Time-dependent density functional theory investigation of the electronic spectra of hexanuclear chalcohalide rhenium(III) clusters

The UV-vis spectra of the hexanuclear chalcohalide rhenium(III) clusters of formula [Re(6)S(8)X(6)](4-) (X(-) = Cl(-), Br(-), I(-)) were investigated at the time-dependent density functional theory (TD-DFT) level employing B3LYP, PBE1PBE, and the double-hybrid B2PLYP functional in combination with the LANL2DZ basis set. We were able to reproduce the red shift experimentally observed when the halide changes from chloride to iodide. However, some discrepancies between experimental results and theory were found. First, we did not observe a remarkable dependence of the experimental ill-resolved bands on the solvent. Indeed, similar spectra were obtained taken CH(2)Cl(2) or CH(3)CN as solvents into account. Second, all calculations explained the origin of the band peaked at the low-energy region in contraposition with the one experimentally assumed by R. Long et al. (J. Am. Chem. Soc. 1996, 118, 4603), and theoretically made available by Arratia-Pe?rez et al. (J. Chem. Phys. 1999, 110, 2529). These authors have proposed a ligand-to-cluster charge transfer (LCCT) for all title complexes. Our findings undoubtedly allow such origin to be discarded. While the HGGA functionals lead to a cluster-to-halide ligand charge transfer (CLCT), an intracluster charge transfer (ICCT) has been considered by employing B2PLYP. This contribution showed B2PLYP in the presence of the solvent to be the best performer in studying the UV-vis spectra of large complexes of rhenium(III) containing the Re-S bond. We strongly recommended the use of the double-hybrid B2PLYP in studying UV-vis spectrum of rhenium complexes of size making the computational cost affordable. We expect that our work stimulates new experimental and theoretical investigations of the title complexes to confirm our assignment.     

DFT Methods to Study the Reaction Mechanism of Iridium‐Catalyzed Hydrogenation of Olefins: Which Functional Should be Chosen?

To enable the selection of more accurate computational methods for the future theoretical exploration of the reaction mechanism of Ir‐catalyzed olefin hydrogenation, we compared high‐level ab initio coupled cluster and DFT calculations with a simplified model of Pfaltz's Ir/P,N‐type catalyst for all four previously proposed Ir^I/Ir^III and Ir^III/Ir^V mechanisms. Through the systematic assessment of the DFT performances, the DFT empirical dispersion correction (DFT‐D3) is found to be indispensable for improving the accuracy of relative energies between the Ir^I/Ir^III and Ir^III/Ir^V mechanisms. After including the DFT‐D3 correction, the three best performing density functionals (DFs) are B2‐PLYP, BP86, and TPSSh. In these recommended DFs, the computationally more expensive double‐hybrid functional B2‐PLYP‐D3 has a balanced and outstanding performance for calculations of the reaction barriers, reaction energies, and energy gaps between different mechanisms, whereas the less costly BP86‐D3 and TPSSh‐D3 methods have outstanding, but relatively less uniform performances.     

Automated and Efficient Generation of General Molecular Aggregate Structures

Modeling intermolecular interactions of complex non-covalent structures is important in many areas of chemistry. To facilitate the generation of reasonable dimer, oligomer, and general aggregate geometries, we introduce an automated computational interaction site screening (aISS) workflow. This easy-to-use tool combines a genetic algorithm employing the intermolecular force-field xTB-IFF for initial search steps with the general force-field GFN-FF and the semi-empirical GFN2-xTB method for geometry optimizations. Compared with the alternative CREST program, aISS yields similar results but with computer time savings of 1–3 orders of magnitude. This allows for the treatment of systems with thousands of atoms composed of elements up to radon, e.g., metal-organic complexes, or even polyhedra and zeolite cut-outs which were not accessible before. Moreover, aISS can identify reactive sites and provides options like site-directed (user-guided) screening.     

Quantum Chemical Study of the Structures and Stability of Copper(II) Bis(diketonate) Dimers

Russian Journal of Coordination Chemistry - The quantum-chemical study of the copper diketonate dimers ([Cu(Acac)2]2 and [Cu(Acac)Hfac)]2) is performed using various functionals (B3LYP, TPSSh,...     

