Scalar Relativistic Effects Research Articles

Anion Photoelectron Spectroscopy and Theoretical Study of HAuCN and [HAuCN]-: Spin-Orbit Coupling and Low-Lying Excited States.

We report a study of the electronic structures and chemical bonding of gaseous [HAuCN]- and the corresponding neutral molecule using photoelectron spectroscopy and relativistic quantum chemistry calculations. The electron affinity of the neutral HAuCN is reported to be 4.75 eV for the first time. The low-lying excited states of neutral molecule are observed and assigned according to the calculations utilizing a sophisticated electron correlation method incorporating both the scalar and spin-orbit relativistic effects. Our theoretical calculations suggest the geometry will be distorted from linear structure to the bent during the process of detaching one electron from the anion. Various chemical bonding analyses based on theoretical calculations have been performed for the titled complexes, and the apparent covalent natures of interactions between gold and the studied ligands have been verified.

Excited-State Switching Frustrates the Tuning of Properties in Triphenylamine-Donor-Ligand Rhenium(I) and Platinum(II) Complexes.

The photophysical properties of a series of rhenium(I) tricarbonyl and platinum(II) bis(acetylide) complexes containing a triphenylamine (TPA)-substituted 1,10-phenanthroline ligand have been examined. The complexes possess both metal-to-ligand charge-transfer (MLCT) and intraligand charge-transfer (ILCT) transitions that absorb in the visible region. The relative energies and ordering of the absorbing CT states have been successfully controlled by changing the metal center and modulating the donating ability of the TPA group through the addition of electron-donating methoxy and electron-withdrawing cyano groups. The ground-state properties behave in a predictable manner as a function of the TPA substituent and are characterized with a suite of techniques including electronic absorption spectroscopy, resonance Raman spectroscopy, electrochemistry, and time-dependent density functional theory calculations. However, systematic control over the ground-state properties of the complexes does not extend to their excited-state behavior. Unexpectedly, despite variation of both the MLCT and ILCT state energies, all of the luminescent complexes displayed near-isoenergetic emission at 298 K, yet the emissive lifetimes of the complexes vary from 290 ns to 3.9 μs. Excited-state techniques including transient absorption and transient resonance Raman, combined with a suite of quantum-chemical calculations, including scalar relativistic effects to elucidate competitive excited-state relaxation pathways, have been utilized to aid in assignment of the long-lived state in the complexes, which was shown to possess differing 3MLCT and 3ILCT contributions across the series.

All-electron basis sets augmented with diffuse functions for He, Ca, Sr, Ba, and lanthanides: application in calculations of atomic and molecular properties.

Non-relativistic and Douglas-Kroll-Hess (DKH) basis sets augmented with diffuse functions for He, Ca, Sr, Ba, and lanthanides are generated. These sets are appropriated to describe electrons away from the nuclei. Using the DKH augmented sets along with the B3LYP functional, bond lengths, dissociation energies, harmonic vibrational frequencies, adiabatic ionization potentials, adiabaticelectron affinities, anddipole moments for CaH, SrH, and BaH are computed. These results agree well with the most recent experimental and benchmark theoretical data published in the literature. The DKH mean dipole polarizabilities reported in this work for some elements are close to the recommended values. Scalar relativistic effects are also estimated.

Splittings of d8 configurations of late-transition metals with EOM-DIP-CCSD and FSCCSD methods.

Multireference methods are usually required for transition metal systems due to the partially filled d electrons. In this work, the single-reference equation-of-motion coupled-cluster method at the singles and doubles level for double ionization potentials (EOM-DIP-CCSD) is employed to calculate energies of states from the d8 configuration of late-transition metal atoms starting from a closed-shell reference. Its results are compared with those from the multireference Fock-space coupled-cluster method at the CCSD level (FSCCSD) for DIP from the same closed-shell reference. Both scalar-relativistic effects and spin-orbit coupling are considered in these calculations. Compared with all-electron FSCCSD results with four-component Dirac-Coulomb Hamiltonian, FSCCSD with relativistic effective core potentials can provide reasonable results, except for atoms with unstable reference. Excitation energies for states in the (n - 1)d8ns2 configuration are overestimated pronouncedly with these two methods, and this overestimation is more severe than those in the (n - 1)d9ns1 configuration. Error of EOM-CCSD on these excitation energies is generally larger than that of FSCCSD. On the other hand, relative energies of most of the states in the d8 configuration with respect to the lowest state in the same configuration are predicted reliably with EOM-DIP-CCSD, except for the 3P0 state of Hg2+ and states in Ir+. FSCCSD can provide reasonable relative energies for the several lowest states, while its error tends to be larger for higher states.

