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New Strategies in Modeling Electronic Structures and Properties with Applications to Actinides

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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

This chapter discusses contemporary quantum chemical methods and provides general insights into modern electronic structure theory with a focus on heavy-element-containing compounds. We first give a short overview of relativistic Hamiltonians that are frequently applied to account for relativistic effects. Then, we scrutinize various quantum chemistry methods that approximate the N-electron wave function. In this respect, we will review the most popular single- and multi-reference approaches that have been developed to model the multi-reference nature of heavy element compounds and their ground- and excited-state electronic structures. Specifically, we introduce various flavors of post-Hartree–Fock methods and optimization schemes like the complete active space self-consistent field method, the configuration interaction approach, the Fock-space coupled cluster model, the pair-coupled cluster doubles ansatz, also known as the antisymmetric product of 1 reference orbital geminal, and the density matrix renormalization group algorithm. Furthermore, we will illustrate how concepts of quantum information theory provide us with a qualitative understanding of complex electronic structures using the picture of interacting orbitals. While modern quantum chemistry facilitates a quantitative description of atoms and molecules as well as their properties, concepts of quantum information theory offer new strategies for a qualitative interpretation that can shed new light onto the chemistry of complex molecular compounds.

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References

  1. Adamo C, Barone V (1999) Toward reliable density functional methods without adjustable parameters: the PBE0 model. Phys Rev Lett 110:6158–6170

    CAS  Google Scholar 

  2. Almond PM, Skanthakumar S, Soderholm L, Burns PC (2007) Cation-cation interactions and antiferromagnetism in Na[Np(V)O\(_2\)(OH)\(_2\)]: synthesis, structure, and magnetic properties. Chem Mater 19:280–285

    Article  CAS  Google Scholar 

  3. Andersson K, Malmqvist PÅ, Roos BO, Sadlej AJ, Woliński K (1990) Second-order perturbation theory with a CASSCF reference function. J Phys Chem 94:5483–5488

    Article  CAS  Google Scholar 

  4. Andersson K, Malmqvist PÅ, Roos BO (1992) Second-order perturbation theory with a complete active space self-consistent field reference function. J Chem Phys 96:1218–1226

    Article  CAS  Google Scholar 

  5. Arnold PL, Love JB, Patel D (2009) Pentavalent uranyl complexes. Coord Chem Rev 253:1973–1978

    Article  CAS  Google Scholar 

  6. Autschbach J, Siekierski S, Seth M, Schwerdtfeger P, Schwarz WHE (2002) Dependence of relativistic effects on electronic configuration in the neutral atoms of d- and f-block elements. J Comput Chem 23:804–813

    Article  CAS  PubMed  Google Scholar 

  7. Barcza G, Legeza Ö, Marti KH, Reiher M (2011) Quantum-information analysis of electronic states of different molecular structures. Phys Rev A 83:012508

    Article  CAS  Google Scholar 

  8. Barcza G, Noack R, Sólyom J, Legeza Ö (2014) Entanglement patterns and generalized correlation functions in quantum many-body systems. Phys Rev B 92:125140

    Article  CAS  Google Scholar 

  9. Barysz M (2003) Two-component methods. In: Kaldor U, Wilson S (eds) Theoretical chemistry and physics of heavy and superheavy elements. Springer, pp 349–397. Chapter 9

    Google Scholar 

  10. Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38:3098–4000

    Article  CAS  Google Scholar 

  11. Boguslawski K (2016) Targeting excited states in all-trans polyenes with electron-pair states. J Chem Phys 145:234105

    Article  PubMed  CAS  Google Scholar 

  12. Boguslawski K (2017) Erratum: “targeting excited states in all-trans polyenes with electron-pair states”. J Chem Phys 147(13):139901

    Article  PubMed  CAS  Google Scholar 

  13. Boguslawski K, Ayers PW (2015) Linearized coupled cluster correction on the antisymmetric product of 1-reference orbital geminals. J Chem Theory Comput 11:5252–5261

    Article  CAS  PubMed  Google Scholar 

  14. Boguslawski K, Reiher M (2014) Chemical bonding in open-shell transition-metal complexes. In: Frenking G, Shaik S (eds) The chemical bond: Chemical bonding across the periodic table, 1st edn. Wiley-VCH Verlag GmbH & Co KGaA, Weinheim, chap 8, pp 219–252

    Google Scholar 

  15. Boguslawski K, Tecmer P (2015) Orbital entanglement in quantum chemistry. Int J Quantum Chem 115:1289–1295

    Article  CAS  Google Scholar 

  16. Boguslawski K, Tecmer P (2017) Erratum: orbital entanglement in quantum chemistry. Int J Quantum Chem 117:e25455

    Article  CAS  Google Scholar 

  17. Boguslawski K, Tecmer P, Legeza Ö, Reiher M (2012) Entanglement measures for single- and multireference correlation effects. J Phys Chem Lett 3:3129–3135

    Article  CAS  PubMed  Google Scholar 

  18. Boguslawski K, Tecmer P, Barcza G, Legeza Ö, Reiher M (2013) Orbital entanglement in bond-formation processes. J Chem Theory Comput 9:2959–2973

    Article  CAS  PubMed  Google Scholar 

  19. Boguslawski K, Tecmer P, Ayers PW, Bultinck P, de Baerdemacker S, van Neck D (2014a) Efficient description of strongly correlated electrons with mean-field cost. Phys Rev B 89:201106