Electron transfer reactions between copper(II) porphyrin complexes and various oxidizing reagents in acetonitrile

Homogeneous electron transfer reactions of the Cu(II) complexes of 5,10,15,20-tetraphenylporphyrin (TPP) and 2,3,7,8,12,13,17,18-octaethylporphyrin (OEP) with various oxidizing reagents were spectrophotometrically investigated in acetonitrile. The reaction products were confirmed to be the pi-cation radicals of the corresponding Cu(II)-porphyrin complexes on the basis of the electronic spectra and the redox potentials of the complexes. The rate of the electron transfer reaction between the Cu(II)-porphyrin complex and solvated Cu(2+) was determined as a function of the water concentration under the pseudo first-order conditions where Cu(2+) is in large excess over the Cu(II)-porphyrin complex. The decrease in the pseudo first-order rate constant with increasing the water concentration was attributed to the stepwise displacement of acetonitrile in [Cu(AN)(6)](2+)(AN = acetonitrile) by water, and it was concluded that only the Cu(2+) species fully solvated by acetonitrile, [Cu(AN)(6)](2+), possesses sufficiently high redox potential for the oxidation of Cu(ii)-OEP and Cu(ii)-TPP. The reactions of the Cu(II)-porphyrin complexes with other oxidizing reagents such as [Ni(tacn)(2)](3+)(tacn = 1,4,7-triazacyclononane) and [Ru(bpy)(3)](3+)(bpy = 2,2'-bipyridine) were too fast to be followed by a conventional stopped-flow technique. Marcus cross relation for the outer-sphere electron transfer reaction was used to estimate the rate constants of the electron self-exchange reaction between Cu(II)-porphyrin and its pi-cation radical: log(k/M(-1) s(-1))= 9.5 +/- 0.5 for TPP and log(k/M(-1) s(-1))= 11.1 +/- 0.5 for OEP at 25.0 degrees C. Such large electron self-exchange rate constants are typical for the porphyrin-centered redox reactions for which very small inner- and outer-sphere reorganization energies are required.     

Sublimation Properties of α,ω-Diamines Revisited from First-Principles Calculations

Sublimation enthalpies of alkane-α,ω-diamines exhibit an odd-even pattern within their homologous series. First-principles calculations coupled with the quasi-harmonic approximation for crystals and with the conformation mixing model for the ideal gas are used to explain this phenomenon from the theoretical point of view. Crystals of the odd and even alkane-α,ω-diamines distinctly differ in their packing motifs. However, first-principles calculations indicate that it is a delicate interplay of the cohesive forces, phonons, molecular vibrations and conformational equilibrium which governs the odd-even pattern of the sublimation enthalpies within the homologous series. High molecular flexibility of the alkane-α,ω-diamines predetermines higher sensitivity of the computational model to the quality of the optimized geometries and relative conformational energies. Performance of high-throughput computational methods, such as the density functional tight binding (DFTB, GFN2-xTB) and the explicitly correlated dispersion-corrected Møller - Plesset perturbative method (MP2C-F12), are benchmarked against the consistent state-of-the-art calculations of conformational energies and interaction energies, respectively.     

Predicting the redox properties of uranyl complexes using electronic structure calculations

A plethora of chemical reactions is redox driven processes. The conversion of toxic and highly soluble U(VI) complexes to nontoxic and insoluble U(IV) form are carried out through proton coupled electron transfer by iron containing cytochromes and mineral surfaces such as machinawite. This redox process takes place through the formation of U(V) species which is unstable and immediately undergo the disproportionation reaction. Thus, theoretical methods are extremely useful to understand the reduction process of U(VI) to U(V) species. We here have carried out the structures and reduction properties of several U(VI) to U(V) complexes using a variety of electronic structure methods. Due to the lack of experimental ionization energies for uranyl (UO₂(V)‐UO₂(VI)) couple, we have benchmarked the current and popularly used density functionals and cost effective ab initio methods against the experimental electron detachment energies of [UO₂F₄]^1‐/2‐ and [UO₂Cl₄]^1‐/2‐. We find that electron detachment energy of U(VI) predicted by RI‐MP2 level on the BP86 geometries correlate nicely with the experimental and CCSD(T) data. Based on our benchmark studies, we have predicted the structures and electron detachment energies of U(V) to U(VI) species for a series of uranium complexes at the RI‐MP2//BP86 level which are experimentally inaccessible till date. We find that the redox active molecular orbital is ligand centered for the oxidation of U(VI) species, where it is metal centered (primarily f‐orbital) for the oxidation of U(V) species. Finally, we have also calculated the detachment energies of a known uranyl [UO₂]¹⁺ complex whose X‐ray crystal structures of both oxidation states are available. The large bulky nature of the ligand stabilizing the uncommon U(V) species which cannot be routinely studied by present day CCSD(T) methods as the system size are more than 20–30 atoms. The success of our efficient computational strategy can be experimentally verified in the near future for the complex as the structures are stable in gas phase which can undergo oxidation.     