Coupled cluster spectroscopic properties of the coinage metal nitrosyls, M–NO (M = Cu, Ag, Au)

Ab initio near-equilibrium potential energy and dipole moment surfaces for the bent CuNO, AgNO, and AuNO molecules have been calculated under the Feller–Peterson–Dixon (FPD) composite framework at the coupled cluster level of theory including complete basis set extrapolation, outer-core correlation, scalar relativistic effects, and spin–orbit coupling. The Brueckner coupled cluster doubles with perturbative triples method, BCCD(T), was used to greatly improve upon CCSD(T), which was particularly problematic for CuNO. In the latter case, the BCCD(T) vibrational frequencies showed significant differences compared to CCSD(T), e.g., nearly 65 cm−1 for the NO stretching frequency, and BCCD(T) also resulted in much better agreement with the available experimental frequencies. A full range of ro-vibrational spectroscopic constants are given for all three molecules of this study using the accurate composite potential energy functions and employing second-order vibrational perturbation theory.

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.

DFT and DFT+U investigation of the effect of spin–orbit interaction and exchange-correlation energy on electronic and magnetic structures of Ir-based double perovskites Ba2TIrO6 (T = Cr, Mn, and Fe)

This study utilizes the generalized gradient approximation (GGA) and GGA+U methods within the first-principles density functional theory to investigate the electronic and magnetic structures of Ir5+-based double perovskites Ba2TIrO6 (T = Cr, Mn, and Fe). Also, we include the spin–orbit (SO) interaction to incorporate the scalar relativistic effect in calculations. The structural optimizations and stability revealed that Ba2TIrO6 exhibits a cubic structure (space group Fm-3m). GGA+U and GGA+SO+U yield quite accurate results of the bandgaps and conduction states as compared to GGA and GGA+SO methods. The total and partial densities of states (DOSs) predict that Ba2TIrO6 shows two behaviors: half-metallic (T = Cr) and metallic (T = Mn and Fe), wholly transforming to the half-metallicity nature when SO and U are jointly turned on within the GGA+SO+U method. Moreover, the results of magnetic structures expose the existence of ferromagnetic (T = Cr and Fe) and antiferromagnetic (T = Mn) orderings in Ba2TIrO6 via 180°-superexchange T3+–O2−–Ir5+. Analysis of the DOSs and magnetic moments shows that the inclusion of the SO interaction has an insignificant effect on Ir-5d4 electrons in all compounds.

Interactions and charge-transfer dynamics of anAl+ion immersed in ultracold Rb and Sr atoms

Atomic clocks based on an Al$^+$ ion sympathetically cooled by a laser-cooled alkaline-earth ion have achieved unprecedented accuracy. Here, we investigate theoretically interactions and charge transfer dynamics of an Al$^+$ ion immersed in an ultracold gas of Rb and Sr atoms. We calculate potential energy curves and transition electric dipole moments for the (Al+Rb)$^+$ and (Al+Sr)$^+$ ion-atom systems using coupled cluster and multireference configuration interaction methods with scalar relativistic effects included within the small-core energy-consistent pseudopotentials in Rb and Sr atoms. The long-range interaction coefficients are also reported. We use the electronic structure data to investigate cold collisions and charge transfer dynamics. Scattering of an Al$^+$ ion with alkali-metal or alkaline-earth-metal atom is governed by one potential energy curve whereas charge transfer can lead to several electronic states mixed by the relativistic spin-orbit coupling. We examine the branching ratios resulting from the interplay of the short- and long-range effects, as well as the prospects for the laser-field control and formation of molecular ions. We propose to employ the atomic clock transition in an Al$^+$ ion to monitor ion-atom scattering dynamics via quantum logic spectroscopy. The presented results pave the way for the application of atomic ions other than alkali-metal and alkaline-earth-metal ones in the field of cold hybrid ion-atom experiments.

Relativistic effects on the aromaticity of E3M3H3 (E = C-Pb; M = N-Bi) benzene analogues.

