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Development of the Analytic Second Derivatives for the Fragment Molecular Orbital Method

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Recent Advances of the Fragment Molecular Orbital Method

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Abstract

The development of the analytic second derivatives of the energy with respect to nuclear coordinates for the fragment molecular orbital method is reviewed, and a summary of equations is provided for Hartree–Fock and density functional theory (DFT). The second derivatives are developed for unrestricted DFT. The accuracy of frequencies, IR intensities, Raman activities, and free energies is evaluated in comparison to unfragmented results.

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References

  1. Deglmann P, Furche F, Ahlrichs R (2002) An efficient implementation of second analytical derivatives for density functional methods. Chem Phys Lett 362:511–518

    Article  CAS  Google Scholar 

  2. Alexeev Y, Schmidt MW, Windus TL, Gordon MS (2007) A parallel distributed data CPHF algorithm for analytic Hessians. J Comput Chem 28:1685–1694

    Article  CAS  PubMed  Google Scholar 

  3. Pulay P (1969) Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. Mol Phys 17:197–204

    Article  CAS  Google Scholar 

  4. Gordon MS, Fedorov DG, Pruitt SR, Slipchenko LV (2012) Fragmentation methods: a route to accurate calculations on large systems. Chem Rev 112:632–672

    Article  CAS  PubMed  Google Scholar 

  5. Sakai S, Morita S (2005) Ab initio integrated multi-center molecular orbitals method for large cluster systems: Total energy and normal vibration. J Phys Chem A 109:8424–8429

    Article  CAS  PubMed  Google Scholar 

  6. Rahalkar AP, Ganesh V, Gadre SR (2008) Enabling ab initio hessian and frequency calculations of large molecules. J Chem Phys 129:234101

    Article  PubMed  CAS  Google Scholar 

  7. Jose KVJ, Raghavachari K (2015) Evaluation of energy gradients and infrared vibrational spectra through molecules-in-molecules fragment-based approach. J Chem Theory Comput 11(3):950–961

    Article  CAS  PubMed  Google Scholar 

  8. Hua W, Fang T, Li W, Yu JG, Li S (2008) Geometry optimizations and vibrational spectra of large molecules from a generalized energy-based fragmentation approach. J Phys Chem A 112(43):10864–10872

    Article  CAS  PubMed  Google Scholar 

  9. Collins MA (2014) Molecular forces, geometries, and frequencies by systematic molecular fragmentation including embedded charges. J Chem Phys 141:094108

    Article  PubMed  CAS  Google Scholar 

  10. Liu J, Zhang JZH, He X (2016) Fragment quantum chemical approach to geometry optimization and vibrational spectrum calculation of proteins. Phys Chem Chem Phys 18:1864–1875

    Article  CAS  PubMed  Google Scholar 

  11. Cui Q, Karplus M (2000) Molecular properties from combined qm/mm methods. I. Analytical second derivative and vibrational calculations. J Chem Phys 112:1133

    Google Scholar 

  12. Li H, Jensen JH (2002) Partial Hessian vibrational analysis: the localization of the molecular vibrational energy and entropy. Theor Chem Acc 107:211–219

    Article  CAS  Google Scholar 

  13. Jensen JH, Li H, Robertson AD, Molina PA (2005) Prediction and rationalization of protein pKa values using QM and QM/MM methods. J Phys Chem A 109:6634–6643

    Article  CAS  PubMed  Google Scholar 

  14. Ghysels A, Woodcock HL III, Larkin JD, Miller BT, Shao Y, Kong J, Neck DV, Speybroeck VV, Waroquier M, Brooks BR (2011) Efficient calculation of QM/MM frequencies with the mobile block Hessian. J Chem Theory Comput 7:496–514

    Google Scholar 

  15. Hafner J, Zheng W (2009) Approximate normal mode analysis based on vibrational subsystem analysis with high accuracy and efficiency. J Chem Phys 130:194111

    Article  PubMed  CAS  Google Scholar 

  16. Ghysels A, Speybroeck VV, Pauwels E, Catak S, Brooks BR, Neck DV, Waroquier M (2010) Comparative study of various normal mode analysis techniques based on partial Hessians. J Comput Chem 31:994–1007

