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

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Transition Metals in Coordination Environments

Part of the book series: Challenges and Advances in Computational Chemistry and Physics ((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.

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References

  1. Kahn O (1993) Molecular magnetism. Wiley, New York

    Google Scholar 

  2. Malrieu JP, Caballol R, Calzado CJ, de Graaf C, Guihéry N (2014) Chem Rev 114:429–492

    Article  CAS  PubMed  Google Scholar 

  3. Moreira IDPR, Illas F (2006) Phys Chem Chem Phys 8:1645–1659

    Google Scholar 

  4. Neese F (2009) Coord Chem Rev 253:526–563

    Article  CAS  Google Scholar 

  5. Illas F, Moreira IDPR, de Graaf C, Barone V (2000) Theor Chem Acc 104:265–272

    Google Scholar 

  6. Caballol R, Castell O, Illas F, Moreira IDPR, Malrieu JP (1997) J Phys Chem A 101:7860–7866

    Google Scholar 

  7. Noodleman L (1981) J Chem Phys 74:5737–5743

    Article  CAS  Google Scholar 

  8. Noodleman L, Davidson ER (1986) Chem Phys 109:131–143

    Article  Google Scholar 

  9. Yamaguchi K, Tsunekawa T, Toyoda Y, Fueno T (1988) Chem Phys Lett 143:371–376

    Article  CAS  Google Scholar 

  10. Yamanaka S, Kawakami T, Nagao H, Yamaguchi K (1994) Chem Phys Lett 231:25–33

    Article  CAS  Google Scholar 

  11. De Loth P, Cassoux P, Daudey JP, Malrieu JP (1981) J Am Chem Soc 103:4007–4016

    Article  Google Scholar 

  12. White SR, Martin RL (1999) J Chem Phys 110:4127–4130

    Article  CAS  Google Scholar 

  13. Schollwöck U (2011) Ann Phys 326:96–192

    Article  CAS  Google Scholar 

  14. Moritz G, Wolf A, Reiher M (2005) J Chem Phys 123:184105

    Article  PubMed  CAS  Google Scholar 

  15. Marti KH, Ondík IM, Moritz G, Reiher M (2008) J Chem Phys 128:014104

    Article  PubMed  CAS  Google Scholar 

  16. Freitag L, Knecht S, Keller SF, Delcey MG, Aquilante F, Pedersen TB, Lindh R, Reiher M, Gonzalez L (2015) Phys Chem Chem Phys 17:14383–14392

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Hu W, Chan GKL (2015) J Chem Theory Comput 11:3000–3009

