Molecular core-valence correlation effects involving the post-d elements Ga–Rn: Benchmarks and new pseudopotential-based correlation consistent basis sets

Equilibrium Values for the Si-H Bond Length and Equilibrium Structures of Silyl Iodide and Halosilylenes

The equilibrium structures of silyl iodide, SiH3I, and silylene halides, SiHX (X = F, Cl, Br, I), were determined by using the mixed regression method, where approximate values of the rotational constants are supplemented by the structural parameters of a different origin. For this goal, it is shown that the r(Si-H) bond length can be determined by using the isolated SiH stretching frequency and that an accurate estimation of the bond angles is obtained by an MP2 calculation with a basis set of triple zeta quality. To check the accuracy of the experimental structures, they were also optimized by means of all electron CCSD(T) calculations using basis sets of quadruple zeta quality.

Exploring the Tl 2 H 2 potential energy surface: A comparative analysis with group 13 systems and experiment

Thallium chemistry is experiencing unprecedented importance. Therefore, it is valuable to characterize some of the simplest thallium compounds. Stationary points along the singlet and triplet Tl  2 H  2 potential energy surface have been characterized. Stationary point geometries were optimized with the CCSD(T)/aug-cc-pwCVQZ-PP method. Harmonic vibrational frequencies were computed at the same level of theory while anharmonic vibrational frequencies were computed at the CCSD(T)/aug-cc-pwCVTZ-PP level of theory. Final energetics were obtained with the CCSDT(Q) method. Basis sets up to augmented quintuple-zeta cardinality (aug-cc-pwCV5Z-PP) were employed to obtain energetics in order to extrapolate to the complete basis set limits using the focal point approach. Zero-point vibrational energy corrections were appended to the extrapolated energies in order to determine relative energies at 0 K. It was found that the planar dibridged isomer lies lowest in energy while the linear structure lies highest in energy. The results were compared to other group 13 M  2 H  2 (M = B, Al, Ga, In, and Tl) theoretical studies and some interesting variations are found. With respect to experiment, incompatibilities exist.

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.

A wealth of structures for the Ge2H2+ radical cation: comparison of theory and experiment

Five structures of Ge2H2 and Ge2H2+ are investigated in this study. Optimized geometries at the CCSD(T)/cc-pwCVQZ-PP level of theory were obtained. Focal point analyses were performed on these optimized geometries to determine relative energies using the CCSD(T) method with polarized basis sets up to quintuple-zeta. Energy corrections include full T and pertubative (Q) coupled-cluster effects plus anharmonic corrections to the zero-point vibrational energy. Relative ordering in energy from lowest to highest of the five Ge2H2+ structures is butterfly, germylidene, monobridged, trans, then linear. In neutral Ge2H2, the monobridged structure lies lower in energy than the germylidene structure. Fundamental vibrational frequencies and IR intensities were computed for the minima at the CCSD(T)/cc-pwCVTZ-PP level of theory to compare with experimental research. Partial atomic charges and natural bonding orbital analyses indicated that the positive charge of Ge2H2+ is contained in the region of the Ge-Ge bond.

Single-Pole Polarization Models: Rapid Evaluation of Electron Affinities of Solvated-Electron and Superatomic Molecular Anionic States

We propose a single-parameter effective one-particle potential, termed the single-pole exchange-correlation (1p-XC), to rapidly evaluate electron affinities (EAs) of nonvalence electronic states of molecular clusters and nanoassemblies. The model combines exact-exchange and the random phase approximation (RPA) correlation potential with a single-pole approximation to model the frequency-dependent polarization function. It captures long-range static and dynamic-frequency effects in the correlation potential, with mean absolute errors of 0.06 eV for EAs of hydrated- and ammoniated-electron clusters with EA values in the range 0.24-1.77 eV. The 1p-XC approximation enables EA estimation with a computational wall-time similar to that of hybrid functionals. The model also provides a compressed-basis, which significantly reduces the rank of higher-level parameter-free one-particle Hamiltonians and further simplifies the computation of EAs. The compressed-basis approach is used to model the hybridization of superatomic molecular states of (C60)2- and (C60)3-, thereby verifying previous model Hamiltonian studies.

Error of relativistic effective core potentials for closed-shell diatomic molecules of p-block heavy and superheavy elements in DFT and TDDFT calculations

Pseudopotentials (PP) are extensively used in electronic structure calculations, particularly for molecules containing heavy elements. Parameters in PPs are mainly determined from ab initio results, and errors of such PPs in density functional theory (DFT) calculations have been studied previously. However, PP errors on results with spin-orbit coupling and those in time-dependent DFT (TDDFT) calculations have not been reported previously. In this work, we investigate the error of the small-core energy-consistent Stuttgart/Koln pseudopotentials in DFT and TDDFT calculations with and without spin-orbit coupling. Ground state bond lengths, harmonic frequencies, dissociation energies, and vertical excitation energies for a series of closed-shell diatomic heavy and superheavy p-block molecules are calculated using several popular exchange-correlation functionals. PP errors are estimated by comparing with results using the all-electron Dirac-Coulomb (-Gaunt) Hamiltonian. Our results show that the difference between ground state properties and most excitation energies in scalar-relativistic calculations with the PP and those of all-electron calculations is quite small. This difference becomes somewhat larger when spin-orbit coupling (SOC) is present, especially for properties that are affected by SOC to some extent. In addition, the errors of the PPs are insensitive to the employed exchange-correlation functionals in most cases. Our results indicate that reasonable DFT and TDDFT results can be obtained using the small-core energy-consistent Stuttgart/Koln pseudopotentials for heavy and super-heavy p-block molecules.