    CAS  PubMed  PubMed Central  Google Scholar 

  17. 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

    CAS  Google Scholar 

  18. 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

    Article  CAS  PubMed  Google Scholar 

  19. Fedorov DG, Nagata T, Kitaura K (2012) Exploring chemistry with the fragment molecular orbital method. Phys Chem Chem Phys 14:7562–7577

    Article  CAS  PubMed  Google Scholar 

  20. Tanaka S, Mochizuki Y, Komeiji Y, Okiyama Y, Fukuzawa K (2014) Electron-correlated fragment-molecular-orbital calculations for biomolecular and nano systems. Phys Chem Chem Phys 16:10310–10344

    Article  CAS  PubMed  Google Scholar 

  21. Fedorov DG (2017) The fragment molecular orbital method: theoretical development, implementation in gamess, and applications. CMS WIREs 7:e1322

    Google Scholar 

  22. Fedorov DG, Asada N, Nakanishi I, Kitaura K (2014) The use of many-body expansions and geometry optimizations in fragment-based methods. Acc Chem Res 47:2846–2856

    CAS  PubMed  Google Scholar 

  23. Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JJ, Koseki S, Matsunaga N, Nguyen KA, Su S, Windus TL, Dupuis M, Montgomery JA (1993) General atomic and molecular electronic structure system. J Comput Chem 14:1347–1363

    Article  CAS  Google Scholar 

  24. Nakata H, Nagata T, Fedorov DG, Yokojima S, Kitaura K, Nakamura S (2013) Analytic second derivatives of the energy in the fragment molecular orbital method. J Chem Phys 138:164103

    Article  PubMed  CAS  Google Scholar 

  25. Green MC, Nakata H, Fedorov DG, Slipchenko LV (2016) Radical damage in lipids investigated with the fragment molecular orbital method. Chem Phys Lett 651:56–61

    Article  CAS  Google Scholar 

  26. Nakata H, Fedorov DG, Yokojima S, Kitaura K, Nakamura S (2014) Efficient vibrational analysis for unrestricted Hartree-Fock based on the fragment molecular orbital method. Chem Phys Lett 603:67–74

    Article  CAS  Google Scholar 

  27. Nakata H, Fedorov DG, Zahariev F, Schmidt MW, Kitaura K, Gordon MS, Nakamura S (2015) Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method. J Chem Phys 142:124101

    Article  PubMed  CAS  Google Scholar 

  28. Nishimoto Y, Fedorov DG, Irle S (2014) Density-functional tight-binding combined with the fragment molecular orbital method. J Chem Theory Comput 10:4801–4812

    Article  CAS  PubMed  Google Scholar 

  29. Nishimoto Y, Nakata H, Fedorov DG, Irle S (2015) Large-scale quantum-mechanical molecular dynamics simulations using density-functional tight-binding combined with the fragment molecular orbital method. J Phys Chem Lett 6:5034–5039

    Article  CAS  PubMed  Google Scholar 

  30. Nakata H, Nishimoto Y, Fedorov DG (2016) Analytic second derivative of the energy for density-functional tight-binding combined with the fragment molecular orbital method. J Chem Phys 145:044113

    Article  PubMed  CAS  Google Scholar 

  31. Nishimoto Y, Fedorov DG (2017) Three-body expansion of the fragment molecular orbital method combined with density-functional tight-binding. J Comput Chem 38:406–418

    Article  CAS  PubMed  Google Scholar 

  32. Nakano T, Kaminuma T, Sato T, Fukuzawa K, Akiyama Y, Uebayasi M, Kitaura K (2002) Fragment molecular orbital method: use of approximate electrostatic potential. Chem Phys Lett 351:475–480

    Article  CAS  Google Scholar 

  33. Nagata T, Fedorov DG, Kitaura K (2010) Importance of the hybrid orbital operator derivative term for the energy gradient in the fragment molecular orbital method. Chem Phys Lett 492:302–308

    Article  CAS  Google Scholar 

  34. Nakano T, Kaminuma T, Sato T, Akiyama Y, Uebayasi M, Kitaura K (2000) Fragment molecular orbital method: application to polypeptides. Chem Phys Lett 318:614–618

    Article  CAS  Google Scholar 

  35. Fedorov DG, Jensen JH, Deka RC, Kitaura K (2008) Covalent bond fragmentation suitable to describe solids in the fragment molecular orbital method. J Phys Chem A 112:11808–11816

