Ab initio calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their derivation

A methodology for the rigorous nonperturbative derivation of magnetic pseudospin Hamiltonians of mononuclear complexes and fragments based on ab initio calculations of their electronic structure is described. It is supposed that the spin-orbit coupling and other relativistic effects are already taken fully into account at the stage of quantum chemistry calculations of complexes. The methodology is based on the establishment of the correspondence between the ab initio wave functions of the chosen manifold of multielectronic states and the pseudospin eigenfunctions, which allows to define the pseudospin Hamiltonians in the unique way. Working expressions are derived for the pseudospin Zeeman and zero-field splitting Hamiltonian corresponding to arbitrary pseudospins. The proposed calculation methodology, already implemented in the SINGLE_ANISO module of the MOLCAS-7.6 quantum chemistry package, is applied for a first-principles evaluation of pseudospin Hamiltonians of several complexes exhibiting weak, moderate, and very strong spin-orbit coupling effects.     

Synthesis and molecular structure of gold triarylcorroles

A number of third-row transition-metal corroles have remained elusive as synthetic targets until now, notably osmium, platinum, and gold corroles. Against this backdrop, we present a simple and general synthesis of β-unsubstituted gold(III) triarylcorroles and the first X-ray crystal structure of such a complex. Comparison with analogous copper and silver corrole structures, supplemented by extensive scalar-relativistic, dispersion-corrected density functional theory calculations, suggests that "inherent saddling" may occur for of all coinage metal corroles. The degree of saddling, however, varies considerably among the three metals, decreasing conspicuously along the series Cu > Ag > Au. The structural differences reflect significant differences in metal-corrole bonding, which are also reflected in the electrochemistry and electronic absorption spectra of the complexes. From Cu to Au, the electronic structure changes from noninnocent metal(II)-corrole(?2-) to relatively innocent metal(III)-corrole(3-).     

Removing critical errors for DFT applications to transition-metal nanoclusters: correct ground-state structures of Ru clusters

As ruthenium plays an important role in heterogeneous catalysis, understanding the structural and electronic properties of Ru clusters is crucial to advancement of technology. Because of its efficiency, density functional theory (DFT) calculations are often utilized in nanoscience, but careful validation is necessary. Recently, small, nonmetallic Ru(n) clusters were reported by Zhang et al. [J. Phys. Chem. B 2004, 108, 2140] to form unusual square and cubic ground-state structures within DFT by treating the exchange-correlation (XC) functional at the level of general-gradient-corrected approximation (GGA). For such clusters, we show that the calculated, energetically preferred structures are sensitive to which XC functional is used and whether relativistic effects are included. We find that a hybrid XC functional with partially exact exchange, such as PBE0, corrects the Ru2 magnetic moment, bond length, and dissociation energy in agreement with experiment and high-level quantum chemistry calculations and changes the Ru4 ground-state structure to a tetrahedron, instead of a square. The change in structural preference is explained by the corrections to the electronic structure of a Ru atom, where the relative position of majority spin s level is shifted with respect to e(g) levels. We also find that standard nonrelativistic DFT-GGA gives similar results to relativistic DFT-PBE0, i.e., relative shifting of s level, but not for the right reasons. Our results again stress the need to validate an XC functional before application to transition-metal nanoclusters.     

Theoretical study of the electronic spectra of square-planar platinum (II) complexes based on the two-component relativistic time-dependent density-functional theory

In the present work the electronic spectra of [PtCl(4)](2-), [PtBr(4)](2-), and [Pt(CN)(4)](2-) are studied with a recently proposed relativistic time-dependent density-functional theory (TDDFT) based on the two-component zeroth-order regular approximation and a noncollinear exchange-correlation (XC) functional. The contribution to the double group excited states in terms of singlet and triplet single group excited states is estimated through the inner product of the transition density matrix obtained from two-component and scalar relativistic TDDFT calculations to better understand the double group excited states. Spin-orbital coupling effects are found to be very important in order to simulate the electronic spectra of these complexes. The results show that the two-component TDDFT formalism can afford excitation energies with high accuracy for the transition-metal systems studied here when use is made of a proper XC potential.     

