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Simulations of radiation damage in single molecule imaging using a X-ray free electron laser use atomic rates calculated in the lowest order. We investigate the difference in ion yield predictions using Hartree-Fock and Hartree-Fock-Slater pproximations for light and heavy elements of biological significance. The results show that for the biologically abundant elements of the second and third rows of the periodic table both approximations agree to about 6%. For the heavier elements beyond the fourth row the discrepancy rices to 11% for the range of the pulse parameters covered in this work. Presented analysis can be used for an error estimation in a wide range of ab initio simulations of the X-ray pulse interaction with biological molecules. We also discuss other atomic structure effects and show that their account has considerably smaller effect on the ion yields of respective elements compared to the choice of the approximation.
An implementation of the Hartree-Fock (HF) method capable of robust convergence for well-behaved arbitrary central potentials is presented. The Hartree-Fock equations are converted to a generalized eigenvalue problem by employing a B-spline basis in
The relation between the correlation energy and the entanglement is analytically constructed for the Moshinskys model of two coupled harmonic oscillators. It turns out that the two quantities are far to be proportional, even at very small couplings.
We prove analytic-type estimates in weighted Sobolev spaces on the eigenfunctions of a class of elliptic and nonlinear eigenvalue problems with singular potentials, which includes the Hartree-Fock equations. Going beyond classical results on the anal
The Hartree-Fock problem provides the conceptual and mathematical underpinning of a large portion of quantum chemistry. As efforts in quantum technology aim to enhance computational chemistry algorithms, the fundamental Hartree-Fock problem is a natu
This work presents an algorithm to evaluate Coulomb and exchange matrices in Fock operator using range separation techniques at various aspects. This algorithm is particularly favorable for the scenario of (1) all-electron calculations or (2) computi