Skip to main content
SpringerLink
Log in

Approximations of Long-Range Interactions in Fragment-Based Quantum Chemical Approaches

  • Chapter
  • First Online:
Linear-Scaling Techniques in Computational Chemistry and Physics

Part of the book series: Challenges and Advances in Computational Chemistry and Physics ((COCH,volume 13))

Abstract

Quantum chemical calculations of very large systems still pose major challenges due to the formidable scaling behavior of standard methods with system size. Here, we will describe how the concept of separating short- and long-range interactions can be used to make such calculations possible nonetheless at least in an approximate way. In mixed quantum mechanical/molecular mechanical (QM/MM) and fragment-based quantum chemical methods, the local surroundings are considered explicitly whereas other parts further away are neglected or included with a lower level of theory, e.g. as interactions with point charges. Different methods to combine these two descriptions, so-called embedding schemes, are outlined. Additionally, the border region problem, how subsystems describable by quantum mechanics can be generated by cleaving and saturating bonds connecting atoms located in the different regions, and proposed solutions are discussed. Finally, with the fragment-based adjustable density matrix assembler (ADMA) method as example, the capacities but also some limitations of the presented approaches will be presented using different test systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 299.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 379.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 379.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Baerends EJ, Ellis DE, Ros P (1973) Chem Phys 2:41–51

