Related papers: An Adaptive Multiscale Approach for Electronic Str…
Multi-configurational electronic structure theory delivers the most versatile approximations to many-electron wavefunctions, flexible enough to deal with all sorts of transformations, ranging from electronic excitations, to open-shell…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
The complex scaling method (CSM) is a useful similarity transformation of the Schr\"odinger equation, in which bound-state spectra are not changed but continuum spectra are separated into resonant and non-resonant continuum ones. Because…
The full-dimensional time-dependent Schrodinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange…
We present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency dependent Sternheimer equation,…
Coupled nonlinear Schr\"odinger equations model various physical phenomena, such as wave propagation in nonlinear optics, multi-component Bose-Einstein condensates, and shallow water waves. Despite their extensive applications, analytical…
In transitions between different environmental settings, a molecular system inevitably undergoes a range of detectable changes, and the ability to accurately simulate such responses, e.g., in the form of shifts to molecular energies,…
Progress toward the solution of the strongly correlated electron problem has been stymied by the exponential complexity of the wave function. Previous work established an exact two-body exponential product expansion for the ground-state…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are…
Electronic structure calculations on small systems such as H$_2$, H$_2$O, LiH, and BeH$_2$ with chemical accuracy are still a challenge for the current generation of the noisy intermediate-scale quantum (NISQ) devices. One of the reasons is…
In this paper, we propose and analyze an adaptive time-stepping fully discrete scheme which possesses the optimal strong convergence order for the stochastic nonlinear Schr\"odinger equation with multiplicative noise. Based on the splitting…
An efficient method for calculating the electronic structure of systems that need a very fine sampling of the Brillouin zone is presented. The method is based on the variational optimization of a "single" (i.e. common to all points in the…
The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
This article deals with the mathematical derivation and the validation over benchmark examples of a numerical method for the solution of a finite-strain holonomic (rate-independent) Cosserat plasticity problem for materials, possibly with…
A numerically implementable Multi-scale Many-Body approach to strongly correlated electron systems is introduced. An extension to quantum cluster methods, it approximates correlations on any given length-scale commensurate with the strength…
An efficient computational algorithm to implement a local operator approach to partitioning electronic energy in general molecular systems is presented. This approach, which rigorously defines the electronic energy on any subsystem within a…
Despite their rich information content, electronic structure data amassed at high volumes in $ab$ $initio$ molecular dynamics simulations are generally under-utilized. We introduce a transferable high-fidelity neural network representation…
A common way to evaluate electronic integrals for polyatomic molecules is to use Becke's partitioning scheme [J. Chem. Phys.88, 2547 (1988)] in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed…