Closed-shell Atoms Research Articles

A Multichannel Least-Squares B-Spline Approach to Molecular Photoionization: Theory, Implementation, and Applications within the Configuration-Interaction Singles Approximation.

We describe, in detail, a basis set approach to the multichannel scattering problem. The full set of linearly independent scattering states at each prefixed energy of the continuum spectrum can be obtained via a least-squares approach. To test the algorithm in a concrete setup, we report a parallel implementation of the close-coupling method in which the final states are treated within the configuration-interaction singles (CIS) approximation. The method requires, as input, a set of orthonormal orbitals, obtained from any quantum chemistry package. A one-center expansion (OCE) basis set consisting of products of radial B-splines and symmetry adapted angular functions is then used to expand the continuum electron wave function. To assess the quality of the CIS approximation, we compute total and partial cross sections and angular asymmetry parameters for the photoionization of a selection of closed-shell atoms (He, Ne, and Ar), H2, H2O, and ethylene. Results are compared with the experimental data and with theoretical predictions obtained with time-dependent density functional theory (TDDFT). It is seen that, generally, the photoionization observables obtained at the CIS level compare well with TDDFT predictions. The same basis can be employed to describe molecular multiphoton or strong field ionization.

Solution of the Kohn–Sham equations for many-electron atoms confined by penetrable walls

The solution of the Kohn–Sham equations in the Roothaan’s context is presented for atoms confined by penetrable walls. A new basis set is employed in this work, which was designed within the Hartree–Fock approach to ensure a correct decay on the electron density. Exchange-correlation functionals from local density and generalized gradient approximation are considered in the implementation of the Kohn–Sham method. The confinement effects on energies (total and orbital) and on the exchange potential are discussed when two exchange-only functionals are compared with the Hartree–Fock method, for closed-shell atoms confined by finite potentials. Clearly, the wrong asymptotic behavior exhibited by the exchange-only Kohn–Sham potentials, considered in this work, has a large impact on orbital energies when several confinements are tested. In fact, such exchange potentials predict orbital energies which are drastically different than those predicted by the Hartree–Fock method. These differences are not restricted just to absolute values, also the trend observed for exchange and orbital energies is quite different than that predicted by Hartree–Fock. Effects of the correlation contribution are also discussed on total and orbital energies, which show same trends than those obtained by exchange-only functionals. Unfortunately, there are no implementations of correlated methods based on the wave-function for this kind of problems, and consequently our results for correlation energy cannot be compared with a reference. With this implementation there is one possibility to test the performance of approximate exchange-correlation functionals, in addition to the sets commonly used in the design of new functionals.

ChemInform Abstract: Experimental and Theoretical Determination of Dissociation Energies of Dispersion‐Dominated Aromatic Molecular Complexes

AbstractReview: 305 refs.

Heavy Element Effects in the Diagonal Born-Oppenheimer Correction within a Relativistic Spin-Free Hamiltonian.

Methodologies beyond the Born-Oppenheimer (BO) approximation are nowadays important to explain high precision spectroscopic measurements. Most previous evaluations of the BO correction are, however, focused on light-element molecules and based on a nonrelativistic Hamiltonian, so no information about the BO approximation (BOA) breakdown in heavy-element molecules is available. The present work is the first to investigate the BOA breakdown for the entire periodic table, by considering scalar relativistic effects in the Diagonal BO correction (DBOC). In closed shell atoms, the relativistic EDBOC scales as Z(1.25) and the nonrelativistic EDBOC scales as Z(1.17), where Z is the atomic number. Hence, we found that EDBOC becomes larger in heavy element atoms and molecules, and the relativistic EDBOC increases faster than nonrelativistic EDBOC. We have further investigated the DBOC effects on properties such as potential energy curves, spectroscopic parameters, and various energetic properties. The DBOC effects for these properties are mostly affected by the lightest atom in the molecule. Hence, in X2 or XAt molecule (X = H, Li, Na, K, Rb, and Cs) the effect of DBOC systematically decreases when X becomes heavier but in HX molecules, the effect of DBOC seems relatively similar among all the molecules.