Prediction of Aqueous Reduction Potentials of X•, ChH•, and XO• Radicals with X = Halogen and Ch = Chalcogen

The aqueous electron affinity and aqueous reduction potentials for F•, Cl•, Br•, I•, OH•, SH•, SeH•, TeH•, ClO•, BrO•, and IO• were calculated using electronic structure methods for explicit cluster models coupled with a self-consistent reaction field (SMD) to treat the aqueous solvent. Calculations were conducted using MP2 and correlated molecular orbital theory up to the CCSD(T)-F12b level for water tetramer clusters and MP2 for octamer cluster. Inclusion of explicit waters was found to be important for accurately predicting the redox potentials in a number of cases. The calculated reduction potentials for X• and ChH• were predicted to within ∼0.1 V of the reported literature values. Fluorine is anomalous due to abstraction of a hydrogen from one of the surrounding water molecules to form a hydroxyl radical and hydrogen fluoride, so its redox potential was calculated using only an implicit model. Larger deviations from experiment were predicted for ClO• and BrO•. These deviations are due to the free energy of solvation of the anion being too negative, as found in the pKa calculations, and that for the neutral being too positive with the current approach.

Quantum computations in heavy noble-gas hydride cations: Reference energies and new spectroscopic data

Computational quantum chemistry has become a powerful tool with a wide range of possibilities to solve chemical-physical problems. As a result of this, the interest in the applications of computational quantum chemistry has expanded considerably, and has opened up novel research opportunities. In particular, those related to the characterization of heavy-atoms complexes, as most electronic structure calculations for such systems struggle with the problem posed by the large number of electrons present in them, and consequently, the introduction of relativistic effects. The present study performed an exhaustive assess to characterized the uncommon NgH+ (Ng = Kr, Xe, and Rn) hydride cations in order to provide accurate rovibrational data of their isotopes to assist in the laboratory characterization or even their astronomical detection. Scalar relativistic effects were included, and the ground and first electronically exited states potential curves were obtained from benchmark ab initio CCSD(T)/CBS and MRCI+Q electronic structure calculations. Next, such interaction potentials, correctly extended to long-range asymptotic regions, were employed in quantum bound state calculations and molecular spectroscopic constants were determined for the most abundance 84Kr, 132Xe, and 222Rn isotopes. Our results were discussed in comparison with available experimental and previous theoretical estimates, aiming to treat accuracy issues. The new sets provide reference data that could serve for spectroscopic characterization of such low abundance and high radioactive species.

Accuracy of Different Electronic Basis Set Families for Anharmonic Molecular Vibrations: A Comprehensive Benchmark Study

In this work, the accuracy and convergence of different electronic basis set families for the computation of anharmonic molecular vibrational spectroscopic calculations are benchmarked. A series of 39 different basis sets from different families following their hierarchy are assessed on VSCF and VSCF-PT2 algorithms with commonly used MP2 and DFT based B3LYP-D potentials for a set of molecular systems. Such an effort has been validated in a previous work ( J. Phys. Chem. A 2020, 124, 9203-9221) with split-valence basis sets for fundamentals and intensities. Here, fundamental transitions, vibrationally excited states, and intensities are compared with the experimental data to estimate the accuracy for a series of Jensen, Dunning, Calendar, Karlsruhe, and Sapporo basis set families. The convergence of basis sets are also compared with the large ANO basis set. Comprehensive statistical error analysis in terms of accuracy and precision was carried out to assess the performance of each basis set. It is observed that the improvement for the calculated harmonic and anharmonic values from the smaller basis sets to the medium (i.e., triple-ξ) is considerable. Beyond this, from medium to large basis sets, the convergence is slow and mostly posits nearly converged values. Basis sets with and without diffuse functions offer characteristically different accuracies and convergence patterns. Finally, recommendations are given on the choice of basis set chosen as black-box which can balance between accuracy and computational time, estimation of the errors, and their selections especially for large molecules.