Kinetics and mechanism of the oxidation of guanosine derivatives by Pt(IV) complexes

The kinetics of redox reactions of the PtIV complexes trans-Pt(d,l)(1,2-(NH2)2C6H10)Cl4 ([PtIVCl4(dach)]) and Pt(NH2CH2CH2NH2)Cl4 ([PtIVCl4(en)]) with 5'- and 3'-dGMP (G) have been studied. These redox reactions involve substitution followed by an inner-sphere electron transfer. The substitution is catalyzed by PtII and follows the classic Basolo-Pearson PtII-catalyzed PtIV-substitution mechanism. We found that the substitutution rates depend on the steric hindrance of PtII, G, and PtIV with the least sterically hindered PtII complex catalyzing at the highest rate. 3'-dGMP undergoes substitution faster than 5'-dGMP, and [PtIVCl4(en)] substitutes faster than [PtIVCl4(dach)]. The enthalpies of activation of the substitution, DeltaH double dagger s, of 3'-dGMP is only 70% greater than that of 5'-dGMP (50.4 vs 30.7 kJ mol(-1)), but the entropy of activation of the substitution, DeltaS double dagger s, of 3'-dGMP is much greater than that of 5'-dGMP (-59.4 vs -129.5 J K(-1) mol(-1)), indicating that steric hindrance plays a major role in the substitution. The enthalpy of activation of electron transfer, DeltaH double dagger e, of 3'-dGMP is smaller than that of 5'-dGMP (88.8 vs 137.8 kJ mol(-1)). The entropy of activation of electron transfer, DeltaS double dagger e, of 3'-dGMP is negative, but that of 5'-dGMP is positive (-27.8 vs +128.8 J K-1 mol-1). The results indicate that 5'-hydroxo has less rotational barrier than 5'-phosphate, but it is geometrically unfavorable for internal electron transfer. The electron-transfer rate also depends on the reduction potential of PtIV. Because of its higher reduction potential, [PtIVCl4(dach)] has a faster electron transfer than [PtIVCl4(en)].     

Analytic derivatives for the XYG3 type of doubly hybrid density functionals: Theory,implementation, and assessment

We present a theoretical development of the equations required to perform an analytic geometry optimization of a molecular system using the XYG3 type of doubly hybrid (xDH) functionals. In contrast to the well‐established B2PLYP type of DH functionals, the energy expressions in the xDH functionals are constructed by using density and orbital information from another standard Kohn–Sham (KS) functional (e.g., B3LYP) for doing the self‐consistent field calculations. Thus, the xDH functionals are nonvariational in both the hybrid density functional part and the second‐order perturbation part, each of which requires formally to solve a coupled‐perturbed KS equation. An implementation is reported here which combines the two parts by defining a total Lagrangian such that only a single set of the Z‐vector equations need to be solved. The computational cost with our implementation is of the same order as those for the conventional Møller–Plesset theory to the second order (MP2) and B2PLYP. Systematic test calculations are provided for covalently bonded molecules as well as compounds involving the intramolecular nonbonded interactions for the main group elements. Satisfactory performance of the xDH functionals demonstrates that the extra computer time on top of the conventional KS procedure is well‐invested, in particular, when the standard KS functionals and MP2 as well, are problematic. © 2013 Wiley Periodicals, Inc.     

Efficient Computation of Geometries for Gold Complexes

Computationally obtaining structural parameters along a reaction coordinate is commonly performed with Kohn-Sham density functional theory which generally provides a good balance between speed and accuracy. However, CPU times still range from inconvenient to prohibitive, depending on the size of the system under study. Herein, the tight binding GFN2-xTB method [C. Bannwarth, S. Ehlert, S. Grimme, J. Chem. Theory Comput. 2019 , 15, 1652] is investigated as an alternative to produce reasonable geometries along a reaction path, that is, reactant, product and transition state structures for a series of transformations involving gold complexes. A small mean error (1 kcal/mol) was found, with respect to an efficient composite hybrid-GGA exchange-correlation functional (PBEh-3c) paired with a double-ζ basis set, which is 2–3 orders of magnitude slower. The outlined protocol may serve as a rapid tool to probe the viability of proposed mechanistic pathways in the field of gold catalysis.     

