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Mixing parameters for geometry optimization using the Hamiltonian algorithm

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Abstract

We study the mixing parameters for the search of an optimal geometry using the Hamiltonian algorithm (HA) combined with ab initio molecular orbital calculations. We choose the C–C–C–C dihedral angle of the butane molecule as an example. HF/3-21G level calculations are employed as the molecular orbital calculations. The distributions of the eigenvalues of mixing coefficients are fitted with the linear, quadratic, and quartic functions. Analyses of HA calculations both up to 2,000 and 60,000 iterative calculations show a possibility that the mixing process reduces the number of iterations. The low energy HF/3-21G, B3LYP/6-31G**, and PCM B3LYP/aug-cc-pVDZ optimized structures of the N-acetyl l-histidine N′-methyl amide and four water molecule supermolecule were also determined using the HA optimization method and compared to the recently determined thought to be global minimum energy structure.

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References

  1. Teramae H, Michl J (1994) Mol Cryst Liq Cryst 256:149

    Article  CAS  Google Scholar 

  2. Neumann F, Teramae H, Downing JW, Michl J (1998) J Am Chem Soc 120:573

    Article  CAS  Google Scholar 

  3. Shinjo K (1999) J Jpn Soc Fuzzy Theory Systems 11(3):382

    Google Scholar 

  4. Saito S, Shinjo K, Oida K, Ohtawara K, Shimogawa S, Hirata K, Kitagawa Y, Kuramochi Y, Onda K, Komatsuzaki A, Noguchi T (2000) In Basics and application of Hamiltonian algorithm, ATR technical report, TR-AC-0049 (in Japanese)

  5. Ohtawara K, Shimogawa S, Shinjo K (2001) Int J Mod Phys C 12:1305

    Article  CAS  Google Scholar 

  6. Ohtawara K, Teramae H (2004) Chem Phys Lett 390:84

    Article  CAS  Google Scholar 

  7. Ishimoto T, Tokiwa H, Teramae H, Nagashima U (2004) Chem Phys Lett 387:460–465

    Article  CAS  Google Scholar 

  8. Ishimoto T, Tokiwa H, Teramae H, Nagashima U (2005) J Chem Phys 122:094905

    Article  Google Scholar 

  9. Sato R, Teramae H, Ishimoto T, Nagashima U (2007) J Comp Chem Jpn 6:295

    Article  CAS  Google Scholar 

  10. Tsuchiya K, Teramae H, Watanabe T, Ishimoto T, Nagashima U (2007) J Comp Chem Jpn 6:275–282 (in Japanese)

    Article  CAS  Google Scholar 

  11. Teramae H, Ohtawara K, Ishimoto T, Nagashima U (2008) Bull Chem Soc Jpn 81:1094

    Article  CAS  Google Scholar 

  12. Shinjo K, Sasada T (1996) Phys Rev E54:4685

    Google Scholar 

  13. Verlet L (1967) Phys Rev 159:98

    Article  CAS  Google Scholar 

  14. Gear CW (1971) Numerical initial value problems in ordinary differential equations. Prentice Hall, Englewood Cliffs

    Google Scholar 

  15. Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH, Koseki S, Matsunaga SN, Nguyen KA, Su S, Windus TL, Dupuis M, Montgomery JA (1993) J Comput Chem 14:1347–1363

    Article  CAS  Google Scholar 

  16. Binkley JS, Pople JA, Hehre WJ (1980) J Am Chem Soc 102:939–947

    Article  CAS  Google Scholar 

  17. 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. 02. Gaussian Inc., Wallingford