Probing C-I bond fission in the UV photochemistry of 2-iodothiophene with core-to-valence transient absorption spectroscopy

The UV photochemistry of small heteroaromatic molecules serves as a testbed for understanding fundamental photo-induced chemical transformations in moderately complex compounds, including isomerization, ring-opening, and molecular dissociation. Here, a combined experimental-theoretical study of 268 nm UV light-induced dynamics in 2-iodothiophene (C4H3IS) is performed. The dynamics are experimentally monitored with a femtosecond extreme ultraviolet (XUV) probe that measures iodine N-edge 4d core-to-valence transitions. Experiments are complemented by density functional theory calculations of both the pump-pulse induced valence excitations and the XUV probe-induced core-to-valence transitions. Possible intramolecular relaxation dynamics are investigated by ab initio molecular dynamics simulations. Gradual absorption changes up to ∼0.5 to 1 ps after excitation are observed for both the parent molecular species and emerging iodine fragments, with the latter appearing with a characteristic rise time of 160 ± 30 fs. Comparison of spectral intensities and energies with the calculations identifies an iodine dissociation pathway initiated by a predominant π → π* excitation. In contrast, initial excitation to a nearby n⟂ → σ* state appears unlikely based on a significantly smaller oscillator strength and the absence of any corresponding XUV absorption signatures. Excitation to the π → π* state is followed by contraction of the C-I bond, enabling a nonadiabatic transition to a dissociative π→σC-I* state. For the subsequent fragmentation, a relatively narrow bond-length region along the C-I stretch coordinate between 230 and 280 pm is identified, where the transition between the parent molecule and the thienyl radical + iodine atom products becomes prominent in the XUV spectrum due to rapid localization of two singly occupied molecular orbitals on the two fragments.

Quantifying the Impact of Halogenation on Intermolecular Interactions and Binding Modes of Aromatic Molecules

Halogenation of aromatic molecules is frequently used to modulate intermolecular interactions with ramifications for optoelectronic and mechanical properties. In this work, we accurately quantify and understand the nature of intermolecular interactions in perhalogenated benzene (PHB) clusters. Using benchmark binding energies from the fixed-node diffusion Monte Carlo (FN-DMC) method, we show that generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA) plus approximate exchange kernel (AKX) provides reliable interaction energies with mean absolute error (MAE) of 0.23 kcal/mol. Using the GKS-spRPA+AXK method, we quantify the interaction energies of several binding modes of PHB clusters ((C₆X₆)_n; X = F, Cl, Br, I; n = 2, 3). For a given binding mode, the interaction energies increase 3-4 times from X = F to X = I; the X-X binding modes have energies in the range of 2-4 kcal/mol, while the π-π binding mode has interaction energies in the range of 4-12 kcal/mol. SAPT-DFT-based energy decomposition analysis is then used to show that the equilibrium geometries are dictated primarily by the dispersion and exchange interactions. Finally, we test the accuracy of several dispersion-corrected density functional approximations and show that only the r2SCAN-D4 method has a low MAE and correct long-range behavior, which makes it suitable for large-scale simulations and for developing structure-function relationships of halogenated aromatic systems.

Electronic Properties of Functionalized Diamanes for Field-Emission Displays

Ultrathin diamond films, or diamanes, are promising quasi-2D materials that are characterized by high stiffness, extreme wear resistance, high thermal conductivity, and chemical stability. Surface functionalization of multilayer graphene with different stackings of layers could be an interesting opportunity to induce proper electronic properties into diamanes. Combination of these electronic properties together with extraordinary mechanical ones will lead to their applications as field-emission displays substituting original devices with light-emitting diodes or organic light-emitting diodes. In the present study, we focus on the electronic properties of fluorinated and hydrogenated diamanes with (111), (110), (0001), (101̅0), and (2̅110) crystallographic orientations of surfaces of various thicknesses by using first-principles calculations and Bader analysis of electron density. We see that fluorine induces an occupied surface electronic state, while hydrogen modifies the occupied bulk state and also induces unoccupied surface states. Furthermore, a lower number of layers is necessary for hydrogenated diamanes to achieve the convergence of the work function in comparison with fluorinated diamanes, with the exception of fluorinated (110) and (2̅110) films that achieve rapid convergence and have the same behavior as other hydrogenated surfaces. This induces a modification of the work function with an increase of the number of layers that makes hydrogenated (2̅110) diamanes the most suitable surface for field-emission displays, better than the fluorinated counterparts. In addition, a quasi-quantitative descriptor of surface dipole moment based on the Tantardini-Oganov electronegativity scale is introduced as the average of bond dipole moments between the surface atoms. This new fundamental descriptor is capable of predicting a priori the bond dipole moment and may be considered as a new useful feature for crystal structure prediction based on artificial intelligence.

The Importance of Tight f Basis Functions for Heavy p-Block Oxides and Halides: A Parallel With Tight d functions in the Second Row

It is well-known that both wave function ab initio and DFT calculations on second-row compounds exhibit anomalously slow basis set convergence unless the basis sets are augmented with additional "tight" (high-exponent) d functions, as in the cc-pV(n+d)Z and aug-cc-pV(n+d)Z basis sets. This has been rationalized as being necessary for a better description of the low-lying 3d orbital, which as the oxidation state increases sinks low enough to act as a back-donation acceptor from chalcogen and halogen lone pairs. This prompts the question whether a similar phenomenon exists for the isovalent compounds of the heavy p-block. We show that for the fourth and fifth row, this is the case, but this time for tight f functions enhancing the description of the low-lying 4f and 5f Rydberg orbitals, respectively. In the third-row heavy p block, the 4f orbitals are too far up, while the 4d orbitals are adequately covered by the basis functions already present to describe the 3d subvalence orbitals.

