A cubic scaling algorithm for excited states calculations in particle–particle random phase approximation

A cubic scaling algorithm for excited states calculations in particle-particle random phase approximation

The particle-particle random phase approximation (pp-RPA) has been shown to be capable of describing double, Rydberg, and charge transfer excitations, for which the conventional time-dependent density functional theory (TDDFT) might not be suitable. It is thus desirable to reduce the computational cost of pp-RPA so that it can be efficiently applied to larger molecules and even solids. This pap...

Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange.

The random-phase approximation with second-order screened exchange (RPA+SOSEX) is a model of electron correlation energy with two caveats: its accuracy depends on an arbitrary choice of mean field, and it scales as O(n(5)) operations and O(n(3)) memory for n electrons. We derive a new algorithm that reduces its scaling to O(n(3)) operations and O(n(2)) memory using controlled approximations and...

Relativistic Pseudopotential Calculations for Electronic Excited States

Relativistic and electron correlation effects play a important role in the electronic structure of molecules containing heavy elements (main group elements, transition metals, lanthanide and actinide complexes). It is therefore mandatory to account for them in quantum mechanical methods used in theoretical chemistry, when investigating for instance the properties of heavy atoms and molecules in...

Excited States Calculations for Protonated PAHs

A -approximation algorithm for Graphic TSP in cubic bipartite graphs

We prove new results for approximating Graphic TSP. Specifically, we provide a polynomialtime 9 7 -approximation algorithm for cubic bipartite graphs and a ( 9 7 + 1 21(k−2) )-approximation algorithm for k-regular bipartite graphs, both of which are improved approximation factors compared to previous results. Our approach involves finding a cycle cover with relatively few cycles, which we are a...