    Google Scholar 

  18. Alexandrova A, Boldyrev A (2005) J Chem Theory Comput 1:566

    Article  CAS  Google Scholar 

  19. Baker J, Wolinski K (2011) J Comp Chem 32:43

    Article  CAS  Google Scholar 

  20. Ohno K, Maeda S (2004) Chem Phys Lett 384:277

    Article  CAS  Google Scholar 

  21. Maeda S, Ohno K (2005) J Phys Chem A 109:5742

    Article  CAS  Google Scholar 

  22. Yang X, Maeda S, Ohno K (2007) J Phys Chem A 111:5099

    Article  CAS  Google Scholar 

  23. Maeda S, Ohno K, Morokuma K (2009) J Phys Chem A 113:1704

    Article  CAS  Google Scholar 

  24. Maeda S, Ohno K, Morokuma K (2009) J Chem Theory Comput 5:2734

    Article  CAS  Google Scholar 

  25. Jalkanen KJ, Suhai S (1996) Chem Phys 208:81–116

    Article  CAS  Google Scholar 

  26. Deng Z, Polavarapu PL, Ford SJ, Hecht L, Barron LD, Ewig CS, Jalkanen KJ (1996) J Phys Chem 100:2025–2034

    Article  CAS  Google Scholar 

  27. Tajkhorshid E, Jalkanen KJ, Suhai S (1998) J Phys Chem B 102:5899–5913

    Article  CAS  Google Scholar 

  28. Han W-G, Jalkanen KJ, Elstner M, Suhai S (1998) J Phys Chem B 102:2587–2602

    Article  CAS  Google Scholar 

  29. Frimand K, Bohr H, Jalkanen KJ, Suhai S (2000) Chem Phys 255:165–194

    Article  CAS  Google Scholar 

  30. Jalkanen KJ, Nieminen RM, Frimand K, Bohr J, Bohr H, Wade RC, Tajkhorshid E, Suhai S (2001) Chem Phys 265:125–151

    Article  CAS  Google Scholar 

  31. Jalkanen KJ (2003) J Phys Condens Matter 15:S1823–S1851

    Article  CAS  Google Scholar 

  32. Jalkanen KJ, Elstner M, Suhai S (2004) J Mol Struct (Theochem) 675:61–77

    Article  CAS  Google Scholar 

  33. Jalkanen KJ, Jurgensen VW, Claussen A, Rahim A, Jensen GM, Wade RC, Nardi F, Jung C, Degtyarenko IM, Nieminen RM, Herrmann F, Knapp-Mohammady M, Niehaus TA, Frimand K, Suhai S (2006) Int J Quantum Chem 106:1160

    Article  CAS  Google Scholar 

  34. Jalkanen KJ, Degtyarenko IM, Nieminen RM, Cao X, Nafie LA, Zhu F, Barron LD (2008) Theor Chem Acc 119:191–210

    Article  CAS  Google Scholar 

  35. Deplazes E, Van Bronswijk W, Zhu F, Barron LD, Ma S, Nafie LA, Jalkanen KJ (2008) Theor Chem Acc 119:155–176

    Article  CAS  Google Scholar 

  36. Guerra CF, Van der Wijst T, Poater J, Swart M, Bickelhaupt FM (2010) Theor Chem Acc 125:245–252

    Article  CAS  Google Scholar 

  37. Jankowski K, Nowakowski K, Grabowski I, Wasilewski J (2010) Theor Chem Acc 125:433–444

    Article  CAS  Google Scholar 

  38. Van Mourik T, Danilov VI, Dailidonis VV, Kurita N, Wakabayashi H, Tsukamoto T (2010) Theor Chem Acc 125:233–244

    Article  CAS  Google Scholar 

  39. Dennington R, Keith T, Millam J (2009) GaussView, Version 5. Semichem Inc., Shawnee Mission

    Google Scholar 

  40. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam NJ, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09, Revision A. 02. Gaussian Inc., Wallingford

    Google Scholar 

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Correspondence to Hiroyuki Teramae.

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Dedicated to Professor Akira Imamura on the occasion of his 77th birthday and published as part of the Imamura Festschrift Issue.

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Teramae, H., Ishimoto, T. & Nagashima, U. Mixing parameters for geometry optimization using the Hamiltonian algorithm. Theor Chem Acc 130, 671–678 (2011). https://doi.org/10.1007/s00214-011-1010-0

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