Excited-state calculations with quantum Monte Carlo

Quantum Monte Carlo methods are first-principle approaches that approximately solve the Schr\"odinger equation stochastically. As compared to traditional quantum chemistry methods, they offer important advantages such as the ability to handle a large variety of many-body wave functions, the favorable scaling with the number of particles, and the intrinsic parallelism of the algorithms which are particularly suitable to modern massively parallel computers. In this chapter, we focus on the two quantum Monte Carlo approaches most widely used for electronic structure problems, namely, the variational and diffusion Monte Carlo methods. We give particular attention to the recent progress in the techniques for the optimization of the wave function, a challenging and important step to achieve accurate results in both the ground and the excited state. We conclude with an overview of the current status of excited-state calculations for molecular systems, demonstrating the potential of quantum Monte Carlo methods in this field of applications

Recipes for sparse LDA of horizontal data

Many important modern applications require analyzing data with more variables than observations, called for short horizontal. In such situation the classical Fisher’s linear discriminant analysis (LDA) does not possess solution because the within-group scatter matrix is singular. Moreover, the number of the variables is usually huge and the classical type of solutions (discriminant functions) are difficult to interpret as they involve all available variables. Nowadays, the aim is to develop fast and reliable algorithms for sparse LDA of horizontal data. The resulting discriminant functions depend on very few original variables, which facilitates their interpretation. The main theoretical and numerical challenge is how to cope with the singularity of the within-group scatter matrix. This work aims at classifying the existing approaches according to the way they tackle this singularity issue, and suggest new ones

Plasma–liquid interactions: a review and roadmap

Plasma–liquid interactions represent a growing interdisciplinary area of research involving plasma science, fluid dynamics, heat and mass transfer, photolysis, multiphase chemistry and aerosol science. This review provides an assessment of the state-of-the-art of this multidisciplinary area and identifies the key research challenges. The developments in diagnostics, modeling and further extensions of cross section and reaction rate databases that are necessary to address these challenges are discussed. The review focusses on non-equilibrium plasmas

Gaussian continuum basis functions for calculating high-harmonic generation spectra

The computation of high\u2010harmonic generation spectra by means of Gaussian basis sets in approaches propagating the time\u2010dependent Schr\uf6dinger equation was explored. The efficiency of Gaussian functions specifically designed for the description of the continuum proposed by Kaufmann et al. (J Phys B 1989, 22, 2223) was investigated. The range of applicability of this approach was assessed by studying the hydrogen atom, that is, the simplest atom for which \u201cexact\u201d calculations on a grid could be performed. The effect of increasing the basis set cardinal number, the number of diffuse basis functions, and the number of Gaussian pseudo\u2010continuum basis functions for various laser parameters was notably studied. The results showed that the latter significantly improved the description of the low\u2010lying continuum states, and provided a satisfactory agreement with grid calculations for laser wavelengths \u3bb0\u2009=\u2009800 and 1064 nm. The Kaufmann continuum functions, therefore, appeared as a promising way of constructing Gaussian basis sets for studying molecular electron dynamics in strong laser fields using time\u2010dependent quantum\u2010chemistry approaches. \ua9 2016 Wiley Periodicals, Inc

Time-Step Targeting Time-Dependent and Dynamical Density Matrix Renormalization Group Algorithms with ab Initio Hamiltonians

We study the dynamical density matrix renormalization group (DDMRG) and time-dependent density matrix renormalization group (td-DMRG) algorithms in the ab initio context to compute dynamical correlation functions of correlated systems. We analyze the strengths and weaknesses of the two methods in small model problems and propose two simple improved formulations, DDMRG⁺⁺ and td-DMRG⁺⁺, that give increased accuracy at the same bond dimension at a nominal increase in cost. We apply DDMRG⁺⁺ to obtain the oxygen core-excitation energy in the water molecule in a quadruple-zeta quality basis, which allows us to estimate the remaining correlation error in existing coupled cluster results. Further, we use DDMRG⁺⁺ to compute the local density of states and gaps and td-DMRG⁺⁺ to compute the complex polarization function, in linear hydrogen chains with up to 50 H atoms, to study metallicity and delocalization as a function of bond length