Quantum chemical topology at the spin–orbit configuration interaction level: Application to astatine compounds

We report a methodology that allows the investigation of the consequences of the spin–orbit coupling by means of the QTAIM and ELF topological analyses performed on top of relativistic and multiconfigurational wave functions. In practice, it relies on the “state‐specific” natural orbitals (NOs; expressed in a Cartesian Gaussian‐type orbital basis) and their occupation numbers (ONs) for the quantum state of interest, arising from a spin–orbit configuration interaction calculation. The ground states of astatine diatomic molecules (AtX with X = AtF) and trihalide anions (IAtI−, BrAtBr−, and IAtBr−) are studied, at exact two‐component relativistic coupled cluster geometries, revealing unusual topological properties as well as a significant role of the spin–orbit coupling on these. In essence, the presented methodology can also be applied to the ground and/or excited states of any compound, with controlled validity up to including elements with active 5d, 6p, and/or 5f shells, and potential limitations starting with active 6d, 7p, and/or 6f shells bearing strong spin–orbit couplings.

[1]  Kerstin Andersson,et al.  Second-order perturbation theory with a CASSCF reference function , 1990 .

[2]  K. Dyall.  Relativistic Quadruple-Zeta and Revised Triple-Zeta and Double-Zeta Basis Sets for the 4p, 5p, and 6p Elements , 2006 .

[3]  W. Schwarz.  An Introduction to Relativistic Quantum Chemistry , 2010 .

[4]  Ph. Durand,et al.  Regular Two-Component Pauli-Like Effective Hamiltonians in Dirac Theory , 1986 .

[5]  G. Schreckenbach,et al.  Computational Studies of the Interaction between Ruthenium Dyes and X− and X2−, X = Br, I, At. Implications for Dye-Sensitized Solar Cells , 2010 .

[6]  A.M.K. Müller,et al.  Explicit approximate relation between reduced two- and one-particle density matrices , 1984 .

[7]  Lucas Visscher,et al.  Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions , 1997 .

[8]  L. Hedin,et al.  Polarization corrections to core levels , 1969 .

[9]  J. Pilmé,et al.  Spin-orbit coupling as a probe to decipher halogen bonding. , 2018, Physical chemistry chemical physics : PCCP.

[10]  Ernest R. Davidson,et al.  Properties and Uses of Natural Orbitals , 1972 .

[11]  J. Pilmé,et al.  On the Interplay Between Charge-Shift Bonding and Halogen Bonding. , 2019, Chemphyschem : a European journal of chemical physics and physical chemistry.

[12]  K. Loos,et al.  Structure of triiodide ion in solution. Raman evidence for the existence of higher polyiodide species , 1974 .

[13]  Hess,et al.  Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators. , 1986, Physical review. A, General physics.

[14]  Evert Jan Baerends,et al.  Relativistic regular two‐component Hamiltonians , 1993 .

[15]  Laura Gagliardi,et al.  Reaching the maximum multiplicity of the covalent chemical bond. , 2007, Angewandte Chemie.

[16]  K. Dyall,et al.  Relativistic and correlation effects on molecular properties. I. The dihalogens F2, Cl2, Br2, I2, and At2 , 1996 .

[17]  B. Shepler,et al.  On the spectroscopic and thermochemical properties of ClO, BrO, IO, and their anions. , 2006, The journal of physical chemistry. A.

[18]  A. Becke.  A New Mixing of Hartree-Fock and Local Density-Functional Theories , 1993 .

[19]  S. Knecht,et al.  Relativistic quantum chemical calculations show that the uranium molecule U2 has a quadruple bond , 2018, Nature Chemistry.

[20]  Yi-Gui Wang,et al.  A practical and efficient method to calculate AIM localization and delocalization indices at post‐HF levels of theory , 2003, J. Comput. Chem..

[21]  Michael W. Schmidt,et al.  Effects of Spin-Orbit Coupling on Covalent Bonding and the Jahn-Teller Effect Are Revealed with the Natural Language of Spinors. , 2011, Journal of chemical theory and computation.

[22]  Sason Shaik,et al.  Charge-shift bonding--a class of electron-pair bonds that emerges from valence bond theory and is supported by the electron localization function approach. , 2005, Chemistry.

[23]  Celestino Angeli,et al.  N-electron valence state perturbation theory: a fast implementation of the strongly contracted variant , 2001 .

[24]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[25]  B. Silvi.  How topological partitions of the electron distributions reveal delocalization , 2004 .

[26]  Trond Saue,et al.  An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation. , 2007, The Journal of chemical physics.

[27]  Evert Jan Baerends,et al.  An approximate exchange-correlation hole density as a functional of the natural orbitals , 2002 .

[28]  M. Vincent,et al.  Revitalizing the concept of bond order through delocalization measures in real space , 2018, Chemical science.

[29]  Eric Renault,et al.  QTAIM Analysis in the Context of Quasirelativistic Quantum Calculations. , 2014, Journal of chemical theory and computation.

[30]  Julien Pilmé,et al.  The bonding picture in hypervalent XF3 (X = Cl, Br, I, At) fluorides revisited with quantum chemical topology , 2017, J. Comput. Chem..

[31]  Richard F. W. Bader.  A quantum theory of molecular structure and its applications , 1991 .

[32]  Pi A. B. Haase,et al.  Relevance of effective bond orders in heterodiatomic molecules and role of the spin-orbit coupling in theAtX(X=At–F)series , 2019, Physical Review A.

[33]  Michael Dolg,et al.  Relativistic pseudopotentials: their development and scope of applications. , 2012, Chemical reviews.

[34]  R. Cimiraglia,et al.  n-electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants , 2002 .

[35]  K. Dyall,et al.  Formulation and implementation of a relativistic unrestricted coupled-cluster method including noniterative connected triples , 1996 .

[36]  P. Hiberty,et al.  WHAT IS PHYSICALLY WRONG WITH THE DESCRIPTION OF ODD-ELECTRON BONDING BY HARTREE-FOCK THEORY ? A SIMPLE NONEMPIRICAL REMEDY , 1995 .

[37]  R. Dreizler,et al.  Density Functional Theory: An Advanced Course , 2011 .

[38]  P. Hiberty,et al.  Charge-Shift Bonding Emerges as a Distinct Electron-Pair Bonding Family from Both Valence Bond and Molecular Orbital Theories. , 2014, Journal of chemical theory and computation.

[39]  Bernard Silvi,et al.  Computational Tools for the Electron Localization Function Topological Analysis , 1999, Comput. Chem..

[40]  Axel D. Becke,et al.  A Simple Measure of Electron Localization in Atomic and Molecular-Systems , 1990 .

[41]  P. Hiberty,et al.  What makes the trifluoride anion F3 - so special? A breathing-orbital valence bond ab initio study. , 2004, Journal of the American Chemical Society.

[42]  Jochen Autschbach,et al.  Magnetic properties and electronic structure of neptunyl(VI) complexes: wavefunctions, orbitals, and crystal-field models. , 2014, Chemistry.

[43]  R. Maurice,et al.  Effective bond orders from two-step spin-orbit coupling approaches: the I2, At2, IO(+), and AtO(+) case studies. , 2015, The Journal of chemical physics.

[44]  J. Murray,et al.  The σ-Hole Coulombic Interpretation of Trihalide Anion Formation. , 2018, Chemphyschem : a European journal of chemical physics and physical chemistry.

[45]  J. Pilmé,et al.  What can tell the quantum chemical topology on carbon–astatine bonds? , 2016 .

[46]  Andreas Savin,et al.  Electron Localization in Solid‐State Structures of the Elements: the Diamond Structure , 1992 .

[47]  Xavier Fradera,et al.  The Lewis Model and Beyond , 1999 .

[48]  B. Roos,et al.  Quantum chemical calculations show that the uranium molecule U2 has a quintuple bond , 2005, Nature.

[49]  Celestino Angeli,et al.  Introduction of n-electron valence states for multireference perturbation theory , 2001 .

[50]  J. Pilmé,et al.  Electronic structures and geometries of the XF3 (X = Cl, Br, I, At) fluorides. , 2015, The Journal of chemical physics.

[51]  B. Roos,et al.  A simple method for the evaluation of the second-order-perturbation energy from external double-excitations with a CASSCF reference wavefunction , 1982 .

[52]  Miquel Solà,et al.  Electron localization function at the correlated level. , 2006, The Journal of chemical physics.

[53]  M. Solà,et al.  The role of electronic delocalization in transition metal complexes from the electron localization function and the quantum theory of atoms in molecules viewpoints , 2009 .

[54]  Marvin Douglas,et al.  Quantum electrodynamical corrections to the fine structure of helium , 1971 .

[55]  J. Karwowski,et al.  Unexpected properties of a density functional , 2005 .

[56]  M. Barysz,et al.  Infinite-order two-component theory for relativistic quantum chemistry , 2002 .

[57]  Juan I. Rodríguez,et al.  Size evolution relativistic DFT-QTAIM study on the gold cluster complexes Au4-S-CnH2n-S'-Au4' (n=2-5) , 2016 .

[58]  Jochen Autschbach,et al.  Magnetic properties and electronic structures of Ar3U(IV)–L Complexes with Ar = C5(CH3)4H(–) or C5H5(–) and L = CH3, NO, and Cl. , 2014, Inorganic chemistry.

[59]  P. Hiberty,et al.  Charge-shift bonding and its manifestations in chemistry. , 2009, Nature chemistry.

