Investigation of ²P Be⁻ Shape Resonances Using a Quadratically Convergent Complex Multiconfigurational Self-Consistent Field Method

Abstract

We develop, implement, and apply a quadratically convergent complex multiconfigurational self-consistent field method (CMCSCF) that uses the complex scaling theorem of Aguilar, Balslev, and Combes within the framework of the multiconfigurational self-consistent field method (MCSCF) in order to theoretically investigate the resonances originated due to scattering of a low-energy electron off of a neutral or an ionic target (atomic or molecular). The need to scale the electronic coordinates of the Hamiltonian as prescribed in the complex scaling theorem requires the use of a modified second quantization algebra suitable for biorthonormal spin orbital bases. In order to control the convergence to a stationary point in the complex energy hypersurface, a modified step-length control algorithm is incorporated. The position and width of 2P Be- shape resonances are calculated by inspecting the continuum states of Be-. To our knowledge, this is the first time that CMCSCF has been directly used to determine electron-atom/molecule scattering resonances. We demonstrate that both relaxation and nondynamical correlation are important for accurately describing shape resonances. For all of the calculations, the quadratically convergent CMCSCF was found to converge to the correct stationary point with a tolerance of 1.0 x 10(-10) au for the energy gradient within 10 iterations or less.

Complex-scaled multireference configuration-interaction method to study Be and Be-like cations' (B, C, N, O, Mg) Auger resonances1s2s22p1Zhang1, Yeager2 2012Phys. Rev. ASelf Cite211110View full textAdd to dashboardCite

“…F and G are the energy gradient vector and Hessian matrix, respectively, which have been explicitly defined in Refs. [8,9,14]. The complex variational principle [17][18][19] ensures that the search for the stationary point may be performed in the same way as MCSCF by setting the first derivative of Q(X)with respect to the step-length vector to zero, which leads to the multidimensional Newton-Raphson equation [8][9][10]14]:…”

“…A step-length control technique based on the Fletcher method [21] adapted for MCSCF by Jorgensen et al [20] was successfully implemented for CMCSCF by Samanta et al [8][9][10] to control the step length outside the quadratic region. When the step length no longer needs to be controlled, the method is quadratically convergent.…”

“…Previously we developed a quadratically convergent complex-scaled multiconfigurational self-consistent field [8,9] method (CMCSCF), "M 1 " [10] method, and the complexscaled multiconfigurational time-dependent Hatree-Fock [11] method (CMCTDHF) [also called the complex-scaled multiconfigurational linear response method (CMCLR)] to obtain the resonance parameters with the trajectory method [12] by determining E(α 0 ,θ 0 ) corresponding to the stability (loops, kinks, inflexions, or any other kind of "slowing down") in the plots of Im(E) as a function of Re(E) evaluated at a series of α values (α trajectories) and a series of θ values (θ trajectories). Both the M 1 and CMCTDHF methods use CMCSCF states as initial states.…”

The effect of metal electron cloud on the luminescence characteristics of organic ligands: An experimental and theoretical investigation

“…Multi-reference approaches such as coupled-cluster with single and double excitations (CCSD) [23], and complete active space self-consistent field (CASSCF) [24][25][26] methods allow very accurate estimates but are limited to small systems because of their large computational cost [27]. An alternative approach that is feasible to use is time-dependent density functional theory (TD-DFT) [28].…”

Configuration interaction calculations on the 2P ground state of boron atom and C+ using Slater orbitals

“…For Be − , a resonance position has been found to be 0.77 eV using a static exchange phase shift method [42], and 0.76 eV using complex SCF method [43]. Recent calculations using the complex MC-SCF method predict two resonances, one resonance position is 0.73 eV and another is 0.31 eV [44].…”