Structure,electronic, and CV properties of hydroxy-naphthaldehyde Schiff-base copper(II) complexes derived from alkyl amines: X-ray structure of bis(n-i-propyl-3-hydroxy-2-naphthaldiminato)copper(II)

Copper(II) complexes with Schiff bases derived from linear and branched amines with 2-hydroxy-1-naphthaldehyde and 3-hydroxy-2-naphthaldehyde were synthesized and characterized by IR and electronic spectroscopies, magnetic susceptibilities, electrochemistry, cyclic voltammetry (CV), X-ray diffraction, and theoretical calculations. Electronic spectra are a function of the R group on the imine nitrogen of the ligand that determines steric effects. Complexes obtained from 3-hydroxy-2-naphthaldehyde ligand are more distorted from planarity in dimethylformamide solutions than those of 2-hydroxy-1-naphthaldehyde for the same R group. As a result, the former are easier to reduce to the related copper(I) complexes than those of 2-hydroxy-1-naphthaldiminate. The structure of bis(N-i-propyl-3-hydroxy-2-naphthaldiminato)copper(II) was determined by single-crystal X-ray diffraction. Its molecular structure can be described as distorted flat tetrahedral influenced by important packing effects and is flatter than that calculated with density functional theory methods. Additional related flat tetrahedral complexes were studied by theoretical calculations and it has been found that electronic effects also play a significant role.     

Solution chemistry of element 106: theoretical predictions of hydrolysis of group 6 cations Mo, W, and Sg

Fully relativistic molecular density-functional calculations of the electronic structure of hydrated and hydrolyzed complexes have been performed for the group 6 elements Mo, W, and element 106, Sg. By use of the electronic density distribution data, relative values of the free energy changes and constants of hydrolysis reactions were defined. The results show hydrolysis of the cationic species with the formation of neutral molecules to decrease in the order Mo > W > Sg, which is in agreement with experiments for Mo, W, and Sg. For the further hydrolysis process with the formation of anionic species, the trend is reversed: Mo > Sg > W. A decisive energetic factor in the hydrolysis process proved to be a predominant electrostatic metal-ligand interaction.     

Role of relativistic effects in the electronic structure and chemical bond of lead hexacyanoferrate

The electronic structure of a large fragment of the Pb₂Fe(CN)₆ crystal lattice with the trigonal structure is studied in the framework of a fully relativistic discrete variational cluster method. On the basis of comparing the results obtained with the data of previous non-relativistic calculations we have considered the relativistic effects on the electronic energy spectrum, the charge density distribution, and Pb-N, N-C, and C-Fe chemical bonding.     

d8和d10配合物激发态性质和金属间弱相互作用的理论研究

随着量子化学理论方法和计算机技术的发展,量子理论模型已成为一种研究分子的高能、不稳定电子态-激发态的最有效手段.通过对一系列d8和d10配合物的激发态电子结构和电子激发前后金属相互作用的理论研究进行了评述.电子吸收和发射是极其复杂的微观过程,涉及到基态与激发态的电子结构性质、金属间弱相互作用、相对论效应等量子理论的基础问题,揭示配合物发光性质的规律性对新型光学材料的探索和设计具有重要指导意义.     

Relativistic four-component DFT calculations of 1H NMR chemical shifts in transition-metal hydride complexes: unusual high-field shifts beyond the Buckingham-Stephens model

State-of-the-art relativistic four-component DFT-GIAO-based calculations of (1)H NMR chemical shifts of a series of 3d, 4d, and 5d transition-metal hydrides have revealed significant spin-orbit-induced heavy atom effects on the hydride shifts, in particular for several 4d and 5d complexes. The spin-orbit (SO) effects provide substantial, in some cases even the dominant, contributions to the well-known characteristic high-field hydride shifts of complexes with a partially filled d-shell, and thereby augment the Buckingham-Stephens model of off-center paramagnetic ring currents. In contrast, complexes with a 4d(10) and 5d(10) configuration exhibit large deshielding SO effects on their hydride (1)H NMR shifts. The differences between the two classes of complexes are attributed to the dominance of π-type d-orbitals for the true transition-metal systems compared to σ-type orbitals for the d(10) systems.     