Role of the electronic properties of azurin active site in the electron‐transfer process

Electron transfer proteins, such as azurin (a blue copper protein), are promising candidates for the implementation of biomolecular nanoelectronic devices. To understand the details of electron transfer in redox active azurin molecules, we performed plane‐wave pseudo‐potential density functional theory (DFT) calculations of the protein active site in the two possible oxidation states Cu(I) and Cu(II). The ab initio results are used to discuss how the electronic spectrum and wavefunctions may mediate the shuttling of electrons through the copper ion. We find that the Cu‐ligand hybridization is very similar in the two charge states of the metal center, but the energy spectrum changes substantially. This result might indicate important effects of electronic correlations in the redox activity and consequent electron transfer through the Cu site. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Bioinorganic chemistry modeled with the TPSSh density functional

In this work, the TPSSh density functional has been benchmarked against a test set of experimental structures and bond energies for 80 transition-metal-containing diatomics. It is found that the TPSSh functional gives structures of the same quality as other commonly used hybrid and nonhybrid functionals such as B3LYP and BP86. TPSSh gives a slope of 0.99 upon linear fitting to experimental bond energies, whereas B3LYP and BP86, representing 20% and 0% exact exchange, respectively, give linear fits with slopes of 0.91 and 1.07. Thus, TPSSh eliminates the large systematic component of the error in other functionals, reducing rms errors from 46-57 to 34 kJ/mol. The nonhybrid version of the functional, TPSS, gives a slope of 1.08, similar to BP86, implying that using 10% exact exchange is the main reason for the success of TPSSh. Typical bioinorganic reactions were then investigated, including spin inversion and electron affinity in iron-sulfur clusters, and breaking or formation of bonds in iron proteins and cobalamins. The results show that differences in reaction energies due to exact exchange can be much larger than the usually cited approximately 20 kJ/mol, sometimes exceeding 100 kJ/mol. The TPSSh functional provides energies approximately halfway between nonhybrids BP86 and TPSS, and 20% exact exchange hybrid B3LYP: Thus, a linear correlation between the amount of exact exchange and the numeric value of the reaction energy is observed in all these cases. For these reasons, TPSSh stands out as a most promising density functional for use and further development within the field of bioinorganic chemistry.     

Redox properties of [Fe2(SC6H5)2(NO)4]: an experimental study and quantum chemical modeling

Reduction of the complex [Fe₂(SC₆H₅)₂(NO)₄] in an aprotic solvent was studied by cyclic voltammetry in a wide range of potential scan rates. It was established that transfer of the first electron is reversible and the redox potential of this reaction was determined. Further reduction of the complex is irreversible because the product of attachment of the second electron is unstable and partially decomposes during the characteristic time of potential scan. The molecular and electronic structures of mono- and dianion of the complex as well as its theoretical redox potential value were calculated using the density functional theory methods with the local (BP86) and hybrid (B3LYP) functionals. The former functional better describes the geometry of the complex while the latter gives a better insight into its electronic structure. The extra negative charge is delocalized over NO groups, phenyl ligands, and iron atoms. The calculated redox potentials of one-electron reduction of the complexes are close to the experimental values obtained by analyzing cyclic voltammograms. Attachment of the second electron opens the decomposition channel of the complex, which is also consistent with experimental data.     

Hydrothermal reaction of Cu(II)/pyrazine-2,3,5-tricarboxylic acid and characterization of the copper(II) complexes

Four copper(II) complexes [Cu3(PZHD)2(2,2'-bpy)2(H2O)2].3H2O (1), [Cu3(DHPZA)2(2,2'-bpy)2] (2), [Cu(C2O4)phen(H2O)].H2O (3), and [Cu3(PZTC)2(2,2'-bpy)2].2H2O (4) were synthesized by hydrothermal reactions, in which the complexes 1-3 were obtained by the in situ Cu(II)/H3PZTC reactions (PZHD3- = 2-hydroxypyrazine-3,5-dicarboxylate, 2,2'-bpy = 2,2'-bipyridine, DHPZA3- = 2,3-dihydroxypyrazine-5-carboxylate, C2O42- = oxalate, phen = 1,10-phenanthroline, and H3PZTC = pyrazine-2,3,5-tricarboxylic acid). The Cu(II)/H3PZTC hydrothermal reaction with 2,2'-bpy, without addition of NaOH, results in the formation of complex 4. The complexes 1-4 and transformations from H3PZTC to PZHD3-, DHPZA3-, and C2O4(2-) were characterized by single-crystal X-ray diffraction and theoretical calculations. In the complexes 1, 2, and 4, the ligands PZHD3-, DPHZA3-, and PZTC3- all show pentadentate coordination to Cu(II) ion forming three different trinuclear units. The trinuclear units in 1 are assembled by hydrogen-bonding and pi-pi stacking to form a 3D supramolecular network. The trinuclear units in 2 acting as building blocks are connected by the carboxylate oxygen atoms forming a 2D metal-organic framework (MOF) with (4,4) topology. While the trinuclear units in 4 are linked together by the carboxylate oxygen atoms to form a novel 2D MOF containing right- and left-handed helical chains. The theoretical characterization testifies that electron transfer between OH- and Cu2+ and redox of Cu 2+ and Cu+ are the most important processes involved in the in situ copper Cu(II)/H3PZTC reactions, forming complexes of 1-3.     