The performance of CCSD(T) for the calculation of dipole moments in diatomics

This work analyzes the accuracy of the coupled cluster with single, double, and perturbative triple excitation [CCSD(T)] method for predicting dipole moments. In particular, we benchmark CCSD(T) predictions for the equilibrium bond length, vibrational frequency, and dipole moment versus accurate experimental data. As a result, we find that CCSD(T) leads to accurate dipole moments. However, in some cases, it disagrees with the experimental values, and the disagreement can not be satisfactorily explained via relativistic or multi-reference effects. Therefore, our results indicate that benchmark studies for energy and geometry properties do not accurately describe other electron density magnitudes.

Active Thermochemical Tables: Enthalpies of Formation of Bromo- and Iodo-Methanes, Ethenes and Ethynes

The thermochemistry of halocarbon species containing iodine and bromine is examined through an extensive interplay between new Feller-Peterson-Dixon (FPD) style composite methods and a detailed analysis of all available experimental and theoretical determinations using the thermochemical network that underlies the Active Thermochemical Tables (ATcT). From the computational viewpoint, a slower convergence of the components of composite thermochemistry methods is observed relative to species that solely contain first row elements, leading to a higher computational expense for achieving comparable levels of accuracy. Potential systematic sources of computational uncertainty are investigated, and, not surprisingly, spin-orbit coupling is found to be a critical component, particularly for iodine containing molecular species. The ATcT analysis of available experimental and theoretical determinations indicates that prior theoretical determinations have significantly larger uncertainties than originally reported, particularly in cases where molecular spin-orbit effects were ignored. Accurate and reliable heats of formation are reported for 38 halogen containing systems, based on combining the current computations with previous experimental and theoretical work via the ATcT approach.

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.

Toward the Observation of the Tin and Lead Analogs of Formaldehyde

Heavy aldehyde and ketone analogues, R₂X═O (X = Si, Ge, Sn, or Pb), differ from their R₂C═O counterparts due to their greater tendency to oligeramize as the X═O bond polarity increases as one goes down the periodic table. To date, H₂Sn═O and H₂Pb═O have eluded experimental detection. Herein we present the most rigorous theoretical study to date on these structures, providing CCSD(T)/pwCVTZ fundamental frequencies computed on CCSD(T)/CBS optimized structures for the H₂X═O (X = Sn, Pb) potential energy surface. The focal point approach is employed to produce the CCSDTQ/CBS relative energies. For the Sn and Pb structures, the carbene-like cis-HXOH was the global minima, with the trans species being less than 0.6 and 1.1 kcal mol^-1 above the cis structures, respectively. The formaldehyde-like H₂X═O structure is in an energy well of at least 34.8 and 25.4 kcal mol^-1 for Sn and Pb, respectively. Our results provide guidance for future work that may detect H₂Sn═O or H₂Pb═O for the first time.

High-Level Theoretical Study of the C1Π States of GaCl, GaBr, InCl, and InBr

For the first singlet excited states C¹Π of IIIA group monohalides GaCl, GaBr, InCl, and InBr, a very shallow potential well may exist in the flat potential energy curve, which poses a challenge to the theoretical accuracy. In this study, high-level theoretical calculations have been performed through the Feller-Peterson-Dixon composite approach to study the C¹Π states, and the obtained spectroscopic constants agree well with the known experimental ones. It is found that the C¹Π states are sensitive to the size of basis functions, spin-orbit coupling, and strong correlations mainly due to triple excitations. The final results show that the C¹Π states of GaCl and InCl are quasi-bound with one (v' = 0) and four (v' = 0-3) vibrational levels, respectively, being consistent with the experimental findings, whereas the C¹Π states of GaBr and InBr are repulsive. Our conclusions deny the existence of higher vibrational levels v' = 1 for GaCl, v' > 3 for InCl, and v' ≥ 0 for InBr in previous experimental and theoretical studies of C¹Π.

Assessment of DLPNO-CCSD(T)-F12 and its use for the formulation of the low-cost and reliable L-W1X composite method

In the present study, we have investigated the performance of RIJCOSX DLPNO-CCSD(T)-F12 methods for a wide range of systems. Calculations with a high-accuracy option ["DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12"] extrapolated to the complete-basis-set limit using the maug-cc-pV[D+d,T+d]Z basis sets provides fairly good agreements with the canonical CCSD(T)/CBS reference for a diverse set of thermochemical and kinetic properties [with mean absolute deviations (MADs) of ~1-2 kJ mol^-1 except for atomization energies]. On the other hand, the low-cost "RIJCOSX DLPNO-CCSD(T)-F12D" option leads to substantial deviations for certain properties, notably atomization energies (MADs of up to tens of kJ mol^-1 ). With the high-accuracy CBS approach, we have formulated the L-W1X method, which further includes a low-cost core-valence plus scalar-relativistic term. It shows generally good accuracy. For improved accuracies in specific cases, we advise replacing maug-cc-pV(n+d)Z with jun-cc-pV(n+d)Z for the calculation of electron affinities, and using well-constructed isodesmic-type reactions to obtain atomization energies. For medium-sized systems, DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 calculations are several times faster than the corresponding canonical computation; the use of the local approximations (RIJCOSX and DLPNO) leads to a better scaling than that for the canonical calculation (from ~6-7 down to ~2-4 for our test systems). Thus, the DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 method, and the L-W1X protocol that based on it, represent a useful means for obtaining accurate thermochemical quantities for larger systems.