Grid-based electronic structure calculations: The tensor decomposition approach

We present a fully grid-based approach for solving Hartree-Fock and all-electron Kohn-Sham equations based on low-rank approximation of three-dimensional electron orbitals. Due to the low-rank structure the total complexity of the algorithm depends linearly with respect to the one-dimensional grid size. Linear complexity allows for the usage of fine grids, e.g. $8192^3$ and, thus, cheap extrapolation procedure. We test the proposed approach on closed-shell atoms up to the argon, several molecules and clusters of hydrogen atoms. All tests show systematical convergence with the required accuracy.

Excitation energies of closed-shell atoms based on equation-of-motion coupled-cluster theory with spin-orbit coupling

Excitation energies of closed-shell atoms based on equation-of-motion coupled-cluster theory with spin-orbit coupling

Structure, Bonding, and Stability of Mercury Complexes with Thiolate and Thioether Ligands from High-Resolution XANES Spectroscopy and First-Principles Calculations.

We present results obtained from high energy-resolution L3-edge XANES spectroscopy and first-principles calculations for the structure, bonding, and stability of mercury(II) complexes with thiolate and thioether ligands in crystalline compounds, aqueous solution, and macromolecular natural organic matter (NOM). Core-to-valence XANES features that vary in intensity differentiate with unprecedented sensitivity the number and identity of Hg ligands and the geometry of the ligand environment. Post-Hartree-Fock XANES calculations, coupled with natural population analysis, performed on MP2-optimized Hg[(SR)2···(RSR)n] complexes show that the shape, position, and number of electronic transitions observed at high energy-resolution are directly correlated to the Hg and S (l,m)-projected empty densities of states and occupations of the hybridized Hg 6s and 5d valence orbitals. Linear two-coordination, the most common coordination geometry in mercury chemistry, yields a sharp 2p to 6s + 5d electronic transition. This transition varies in intensity for Hg bonded to thiol groups in macromolecular NOM. The intensity variation is explained by contributions from next-nearest, low-charge, thioether-type RSR ligands at 3.0-3.3 Å from Hg. Thus, Hg in NOM has two strong bonds to thiol S and k additional weak Hg···S contacts, or 2 + k coordination. The calculated stabilization energy is -5 kcal/mol per RSR ligand. Detection of distant ligands beyond the first coordination shell requires precise measurement of, and comparison to, spectra of reference compounds as well as accurate calculation of spectra for representative molecular models. The combined experimental and theoretical approaches described here for Hg can be applied to other closed-shell atoms, such as Ag(I) and Au(I). To facilitate further calculation of XANES spectra, experimental data, a new crystallographic structure of a key mercury thioether complex, Cartesian coordinates of the computed models, and examples of input files are provided as Supporting Information .

Relativistic Many-body Calculations for Electric Dipole Moments in \(^{129}\)Xe, \(^{199}\)Hg, \(^{223}\)Rn, \(^{225}\)Ra and \(^{171}\)Yb Atom

We present and compare the results of permanent electric dipole moments (EDMs) of various closed-shell atoms due to the nuclear Schiff moment (NSM) and the tensor-pseudotensor (T-PT) interactions between the atomic nuclei and electrons. In order to highlight the role of electron-correlation effects in obtaining accurate EDM results, we employ a number of relativistic many-body methods including coupled-cluster theory at different degrees of approximation. On combining our results obtained from the relativistic coupled-cluster (RCC) at the levels of singles and doubles excitations (CCSD method) with the available EDM measurements we obtain accurate bounds on the couplings \(S\) and \(C_T\) associated with the respective NSM and T-PT interactions. The most precise EDM measurement on \(^{199}\)Hg in combination with our CC results yield limits on the above couplings as \(S<1.45 \times 10^{-12}|e|\)fm\(^3\) and \(C_T < 2.09 \times 10^{-9}\) respectively. Further combining these bounds with the latest nuclear structure and quantum chromodynamics calculations we infer limits on the strong CP-violating parameter and for the combined up- and down- quark chromo-EDMs as \(|\bar{\theta}| < 1.1 \times 10^{-9}\) and \(|\widetilde{d}_u - \widetilde{d}_d| < 2.8 \times 10^{-26} |e|\)cm, respectively.