    Article  CAS  Google Scholar 

  20. Boguslawski K, Tecmer P, Limacher PA, Johnson PA, Ayers PW, Bultinck P, de Baerdemacker S, van Neck D (2014b) Nonvariational orbital optimization techniques for the AP1roG wave function. J Chem Theory Comput 10:4873–4882

    Article  CAS  PubMed  Google Scholar 

  21. Boguslawski K, Tecmer P, Limacher PA, Johnson PA, Ayers PW, Bultinck P, de Baerdemacker S, van Neck D (2014c) Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal. J Chem Phys 140:214114

    Article  PubMed  CAS  Google Scholar 

  22. Boguslawski K, Réal F, Tecmer P, Duperrouzel C, Gomes ASP, Legeza Ö, Ayers PW, Vallet V (2017) On the multi-reference nature of plutonium oxides: PuO\(_2^{2+}\), PuO\(_2\), PuO\(_3\), and PuO\(_2\)(OH)\(_2\). Phys Chem Chem Phys 19:4317–4329

    Article  CAS  PubMed  Google Scholar 

  23. Breit G (1929) The effect of retardation on the interaction of two electrons. Phys Rev 34:553–573

    Article  CAS  Google Scholar 

  24. Bytautas L, Henderson TM, Jiménez-Hoyos CA, Ellis JK, Scuseria GE (2011) Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy. J Chem Phys 135:044119

    Article  PubMed  CAS  Google Scholar 

  25. Chan GKL, Sharma S (2011) The density matrix renormalization group in quantum chemistry. Annu Rev Phys Chem 62:465–481

    Article  CAS  PubMed  Google Scholar 

  26. Chang C, Pelissier M, Durand P (1986) Regular two-component Pauli-like effective hamiltonians in Dirac theory. Phys Scr 34:394–404

    Article  CAS  Google Scholar 

  27. Chatterjee K, Pastorczak E, Jawulski K, Pernal K (2016) A minimalistic approach to static and dynamic electron correlations: amending generalized valence bond method with extended random phase approximation correlation correction. J Chem Phys 113:2960–2963

    Google Scholar 

  28. Choppin GR, Rao LF (1984) Complexation of pentavalent and hexavalent actinides by fluoride. Radiochim Acta 37:143–146

    Article  CAS  Google Scholar 

  29. Cohen AJ, Mori-Sánchez P, Yang W (2012) Challenges for density functional theory. Chem Rev 112:289–320

    Article  CAS  PubMed  Google Scholar 

  30. Coleman AJ (1965) Structure of fermion density matrices. II. Antisymmetrized geminal powers. J Math Phys 6:1425–1431

    Article  Google Scholar 

  31. Cremer D (2001) Density functional theory: coverage of dynamic and non-dynamic electron correlation effects. Mol Phys 99:1899–1940

    Article  CAS  Google Scholar 

  32. de Jong WA, Visscher L, Nieuwpoort WC (1999) On the bonding and the electric field gradient of the uranyl ion. J Mol Struct (Theochem) 458:41–52

    Article  Google Scholar 

  33. Denning RG (1992) Electronic structure and bonding in actinyl ions, vol 79. Springer, Berlin, Heidelberg, pp 313–336

    Google Scholar 

  34. Denning RG (2007) Electronic structure and bonding in actinyl ions and their analogs. J Phys Chem A 111:4125–4143

    Article  CAS  PubMed  Google Scholar 

  35. Dirac PAM (1928) The quantum theory of the electron. Proc Roy Soc Lond A 117:610–624

    Article  Google Scholar 

  36. Diwu J, Wang S, Albrecht-Schmitt TE (2012) Periodic trends in hexanuclear actinide clusters. Inorg Chem 51:4088–4093

    Article  CAS  PubMed  Google Scholar 

  37. Dolg M, Cao X (2012) Relativistic pseudopotentials: their development and scope of applications. Chem Rev 112:403–480

    Article  CAS  PubMed  Google Scholar 

  38. Douglas N, Kroll NM (1974) Quantum electrodynamical corrections to fine-structure of helium. Ann Phys 82:89–155

    Article  CAS  Google Scholar 

  39. Duperrouzel C, Tecmer P, Boguslawski K, Barcza G, Legeza Ö, Ayers PW (2015) A quantum informational approach for dissecting chemical reactions. Chem Phys Lett 621:160–164

    Article  CAS  Google Scholar 

  40. Foldy LL, Wouthuysen SA (1950) On the Dirac theory of spin 1/2 particles and its non-relativistic limit. Phys Rev 78:29–36

    Article  Google Scholar 

  41. Forbes TZ, Burns PC, Soderholm L, Skanthakumar S (2006) Crystal structures and magnetic properties of NaK\(_3\)(NpO\(_2\))\(_4\)(SO\(_4\))\(_4\)(H\(_2\)O)\(_2\) and NaNpO\(_2\)SO\(_4\)H\(_2\)O: cation-cation interactions in a neptunyl sulfate framework. Chem Mater 18:1643–1649

    Article  CAS  Google Scholar 

  42. Fortier S, Hayton TW (2010) Oxo ligand functionalization in the uranyl ion (UO\(_2^{2+}\)). Coord Chem Rev 254:197

    Article  CAS  Google Scholar 

  43. Gainar I, Sykes KW (1964) The spectra and stability of some neptunium complex ions in water and methanol. J Chem Soc 9:4452–4459

