Embedding Methods in Quantum Chemistry

Chapter

Abstract

An overview over different embedding schemes for electronic-structure calculations is given, with the main focus on methods used for molecular systems. The in-principle exact subsystem DFT formalism is used as a reference point to classify the different approaches according to their components of the exact embedding potential. Special attention is paid to recently proposed ideas from the field of density-based embedding and density matrix reconstruction approaches.

Keywords

Embedding methods Subsystem methods Fragmentation methods 

References

  1. 1.
    M.S. Gordon, L.V. Slipchenko, Chem. Rev. 115, 5605–5606 (2015)CrossRefGoogle Scholar
  2. 2.
    A.V. Akimov, O.V. Prezhdo, Chem. Rev. 115, 5797–5890 (2015)CrossRefGoogle Scholar
  3. 3.
    K. Raghavachari, A. Saha, Chem. Rev. 115, 5643–5677 (2015)CrossRefGoogle Scholar
  4. 4.
    M.A. Collins, R.P.A. Bettens, Chem. Rev. 115, 5607–5642 (2015)CrossRefGoogle Scholar
  5. 5.
    L.W. Chung, W.M.C. Sameera, R. Ramozzi, A.J. Page, M. Hatanaka, G.P. Petrova, T.V. Harris, X. Li, Z. Ke, F. Liu, H.-B. Li, L. Ding, K. Morokuma, Chem. Rev. 115, 5678–5796 (2015)CrossRefGoogle Scholar
  6. 6.
    T.A. Wesołowski, S. Shedge, X. Zhou, Chem. Rev. 115, 5891–5928 (2015)CrossRefGoogle Scholar
  7. 7.
    E. Brunk, U. Rothlisberger, Chem. Rev. 115, 6217–6263 (2015)CrossRefGoogle Scholar
  8. 8.
    P. Huang, E.A. Carter, Annu. Rev. Phys. Chem. 59, 261–290 (2008)CrossRefGoogle Scholar
  9. 9.
    A.S.P. Gomes, C.R. Jacob, Annu. Rep. Prog. Chem. C 108, 222–277 (2012)CrossRefGoogle Scholar
  10. 10.
    C.R. Jacob, J. Neugebauer, WIREs Comput. Mol. Sci. 4, 325–362 (2014)CrossRefGoogle Scholar
  11. 11.
    Q. Sun, G.K.-L. Chan, Acc. Chem. Res. (2016) (in press)Google Scholar
  12. 12.
    W. Li, S. Li, Y. Jiang, J. Phys. Chem. A 111, 2193–2199 (2007)CrossRefGoogle Scholar
  13. 13.
    M.S. Gordon, D.G. Fedorov, S.R. Pruitt, L.V. Slipchenko, Chem. Rev. 112, 632–672 (2012)CrossRefGoogle Scholar
  14. 14.
    A.M. Gao, D.W. Zhang, J.Z. Zhang, Y. Zhang, Chem. Phys. Lett. 394, 293–297 (2004)CrossRefGoogle Scholar
  15. 15.
    E. Suárez, N. Díaz, D. Suárez, J. Chem. Theory Comput. 5, 1667–1679 (2009)CrossRefGoogle Scholar
  16. 16.
    N.J. Mayhall, K. Raghavachari, J. Chem. Theory Comput. 8, 2669–2675 (2012)CrossRefGoogle Scholar
  17. 17.
    R.M. Richard, J.M. Herbert, J. Chem. Phys. 137, 064113 (2012)CrossRefGoogle Scholar
  18. 18.
    G. Senatore, K.R. Subbaswamy, Phys. Rev. B 34, 5754–5757 (1986)CrossRefGoogle Scholar
  19. 19.
    P. Cortona, Phys. Rev. B 44, 8454–8458 (1991)CrossRefGoogle Scholar
  20. 20.
    T.A. Wesołowski, J. Weber, Chem. Phys. Lett. 248, 71–76 (1996)CrossRefGoogle Scholar
  21. 21.
    T.A. Wesołowski, A. Warshel, J. Phys. Chem. 97, 8050–8053 (1993)CrossRefGoogle Scholar
  22. 22.
    B. Jeziorski, R. Moszynski, K. Szalewicz, Chem. Rev. 94, 1887–1930 (1994)CrossRefGoogle Scholar
  23. 23.
    P. Elliott, M.H. Cohen, A. Wasserman, K. Burke, J. Chem. Theory Comput. 5, 827–833 (2009)CrossRefGoogle Scholar
  24. 24.
    P. Elliott, K. Burke, M.H. Cohen, A. Wasserman, Phys. Rev. A 82, 024501 (2010)CrossRefGoogle Scholar
  25. 25.
    C. Huang, M. Pavone, E.A. Carter, J. Chem. Phys. 134, 154110 (2011)CrossRefGoogle Scholar
  26. 26.
    M.L. Connolly, Science 221, 709–713 (1983)CrossRefGoogle Scholar
  27. 27.
    M.L. Connolly, J. Appl. Crystallogr. 16, 548–558 (1983)CrossRefGoogle Scholar
  28. 28.
    J. Tomasi, B. Mennucci, R. Cammi, Chem. Rev. 105, 2999–3094 (2005)CrossRefGoogle Scholar
  29. 29.
    S. Miertuš, E. Scrocco, J. Tomasi, Chem. Phys. 55, 117–129 (1981)CrossRefGoogle Scholar
  30. 30.
    B. Mennucci, E. Cancès, J. Tomasi, J. Phys. Chem. B 101, 10506–10517 (1997)CrossRefGoogle Scholar
  31. 31.
    V. Barone, M. Cossi, J. Phys. Chem. A 102, 1995–2001 (1998)CrossRefGoogle Scholar
  32. 32.
    B. Mennucci, WIREs Comput. Mol. Sci. 2, 386–404 (2012)CrossRefGoogle Scholar
  33. 33.
    A. Klamt, G. Schüürmann, J. Chem. Soc., Perkin Trans. 2, 799–805 (1993)CrossRefGoogle Scholar
  34. 34.
    E.V. Stefanovich, T.N. Truong, Chem. Phys. Lett. 244, 65–74 (1995)CrossRefGoogle Scholar
  35. 35.
    A. Klamt, J. Phys. Chem. 99, 2224–2235 (1995)CrossRefGoogle Scholar
  36. 36.
    A. Klamt, WIREs Comput. Mol. Sci. 1, 699–709 (2011)CrossRefGoogle Scholar
  37. 37.
    S.-T. Lin, S.I. Sandler, Ind. Eng. Chem. Res. 41, 899–913 (2002)CrossRefGoogle Scholar
  38. 38.
    A. Klamt, J. Phys. Chem. 100, 3349–3353 (1996)CrossRefGoogle Scholar
  39. 39.
    S. Sinnecker, A. Rajendran, A. Klamt, M. Diedenhofen, F. Neese, J. Phys. Chem. A 110, 2235–2245 (2006)CrossRefGoogle Scholar
  40. 40.
