. Korchowiec J, Lewandowski J, Makowski M, Gu FL, Aoki Y (2009) Elongation cutoff technique armed with quantum fast multipole method for linear scaling. J Comput Chem 30: 2515-2525.
35. Korchowiec J, Silva P, Makowski M, Gu FL, Aoki Y (2010) Elongation cutoff technique at Kohn-Sham level of theory. Int J Quantum Chem 110: 2130-2139.
36. Gu FL, Aoki Y, Imamura A, Bishop DM, Kirtman B (2003) Application of the elongation method to nonlinear optical properties: finite field approach for calculating static electric (hyper)polarizabilities. Mol Phys 101: 1487-1494.
37. Ohnishi S, Gu FL, Naka K, Imamura A, Kirtman B, Aoki Y (2004) Calculation of static (Hyper) polarizabilities for π-conjugated donor/acceptor molecules and block copolymers by the elongation finite-field method. J Phys Chem A 108: 8478-8484.
38. Gu FL, Guillaume M, Botek E, Champagne B, Castet F, Ducasse L, Aoki Y (2006) Elongation method and supermolecule approach for the calculation of nonlinear susceptibilities. Application to the 3-methyl-4-nitropyridine 1-oxide and 2-methyl-4-nitroaniline crystals. J Comput Method Sci Eng 6: 171-188. http://iospress. metapress. com/content/fwabp9hpr2nr7mhh/fulltext. pdf.
39. Ohnishi S, Orimoto Y, Gu FL, Aoki Y (2007) Nonlinear optical properties of polydiacetylene with donor-acceptor substitution block. J Chem Phys 127: 084702.
40. Chen W, Yu G-T, Gu FL, Aoki Y (2009) Investigation on the electronic structures and nonlinear optical properties of pristine boron nitride and boron nitride-carbon heterostructured single-wall nanotubes by the elongation method. J Phys Chem C 113: 8447-8454.
41. Yan LK, Pomogaeva A, Gu FL, Aoki Y (2010) Theoretical study on nonlinear optical properties of metalloporphyrin using elongation method. Theor Chem Acc 125: 511-520.
42. Pomogaeva A, Gu FL, Imamura A, Aoki Y (2010) Electronic structures and nonlinear optical properties of supramolecular associations of benzo-2, 1, 3-chalcogendiazoles by the elongation method. Theor Chem Acc 125: 453-460.
43. Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH, Koseki S, Matsunaga N, Nguyen KA, Su SJ, Windus TL, Dupuis M, Montgomery JA (1993) General atomic and molecular electronic structure system. J Comput Chem 14: 1347-1363. http://www. msg. ameslab. gov/gamess/index. html.
44. Blase X, Charlier JC, De Vita A, Car R (1999) Structural and electronic properties of composite BxCyNz nanotubes and heterojunctions. Appl Phys A 68: 293-300.
45. Terrones M, Romo-Herrera JM, Cruz-Silva E, Lopez-Urias F, Munoz-Sandoval E, Velazquez-Salazar JJ, Terrones H, Bando Y, Golberg D (2007) Pure and doped boron nitride nanotubes. Mater Today 10: 30-38.
46. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene Li X, Knox JE, Hratchian HP, Cross JB, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2004) Gaussian 03, Revision C. 02. Gaussian, Inc., Wallingford, CT.
47. http://xray. bmc. uu. se/hicup/LYC/index. html#COO.
48. Liao M-S, Watts JD, Huang M-J (2009) Dispersion-corrected DFT calculations on C60-porphyrin complexes. Phys Chem Chem Phys 11: 4365-4374.
49. Loboda O, Zalesny R, Avramopoulos A, Papadopoulos MG, Artacho E (2009) Linear-scaling calculations of linear and nonlinear optical properties of [60]fullerene derivatives. In Maroulis G, Simos TE (ed) Computational methods in sciences and engineering, advances in computational science book series: AIP conference proceedings 1108: 198-204. http://link. aip. org/link/?APCPCS/1108/198/1.
50. Loboda O, Zaleśny Avramopoulos A, Luis J-M, Kirtman B, Tagmatarchis N, Reis H, Papadopoulos MG (2009) Linear and nonlinear optical properties of [60]fullerene derivatives. J Phys Chem A 113: 1159-1170.
51. Zaleśny R, Loboda O, Iliopoulos K, Chatzikyriakos G, Couris S, Rotas G, Tagmatarchis N, Avramopoulose A, Papadopoulos MG (2010) Linear and nonlinear optical properties of triphenylamine-functionalized C60: insights from theory and experiment. Phys Chem Chem Phys 12: 373-381.
52. Palummo M, Hogan C, Sottile F, Bagalá P, Rubio A (2009) Ab initio electronic and optical spectra of free-base porphyrins: the role of electronic correlation. J Chem Phys 131: 084102.
53. Yeon KY, Jeong D, Kim SK (2010) Intrinsic lifetimes of the Soret bands of the free-base tetraphenylporphine (H2TPP) and Cu(II)TPP in the condensed phase. Chem Commun 46: 5572-5574.
54. Li C, Ly J, Lei B, Fan W, Zhang D, Han J, Mayyappan M, Thompson C, Zhou M (2004) Data storage studies on nanowire transistors with self-assembled porphyrin molecules. J Phys Chem B 108: 9646-9649.
55. Kwok KS (2003) Materials for future electronics. Mater Today 6: 20-27.
56. Duan X, Huang Y, Lieber CM (2002) Nonvolatile memory and programmable logic from molecule-gated nanowires. Nano Lett 2: 487-490.
57. Meier H, Mühling B (2009) Synthesis and properties of oligo (2, 5-thienylene)s. In Waring A (ed) ARKIVOC: Special issue '5th Eurasian conference on heterocyclic chemistry' ix: 57-69. http://www. arkat-usa. org/get-file/25267/.
58. Obara Y, Takimiya K, Aso Y, Otsubo T (2001) Synthesis and photophysical properties of [60]fullerene-oligo(thienylene-ethynylene) dyads. Tetrahedron Lett 42: 6877-6881.
59. Tormos GV, Nugara PN, Lakshmikantham MV, Gava MP (1993) Poly(2, 5-thienylene ethynylene) and related oligomers. Synth Met 53: 271-281.
60. Shirakawa H, Louis EJ, MacDiarmid AG, Chiang CK., Heeger AJ (1977) Synthesis of electrically conducting organic polymers: halogen derivatives of polyacetylene, (CH)x. J Chem Soc Chem Commun 1977: 578-580.
61. Chiang CK, Druy MA, Gau SC, Heeger AJ, Louis EJ, MacDiarmid AG, Park YW, Shirakawa H (1978) Synthesis of highly conducting films of derivatives of polyacetylene, (CH)x. J Am Chem Soc 100: 1013-1015.
62. MacDiarmid AG (2001) Synthetic metals: a novel role for organic polymers. Synth Met 125: 11-22.