The relativistic effects on the aromaticity of a set of benzene analogues, E3M3H3 (E = C-Pb; M = N-Bi) heterocycles, using magnetically induced current density (MICD) and the NICSzz component of the conventional nucleus independent chemical shift (NICS), is hereby examined. The relativistic effects were evaluated by means of four-component relativistic MICD, and two-component NMR relativistic shielding tensor methods. MICD and NICS were also computed in a non-relativistic fashion, to assess the influence of scalar-relativistic and spin-orbit effects. Most of the studied compounds exhibit a net diatropic ring current (aromatic), excluding the nitrogen-containing compounds which are non-aromatic (except for C3N3H3), in agreement with their higher E-N electronegativity difference. Only in the case of bismuth compounds, E3Bi3H3, aromaticity is substantially decreased when relativistic effects are included (mainly due to the spin-orbit contribution). The larger the mass of the system, the larger the magnitude of this change, in line with the expected relativistic effects for heavier elements. The analysis based on the NICSzz computations agrees with that of the MICD, thus supporting both the magnetic behavior and the aromatic character of these compounds.

Polarizabilities, dispersion coefficients, and retardation functions at the complete basis set CCSD limit: From Be to Ba plus Yb.

Static and dynamic polarizabilities of alkaline earth metal atoms Be-Ba and of the Yb atom, as well as dispersion coefficients and retardation functions for their long-range interactions, are used as a benchmark for the restricted coupled cluster method with singles and doubles (CCSD) and noniterative triples added [CCSD(T)] and related polarization propagator CCSD(3) methods at the complete basis set limit. The latter is attained through the sequence of the augmented correlation-consistent polarized weighted core valence n-zeta basis sets with the exact 2-component approximation for the scalar relativistic effects and with the small-core effective core potentials (for Ca, Sr, and Ba). At the converged level of core correlation treatment, the finite-field CCSD(T) method reproduces the best available data for the static dipole and quadrupole polarizabilities better than 1% and 4%, respectively. Systematic cancelation of the triple contribution in the CCSD(3) calculations of the dynamic polarizabilities of alkaline earth metal atoms makes their dispersion coefficients accurate within 3%. The retardation functions are computed and used for the analysis of the long-range interactions in the homonuclear dimers. Implications to accurate ab initio calculations of the global interaction potentials are discussed.

Formation of Al + (C 6 H 6 ) 13 : The Origin of Magic Number in Metal–Benzene Clusters Determined by the Nature of the Core

The identification of highly abundant, “magic” species in the mass spectra of clusters have proven to be valuable in nanoscience, leading to the discovery of new stable species such as fullerenes a...

The ANO-R Basis Set.

In this work, the new ANO-R basis set for all elements of the first six periods is introduced. The ANO-R basis set is an all-electron basis set that was constructed including scalar-relativistic effects of the exact-two component (X2C) Hamiltonian and modeling the atomic nucleus by a Gaussian charge distribution, which makes the basis set suitable for calculations of both light and heavy elements. For high accuracy, it takes advantage of the general contraction scheme and was developed at the CASSCF/CASPT2 level of theory. The distinguishing feature of the ANO-R basis set is its compactness in terms of both primitive and contracted basis functions, thus containing no superfluous functions for a given quality. An optimum number of primitive basis functions was selected based on studying the convergence toward the complete basis set limit for each element individually. The primitive basis sets were then contracted using the density-averaged atomic-natural-orbital (ANO) scheme, and suitable contraction levels were determined solely based on the natural orbital occupation numbers that describe the contribution of each natural orbital to the one-particle density matrix. Rather than following the common "split-valence n-tuple zeta plus polarization functions" structure, the resulting basis sets ANO-R0 to ANO-R3 possess a unique composition for each element, ensuring that no unnecessary functions are included while the basis sets are still balanced across the first six periods (H-Rn).

Copernicium: A Relativistic Noble Liquid.

The chemical nature and aggregate state of superheavy copernicium (Cn) have been subject of speculation for many years. While strong relativistic effects render Cn chemically inert, which led Pitzer to suggest a noble‐gas‐like behavior in 1975, Eichler and co‐workers in 2008 reported substantial interactions with a gold surface in atom‐at‐a‐time experiments, suggesting a metallic character and a solid aggregate state. Herein, we explore the physicochemical properties of Cn by means of first‐principles free‐energy calculations, which confirm Pitzer's original hypothesis: With predicted melting and boiling points of 283±11 K and 340±10 K, Cn is indeed a volatile liquid and exhibits a density very similar to that of mercury. However, in stark contrast to mercury and the lighter Group 12 metals, we find bulk Cn to be bound by dispersion and to exhibit a large band gap of 6.4 eV, which is consistent with a noble‐gas‐like character. This non‐group‐conforming behavior is eventually traced back to strong scalar‐relativistic effects, and in the non‐relativistic limit, Cn appears as a common Group 12 metal.