    Google Scholar 

  18. Kurashige Y, Yanai T (2009) J Chem Phys 130:234114

    Article  PubMed  CAS  Google Scholar 

  19. Kurashige Y, Chan GKL, Yanai T (2013) Nat Chem 5:660–666

    Google Scholar 

  20. Sharma S, Sivalingam K, Neese F, Chan GKL (2014) Nat Chem 6:927–933

    Google Scholar 

  21. Paul S, Cox N, Pantazis DA (2017) Inorg Chem 56:3875–3888

    Article  CAS  PubMed  Google Scholar 

  22. Harris TV, Kurashige Y, Yanai T, Morokuma K (2014) J Chem Phys 140:054303

    Article  PubMed  CAS  Google Scholar 

  23. Roemelt M, Krewald V, Pantazis DA (2018) J Chem Theory Comput 14:166–179

    Article  CAS  PubMed  Google Scholar 

  24. Chan GKL, Head-Gordon M (2002) J Chem Phys 116:4462–4476

    Google Scholar 

  25. Olivares-Amaya R, Hu W, Nakatani N, Sharma S, Yang J, Chan GKL (2015) J Chem Phys 142:034102

    Google Scholar 

  26. Keller SF, Reiher M (2014) Chimia 68:200–203

    Article  CAS  PubMed  Google Scholar 

  27. Knecht S, Hedegård ED, Keller S, Kovyrshin A, Ma Y, Muolo A, Stein CJ, Reiher M (2016) Chimia 70:244–251

    Article  CAS  PubMed  Google Scholar 

  28. Bencini A, Gatteschi D (1990) EPR of exchange coupled systems. Springer Verlag, Berlin

    Google Scholar 

  29. Pantazis DA, Orio M, Petrenko T, Zein S, Bill E, Lubitz W, Messinger J, Neese F (2009) Chem Eur J 15:5108–5123

    Google Scholar 

  30. Ginsberg AP (1980) J Am Chem Soc 102:111–117

    Article  CAS  Google Scholar 

  31. Mouesca JM, Noodleman L, Case DA, Lamotte B (1995) Inorg Chem 34:4347–4359

    Article  CAS  Google Scholar 

  32. Noodleman L, Post D, Baerends EJ (1982) Chem Phys 64:159–166

    Article  CAS  Google Scholar 

  33. Neese F (2004) J Phys Chem Solids 65:781–785

    Article  CAS  Google Scholar 

  34. Dai D, Whangbo M-H (2003) J Chem Phys 118:29–39

    Article  CAS  Google Scholar 

  35. Ruiz E, Cano J, Alvarez S, Alemany P (1999) J Comput Chem 20:1391–1400

    Article  CAS  Google Scholar 

  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 155–184

    Chapter  Google Scholar 

  37. Golub GH, Reinsch C (1970) Numer Math 14:403–420

    Article  Google Scholar 

  38. Pantazis DA, Orio M, Petrenko T, Zein S, Lubitz W, Messinger J, Neese F (2009) Phys Chem Chem Phys 11:6788–6798

    Article  CAS  PubMed  Google Scholar 

  39. Shoji M, Koizumi K, Kitagawa Y, Kawakami T, Yamanaka S, Okumura M, Yamaguchi K (2006) Chem Phys Lett 432:343–347

    Article  CAS  Google Scholar 

  40. Desplanches C, Ruiz E, Alvarez S (2003) Eur J Inorg Chem 2003:1756–1760

    Article  CAS  Google Scholar 

  41. Hubner O, Fink K, Klopper W (2007) Phys Chem Chem Phys 9:1911–1920

    Article  PubMed  Google Scholar 

  42. Coulaud E, Malrieu J-P, Guihéry N, Ferré N (2013) J Chem Theory Comput 9:3429–3436

    Article  CAS  PubMed  Google Scholar 

  43. Gutierrez L, Alzuet G, Real JA, Cano J, Borrás J, Castiñeiras A (2000) Inorg Chem 39:3608–3614

    Article  CAS  PubMed  Google Scholar 

  44. Rodríguez-Fortea A, Alemany P, Alvarez S, Ruiz E (2001) Chem Eur J 7:627–637

    Google Scholar 

  45. Pantazis DA, Krewald V, Orio M, Neese F (2010) Dalton Trans 39:4959–4967

    Article  CAS  PubMed  Google Scholar 

  46. Coulaud E, Guihéry N, Malrieu J-P, Hagebaum-Reignier D, Siri D, Ferré N (2012) J Chem Phys 137:114106

    Article  PubMed  CAS  Google Scholar 

  47. Krewald V, Neese F, Pantazis DA (2013) J Am Chem Soc 135:5726–5739

    Article  CAS  PubMed  Google Scholar 

  48. Orio M, Pantazis DA, Petrenko T, Neese F (2009) Inorg Chem 48:7251–7260

    Article  CAS  PubMed  Google Scholar 

  49. Ciofini I, Daul CA (2003) Coord Chem Rev 238–239:187–209

    Article  CAS  Google Scholar 

  50. Bencini A, Totti F (2009) J Chem Theory Comput 5:144–154

    Article  CAS  PubMed  Google Scholar 

