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Register a new userInvestigating properties of Cl$^-$ and Au$^-$ ions using relativistic many-body methods
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B. K. Sahoo
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We investigate ground state properties of singly charged chlorine (Cl$^-$) and gold (Au$^-$) negative ions by employing four-component relativistic many-body methods. In our approach, we attach an electron to the respective outer orbitals of chlorine (Cl) and gold (Au) atoms to determine the Dirac-Fock (DF) wave functions of the ground state configurations of Cl$^-$ and Au$^-$, respectively. As a result, all the single-particle orbitals see the correlation effects due to the appended electron of the negative ion. After obtaining the DF wave functions, lower-order many-body perturbation methods, random-phase approximation, and coupled-cluster (CC) theory in the singles and doubles approximation are applied to obtain the ground state wave functions of both Cl$^-$ and Au$^-$ ions. Then, we adopt two different approaches to the CC theory -- a perturbative approach due to the dipole operator to determine electric dipole polarizability and an electron detachment approach in the Fock-space framework to estimate ionization potential. Our calculations are compared with the available experimental and other theoretical results.
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We have carried out theoretical investigations of electron correlation effects on the atomic properties of the Ca atom trapped inside an attractive spherically symmetric potential well of an endohedral fullerene C$_{60}$ cluster. Relativistic coupled-cluster (RCC) theory has been employed to obtain electron correlation energy, ionization potential and dipole polarizability of this atom. We have also performed calculations using the Dirac-Hartree-Fock (DF), relativistic second-order many-body perturbation theory (RMBPT(2) method) and relativistic random phase approximation (RRPA) to demonstrate propagation of the correlation effects in these properties. Our results are compared with the reported calculations employing multi-configuration Hartree-Fock (MCHF) method in Phys. Rev. A {bf 87}, 013409 (2016). We found trends in correlation energy with respect to the potential depth are same, but magnitudes are very large in the relativistic calculations. We have also determined the differential and total cross-sections for elastic scattering of electrons from the free and confined Ca atoms using the electronic charge densities from the Dirac-Hartree core-potential (DFCP) and RCC methods to demonstrate role of potential depth in these properties.
The relativistic coupled-cluster (RCC) method is a powerful many-body method, particularly in the evaluation of electronic wave functions of heavy atoms and molecules, and can be used to calculate various atomic and molecular properties. One such atomic property is the enhancement factor (R) of the atomic electric dipole moment (EDM) due to an electron EDM needed in electron EDM searches. The EDM of the electron is a sensitive probe of CP-violation, and its search could provide insights into new physics beyond the Standard Model, as well as open questions in cosmology. Electron EDM searches using atoms require the theoretical evaluation of R to provide an upper limit for the magnitude of the electron EDM. In this work, we calculate R of 210Fr in the ground state using an improved RCC method, and perform an analysis on the many-body processes occurring within the system. The RCC method allows one to capture the effects of both the electromagnetic interaction and P- and T-violating interactions, and our work develops this method beyond what had been implemented in the previous works. We also perform calculations of hyperfine structure constants, electric dipole transition matrix elements, and excitation energies, to assess the accuracy of R and the success of our improved method. Finally, we present calculations of R with corrections due to Breit interaction effects, approximate quantum electrodynamics (QED) effects, and some leading triple excitation terms added perturbatively, to assess how significantly these terms contribute to the result. We obtain a final value of R = 799, with an estimated 3% error, which is about 11% smaller than a previously reported theoretical calculation.
The emerging field of quantum simulation of many-body systems is widely recognized as a very important application of quantum computing. A crucial step towards its realization in the context of many-electron systems requires a rigorous quantum mechanical treatment of the different interactions. In this pilot study, we investigate the physical effects beyond the mean-field approximation, known as electron correlation, in the ground state energies of atomic systems using the classical-quantum hybrid variational quantum eigensolver (VQE) algorithm. To this end, we consider three isoelectronic species, namely Be, Li-, and B+. This unique choice spans three classes, a neutral atom, an anion, and a cation. We have employed the unitary coupled-cluster (UCC) ansatz to perform a rigorous analysis of two very important factors that could affect the precision of the simulations of electron correlation effects within a basis, namely mapping and backend simulator. We carry out our all-electron calculations with four such basis sets. The results obtained are compared with those calculated by using the full configuration interaction, traditional coupled-cluster and the UCC methods, on a classical computer, to assess the precision of our results. A salient feature of the study involves a detailed analysis to find the number of shots (the number of times a VQE algorithm is repeated to build statistics) required for calculations with IBM Qiskits QASM simulator backend, which mimics an ideal quantum computer. When more qubits become available, our study will serve as among the first steps taken towards computing other properties of interest to various applications such as new physics beyond the Standard Model of elementary particles and atomic clocks using the VQE algorithm.
Molecular adsorption on surfaces plays a central role in catalysis, corrosion, desalination, and many other processes of relevance to industry and the natural world. Few adsorption systems are more ubiquitous or of more widespread importance than those involving water and carbon, and for a molecular level understanding of such interfaces water monomer adsorption on graphene is a fundamental and representative system. This system is particularly interesting as it calls for an accurate treatment of electron correlation effects, as well as posing a practical challenge to experiments. Here, we employ many-body electronic structure methodologies that can be rigorously converged and thus provide faithful references for the molecule-surface interaction. In particular, we use diffusion Monte-Carlo (DMC), coupled cluster (CCSD(T)), as well as the random phase approximation (RPA) to calculate the strength of the interaction between water and an extended graphene surface. We establish excellent, sub-chemical, agreement between the complementary high-level methodologies, and an adsorption energy estimate in the most stable configuration of approximately -100,meV is obtained. We also find that the adsorption energy is rather insensitive to the orientation of the water molecule on the surface, despite different binding motifs involving qualitatively different interfacial charge reorganisation. In producing the first demonstrably accurate adsorption energies for water on graphene this work also resolves discrepancies amongst previously reported values for this widely studied system. It also paves the way for more accurate and reliable studies of liquid water at carbon interfaces with cheaper computational methods, such as density functional theory and classical potentials.
We present electric dipole polarizabilities ($alpha_d$) of the alkali-metal negative ions, from H$^-$ to Fr$^-$, by employing four-component relativistic many-body methods. Differences in the results are shown by considering Dirac-Coulomb (DC) Hamiltonian, DC Hamiltonian with the Breit interaction, and DC Hamiltonian with the lower-order quantum electrodynamics interactions. At first, these interactions are included self-consistently in the Dirac-Hartree-Fock (DHF) method, and then electron correlation effects are incorporated over the DHF wave functions in the second-order many-body perturbation theory, random phase approximation and coupled-cluster (CC) theory. Roles of electron correlation effects and relativistic corrections are analyzed using the above many-body methods with size of the ions. We finally quote precise values of $alpha_d$ of the above negative ions by estimating uncertainties to the CC results, and compare them with other calculations wherever available.
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