    Article  Google Scholar 

  44. Garza AJ, Bulik IW, Henderson TM, Scuseria GE (2015a) Range separated hybrids of pair coupled cluster doubles and density functionals. Phys Chem Chem Phys 17:22412–22422

    Article  CAS  PubMed  Google Scholar 

  45. Garza AJ, Bulik IW, Henderson TM, Scuseria GE (2015b) Synergy between pair coupled cluster doubles and pair density functional theory. J Chem Phys 142:044109

    Article  PubMed  CAS  Google Scholar 

  46. Garza AJ, Sousa Alencar AG, Scuseria GE (2015c) Actinide chemistry using singlet-paired coupled cluster and its combinations with density functionals. J Chem Phys 143:244106

    Article  PubMed  CAS  Google Scholar 

  47. Garza AJ, Bulik IW, Alencar AGS, Sun J, Perdew JP, Scuseria GE (2016) Combinations of coupled cluster, density functionals, and the random phase approximation for describing static and dynamic correlation, and van der Waals interactions. Mol Phys 114:997–1018

    Article  CAS  Google Scholar 

  48. Gaunt JA (1929) The triplets of helium. Proc Roy Soc Lond A 122:513–532

    Article  CAS  Google Scholar 

  49. Goddard WA, Dunning TH Jr, Hunt WJ, Hay PJ (1973) Generalized valence bond description of bonding in low-lying states of molecules. Acc Chem Res 6:368–376

    Article  CAS  Google Scholar 

  50. Gomes ASP, Jacob CR, Visscher L (2008) Calculation of local excitations in large systems by embedding wave-function theory in density-functional theory. Phys Chem Chem Phys 10:5353–5362

    Article  CAS  PubMed  Google Scholar 

  51. Gomes ASP, Jacob CR, Réal F, Visscher L, Vallet V (2013) Towards systematically improvable models for actinides in condensed phase: the electronic spectrum of uranyl in Cs\(_2\)UO\(_2\)Cl\(_4\) as a test case. Phys Chem Chem Phys 15:15153–15162

    Article  CAS  PubMed  Google Scholar 

  52. Goncharov V, Han J, Kaledin LA, Heaven MC (2005) Ionization energy measurements and electronic spectra for ThO. J Chem Phys 122:204311

    Article  PubMed  CAS  Google Scholar 

  53. Goncharov V, Kaledin LA, Heaven MC (2006) Probing the electronic structure of UO\(^+\) with high-resolution photoelectron spectroscopy. J Phys Chem 125:133202

    Article  CAS  Google Scholar 

  54. Guillaume B, Hobart DE, Bourges JY (1981) “Cation-cation” complexes of pentavalent actinides—II Spectrophotometric study of complexes of americium(V) with uranyl(VI) and neptunyl(VI) ions in aqueous perchlorate solution. J Inorg Nucl Chem 43:3295–3299

    Article  CAS  Google Scholar 

  55. Häller LJL, Kaltsoyannis N, Sarsfield MJ, May I, Cornet SM, Redmond MP, Helliwell M (2007) A structural and theoretical investigation of equatorial cis and trans uranyl phosphinimine and uranyl phosphine oxide complexes UO\(_2\)Cl\(_2\)(Cy\(_3\)PNH)\(_2\) and UO\(_2\)Cl\(_2\)(Cy\(_3\)PO)\(_2\). Inorg Chem 46:4868–4875

    Article  PubMed  CAS  Google Scholar 

  56. Halperin J, Oliver JH (1983) Sulfate complexation of neptunium(V) in aqueous solution. Radiochim Acta 33:29–33

    Article  CAS  Google Scholar 

  57. Hay PJ, Hunt WJ, Goddard WA (1972) Generalized valence bond wavefunctions for the low lying states of methylene. Chem Phys Lett 13:30–35

    Article  CAS  Google Scholar 

  58. Hayton TW (2013) Uranium chemistry: an actinide milestone. Nat Chem 5:451–452

    Article  CAS  PubMed  Google Scholar 

  59. Hégely B, Nagy PR, Ferenczy GG, Kállay M (2016) Exact density functional and wave function embedding schemes based on orbital localization. J Chem Phys 145(6):064107

    Article  CAS  Google Scholar 

  60. Helgaker T, Jørgensen P, Olsen J (2000) Molecular electronic-structure theory. Wiley, New York

    Book  Google Scholar 

  61. Hess BA (1986) Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators. Phys Rev A 33:3742–3748

    Article  CAS  Google Scholar 

  62. Hess BA, Marian CM, Wahlgren U, Gropen O (1996) A mean-field spin-orbit method applicable to correlated wavefunctions. Chem Phys Lett 251:365–371

    Article  CAS  Google Scholar 

  63. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871

    Article  Google Scholar 

  64. Hurley AC, Lennard-Jones J, Pople JA (1953) The molecular orbital theory of chemical valency XIV. Paired electrons in the presence of two unlike attracting centres. Proc R Soc Lond Ser A 220:446–455

    Article  CAS  Google Scholar 

  65. Ilias̆ M, Saue T (2007) An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation. J Chem Phys 126:064102

    Google Scholar 

  66. Infante I, Gomes ASP, Visscher L (2006) On the performance of the intermediate Hamiltonian Fock-space coupled-cluster method on linear triatomic molecules: the electronic spectra of NpO\(_2^+\), NpO\(_2^{2+}\), and PuO\(_2^{2+}\). J Chem Phys 125:074301

