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Applications of the Density Matrix Renormalization Group to Exchange-Coupled Transition Metal Systems

  • Vera Krewald
  • Dimitrios A. PantazisEmail author
Chapter
Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 29)

Abstract

Transition metal complexes containing magnetically interacting open-shell ions are important for diverse areas of molecular science. The reliable prediction and computational analysis of their electronic structure and magnetic properties, either in qualitative or quantitative terms, remain a central challenge for theoretical chemistry. The use of multireference methods is in principle the ideal approach to the inherently multireference problem of exchange coupling in oligonuclear transition metal complexes; however, the applicability of such methods has been severely restricted due to their computational cost. In recent years, the introduction of the density matrix renormalization group (DMRG) to quantum chemistry has enabled the multireference treatment of chemical problems with previously unattainable numbers of active electrons and orbitals. This development also paved the way for the first-principles multireference treatment of magnetic properties in the case of exchange-coupled transition metal systems. Here, the first detailed applications of DMRG-based methods to exchange-coupled systems are reviewed and the lessons learned so far regarding the applicability, apparent limitations, and future promise of this approach are discussed.

Keywords

Density Matrix Renormalization Group (DMRG) Multireference calculations Exchange coupling NEVPT2 Antiferromagnetism 

References

  1. 1.
    Kahn O (1993) Molecular magnetism. Wiley, New YorkGoogle Scholar
  2. 2.
    Malrieu JP, Caballol R, Calzado CJ, de Graaf C, Guihéry N (2014) Chem Rev 114:429–492PubMedCrossRefGoogle Scholar
  3. 3.
    Moreira IDPR, Illas F (2006) Phys Chem Chem Phys 8:1645–1659Google Scholar
  4. 4.
    Neese F (2009) Coord Chem Rev 253:526–563CrossRefGoogle Scholar
  5. 5.
    Illas F, Moreira IDPR, de Graaf C, Barone V (2000) Theor Chem Acc 104:265–272Google Scholar
  6. 6.
    Caballol R, Castell O, Illas F, Moreira IDPR, Malrieu JP (1997) J Phys Chem A 101:7860–7866Google Scholar
  7. 7.
    Noodleman L (1981) J Chem Phys 74:5737–5743CrossRefGoogle Scholar
  8. 8.
    Noodleman L, Davidson ER (1986) Chem Phys 109:131–143CrossRefGoogle Scholar
  9. 9.
    Yamaguchi K, Tsunekawa T, Toyoda Y, Fueno T (1988) Chem Phys Lett 143:371–376CrossRefGoogle Scholar
  10. 10.
    Yamanaka S, Kawakami T, Nagao H, Yamaguchi K (1994) Chem Phys Lett 231:25–33CrossRefGoogle Scholar
  11. 11.
    De Loth P, Cassoux P, Daudey JP, Malrieu JP (1981) J Am Chem Soc 103:4007–4016CrossRefGoogle Scholar
  12. 12.
    White SR, Martin RL (1999) J Chem Phys 110:4127–4130CrossRefGoogle Scholar
  13. 13.
    Schollwöck U (2011) Ann Phys 326:96–192CrossRefGoogle Scholar
  14. 14.
    Moritz G, Wolf A, Reiher M (2005) J Chem Phys 123:184105PubMedCrossRefGoogle Scholar
  15. 15.
    Marti KH, Ondík IM, Moritz G, Reiher M (2008) J Chem Phys 128:014104PubMedCrossRefGoogle Scholar
  16. 16.
    Freitag L, Knecht S, Keller SF, Delcey MG, Aquilante F, Pedersen TB, Lindh R, Reiher M, Gonzalez L (2015) Phys Chem Chem Phys 17:14383–14392PubMedPubMedCentralCrossRefGoogle Scholar
  17. 17.
    Hu W, Chan GKL (2015) J Chem Theory Comput 11:3000–3009Google Scholar
  18. 18.