    T. Sachsenhauser, S. Rehfeldt, A. Klamt, F. Eckert, H. Klein, Fluid Phase Equilibr. 382, 89–99 (2014)CrossRefGoogle Scholar
  41. 41.
    A. Klamt, J. Phys. Chem. A 120, 2049–2056 (2016)CrossRefGoogle Scholar
  42. 42.
    E. Cancès, Y. Maday, B. Stamm, J. Chem. Phys. 139, 054111 (2013)CrossRefGoogle Scholar
  43. 43.
    F. Lipparini, B. Stamm, E. Cancès, Y. Maday, B. Mennucci, J. Chem. Theory Comput. 9, 3637–3648 (2013)CrossRefGoogle Scholar
  44. 44.
    F. Lipparini, L. Lagardère, G. Scalmani, B. Stamm, E. Cancès, Y. Maday, J.-P. Piquemal, M.J. Frisch, B. Mennucci, J. Phys. Chem. Lett. 5, 953–958 (2014)CrossRefGoogle Scholar
  45. 45.
    F. Lipparini, G. Scalmani, L. Lagardère, B. Stamm, E. Cancès, Y. Maday, J.-P. Piquemal, M.J. Frisch, B. Mennucci, J. Chem. Phys. 141, 184108 (2014)CrossRefGoogle Scholar
  46. 46.
    A. Goez, J. Neugebauer, J. Chem. Theory Comput. 11, 5277–5290 (2015)CrossRefGoogle Scholar
  47. 47.
    D.M. Chipman, J. Chem. Phys. 106, 10194–10206 (1997)CrossRefGoogle Scholar
  48. 48.
    C.-G. Zhan, J. Bentley, D.M. Chipman, J. Chem. Phys. 108, 177–192 (1998)CrossRefGoogle Scholar
  49. 49.
    D.M. Chipman, J. Chem. Phys. 112, 5558–5565 (2000)CrossRefGoogle Scholar
  50. 50.
    E. Cancès, B. Mennucci, J. Chem. Phys. 114, 4744–4745 (2001)CrossRefGoogle Scholar
  51. 51.
    C.J. Cramer, D.G. Truhlar, J. Am. Chem. Soc. 113, 8552–8554 (1991)CrossRefGoogle Scholar
  52. 52.
    C.J. Cramer, D.G. Truhlar, Acc. Chem. Res. 41, 760–768 (2008)CrossRefGoogle Scholar
  53. 53.
    A.V. Marenich, C.J. Cramer, D.G. Truhlar, J. Chem. Theory Comput. 9, 609–620 (2013)CrossRefGoogle Scholar
  54. 54.
    A.V. Marenich, C.J. Cramer, D.G. Truhlar, J. Phys. Chem. B 113, 6378–6396 (2009)CrossRefGoogle Scholar
  55. 55.
    A.V. Marenich, R.M. Olson, C.P. Kelly, C.J. Cramer, D.G. Truhlar, J. Chem. Theory Comput. 3, 2011–2033 (2007)CrossRefGoogle Scholar
  56. 56.
    A. Warshel, M. Karplus, J. Am. Chem. Soc. 94, 5612–5625 (1972)CrossRefGoogle Scholar
  57. 57.
    A. Warshel, M. Levitt, J. Mol. Biol. 103, 227–249 (1976)CrossRefGoogle Scholar
  58. 58.
    H.M. Senn, W. Thiel, Angew. Chem. Int. Edit. 48, 1198–1229 (2009)CrossRefGoogle Scholar
  59. 59.
    T. Steinbrecher, M. Elstner, QM and QM/MM Simulations of Proteins, in Biomolecular Simulations: Methods and Protocols, ed. by L. Monticelli, E. Salonen (Humana Press, Totowa, NJ, 2013)Google Scholar
  60. 60.
    M.G. Quesne, T. Borowski, S.P. deVisser, Chem. Eur. J. 22, 2562–2581 (2016)Google Scholar
  61. 61.
    F. Maseras, K. Morokuma, J. Comput. Chem. 16, 1170–1179 (1995)CrossRefGoogle Scholar
  62. 62.
    M. Svensson, S. Humbel, R.D.J. Froese, T. Matsubara, S. Sieber, K. Morokuma, J. Phys. Chem. 100, 19357–19363 (1996)CrossRefGoogle Scholar
  63. 63.
    M. Svensson, S. Humbel, K. Morokuma, J. Chem. Phys. 105, 3654–3661 (1996)CrossRefGoogle Scholar
  64. 64.
    D. Bakowies, W. Thiel, J. Phys. Chem. 100, 10580–10594 (1996)CrossRefGoogle Scholar
  65. 65.
    T. Vreven, K.S. Byun, I. Komromi, S. Dapprich, J.A. Montgomery, K. Morokuma, M.J. Frisch, J. Chem. Theory Comput. 2, 815–826 (2006)CrossRefGoogle Scholar
  66. 66.
    S. Humbel, S. Sieber, K. Morokuma, J. Chem. Phys. 105, 1959–1967 (1996)CrossRefGoogle Scholar
  67. 67.
    P. Tao, J.F. Fisher, Q. Shi, T. Vreven, S. Mobashery, H.B. Schlegel, Biochemistry 48, 9839–9847 (2009)CrossRefGoogle Scholar
  68. 68.
    S. Caprasecca, S. Jurinovich, L. Viani, C. Curutchet, B. Mennucci, J. Chem. Theory Comput. 10, 1588–1598 (2014)CrossRefGoogle Scholar
  69. 69.
    S. Dapprich, I. Komromi, K. Byun, K. Morokuma, M.J. Frisch, J. Mol. Struct. Theochem 461–462, 1–21 (1999)CrossRefGoogle Scholar
  70. 70.
    T. Vreven, B. Mennucci, C.O. da Silva, K. Morokuma, J. Tomasi, J. Chem. Phys. 115, 62–72 (2001)CrossRefGoogle Scholar
  71. 71.
    T. Kerdcharoen, K. Morokuma, Chem. Phys. Lett. 355, 257–262 (2002)CrossRefGoogle Scholar
  72. 72.
    B.W. Hopkins, G.S. Tschumper, J. Comput. Chem. 24, 1563–1568 (2003)CrossRefGoogle Scholar
  73. 73.
    L.W. Chung, H. Hirao, X. Li, K. Morokuma, WIREs Comput. Mol. Sci. 2, 327–350 (2012)CrossRefGoogle Scholar
  74. 74.
    M. Swart, F.M. Bickelhaupt, J. Comput. Chem. 29, 724–734 (2008)CrossRefGoogle Scholar
  75. 75.
    V. Luzhkov, A. Warshel, J. Am. Chem. Soc. 113, 4491–4499 (1991)CrossRefGoogle Scholar
  76. 76.