[60]  É. Renault,et al.  Assessment of an effective quasirelativistic methodology designed to study astatine chemistry in aqueous solution. , 2011, Physical chemistry chemical physics : PCCP.

[61]  P. Salvador,et al.  Benchmark calculations of metal carbonyl cations: relativistic vs. electron correlation effects. , 2013, Physical chemistry chemical physics : PCCP.

[62]  R. Bader,et al.  Spatial localization of the electronic pair and number distributions in molecules , 1975 .

[63]  Kenneth G. Dyall,et al.  The choice of a zeroth-order Hamiltonian for second-order perturbation theory with a complete active space self-consistent-field reference function , 1995 .

[64]  J. Pilmé,et al.  Introducing the ELF Topological Analysis in the Field of Quasirelativistic Quantum Calculations. , 2012, Journal of chemical theory and computation.

[65]  Andreas Hansen,et al.  A diuranium carbide cluster stabilized inside a C80 fullerene cage , 2018, Nature Communications.

[66]  A. Savin,et al.  Classification of chemical bonds based on topological analysis of electron localization functions , 1994, Nature.

[67]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[68]  Andreas Savin,et al.  Topological analysis of the electron localization function applied to delocalized bonds , 1996 .

[69]  H. Quiney,et al.  Charge-Displacement Analysis via Natural Orbitals for Chemical Valence in the Four-Component Relativistic Framework. , 2018, Journal of chemical theory and computation.

[70]  R. Maurice,et al.  Experimental and computational evidence of halogen bonds involving astatine , 2018, Nature Chemistry.

[71]  J. Autschbach.  Orbitals for Analyzing Bonding and Magnetism of Heavy-Metal Complexes , 2016 .

[72]  R. Maurice,et al.  Unraveling the hydration-induced ground-state change of AtO+ by relativistic and multiconfigurational wave-function-based methods. , 2016, Physical chemistry chemical physics : PCCP.

[73]  H. Stoll,et al.  Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post-d group 16–18 elements , 2003 .

[74]  K. Dyall.  Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the light elements H–Ar , 2016, Theoretical Chemistry Accounts.

[75]  Miquel Solà,et al.  Electron Localization Function at the Correlated Level: A Natural Orbital Formulation. , 2010, Journal of chemical theory and computation.

[76]  Xinying Li,et al.  Metalophilic interaction in gold halide: Quantum chemical study of AuX (X = Fat) , 2014, J. Comput. Chem..

[77]  J. Graton,et al.  Quantum calculations of At-mediated halogen bonds: on the influence of relativistic effects , 2018 .

[78]  James S. M. Anderson,et al.  Molecular QTAIM Topology Is Sensitive to Relativistic Corrections. , 2019, Chemistry.

[79]  R. Maurice,et al.  Towards a stronger halogen bond involving astatine: unexpected adduct with Bu3PO stabilized by hydrogen bonding. , 2019, Chemistry.

[80]  J. Barbet,et al.  (211)At-labeled agents for alpha-immunotherapy: On the in vivo stability of astatine-agent bonds. , 2016, European journal of medicinal chemistry.

[81]  Björn O. Roos,et al.  Second-order perturbation theory with a complete active space self-consistent field reference function , 1992 .

[82]  Ingvar Lindgren,et al.  Diagonalisation of the Dirac Hamiltonian as a basis for a relativistic many-body procedure , 1986 .

[83]  The Heaviest Possible Ternary Trihalogen Species, IAtBr- , Evidenced in Aqueous Solution: An Experimental Performance Driven by Computations. , 2016, Angewandte Chemie.

[84]  Harrison Shull,et al.  NATURAL ORBITALS IN THE QUANTUM THEORY OF TWO-ELECTRON SYSTEMS , 1956 .

[85]  Bernd A. Hess,et al.  Revision of the Douglas-Kroll transformation. , 1989, Physical review. A, General physics.

[86]  M. Reiher,et al.  Relativistic Effects on the Topology of the Electron Density. , 2007, Journal of chemical theory and computation.

[87]  Jochen Autschbach,et al.  Ab Initio Study of Covalency in the Ground versus Core-Excited States and X-ray Absorption Spectra of Actinide Complexes. , 2018, The journal of physical chemistry letters.

[88]  P. Hiberty,et al.  Application of the valence bond mixing configuration diagrams to hypervalency in trihalide anions: a challenge to the Rundle-Pimentel model. , 2008, The journal of physical chemistry. A.

[89]  R. Cimiraglia,et al.  Electronic structure investigation of the evanescent AtO(+) ion. , 2013, Physical chemistry chemical physics : PCCP.

[90]  Marc J. A. Johnson,et al.  Uncovering the Uranium-Nitrogen Triple Bond , 2012, Science.