  51. Ruiz E (2004) Struct Bond 113:91–102

    Google Scholar 

  52. Comba P, Hausberg S, Martin B (2009) J Phys Chem A 113:6751–6755

    Article  CAS  PubMed  Google Scholar 

  53. Illas F, Moreira IDPR, Bofill JM, Filatov M (2004) Phys Rev B 70:132414

    Google Scholar 

  54. Illas F, Moreira IDPR, Bofill JM, Filatov M (2006) Theor Chem Acc 116:587–597

    Google Scholar 

  55. Zein S, Poor Kalhor M, Chibotaru LF, Chermette H (2009) J Chem Phys 131:224316

    Article  PubMed  CAS  Google Scholar 

  56. Neese F (2006) J Biol Inorg Chem 11:702–711

    Article  CAS  PubMed  Google Scholar 

  57. Amos AT, Hall GG (1961) Proc R Soc Lond A 263:483–493

    Google Scholar 

  58. Malmqvist P-Å, Roos BO (1989) Chem Phys Lett 155:189–194

    Article  CAS  Google Scholar 

  59. Roos BO, Taylor PR, Siegbahn PEM (1980) Chem Phys 48:157–173

    Article  CAS  Google Scholar 

  60. Andersson K, Roos BO (1992) Chem Phys Lett 191:507–514

    Article  CAS  Google Scholar 

  61. Pierloot K, Persson BJ, Roos BO (1995) J Phys Chem 99:3465–3472

    Article  CAS  Google Scholar 

  62. Andersson K, Malmqvist PA, Roos BO, Sadlej AJ, Wolinski K (1990) J Phys Chem 94:5483–5488

    Article  CAS  Google Scholar 

  63. Finley J, Malmqvist P-Å, Roos BO, Serrano-Andrés L (1998) Chem Phys Lett 288:299–306

    Article  CAS  Google Scholar 

  64. Angeli C, Cimiraglia R, Evangelisti S, Leininger T, Malrieu JP (2001) J Chem Phys 114:10252–10264

    Article  CAS  Google Scholar 

  65. Angeli C, Cimiraglia R, Malrieu J-P (2002) J Chem Phys 117:9138–9153

    Article  CAS  Google Scholar 

  66. Miralles J, Daudey JP, Caballol R (1992) Chem Phys Lett 198:555–562

    Article  CAS  Google Scholar 

  67. Miralles J, Castell O, Caballol R, Malrieu JP (1993) Chem Phys 172:33–43

    Article  CAS  Google Scholar 

  68. Castell O, Caballol R (1999) Inorg Chem 38:668–673

    Article  CAS  Google Scholar 

  69. Calzado CJ, Cabrero J, Malrieu JP, Caballol R (2002) J Chem Phys 116:2728–2747

    Article  CAS  Google Scholar 

  70. Calzado CJ, Cabrero J, Malrieu JP, Caballol R (2002) J Chem Phys 116:3985–4000

    Article  CAS  Google Scholar 

  71. Calzado CJ, Angeli C, Taratiel D, Caballol R, Malrieu JP (2009) J Chem Phys 131:044327

    Article  PubMed  CAS  Google Scholar 

  72. Queralt N, Taratiel D, de Graaf C, Caballol R, Cimiraglia R, Angeli C (2008) J Comput Chem 29:994–1003

    Article  CAS  PubMed  Google Scholar 

  73. Olsen J, Roos BO, Jørgensen P, Jensen HJA (1988) J Chem Phys 89:2185–2192

    Article  CAS  Google Scholar 

  74. Malmqvist PA, Rendell A, Roos BO (1990) J Phys Chem 94:5477–5482

    Article  CAS  Google Scholar 

  75. Ma D, Li Manni G, Gagliardi L (2011) J Chem Phys 135:044128

    Article  PubMed  CAS  Google Scholar 

  76. Li Manni G, Aquilante F, Gagliardi L (2011) J Chem Phys 134:034114

    Article  PubMed  CAS  Google Scholar 

  77. Li Manni G, Ma D, Aquilante F, Olsen J, Gagliardi L (2013) J Chem Theory Comput 9:3375–3384

    Article  CAS  PubMed  Google Scholar 

  78. Thomas RE, Sun Q, Alavi A, Booth GH (2015) J Chem Theory Comput 11:5316–5325

    Article  CAS  PubMed  Google Scholar 

  79. Li Manni G, Smart SD, Alavi A (2016) J Chem Theory Comput 12:1245–1258

    Article  PubMed  CAS  Google Scholar 

  80. Moritz G, Hess BA, Reiher M (2005) J Chem Phys 122:024107

    Article  PubMed  CAS  Google Scholar 

  81. Zgid D, Nooijen M (2008) J Chem Phys 128:014107

    Article  PubMed  CAS  Google Scholar 

  82. Chan GKL, Sharma S (2011) Annu Rev Phys Chem 62:465–481

    Google Scholar 

  83. Boguslawski K, Tecmer P, Legeza Ö, Reiher M (2012) J Phys Chem Lett 3:3129–3135

    Article  CAS  PubMed  Google Scholar 

  84. Stein CJ, Reiher M (2016) J Chem Theory Comput 12:1760–1771