Observation of Selectively Populated Monohalide Excited States from the Reactions of Group 3 Metal (Sc, Y, and La) Monomers and Dimers with Halogen-Containing Molecules

The chemiluminescent reactions of the group 3 metals Sc and Y with F₂, Cl₂, Br₂, ClF, ICl (Sc), IBr (Y), and SF₆ and La with F₂, SF₆, Cl₂, and ClF have been studied at low pressures (6 × 10^-6 to 4 × 10^-4 Torr) using a beam-gas arrangement and extended to the 10^-3 Torr multiple collision pressure range. Contrary to previous reports, the observed chemiluminescent spectra are primarily attributed to emission from the metal monohalides. Extensive pressure and temperature dependence studies and high-level correlated molecular orbital theory calculations of the bond dissociation energies support this conclusion and the attribution of the chemiluminescence. Evidence for the "selective" production of a monohalide excited electronic state is obtained for several of the Sc and Y reactions. All reactions producing the metal monofluorides are first order with respect to the oxidant, while reactions producing the monochlorides and monobromides are found to be "faster than first order" with respect to the oxidant. This difference is associated with the metal halide bond dissociation energies and the metal halide product internal density of states. Analysis of the temperature dependence for six representative reactions indicates that the "selective" excited-state formation of the metal monohalides proceeds via a direct mechanism with negligible activation energy. We compare and contrast the present results with previous experiments and interpretations which have assigned the selective emission from these systems to the group 3 dihalides produced in a two-step reaction sequence analogous to an electron jump process. The current results suggest a distinctly different interpretation of the observed processes in these systems. The observed selectivity observed in these studies is remarkable given the significant number of known and potential excited states in the scandium and yttrium halides as well as their different electronic configurations.

Intermediate Hamiltonian Fock-space coupled-cluster theory for excitation energies, double ionization potentials, and double electron attachments with spin–orbit coupling

The intermediate Hamiltonian Fock-space coupled-cluster methods at the singles and doubles level (IHFSCCSD) for excitation energies in the (1p, 1h) sector, double ionization potentials in the (0p, 2h) sector, and double electron attachments in the (2p, 0h) sector of the Fock space are implemented based on the CCSD method with spin–orbit coupling (SOC) included in the post-Hartree–Fock treatment using a closed-shell reference in this work. The active space is chosen to contain those orbitals that have the largest contribution to principal ionized or electron-attached states obtained from the equation-of-motion coupled-cluster calculations. Both time-reversal symmetry and spatial symmetry are exploited in the implementation. Our results show that the accuracy of IHFSCCSD results is closely related to the active space, and the sufficiency of the active space can be assessed from the percentage of transitions within the active space. In addition, unreasonable results may be encountered when the ionized or electron-attached states with a somewhat larger contribution from double excitations are included to determine the active space and cluster operators in the (0p, 1h) or (1p, 0h) sector of the Fock space. A larger active space may be required to describe SO splitting reliably than that in the scalar-relativistic calculations in some cases. The IHFSCCSD method with SOC developed in this work can provide reliable results for heavy-element systems when a sufficient active space built upon the principal ionization potential/electron affinity states is adopted.

Ab initio calculations in atoms, molecules, and solids, treating spin-orbit coupling and electron interaction on an equal footing

We incorporate explicit, non-perturbative treatment of spin-orbit coupling into ab initio auxiliary-field quantum Monte Carlo (AFQMC) calculations. The approach allows a general computational framework for molecular and bulk systems in which material specificity, electron correlation, and spin-orbit coupling effects can be captured accurately and on an equal footing, with favorable computational scaling vs system size. We adopt relativistic effective-core potentials that have been obtained by fitting to fully relativistic data and that have demonstrated a high degree of reliability and transferability in molecular systems. This results in a two-component spin-coupled Hamiltonian, which is then treated by generalizing the ab initio AFQMC approach. We demonstrate the method by computing the electron affinity in Pb, the bond dissociation energy in Br₂ and I₂, and solid Bi.

Theoretical investigation of the low lying electronic states of MgGa

In this work, we investigate the low-lying electronic states correlated to the first and the second dissociation channels of MgGa molecule, neglecting and including the spin-orbit coupling effect. High-level ab initio calculations have been performed by using the icMRCI + Q method. Potential energy curves, spectroscopic constants, electron configurations and dipole moments are derived and discussed. Molecular structures of several magnesium-group 13 diatomics have been probed and analyzed. Information associated with transition dipole moments, Franck-Condon factors, vibrational branching ratios and radiative lifetimes between the Ω states are also well characterized. It is anticipated this work will provide some inspiration for further studies on MgGa.