    Article  CAS  PubMed  Google Scholar 

  36. Nishimoto Y, Fedorov DG (2018) Adaptive frozen orbital treatment for the fragment molecular orbital method combined with density-functional tight-binding. J Chem Phys 148:064115

    Article  PubMed  CAS  Google Scholar 

  37. Yamaguchi Y, Schaefer HF III, Osamura Y, Goddard J (1994) A new dimension to quantum chemistry: analytical derivative methods in ab initio molecular electronic structure theory. Oxford University Press, New York

    Google Scholar 

  38. Nagata T, Brorsen K, Fedorov DG, Kitaura K, Gordon MS (2011) Fully analytic energy gradient in the fragment molecular orbital method. J Chem Phys 134:124115

    Article  PubMed  CAS  Google Scholar 

  39. Nagata T, Fedorov DG, Kitaura K (2009) Derivatives of the approximated electrostatic potentials in the fragment molecular orbital method. Chem Phys Lett 475:124–131

    Article  CAS  Google Scholar 

  40. Nagata T, Fedorov DG, Kitaura K (2012) Analytic gradient for the embedding potential with approximations in the fragment molecular orbital method. Chem Phys Lett 544:87–93

    Article  CAS  Google Scholar 

  41. Nakata H, Fedorov DG (2018) Analytic second derivatives for the efficient electrostatic embedding in the fragment molecular orbital method. J Comput Chem 39:2039–2050

    Google Scholar 

  42. Fedorov DG, Alexeev Y, Kitaura K (2011) Geometry optimization of the active site of a large system with the fragment molecular orbital method. J Phys Chem Lett 2:282–288

    Article  CAS  Google Scholar 

  43. Fedorov DG, Ishida T, Kitaura K (2005) Multilayer formulation of the fragment molecular orbital method (FMO). J Phys Chem A 109:2638–2646

    Article  CAS  PubMed  Google Scholar 

  44. Aikens CM, Webb SP, Bell RL, Fletcher GD, Schmidt MW, Gordon MS (2003) A derivation of the frozen-orbital unrestricted open-shell and restricted closed-shell second-order perturbation theory analytic gradient expressions. Theor Chem Acc 110:233–253

    Article  CAS  Google Scholar 

  45. Handy NC, Schaefer HF III (1984) On the evaluation of analytic energy derivatives for correlated wave functions. J Chem Phys 81:5031–5033

    Article  CAS  Google Scholar 

  46. Nagata T, Fedorov DG, Ishimura K, Kitaura K (2011) Analytic energy gradient for second-order Møller-Plesset perturbation theory based on the fragment molecular orbital method. J Chem Phys 135:044110

    Article  PubMed  CAS  Google Scholar 

  47. Fedorov DG, Kitaura K (2004) The importance of three-body terms in the fragment molecular orbital method. J Chem Phys 120:6832–6840

    Google Scholar 

  48. 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

    Google Scholar 

  49. Nakata H, Fedorov DG, Nagata T, Yokojima S, Ogata K, Kitaura K, Nakamura S (2012) Unrestricted Hartree-Fock based on the fragment molecular orbital method: energy and its analytic gradient. J Chem Phys 137:044110

    Article  PubMed  CAS  Google Scholar 

  50. Komornicki A, McIver JW (1979) An efficient abinitio method for computing infrared and Raman intensities: application to ethylene. J Chem Phys 70(4):2014–2016

    Article  CAS  Google Scholar 

  51. Bacskay GB, Saebø S, Taylor PR (1984) On the calculation of dipole moment and polarizability derivatives by the analytical energy gradient method: application to the formaldehyde molecule. Chem Phys 90:215–224

    Article  CAS  Google Scholar 

  52. Nakata H, Fedorov DG, Yokojima S, Kitaura K, Nakamura S (2014) Simulations of Raman spectra using the fragment molecular orbital method. J Chem Theory Comput 10(9):3689–3698

    Article  CAS  PubMed  Google Scholar 

  53. Jacob CR, Luber S, Reiher M (2009) Analysis of secondary structure effects on the IR and Raman spectra of polypeptides in terms of localized vibrations. J Phys Chem B 113(18):6558–6573