    Kurashige Y, Yanai T (2009) J Chem Phys 130:234114PubMedCrossRefGoogle Scholar
  19. 19.
    Kurashige Y, Chan GKL, Yanai T (2013) Nat Chem 5:660–666Google Scholar
  20. 20.
    Sharma S, Sivalingam K, Neese F, Chan GKL (2014) Nat Chem 6:927–933Google Scholar
  21. 21.
    Paul S, Cox N, Pantazis DA (2017) Inorg Chem 56:3875–3888PubMedCrossRefGoogle Scholar
  22. 22.
    Harris TV, Kurashige Y, Yanai T, Morokuma K (2014) J Chem Phys 140:054303PubMedCrossRefGoogle Scholar
  23. 23.
    Roemelt M, Krewald V, Pantazis DA (2018) J Chem Theory Comput 14:166–179PubMedCrossRefGoogle Scholar
  24. 24.
    Chan GKL, Head-Gordon M (2002) J Chem Phys 116:4462–4476Google Scholar
  25. 25.
    Olivares-Amaya R, Hu W, Nakatani N, Sharma S, Yang J, Chan GKL (2015) J Chem Phys 142:034102Google Scholar
  26. 26.
    Keller SF, Reiher M (2014) Chimia 68:200–203PubMedCrossRefGoogle Scholar
  27. 27.
    Knecht S, Hedegård ED, Keller S, Kovyrshin A, Ma Y, Muolo A, Stein CJ, Reiher M (2016) Chimia 70:244–251PubMedCrossRefGoogle Scholar
  28. 28.
    Bencini A, Gatteschi D (1990) EPR of exchange coupled systems. Springer Verlag, BerlinGoogle Scholar
  29. 29.
    Pantazis DA, Orio M, Petrenko T, Zein S, Bill E, Lubitz W, Messinger J, Neese F (2009) Chem Eur J 15:5108–5123Google Scholar
  30. 30.
    Ginsberg AP (1980) J Am Chem Soc 102:111–117CrossRefGoogle Scholar
  31. 31.
    Mouesca JM, Noodleman L, Case DA, Lamotte B (1995) Inorg Chem 34:4347–4359CrossRefGoogle Scholar
  32. 32.
    Noodleman L, Post D, Baerends EJ (1982) Chem Phys 64:159–166CrossRefGoogle Scholar
  33. 33.
    Neese F (2004) J Phys Chem Solids 65:781–785CrossRefGoogle Scholar
  34. 34.
    Dai D, Whangbo M-H (2003) J Chem Phys 118:29–39CrossRefGoogle Scholar
  35. 35.
    Ruiz E, Cano J, Alvarez S, Alemany P (1999) J Comput Chem 20:1391–1400CrossRefGoogle Scholar
  36. 36.
    Yamaguchi K, Takahara Y, Fueno T (1986) Ab-initio molecular orbital studies of structure and reactivity of transition metal-oxo compounds. In: Smith VH Jr, Scheafer HF III, Morokuma K (eds) Applied quantum chemistry. D. Reidel, Boston, pp 155–184CrossRefGoogle Scholar
  37. 37.
    Golub GH, Reinsch C (1970) Numer Math 14:403–420CrossRefGoogle Scholar
  38. 38.
    Pantazis DA, Orio M, Petrenko T, Zein S, Lubitz W, Messinger J, Neese F (2009) Phys Chem Chem Phys 11:6788–6798PubMedCrossRefGoogle Scholar
  39. 39.
    Shoji M, Koizumi K, Kitagawa Y, Kawakami T, Yamanaka S, Okumura M, Yamaguchi K (2006) Chem Phys Lett 432:343–347CrossRefGoogle Scholar
  40. 40.
    Desplanches C, Ruiz E, Alvarez S (2003) Eur J Inorg Chem 2003:1756–1760CrossRefGoogle Scholar
  41. 41.
    Hubner O, Fink K, Klopper W (2007) Phys Chem Chem Phys 9:1911–1920PubMedCrossRefGoogle Scholar
  42. 42.