Group 15 and 16 Nitrene-Like Pnictinidenes

Pnictinidenes are an increasingly relevant species in main group chemistry and generally exhibit proclivity for the triplet electronic ground state. However, the elusive singlet electronic states are often desired for chemical applications. We predict the singlet-triplet energy differences (ΔE_ST =E_Singlet -E_Triplet ) of simple group 15 and 16 substituted pnictinidenes (Pn-R; Pn=P, As, Sb, or Bi) with highly reliable focal-point analyses targeting the CCSDTQ/CBS level of theory. The only cases we predict to have favorable singlet states are P-PH₂ (-3.2 kcal mol^-1 ) and P-NH₂ (-0.2 kcal mol^-1 ). ΔE_ST trends are discussed in light of the geometric predictions as well as qualitative natural bond order analysis to elucidate some of the important electronic structure features. Our work provides a rigorous benchmark for the ΔE_ST of fundamental Pn-R moieties and provides a firm foundation for the continued study of heavier pnictinidenes.

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.

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.

Highly Strained Pn(CH)3 (Pn = N, P, As, Sb, Bi) Tetrahedranes: Theoretical Characterization

Recent experimental research by Cummins and co-workers has established the existence of a tetrahedrane molecule with one CH moiety replaced by phosphorus. We present here the first theoretical studies of the entire Pn(CH)₃ (Pn = N, P, As, Sb, Bi) class of molecules. Geometries are obtained at the highly reliable CCSD(T)/aug-cc-pwCVTZ(-PP) level of theory. Harmonic vibrational frequencies are determined and analyzed to confirm the nature of each stationary point and provide helpful findings that may aid in the detection of each species. Most notable is the result that the geometric parameters associated with the (CH)₃ moiety in the tetrahedranes exhibit little change under pnictogen substitution, while the Pn-C bonds and C-Pn-C bond angles greatly increase and decrease, respectively. Strain energies are predicted and range from 122.3 kcal mol^-1 (N(CH)₃) to 99.4 kcal mol^-1 (Bi(CH)₃) at the DF-CCSD(T)//B3LYP-D3/aug-cc-pV(T+d)Z(-PP) level of theory. The obtained geometries are further analyzed with Natural Bond Orbital (NBO) methods to understand the bonding and electronic structure of each species. We also provide insight into how different substituents can help make the tetrahedrane structure more energetically favorable due to electron delocalization into substituent antibonding orbitals. The effect of additional delocalization also weakens the Pn-C bonds, especially for the heavier pnictogens. This work concludes with a list of considerations that summarize our key findings and motivate future work aimed at producing novel pnictogen-substituted tetrahedrane molecules.

Theoretical investigation on the low-lying electronic states of diatomic magnesium bismuthide including the spin-orbit coupling effect

High-level ab initio computations have been performed to investigate molecular structures, potential energy curves, vibrational energy levels and spectroscopic constants for twelve Λ-S states of the first four dissociation limits of MgBi. Characterizations of seven Ω states, corresponding to the first and the second Λ-S dissociation limits, have been explored for the first time. The spin-orbit coupling effect is revealed to have introduced a significant impact on the pattern of these electronic states and interactions among them. Our predictions for molecular structures and spectroscopic constants of MgBi are compared with available data of other magnesium-group 18 family species. Regular tendencies of these parameters are clearly exhibited when the group 18 atom is replaced by another one in the group. Information associated with transition dipole moments, Franck-Condon factors, vibrational branching ratios and radiative lifetimes between the Ω states are obtained and their transitional properties are analyzed and discussed. The results and data determined in this work are expected to guide and assist laboratorial detections of MgBi and to extend our understanding for the magnesium-group 18 species.

Quantum chemical benchmark databases of gold-standard dimer interaction energies

Advances in computational chemistry create an ongoing need for larger and higher-quality datasets that characterize noncovalent molecular interactions. We present three benchmark collections of quantum mechanical data, covering approximately 3,700 distinct types of interacting molecule pairs. The first collection, which we refer to as DES370K, contains interaction energies for more than 370,000 dimer geometries. These were computed using the coupled-cluster method with single, double, and perturbative triple excitations [CCSD(T)], which is widely regarded as the gold-standard method in electronic structure theory. Our second benchmark collection, a core representative subset of DES370K called DES15K, is intended for more computationally demanding applications of the data. Finally, DES5M, our third collection, comprises interaction energies for nearly 5,000,000 dimer geometries; these were calculated using SNS-MP2, a machine learning approach that provides results with accuracy comparable to that of our coupled-cluster training data. These datasets may prove useful in the development of density functionals, empirically corrected wavefunction-based approaches, semi-empirical methods, force fields, and models trained using machine learning methods.

