This thesis is part of an effort to enable large–scale Hartree–Fock/Kohn–Sham (HF/KS) calculations. The objective is to model molecules and materials containing thousands of atoms at the quantum mechanical level. HF/KS calculations are usually performed with the Self-Consistent Field (SCF) method. This method involves two computationally intensive steps. These steps are the construction of the ...

We propose a novel hybrid loss for multiclass and structured prediction problems that is a convex combination of log loss for Conditional Random Fields (CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs). We provide a sufficient condition for when the hybrid loss is Fisher consistent for classification. This condition depends on a measure of dominance between labels – specific...

We formulate a self-consistent field theory for polyelectrolyte brushes in the presence of counterions. We numerically solve the self-consistent field equations and study the monomer density profile, the distribution of counterions, and the total charge distribution. We study the scaling relations for the brush height and compare them to the prediction of other theories. We find a weak dependen...

Unparameterized and parameterized versions are outlined of a new method for approximating self-consistent field wavefunctions from first principles at the minimum basis set level for complex molecules containing hydrogen and first-row atoms. The Hartree-Fock self-consistent field equations for closed-shell molecules are solved, retaining all one-electron integrals, and approximating the two-ele...

These notes describe the multiconfigurational self-consistent-field (MCSCF) method, which is a general approach for describing chemical systems in which a single electron configuration is no longer an adequate description of the electronic structure. This commonly happens in reactions that break or form chemical bonds, diradicals, and metals of the first transition row. A single-determinant, re...

Spatially Coherent Random Forest (SCRF) extends Random Forest to create spatially coherent labeling. Each split function in SCRF is evaluated based on a traditional information gain measure that is regularized by a spatial coherency term. This way, SCRF is encouraged to choose split functions that cluster pixels both in appearance space and in image space. In particular, we use SCRF to detect c...

The reaction of ammonia and pyridine with trimethylsulfonium ion has been studied in gas phase and solution. Density functional theory at the B3LYP/6-31+G level was used to describe the energy changes along the reaction coordinate in the gas phase, and the self-consistent isodensity polarizable continuum model (SCI-PCM) was used to calculate the effect of cyclohexane and dimethyl sulfoxide as t...

The multiconfigurational self-consistent field theory is considered the standard starting point for almost all multireference approaches required for strongly correlated molecular problems. The limitation of the approach is generally given by the number of strongly correlated orbitals in the molecule, since its cost will grow exponentially with this number. We present a new multiconfigurational...

Recent developments in off-lattice self-consistent field theories for inhomogeneous complex fluids are reviewed. Particular emphasis is given to the treatment of intermolecular interactions and compressibility, to the role of fluctuations, and to the discussion of the coarse-graining length which is inherent to the theory. Valuable insight can be gained from the comparison of self-consistent fi...