    V. Luzhkov, A. Warshel, J. Comput. Chem. 13, 199–213 (1992)CrossRefGoogle Scholar
  77. 77.
    M.A. Thompson, G.K. Schenter, J. Phys. Chem. 99, 6374–6386 (1995)CrossRefGoogle Scholar
  78. 78.
    M.A. Thompson, J. Phys. Chem. 100, 14492–14507 (1996)CrossRefGoogle Scholar
  79. 79.
    C. Curutchet, A. Muñoz-Losa, S. Monti, J. Kongsted, G.D. Scholes, B. Mennucci, J. Chem. Theory Comput. 5, 1838–1848 (2009)CrossRefGoogle Scholar
  80. 80.
    S. Caprasecca, C. Curutchet, B. Mennucci, J. Chem. Theory Comput. 8, 4462–4473 (2012)CrossRefGoogle Scholar
  81. 81.
    Q. Zeng, W. Liang, J. Chem. Phys. 143, 134104 (2015)CrossRefGoogle Scholar
  82. 82.
    J.H. Jensen, P.N. Day, M.S. Gordon, H. Basch, D. Cohen, D.R. Garmer, M. Kraus, W.J. Stevens, Effective fragment method for modeling intermolecular hydrogen-bonding effects on quantum mechanical calculations, in Modeling the Hydrogen Bond, ed. by D.A. Smith (American Chemical Society, Washington, DC, 1994), Chapter 10, pp. 139–151Google Scholar
  83. 83.
    P.N. Day, J.H. Jensen, M.S. Gordon, S.P. Webb, W.J. Stevens, M. Krauss, D. Garmer, H. Basch, D. Cohen, J. Chem. Phys. 105, 1968–1986 (1996)CrossRefGoogle Scholar
  84. 84.
    M.S. Gordon, M.A. Freitag, P. Bandyopadhyay, J.H. Jensen, V. Kairys, W.J. Stevens, J. Phys. Chem. A 105, 293–307 (2001)CrossRefGoogle Scholar
  85. 85.
    L.V. Slipchenko, M.S. Gordon, J. Comput. Chem. 28, 276–291 (2007)CrossRefGoogle Scholar
  86. 86.
    M.A. Freitag, M.S. Gordon, J.H. Jensen, W.J. Stevens, J. Chem. Phys. 112, 7300–7306 (2000)CrossRefGoogle Scholar
  87. 87.
    L.V. Slipchenko, M.S. Gordon, Mol. Phys. 107, 999–1016 (2009)CrossRefGoogle Scholar
  88. 88.
    I. Adamovic, M.S. Gordon, Mol. Phys. 103, 379–387 (2005)CrossRefGoogle Scholar
  89. 89.
    J.H. Jensen, J. Chem. Phys. 114, 8775–8783 (2001)CrossRefGoogle Scholar
  90. 90.
    H. Li, M.S. Gordon, J.H. Jensen, J. Chem. Phys. 124, 214108 (2006)CrossRefGoogle Scholar
  91. 91.
    M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comput. Chem. 14, 1347–1363 (1993)CrossRefGoogle Scholar
  92. 92.
    M.S. Gordon, M.W. Schmidt, Advances in electronic structure theory: GAMESS a decade later, in Theory and Applications of Computational Chemistry, ed. by C.E. Dykstra, G. Frenking, K.S. Kim, G.E. Scuseria (Elsevier, Amsterdam, 2005)Google Scholar
  93. 93.
    H. Li, H.M. Netzloff, M.S. Gordon, J. Chem. Phys. 125, 194103 (2006)CrossRefGoogle Scholar
  94. 94.
    H. Li, M.S. Gordon, Theor. Chem. Acc. 115, 385–390 (2006)CrossRefGoogle Scholar
  95. 95.
    P. Arora, L.V. Slipchenko, S.P. Webb, A. DeFusco, M.S. Gordon, J. Phys. Chem. A 114, 6742–6750 (2010)CrossRefGoogle Scholar
  96. 96.
    C.H. Choi, S. Re, M. Feig, Y. Sugita, Chem. Phys. Lett. 539–540, 218–221 (2012)CrossRefGoogle Scholar
  97. 97.
    D.D. Kemp, J.M. Rintelman, M.S. Gordon, J.H. Jensen, Theor. Chem. Acc. 125, 481–491 (2010)CrossRefGoogle Scholar
  98. 98.
    Q.A. Smith, K. Ruedenberg, M.S. Gordon, L.V. Slipchenko, J. Chem. Phys. 136, 244107 (2012)CrossRefGoogle Scholar
  99. 99.
    M.S. Gordon, Q.A. Smith, P. Xu, L.V. Slipchenko, Annu. Rev. Phys. Chem. 64, 553–578 (2013)CrossRefGoogle Scholar
  100. 100.
    V. Kairys, J.H. Jensen, J. Phys. Chem. A 104, 6656–6665 (2000)CrossRefGoogle Scholar
  101. 101.
    P.K. Gurunathan, A. Acharya, D. Ghosh, D. Kosenkov, I. Kaliman, Y. Shao, A.I. Krylov, L.V. Slipchenko, J. Phys. Chem. B 120, 6562–6574 (2016)CrossRefGoogle Scholar
  102. 102.
    C. Steinmann, D.G. Fedorov, J.H. Jensen, J. Phys. Chem. A 114, 8705–8712 (2010)CrossRefGoogle Scholar
  103. 103.
    S.R. Pruitt, C. Steinmann, J.H. Jensen, M.S. Gordon, J. Chem. Theory Comput. 9, 2235–2249 (2013)CrossRefGoogle Scholar
  104. 104.
    J.M. Olsen, K. Aidas, J. Kongsted, J. Chem. Theory Comput. 6, 3721–3734 (2010)CrossRefGoogle Scholar
  105. 105.
    L. Gagliardi, R. Lindh, G. Karlström, J. Chem. Phys. 121, 4494–4500 (2004)CrossRefGoogle Scholar
  106. 106.
    J.M.H. Olsen, J. Kongsted, Molecular properties through polarizable embedding, in Advances in Quantum Chemistry, ed. by J.R. Sabin, E. Brändas, vol. 61 (Academic Press, New York, 2011)Google Scholar
  107. 107.
    K. Sneskov, T. Schwabe, J. Kongsted, O. Christiansen, J. Chem. Phys. 134, 104108 (2011)CrossRefGoogle Scholar
  108. 108.
    T. Schwabe, K. Sneskov, J.M.H. Olsen, J. Kongsted, O. Christiansen, C. Hättig, J. Chem. Theory Comput. 8, 3274–3283 (2012)CrossRefGoogle Scholar
  109. 109.
    E.D. Hedegård, N.H. List, H.J.A. Jensen, J. Kongsted, J. Chem. Phys. 139, 044101 (2013)CrossRefGoogle Scholar
  110. 110.
    E.D. Hedegård, M. Reiher, J. Chem. Theory Comput. 12, 4242–4253 (2016)CrossRefGoogle Scholar
  111. 111.
