Application of explicitly correlated coupled-cluster methods to molecules containing post-3d main group elements

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.

Correlation Consistent Basis Sets for Explicitly Correlated Theory: The Transition Metals

We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. The cc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wis are [9s8p6d3f2g] for the 3d-block elements and [7s7p6d3f2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wis basis sets are evaluated on challenging test sets for metal-organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of main-group elements; however, it is somewhat more significant for metal clusters.

Atomic Mean-Field Approach within Exact Two-Component Theory Based on the Dirac-Coulomb-Breit Hamiltonian

An extension of the exact two-component theory with atomic mean-field integrals (the X2CAMF scheme) to the treatment of the Breit term together with efficient implementation using an atomic Dirac-Coulomb-Breit Hartree-Fock program is reported. The accuracy of the X2CAMF scheme for treating the contributions from the Breit term to the molecular properties is demonstrated using benchmark calculations of equilibrium bond lengths, harmonic frequencies, and dipole moments for molecules containing elements across the periodic table. Calculations of the properties for molecules containing period four elements aiming at high accuracy as well as for Th- and U-containing molecules are also presented and compared with experimental results to demonstrate the usefulness of the X2CAMF scheme in combination with accurate treatments of electron correlation by the coupled-cluster (CC) methods. The combination of CC methods and the X2CAMF scheme shows potential to extend the accuracy of CC calculations to heavy elements, e.g., to computational heavy-element thermochemistry.

Fluoro-nitrogen Cations

The crystal structures of [NH 3 F] + [CF 3 SO 3 ] - , [NH 2 F 2 ] + [SbF 6 ] - , and [N 2 F 3 ] + [Sb 3 F 16 ] - have been determined, representing the first structural characterizations of these simple fluoro-nitrogen cations. The influences of the hybridization of the central nitrogen atom and of the number of fluorine substituents on the N-F bond lengths are evaluated for the series N 2 F + , N 2 F 3 + , NF 2 O + , NH 3 F + , NH 2 F 2 + , and NF 4 + . It is shown that the N-F bond length decreases from 1.40 Å to 1.26 Å with increasing fluorine substitution and increasing s-character of the nitrogen atom, and that unusual N-F bond lengths reported in the previous literature are caused by disorder problems.

Correlation consistent basis sets for explicitly correlated wavefunctions: Pseudopotential-based basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements

New correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements have been developed specifically for use in explicitly correlated F12 calculations. This includes orbital basis sets for valence only (cc-pVnZ-PP-F12, n = D, T, Q) and outer core-valence (cc-pCVnZ-PP-F12) correlation, along with both of these augmented with additional high angular momentum diffuse functions. Matching auxiliary basis sets required for density fitting and resolution-of-the-identity approaches to conventional and F12 integrals have also been optimized. All of the basis sets are to be used in conjunction with small-core relativistic pseudopotentials [Figgen et al., Chem. Phys. 311, 227 (2005)]. The accuracy of the basis sets is determined through benchmark calculation at the explicitly correlated coupled-cluster level of theory for various properties of atoms and diatomic molecules. The convergence of the properties with respect to the basis set is dramatically improved compared to conventional coupled-cluster calculations, with cc-pVTZ-PP-F12 results close to conventional estimates of the complete basis set limit. The patterns of convergence are also greatly improved compared to those observed from the use of conventional correlation consistent basis sets in F12 calculations.

Accurate Thermochemistry for Main-Group Elements up to Xenon with the Wn-P34 Series of Composite Methods

In the present study, we introduce the accurate Wn-P34 quantum chemistry composite methods with applicability to heavy p-block elements up to xenon. For a set of thermochemical properties for prototypical third- and fourth-row species and for a diverse set of small light-main-group species, they show accuracies of ∼3 kJ mol^-1 or better. Overall, the Wn-P34 methods are comparable in accuracy to Wn, with a widened applicability to heavier elements. We have used Wn-P34 to compile the P34 set of accurate thermochemical values for heavy p-block species, and we have applied this set to assess a wide range of lower-cost methods. The results of our assessment show that the G4(MP2)-XK composite method provides adequate treatments for these species, but several widely used double-hybrid density functional theory (DH-DFT) methods show uncharacteristically large deviations. In contrast, we find it presently surprising that some pure and hybrid DFT methods such as TPSS and SCANh perform quite well. We hope that our findings and new tools would facilitate the application of computational chemistry for heavy elements, of which the properties are yet to be broadly explored.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Characterizing structures, energetics, and spectra of species on the 1,3[H, C, As] potential energy surfaces: A high-level theoretical contribution

