Closed-shell Atoms Research Articles

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

We assess a variant of linear-response range-separated time-dependent density-functional theory (TDDFT), combining a long-range Hartree-Fock (HF) exchange kernel with a short-range adiabatic exchange-correlation kernel in the local-density approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closed-shell atoms and small molecules. This range-separated TDDFT tends to give underestimated C6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to time-dependent Hartree-Fock which has a mean absolute percentage error of about 6%. These results thus show that introduction of long-range HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of range-separated TDDFT is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.

Looking for Atoms that Pack By the Rules

Finding the most energetically favorable crystal structure of closed-shell atoms is a long-standing problem where experiment and theory don’t agree, but a study of argon nanoclusters is providing new insight into the discrepancy.

Relativistic linearized coupled-cluster single-double calculations of positron-atom bound states

Relativistic coupled-cluster single-double approximation is used to calculate positron-atom bound states. The method is tested on closed-shell atoms such as Be, Mg, Ca, Zn, Cd, and Hg where a number of accurate calculations is available. It is then used to calculate positron binding energies for a range of open-shell transition metal atoms from Sc to Cu, from Y to Pd, and from Lu to Pt. These systems possess Feshbach resonances, which can be used to search for positron-atom binding experimentally through resonant annihilation or scattering.

Ab initiostudies of electron correlation effects in heavier closed-shell atoms: Structure of the all-electron correlation energies of Zn2+and Zn

To provide reliable reference results for various components of the electron correlation energies of Zn${}^{2+}$ and Zn, which play a similar role for $3d$-electron systems as Ne and Mg do for lighter atoms, we have performed extensive calculations of the all-electron correlation energy and of its various components with several state-of-the-art ab initio techniques. Two pairs of basis-set sequences that systematically converge to the complete basis set (CBS) limit have been employed in the calculations. One pair [cc-pV$n$Z and aug-cc-pV$n$Z (correlation consistent polarized valence $n$-zeta and augmented cc-pV$n$Z with $n=$ D, T, Q, 5, $6(\ensuremath{-}k)$)] is oriented towards the description of valence electron correlation. The second pair of sequences [cc-pCCV$n$Z and aug-cc-pCCV$n$Z (core core-valence $n$-zeta, with $n$ = D, T, Q, 5, $6(\ensuremath{-}k)$)] is developed for the description of all-electron correlation effects. The correlation energies have been determined with second-order M\o{}ller-Plesset perturbation theory (MP2) and several single-reference coupled-cluster (CC) methods. The present correlation energies represent accurate post-MP2 correlation energies for closed-shell atoms including 3$d$ electrons both at the all-electron and subshell levels and should be useful benchmark results for various transitions. We have also employed the present results for assessments of the focal-point approximation (FPA), broadly used in approximations of difference correlation effects for molecular interaction problems, in applications aiming at estimating correlation effects in heavier atoms. Our results indicate that for the systems considered, the magnitudes of the MP2 correlation energies overestimate the magnitudes of the CC values for all electrons correlated as well as of their various subsets. For the all-electron correlation energies of the Zn atom, our result confirms the finding of S. P. McCarthy and A. J. Thakkar [J. Chem. Phys. 134, 044102 (2011)] obtained by means of non--ab initio approaches for all heavy closed-shell atoms from Zn to Rn. We have shown that for both Zn${}^{2+}$ and Zn this overestimation is directly caused by the presence of the $3{d}^{10}$ electron configuration.

Atomic C 6 dispersion coefficients: a four-component relativistic Kohn–Sham study

We present C 6 homo- and heteroatomic dispersion coefficients for all closed-shell atoms of the periodic table based on dipole–dipole polarizabilities at imaginary frequencies calculated using our recent extension of the complex polarization propagator approach to the four-component relativistic Kohn–Sham approach. Lack of proper reference data bars definite conclusions as to which density functional shows the overall best performance, and we therefore call for state-of-the-art wave function-based correlated calculations of dispersion coefficients. Scalar relativistic effects are significant already for elements as light as zinc, whereas spin–orbit effects must be taken into account only for very heavy elements.

