The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

Investigating the Heaviest Halogen: Lessons Learned from Modeling the Electronic Structure of Astatine's Small Molecules

We present a systematic study of electron-correlation and relativistic effects in diatomic molecular species of the heaviest halogen astatine (At) within relativistic single- and multireference coupled-cluster approaches and relativistic density functional theory. We establish revised reference ab initio data for the ground states of At₂, HAt, AtAu, and AtO⁺ using a highly accurate relativistic effective core potential model and in-house basis sets developed for accurate modeling of molecules with large spin-orbit effects. Spin-dependent relativistic effects on chemical bonding in the ground state are comparable to the binding energy or even exceed it in At₂. Electron-correlation effects near the equilibrium internuclear separation are mostly dynamical and can be adequately captured using single-reference CCSD(T). However, bond elongation in At₂ and, especially, AtO⁺ results in rapid manifestation of its multireference character. While useful for evaluating the spin-orbit effects on the ground-state bonding and properties, the two-component density functional theory lacks predictive power, especially in combination with popular empirically adjusted exchange-correlation functionals. This drawback supports the necessity to develop new functionals for reliable quantum-chemical models of heavy-element compounds with strong relativistic effects.

A molecular modeling of iodinated organic compounds

Thermodynamic quantities of some iodinated compounds have been studied by means of ab initio and density functional theory calculations. Since there are some limitations for heavy elements in the fifth row of periodic table such as the iodine atom, a high level of ab initio theory is developed to calculate the energy of iodinated compounds. The standard enthalpies of formation for alkyl iodides and other iodinated organic compounds have been computed and compared with available experimental data. The impact of iodine atoms on the change of enthalpies for deprotonation of iodobenzenes has been studied and a mathematical model is proposed for the effect of iodine on the change of deprotonation. The acidity of diiodophenols as a model for thyroxin hormone has been successfully calculated. The barriers for nucleophilic reactions of substituted methyl iodides are investigated and the energy profiles are characterized by double-well potentials which correspond to pre-reaction and post-reaction complexes, separated by a transition state.

Bond Dissociation Energies in Heavy Element Chalcogen and Halogen Small Molecules

Thermodynamic properties including bond dissociation energies (BDEs), heats of formation, and gas-phase acidities for the hydrides and dimers of chalcogens and halogens, H₂Y, HX, Y₂, and X₂ for Y = Se, Te, and At and X = Br, I, and At, have been predicted using the Feller-Peterson-Dixon composite-correlated molecular orbital theory approach. A full four-component CCSD(T) approach was used to calculate the spin-orbit effects on thermodynamic properties, except for Se₂, where the AoC-DHF value was used due to strong multireference effects in Se₂ for the SO calculations. The calculated results show that the At₂ BDE is quite small, 19.5 kcal/mol, with much of the low bond energy due to spin-orbit effects. H₂Po is not predicted to be stable to dehydrogenation to Po + H₂ in terms of the free energy at 298 K. In the gas phase, HAt is predicted to be a stronger acid than H₂SO₄. The current results provide insights into potential difficulties in the actual experimental observation of such species for heavy elements.

Relativistic four-component potential energy curves for the lowest 23 covalent states of molecular astatine (At2)

The potential energy curves (PECs) of all covalent states of Molecular Astatine (At₂) have been investigated in this work within a four-component relativistic framework using the MOLFDIR program package. The ground state was determined using multireference configuration interaction with all single and double excitations including Davidson size-extensivity correction (MRCISD+Q) whereas the 22 excited states were treated by complete open shell configuration interaction (COSCI). Spectroscopic constants (R_e,ω_e,ω_ex_e,ω_ey_e, D_e,B_e,α_e,β_e,T_e) are presented for all states as well as vertical excitations obtained at COSCI, MRCISD and MRCISD+Q levels. In addition, it is also presented accurate extended Rydberg analytical form for the ground state X: (1)0_g⁺.

Beyond chemical accuracy in the heavy p-block: The first ionization potentials and electron affinities of Ga-Kr, In-Xe, and Tl-Rn

A relativistic coupled-cluster version of the Feller-Peterson-Dixon composite method has been used to accurately calculate the first ionization potentials (IPs) and electron affinities (EAs) of the post-d, p-block elements Ga-Rn. Complete basis set extrapolations including outer-core correlation at the CCSD(T) level of theory were combined with contributions from higher order electron correlation up to CCSDTQ, quantum electrodynamic effects (Lamb shift), and spin-orbit (SO) coupling including the Gaunt contribution. Several methods for including SO were investigated, in which all involved the four-component (4c) Dirac-Coulomb (DC) Hamiltonian. The treatment of SO coupling was the contribution that limited the final accuracy of the present results. In the cases where 4c-DC-CCSD(T) could be reliably used for the SO contributions, the final composite IPs and EAs agreed with the available experimental values to within an unsigned average error of just 0.16 and 0.20 kcal/mol, respectively. In all cases, the final IPs and EAs were within 1 kcal/mol of the available experimental values, except for the EAs of the group 13 elements (Ga, In, and Tl), where the currently accepted experimental values appear to be too large by as much as 4 kcal/mol. The values predicted in this work, which have estimated uncertainties of ±0.5 kcal/mol, are 5.25 (Ga), 7.69 (In), and 7.39 (Tl) kcal/mol. For the EAs of Po and At, which do not have experimental values, the current calculations predict values of 34.2 and 55.8 kcal/mol with estimated uncertainties of ±0.6 and ±0.3 kcal/mol, respectively.

The bismuth tetramer Bi4: the ν3 key to experimental observation

The spectroscopic identification of Bi₄ has been very elusive. Two constitutional Bi₄ isomers of T_d and C_2v symmetry are investigated and each is found to be a local energetic minimum.

Exploring the potential energy surface of small lead clusters using the gradient embedded genetic algorithm and an adequate treatment of relativistic effects

Theoretical inclusion of relativistic effects (scalar and spin–orbit) play a crucial role to assure an adequate structural assignment on lead clusters.

Scrutinizing "Invisible" astatine: A challenge for modern density functionals

The main-group 6p elements did not receive much attention in the development of recent density functionals. In many cases it is still difficult to choose among the modern ones a relevant functional for various applications. Here, we illustrate the case of astatine species (At, Z = 85) and we report the first, and quite complete, benchmark study on several properties concerning such species. Insights on geometries, transition energies and thermodynamic properties of a set of 19 astatine species, for which reference experimental or theoretical data has been reported, are obtained with relativistic (two-component) density functional theory calculations. An extensive set of widely used functionals is employed. The hybrid meta-generalized gradient approximation (meta-GGA) PW6B95 functional is overall the best choice. It is worth noting that the range-separated HSE06 functional as well as the old and very popular B3LYP and PBE0 hybrid-GGAs appear to perform quite well too. Moreover, we found that astatine chemistry in solution can accurately be predicted using implicit solvent models, provided that specific parameters are used to build At cavities. © 2016 Wiley Periodicals, Inc.