    Coulaud E, Malrieu J-P, Guihéry N, Ferré N (2013) J Chem Theory Comput 9:3429–3436PubMedCrossRefGoogle Scholar
  43. 43.
    Gutierrez L, Alzuet G, Real JA, Cano J, Borrás J, Castiñeiras A (2000) Inorg Chem 39:3608–3614PubMedCrossRefGoogle Scholar
  44. 44.
    Rodríguez-Fortea A, Alemany P, Alvarez S, Ruiz E (2001) Chem Eur J 7:627–637Google Scholar
  45. 45.
    Pantazis DA, Krewald V, Orio M, Neese F (2010) Dalton Trans 39:4959–4967PubMedCrossRefGoogle Scholar
  46. 46.
    Coulaud E, Guihéry N, Malrieu J-P, Hagebaum-Reignier D, Siri D, Ferré N (2012) J Chem Phys 137:114106PubMedCrossRefGoogle Scholar
  47. 47.
    Krewald V, Neese F, Pantazis DA (2013) J Am Chem Soc 135:5726–5739PubMedCrossRefGoogle Scholar
  48. 48.
    Orio M, Pantazis DA, Petrenko T, Neese F (2009) Inorg Chem 48:7251–7260PubMedCrossRefGoogle Scholar
  49. 49.
    Ciofini I, Daul CA (2003) Coord Chem Rev 238–239:187–209CrossRefGoogle Scholar
  50. 50.
    Bencini A, Totti F (2009) J Chem Theory Comput 5:144–154PubMedCrossRefGoogle Scholar
  51. 51.
    Ruiz E (2004) Struct Bond 113:91–102Google Scholar
  52. 52.
    Comba P, Hausberg S, Martin B (2009) J Phys Chem A 113:6751–6755PubMedCrossRefGoogle Scholar
  53. 53.
    Illas F, Moreira IDPR, Bofill JM, Filatov M (2004) Phys Rev B 70:132414Google Scholar
  54. 54.
    Illas F, Moreira IDPR, Bofill JM, Filatov M (2006) Theor Chem Acc 116:587–597Google Scholar
  55. 55.
    Zein S, Poor Kalhor M, Chibotaru LF, Chermette H (2009) J Chem Phys 131:224316PubMedCrossRefGoogle Scholar
  56. 56.
    Neese F (2006) J Biol Inorg Chem 11:702–711PubMedCrossRefGoogle Scholar
  57. 57.
    Amos AT, Hall GG (1961) Proc R Soc Lond A 263:483–493Google Scholar
  58. 58.
    Malmqvist P-Å, Roos BO (1989) Chem Phys Lett 155:189–194CrossRefGoogle Scholar
  59. 59.
    Roos BO, Taylor PR, Siegbahn PEM (1980) Chem Phys 48:157–173CrossRefGoogle Scholar
  60. 60.
    Andersson K, Roos BO (1992) Chem Phys Lett 191:507–514CrossRefGoogle Scholar
  61. 61.
    Pierloot K, Persson BJ, Roos BO (1995) J Phys Chem 99:3465–3472CrossRefGoogle Scholar
  62. 62.
    Andersson K, Malmqvist PA, Roos BO, Sadlej AJ, Wolinski K (1990) J Phys Chem 94:5483–5488CrossRefGoogle Scholar
  63. 63.
    Finley J, Malmqvist P-Å, Roos BO, Serrano-Andrés L (1998) Chem Phys Lett 288:299–306CrossRefGoogle Scholar
  64. 64.
    Angeli C, Cimiraglia R, Evangelisti S, Leininger T, Malrieu JP (2001) J Chem Phys 114:10252–10264CrossRefGoogle Scholar
  65. 65.
    Angeli C, Cimiraglia R, Malrieu J-P (2002) J Chem Phys 117:9138–9153CrossRefGoogle Scholar
  66. 66.