A quantum chemical study of aluminum–nitrogen bonds in three-coordinate aluminum compounds

DFT and HF methods implemented in the PC GAMESS-Firefly program package are employed to calculate the spatial and electronic structures of molecules of three-coordinate aluminum compounds with Al–N bonds. NBO and AIM methods are applied to determine the main characteristics of Al–N and N–C bonds in these molecules. It is shown that Al and N atoms interact with each other as closed shell atoms. The N–C bonds are close to covalent ones.

Similarity between the angular distributions of the first- and second-step electrons in sequential two-photon atomic double ionization

Angular distributions of electrons produced in sequential two-photon atomic double ionization are considered theoretically by comparing the results obtained for the first and the second electron. It is shown analytically that the angular distributions of the two emitted electrons in many cases are similar for ionization from a closed-shell atom. Numerical examples of this counter-intuitive similarity are presented. In addition, examples are given demonstrating the difference between the angular distributions of the first photoelectron in sequential two-photon double ionization and in conventional one-photon single ionization.

Van der Waals coefficients for positronium interactions with atoms

The random-phase approximation with exchange (RPAE) is used with a $B$-spline basis to compute dynamic dipole polarizabilities of noble-gas atoms and several other closed-shell atoms (Be, Mg, Ca, Zn, Sr, Cd, and Ba). From these, values of the van der Waals ${C}_{6}$ constants for positronium interactions with these atoms are determined and compared with existing data. After correcting the RPAE polarizabilities to fit the most accurate static polarizability data, our best predictions of ${C}_{6}$ for Ps--noble-gas pairs are expected to be accurate to within 1%, and to within a few percent for the alkaline-earth metals. We also used accurate dynamic dipole polarizabilities from the literature to compute the ${C}_{6}$ coefficients for the alkali-metal atoms. Implications of increased ${C}_{6}$ values for Ps scattering from more polarizable atoms are discussed.

Tunable Magnetism in Transition-Metal-Decorated Phosphorene

We present a density functional theory study of 3d transition-metal (TM) atoms (Sc–Zn) adsorbed on a phosphorene sheet. We show that due to the existence of lone pair electrons on P atoms in phosphorene, all the TM atoms, except the closed-shell Zn atom, can bond strongly to the phosphorene with sizable binding energies. Moreover, the TM@phosphorene systems for TM from Sc to Co exhibit interesting magnetic properties, which arise from the exchange splitting of the TM 3d orbitals. We also find that strain is an effective way to control the magnetism of TM@phosphorene systems by tuning the interaction of the TM with phosphorene and, thus, the relative positions of in-gap TM 3d orbitals. In particular, a small biaxial strain could induce a magnetic transition from a low-spin to a high-spin state in phosphorene decorated by Sc, V, or Mn. These results clearly establish the potential for phosphorene utilization in innovative spintronic devices.

Fermi orbital derivatives in self-interaction corrected density functional theory: Applications to closed shell atoms.

A recent modification of the Perdew-Zunger self-interaction-correction to the density-functional formalism has provided a framework for explicitly restoring unitary invariance to the expression for the total energy. The formalism depends upon construction of Löwdin orthonormalized Fermi-orbitals which parametrically depend on variational quasi-classical electronic positions. Derivatives of these quasi-classical electronic positions, required for efficient minimization of the self-interaction corrected energy, are derived and tested, here, on atoms. Total energies and ionization energies in closed-shell singlet atoms, where correlation is less important, using the Perdew-Wang 1992 Local Density Approximation (PW92) functional, are in good agreement with experiment and non-relativistic quantum-Monte-Carlo results albeit slightly too low.