Biliverdine-based metalloradicals: sterically enhanced noninnocence

This is a first density functional theory survey of transition-metal biliverdines (Blv), where we have chosen to focus on key Mn, Fe, Co, and Cu complexes. According to the calculations, the complexes are invariably noninnocent, featuring Blv*2- ligand radicals. In this, biliverdine complexes resemble metallocorroles, but the parallels are only approximate. Briefly, metallobiliverdines exhibit a much greater tendency to adopt noninnocent electronic structures than analogous metallocorroles. The O...O nonbonded contacts in biliverdines apparently preclude the formation of short metal-N bonds that, in turn, could stabilize high-valent metal ions. Thus, while most copper corroles (Cor) exhibit diamagnetic CuIII ground states, copper biliverdines are clearly Cu(II)Blv*2- species. In the same spirit, while chloroiron corroles are best described as FeIII(S = 3/2)Cor*2-,the analogous biliverdine derivative seems best described as Fe(III)(S = 5/2)Blv*2-, i.e., featuring a high-spin FeIII center with long (>2.0 A) Fe-N bond distances. Overall, the results highlight the important role that steric effects may play in modulating the electronic structures and the potentially noninnocent nature of transition-metal complexes.     

Relativistic quantum chemistry and rigorous variational analysis

A brief review of relativistic quantum chemistry is given here. Relativistic effects and their importance in chemistry are discussed. An outline of different theoretical aspects is presented. Aspects of variation techniques relevant to relativistic calculations are discussed in detail. These involve the derivation of min-max theorems for Dirac, Dirac-Hartree-Fock and Dirac-Coulomb calculations. The consequence of relativistic Hamiltonians being unbounded are also discussed for other lines of investigation. The upper bounds derived are physically interpreted. Sample Dirac-Hartree-Fock results for the Be atom, calculated using both STO and GTO bases for the nonrelativistic orbitals and the upper components of the relativistic orbitals, are given. The inadequacy of the so-called kinetically balanced basis set is discussed and illustrated with these results. The importance of the variational or dynamical balance and hence the merit of the LCAS-MS scheme is pointed out. The possibility of calculating quantum electrodynamical pair energy from relativistic configuration interaction calculations on a two-electron atom is discussed and exemplified. The present status of relativistic molecular calculations is briefly reviewed. Conclusions on the aspects of variational analysis and molecular calculations are enclosed.     

Probing actinide electronic structure using fluorescence and multi-photon ionization spectroscopy

The role of the 5f orbitals in actinide bond formation is one of the central issues of actinide chemistry. This question can be explored using relativistic quantum chemistry calculations, but the theoretical methods must be validated using definitive experimental data. For simple ionic compounds such as actinide oxides and halides, the electronic structure can be examined using electronic and photoelectron spectroscopy of gas phase molecules. The present article surveys recent spectroscopic and theoretical studies of the oxides of thorium and uranium. The results show that the 5f-like states are spectators and that the complex patterns of low-lying electronic states for these molecules can be understood in terms of a semi-empirical ligand field model. Comparisons with recent high-level theoretical calculations are presented and discussed.     

Solvent effects and dynamic averaging of 195Pt NMR shielding in cisplatin derivatives

The influences of solvent effects and dynamic averaging on the (195)Pt NMR shielding and chemical shifts of cisplatin and three cisplatin derivatives in aqueous solution were computed using explicit and implicit solvation models. Within the density functional theory framework, these simulations were carried out by combining ab initio molecular dynamics (aiMD) simulations for the phase space sampling with all-electron relativistic NMR shielding tensor calculations using the zeroth-order regular approximation. Structural analyses support the presence of a solvent-assisted "inverse" or "anionic" hydration previously observed in similar square-planar transition-metal complexes. Comparisons with computationally less demanding implicit solvent models show that error cancellation is ubiquitous when dealing with liquid-state NMR simulations. After aiMD averaging, the calculated chemical shifts for the four complexes are in good agreement with experiment, with relative deviations between theory and experiment of about 5% on average (1% of the Pt(II) chemical shift range).     