    Miralles J, Daudey JP, Caballol R (1992) Chem Phys Lett 198:555–562CrossRefGoogle Scholar
  67. 67.
    Miralles J, Castell O, Caballol R, Malrieu JP (1993) Chem Phys 172:33–43CrossRefGoogle Scholar
  68. 68.
    Castell O, Caballol R (1999) Inorg Chem 38:668–673CrossRefGoogle Scholar
  69. 69.
    Calzado CJ, Cabrero J, Malrieu JP, Caballol R (2002) J Chem Phys 116:2728–2747CrossRefGoogle Scholar
  70. 70.
    Calzado CJ, Cabrero J, Malrieu JP, Caballol R (2002) J Chem Phys 116:3985–4000CrossRefGoogle Scholar
  71. 71.
    Calzado CJ, Angeli C, Taratiel D, Caballol R, Malrieu JP (2009) J Chem Phys 131:044327PubMedCrossRefGoogle Scholar
  72. 72.
    Queralt N, Taratiel D, de Graaf C, Caballol R, Cimiraglia R, Angeli C (2008) J Comput Chem 29:994–1003PubMedCrossRefGoogle Scholar
  73. 73.
    Olsen J, Roos BO, Jørgensen P, Jensen HJA (1988) J Chem Phys 89:2185–2192CrossRefGoogle Scholar
  74. 74.
    Malmqvist PA, Rendell A, Roos BO (1990) J Phys Chem 94:5477–5482CrossRefGoogle Scholar
  75. 75.
    Ma D, Li Manni G, Gagliardi L (2011) J Chem Phys 135:044128PubMedCrossRefGoogle Scholar
  76. 76.
    Li Manni G, Aquilante F, Gagliardi L (2011) J Chem Phys 134:034114PubMedCrossRefGoogle Scholar
  77. 77.
    Li Manni G, Ma D, Aquilante F, Olsen J, Gagliardi L (2013) J Chem Theory Comput 9:3375–3384PubMedCrossRefGoogle Scholar
  78. 78.
    Thomas RE, Sun Q, Alavi A, Booth GH (2015) J Chem Theory Comput 11:5316–5325PubMedCrossRefGoogle Scholar
  79. 79.
    Li Manni G, Smart SD, Alavi A (2016) J Chem Theory Comput 12:1245–1258PubMedCrossRefGoogle Scholar
  80. 80.
    Moritz G, Hess BA, Reiher M (2005) J Chem Phys 122:024107PubMedCrossRefGoogle Scholar
  81. 81.
    Zgid D, Nooijen M (2008) J Chem Phys 128:014107PubMedCrossRefGoogle Scholar
  82. 82.
    Chan GKL, Sharma S (2011) Annu Rev Phys Chem 62:465–481Google Scholar
  83. 83.
    Boguslawski K, Tecmer P, Legeza Ö, Reiher M (2012) J Phys Chem Lett 3:3129–3135PubMedCrossRefGoogle Scholar
  84. 84.
    Stein CJ, Reiher M (2016) J Chem Theory Comput 12:1760–1771PubMedCrossRefGoogle Scholar
  85. 85.
    Ma Y, Knecht S, Keller S, Reiher M (2017) J Chem Theory Comput 13:2533–2549PubMedCrossRefGoogle Scholar
  86. 86.
    Baiardi A, Stein CJ, Barone V, Reiher M (2017) J Chem Theory Comput 13:3764–3777PubMedCrossRefGoogle Scholar
  87. 87.
    Battaglia S, Keller S, Knecht S (2018) J Chem Theory Comput 14:2353–2369PubMedCrossRefGoogle Scholar
  88. 88.
    Moritz G, Reiher M (2007) J Chem Phys 126:244109PubMedCrossRefGoogle Scholar
  89. 89.
    Sobczak P, Barasiński A, Drzewiński A, Kamieniarz G, Kłak J, Bieńko A, Mroziński J (2009) Polyhedron 28:1838–1841CrossRefGoogle Scholar
  90. 90.