    Article  CAS  Google Scholar 

  2. Sambe H, Felton RH (1975) J Chem Phys 62:1122–1126

    Article  CAS  Google Scholar 

  3. Dunlap BI, Connolly JWD, Sabin JRJ (1979) Chem Phys 71:3396–3402

    CAS  Google Scholar 

  4. Dyczmons V (1973) Theor Chem Acc 28:307–310

    Article  CAS  Google Scholar 

  5. Ahlrichs R (1974) Theor Chem Acc 33 157–167

    Article  CAS  Google Scholar 

  6. Lambrecht DS, Ochsenfeld CJ (2005) Chem Phys 123:184101–184114

    Google Scholar 

  7. Ochsenfeld C, White CA, Head-Gordon M (1998) J Chem Phys 109:1663–1669

    Article  CAS  Google Scholar 

  8. Maslen PE, Ochsenfeld C, White CA, Lee MS, Head-Gordon M (1998) J Phys Chem A 102:2215–2222

    Article  CAS  Google Scholar 

  9. Challacombe M, Schwegler E (1997) J Chem Phys 106:5526–5536

    Article  CAS  Google Scholar 

  10. White CA, Johnson BG, Gill PMW, Head-Gordon M (1994) Chem Phys Lett 230:8–16

    Article  CAS  Google Scholar 

  11. White CA, Johnson BG, Gill PMW, Head-Gordon M (1996) Chem Phys Lett 253:268–278

    Article  CAS  Google Scholar 

  12. Scuseria GE (1999) J Phys Chem A 103:4782–4790

    Article  CAS  Google Scholar 

  13. Strain MCG, Scuseria E, Frisch MJ (1996) Science 271:51–53

    Article  CAS  Google Scholar 

  14. Schwegler E, Challacombe M (1999) J Chem Phys 111:6223–6229

    Article  CAS  Google Scholar 

  15. Burant JC, Strain MC, Scuseria GE, Frisch MJ (1996) Chem Phys Lett 248:43–49

    Article  CAS  Google Scholar 

  16. Shao Y, White, CA, Head-Gordon M (2001) J Chem Phys 114:6572–6577

    Article  CAS  Google Scholar 

  17. Greengard L, Rokhlin V (1987) J Comp Phys 73:325–348

    Article  Google Scholar 

  18. Schmidt KE, Lee MA (1991) J Stat Phys 63:1223–1235

    Article  Google Scholar 

  19. Petersen HG, Soelvason D, Perram JW, Smith ER (1994) J Chem Phys 101:8870–8876

    Article  CAS  Google Scholar 

  20. White CA, Head-Gordon M (1994) J Chem Phys 101:6593–6605

    Article  Google Scholar 

  21. White CA, Head-Gordon M (1996) J Phys Chem 105:5061–5067

    Article  CAS  Google Scholar 

  22. Yang W (1991) Phys Rev Lett 66:1438

    Article  CAS  Google Scholar 

  23. Yang W, Lee TS (1995) J Chem Phys 103:5674–5678

    Article  CAS  Google Scholar 

  24. Lee C, Yang W (1992) J Chem Phys 96:2408–2411

    Article  CAS  Google Scholar 

  25. Gogonea V, Westerhoff LM, Merz J (2000) J Chem Phys 113:5604–5613

    Article  CAS  Google Scholar 

  26. Kobayashi M, Nakai H (2009) Int J Quantum Chem 109:2227–2237

    Article  CAS  Google Scholar 

  27. Akama T, Fujii A, Kobayashi M, Nakai H (2007) Mol Phys 105:2799–2804

    Article  CAS  Google Scholar 

  28. Akama T, Kobayashi M, Nakai H (2007) J Comp Chem 28:2003–2012

    Article  CAS  Google Scholar 

  29. Kobayashi M, Akama T, Nakai H (2006) J Chem Phys 125:204106–204108

    Article  Google Scholar 

  30. He X, Merz KM (2010) J Chem Theor Comp 6:405–411

    Article  CAS  Google Scholar 

  31. St-Amant A (2002) In: Laird BB, Ross RB, Ziegler T (eds) Chemical apllications of density-functional theory. ACS Symposium Series 629. American Chemical Society, Washington, DC, pp. 70–84

    Google Scholar 

  32. Dixon SL, Merz J (1996) J Chem Phys 104:6643–6649

    Article  CAS  Google Scholar 

  33. Dixon SL, Merz KM Jr (1998) In: Schleyer PvR, Allinger NC, Clark T, Gasteiger J, Kollmann PA, Schaefer HF III, Schreiner, PR (eds) The encyclopedia of computational chemistry. Wiley, Chichester, pp. 762–776

    Google Scholar 

  34. Mezey PG (1996) Adv Quant Chem 27:163–222

    Article  Google Scholar 

  35. Mezey PG (1997) Intern Rev Phys Chem 16:361–388

    Article  CAS  Google Scholar 

  36. Mezey PG (1995) J Math Chem 18:141–168

    Article  CAS  Google Scholar 

  37. Mezey PG (1997) Int J Quantum Chem 63:39–48

    Article  CAS  Google Scholar 

  38. Walker PD, Mezey PG (1993) J Amer Chem Soc 115:12423–12430

    Article  CAS  Google Scholar 

  39. Walker PD, Mezey PG (1994) Can J Chem 72:2531–2536

    Article  CAS  Google Scholar 

  40. Walker PD, Mezey PG (1994) J Amer Chem Soc 116:12022–12032

    Article  CAS  Google Scholar 

  41. Szekeres Z, Exner TE, Mezey PG (2005) Int J Quantum Chem 104:847–860

    Article  CAS  Google Scholar 

  42. Exner TE, Mezey PG (2004) J Phys Chem A 108:4301–4309

    Article  CAS  Google Scholar 

  43. Exner TE, Mezey PG (2005) Phys Chem Chem Phys:7:4061–4069

    Article  CAS  Google Scholar 

  44. Exner TE, Mezey PG (2002) J Phys Chem A 106:11791–11800

    Article  CAS  Google Scholar 

  45. Exner TE, Mezey PG (2003) J Comp Chem 24:1980–1986

    Article  CAS  Google Scholar 

  46. Gadre SR, Shirsat RN, Limaye AC (1994) J Phys Chem 98:9165–9169

    Article  CAS  Google Scholar 

  47. Babu K, Gadre SR (2003) J Comp Chem 24:484–495

    Article  CAS  Google Scholar 

  48. Gao B, Jiang J, Liu K, Wu Z, Lu W, Luo Y (2008) J Comp Chem 29:434–444

    Article  CAS  Google Scholar 

  49. Li W, Fang T, Li S (2006) J Chem Phys 124:154102–154106

    Article  Google Scholar 

  50. Li W, Li S (2005) J Chem Phys 122:194109–6

    Google Scholar 

  51. Kitaura K, Ikeo E, Asada T, Nakano T, Uebayasi M (1999) Chem Phys Lett 313:701–706

    Article  CAS  Google Scholar 

  52. Kitaura K, Sawai T, Asada T, Nakano T, Uebayasi M (1999) Chem Phys Lett 312:319–324

    Article  CAS  Google Scholar 

  53. Nakano T, Kaminuma T, Sato T, Akiyama Y, Uebayasi M, Kitaura K (2000) Chem Phys Lett 318:614–618

    Article  CAS  Google Scholar 

  54. Kitaura K, Sugiki S-I, Nakano T, Komeiji Y, Uebayasi M (2001) Chem Phys Lett 336:163–170

    Article  CAS  Google Scholar 

  55. Nakano T, Kaminuma T, Sato T, Fukuzawa K, Akiyama Y, Uebayasi M, Kitaura K (2002) Chem Phys Lett 351:475–480

    Article  CAS  Google Scholar 

  56. Inadomi Y, Nakano T, Kitaura K, Nagashima U (2002) Chem Phys Lett 364:139–143

    Article  CAS  Google Scholar 

  57. Komeiji Y, Nakano T, Fukuzawa K, Ueno Y, Inadomi Y, Nemoto T, Uebayasi M, Fedorov DG, Kitaura K (2003) Chem Phys Lett 372:342–347