    N.H. List, M.T.P. Beerepoot, J.M.H. Olsen, B. Gao, K. Ruud, H.J.A. Jensen, J. Kongsted, J. Chem. Phys. 142, 034119 (2015)CrossRefGoogle Scholar
  112. 112.
    N.H. List, J.M.H. Olsen, J. Kongsted, Phys. Chem. Chem. Phys. 18, 20234–20250 (2016)CrossRefGoogle Scholar
  113. 113.
    J.M.H. Olsen, C. Steinmann, K. Ruud, J. Kongsted, J. Phys. Chem. A 119, 5344–5355 (2015)CrossRefGoogle Scholar
  114. 114.
    D.W. Zhang, J.Z.H. Zhang, J. Chem. Phys. 119, 3599–3605 (2003)CrossRefGoogle Scholar
  115. 115.
    X. He, J.Z.H. Zhang, J. Chem. Phys. 122, 031103 (2005)CrossRefGoogle Scholar
  116. 116.
    X. Chen, Y. Zhang, J.Z.H. Zhang, J. Chem. Phys. 122, 184105 (2005)CrossRefGoogle Scholar
  117. 117.
    C.R. Jacob, L. Visscher, J. Chem. Phys. 128, 155102 (2008)CrossRefGoogle Scholar
  118. 118.
    P. Söderhjelm, U. Ryde, J. Phys. Chem. A 113, 617–627 (2009)CrossRefGoogle Scholar
  119. 119.
    X.H. Chen, D.W. Zhang, J.Z.H. Zhang, J. Chem. Phys. 120, 839–844 (2004)CrossRefGoogle Scholar
  120. 120.
    S. Li, W. Li, T. Fang, J. Am. Chem. Soc. 127, 7215–7226 (2005)CrossRefGoogle Scholar
  121. 121.
    X.H. Chen, J.Z.H. Zhang, J. Chem. Phys. 125, 044903 (2006)CrossRefGoogle Scholar
  122. 122.
    N. Jiang, J. Ma, Y. Jiang, J. Chem. Phys. 124, 114112 (2006)CrossRefGoogle Scholar
  123. 123.
    X. He, J.Z.H. Zhang, J. Chem. Phys. 124, 184703 (2006)CrossRefGoogle Scholar
  124. 124.
    X. Wang, J. Liu, J.Z.H. Zhang, X. He, J. Phys. Chem. A 117, 7149–7161 (2013)CrossRefGoogle Scholar
  125. 125.
    Y. Mei, C. Ji, J.Z.H. Zhang, J. Chem. Phys. 125, 094906 (2006)CrossRefGoogle Scholar
  126. 126.
    X. Jia, X. Wang, J. Liu, J.Z.H. Zhang, Y. Mei, X. He, J. Chem. Phys. 139, 214104 (2013)CrossRefGoogle Scholar
  127. 127.
    J. Liu, J.Z.H. Zhang, X. He, Phys. Chem. Chem. Phys. 18, 1864–1875 (2016)CrossRefGoogle Scholar
  128. 128.
    J. Liu, T. Zhu, X. Wang, X. He, J.Z.H. Zhang, J. Chem. Theory Comput. 11, 5897–5905 (2015)CrossRefGoogle Scholar
  129. 129.
    C. Ji, Y. Mei, J.Z.H. Zhang, Biophys. J. 95, 1080–1088 (2008)CrossRefGoogle Scholar
  130. 130.
    W. Hua, T. Fang, W. Li, J.-G. Yu, S. Li, J. Phys. Chem. A 112, 10864–10872 (2008)CrossRefGoogle Scholar
  131. 131.
    S. Hua, W. Hua, S. Li, J. Phys. Chem. A 114, 8126–8134 (2010)CrossRefGoogle Scholar
  132. 132.
    S. Hua, W. Li, S. Li, ChemPhysChem 14, 108–115 (2013)CrossRefGoogle Scholar
  133. 133.
    H. Li, W. Li, S. Li, J. Ma, J. Phys. Chem. B 112, 7061–7070 (2008)CrossRefGoogle Scholar
  134. 134.
    T. Fang, W. Li, F. Gu, S. Li, J. Chem. Theory Comput. 11, 91–98 (2015)CrossRefGoogle Scholar
  135. 135.
    S. Li, W. Li, J. Ma, Acc. Chem. Res. 47, 2712–2720 (2014)CrossRefGoogle Scholar
  136. 136.
    K. Kitaura, E. Ikeo, T. Asada, T. Nakano, M. Uebayasi, Chem. Phys. Lett. 313, 701–706 (1999)CrossRefGoogle Scholar
  137. 137.
    K. Kitaura, T. Sawai, T. Asada, T. Nakano, M. Uebayasi, Chem. Phys. Lett. 312, 319–324 (1999)CrossRefGoogle Scholar
  138. 138.
    T. Nakano, T. Kaminuma, T. Sato, Y. Akiyama, M. Uebayasi, K. Kitaura, Chem. Phys. Lett. 318, 614–618 (2000)CrossRefGoogle Scholar
  139. 139.
    D.G. Fedorov, J.H. Jensen, R.C. Deka, K. Kitaura, J. Phys. Chem. A 112, 11808–11816 (2008)CrossRefGoogle Scholar
  140. 140.
    D.G. Fedorov, T. Ishida, K. Kitaura, J. Phys. Chem. A 109, 2638–2646 (2005)CrossRefGoogle Scholar
  141. 141.
    D.G. Fedorov, K. Kitaura (eds.), The Fragment Molecular Orbital Method: Practical Applications to Large Molecular Systems (CRC Press, Boca Raton, FL, 2009)Google Scholar
  142. 142.
    D.G. Fedorov, K. Kitaura, J. Chem. Phys. 120, 6832–6840 (2004)CrossRefGoogle Scholar
  143. 143.
    T. Nakano, Y. Mochizuki, K. Yamashita, C. Watanabe, K. Fukuzawa, K. Segawa, Y. Okiyama, T. Tsukamoto, S. Tanaka, Chem. Phys. Lett. 523, 128–133 (2012)CrossRefGoogle Scholar
  144. 144.
    T. Nakano, T. Kaminuma, T. Sato, K. Fukuzawa, Y. Akiyama, M. Uebayasi, K. Kitaura, Chem. Phys. Lett. 351, 475–480 (2002)CrossRefGoogle Scholar
  145. 145.
    D.G. Fedorov, L.V. Slipchenko, K. Kitaura, J. Phys. Chem. A 114, 8742–8753 (2010)CrossRefGoogle Scholar
  146. 146.
    D.G. Fedorov, K. Kitaura, Chem. Phys. Lett. 433, 182–187 (2006)CrossRefGoogle Scholar
  147. 147.
    D.G. Fedorov, K. Kitaura, J. Chem. Phys. 131, 171106 (2009)CrossRefGoogle Scholar
  148. 148.