Canonical and DLPNO-Based Composite Wavefunction Methods Parametrized against Large and Chemically Diverse Training Sets. 2: Correlation-Consistent Basis Sets, Core-Valence Correlation, and F12 Alternatives

A hierarchy of wavefunction composite methods (cWFT), based on G4-type cWFT methods available for elements H through Rn, was recently reported by the present authors [J. Chem. Theor. Comput.2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Møller–Plesset correction and replacing the Weigend–Ahlrichs def2-mZVPP(D) basis sets used with complete basis set extrapolation from augmented correlation-consistent core–valence triple-ζ, aug-cc-pwCVTZ(-PP), and quadruple-ζ, aug-cc-pwCVQZ(-PP), basis sets, thus creating cc-G4-type methods. For the large and chemically diverse GMTKN55 benchmark suite, they represent a substantial further improvement and bring WTMAD2 (weighted mean absolute deviation) down below 1 kcal/mol. Intriguingly, the lion’s share of the improvement comes from better capture of valence correlation; the inclusion of core–valence correlation is almost an order of magnitude less important. These robust correlation-consistent cWFT methods approach the CCSD(T) complete basis limit with just one or a few fitted parameters. Particularly, the DLPNO variants such as cc-G4-T-DLPNO are applicable to fairly large molecules at a modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component.

Equation-of-motion coupled-cluster theory for double electron attachment with spin-orbit coupling

We report implementation of the equation-of-motion coupled-cluster (EOM-CC) method for double electron-attachment (DEA) with spin-orbit coupling (SOC) at the CC singles and doubles (CCSD) level using a closed-shell reference in this work. The DEA operator employed in this work contains two-particle and three-particle one-hole excitations, and SOC is included in post-Hartree-Fock treatment. Time-reversal symmetry and spatial symmetry are exploited to reduce computational cost. The EOM-DEA-CCSD method with SOC allows us to investigate SOC effects of systems with two-unpaired electrons. According to our results on atoms, double ionization potentials (DIPs), excitation energies (EEs), and SO splittings of low-lying states are calculated reliably using the EOM-DEA-CCSD method with SOC. Its accuracy is usually higher than that of EOM-CCSD for EEs or DIPs if the same target can be reached from single excitations by choosing a proper closed-shell reference. However, performance of the EOM-DEA-CCSD method with SOC on molecules is not as good as that for atoms. Bond lengths for the ground and the several lowest excited states of GaH, InH, and TlH are underestimated pronouncedly, although reasonable EEs are obtained, and splittings of the ³Σ^- state from the π² configuration are calculated to be too small with EOM-DEA-CCSD.

Gas-Phase Thermochemistry of MX3 and M2X6 (M = Sc, Y; X = F, Cl, Br, I) from a Composite Reaction-Based Approach: Homolytic versus Heterolytic Cleavage

A domain-based local-pair natural-orbital coupled-cluster approach with single, double, and improved linear-scaling perturbative triple correction via an iterative algorithm, DLPNO-CCSD(T₁), was applied within the framework of the Feller-Peterson-Dixon approach to derive gas-phase heats of formation of scandium and yttrium trihalides and their dimers via a set of homolytic and heterolytic dissociation reactions. All predicted heats of formation moderately depend on the reaction type with the most and least negative values obtained for homolytic and heterolytic dissociation, respectively. The basis set size dependence, as well as the influence of static correlation effects not covered by the standard (DLPNO-)CCSD(T) approach, suggests that exploitation of the heterolytic dissociation reactions with the formation of M³⁺ and X^- ions leads to the most robust heats of formation. The gas-phase formation enthalpies ΔH_f°(0 K)/ΔH_f°(298.15 K) and absolute entropies S°(298.15 K) were obtained for the first time for the Sc₂F₆, Sc₂Br₆, and Sc₂I₆ species. For ScBr₃, ScI₃, Sc₂Cl₆, and Y₂Cl₆, we suggest a reexamination of the experimental heats of formation available in the literature. For other compounds, the predicted values were found to be in good agreement with the experimental estimates. Extracted MX₃ (M = Sc, Y; X = F, Cl, Br, and I) 0 K atomization enthalpies indicate weaker bonding when moving from fluorine to iodine and from yttrium to scandium. Likewise, the stability of yttrium trihalide dimers degrades when going from fluorine to iodine. Respective scandium trihalide dimers are less stable, with 0 K dimer dissociation energy decreasing in the row fluorine - chlorine - bromine ≈ iodine. Correlation of the (n - 1)s²p⁶ electrons on bromine and iodine, inclusion of zero-point energy, relativistic effects, and the effective-core-potential correction as well as amelioration of the DLPNO localization inaccuracy are shown to be of similar magnitude, which is critical if accurate heats of formation are a goal.

Finite-Field Calculations of Transition Properties by the Fock Space Relativistic Coupled Cluster Method: Transitions between Different Fock Space Sectors

Reliable information on transition matrix elements of various property operators between molecular electronic states is of crucial importance for predicting spectroscopic, electric, magnetic and radiative properties of molecules. The finite-field technique is a simple and rather accurate tool for evaluating transition matrix elements of first-order properties in the frames of the Fock space relativistic coupled cluster approach. We formulate and discuss the extension of this technique to the case of transitions between the electronic states associated with different sectors of the Fock space. Pilot applications to the evaluation of transition dipole moments between the closed-shell-like states (vacuum sector) and those dominated by single excitations of the Fermi vacuum (the 1h1p sector) in heavy atoms (Xe and Hg) and simple molecules of heavy element compounds (I2 and TlF) are reported.

