Complex scaling method for molecules in intense laser fields

Abstract

This work consists of two parts: In the first part we report new full 3D correlated two-electron ab-initio calculations for diatomic systems including the symmetric molecular hydrogen H[subscript 2] and its extension to nonsymmetric molecule HeH[superscript +] . We use a numerical spectral method of configuration interaction (CI) type to solve stationary Schrödinger equations (SSE) via expansion of two-electron wave function on basis of associated Laguerre polynomials and Legendre functions. We use the complex scaling method for our basis function expansion in order to describe the decaying behavior of resonance states correctly. From solving SSE, we have been able to compute the energy levels for the ground state, many high lying excited states, double excited states, and transition dipole moments. The accuracy of our results shows the efficiency of our numerical method and the wave function expansion. Then, we solve time-dependent Schrödinger equations (TDSE) by using high-order Runge-Kutta method with adaptative step size. In the case of TDSE the complex scaling of the basis functions also prevents the reflection of the wave function during time propagation, so a smaller basis expansion is sufficient to study the physical phenomena. The preliminary results for total ionization show very good accuracy. We have implemented our CI based algorithm for the solution of SSE's and TDSE's for diatomic molecules, the symmetric case (H[subscript 2]) and the nonsymmetric case (HeH[superscript +]), based on FORTRAN77. Our algorithm is highly optimized and also we parallelized it with OPENMP method, so it is very efficient. Then, by having final two-electron wave functions of diatomic molecules at the end of laser pulse and the corresponding eigenvalues and eigenfunctions of one-electron systems in hand we used projection methods to compute single (SI) and double (DI) ionization probabilities at the end of laser pulse. Our results for ionization and excitation probabilities (at 800 nm and 400 nm) show a strong evidence of enhanced ionization (EI), in both single and double ionization, as well as enhanced excitation (EE), in single and double excitation, as the internuclear distance R of diatomic systems (H[subscript 2] and HeH[superscript +]) increases from the equilibrium value R[subscript e]. The enhancement of all these molecular processes exhibits a maximum at a critical distance R[subscript c] which can be predicted from simple electrostatic and recollision models. We also computed the molecular high-order harmonic spectra, MHOHG, for H[subscript 2] at different laser intensities confirming the spectra satisfy a cut-off law. In the second part we have derived new integration schemes based on exponential decomposition of evolution operators. We have shown that in order to avoid negative time steps, complex time steps a « ib with positive real part a > 0 can give very accurate wave functions with high order efficiency for small errors. Of note is that the new operators S[superscript A,B][subscript 3], S?[subscript 3], S?[subscript 4] have all been obtained from combinations of lower order S[superscript A,B][subscript 2] with complex time step [gamma] = a « ib and a > 0.This suggests that these low order operators with complex time steps are basic generators of higher order accuracy exponential integrators.