    Barasiński A, Sobczak P, Drzewiński A, Kamieniarz G, Bieńko A, Mroziński J, Gatteschi D (2010) Polyhedron 29:1485–1491CrossRefGoogle Scholar
  91. 91.
    Schnack J, Ummethum J (2013) Polyhedron 66:28–33CrossRefGoogle Scholar
  92. 92.
    Keller S, Boguslawski K, Janowski T, Reiher M, Pulay P (2015) J Chem Phys 142:244104PubMedCrossRefGoogle Scholar
  93. 93.
    Sayfutyarova ER, Sun Q, Chan GK, Knizia G (2017) J Chem Theory Comput 13:4063–4078PubMedCrossRefGoogle Scholar
  94. 94.
    Bao JJ, Dong SS, Gagliardi L, Truhlar DG (2018) J Chem Theory Comput 14:2017–2025PubMedCrossRefGoogle Scholar
  95. 95.
    Barcza G, Legeza Ö, Marti KH, Reiher M (2011) Phys Rev A 83Google Scholar
  96. 96.
    Saitow M, Kurashige Y, Yanai T (2015) J Chem Theory Comput 11:5120–5131PubMedCrossRefGoogle Scholar
  97. 97.
    Guo S, Watson MA, Hu W, Sun Q, Chan GKL (2016) J Chem Theory Comput 12:1583–1591Google Scholar
  98. 98.
    Roemelt M, Guo S, Chan GKL (2016) J Chem Phys 144:204113PubMedCrossRefGoogle Scholar
  99. 99.
    Yanai T, Saitow M, Xiong XG, Chalupský J, Kurashige Y, Guo S, Sharma S (2017) J Chem Theory Comput 13:4829–4840PubMedCrossRefGoogle Scholar
  100. 100.
    Boguslawski K, Tecmer P, Barcza G, Legeza Ö, Reiher M (2013) J Chem Theory Comput 9:2959–2973PubMedCrossRefGoogle Scholar
  101. 101.
    Wouters S, Bogaerts T, Van Der Voort P, Van Speybroeck V, Van Neck D (2014) J Chem Phys 140:241103PubMedCrossRefGoogle Scholar
  102. 102.
    Kurashige Y, Saitow M, Chalupský J, Yanai T (2014) Phys Chem Chem Phys 16:11988–11999PubMedCrossRefGoogle Scholar
  103. 103.
    Chalupský J, Rokob TA, Kurashige Y, Yanai T, Solomon EI, Rulíšek L, Srnec M (2014) J Am Chem Soc 136:15977–15991PubMedCrossRefGoogle Scholar
  104. 104.
    Ma Y, Knecht S, Reiher M (2017) Chem Phys Chem 18:384–393PubMedCrossRefGoogle Scholar
  105. 105.
    Phung QM, Domingo A, Pierloot K (2018) Chem Eur J 24:5183–5190Google Scholar
  106. 106.
    Phung QM, Pierloot K (2018) Phys Chem Chem Phys 20:17009–17019PubMedCrossRefGoogle Scholar
  107. 107.
    Dong G, Phung QM, Hallaert SD, Pierloot K, Ryde U (2017) Phys Chem Chem Phys 19:10590–10601PubMedCrossRefGoogle Scholar
  108. 108.
    Zhang C, Chen C, Dong H, Shen JR, Dau H, Zhao J (2015) Science 348:690–693PubMedCrossRefGoogle Scholar
  109. 109.
    Paul S, Neese F, Pantazis DA (2017) Green Chem 19:2309–2325CrossRefGoogle Scholar
  110. 110.
    Umena Y, Kawakami K, Shen J-R, Kamiya N (2011) Nature 473:55–60PubMedCrossRefPubMedCentralGoogle Scholar
  111. 111.
    Pantazis DA, Ames W, Cox N, Lubitz W, Neese F (2012) Angew Chem Int Ed 51:9935–9940Google Scholar
  112. 112.