CI−RMBPT neon g-factors

Previously, we obtained accurate energies and oscillator strengths for many energy levels and transitions in neon and argon with CI+RMBPT particle–hole ab initio theory. In this paper, we demonstrate that this theory also predicts accurately g-factors for neon transitions. The theory can be extended to other closed-shell atoms and ions. Calculations are performed relativistically in the jj-coupling scheme without conversion into LS-coupling.

When does the non-variational nature of second-order Møller-Plesset energies manifest itself? All-electron correlation energies for open-shell atoms from K to Br

All-electron correlation energies E(c) are not very well known for open-shell atoms with more than 18 electrons. The complete basis-set (CBS) limits of second-order Møller-Plesset (MP2) perturbation theory energies are obtained for open-shell atoms by computations in large basis sets combined with a knowledge of the MP2/CBS limit for the next larger closed-shell atom with the same valence shell structure. Then higher-order correlation corrections are found by coupled-cluster calculations using basis sets that are not quite as large. The method is validated for the open-shell atoms from Al to Cl for which E(c) is reasonably well established. Then, the method is used to obtain non-relativistic E(c) values, probably accurate to 3%, for the open-shell atoms of the fourth period: K, Sc-Cu, and Ga-Br. These energies are compared with the predictions of 19 density functionals and may be useful for the parameterization of new ones. The results show that MP2 overestimates |E(c)| for atoms heavier than Fe.

Exchange-only optimized-effective-potential calculations using Slater-type basis functions: Atoms and diatomic molecules

The exchange-only optimized-effective-potential method is implemented with the use of Slater-type basis functions, seeking an alternative to the standard methods of solution with some computational advantages. This procedure has been tested in a small group of closed-shell atoms and diatomic molecules, for which numerical solutions are available. The results obtained with this implementation have been compared to the exact numerical solutions and to the results obtained when the optimized effective equations are solved using the Gaussian-type basis sets. This Slater-type basis approach leads to a more compact expansion space for representing the potential of the optimized-effective-potential method and to considerable computational savings when compared to both the numerical solution and the more traditional one in terms of the Gaussian basis sets.

Basis set effects on the Hartree–Fock description of confined many-electron atoms

In this work, the basis sets designed by Clementi, Bunge and Thakkar, for atomic systems, have been used to obtain the electronic structure of confined many-electron atoms by using Roothaan's approach in the Hartree–Fock context with a new code written in C, which uses the message-passing interface library. The confinement was imposed as Ludeña suggested to simulate walls with infinity potential. For closed-shell atoms, the Thakkar basis set functions give the best total energies (TE) as a function of the confinement radius, obtaining the following ordering: TE(Thakkar) < TE(Bunge) < TE(Clementi). However, for few open-shell atoms this ordering is not preserved and a trend, for the basis sets, is not observed. Although there are differences between the TE predicted by these basis set functions, the corresponding pressures are similar to each other; it means that changes in the total energy are described almost in the same way by using any of these basis sets. By analysing the total energy as a function of the inverse of the volume we propose an equation of state; for regions of small volumes, this equation predicts that the pressure is inversely proportional to the square of the volume.

Defects in ion-implanted hcp-titanium: A first-principles study of electronic structures

The electronic structures of hexagonal closed-packed (h.c.p) titanium containing a vacancy and krypton impurity atoms at various insertion sites are calculated by first-principles methods in the framework of the density-functional theory (DFT). The density of states (DOS) for titanium containing a vacancy defect shows resonance-like features. Also, the bulk electron density decreases from ∼0.15/Å 3 to ∼0.05/Å 3 at the vacancy centre. Electronic structure calculations have been performed to investigate what underlies the krypton site preference in titanium. The DOS of the nearest-neighbour (NN) titanium atoms to the octahedral krypton appears to be less distorted (relative to pure titanium) when compared to the NN titanium atoms to the tetrahedral krypton. The electronic density deformation maps show that polarization of the titanium atoms is stronger when the krypton atom is located at the tetrahedral site. Since krypton is a closed-shell atom, thus precluding any bonding with the titanium atoms, we may conclude that the polarization of the electrons in the vicinity of the inserted krypton atoms and the distortion of the DOS of the NN titanium atoms to the krypton serve to indicate which defect site is preferred when a krypton atom is inserted into titanium. Based on these considerations, we conclude that the substitutional site is the most favourable one, and the octahedral is the preferred interstitial site, in agreement with recent DFT calculations of the energetics of krypton impurity sites.

Unique Solutions to Hartree–Fock Equations for Closed Shell Atoms

In this paper we study the problem of uniqueness of solutions to the Hartree and Hartree-Fock equations of atoms. We show, for example, that the Hartree-Fock ground state of a closed shell atom is unique provided the atomic number $Z$ is sufficiently large compared to the number $N$ of electrons. More specifically, a two-electron atom with atomic number $Z\geq 35$ has a unique Hartree-Fock ground state given by two orbitals with opposite spins and identical spatial wave functions. This statement is wrong for some $Z>1$, which exhibits a phase segregation.

Coupled cluster study of structural properties of RgI and RgI− (Rg = He, Ne, Ar) weakly bound molecules

Structural properties, spectroscopic constants and the interaction between rare-gas atom and open and closed-shell iodine atom of weakly bound van der Waals molecules have been studied in details using CCSD(T) method. The Lennard-Jones potential is used to study the interaction and spectroscopic constants of the neutral and anionic systems. The spectroscopic constants and the interacting force between the two atoms of RgI and RgI− (Rg = He, Ne and Ar) have been calculated using our method developed recently for the weakly bound molecule in Lennard-Jones potential. The results have been compared with the theoretical and experimental data wherever available. Most of the spectroscopic constants are first reported.

Accurate all-electron correlation energies for the closed-shell atoms from Ar to Rn and their relationship to the corresponding MP2 correlation energies

All-electron correlation energies E(c) are not very well-known for atoms with more than 18 electrons. Hence, coupled-cluster calculations in carefully designed basis sets are combined with fully converged second-order Møller-Plesset perturbation theory (MP2) computations to obtain fairly accurate, nonrelativistic E(c) values for the 12 closed-shell atoms from Ar to Rn. These energies will be useful for the evaluation and parameterization of density functionals. The results show that MP2 overestimates ∣E(c)∣ for heavy atoms. Spin-component scaling of the MP2 correlation energy is used to provide a simple explanation for this overestimation.

Ultracold RbSr Molecules Can Be Formed by Magnetoassociation

We investigate the interactions between ultracold alkali-metal atoms and closed-shell atoms using electronic structure calculations on the prototype system Rb+Sr. There are molecular bound states that can be tuned across atomic thresholds with a magnetic field and previously neglected terms in the collision Hamiltonian that can produce zero-energy Feshbach resonances with significant widths. The largest effect comes from the interaction-induced variation of the Rb hyperfine coupling. The resonances may be used to form paramagnetic polar molecules if the magnetic field can be controlled precisely enough.

Magnetic shielding constants calculated by the infinite-order Douglas–Kroll–Hess method with electron-electron relativistic corrections

We presented a two-component relativistic quantum-chemical theory for magnetic shielding constants, which is based on the infinite-order Douglas-Kroll (IODK) transformation. Two-electron relativistic corrections were also generated using the IODK transformation, although negligibly small terms were discarded. The use of small-component basis functions was completely excluded from the present theory. We examined the combination of the levels of relativistic one- and two-electron terms and magnetic interaction terms using the first-order Foldy-Wouthuysen (FW1), the second-order Douglas-Kroll (DK2), and the infinite-order Douglas-Kroll (IODK) transformations, as well as the lowest-order (c(-2)) Breit-Pauli approximation. We calculated the magnetic shielding constants of several closed-shell atoms using the FW1, DK2, IODK, and Breit-Pauli Hamiltonians. The IODK Hamiltonian reproduced well the results calculated by the four-component Dirac-Fock-Coulomb theory: The maximum deviation is only about 2.2%. We found that the accuracy of the magnetic shielding constants is strongly affected by the relativistic treatments of one-electron magnetic interaction, while the effect of the two-component two-electron relativistic corrections is relatively small. We also discussed the picture change effect on magnetic operators.