    Y. Inadomi, T. Nakano, K. Kitaura, U. Nagashima, Chem. Phys. Lett. 364, 139–143 (2002)CrossRefGoogle Scholar
  149. 149.
    S. Sugiki, N. Kurita, Y. Sengoku, H. Sekino, Chem. Phys. Lett. 382, 611–617 (2003)CrossRefGoogle Scholar
  150. 150.
    D.G. Fedorov, K. Kitaura, J. Chem. Phys. 121, 2483–2490 (2004)CrossRefGoogle Scholar
  151. 151.
    D.G. Fedorov, K. Kitaura, J. Chem. Phys. 123, 134103 (2005)CrossRefGoogle Scholar
  152. 152.
    D.G. Fedorov, K. Kitaura, J. Chem. Phys. 122, 054108 (2005)CrossRefGoogle Scholar
  153. 153.
    Y. Nishimoto, D.G. Fedorov, S. Irle, J. Chem. Theory Comput. 10, 4801–4812 (2014)CrossRefGoogle Scholar
  154. 154.
    Y. Nishimoto, D.G. Fedorov, S. Irle, Chem. Phys. Lett. 636, 90–96 (2015)CrossRefGoogle Scholar
  155. 155.
    K. Kitaura, S.-I. Sugiki, T. Nakano, Y. Komeiji, M. Uebayasi, Chem. Phys. Lett. 336, 163–170 (2001)CrossRefGoogle Scholar
  156. 156.
    T. Nagata, K. Brorsen, D.G. Fedorov, K. Kitaura, M.S. Gordon, J. Chem. Phys. 134, 124115 (2011)CrossRefGoogle Scholar
  157. 157.
    D.G. Fedorov, T. Ishida, M. Uebayasi, K. Kitaura, J. Phys. Chem. A 111, 2722–2732 (2007)CrossRefGoogle Scholar
  158. 158.
    Y. Komeiji, T. Nakano, K. Fukuzawa, Y. Ueno, Y. Inadomi, T. Nemoto, M. Uebayasi, D.G. Fedorov, K. Kitaura, Chem. Phys. Lett. 372, 342–347 (2003)CrossRefGoogle Scholar
  159. 159.
    Y. Komeiji, Y. Mochizuki, T. Nakano, D.G. Fedorov, J. Mol. Struct. Theochem 898, 2–7 (2009)CrossRefGoogle Scholar
  160. 160.
    D.G. Fedorov, K. Kitaura, H. Li, J.H. Jensen, M.S. Gordon, J. Comput. Chem. 27, 976–985 (2006)CrossRefGoogle Scholar
  161. 161.
    T. Fujita, T. Nakano, S. Tanaka, Chem. Phys. Lett. 506, 112–116 (2011)CrossRefGoogle Scholar
  162. 162.
    Y. Mochizuki, S. Koikegami, S. Amari, K. Segawa, K. Kitaura, T. Nakano, Chem. Phys. Lett. 406, 283–288 (2005)CrossRefGoogle Scholar
  163. 163.
    M. Chiba, D.G. Fedorov, K. Kitaura, Chem. Phys. Lett. 444, 346–350 (2007)CrossRefGoogle Scholar
  164. 164.
    D.G. Fedorov, K. Kitaura, J. Phys. Chem. A 111, 6904–6914 (2007)CrossRefGoogle Scholar
  165. 165.
    D.G. Fedorov, T. Nagata, K. Kitaura, Phys. Chem. Chem. Phys. 14, 7562–7577 (2012)CrossRefGoogle Scholar
  166. 166.
    T. Nagata, D.G. Fedorov, K. Kitaura, M.S. Gordon, J. Chem. Phys. 131, 024101 (2009)CrossRefGoogle Scholar
  167. 167.
    S. Hirata, M. Valiev, M. Dupuis, S.S. Xantheas, S. Sugiki, H. Sekino, Mol. Phys. 103, 2255–2265 (2005)CrossRefGoogle Scholar
  168. 168.
    M. Kamiya, S. Hirata, M. Valiev, J. Chem. Phys. 128, 074103 (2008)CrossRefGoogle Scholar
  169. 169.
    E.E. Dahlke, D.G. Truhlar, J. Chem. Theory Comput. 3, 46–53 (2007)CrossRefGoogle Scholar
  170. 170.
    G.J.O. Beran, J. Chem. Phys. 130, 164115 (2009)CrossRefGoogle Scholar
  171. 171.
    S.R. Gadre, R.N. Shirsat, A.C. Limaye, J. Phys. Chem. 98, 9165–9169 (1994)CrossRefGoogle Scholar
  172. 172.
    K. Babu, S.R. Gadre, J. Comput. Chem. 24, 484–495 (2003)CrossRefGoogle Scholar
  173. 173.
    V. Ganesh, R.K. Dongare, P. Balanarayan, S.R. Gadre, J. Chem. Phys. 125, 104109 (2006)CrossRefGoogle Scholar
  174. 174.
    N. Sahu, S.R. Gadre, Acc. Chem. Res. 47, 2739–2747 (2014)CrossRefGoogle Scholar
  175. 175.
    A.P. Rahalkar, V. Ganesh, S.R. Gadre, J. Chem. Phys. 129, 234101 (2008)CrossRefGoogle Scholar
  176. 176.
    A.P. Rahalkar, M. Katouda, S.R. Gadre, S. Nagase, J. Comput. Chem. 31, 2405–2418 (2010)Google Scholar
  177. 177.
    J.P. Furtado, A.P. Rahalkar, S. Shanker, P. Bandyopadhyay, S.R. Gadre, J. Phys. Chem. Lett. 3, 2253–2258 (2012)CrossRefGoogle Scholar
  178. 178.
    N. Sahu, S.R. Gadre, J. Chem. Phys. 142, 014107 (2015)CrossRefGoogle Scholar
  179. 179.
    N. Sahu, S.R. Gadre, J. Chem. Phys. 144, 114113 (2016)CrossRefGoogle Scholar
  180. 180.
    N. Sahu, G. Singh, A. Nandi, S.R. Gadre, J. Phys. Chem. A 120, 5706–5714 (2016)CrossRefGoogle Scholar
  181. 181.
    M. Isegawa, B. Wang, D.G. Truhlar, J. Chem. Theory Comput. 9, 1381–1393 (2013)CrossRefGoogle Scholar
  182. 182.
    A.P. Rahalkar, S.D. Yeole, V. Ganesh, S.R. Gadre, Molecular tailoring: an art of the possible for ab initio treatment of large molecules and molecular clusters, in Linear-Scaling Techniques in Computational Chemistry and Physics: Methods and Applications, ed. by R. Zalesny, M.G. Papadopoulos, P.G. Mezey, J. Leszczynski (Springer, Netherlands, Dordrecht, 2011)Google Scholar
  183. 183.