    Article  CAS  Google Scholar 

  58. Fedorov DG, Kitaura K, Li H, Jensen JH, Gordon MS (2006) J Comp Chem 27:976–985

    Article  CAS  Google Scholar 

  59. Stoll H (1992) Phys Rev B 46:6700

    Article  CAS  Google Scholar 

  60. Stoll H (1992) Chem Phys Lett 191:548

    Article  CAS  Google Scholar 

  61. Stoll H (1992) Chem Phys 97:8449

    CAS  Google Scholar 

  62. Paulus B (2006) Phys Rep 428:1–52

    Article  CAS  Google Scholar 

  63. Fedorov DG, Kitaura K (2004) J Chem Phys 121:2483–2490

    Article  CAS  Google Scholar 

  64. Fedorov DG, Kitaura K (2005) J Chem Phys 123:134103–134111

    Article  Google Scholar 

  65. Ranganathan S, Gready JE (1997) J Phys Chem B 101:5614–5618

    Article  CAS  Google Scholar 

  66. Gready JE, Ranganathan S (1994) Gre Faraday Trans 90:2047–2056

    Article  Google Scholar 

  67. Zhang DW, Zhang JZH (2003) J Chem Phys 119:3599–3605

    Article  CAS  Google Scholar 

  68. Jiang N, Ma J, Jiang Y (2006) J Chem Phys 124:114112–114119

    Article  Google Scholar 

  69. Hyperchem 7.5. (2003) Hypercube, Inc., 1115 NW 4th Street, Gainesville, FL 32601, USA. Ref Type: Computer Program

    Google Scholar 

  70. Zhang Y, Lee TS, Yang W (1999) J Chem Phys 110:46–54

    Article  CAS  Google Scholar 

  71. Zhang Y (2005) J Chem Phys 122:024114

    Article  Google Scholar 

  72. Zhang Y (2006) Theor Chem Acc 116:43–50

    Article  CAS  Google Scholar 

  73. Jardillier N, Goursot A (2008) Chem Phys Lett 454:65–69

    Article  CAS  Google Scholar 

  74. DiLabio GA, Hurley MM, Christiansen PA (2002) J Chem Phys 116:9578–9584

    Article  CAS  Google Scholar 

  75. Antes I, Thiel W (1999) J Phys Chem A 103:9290–9295

    Article  CAS  Google Scholar 

  76. Poteau R, Ortega I, Alary F, Ramirez Solis A, Barthelat JC, Daudey J-P (2001) J Phys Chem A 105:198–205

    Article  CAS  Google Scholar 

  77. Yasuda K, Yamaki D (2004) J Chem Phys 121:3964–3972

    Article  CAS  Google Scholar 

  78. Slavicek P, Martinez TJ (2006) J Chem Phys 124:084107

    Article  Google Scholar 

  79. Assfeld X, Ferre N, Rivail J (1998) In: Combined quantum mechanical and molecular mechanical methods. American Chemical Society, Washington, DC, pp. 234–249

