Density fitting (DF), also known as the resolution of identity (RI), is a widely used technique in quantum chemical calculations with various types atomic basis sets─Gaussian-type orbitals, Slater-type well numerical orbitals─to speed up density functional, Hartree–Fock (HF), and post-HF calculations. Traditionally, custom auxiliary sets are hand-optimized for each orbital set; however, some au...

Geometry optimizations were carried out for the (HF)2, (H2O)2, and HF–H2O intermolecular complexes using the MP2/aug-cc-pVXZ {X = 2, 3, 4, and 5} theoretical models on both the uncorrected and counterpoise (CP) corrected potential energy hypersurfaces (PES). Our results and the available literature data clearly show that extrapolation of intermolecular distances to the complete basis set (CBS) ...

We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb operator [T. Limpanuparb, A. T. B. Gilbert, and P. M. W. Gill, J. Chem. Theory Comput. 7, 830 (2011)] and the long-range Ewald operator [T. Limpanuparb and P. M. W. Gill, J. Chem. Theory Comput. 7, 2353 (2011)]) are employed in quantum chemical calcula...

We report Hartree-Fock HF -based pseudopotentials suitable for plane-wave calculations. Unlike typical effective core potentials, the present pseudopotentials are finite at the origin and exhibit rapid convergence in a plane-wave basis; the optimized pseudopotential method A. M. Rappe et al., Phys. Rev. B 41, 1227 1990 improves plane-wave convergence. Norm-conserving HF pseudopotentials are fou...

ACES III is a newly written program in which the computationally demanding components of the computational chemistry code ACES II [J. F. Stanton et al., Int. J. Quantum Chem. 526, 879 (1992); [ACES II program system, University of Florida, 1994] have been redesigned and implemented in parallel. The high-level algorithms include Hartree-Fock (HF) self-consistent field (SCF), second-order many-bo...

Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately quantify the uncertainty that results from the cost of the original simulator, and thus the inability to evaluate it on the whole input space. However, it is ...

One common problem in building deep learning architectures is the choice of the hyper-parameters. Among the various existing strategies, we propose to combine two complementary ones. On the one hand, the Hyperband method formalizes hyper-parameter optimization as a resource allocation problem, where the resource is the time to be distributed between many configurations to test. On the other han...

Recently, several researchers have reported encouraging experimental results when using Gaussian or bump-like activation functions in multilayer perceptrons. Networks of this type usually require fewer hidden layers and units and often learn much faster than typical sigmoidal networks. To explain these results we consider a hyper-ridge network, which is a simple perceptron with no hidden units ...

We investigate the statistical modeling of hyper-spectral data. The accurate modeling of experimental data is critical in target detection and classification applications. In fact, having a statistical model that is capable of properly describing data variability leads to the derivation of the best decision strategies together with a reliable assessment of algorithm performance. Most existing c...

in this note first we define the notions of fuzzy positive implicativehyper bck-ideals of types 1,2,3 and 4. then we prove some theorems whichcharacterize the above notions according to the level subsets. also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperbck-ideals and fuzzy positive implicative hyper bck-ideals of types 5,6,7and 8. then, we define the no...