Accurate calculations of interstellar lines of Mg<SUP>+</SUP> using the coupled cluster approach

One of the most successful ab initio, highly correlated all-order many-body methods, the relativistic coupled cluster theory, is employed to calculate excitation energies of the doublet states of Mg+ and allowed transitions among them that are of interest in astrophysical problems. We have also calculated oscillator strength for the 3s-4p doublet transitions, which is improved over the existing results. These transition lines have been sought after in astronomical observations because they represent the best column density identifier in the interstellar medium. Our calculated oscillator strength (9.3 &#215; 10-4) and branching ratio (1.80) of these doublet lines matches well with the recent empirical and semiempirical calculations

Relativistic coupled-cluster-based linear response theory for ionization potentials of alkali-metal and alkaline-earth-metal atoms

We have developed and applied the relativistic coupled-cluster-based linear response theory (RCCLRT) for computing the principal as well as the shake-up ionization potentials (IP's) of Li, Be, Na, and Mg where the single-particle orbitals are generated by solving the relativistic Hartree-Fock-Roothaan equations using the Gaussian basis functions on a grid. The computed principal and shake-up ionization energies by the RCCLRT approach are in favorable agreement with the experimental results. Since for the (one-valence) IP problem, there is a formal equivalence between the principal IP values as obtained from the CCLRT and those obtained as eigenvalues of the multireference coupled-cluster theory, the computed quantities are fully size extensive. The approach via the RCCLRT has the additional advantage of providing the shake-up IP's as well. These are, however, not fully size extensive, but the error scales as the number of valence excitations (2h-1p), so the inextensivity error is rather small

Core effects on ionization potentials in thallium

Ionization potentials (IP's) are evaluated for various excited states of Tl using the relativistic coupled cluster (CCCD) theory in the even-parity pair channel approximation (CCSD-EPC). An average accuracy below half a percent is reached. The effect of deep core electrons on the core-valence correlations is investigated. It is found that electrons in the third subshell (n=3) modify the IP's of the 6p orbitals by 100 cm-1. By comparison with calculations made in the linearized CCSD (LCCSD) approximation it is demonstrated that nonlinear contributions are mandatory to reach an accuracy below half a percent for the 6p&#189; orbital

Relativistic coupled cluster calculations of the energies for rubidium and cesium atoms

Ionization potentials and excitation energies of rubidium and cesium atoms are computed using the relativistic coupled cluster (CC) method. The effect of electron correlations on the ground and excited state properties is investigated using different levels of CC approximations and truncation schemes. The present work demonstrates that the even-parity channel truncation scheme produces results almost as accurate as obtained from the all-parity channel approximation scheme at a reduced computational cost. The present study also indicates that for a given basis the linearized CC method tends to overestimate the ground and excited state properties compared to the full CC method

A linear response theory for excited state energies for systems with a strongly correlated ground state

1-8In this paper we apply our recently developed state-specific multi-reference coupled cluster based linear response method to compute excited state energies for systems whose ground state has a pronounced multi-reference character. The parent state-specific theory is built on complete active space reference functions, and is designed to treat quasi-degeneracy of varying degrees while bypassing the intruder problem. The response theory based on such a function offers thus a very convenient tool for generating potential energy surfaces (PES) for excited states where a traditional response formulation based on a single reference theory will fail due to the quas-idegeneracy in some regions of the PES and the effective hamiltonian based response methods would be beset by intruders. A succinct summary of the response formalism is presented to both underline the basic issues and the mode of approach. Illustrative numerical results are presented for the PES of the excited states as a function of the angle opening for the paradigm system H4 in trapezoidal geometry (H4), whose ground state requires a two-configuration description at the rectangular geomet ry, and has intruders at an intermediate trapezoidal geometry. A comparison with the full CI results in the same bas is indicates the efficacy of the method

Development of a size-consistent state-specific multireference perturbation theory with relaxed model-space coefficients

We explore the Rayleigh-Schrodinger and the Brillouin-Wigner perturbative counterparts of our recently developed state-specific coupled-cluster formalism with a complete active space. It is size-extensive and designed to avoid intruders. For each reference determinant &#966;&#956;, there is a separate cluster operator T&#956;. The redundancy inherent in such a choice is resolved by postulating suitable sufficiency conditions which at the same time ensure size-extensivity and size-consistency. The combining coefficients c&#956; for &#966;&#956;s are completely relaxed and obtained by diagonalizing an effective operator in the model space, one root of which is the target eigenvalue of the state. We illustrate size-consistency of the perturbative formalisms with an example model problem

A compact spin-free cluster expansion formalism for simple open-shell configurations

A compact spin-free coupled cluster (CC) approach is presented for simple open-shell configurations such as doublets or h-p excited singlets/triplets, using a new cluster Ansaz for the wave-operator. Unlike the extant methods, the CC equations for state energies are at most quartic in the cluster amplitudes, analogous to the closed-shell theory. It can also be utilized for energy differences relative to a closed-shell singlet. The Ansaz allows contractions between cluster operators via spectator orbitals, taking care of relaxation and correlation effects very efficiently. Applications to IP and doublet energies demonstrate its efficacy for outer, inner and core ionizations

State-specific multi-reference coupled electron-pair approximation like methods: formulation and molecular applications

We present two variants of state-specific multi-reference coupled electron-pair type approximants (SS-MRCEPA) of our recently formulated state-specific multi-reference coupled-cluster (SS-MRCC) theory. Just like the parent SS-MRCC theory, these are formulated with a complete active space, and are rigorously size-extensive and size-consistent. They also bypass the intruder problem very efficiently. The efficacy of the methods is illustrated with the computation of the ground state potential energy surface of the trapezoidal H4 model, where the ground state requires a two-determinantal model space and the effective hamiltonian methods face intruders