Expectation values in two-component relativistic theories

We examined numerically the equivalence between the expectation values calculated by the four-component wave function and those calculated by the two-component wave functions generated by the infinite-order Douglas-Kroll (IODK) transformation. We showed the expectation values <r(-1)> and <delta(r-R)> in several closed-shell atoms using the so-called picture-changed 2x2 operators at some levels of approximation. The effect of the two-electron Coulomb term was also discussed. The numerical results indicated that the accuracy of <r(-1)> mainly depends on the level of the wave functions, while that of <delta(r-R)> is affected by the accuracy of both the wave functions and the picture-changed operators. As expected, the picture-changed operators and the IODK wave functions generate essentially equivalent expectation values in comparison with those calculated by the four-component Dirac-type method.

Elastic scattering of positrons by helium, neon, argon and krypton atoms

An elaborate computer code is constructed for the investigation of the elastic scattering of positrons from noble gases using an iterative Green's function partial-wave expansion formalism. Model static and polarization potentials are derived for describing the interactions of positrons with closed shell atoms. Quite accurate variational pictures are employed for describing the atomic targets. The efficiency of the developed code is tested by investigating the collisions of positrons from the atoms of four ideal gases, namely, helium, neon, argon and krypton. In each case, sufficient integration range and number of iterations are used for calculating the elastic phase shifts of 8 partial waves as well as the total elastic cross sections for an extended range of incident energies. Comparison between our results and both experimental and theoretical values available in the literature indicates that our results are very close to the experimental ones. They are as accurate as the theoretical results obtained with more complicated approaches.

Model Analysis of Rotationally Inelastic Ar + H2O Scattering in an Electric Field

We develop an analytic model of thermal state-to-state rotationally inelastic collisions of asymmetric-top molecules with closed-shell atoms in electric fields and apply it to the Ar−H2O collision system. The predicted cross sections as well as the steric asymmetry of the collisions show at fields up to 150 kV/cm characteristic field-dependent features which can be experimentally tested. Particularly suitable candidates for such tests are the 000 → 220 and 101 → 221 channels, arising from the relaxation of the field-free selection rules due to the hybridization of J states by the field. Averaging over the M′ product channels is found to largely obliterate the orientation effects brought about by the field.

Toward improved density functionals for the correlation energy

Eleven density functionals, including some of the most widely used ones, are tested on their ability to predict nonrelativistic, electron correlation energies for the 17 atoms from He to Ar, the 17 cations from Li(+) to K(+), and 11 (1)S state atoms from Ca to Rn. They all lead to relatively poor predictions for the heavier atoms. Reparametrization of these functionals improves their performance for light atoms but does not alleviate their problems with the heavier, closed-shell atoms. Several novel, few-parameter, density functionals for the correlation energy are developed heuristically. Four new functionals lead to qualitatively improved predictions for the heavier atoms without unreasonably compromising accuracy for the lighter atoms. Further progress would be facilitated by reliable estimates of electron correlation energies for more atoms, particularly heavy ones.

A simple cross-correlation technique between infrared and hard x-ray pulses

We report a gas phase technique to establish the temporal overlap of ultrafast infrared laser and hard x-ray pulses. We use tunnel ionization of a closed shell atom in the strong field at the focus of an infrared laser beam to open a distinct x-ray absorption resonance channel with a clear fluorescence signature. The technique has an intrinsic response of a few femtoseconds and is nondestructive to the two beams. It provides a step-functionlike cross-correlation result. The details of the transient provide a diagnostic of the temporal overlap of the two pulses.