    Article  CAS  PubMed  Google Scholar 

  85. Ma Y, Knecht S, Keller S, Reiher M (2017) J Chem Theory Comput 13:2533–2549

    Article  CAS  PubMed  Google Scholar 

  86. Baiardi A, Stein CJ, Barone V, Reiher M (2017) J Chem Theory Comput 13:3764–3777

    Article  CAS  PubMed  Google Scholar 

  87. Battaglia S, Keller S, Knecht S (2018) J Chem Theory Comput 14:2353–2369

    Article  CAS  PubMed  Google Scholar 

  88. Moritz G, Reiher M (2007) J Chem Phys 126:244109

    Article  PubMed  CAS  Google Scholar 

  89. Sobczak P, Barasiński A, Drzewiński A, Kamieniarz G, Kłak J, Bieńko A, Mroziński J (2009) Polyhedron 28:1838–1841

    Article  CAS  Google Scholar 

  90. Barasiński A, Sobczak P, Drzewiński A, Kamieniarz G, Bieńko A, Mroziński J, Gatteschi D (2010) Polyhedron 29:1485–1491

    Article  CAS  Google Scholar 

  91. Schnack J, Ummethum J (2013) Polyhedron 66:28–33

    Article  CAS  Google Scholar 

  92. Keller S, Boguslawski K, Janowski T, Reiher M, Pulay P (2015) J Chem Phys 142:244104

    Article  PubMed  CAS  Google Scholar 

  93. Sayfutyarova ER, Sun Q, Chan GK, Knizia G (2017) J Chem Theory Comput 13:4063–4078

    Article  CAS  PubMed  Google Scholar 

  94. Bao JJ, Dong SS, Gagliardi L, Truhlar DG (2018) J Chem Theory Comput 14:2017–2025

    Article  CAS  PubMed  Google Scholar 

  95. Barcza G, Legeza Ö, Marti KH, Reiher M (2011) Phys Rev A 83

    Google Scholar 

  96. Saitow M, Kurashige Y, Yanai T (2015) J Chem Theory Comput 11:5120–5131

    Article  CAS  PubMed  Google Scholar 

  97. Guo S, Watson MA, Hu W, Sun Q, Chan GKL (2016) J Chem Theory Comput 12:1583–1591

    Google Scholar 

  98. Roemelt M, Guo S, Chan GKL (2016) J Chem Phys 144:204113

    Article  PubMed  CAS  Google Scholar 

  99. Yanai T, Saitow M, Xiong XG, Chalupský J, Kurashige Y, Guo S, Sharma S (2017) J Chem Theory Comput 13:4829–4840

    Article  CAS  PubMed  Google Scholar 

  100. Boguslawski K, Tecmer P, Barcza G, Legeza Ö, Reiher M (2013) J Chem Theory Comput 9:2959–2973

    Article  CAS  PubMed  Google Scholar 

  101. Wouters S, Bogaerts T, Van Der Voort P, Van Speybroeck V, Van Neck D (2014) J Chem Phys 140:241103

    Article  PubMed  CAS  Google Scholar 

  102. Kurashige Y, Saitow M, Chalupský J, Yanai T (2014) Phys Chem Chem Phys 16:11988–11999

    Article  CAS  PubMed  Google Scholar 

  103. Chalupský J, Rokob TA, Kurashige Y, Yanai T, Solomon EI, Rulíšek L, Srnec M (2014) J Am Chem Soc 136:15977–15991

    Article  PubMed  CAS  Google Scholar 

  104. Ma Y, Knecht S, Reiher M (2017) Chem Phys Chem 18:384–393

    Article  CAS  PubMed  Google Scholar 

  105. Phung QM, Domingo A, Pierloot K (2018) Chem Eur J 24:5183–5190

    Google Scholar 

  106. Phung QM, Pierloot K (2018) Phys Chem Chem Phys 20:17009–17019

    Article  CAS  PubMed  Google Scholar 

  107. Dong G, Phung QM, Hallaert SD, Pierloot K, Ryde U (2017) Phys Chem Chem Phys 19:10590–10601

    Article  CAS  PubMed  Google Scholar 

  108. Zhang C, Chen C, Dong H, Shen JR, Dau H, Zhao J (2015) Science 348:690–693

    Article  CAS  PubMed  Google Scholar 

  109. Paul S, Neese F, Pantazis DA (2017) Green Chem 19:2309–2325

    Article  CAS  Google Scholar 

  110. Umena Y, Kawakami K, Shen J-R, Kamiya N (2011) Nature 473:55–60

    Article  CAS  PubMed  Google Scholar 

  111. Pantazis DA, Ames W, Cox N, Lubitz W, Neese F (2012) Angew Chem Int Ed 51:9935–9940

    Google Scholar 

  112. Krewald V, Retegan M, Pantazis DA (2016) Top Curr Chem 371:23–48

    Article  CAS  PubMed  Google Scholar 

  113. Beinert H, Holm RH, Münck E (1997) Science 277:653–659

    Article  CAS  PubMed  Google Scholar 

  114. Lledós A, Moreno-Mañas M, Sodupe M, Vallribera A, Mata I, Martínez B, Molins E (2003) Eur J Inorg Chem 2003:4187–4194