Assessing conformer energies using electronic structure and machine learning methods

We have performed a large‐scale evaluation of current computational methods, including conventional small‐molecule force fields; semiempirical, density functional, ab initio electronic structure methods; and current machine learning (ML) techniques to evaluate relative single‐point energies. Using up to 10 local minima geometries across ~700 molecules, each optimized by B3LYP‐D3BJ with single‐point DLPNO‐CCSD(T) triple‐zeta energies, we consider over 6500 single points to compare the correlation between different methods for both relative energies and ordered rankings of minima. We find that the current ML methods have potential and recommend methods at each tier of the accuracy‐time tradeoff, particularly the recent GFN2 semiempirical method, the B97‐3c density functional approximation, and RI‐MP2 for accurate conformer energies. The ANI family of ML methods shows promise, particularly the ANI‐1ccx variant trained in part on coupled‐cluster energies. Multiple methods suggest continued improvements should be expected in both performance and accuracy.     

Theoretical studies on structures and reactivities of organocuprate(I) and organocopper(III) species

Systematic evaluation of method and basis set on the structure and energetics of organocuprate(I) and organocopper(III) species has been carried out. Various structures of organocuprate(I) and organocuprate(III) complexes were optimized with the HF, MP2, and B3LYP methods, and compared with the structures determined by X-ray crystallography (i.e., Me(2)Cu(I)(-), (CF(3))(4)Cu(III)(-)). Both the MP2 and B3LYP methods reasonably reproduce the X-ray structures while the HF method does not. Using larger basis set and incorporating the relativistic effects for Cu afford the best results. In the studies on the energetics of a Libond;Cu cluster model (Me(2)CuLi. LiCl) and Me(3)Cu model with the MP2, MP3, MP4DQ, MP4SDQ, CCSD(T), and B3LYP methods, the B3LYP method gives energetics similar to those obtained with the CCSD(T) method with much less cost, and hence, is judged to be the best practical method. The studies have shown that B3LYP method with the basis set incorporating the relativistic effective core potentials for Cu and the 6-31G* basis set for the rest is the theoretical method that is the most cost-effective for the studies of the structure and energetics of organocuprate(I) and organocopper(III) species.     

Synthesis of two new linear trinuclear Cu(II) complexes: mechanism of magnetic coupling through hybrid B3LYP functional and CShM studies

Two new Cu(II) linear trinuclear Schiff base complexes, [Cu3(L)2(CH3COO)2] (1) and [Cu3(L)2(CF3COO)2] (2), have been prepared using a symmetrical Schiff base ligand H2L [where H2L = N,N'-bis(2-hydroxyacetophenone)propylenediimine]. Both of the complexes have been characterized by elemental analyses, Fourier transform IR, UV/vis, and electron paramagnetic resonance spectroscopy. Single-crystal X-ray structures show that the adjacent Cu(II) ions are linked by double phenoxo bridges and a mu(2)-eta(1):eta(1) carboxylato bridge. In each complex, the central copper atom is located in an inversion center with distorted octahedral coordination geometry, while the terminal copper atoms have square-pyramidal geometry. Cryomagnetic susceptibility measurements over a wide range of temperature exhibit a distinct antiferromagnetic interaction of J = -36.5 and -72.3 cm(-1) for 1 and 2, respectively. Density functional theory calculations (B3LYP functional) and continuous-shape measurement (CShM) studies have been performed on the trinuclear unit to provide a qualitative theoretical interpretation of the antiferromagnetic behavior shown by the complexes.