1. Divide and Conquer QM Development Muller, Ward, Goddard Linear Scaling Massive Parallelizability Form H Diagonalize  Did  Change? Guess  No Done Yes O(N 4 ) PS/Jaguar  O(N 2 ) O(N 3 ) Difficult to reduce: Krylof space, Conjugate gradient Currently only important if N > 2000

2. Divide and Conquer Methods Break a big problem into small problems Physically based in quantum chemistry Divide and Conquer H Hamiltonian: Divided into fragments and buffer zones nbf

3. Divide and Conquer Results Linear Alkanes –14-98 atoms –170-817 bfns Linear scaling AND parallel!

4. Divide, Conquer, and Recombine Buffer zones don’t scale –Metallic Systems –Same problem n times Hierarchically recombine –E-value decomp of off- diagonal sections –Can also approximate.