    Article  PubMed  CAS  Google Scholar 

  67. Ingram KIM, Kaltsoyannis N, Gaunt AJ, Neu MP (2007) Covalency in the f-element-chalcogen bond computational studies of [M(N(EPH\(_2\))\(_2\))\(_3\)] (M = La, U, Pu; E = O, S, Se, Te). J Alloys Compd 444–445:369–375

    Article  CAS  Google Scholar 

  68. Ingram KIM, Tassell MJ, Gaunt AJ, Kaltsoyannis N (2008) Covalency in the f element-chalcogen bond. Computational studies of M[N(EPR\(_2\))\(_2\)]\(_3\) (M = La, Ce, Pr, Pm, Eu, U, Np, Pu, Am, Cm; E = O, S, Se, Te; R = H, (i)Pr, Ph). Inorg Chem 47:7824–7833

    Article  CAS  PubMed  Google Scholar 

  69. Jackson VE, Craciun R, Dixon DA, Peterson K, de Jong WB (2008) Prediction of Vibrational Frequencies of UO\(_2^{2+}\) at the CCSD(T) Level. J Phys Chem A 112:4095–4099

    Google Scholar 

  70. Jeszenszki P, Nagy PR, Zoboki T, Szabados A, Surján PR (2014) Perspectives of APSG-based multireference perturbation theories. Int J Quantum Chem 114:1048–1052

    Article  CAS  Google Scholar 

  71. Jin GB, Skanthakumar S, Soderholm L (2011a) Cation-cation interactions: crystal structures of neptunyl(V) selenate hydrates, (NpO\(_2\))\(_2\)(SeO\(_4\))(H\(_2\)O)\(_n\) (\(n\) = 1, 2, and 4). Inorg Chem 50:5203–5214

    Article  CAS  PubMed  Google Scholar 

  72. Jin GB, Skanthakumar S, Soderholm L (2011b) Two new neptunyl(V) selenites: a novel cation-cation interaction framework in (NpO\(_2\))\(_3\)(OH)(SeO\(_3\))(H\(_2\)O)\(_2\cdot \)H\(_2\)O and a uranophane-type sheet in Na(NpO\(_2\))(SeO\(_3\))(H\(_2\)O). Inorg Chem 50:6297–6303

    Article  CAS  PubMed  Google Scholar 

  73. Johnson PA, Ayers PW, Limacher PA, de Baerdemacker S, van Neck D, Bultinck P (2013) A size-consistent approach to strongly correlated systems using a generalized antisymmetrized product of nonorthogonal geminals. J Chem Theor Comput 1003:101–113

    Article  CAS  Google Scholar 

  74. Keller S, Boguslawski K, Janowski T, Reiher M, Pulay P (2015) Selection of active spaces for multiconfigurational wavefunctions. J Chem Phys 142:244104

    Article  PubMed  CAS  Google Scholar 

  75. Kędziera D (2006) Solving of the infinite-order two-component method equations. In: Recent progess in computational sciences and engineering, VSP BV-C/O BRILL ACAD PUBL, Leiden, The Netherlands, Lecture series on computer and computational sciences, vol 7A–B, pp 252–255

    Google Scholar 

  76. Kędziera D, Barysz M (2007) Non-iterative approach to the infinite-order two-component (IOTC) relativistic theory and the non-symmetric algebraic Riccati equation. Chem Phys Lett 446:176–181

    Google Scholar 

  77. Knecht S, Keller S, Autschbach J, Reiher M (2016) A nonorthogonal state-interaction approach for matrix product state wave functions. J Chem Theory Comput 12:5881–5894

    Article  CAS  PubMed  Google Scholar 

  78. Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133–A1138

    Article  Google Scholar 

  79. Kovács A, Konings RJM, Raab J, Gagliardi L (2008) A theoretical study of AmO\(_n\) and CmO\(_n\) (n = 1, 2). Phys Chem Chem Phys 10:1114–1117

    Article  PubMed  Google Scholar 

  80. Krylov AI (2006) Spin-flip equation-of-motion coupled-cluster electronic structure method for a description of excited states, bond breaking, diradicals, and triradicals. Acc Chem Res 39:83–91

    Article  CAS  PubMed  Google Scholar 

  81. Kümmel S, Kronik L (2008) Orbital-dependent density functionals: theory and applications. Rev Mod Phys 80:3–60

    Article  CAS  Google Scholar 

  82. Kurashige Y, Yanai T (2011) Second-order perturbation theory with density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer. J Chem Phys 135:094104

    Article  PubMed  CAS  Google Scholar 

  83. Kutepov AL (2007) The effect of exact calculation of exchange interaction upon calculated electronic structure of actinides. J Alloys Compd 444–445:174–176

    Article  CAS  Google Scholar 

  84. Kutzelnigg W (1964) Direct determination of natural orbitals and natural expansion coefficients of many-electron wavefunctions. I. Natural orbitals in the geminal product spproximation. J Chem Phys 40:3640–3647

    Article  CAS  Google Scholar 

  85. Kutzelnigg W (1965) On the validity of the electron pair approximation for the beryllium ground state. Theor Chim Acta 3:241–253

    Article  CAS  Google Scholar 

  86. Łachmanska A, Tecmer P, Legeza Ö, Boguslawski K (2018) Elucidating cation–cation interactions in neptunyl dications using multireference ab initio theory. Phys Chem Chem Phys 21:744–759