Assessment of higher-order spin�Corbit effects on electronic g-tensors of d 1 transition-metal complexes by relativistic two- and four-component methods

The electronic g-tensors of a series of V, Cr, Mo, W, Tc, and Re d¹ transition-metal complexes have been studied systematically by density functional theory (DFT) methods. The comparison between one-component second-order perturbation theory calculations with two- and four-component first-order perturbation calculations has allowed an assessment of the importance of higher-order spin-orbit contributions. Using an efficient matrix Dirac?CKohn?CSham implementation with relativistic kinetic balance basis sets, it has been possible for the first time to apply four-component DFT also to g-tensors of larger models for biological vanadium, molybdenum, and tungsten metal sites. Higher-order spin?Corbit effects are generally crucial for an accurate determination of the g-tensors in such complexes, in many cases more important than the choice of non-hybrid or hybrid density functional. A systematic scaling analysis of the spin?Corbit integrals shows that second-order spin?Corbit effects may be of the same size as the leading first-order effects and thus alter the computed g-tensors fundamentally, in particular for the 5d species. In the latter case, even third-order effects may be non-negligible.     

Structure of the HOOO radical in liquid water: a theoretical study.

The HOOO radical is supposed to play a role in ozone chemistry, both in the gas phase and aqueous media. We discuss the influence of the solvent on the electronic and geometrical structure of this radical using density functional and high-level ab initio calculations together with continuum, discrete, and discrete-continuum solvent models. Solute-solvent electrostatic interactions are shown to be fundamental, and lead to a noticeable stabilization of the radical, which should adopt a trans conformation in aqueous media. In fact, no energy minimum for the cis conformation is predicted in these conditions.     

Spectroscopic methods in bioinorganic chemistry: blue to green to red copper sites

A wide variety of spectroscopic methods are now available that provide complimentary insights into the electronic structures of transition-metal complexes. Combined with calculations, these define key bonding interactions, enable the evaluation of reaction coordinates, and determine the origins of unique spectroscopic features/electronic structures that can activate metal centers for catalysis. This presentation will summarize the contributions of a range of spectroscopic methods combined with calculations in elucidating the electronic structure of an active site using the blue copper site as an example. The contribution of electronic structure to electron-transfer reactivity will be considered in terms of anisotropic covalency, electron-transfer pathways, reorganization energy, and protein contributions to the geometric and electronic structures of blue-copper-related active sites.     

Elongated dihydrogen versus compressed dihydride complexes: the temperature dependence of the H-D spin-spin coupling constant as a criterion to distinguish between them

To be able to propose experimental tests to distinguish elongated dihydrogen transition-metal complexes from compressed dihydride transition-metal complexes, a thorough density functional study of the electronic structure in combination with quantum nuclear dynamics calculations have been performed for complexes [Cp*Ru(H2PCH2PCH2(H2)]+ and [CpRe(CO)2H2]. The results of this study suggest that elongated dihydrogen complexes and compressed dihydride complexes have different properties and that it should be possible to distinguish between them experimentally. In particular, different behavior is predicted with respect to 1) the sign of the isotope geometric effect on the H-H distance at 0 K, 2) the temperature dependence of the H-H distance, and 3) the temperature dependence of the H-D spin-spin coupling constant in 1H NMR spectroscopy.     

Cationic,Two‐Coordinate Gold π Complexes

Cationic, two‐coordinate gold π complexes that contain a phosphine or N‐heterocyclic supporting ligand have attracted considerable attention recently owing to the potential relevance of these species as intermediates in the gold‐catalyzed functionalization of C? C multiple bonds. Although neutral two‐coordinate gold π complexes have been known for over 40 years, examples of the cationic two‐coordinate gold(I) π complexes germane to catalysis remained undocumented prior to 2006. This situation has changed dramatically in recent years and well‐defined examples of two‐coordinate, cationic gold π complexes containing alkene, alkyne, diene, allene, and enol ether ligands have been documented. This Minireview highlights this recent work with a focus on the structure, bonding, and ligand exchange behavior of these complexes.