Coordinate rotation studies of H⁻, He⁻, Be⁻, Mg⁻ resonances: Basis set and configuration list dependence

Abstract

We have performed coordinate rotated configuration interaction calculations on well-studied Feshbach resonances of H-and He-and on *P shape resonances of Be-and Mg-. The focus of our efforts was the dependence of computed resonance energies on both the quality of the atomicorbital basis and the level of treatment of electron correlation. Our results indicate that great care must be taken to guarantee that a basis is adequate; commonly used quantum-chemistry bases are probably far from satisfactory. Our findings also indicate that a proper treatment of inner-shell orbitals within coordinate rotation calculations is a formidable task. We are therefore encouraged to look carefully for modified coordinate rotation techniques that focus on the active valence-level orbitals and may avoid spurious complex energies arising from improper treatment of inner shells. 2 ~~

Complex absorbing potentials within EOM-CC family of methods: Theory, implementation, and benchmarks

“…Once the density matrix is computed, the energy of the resonance state is corrected according to Eqs. (7) and (8).…”

“…5 One can avoid the inconveniences of working with continuum functions or fiddling with boundary conditions by reformulating the problem using complex variables. [2][3][4] The most rigorous approach is the complex-scaling formalism 2,6 in which all coordinates are scaled by a complex number e −iθ ; however, practical applications of this method are limited by its extreme sensitivity to the one-electron basis set [7][8][9][10][11] as well as conceptual difficulties regarding the separation of nuclear and electronic motions of the scaled Hamiltonian. [12][13][14][15] These problems are avoided in an alternative approach in which the original (non-scaled) Hamiltonian is augmented by a complex potential −iηŴ devised to absorb the diverging tail of the resonance wave function.…”

Complex-scaled equation-of-motion coupled-cluster method with single and double substitutions for autoionizing excited states: Theory, implementation, and examples

“…Second, although complex-scaling does not change the eigenvalues of bound states (in the complete one-and many-electron limit), it does change the corresponding wave functions introducing oscillatory behavior, which is most prominent for core electrons in many-electron systems. [62][63][64] To accurately describe these changes of the wave function along θ -trajectories, sufficiently flexible bases are necessary. Finally, as demonstrated below, for Feshbach resonances (whose lifetimes are determined by electron correlation), basis sets need to be capable of describing both radial and angular correlation accurately and in a balanced way.…”

“…A number of approaches have been developed to tackle the core electrons problem, 63 the simplest of which is a subtracted-core technique; it can be easily applied in complex-scaled EOM-EE-CCSD by freezing core electrons in post-cs-HF calculations.…”

Many‐electron theory of autoionizing states using complex coordinates: The position and the partial and total widths of the Ne+ 1s hole state

“…For example, in 1977 Ho, Bhatia, and Temkin [26], having carried out large configuration-interaction calculations with Hylleraas basis sets, stated that "the full advantages of the complex rotation method for more than two-electron systems have yet to be realized." Similarly, in a recent publication, Chuljian and Simons [36] concluded that for N-electron autoionizing states "commonly used quantum-chemistry bases are probably far from satisfactory. Our findings also indicate that a proper treatment of innershell orbitals within coordinate rotation calculations is a formidable task."…”