Relativistic Real-Time Time-Dependent Equation-of-Motion Coupled-Cluster

We present a relativistic time-dependent equation-of-motion coupled-cluster with single and double excitations (TD-EOM-CCSD) formalism. Unlike other explicitly time-dependent quantum chemical methods, the present approach considers the time correlation function of the dipole operator, as opposed to the expectation value of the time-dependent dipole moment. We include both scalar relativistic effects and spin-orbit coupling variationally in this scheme via the use of the exact two-component (X2C) wave function as the reference that enters the coupled-cluster formalism. In order to evaluate the accuracy of X2C-TD-EOM-CCSD, we compare zero-field splitting in atomic absorption spectra of open-shell systems (Na, K, Mg+, and Ca+) with values obtained from experiment. In closed-shell species (Na+, K+, Mg2+, and Ca2+), we observe singlet-triplet mixing in the X2C-TD-EOM-CC calculations, which results from the use of the X2C reference. The effects of the X2C reference are evaluated by comparing spectra derived from X2C-TD-EOM-CC calculations to those from TD-EOM-CC calculations using a complex generalized Hartree-Fock ([Formula: see text]-GHF) reference.

A new generation of effective core potentials from correlated calculations: 4s and 4p main group elements and first row additions.

Recently, we developed a new method for generating effective core potentials (ECPs) using valence energy isospectrality with explicitly correlated all-electron (AE) excitations and norm-conservation criteria. We apply this methodology to the 3rd-row main group elements, creating new correlation consistent ECPs (ccECPs) and also deriving additional ECPs to complete the ccECP table for H-Kr. For K and Ca, we develop Ne-core ECPs, and for the 4p main group elements, we construct [Ar]3d10-core potentials. Scalar relativistic effects are included in their construction. Our ccECPs reproduce AE spectra with significantly better accuracy than many existing pseudopotentials and show better overall consistency across multiple properties. The transferability of ccECPs is tested on monohydride and monoxide molecules over a range of molecular geometries. For the constructed ccECPs, we also provide optimized DZ-6Z valence Gaussian basis sets.

Relevance of effective bond orders in heterodiatomic molecules and role of the spin-orbit coupling in theAtX(X=At–F)series

Scalar and spin-dependent relativistic effects can influence the geometries and wave functions of the ground and excited states of molecular systems in a way that is not always trivial. However, it is still common for researchers, in particular within the quantum chemistry community, to neglect the spin-dependent effects while discussing the binding between atoms in heavy-element systems. Within multiconfigurational self-consistent field frameworks, the binding in diatomic molecules can be derived from the occupation of the natural orbitals, which by definition form a basis that diagonalizes the one-body density matrix. This does not fully prevent arbitrariness, and the first objective of the present paper will be to review the concept of effective bond order, in particular with respect to the rounding up rule. Then, the respective roles of the scalar and the spin-dependent relativistic effects on the bond lengths are investigated by means of state-of-the-art nonrelativistic, scalar-relativistic, and exact two-component coupled-cluster calculations, providing reference molecular geometries for the whole $\mathrm{At}X$ ($X$ = At -- F) series. A diagnostic of relevance for defining effective bond orders in heterodiatomic molecules is introduced and applied to this series, showing that the more dissymmetric the system, the less defined the effective bond order is. Finally, the role of the spin-orbit coupling on the effective bond orders is discussed. AtI appears as a key intermediate in the series in terms of the ground-state $\ensuremath{\pi}$ bonding or antibonding character. Although emphasis will be put on ground states, the present methodology is readily applicable to the description of excited states.

Theoretical investigations of structural, thermal properties and stability of the group 12 metal M(XH) isomers in atmosphere: M = (Zn, Cd, Hg) and XH = (OH, SH)

Electronic structure calculations have been performed of the group 12 metal (Zn, Cd, Hg) reaction between hydroxyl OH and hydrosulfide SH to understand the processes of transformation in the atmosphere. DFT/B3LYP methods are employed to calculate the structure of reactants, intermediates, transition states and products as well as their equilibrium geometries, electronic properties, dissociation energy. The scalar relativistic effects have been accurately included by making use of the relativistic effective potentials. The computing results obtained at B3LYP/MWB level of M(OH) and M(SH) for doublet and quartet (2,4∑+, 2A′, 4A″ and 2,4∏) state suggest that the doublet states are most stable than the quartet. The computed potential hypersurface 2A′ indicates four stationary points; two of them correspond to the stable structures with symmetries: MOH/MSH(2A′) and OMH/SMH(2∏), and two points correspond to transition states with the symmetries: MOH/MSH(2∑+) and MOH/MSH(2A′). The isomerization process MXH(2A′) → XMH(2∏) via the transition state and the atmospheric stability of M(XH) are also discussed. Examination of dissociation energy, enthalpy of reaction and wavelength from linear form OMH/SMH(2∏) estimate that the molecule has appreciable stability. As for the angled form MOH/MSH(2A′), the values obtained suggest that it is easily dissociable in the presence of solar radiation. Our results are compared with previous work, when available.