Equation-of-Motion Coupled-Cluster Theory for Excitation Energies of Closed-Shell Systems with Spin–Orbit Coupling

Excitation energies of closed-shell systems based on the equation-of-motion (EOM) coupled-cluster theory at the singles and doubles (CCSD) level with spin-orbit coupling (SOC) included in the post-Hartree-Fock treatment are implemented in the present work. SOC can be included in both the CC and EOM steps (EOM-SOC-CCSD) or only in the EOM part (SOC-EOM-CCSD). The latter approach is an economical way to account for SOC effects, but excitation energies with this approach are not size-intensive. When the unlinked term in the latter approach is neglected (cSOC-EOM-CCSD), size-intensive excitation energies can be obtained. Time-reversal symmetry and spatial symmetry are exploited to reduce the computational effort. Imposing time-reversal symmetry results in a real matrix representation for the similarity-transformed Hamiltonian, which facilitates the requirement of time-reversal symmetry for new trial vectors in Davidson's algorithm. Results on some closed-shell atoms and molecules containing heavy elements show that EOM-SOC-CCSD can provide excitation energies and spin-orbit splittings with reasonable accuracy. On the other hand, the SOC-EOM-CCSD approach is able to afford accurate estimates of SOC effects for valence electrons of systems containing elements up to the fifth row, while cSOC-EOM-CCSD is less accurate for spin-orbit splittings of transitions involving p1/2 spinors, even for Kr.

Relativistic equation-of-motion coupled-cluster method for the double-ionization potentials of closed-shell atoms

We report the general implementation of the relativistic equation-of-motion coupled-cluster method to calculate double ionization spectra (DI-EOMCC) of atomic and molecular systems. As a first application, this method is employed to calculate the principal valence double ionization potential values of He and alkaline earth metal (Be, Mg, Ca, Sr and Ba) atoms. Our results are compared with the results available from the national institute of standards and technology (NIST) database and other ab initio calculations. We have achieved an accuracy of ~ 0.1%, which is an improvement over the first principles T-matrix calculations [J. Chem. Phys. 123, 144112 (2005)]. We also present results using the second-order many-body perturbation theory and the random- phase approximation in the equation-of-motion framework and these results are compared with the DI-EOMCC results.

Photo-induced strengthening of weak bonding in noble gas dimers

We demonstrate through extensive first-principles time-dependent density functional calculations that attractive van der Waals interaction between closed-shell atoms can be enhanced by light with constant spatial intensity. We illustrate this general phenomenon for a He dimer as a prototypical case of complex van der Waals interactions and show that when excited by light with a frequency close to the 1s → 2p He-atomic transition, an attractive force larger than 7 pN is produced. This force gain is manifested as a larger acceleration of He-He contraction under an optical field. The concerted dynamical motions of the He atoms together with polarity switching of the charge-induced dipole cause the contraction of the dimer. These findings are relevant for the photo-induced control of weakly bonded molecular species, either in gas phase or in solution.

Relativistic equation-of-motion coupled-cluster method: Application to closed-shell atomic systems

We report our successful implementation of the relativistic equation-of-motion coupled-cluster (EOMCC) method. This method is employed to compute the principal ionization potentials (IPs) of closed-shell rare-gas atoms, He-like ions, Be-like ions, along with Na${}^{+}$, Al${}^{+}$, K${}^{+}$, Be, and Mg. Four-component Dirac spinors are used in the calculations, and the one- and two-electron integrals are evaluated using the Dirac-Coulomb Hamiltonian. Our results are in excellent agreement with available measurements, which are taken from the National Institute of Science and Technology database. The accuracies of the calculations are estimated to be within one half of a percent for He-like and Be-like ions and 1% for the heavier systems. We also present results using the second-order many-body perturbation theory and random-phase approximation in the EOMCC framework. These results are compared with those of EOMCC at the level of single and double excitations in order to assess the role of the electron correlation effects in the intermediate schemes considered in our calculations.

Testing Noncollinear Spin-Flip, Collinear Spin-Flip, and Conventional Time-Dependent Density Functional Theory for Predicting Electronic Excitation Energies of Closed-Shell Atoms.

