Related papers: Analytic gradients for spin multiplets in natural …
We report a variational approach to the nonlinearly screened interaction of charged particles with a many-electron system. This approach has been developed by introducing a modification of the Schwinger variational principle of scattering…
Understanding the quantum dynamics of spin defects and their coherence properties requires accurate modeling of spin-spin interaction in solids and molecules, for example by using spin Hamiltonians with parameters obtained from…
X-ray photoelectron spectra provide a wealth of information on the electronic structure. The extraction of molecular details requires adequate theoretical methods, which in case of transition metal complexes has to account for effects due…
For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…
Simplex gradients are an essential feature of many derivative free optimization algorithms, and can be employed, for example, as part of the process of defining a direction of search, or as part of a termination criterion. The calculation…
Integrated gradients are widely employed to evaluate the contribution of input features in classification models because it satisfies the axioms for attribution of prediction. This method, however, requires an appropriate baseline for…
We describe the implementation of analytical Hartree-Fock gradients for periodic systems in the code CRYSTAL, emphasizing the technical aspects of this task. The code is now capable of calculating analytical derivatives with respect to…
The orbital, spin and valley degrees of freedom in silicon quantum dots support many modes of spin qubit operation. However, it is generally challenging to obtain information about the energy level spectrum over large ranges of parameter…
We consider the effective dynamics obtained by double-passing a far-detuned laser probe through a large atomic spin system. The net result of the atom-field interaction is a type of coherent positive feedback that amplifies the values of…
A computational procedure is developed for the efficient calculation of derivatives of integrals over non-separable Gaussian-type basis functions, used for the evaluation of gradients of the total energy in quantum-mechanical simulations.…
We introduce an algorithm for the solution of a system of radial Schr\"odinger equations describing the inelastic scattering of particles with spin in a partial wave with definite total angular momentum. The system of differential equations…
A new integral formula, which has not been compiled in any integral tables or mathematical softwares, is proposed to obtain the analytical energy-angular spectra of the particles that are sequentially emitted from the discrete energy levels…
Multi-reference calculations along the lines of the Generator Coordinate Method or the restoration of broken symmetries within the nuclear Energy Density Functional (EDF) framework are becoming a standard tool in nuclear structure physics.…
A theoretical study of spin dynamics in non-relativistic particle beams with interacting angular momenta traversing static, spatially varying magnetic fields is presented. The computational framework evaluates sinusoidal magnetic field…
We develop an alternative formulation in the energy-domain to calculate the second order M{\o}ller-Plesset (MP2) perturbation energies. The approach is based on repeatedly choosing four random energies using a non-separable guiding…
We study multiplicative dependence between elements in orbits ofalgebraic dynamical systems over number fields modulo a finitely generated multiplicative subgroup of the field. We obtain a series of results, many of which may be viewed as a…
The irregular solutions of the stationary Schr\"odinger equation are important for the fundamental formal development of scattering theory. They are also necessary for the analytical properties of the Green function, which in practice can…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
In previous work, the necessary integrals arising from correlated wavefunctions were expressed in forms suitable for numerical integration. For the evaluation of $r_{12}$ and $1/r_{12}$ integrals an analytic formula is derived.…
Analytical expressions are derived for classical trajectories in repulsive Coulomb plus multi-step attractive potentials. Thereafter the closed form expressions are obtained for classical deflection functions. The expressions are expected…