    L. Huang, L. Massa, J. Karle, Int. J. Quantum Chem. 103, 808–817 (2005)CrossRefGoogle Scholar
  184. 184.
    L. Huang, L. Massa, J. Karle, Biochemistry 44, 16747–16752 (2005)CrossRefGoogle Scholar
  185. 185.
    L. Huang, L. Massa, J. Karle, Proc. Natl. Acad. Sci. USA 105, 1849–1854 (2008)CrossRefGoogle Scholar
  186. 186.
    V. Deev, M.A. Collins, J. Chem. Phys. 122, 154102 (2005)CrossRefGoogle Scholar
  187. 187.
    M.A. Collins, V.A. Deev, J. Chem. Phys. 125, 104104 (2006)CrossRefGoogle Scholar
  188. 188.
    L. Huang, L. Massa, Int. J. Quantum Chem. 111, 2180–2186 (2011)CrossRefGoogle Scholar
  189. 189.
    L. Huang, H.J. Bohorquez, C.F. Matta, L. Massa, Int. J. Quantum Chem. 111, 4150–4157 (2011)CrossRefGoogle Scholar
  190. 190.
    L. Huang, L. Massa, J. Karle, Int. J. Quantum Chem. 106, 447–457 (2006)CrossRefGoogle Scholar
  191. 191.
    L. Huang, C. Matta, L. Massa, Struct. Chem. 26, 1433–1442 (2015)CrossRefGoogle Scholar
  192. 192.
    R.M. Richard, J.M. Herbert, J. Chem. Theory Comput. 9, 1408–1416 (2013)CrossRefGoogle Scholar
  193. 193.
    J.M. Mullin, L.B. Roskop, S.R. Pruitt, M.A. Collins, M.S. Gordon, J. Phys. Chem. A 113, 10040–10049 (2009)CrossRefGoogle Scholar
  194. 194.
    M.A. Collins, Phys. Chem. Chem. Phys. 14, 7744–7751 (2012)CrossRefGoogle Scholar
  195. 195.
    H.-A. Le, H.-J. Tan, J.F. Ouyang, R.P.A. Bettens, J. Chem. Theory Comput. 8, 469–478 (2012)CrossRefGoogle Scholar
  196. 196.
    M.A. Collins, M.W. Cvitkovic, R.P.A. Bettens, Acc. Chem. Res. 47, 2776–2785 (2014)CrossRefGoogle Scholar
  197. 197.
    J. Řezáč, D.R. Salahub, J. Chem. Theory Comput. 6, 91–99 (2010)CrossRefGoogle Scholar
  198. 198.
    N.J. Mayhall, K. Raghavachari, J. Chem. Theory Comput. 7, 1336–1343 (2011)CrossRefGoogle Scholar
  199. 199.
    K.V.J. Jose, K. Raghavachari, J. Chem. Theory Comput. 11, 950–961 (2015)CrossRefGoogle Scholar
  200. 200.
    K.V.J. Jose, D. Beckett, K. Raghavachari, J. Chem. Theory Comput. 11, 4238–4247 (2015)CrossRefGoogle Scholar
  201. 201.
    K.V.J. Jose, K. Raghavachari, Mol. Phys. 113, 3057–3066 (2015)CrossRefGoogle Scholar
  202. 202.
    K.V.J. Jose, K. Raghavachari, J. Chem. Theory Comput. 12, 585–594 (2016)CrossRefGoogle Scholar
  203. 203.
    W. Yang, Phys. Rev. Lett. 66, 1438–1441 (1991)CrossRefGoogle Scholar
  204. 204.
    W. Yang, T. Lee, J. Chem. Phys. 103, 5674–5678 (1995)CrossRefGoogle Scholar
  205. 205.
    W. Yang, Phys. Rev. A 44, 7823–7826 (1991)CrossRefGoogle Scholar
  206. 206.
    S.L. Dixon, K.M. Merz, J. Chem. Phys. 104, 6643–6649 (1996)CrossRefGoogle Scholar
  207. 207.
    S.L. Dixon, K.M. Merz, J. Chem. Phys. 107, 879–893 (1997)CrossRefGoogle Scholar
  208. 208.
    T. Lee, D.M. York, W. Yang, J. Chem. Phys. 105, 2744–2750 (1996)CrossRefGoogle Scholar
  209. 209.
    P.D. Walker, P.G. Mezey, J. Am. Chem. Soc. 115, 12423–12430 (1993)CrossRefGoogle Scholar
  210. 210.
    P.G. Mezey, Local-shape analysis of macromolecular electron densities, in Computational Chemistry: Reviews of Current Trends (World Scientific Publishing, Singapore, 1996)Google Scholar
  211. 211.
    P.G. Mezey, J. Math. Chem. 18, 141–168 (1995)CrossRefGoogle Scholar
  212. 212.
    T.E. Exner, P.G. Mezey, J. Phys. Chem. A 108, 4301–4309 (2004)CrossRefGoogle Scholar
  213. 213.
    W. Li, S. Li, J. Chem. Phys. 121, 6649–6657 (2004)CrossRefGoogle Scholar
  214. 214.
    T. Akama, M. Kobayashi, H. Nakai, J. Comput. Chem. 28, 2003–2012 (2007)CrossRefGoogle Scholar
  215. 215.
    M. Kobayashi, T. Akama, H. Nakai, J. Chem. Phys. 125, 204106 (2006)CrossRefGoogle Scholar
  216. 216.
    M. Kobayashi, Y. Imamura, H. Nakai, J. Chem. Phys. 127, 074103 (2007)CrossRefGoogle Scholar
  217. 217.
    M. Kobayashi, H. Nakai, J. Chem. Phys. 129, 044103 (2008)CrossRefGoogle Scholar
  218. 218.
    M. Kobayashi, H. Nakai, J. Chem. Phys. 131, 114108 (2009)CrossRefGoogle Scholar
  219. 219.
    M. Kobayashi, H. Nakai, Int. J. Quantum Chem. 109, 2227–2237 (2009)CrossRefGoogle Scholar
  220. 220.
    G.-L. Song, Z.H. Li, Z.-P. Liu, X.-M. Cao, W. Wang, K.-N. Fan, Y. Xie, H.F. Schaefer, J. Chem. Theory Comput. 4, 2049–2056 (2008)CrossRefGoogle Scholar
  221. 221.
    M. Guidon, J. Hutter, J. VandeVondele, J. Chem. Theory Comput. 6, 2348–2364 (2010)CrossRefGoogle Scholar
  222. 222.
    T. Touma, M. Kobayashi, H. Nakai, Chem. Phys. Lett. 485, 247–252 (2010)CrossRefGoogle Scholar
  223. 223.
    M. Kobayashi, T. Touma, H. Nakai, J. Chem. Phys. 136, 084108 (2012)CrossRefGoogle Scholar
  224. 224.
    T. Yoshikawa, H. Nakai, J. Comput. Chem. 36, 164–170 (2015)CrossRefGoogle Scholar
  225. 225.