    Google Scholar 

  87. Langhoff SR, Davidson ER (1974) Configuration interaction calculations on the nitrogen molecule. Int J Quantum Chem 8:61–72

    Article  CAS  Google Scholar 

  88. Lawler KV, Beran GJO, Head-Gordon M (2008) Symmetry breaking in benzene and larger aromatic molecules within generalized valence bond coupled cluster methods. J Chem Phys 128:024107

    Article  PubMed  CAS  Google Scholar 

  89. Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785–789

    Article  CAS  Google Scholar 

  90. Legeza Ö, Sólyom J (2003) Optimizing the density-matrix renormalization group method using quantum information entropy. Phys Rev B 68:195116

    Article  CAS  Google Scholar 

  91. Legeza Ö, Noack R, Sólyomand J, Tincani L (2005) Applications of quantum information in the density-matrix renormalization group. In: Fehske H, Schneider R, Weiße A (eds) Computational many-particle physics. Springer, Berlin/Heidelberg, chap 24, pp 653–664

    Google Scholar 

  92. Legeza Ö, Barcza G, Noack RM, Sólyom J (2013) Entanglement topology of strongly correlated systems. Korrelationstage MPIPKS, Dresden

    Google Scholar 

  93. Li J, Bursten BE, Liang B, Andrews L (2002) Noble gas-actinide compounds: complexation of the CUO molecule by Ar, Kr, and Xe atoms in noble gas matrices. Science 295:2242–2245

    Article  CAS  PubMed  Google Scholar 

  94. Liang B, Andrews L, Li J, Bursten BE (2002) Noble gas-actinide compounds: evidence for the formation of distinct CUO(Ar)\(_{4-n}\)(Xe)\(_n\) and CUO(Ar)\(_{4-n}\)(Xe)\(_n\) (n = 1, 2, 3, 4) complexes. J Am Chem Soc 124:9016–9017

    Article  CAS  PubMed  Google Scholar 

  95. Limacher P, Ayers P, Johnson P, de Baerdemacker S, van Neck D, Bultinck P (2014) Simple and inexpensive perturbative correction schemes for antisymmetric products of nonorthogonal geminals. Phys Chem Chem Phys 16:5061–5065

    Article  CAS  PubMed  Google Scholar 

  96. Limacher PA, Ayers PW, Johnson PA, de Baerdemacker S, van Neck D, Bultinck P (2013) A new mean-field method suitable for strongly correlated electrons: computationally facile antisymmetric products of nonorthogonal geminals. J Chem Theor Comput 9:1394–1401

    Article  CAS  Google Scholar 

  97. Malmqvist PÅ, Roos BO, Schimmelpfennig B (2002) The restricted active space (RAS) state interaction approach with spin-orbit coupling. Chem Phys Lett 357:230–240

    Article  CAS  Google Scholar 

  98. Marian CM, Wahlgren U (1996) A new mean-field and ECP-based spin-orbit method. Applications to Pt and PtH. Chem Phys Lett 251:357–364

    Article  CAS  Google Scholar 

  99. Marti KH, Reiher M (2010) The density matrix renormalization group algorithm in quantum chemistry. Z Phys Chem 224:583–599

    Article  CAS  Google Scholar 

  100. Matsika S, Zhang Z, Brozell SR, Bladeau JP, Pitzer RM (2001) Electronic structure and spectra of actinyl ions. J Phys Chem A 105:3825–3828

    Article  CAS  Google Scholar 

  101. Meissner L, Musiał M (2010) Intermediate Hamiltonian formulations of the Fock-space coupled-cluster method: details, comparisons, examples. In: Recent progress in coupled cluster methods. Springer, p 395

    Google Scholar 

  102. Mikheev NB, Kulyukhin SA, Melikhov IV (2007) Lanthanides and actinides among other groups of elements of the periodic table. Radioch 49:449–463

    Article  CAS  Google Scholar 

  103. Mottet M, Tecmer P, Boguslawski K, Legeza Ö, Reiher M (2014) Quantum entanglement in carbon-carbon, carbon-phosphorus, and silicon-silicon bonds. Phys Chem Chem Phys 16:8872–8880

    Article  CAS  PubMed  Google Scholar 

  104. Murg V, Verstraete F, Schneider R, Nagy PR, Legeza O (2015) Tree tensor network state with variable tensor order: an efficient multireference method for strongly correlated systems. J Chem Theory Comput 11:1027–1036

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  105. Musiał M, Bartlett RJ (2011) Multi-reference fock space coupled-cluster method in the intermediate hamiltonian formulation for potential energy surfaces. J Chem Phys 135(4):044121

    Article  PubMed  CAS  Google Scholar 

  106. Neuscamman E, Yanai T, Chan GKL (2010) A review of canonical transformation theory. Int Rev Phys Chem 29:231–271

    Article  CAS  Google Scholar 

  107. Parks JM, Parr RG (1958) Theory of separated electron pairs. J Chem Phys 28:335–345

    Article  CAS  Google Scholar 

  108. Parr RG, Ellison FO, Lykos PG (1956) Generalized antisymmetrized product wave functions for atoms and molecules. J Chem Phys 24:1106–1106

    Article  CAS  Google Scholar 

  109. Pastorczak E, Pernal K (2015) ERPA-APSG: a computationally efficient geminal-based method for accurate description of chemical systems. Phys Chem Chem Phys 17:8622–8626