    Book  Google Scholar 

  80. Gorb LG, Rivail JL, Thery V, Rinaldi D (1996) Int J Quantum Chem 60:1525–1536

    Article  Google Scholar 

  81. Rivail JL (1999) J Mol Struct THEOCHEM 463:3

    Article  CAS  Google Scholar 

  82. Thery V, Rinaldi D, Rivail JL, Maigret B, Ferenczy GG (1994) J Comp Chem 15:269–282

    Article  CAS  Google Scholar 

  83. Ferenczy GG, Rivail JL, Surjan PR, Naray-Szabo G (1992) J Comp Chem 13:830–837

    Article  CAS  Google Scholar 

  84. Philipp DM, Friesner RA (1999) J Comp Chem 20:1468–1494

    Article  CAS  Google Scholar 

  85. Murphy RB, Philipp DM, Friesner RA (2000) J Comp Chem 21:1442–1457

    Article  CAS  Google Scholar 

  86. Pu J, Gao J, Truhlar DG (2004) J Phys Chem A 108:632–650

    Article  CAS  Google Scholar 

  87. Pernal K, Wesolowski TA (2009) Int J Quantum Chem 109:2520–2525

    Article  CAS  Google Scholar 

  88. Wesolowski TA (2008) Phys Rev A 77:012504

    Article  Google Scholar 

  89. Case DA, Darden TA, Cheatham III TE, Simmerling CL, Wang J, Duke RE, Luo R, Crowley M, Walker RC, Zhang W, Merz KM, Wang B, Hayik S, Roitberg A, Seabra G, Kolossvary I, Wong KF, Paesani F, Vanicek J, Wu X, Brozell SR, Steinbrecher T, Gohlke H, Yang L, Tan C, Mongan J, Hornak V, Cui G, Mathews DH, Seetin MG, Sagui C, Babin V, Kollman PA (2008) AMBER 10. University of California, San Francisco, CA. Ref Type: Computer Program

    Google Scholar 

  90. Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983) J Comp Chem 4:187–217

    Article  CAS  Google Scholar 

  91. Zhang Y, Lee TS, Yang W (1999) J Chem Phys 110:46–54

    Article  CAS  Google Scholar 

  92. Exner TE (2010) Int J Quantum Chem. doi: 10.1002/qua.22473

    Google Scholar 

  93. Eckard S, Exner TE (2006) Z Phys Chem 220:927–944

    Article  CAS  Google Scholar 

  94. Eckard S, Exner TE (2009) Int J Quantum Chem 109:1451–1463

    Article  CAS  Google Scholar 

  95. McWeeny R (1962) Phys Rev 126:1028

    Article  Google Scholar 

  96. Ditchfield R (1974) Mol Phys 27:789–807

    Article  CAS  Google Scholar 

  97. Wolinski K, Sadlej AJ (1980) Mol Phys 41:1419–1430

    Article  CAS  Google Scholar 

  98. Wolinski K, Hinton JF, Pulay P 1990 J Amer Chem Soc 112:8251–8260

    Article  CAS  Google Scholar 

  99. 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 M, Li X, Knox JE, Hratchian HP, Cross JB, Bakken V, 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.2). Wallingford CT, Gaussian, Inc. Ref Type: Computer Program

    Google Scholar 

  100. Cances E, Mennucci B, Tomasi J (1997) J Chem Phys 107:3032–3041

    Article  CAS  Google Scholar 

  101. Cossi M, Barone V, Mennucci B, Tomasi J (1998) Chem Phys Lett 286:253–260

    Article  CAS  Google Scholar 

  102. Mennucci B, Tomasi J (1997) J Chem Phys 106:5151–5158

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The authors thank Paul G. Mezey, Raymond A. Poirier, and Peter L. Warburton for fruitful discussions. The work was supported by the Deutsche Forschungsgemeinschaft, Priority Program SPP 1145 “Modern and Universal First-Principles Methods for Many-Electron Systems in Chemistry and Physics” and the Juniorprofessorenprogramm des Landes Baden-Württemberg. Simon Eckard gratefully acknowledges the Fonds der Chemischen Industrie for a PhD fellowship and the German Academic Exchange Service (DAAD) for a short-term PhD student fellowship.

Author information

Authors and Affiliations

  1. Department of Chemistry and Zukunftskolleg, University of Konstanz, D-78457, Konstanz, Germany

    Andrea Frank, Ionut Onila & Thomas E. Exner

  2. Institute of Physical Chemistry, University of Zurich, 8057, Zürich, Switzerland

    Simon M. Eckard

Authors
  1. Simon M. Eckard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Frank
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ionut Onila
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thomas E. Exner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas E. Exner .

Editor information

Editors and Affiliations

  1. Inst. Physical & Theoretical Chemistry, Wroclaw University of Technology, Wyb. Wyspianskiego 27, Warszawa, 50-370, Poland

    Robert Zalesny

  2. Institute of Organic &, Pharmaceutical Chemistry, National Hellenic Research Foundation, Vas. Constantinou Ave. 48, Athens, 116 35, Greece

    Manthos G. Papadopoulos

  3. Dept. Chemistry, University of Saskatchewan, Saskatoon, S7N 0W0, Saskatchewan, Canada

    Paul G. Mezey

  4. Jackson State University, J. R. Lynch St. 1325, Jackson, 39217, Mississippi, USA

    Jerzy Leszczynski

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Eckard, S.M., Frank, A., Onila, I., Exner, T.E. (2011). Approximations of Long-Range Interactions in Fragment-Based Quantum Chemical Approaches. 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_8

Download citation

Publish with us

Policies and ethics

Search

Navigation