    F. Shimojo, S. Hattori, R.K. Kalia, M. Kunaseth, W. Mou, A. Nakano, K.-I. Nomura, S. Ohmura, P. Rajak, K. Shimamura, P. Vashishta, J. Chem. Phys. 140, 18A529 (2014)CrossRefGoogle Scholar
  226. 226.
    H. Nishizawa, Y. Nishimura, M. Kobayashi, S. Irle, H. Nakai, J. Comput. Chem. 37, 1983–1992 (2016)CrossRefGoogle Scholar
  227. 227.
    M.E. Fornace, J. Lee, K. Miyamoto, F.R. Manby, T.F. Miller, J. Chem. Theory Comput. 11, 568–580 (2015)CrossRefGoogle Scholar
  228. 228.
    M. Kobayashi, H. Nakai, Phys. Chem. Chem. Phys. 14, 7629–7639 (2012)CrossRefGoogle Scholar
  229. 229.
    K.M. Merz Jr., Acc. Chem. Res. 47, 2804–2811 (2014)CrossRefGoogle Scholar
  230. 230.
    G. Knizia, G.K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)CrossRefGoogle Scholar
  231. 231.
    G. Knizia, G.K.-L. Chan, J. Chem. Theory Comput. 9, 1428–1432 (2013)CrossRefGoogle Scholar
  232. 232.
    G. Kotliar, S.Y. Savrasov, K. Haule, V.S. Oudovenko, O. Parcollet, C.A. Marianetti, Rev. Mod. Phys. 78, 865–951 (2006)CrossRefGoogle Scholar
  233. 233.
    D. Zgid, G.K.-L. Chan, J. Chem. Phys. 134, 094115 (2011)CrossRefGoogle Scholar
  234. 234.
    A.A. Kananenka, E. Gull, D. Zgid, Phys. Rev. B 91, 121111 (2015)CrossRefGoogle Scholar
  235. 235.
    T.N. Lan, A.A. Kananenka, D. Zgid, J. Chem. Phys. 143, 241102 (2015)CrossRefGoogle Scholar
  236. 236.
    T. Nguyen Lan, A.A. Kananenka, D. Zgid, J. Chem. Theory Comput. 12, 4856–4870 (2016)CrossRefGoogle Scholar
  237. 237.
    B.-X. Zheng, G.K.-L. Chan, Phys. Rev. B 93, 035126 (2016)CrossRefGoogle Scholar
  238. 238.
    S. Wouters, C.A. Jiménez-Hoyos, Q. Sun, G.K.-L. Chan, J. Chem. Theory Comput. 12, 2706–2719 (2016)CrossRefGoogle Scholar
  239. 239.
    I.W. Bulik, W. Chen, G.E. Scuseria, J. Chem. Phys. 141, 054113 (2014)CrossRefGoogle Scholar
  240. 240.
    M. Welborn, T. Tsuchimochi, T. Van Voorhis, J. Chem. Phys. 145, 074102 (2016)CrossRefGoogle Scholar
  241. 241.
    J.W. Kaminski, S. Gusarov, T.A. Wesołowski, A. Kovalenko, J. Phys. Chem. A 114, 6082–6096 (2010)CrossRefGoogle Scholar
  242. 242.
    M. Humbert-Droz, X. Zhou, S.V. Shedge, T.A. Wesołowski, Theor. Chem. Acc. 133, 1405 (2013)CrossRefGoogle Scholar
  243. 243.
    T. Dresselhaus, J. Neugebauer, Theor. Chem. Acc. 134, 97 (2015)CrossRefGoogle Scholar
  244. 244.
    S. Laricchia, E. Fabiano, F. Della Sala, J. Chem. Phys. 133, 164111 (2010)CrossRefGoogle Scholar
  245. 245.
    S. Laricchia, E. Fabiano, F. Della Sala, Chem. Phys. Lett. 518, 114–118 (2011)CrossRefGoogle Scholar
  246. 246.
    S. Laricchia, E. Fabiano, F. Della Sala, J. Chem. Phys. 137, 14102 (2012)CrossRefGoogle Scholar
  247. 247.
    S. Kümmel, L. Kronik, Rev. Mod. Phys. 80, 3–60 (2008)CrossRefGoogle Scholar
  248. 248.
    L.H. Thomas, Math. Proc. Cambridge 23, 542–548 (1927)CrossRefGoogle Scholar
  249. 249.
    E. Fermi, Z. Phys. 48, 73–79 (1928)CrossRefGoogle Scholar
  250. 250.
    S. Fux, K. Kiewisch, C.R. Jacob, J. Neugebauer, M. Reiher, Chem. Phys. Lett. 461, 353–359 (2008)CrossRefGoogle Scholar
  251. 251.
    D. Schlüns, K. Klahr, C. Mück-Lichtenfeld, L. Visscher, J. Neugebauer, Phys. Chem. Chem. Phys. 17, 14323–14341 (2015)CrossRefGoogle Scholar
  252. 252.
    A. Lembarki, H. Chermette, Phys. Rev. A 50, 5328–5331 (1994)CrossRefGoogle Scholar
  253. 253.
    S. Fux, C.R. Jacob, J. Neugebauer, L. Visscher, M. Reiher, J. Chem. Phys. 132, 164101 (2010)CrossRefGoogle Scholar
  254. 254.
    C.R. Jacob, L. Visscher, Towards the description of covalent bonds in subsystem density-functional theory, in Recent Progress in Orbital-free Density Functional Theory, ed. by T.A. Wesołowski, Y.A. Wang (World Scientific Publishing, Singapore, 2013)Google Scholar
  255. 255.
    O. Roncero, M.P. de Lara-Castells, P. Villarreal, F. Flores, J. Ortega, M. Paniagua, A. Aguado, J. Chem. Phys. 129, 184104 (2008)CrossRefGoogle Scholar
  256. 256.
    J.D. Goodpaster, N. Ananth, F.R. Manby, T.F. Miller III, J. Chem. Phys. 133, 084103 (2010)CrossRefGoogle Scholar
  257. 257.
    P.K. Tamukong, Y.G. Khait, M.R. Hoffmann, J. Phys. Chem. A 118, 9182–9200 (2014)CrossRefGoogle Scholar
  258. 258.
    D.V. Chulhai, L. Jensen, J. Chem. Theory Comput. 11, 3080–3088 (2015)CrossRefGoogle Scholar
  259. 259.
    J.P. Unsleber, J. Neugebauer, C.R. Jacob, Phys. Chem. Chem. Phys. 18, 21001–21009 (2016)CrossRefGoogle Scholar
  260. 260.
    F.R. Manby, M. Stella, J.D. Goodpaster, T.F. Miller, J. Chem. Theory Comput. 8, 2564–2568 (2012)CrossRefGoogle Scholar
  261. 261.