    Article  CAS  PubMed  Google Scholar 

  110. Perdew JP (1986) Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys Rev B 33:8822–8824

    Article  CAS  Google Scholar 

  111. Perdew JP, Zunger A (1981) Self-interaction correction to density-functional approximations for many-electron systems. Phys Rev B 23:5048

    Article  CAS  Google Scholar 

  112. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868

    Article  CAS  PubMed  Google Scholar 

  113. Perdew JP, Burke K, Ernzerhof M (1997) Generalized gradient approximation made simple. Phys Rev Lett 78:1396

    Article  CAS  Google Scholar 

  114. Pernal K (2014) Intergeminal correction to the antisymmetrized product of strongly orthogonal geminals derived from the extended random phase approximation. J Chem Theory Comput 10:4332–4341

    Article  CAS  PubMed  Google Scholar 

  115. Peyerimhoff SD, Buenker RJ (1969) Study of the geometry and spectra of the allylic systems by ab initio methods. J Chem Phys 51:2528–2537

    Article  CAS  Google Scholar 

  116. Pierloot K, van Besien E (2005) Electronic spectrum of UO\(_2^{2+}\) and [UO\(_2\)Cl\(_4\)]\(^{2-}\). J Phys Chem 123:204309

    Article  CAS  Google Scholar 

  117. Pierloot K, van Besien E, van Lenthe E, Baerends EJ (2007) Electronic structure and spectrum of UO\(_2^{+2}\) 2 and UO\(_2\)Cl\(_4^{2-}\) calculated with time-dependent density functional theory. J Chem Phys 126:194311

    Article  PubMed  CAS  Google Scholar 

  118. Rao PRV, Gudi NM, Bagawde SV, Patil SK (1979) The complexing of neptunium(V) by some inorganic ligands. J Inorg Nucl Chem 41:235–239

    Article  CAS  Google Scholar 

  119. Rassolov VA (2002) A geminal model chemistry. J Chem Phys 117:5978–5987

    Article  CAS  Google Scholar 

  120. Rassolov VA, Xu F, Garashchuk S (2004) Geminal model chemistry II. Perturbative corrections. J Chem Phys 120:10385–10394

    Article  CAS  PubMed  Google Scholar 

  121. Réal F, Vallet V, Marian C, Wahlgren U (2007) On the bonding and the electric field gradient of the uranyl ion. J Phys Chem 127:214302

    Article  CAS  Google Scholar 

  122. Réal F, Gomes ASP, Visscher L, Vallet V, Eliav EJ (2009) Benchmarking electronic structure calculations on the bare UO\(_2^{2+}\) ion: how different are single and multireference electron correlation methods? J Phys Chem A 113:12504–12511

    Article  PubMed  CAS  Google Scholar 

  123. Reiher M (2006) Douglas-Kroll-Hess Theory: a relativistic electrons-only theory for chemistry. Theor Chem Acc 116:241–252

    Article  CAS  Google Scholar 

  124. Reiher M (2012) Relativistic Douglas-Kroll-Hess theory. WIREs Comput Mol Sci 2:139–149

    Article  CAS  Google Scholar 

  125. Rissler J, Noack RM, White SR (2006) Measuring orbital interaction using quantum information theory. Chem Phys 323:519–531

    Article  CAS  Google Scholar 

  126. Roesch F, Dittrich S, Buklanov GV, Milanov M, Khalkin VA, Dreyer R (1990) Electromigration of carrier-free radionuclides. 12. Reactions of neptunium-239(V) with acetate and citrate ligands in neutral solutions. Radiochim Acta 49:29–34

    CAS  Google Scholar 

  127. Rosta E, Surján PR (2002) Two-body zeroth order hamiltonians in multireference perturbation theory: the APSG reference state. J Chem Phys 116:878–889

    Article  CAS  Google Scholar 

  128. Saitow M, Kurashige Y, Yanai T (2013) Multireference configuration intaraction theory using cumulant reconstruction with internal contraction of density matrix renormalization group wave function. J Chem Phys 139:044118

    Article  PubMed  CAS  Google Scholar 

  129. Saue T (2012) Relativistic hamiltonians for chemistry: a primer. Chem Phys Chem 3:3077–3094

    Google Scholar 

  130. Schimmelpfennig B, Maron L, Wahlgren U, Teichteil C, Fagerli H, Gropen O (1998) On the combination of ECP-based CI calculations with all-electron spin-orbit mean-field integrals. Chem Phys Lett 286:267–271

    Article  CAS  Google Scholar 

  131. Schollwöck U (2005) The density-matrix renormalization group. Rev Mod Phys 77:259–315

    Article  CAS  Google Scholar 

  132. Sharma S, Chan G (2014) Communication: a flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states. J Chem Phys 141:111101

    Article  PubMed  CAS  Google Scholar 

  133. Sikkema J, Visscher L, Saue T, Ilias̆ M, (2009) The molecular mean-field approach for correlated relativistic calculations. J Chem Phys 131:124116

    Google Scholar 

  134. Skanthakumar S, Antonio MR, Soderholm L (2008) A comparison of neptunyl(V) and neptunyl(VI) solution coordination: the stability of cation-cation interactions. Inorg Chem 47:4591–4595