    Krewald V, Retegan M, Pantazis DA (2016) Top Curr Chem 371:23–48PubMedCrossRefGoogle Scholar
  113. 113.
    Beinert H, Holm RH, Münck E (1997) Science 277:653–659PubMedCrossRefGoogle Scholar
  114. 114.
    Lledós A, Moreno-Mañas M, Sodupe M, Vallribera A, Mata I, Martínez B, Molins E (2003) Eur J Inorg Chem 2003:4187–4194CrossRefGoogle Scholar
  115. 115.
    Boguslawski K, Marti KH, Reiher M (2011) J Chem Phys 134:224101PubMedCrossRefGoogle Scholar
  116. 116.
    Bencini A, Totti F (2008) Inorg Chim Acta 361:4153–4156CrossRefGoogle Scholar
  117. 117.
    Bastardis R, Guihéry N, de Graaf C (2008) J Chem Phys 129:104102PubMedCrossRefGoogle Scholar
  118. 118.
    Spivak M, Angeli C, Calzado CJ, de Graaf C (2014) J Comput Chem 35:1665–1671PubMedCrossRefGoogle Scholar
  119. 119.
    Bossek U, Weyhermueller T, Wieghardt K, Nuber B, Weiss J (1990) J Am Chem Soc 112:6387–6388CrossRefGoogle Scholar
  120. 120.
    Kanady JS, Tsui EY, Day MW, Agapie T (2011) Science 333:733–736PubMedCrossRefGoogle Scholar
  121. 121.
    Mukherjee S, Stull JA, Yano J, Stamatatos TC, Pringouri K, Stich TA, Abboud KA, Britt RD, Yachandra VK, Christou G (2012) Proc Natl Acad Sci USA 109:2257–2262PubMedCrossRefGoogle Scholar
  122. 122.
    Krewald V, Retegan M, Neese F, Lubitz W, Pantazis DA, Cox N (2016) Inorg Chem 55:488–501PubMedCrossRefGoogle Scholar
  123. 123.
    Stein CJ, von Burg V, Reiher M (2016) J Chem Theory Comput 12:3764–3773PubMedCrossRefGoogle Scholar
  124. 124.
    Angeli C, Calzado CJ (2012) J Chem Phys 137:034104PubMedCrossRefGoogle Scholar
  125. 125.
    Bjornsson R, Lima FA, Spatzal T, Weyhermüller T, Glatzel P, Bill E, Einsle O, Neese F, DeBeer S (2014) Chem Sci 5:3096–3103CrossRefGoogle Scholar
  126. 126.
    Domingo A, Specklin D, Rosa V, Mameri S, Robert V, Welter R (2014) Eur J Inorg Chem 2014:2552–2560CrossRefGoogle Scholar
  127. 127.
    Kurashige Y, Yanai T (2011) J Chem Phys 135:094104PubMedCrossRefGoogle Scholar
  128. 128.
    Saitow M, Kurashige Y, Yanai T (2013) J Chem Phys 139:044118PubMedCrossRefGoogle Scholar
  129. 129.
    Sharma S, Chan GKL (2014) J Chem Phys 141:111101Google Scholar
  130. 130.
    Yanai T, Kurashige Y, Mizukami W, Chalupský J, Lan TN, Saitow M (2015) Int J Quantum Chem 115:283–299CrossRefGoogle Scholar
  131. 131.
    Veis L, Antalík A, Brabec J, Neese F, Legeza Ö, Pittner J (2016) J Phys Chem Lett 7:4072–4078PubMedCrossRefGoogle Scholar
  132. 132.
    Phung QM, Wouters S, Pierloot K (2016) J Chem Theory Comput 12:4352–4361PubMedCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Fachbereich Chemie, Technische Universität DarmstadtDarmstadtGermany
  2. 2.Max-Planck-Institut Für KohlenforschungMülheim an der RuhrGermany

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