    Article  CAS  Google Scholar 

  115. Boguslawski K, Marti KH, Reiher M (2011) J Chem Phys 134:224101

    Article  PubMed  CAS  Google Scholar 

  116. Bencini A, Totti F (2008) Inorg Chim Acta 361:4153–4156

    Article  CAS  Google Scholar 

  117. Bastardis R, Guihéry N, de Graaf C (2008) J Chem Phys 129:104102

    Article  PubMed  CAS  Google Scholar 

  118. Spivak M, Angeli C, Calzado CJ, de Graaf C (2014) J Comput Chem 35:1665–1671

    Article  CAS  PubMed  Google Scholar 

  119. Bossek U, Weyhermueller T, Wieghardt K, Nuber B, Weiss J (1990) J Am Chem Soc 112:6387–6388

    Article  CAS  Google Scholar 

  120. Kanady JS, Tsui EY, Day MW, Agapie T (2011) Science 333:733–736

    Article  CAS  PubMed  Google Scholar 

  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 109:2257–2262

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  122. Krewald V, Retegan M, Neese F, Lubitz W, Pantazis DA, Cox N (2016) Inorg Chem 55:488–501

    Article  CAS  PubMed  Google Scholar 

  123. Stein CJ, von Burg V, Reiher M (2016) J Chem Theory Comput 12:3764–3773

    Article  CAS  PubMed  Google Scholar 

  124. Angeli C, Calzado CJ (2012) J Chem Phys 137:034104

    Article  PubMed  CAS  Google Scholar 

  125. Bjornsson R, Lima FA, Spatzal T, Weyhermüller T, Glatzel P, Bill E, Einsle O, Neese F, DeBeer S (2014) Chem Sci 5:3096–3103

    Article  CAS  Google Scholar 

  126. Domingo A, Specklin D, Rosa V, Mameri S, Robert V, Welter R (2014) Eur J Inorg Chem 2014:2552–2560

    Article  CAS  Google Scholar 

  127. Kurashige Y, Yanai T (2011) J Chem Phys 135:094104

    Article  PubMed  CAS  Google Scholar 

  128. Saitow M, Kurashige Y, Yanai T (2013) J Chem Phys 139:044118

    Article  PubMed  CAS  Google Scholar 

  129. Sharma S, Chan GKL (2014) J Chem Phys 141:111101

    Google Scholar 

  130. Yanai T, Kurashige Y, Mizukami W, Chalupský J, Lan TN, Saitow M (2015) Int J Quantum Chem 115:283–299

    Article  CAS  Google Scholar 

  131. Veis L, Antalík A, Brabec J, Neese F, Legeza Ö, Pittner J (2016) J Phys Chem Lett 7:4072–4078

    Article  CAS  PubMed  Google Scholar 

  132. Phung QM, Wouters S, Pierloot K (2016) J Chem Theory Comput 12:4352–4361

    Article  CAS  PubMed  Google Scholar 

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Authors and Affiliations

  1. Fachbereich Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 4, 64287, Darmstadt, Germany

    Vera Krewald

  2. Max-Planck-Institut Für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470, Mülheim an der Ruhr, Germany

    Dimitrios A. Pantazis

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  1. Vera Krewald
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Correspondence to Dimitrios A. Pantazis .

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Editors and Affiliations

  1. Jerzy Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Kraków, Poland

    Ewa Broclawik

  2. Jerzy Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Kraków, Poland

    Tomasz Borowski

  3. Faculty of Chemistry, Jagiellonian University, Kraków, Poland

    Mariusz Radoń

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Krewald, V., Pantazis, D.A. (2019). Applications of the Density Matrix Renormalization Group to Exchange-Coupled Transition Metal Systems. In: Broclawik, E., Borowski, T., Radoń, M. (eds) Transition Metals in Coordination Environments. Challenges and Advances in Computational Chemistry and Physics, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-030-11714-6_4

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