    Article  CAS  PubMed  Google Scholar 

  135. Stein CJ, Reiher M (2016) Automated selection of active orbital spaces. J Chem Theory Comput 12:1760–1771

    Article  CAS  PubMed  Google Scholar 

  136. Stein T, Henderson TM, Scuseria GE (2014) Seniority-based coupled cluster theory. J Chem Phys 140:214113

    Article  PubMed  CAS  Google Scholar 

  137. Straka M, Hrobarik P, Kaupp M (2005) Understanding structure and bonding in early actinide 6d\(^0\)5f\(^0\) MX\(_6^q\) (M = Th-Np; X = H, F) complexes in comparison with their transition metal 5d\(^0\) analogues. J Am Chem Soc 127:2591–2599

    Article  CAS  PubMed  Google Scholar 

  138. Sullivan JC (1962) Complex-ion formation between cations. Spectra and identification of a Np(V)-Cr(III) complex. J Am Chem Soc 84:4256–4259

    Article  CAS  Google Scholar 

  139. Sullivan JC, Hindman JC, Zielen AJ (1960) Kinetics of the reduction of neptunium(VI) by uranium(IV). J Am Chem Soc 82:5288–5292

    Article  CAS  Google Scholar 

  140. Sullivan JC, Hindman JC, Zielen AJ (1961) Specific interaction between Np(V) and U(VI) in aqueous perchloric acid media. J Am Chem Soc 83:3373–3378

    Article  CAS  Google Scholar 

  141. Surján PR, Jeszenszki P, Szabados Á (2015) Role of triplet states in geminal-based perturbation theory. Mol Phys 113:2960–2963

    Article  CAS  Google Scholar 

  142. Szalay S, Pfeffer M, Murg V, Barcza G, Verstraete F, Schneider R, Legeza Ö (2015) Tensor product methods and entanglement optimization for ab initio quantum chemistry. Int J Quantum Chem 115:1342–1391

    Article  CAS  Google Scholar 

  143. Szalay S, Barcza G, Szilvási T, Veis L, Legeza Ö (2017) The correlation theory of the chemical bond. Sci Rep 7:2237

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  144. Tecmer P, González-Espinoza CE (2018) Electron correlation effects of the ThO and ThS molecules in the spinor basis. A relativistic coupled cluster study of ground and excited states properties. Phys Chem Chem Phys 20:23424–23432

    Article  CAS  PubMed  Google Scholar 

  145. Tecmer P, Gomes ASP, Ekström U, Visscher L (2011) Electronic spectroscopy of UO\(_2^{2+}\), NUO\(^+\) and NUN: an evaluation of time-dependent density functional theory for actinides. Phys Chem Chem Phys 13:6249–6259

    Article  CAS  PubMed  Google Scholar 

  146. Tecmer P, Bast R, Ruud K, Visscher L (2012a) Charge-transfer excitations in uranyl tetrachloride \(([{\rm UO}_{2}{\rm Cl}_{4}]^{2-})\): How reliable are electronic spectra from relativistic time-dependent density functional theory? J Phys Chem A 116:7397–7404

    Article  CAS  PubMed  Google Scholar 

  147. Tecmer P, van Lingen H, Gomes ASP, Visscher L (2012b) The electronic spectrum of CUONg4 (Ng = Ne, Ar, Kr, Xe): new insights in the interaction of the CUO molecule with noble gas matrices. J Chem Phys 137:084308

    Article  PubMed  CAS  Google Scholar 

  148. Tecmer P, Govind N, Kowalski K, de Jong WA, Visscher L (2013) Reliable modeling of the electronic spectra of realistic uranium complexes. J Chem Phys 139:034301

    Article  PubMed  CAS  Google Scholar 

  149. Tecmer P, Boguslawski K, Johnson PA, Limacher PA, Chan M, Verstraelen T, Ayers PW (2014a) Assessing the accuracy of new geminal-based approaches. J Phys Chem A 118:9058–9068

    Article  CAS  PubMed  Google Scholar 

  150. Tecmer P, Boguslawski K, Legeza Örs, Reiher M (2014b) Unravelling the quantum-entanglement effect of noble gas coordination on the spin ground state of CUO. Phys Chem Chem Phys 16:719–727

    Article  CAS  PubMed  Google Scholar 

  151. Tecmer P, Gomes ASP, Knecht S, Visscher L (2014c) Communication: Relativistic fock-space coupled cluster study of small building blocks of larger uranium complexes. J Chem Phys 141:041107

    Article  PubMed  CAS  Google Scholar 

  152. Tecmer P, Boguslawski K, Ayers PW (2015) Singlet ground state actinide chemistry with geminals. Phys Chem Chem Phys 17:14427–14436

    Article  CAS  PubMed  Google Scholar 

  153. Tecmer P, Boguslawski K, Kȩdziera D (2017) Relativistic methods in computational quantum chemistry. In: Leszczyński J (ed) Handbook of computational chemistry, vol 2. Springer. Netherlands, Dordrecht, pp 885–926

    Chapter  Google Scholar 

  154. Vallet V, Maron L, Teichteil C, Flament JP (2000) A two-step uncontracted determinantal effective Hamiltonian-based SO-CI method. J Chem Phys 113:1391–1402

    Article  CAS  Google Scholar 

  155. Vallet V, Privalov T, Wahlgren U, Grenthe I (2004) The mechanism of water exchange in AmO\(_2\)(H\(_2\)O)\(_5^{(2+)}\) and in the isoelectronic UO\(_2\)(H\(_2\)O)\(_5^{(+)}\) and NpO\(_2\)(H\(_2\)O)\(_5^{(2+)}\) complexes as studied by quantum chemical methods. J Am Chem Soc 126:7766–7767

