1. Ludwik Adamowicz and Michele Pavanello, Department of Chemistry and Biochemistry February 9th, 2012

2. UA SUPERCOMPUTERS Shared Memory - SGI Altix 4700 Marin - Interactive Front End, Altix 4700, 100- core Itanium2, 160 GB memory Bora - Batch System, Altix 4700, 512-core Itanium2, 1024 GB memory Cluster - SGI Altix ICE 8200 Ice - Interactive Front End, 3 "round-robin" login nodes cluster 1392-core, quad-core Xeon (Harpertown), 2 GB memory/core New Cluster - SGI Altix ICE 8400 2112-core, 6-core INTEL Xeon Soon To Be Installed SGI Altix UV IBM: DataPlex HTC

3. Goal: Accurate PES of H 3 + Motivation Interstellar chemistry: (H n ) + Spectroscopy: H 3 + What has been done in the past? MethodSingle Point (cm -1 )PES (cm -1 ) CI, (CC), (MPn) 200 – 10 R12 – CI, (CC, MPn) <10 ECGs*< 10 -3 0.02 Our work?? *Cencek JCP, 108, 2831 (1998) ; Explicitly Correlated Gaussians (ECGs)

4. Expansion in terms of basis functions The basis set is made of explicitly correlated Gaussians with floating centers linear and non-linear parameters The case of H 3 + Atoms Molecules

5. 1.Electron-Nucleous cusp 2.Electron-Electron cusp Kato’s condition* *T. Kato (1957) Cusp function: The derivative of Ψ in this point counts!

6. Energy E Gradient G Determine the step size and move The step size is determined as a function of G and E.

7. Variational Principle Basis sizeCPU Time (days) Energy 1 (au) Energy 2 (au) 1508-1.343 835 599 83-1.343 835 540 30040-1.343 835 623 08-1.343 835 615 6008-1.343 835 624 94-1.343 835 624 10000.1-1.343 835 625 02NA 1) Pavanello et. al. J. Chem. Phys., 130, 034104 (2009) 2) Cencek et al. Chem. Phys. Lett. 246, 417-420 (1995) 1.Non-linearity: M*7 parameters 2.Encounter linear dependencies

8. 5 or 6 electrons maximum I.Antisymmetrize electrons: n e ! II.Basis set size: M 2 Schrödinger Equation I.Born-Oppenheimer approximation II.Relativity III.Coulomb Hamiltonian Implementation – Parallelization – Numerical Instability I.Encounter linear dependencies II.Memory constraints

9. 1.Re-optimize from scratch the basis set for each PES grid point. a.Takes a long time to optimize the basis set b.Hundreds, sometimes thousands of geometries need to be considered 2.Guess the basis set from nearby geometries a.How? b.Is it precise? c.Is the precision maintained for each grid point? We need a benchmark!

10. Generated a 377-point PES The wavefunction at a certain geometry was generated from one of a nearby geometry Pavanello et al. J. Chem. Phys. 130, 001033 (2009) The spring model Convergence dictated by the value of the analytical gradient ( G T G < 10 -11 a.u. ) and not of the energy M=900 6300 parameters

11. Total Energy (a.u.) ΔE(a.u. x 10 -8 ) We notice: Our energies are always 0.01 cm -1 below the best in the literature. Stretched geometries seem to show better improvement The more negative the better!

12. asymmetric C 2v 3C 2v 4

13. Total Energy (a.u.) ρ (a.u.) R 12 R 13 R 23 Viegas, Alijah and Varandas, JCP (2007) Johnson, JCP (1980) Whitten and Smith (1968) Alijah at al. used MR-CI with cc-pV5Z

14. Alijah’s most diffuse function H3+H3+ [H H H] + 2H+H + 20 cm -1 Alijah et al. Our work (ECGs) Energy Difference (a.u.)

16. We developed: ECG with analytical gradients, tested on single point calculations Spring method to calculate PESs, tested on a 69 point PES portion of H 3 + The code is applicable to any (n e <7) molecular system We achieved: Most accurate variational energies to date Most accurate (≈ 0.01cm -1 ) and extensive PES (42000 grid points) of H 3 +

17. To be developed: Leading relativistic corrections Non-adiabatic corrections Leading QED corrections

18. The total laboratory-frame nonrelativistic Hamiltonian:

24. H3+H3+H3+H3+

26. Coworkers: Pawel Kozlowski Donald Kinghorn Mauricio Cafiero Sergiy Bubin Michele Pavanello Wei-Cheng Tung Collaborators: Alexander Alijah Nikolai Zobov Irina I. Mizus Oleg Polyansky Jonathan Tennyson Tamás Szidarovzsky Attila Császár Max Berg Annemieke Petrignani Andreas Wolf Support: NSF