Complex Multiconfigurational Self‐Consistent Field‐Based Methods to Investigate Electron‐Atom/Molecule Scattering Resonances

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.…”

Electron-atom resonances: The complex-scaled multiconfigurational spin-tensor electron propagator method for the2PBe−shape resonance problem

“…In real space, MCSCF with a small complete active space (CAS) has been proven to be a very effective method to describe nondynamical and some dynamical correlation correctly and is computationally cheaper than very large or full configuration interaction (CI) calculations [12] while still incorporating the fundamental physics of what is going on. Based on the CMCSCF initial state, we also developed a new method termed as the M 1 method [11,13], in which the complex M 1 matrix is constructed from the first block of the M matrix defined in MCSTEP [14][15][16][17][18]. This block allows for only simple electron removal and addition to orbitals with no more complicated processes allowed to mix in.…”

“…In addition to simple electron addition operators to all orbitals as in the M1 method, MC-STEP includes operators the allow for electron removal and electron addition to all orbitals to excited states within the CAS [14][15][16][17][18]. In complex space, the M 1 and CMCSTEP methods use CMCSCF states as reference or initial state along with H. Both the CMCSCF and M 1 methods have been previously efficiently used to study the 2 P Be − shape resonance [10,11,13].…”