Jahn-Teller effect versus spin-orbit coupling: The structure of the free molybdenum pentafluoride molecule

The complete active space self-consistent field (CASSCF) and multiconfigurational quasi-degenerate second-order perturbation (MCQDPT2) calculations have been used to study the ground and low-lying excited electronic states of MoF5. Scalar-relativistic effects and spin-orbit coupling (SOC) have been taken into account employing the third-order Douglas-Kroll-Hess (DKH) Hamiltonian and full Breit-Pauli operator, respectively. The optimization and the calculation of the Hessian matrix have been performed by non-routine procedure employing the symmetry coordinates for all considered (D3h, C2v and C4v) geometrical configurations. The trigonal bipyramidal D3h structure of molybdenum pentafluoride MoF5 possesses two-fold degenerate ground first excited electronic orbital state and undergoes Jahn-Teller distortion to the C2v configurations. Accounting of SOC quenches the JT effect. As a result the D3h structure of MoF5 is no longer the conical intersection of two adiabatic potential energy surfaces (APES) but two separated APES corresponding to ground (12E1/2) and nearest excited (12E3/2) spin-orbit states are appeared instead. The D3h trigonal bipyramidal structure in the ground spin-orbit state corresponds to the 2-nd order saddle point on APES and lies above the minima (C2v structure, 12E1/2 state) by 244 cm−1. The warping barrier (another C2v structure) in the trough of APES and the Berry pseudorotation barrier (C4v structure, ground spin-orbit state 2E3/2) are 19 and 310 cm−1, respectively. Therefore MoF5 molecule is characterized in the gas phase by a large-amplitude motion of fluorine atoms in the equatorial plane and non-rigid intramolecular rearrangement by Berry mechanism. Despite such non-rigid nuclei dynamic, the calculated harmonic frequencies of MoF5 molecule do not contradict to available experimental IR spectrum. The repeat refinement of MoF5 gas electron diffraction data has been carried out using static and pseudoconformer models based on the SO-MCQDPT2 results. Corresponding to only extreme points on APES the configurations have been included into the pseudoconformer model. The both models have been fitted to the experimental data by the same quality.

Ab Initio Ground-State Potential Energy Function and Vibration-Rotation Energy Levels of Aluminum Monohydride.

The accurate ground-state potential energy function of aluminum monohydride (AlH) has been determined from ab initio calculations using the multireference averaged coupled-pair functional (MR-ACPF) method in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. The vibration-rotation energy levels of the two isotopologues, AlH and AlD, were predicted to near the "spectroscopic" accuracy. The importance of electron correlation beyond the MR-ACPF level of approximation, the scalar relativistic, spin-orbit, adiabatic, and nonadiabatic effects was discussed. © 2019 Wiley Periodicals, Inc.

An accurate ab initio electronic structure calculation for interstellar argonium

A high level electronic structure calculation of the Born–Oppenheimer (BO) potential, scalar-relativistic effect and adiabatic correction is performed for the X1Σ+ ground state of astronomically important isotopologues of the ArH+ cation. Particular attention is paid to both short and long distances, where experimental spectroscopic data is not yet available. The BO energy is obtained over a wide range of interatomic distances (R ∈ [0.5, 20] Å) in the framework of multi-reference coupled pair functional (MR-ACPF) and single-reference coupled-cluster (CCSD(T)) methods. The all-electrons basis sets of the def2-nZVPP (n=3,4) and nZaPa-NR, aug-cc-pCVnZ (n=3−6) quality are used to monitor energy convergence. The BO energies are corrected for the basis set superposition error (BSSE) via the counterpoise method and are reduced to the complete basis set (CBS) limit using alternative extrapolating schemes. The permanent dipole moment d(R) and static dipole polarizability α(R) are calculated using a finite-field method. The molecular structure parameters coincide with their empirical counterparts for low vibrational levels to within 0.1%. Implementation of the ab initio results to circumscribe our understanding of the chemical networks in interstellar space is discussed.