The ground and the low lying electronic states of structures on the ^1,3[H, C, As] potential energy surfaces were investigated with the highly correlated theoretical approaches CCSD(T), CCSD(T)-F12b, and CASSCF/MRCI along with the series of correlation consistent (aug-cc-pVnZ, n = D, T, Q, 5) basis sets. Energetic and spectroscopic parameters were obtained at the complete basis set limit, and the effect of core-valence correlation on these properties evaluated. Fundamental frequencies were also computed with the variational configuration interaction (VCI) approach. Heats of formation at 0 and 298.15 K were estimated for HCAs and CH, AsH, CAs, and HCAs, as well as the calculation of ionization potentials for HCAs. Comparisons of the present results with literature ones for the systems HCN/HNC, HCP/HPC highlight similarities and differences among these systems. Altogether, this investigation provides a very reliable characterization of the species on the surfaces and should guide future experimental studies on these systems.

A variationally computed room temperature line list for AsH3

Calculations are reported on the rotation–vibration energy levels of the arsine molecule with associated transition intensities.

A comparison between hydrogen and halogen bonding: the hypohalous acid–water dimers, HOX⋯H2O (X = F, Cl, Br)

Hypohalous acids (HOX) are a class of molecules that play a key role in the atmospheric seasonal depletion of ozone and have the ability to form both hydrogen and halogen bonds.

Near-UV photodissociation dynamics of CH2I2

The near-UV photodissociation dynamics of CH₂I₂has been investigated using a combination of velocity-map (slice) ion imaging andab initiocalculations characterizing the excited states.

Energy disposal and thermal rate constants for the OH + HBr and OH + DBr reactions: quasiclassical trajectory calculations on an accurate potential energy surface

We report reaction cross sections, energy disposal, and rate constants for the OH + HBr → Br + H2O and OH + DBr → Br + HDO reactions from quasiclassical trajectory calculations using an ab initio potential energy surface [ de Oliveira-Filho , A. G. S. ; Ornellas , F. R. ; Bowman , J. M. J. Phys. Chem. Lett. 2014 , 5 , 706 - 712 ]. Comparison with available experiments are made and generally show good agreement.

Quasiclassical Trajectory Calculations of the Rate Constant of the OH + HBr → Br + H2O Reaction Using a Full-Dimensional Ab Initio Potential Energy Surface Over the Temperature Range 5 to 500 K

We report a permutationally invariant, ab initio potential energy surface (PES) for the OH + HBr → Br + H2O reaction. The PES is a fit to roughly 26 000 spin-free UCCSD(T)/cc-pVDZ-F12a energies and has no classical barrier to reaction. It is used in quasiclassical trajectory calculations with a focus on the thermal rate constant, k(T), over the temperature range 5 to 500 K. Comparisons with available experimental data over the temperature range 23 to 416 K are made using three approaches to treat the OH rotational and associated electronic partition function. All display an inverse temperature dependence of k(T) below roughly 160 K and a nearly constant temperature dependence above 160 K, in agreement with experiment. The calculated rate constant with no treatment of spin-orbit coupling is overall in the best agreement with experiment, being (probably fortuitously) within 20% of it.

Is near-"spectroscopic accuracy" possible for heavy atoms and coupled cluster theory? An investigation of the first ionization potentials of the atoms Ga-Kr

Recent developments in ab initio coupled cluster (CC) theory and correlation consistent basis sets have ushered in an era of unprecedented accuracy when studying the spectroscopy and thermodynamics of molecules containing main group elements. These same developments have recently seen application to heavier inorganic or transition metal-containing species. The present work benchmarks conventional single reference coupled cluster theory (up to full configuration interaction for valence electron correlation and coupled cluster with up to full pentuple excitations (CCSDTQP) for core-valence correlation) and explicitly correlated coupled cluster methods [CC with single, double, and perturbative triple substitutions (CCSD(T)-F12)] for the atomic ionization potentials of the six 4p elements (Ga-Kr), a property with experimental error bars no greater than a few cm(-1). When second-order spin orbit coupling effects are included, a composite methodology based on CCSD(T) calculations yielded a mean signed error of just -0.039 kcal mol(-1) and a mean unsigned error of 0.043 kcal mol(-1). Inclusion of post-CCSD(T) correlation corrections reduced both of these values to -0.008 kcal mol(-1) and 0.025 kcal mol(-1), respectively, with the latter corresponding to an average error of just 9 cm(-1). The maximum signed error in the latter scheme was just -0.043 kcal mol(-1) (15 cm(-1)).