    A. Solovyeva, M. Pavanello, J. Neugebauer, J. Chem. Phys. 136, 194104 (2012)CrossRefGoogle Scholar
  262. 262.
    T.A. Wesołowski, One-electron equations for embedded electron density: challenge for theory and practical payoffs in multi-level modelling of complex polyatomic systems, in Computational Chemistry: Reviews of Current Trends (World Scientific, Singapore, 2011)Google Scholar
  263. 263.
    M.E. Casida, T.A. Wesołowski, Int. J. Quantum Chem. 96, 577–588 (2004)CrossRefGoogle Scholar
  264. 264.
    T.A. Wesołowski, J. Am. Chem. Soc. 126, 11444–11445 (2004)CrossRefGoogle Scholar
  265. 265.
    J. Neugebauer, M.J. Louwerse, E.J. Baerends, T.A. Wesołowski, J. Chem. Phys. 122, 094115 (2005)CrossRefGoogle Scholar
  266. 266.
    C.R. Jacob, L. Visscher, J. Chem. Phys. 125, 194104 (2006)CrossRefGoogle Scholar
  267. 267.
    J. Neugebauer, J. Chem. Phys. 126, 134116 (2007)CrossRefGoogle Scholar
  268. 268.
    J. Neugebauer, ChemPhysChem 10, 3148–3173 (2009)CrossRefGoogle Scholar
  269. 269.
    C. König, J. Neugebauer, ChemPhysChem 13, 386–425 (2012)CrossRefGoogle Scholar
  270. 270.
    A. Kovyrshin, J. Neugebauer, J. Chem. Phys. 133, 174114 (2010)CrossRefGoogle Scholar
  271. 271.
    C. König, N. Schlüter, J. Neugebauer, J. Chem. Phys. 138, 034104 (2013)CrossRefGoogle Scholar
  272. 272.
    C. Daday, C. König, O. Valsson, J. Neugebauer, C. Filippi, J. Chem. Theory Comput. 9, 2355–2367 (2013)CrossRefGoogle Scholar
  273. 273.
    M. Pavanello, J. Chem. Phys. 138, 204118 (2013)CrossRefGoogle Scholar
  274. 274.
    D.G. Artiukhin, C.R. Jacob, J. Neugebauer, J. Chem. Phys. 142, 234101 (2015)CrossRefGoogle Scholar
  275. 275.
    C. König, J. Neugebauer, J. Chem. Theory Comput. 9, 1808–1820 (2013)CrossRefGoogle Scholar
  276. 276.
    A. Goez, C.R. Jacob, J. Neugebauer, Comput. Theor. Chem. 1040–1041, 347–359 (2014)CrossRefGoogle Scholar
  277. 277.
    M. Pavanello, J. Neugebauer, J. Chem. Phys. 135, 234103 (2011)CrossRefGoogle Scholar
  278. 278.
    A. Solovyeva, M. Pavanello, J. Neugebauer, J. Chem. Phys. 140, 164103 (2014)CrossRefGoogle Scholar
  279. 279.
    P. Ramos, M. Pavanello, Phys. Chem. Chem. Phys. 18, 21172–21178 (2016)CrossRefGoogle Scholar
  280. 280.
    N. Govind, Y.A. Wang, A.J.R. da Silva, E.A. Carter, Chem. Phys. Lett. 295, 129–134 (1998)CrossRefGoogle Scholar
  281. 281.
    N. Govind, Y.A. Wang, E.A. Carter, J. Chem. Phys. 110, 7677–7688 (1999)CrossRefGoogle Scholar
  282. 282.
    P. Huang, E.A. Carter, J. Chem. Phys. 125, 084102 (2006)CrossRefGoogle Scholar
  283. 283.
    T. Klüner, N. Govind, Y.A. Wang, E.A. Carter, Phys. Rev. Lett. 86, 5954–5957 (2001)CrossRefGoogle Scholar
  284. 284.
    T. Klüner, N. Govind, Y.A. Wang, E.A. Carter, J. Chem. Phys. 116, 42–54 (2002)CrossRefGoogle Scholar
  285. 285.
    Y.G. Khait, M.R. Hoffmann, J. Chem. Phys. 133, 044107 (2010)CrossRefGoogle Scholar
  286. 286.
    S. Höfener, A.S.P. Gomes, L. Visscher, J. Chem. Phys. 136, 044104 (2012)CrossRefGoogle Scholar
  287. 287.
    S. Höfener, L. Visscher, J. Chem. Theory Comput. 12, 549–557 (2016)CrossRefGoogle Scholar
  288. 288.
    J.D. Goodpaster, T.A. Barnes, F.R. Manby, T.F. Miller, J. Chem. Phys. 137, 224113 (2012)CrossRefGoogle Scholar
  289. 289.
    K. Kiewisch, C.R. Jacob, L. Visscher, J. Chem. Theory Comput. 9, 2425–2440 (2013)CrossRefGoogle Scholar
  290. 290.
    A. Goez, J. Neugebauer, Mol. Phys. (2016) (in press)Google Scholar
  291. 291.
    A. Goez, J. Neugebauer, J. Chem. Theory Comput. 12, 4843–4855 (2016)CrossRefGoogle Scholar
  292. 292.
    T.A. Wesołowski, A. Goursot, J. Weber, J. Chem. Phys. 115, 4791–4797 (2001)CrossRefGoogle Scholar
  293. 293.
    M. Dułak, J.W. Kamiński, T.A. Wesołowski, J. Chem. Theory Comput. 3, 735–745 (2007)CrossRefGoogle Scholar
  294. 294.
    M. Iannuzzi, B. Kirchner, J. Hutter, Chem. Phys. Lett. 421, 16–20 (2006)CrossRefGoogle Scholar
  295. 295.
    S. Andermatt, J. Cha, F. Schiffmann, J. VandeVondele, J. Chem. Theory Comput. 12, 3214–3227 (2016)CrossRefGoogle Scholar
  296. 296.
    D. Schlüns, M. Franchini, A.W. Götz, J. Neugebauer, C.R. Jacob, L. Visscher, J. Comput. Chem. 2016 (in press)Google Scholar
  297. 297.
    J. Heuser, S. Höfener, J. Comput. Chem. 37, 1092–1101 (2016)CrossRefGoogle Scholar
  298. 298.
    T. Dresselhaus, J. Neugebauer, S. Knecht, S. Keller, Y. Ma, M. Reiher, J. Chem. Phys. 142, 044111 (2015)CrossRefGoogle Scholar
  299. 299.
    S. Prager, A. Zech, F. Aquilante, A. Dreuw, T.A. Wesołowski, J. Chem. Phys. 144, 204103 (2016)CrossRefGoogle Scholar
  300. 300.
    A. Kovyrshin, J. Neugebauer, Phys. Chem. Chem. Phys. 18, 20955–20975 (2016)CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.WWU Münster, Organisch-Chemisches Institut and Center for Multiscale Theory and ComputationMünsterGermany

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