    Article  CAS  PubMed  Google Scholar 

  54. Weymuth T, Jacob CR, Reiher M (2010) A local-mode model for understanding the dependence of the extended amide III vibrations on protein secondary structure. J Phys Chem B 114:10649–10660

    Article  CAS  PubMed  Google Scholar 

  55. Weymuth T, Haag MP, Kiewisch K, Luber S, Schenk S, Jacob CR, Herrmann C, Neugebauer J, Reiher M (2012) Movipac: vibrational spectroscopy with a robust meta-program for massively parallel standard and inverse calculations. J Comput Chem 33:2186–2198

    Article  CAS  PubMed  Google Scholar 

  56. Nakata H, Fedorov DG, Nagata T, Kitaura K, Nakamura S (2015) Simulations of chemical reactions with the frozen domain formulation of the fragment molecular orbital method. J Chem Theory Comput 11:3053–3064

    Article  CAS  PubMed  Google Scholar 

  57. Albery WJ, Knowles JR (1976) Free-energy profile for the reaction catalyzed by triosephosphate isomerase. Biochemistry 15:5627–5631

    Article  CAS  PubMed  Google Scholar 

  58. Zhang Y, Liu H, Yang W (2000) Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface. J Chem Phys 112:3483–3492

    Article  CAS  Google Scholar 

  59. Ishida T, Fedorov DG, Kitaura K (2006) All electron quantum chemical calculation of the entire enzyme system confirms a collective catalytic device in the chorismate mutase reaction. J Phys Chem B 110:1457–1463

    Article  CAS  PubMed  Google Scholar 

  60. Ito M, Brinck T (2014) Novel approach for identifying key residues in enzymatic reactions: proton abstraction in ketosterbid isomerase. J Phys Chem B 118:13050–13058

    Article  CAS  PubMed  Google Scholar 

  61. Jensen JH, Willemos M, Winther JR, De Vico L (2014) In silico prediction of mutant HIV-1 proteases cleaving a target sequence. PLoS ONE 9:e95833

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  62. Fedorov DG, Kitaura K (2007) Pair interaction energy decomposition analysis. J Comput Chem 28:222–237

    Article  CAS  PubMed  Google Scholar 

  63. Ahmed Z, Beta IA, Mikhonin AV, Asher SA (2005) UV resonance Raman thermal unfolding study of Trp-cage shows that it is not a simple two-state miniprotein. J Am Chem Soc 127:10943–10950

    Article  CAS  PubMed  Google Scholar 

  64. Scott AP, Radom L (1996) Harmonic vibrational frequencies: an evaluation of Hartree-Fock, Møller-Plesset, quadratic configuration interaction, density functional theory, and semiempirical scale factors. J Phys Chem 100:16502–16513

    Article  CAS  Google Scholar 

  65. Grimme S, Antony J, Ehrlich S, Krieg H (2010) A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J Chem Phys 132:154104

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

This research used the computational resources of the Supercomputer system ITO in R.I.I.T at Kyushu University as a national joint-usage/research center.

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Authors and Affiliations

  1. Department of Fundamental Technology Research, Research and Development Center Kagoshima, Kyocera Corporation, 1-4 Kokubu Yamashita-cho, Kirishima-shi, Kagoshima, 899-4312, Japan

    Hiroya Nakata

  2. CD-FMat, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan

    Dmitri G. Fedorov

Authors
  1. Hiroya Nakata
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  2. Dmitri G. Fedorov
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Correspondence to Hiroya Nakata .

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Editors and Affiliations

  1. Department of Chemistry, Faculty of Science, Rikkyo University, Tokyo, Japan

    Yuji Mochizuki

  2. Graduate School of System Informatics, Kobe University, Kobe, Japan

    Shigenori Tanaka

  3. School of Pharmacy and Pharmaceutical Sciences, Hoshi University, Tokyo, Japan

    Kaori Fukuzawa

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Nakata, H., Fedorov, D.G. (2021). Development of the Analytic Second Derivatives for the Fragment Molecular Orbital Method. In: Mochizuki, Y., Tanaka, S., Fukuzawa, K. (eds) Recent Advances of the Fragment Molecular Orbital Method. Springer, Singapore. https://doi.org/10.1007/978-981-15-9235-5_22

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