Co-iterative augmented Hessian method for orbital optimization

Orbital optimization procedure is widely called in electronic structure simulation. To efficiently find the orbital optimization solution, we developed a new second order orbital optimization algorithm, co-iteration augmented Hessian (CIAH) method. In this method, the orbital optimization is embedded in the diagonalization procedure for augmented Hessian (AH) eigenvalue equation. Hessian approximations can be easily employed in this method to improve the computational costs. We numerically performed the CIAH algorithm with SCF convergence of 20 challenging systems and Boys localization of C60 molecule. We found that CIAH algorithm has better SCF convergence and less computational costs than direct inversion iterative subspace (DIIS) algorithm. The numerical tests suggest that CIAH is a stable, reliable and efficient algorithm for orbital optimization problem

Bellus Mortis

Life and death have long been the focus and inspiration for artists, composers, and philosophers. To live and die is the inevitable condition for all sentient beings. Life is largely celebrated, praised and is generally associated with joy, beauty, and virtue. Death, on the other hand, evokes horror, anguish, and despair. Death is feared and reviled by much of humanity. However, what if the dichotomy between life and death is not as unambiguous as people thought it to be? Why is the alternative term for “Death” called “Afterlife”? People glorify life whilst they demonize death. They usually fail to realize, that life and death are merely two inseparable faces of the same coin: they are indeed mutually exclusive, but neither could exist without another. The paintings that constitute my thesis exhibition Bellus Mortis strive to scrutinize the complex nature of life and death and to sift through divergent aspects of death. In my imagery, I have consciously chosen to explore theatrical depictions of various esoteric cultural practices associated with dying. I am also interested in investigating the chronological pictorial representations of Eastern philosophical perspectives of death. Utilizing cryptic and allegorical visual language, I attempt to represent death in a personal and neutral manner that is free from predetermined negativities, prejudice, and stereotypes. My artistic goal is to blur the boundary between the two and to visualize the unappreciated beauty, and tranquility of death. Additionally, my art is intended to demonstrate that life is not always the sublime gift brimming with ethereal delight that people choose to believe in unquestioningly. Ignore its flaws, an endless life will simply become an eternal torment

Long-Range Density Fitting

By separating the short-range and long-range components of the Coulomb potential, it becomes possible to compute electron repulsion integrals for each component using different methods. The short-range part can be computed analytically, while the long-range part can be approximated using the density fitting method. This combination provides a reliable approximation to the full-range electron repulsion integrals, with an error in the HF energy around 0.1 $\mu E_h$ per atom. Additionally, this method provides more than twice the overall performance compared to HF with conventional integral evaluation schemes

A general second order complete active space self-consistent-field solver for large-scale systems

We present a new second order complete active space self-consistent field implementation to converge wavefunctions for both large active spaces and large atomic orbital (AO) bases. Our algorithm decouples the active space wavefunction solver from the orbital optimization in the microiterations, and thus may be easily combined with various modern active space solvers. We also introduce efficient approximate orbital gradient and Hessian updates, and step size determination. We demonstrate its capabilities by calculating the low-lying states of the Fe(\Roman{2})-porphine complex with modest resources using a density matrix renormalization group solver in a CAS(22,27) active space and a 3000 AO basis

Electronic landscape of the P-cluster of nitrogenase as revealed through many-electron quantum wavefunctions

The electronic structure of the nitrogenase metal cofactors is central to nitrogen fixation. However, the P-cluster and iron molybdenum cofactor, each containing eight irons, have resisted detailed characterization of their electronic properties. Through exhaustive many-electron wavefunction simulations enabled by new theoretical methods, we report on the low-energy electronic states of the P-cluster in three oxidation states. The energy scales of orbital and spin excitations overlap, yielding a dense spectrum with features we trace to the underlying atomic states and recouplings. The clusters exist in superpositions of spin configurations with non-classical spin correlations, complicating interpretation of magnetic spectroscopies, while the charges are mostly localized from reorganization of the cluster and its surroundings. Upon oxidation, the opening of the P-cluster significantly increases the density of states, which is intriguing given its proposed role in electron transfer. These results demonstrate that many-electron simulations stand to provide new insights into the electronic structure of the nitrogenase cofactors.Comment: 23 pages, 5 figure

Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory

We determine the ground-state phase diagram of the three-band Hubbard model across a range of model parameters using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AFM) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. All parametrizations of the model display AFM and SC phases, but the decay of AFM order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AFM and SC orders occurs in all parameter sets. The local magnetic moment localizes entirely at the copper sites. The magnetic phase diagram is particularly sensitive to Δ_(pd) and t_(pp), and existing estimates of the charge transfer gap Δ_(pd) appear too large in so-called minimal model parametrizations. The electron-doped side of the phase diagram is qualitatively distinct from the hole-doped side and we find an unusual two-peak structure in the SC in the full model parametrization. Examining the SC order at the atomic scale, within the larger scale d_(x²−y²)-wave SC pairing order between Cu-Cu and O-O, we also observe a local p_(x(y)) [or d_(xz(yz))] symmetry modulation of the pair density on the Cu-O bonds. Our work highlights some of the features that arise in a three-band versus one-band picture, the role of the oxygen degrees of freedom in new kinds of atomic-scale SC orders, and the necessity of re-evaluating current parametrizations of the three-band Hubbard model

Gaussian and plane-wave mixed density fitting for periodic systems

We introduce a mixed density fitting scheme that uses both a Gaussian and a plane-wave fitting basis to accurately evaluate electron repulsion integrals in crystalline systems. We use this scheme to enable efficient all-electron Gaussian based periodic density functional and Hartree-Fock calculations