Ab initio relativistic potential energy surfaces of benzene-Xe complex with application to intermolecular vibrations

The benzene-Xe (BXe) complex in its electronic ground state is studied using ab initio methods. Since this complex contains the heavy Xe atom, the relativistic effects cannot be neglected. We test two different approaches that describe the scalar relativistic effects in the framework of the coupled-cluster level of theory with single, double, and perturbative triple excitations, used for the interaction energy calculations. The first one is based on the small core pseudopotential (PP), and the second one is based on the explicit treatment of scalar relativistic effects using the Douglas-Kroll-Hess (DKH) Hamiltonian. A few basis sets are tested with the PP and DKH, and for each one, the analytical potential energy surface (PES) is constructed. It is shown that the difference between PESs determined with PP and DKH methods is small, if the orbitals of the 4d subshell in Xe are correlated. We select the most appropriate approach for the calculation of the potential energy surface of BXe, with respect to accuracy and computational cost. The optimal level of theory includes a small Dunning's basis set for the benzene monomer and a larger PP basis set for Xe supplemented by midbond functions. The PES obtained using such an approach provides a reasonable accuracy when compared to the empirical one derived from the microwave spectra of BXe. The empirical and the theoretical values of intermolecular vibrational energies agree within 0.5 cm^-1 up to second overtones. The vibrational energy level pattern of BXe is characterized by a distinct polyad structure.

Characterization of the low-lying electronic states of tin monohydride cation including the spin-orbit coupling effect: A theoretical perspective

High-level ab initio computations have been performed on SnH⁺. The potential energy curves and spectroscopic constants of the low-lying Λ-S electronic states, as well as their associated Ω states, are derived at the icMRCI + Q level employing basis sets of quintuple-ζ quality. The transition dipole moments, Einstein coefficients, radiative lifetimes and Franck-Condon factors of three spin-forbidden transition bands ( [Formula: see text] , [Formula: see text] and [Formula: see text] ) are determined. Comparisons between our predictions and available experimental results indicate reasonable agreement. The spin-orbit coupling effect has been proved to affect these low-lying electronic states significantly.

The study of laser cooling of TeH- anion in theoretical approach

The probabilities of laser cooling of TeH^- anion via a spin-forbidden transition and a three-electronic-level transition are proposed. The potential energy curves of the X¹Σ⁺, a³∏, A¹∏, and b³Σ⁺ electronic states of tellurium monohydride anion (TeH^-) are calculated using multi-reference configuration interaction method. Davidson corrections, core-valence correlations and spin-orbit coupling effects are also considered. The AWCV5Z-PP pseudopotential basis set of Te atom is used. Spectroscopic parameters of the Λ-S and Ω states are obtained by solving radial Schrodinger equation. These results are reported at the first time. Permanent dipole moments of the Ω states and transition dipole moments of the a₂1↔X0⁺ and A1↔X0⁺ transitions are also calculated. Highly diagonally distributed Franck-Condon factors of the a₂1↔X0⁺ and A1↔X0⁺ transitions are obtained, the value of f₀₀ is 0.9970 and 0.9980, respectively. Spontaneous radiative lifetimes of the a₂1 and A1 excited states are predicted. i.e. τ(a₂1) = 200.3 ns and τ(A1) = 84.3 ns. Only the main pump laser is required to driving a₂1↔X0⁺ and A1↔X0⁺ transitions. The laser wavelengths both are in the visible region. Doppler temperatures and recoil temperatures of laser cooling TeH^- anion are also predicted.

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.

Ab initio investigation on the low-lying electronic states of magnesium antimonide

The twelve Λ-S electronic states of the first four dissociation limits of the MgSb molecule have been examined at the icMRCI+Q level employing basis sets of quintuple-ζ quality. The potential energy curves, vibrational levels and spectroscopic constants of the species have been investigated. The permanent dipole moments of the interested states are derived, and the transition dipole moments, Einstein emission coefficients, radiation lifetimes and Franck-Condon factors between selected states are also determined. Four Λ-S states of the first two dissociation limits split into seven Ω states under the effect of spin-orbit coupling. Characterizations of the MgSb low-lying Ω states are performed for the first time. In addition, the results and relevant data provided in this work on MgSb are compared with the antimony-IIA group and magnesium-VA group diatomic species. It is anticipated that this work will shed some light on further investigations of MgSb and other antimony-IIA group systems.

Evaluation of bismuth-based dispersion energy donors – synthesis, structure and theoretical study of 2-biphenylbismuth(iii) derivatives

Intramolecular Bi⋯π arene London dispersion interactions in (biphenyl)_3−xBiX_x amount to ca. 20 kJ mol⁻¹ with distances of 3.8–4.0 Å.

Single-precision open-shell CCSD and CCSD(T) calculations on graphics processing units

It has been shown that coupled-cluster calculations with single-precision data are able to provide correlation energy with insignificant loss of accuracy.