Conventional time-dependent density functional theory (TDDFT) is based on a closed-shell Kohn-Sham (KS) singlet ground state with the adiabatic approximation, using either linear response (KS-LR) or the Tamm-Dancoff approximation (KS-TDA); these methods can only directly predict singly excited states. This deficiency can be overcome by using a triplet state as the reference in the KS-TDA approximation and "exciting" the singlet by a spin flip (SF) from the triplet; this is the method suggested by Krylov and co-workers, and we abbreviate this procedure as SF-KS-TDA. SF-KS-TDA can be applied either with the original collinear kernel of Krylov and co-workers or with a noncollinear kernel, as suggested by Wang and Ziegler. The SF-KS-TDA method does bring some new practical difficulties into play, but it can at least formally model doubly excited states and states with double-excitation character, so it might be more useful than conventional TDDFT (both KS-LR and KS-TDA) for photochemistry if these additional difficulties can be surmounted and if it is accurate with existing approximate exchange-correlation functionals. In the present work, we carried out calculations specifically designed to understand better the accuracy and limitations of the conventional TDDFT and SF-KS-TDA methods; we did this by studying closed-shell atoms and closed-shell monatomic cations because they provide a simple but challenging testing ground for what we might expect in studying the photochemistry of molecules with closed-shell ground states. To test their accuracy, we applied conventional KS-LR and KS-TDA and 18 versions of SF-KS-TDA (nine collinear and nine noncollinear) to the same set of vertical excitation energies (including both Rydberg and valence excitations) of Be, B(+), Ne, Na(+), Mg, and Al(+). We did this for 10 exchange-correlation functionals of various types, both local and nonlocal. We found that the GVWN5 and M06 functionals with nonlocal kernels in spin-flip calculations can both have accuracy competitive to CASPT2 calculations. When the results were averaged over all 36 test energy differences, seven (GVWN5, M06, B3PW91, LRC-ωPBE, LRC-ωPBEh, PBE, and M06-2X) of the 10 studied density functionals had smaller mean unsigned errors for noncollinear calculations than the mean unsigned error of the best functional (M06-2X) for either conventional KS-TDA or KS-LR.

Correlation trends in the ground-state static electric dipole polarizabilities of closed-shell atoms and ions

We employ the closed-shell perturbed relativistic coupled-cluster (RCC) theory developed by us earlier [Phys. Rev. A 77, 062516 (2008)] to evaluate the ground-state static electric dipole polarizabilities ($\ensuremath{\alpha}$s) of several atomic systems. In this work, we have incorporated a class of higher-order many-body effects in our calculations that had not been taken into account in the above paper. We highlight their importance in improving the accuracies of $\ensuremath{\alpha}$s. We also calculate the ground state $\ensuremath{\alpha}$s of the inert gas atoms and several isoelectronic singly and doubly charged ions in order to make a comparative study of the trends of the correlation effects. Furthermore, we have developed a method to construct intermediate diagrams that are required for the computations of the unperturbed single and doubl coupled-cluster amplitudes. Our RCC results are compared with those of many-body perturbation theory at different orders to demonstrate the importance of higher-order correlation effects for the accurate determination of ($\ensuremath{\alpha}$s) of the systems that we have considered.

Communication: Nuclear quadrupole moment-induced Cotton-Mouton effect in noble gas atoms

New, high-sensitivity and high-resolution spectroscopic and imaging methods may be developed by exploiting nuclear magneto-optic effects. A first-principles electronic structure formulation of nuclear electric quadrupole moment-induced Cotton-Mouton effect (NQCME) is presented for closed-shell atoms. In NQCME, aligned quadrupole moments alter the index of refraction of the medium along with and perpendicular to the direction of nuclear alignment. The roles of basis-set convergence, electron correlation, and relativistic effects are investigated for three quadrupolar noble gas isotopes: (21)Ne, (83)Kr, and (131)Xe. The magnitude of the resulting ellipticities is predicted to be 10(-4)-10(-6) rad/(M cm) for fully spin-polarized nuclei. These should be detectable in the Voigt setup. Particularly interesting is the case of (131)Xe, in which a high degree of spin polarization can be achieved via spin-exchange optical hyperpolarization.