    Article  CAS  PubMed  Google Scholar 

  156. van Lenthe E, Baerends EJ, Snijders JG (1994) Relativistic total energy using regular approximations. J Chem Phys 101:9783

    Article  Google Scholar 

  157. van Wüllen C (2002) Relation between different variants of the generalized Douglas-Kroll transformation through sixth order. J Chem Phys 120:7307–7313

    Article  CAS  Google Scholar 

  158. Visscher L (2017) An introduction to relativistic quantum chemistry. In: Reine S, Saue T (eds) European summerschool in quantum chemistry 2017—book III, 10th edn. ESQC committee—2017, chap 7, pp 605–646

    Google Scholar 

  159. Vlaisavljevich B, Miró P, Ma D, Sigmon GE, Burns PC, Cramer CJ, Gagliardi L (2013) Synthesis and characterization of the first 2D neptunyl structure stabilized by side-on cation-cation interactions. Chem Eur J 19:2937–2941

    Article  CAS  PubMed  Google Scholar 

  160. Wang D, van Gunsteren WF, Chai Z (2012a) Recent advances in computational actinoid chemistry. Chem Soc Rev 41:5836–5865

    Article  CAS  PubMed  Google Scholar 

  161. Wang S, Alekseev EV, Depmeier W, Albrecht-Schmitt TE (2011) Surprising coordination for plutonium in the first plutonium(III) borate. Inorg Chem 50:4692–4694

    Article  CAS  PubMed  Google Scholar 

  162. Wang S, Diwu J, Alekseev EV, Jouffret LJ, Depmeier W, Albrecht-Schmitt TE (2012b) Cation-cation interactions between neptunyl(VI) units. Inorg Chem 51:7016–7018

    Article  CAS  PubMed  Google Scholar 

  163. Wei F, Wu G, Schwarz WH, Li J (2011) Geometries, electronic structures, and excited states of UN\(_2\), NUO\(^+\), and UO\(_2^{2+}\): A combined CCSD(T), RAS/CASPT2 and TDDFT study. Theor Chem Acc 129:467–481

    Article  CAS  Google Scholar 

  164. Wilson RE, Sio SD, Vallet V (2018) Protactinium and the intersection of actinide and transition metal chemistry. Nat Chem 9:622

    Google Scholar 

  165. Wolf A, Reiher M, Hess BA (2002) The generalized Douglas-Kroll transformation. J Chem Phys 117:9215–9226

    Article  CAS  Google Scholar 

  166. Wouters S, van Neck D (2014) The density matrix renormalization group for ab initio quantum chemistry. Eur Phys J D 68:272

    Article  CAS  Google Scholar 

  167. Wåhlin P, Danilo C, Vallet V, Réal F, Flament JP, Wahlgren U (2008) An investigation of the accuracy of different DFT functionals on the water exchange reaction in hydrated uranyl(VI) in the ground state and the first excited state. J Chem Theory Comput 4:569–577

    Article  PubMed  CAS  Google Scholar 

  168. Yabushita S, Zhang Z, Pitzer RM (1999) Spin-orbit configuration interaction using the graphical unitary group approach and relativistic core potential and spin-orbit operators. J Phys Chem A 103:5791–5800

    Article  CAS  Google Scholar 

  169. Yanai T, Tew DP, Handy NC (2004) A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem Phys Lett 393:51–57

    Article  CAS  Google Scholar 

  170. Yanai T, Kurashige Y, Mizukami W, Chalupský J, Lan TN, Saitow M (2015) Density matrix renormalization group for ab initio calculations and associated dynamic correlation methods: a review of theory and applications. Int J Quantum Chem 115:283–299

    Article  CAS  Google Scholar 

  171. Zhou MF, Andrews L, Li J, Bursten BE (1999) Reaction of laser-ablated uranium atoms with CO: infrared spectra of the CUO, CUO\(^-\), OUCCO, (\(\eta ^2\)-C\(_2\))UO\(_2\), and U(CO)\(_x\) (x = 1–6) molecules in solid neon. J Am Chem Soc 121:9712–9721

    Article  CAS  Google Scholar 

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Acknowledgements

A. Ł. and K. B. acknowledge financial support from the National Science Centre, Poland (SONATA BIS 5 Grant No. 2015/18/E/ST4/00584). K. B. gratefully acknowledges funding from a Marie-Skłodowska-Curie Individual Fellowship project no. 702635–PCCDX and a scholarship for outstanding young scientists from the Ministry of Science and Higher Education. P. T. thanks the POLONEZ fellowship program of the National Science Center, Poland, No. 2015/19/P/ST4/02480. This project had received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska–Curie grant agreement No. 665778.

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  1. Faculty of Physics, Astronomy and Informatics, Institute of Physics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100, Toruń, Poland

    Aleksandra Leszczyk, Paweł Tecmer & Katharina Boguslawski

  2. Faculty of Chemistry, Nicolaus Copernicus University in Torun, Gagarina 7, 87-100, Toruń, Poland

    Katharina Boguslawski

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  1. Aleksandra Leszczyk
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  2. Paweł Tecmer
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  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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Leszczyk, A., Tecmer, P., Boguslawski, K. (2019). New Strategies in Modeling Electronic Structures and Properties with Applications to Actinides. 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_5

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