Why H Using Diffusion Monte Carlo DMC 3

+? ? ? Why H Using Diffusion Monte Carlo (DMC) 3 to Probe the Rotationally Excited + States of H 3 Bethany A. Wellen, Andrew S. Petit, and Anne B. Mc. Coy The Ohio State University

++? ? ? Why H Why 33 ? ? ?

Why H 3+? ? ? B. J. Mc. Call, Spectroscopy of H 3+ in Laboratory and Astrophysical Plasmas, Ph. D. Thesis, University of Chicago, (2001).

Why ? ? ? Why H 33++? ? ? B. J. Mc. Call, T. R. Geballe, K. H. Hinkle, and T. Oka, Science, 279, 1910 (1998).

Why ? ? ? Why H 33++? ? ? Ortho Para B. J. Mc. Call, T. R. Geballe, K. H. Hinkle, and T. Oka, Science, 279, 1910 (1998).

Why ? ? ? Why H 33++? ? ? Ortho Para B. J. Mc. Call, T. R. Geballe, K. H. Hinkle, and T. Oka, Science, 279, 1910 (1998).

Why ? ? ? Why H 33++? ? ? Ortho Para B. J. Mc. Call, T. R. Geballe, K. H. Hinkle, and T. Oka, Science, 279, 1910 (1998).

Why ? ? ? Why H 33++? ? ? Ortho Para B. J. Mc. Call, T. R. Geballe, K. H. Hinkle, and T. Oka, Science, 279, 1910 (1998). K. N. Crabtree, N. Indriolo, H. Kreckel, B. A. Tom, and B. J. Mc. Call, The Astrophysical Journal, 729, 1 (2011).

Why ? ? ? Why H 33++? ? ? Ortho Para B. J. Mc. Call, T. R. Geballe, K. H. Hinkle, and T. Oka, Science, 279, 1910 (1998). K. N. Crabtree, N. Indriolo, H. Kreckel, B. A. Tom, and B. J. Mc. Call, The Astrophysical Journal, 729, 1 (2011).

++? ? ? Why H Why 33 ? ? ?

++? ? ? Why H Why 33 ? ? ? H 5+

++? ? ? Why H Why 33 ? ? ? H 5+

++? ? ? Why H Why 33 ? ? ? H 5+

++? ? ? Why H Why 33 ? ? ? H 5+

+? ? ? Why H Diffusion Monte Carlo 3 J. B. Anderson J. Chem. Phys. , 63, 1499 (1975). J. B. Anderson J. Chem. Phys. , 65, 4121 (1976).

+? ? ? Why H Diffusion Monte Carlo 3 J. B. Anderson J. Chem. Phys. , 63, 1499 (1975). J. B. Anderson J. Chem. Phys. , 65, 4121 (1976).

+? ? ? Why H Diffusion Monte Carlo 3 J. B. Anderson J. Chem. Phys. , 63, 1499 (1975). J. B. Anderson J. Chem. Phys. , 65, 4121 (1976).

+? ? ? Why H Diffusion Monte Carlo 3 J. B. Anderson J. Chem. Phys. , 63, 1499 (1975). J. B. Anderson J. Chem. Phys. , 65, 4121 (1976).

+? ? ? Why H Diffusion Monte Carlo 3 J. B. Anderson J. Chem. Phys. , 63, 1499 (1975). J. B. Anderson J. Chem. Phys. , 65, 4121 (1976).

+? ? ? Why H Diffusion Monte Carlo 3 J. B. Anderson J. Chem. Phys. , 63, 1499 (1975). J. B. Anderson J. Chem. Phys. , 65, 4121 (1976).

+? ? ? Why H Diffusion Monte Carlo 3 J. B. Anderson J. Chem. Phys. , 63, 1499 (1975). J. B. Anderson J. Chem. Phys. , 65, 4121 (1976).

+? ? ? Why H Diffusion Monte Carlo 3 Eref

+? ? ? Why H Taking Diffusion 3 Monte Carlo to Excited States and Beyond!!!

+? ? ? Why H Taking Diffusion 3 Monte Carlo to Excited States and Beyond!!!

+? ? ? Why H Taking Diffusion 3 Monte Carlo to Excited States and Beyond!!! = +

+? ? ? Why H Taking Diffusion 3 Monte Carlo to Excited States and Beyond!!! = +

+? ? ? Why H Taking Diffusion 3 Monte Carlo to Excited States and Beyond!!! = + If rnode is correct, then the average energy in each nodal region MUST be identical

+? ? ? Why H Taking Diffusion 3 Monte Carlo to Excited States and Beyond!!! = + If rnode is correct, then the average energy in each nodal region MUST be identical

+? ? ? Why H Our Rotational 3 DMC Ansatz C B A

+? ? ? Why H Our Rotational 3 DMC Ansatz C C C B B A A

+? ? ? Why H Our Rotational 3 DMC Ansatz C C C B B A A

+? ? ? Why H Our Rotational 3 DMC Ansatz C C C B B A A Eckart frame employed to maximize separation of rotational and vibrational motion

+? ? ? Why H Our Rotational 3 DMC Ansatz C C C B B A A Eckart frame employed to maximize separation of rotational and vibrational motion Focusing on M=0 states

+? ? ? Why H Our Rotational 3 DMC Ansatz Two Key Assumptions:

+? ? ? Why H Our Rotational 3 DMC Ansatz Two Key Assumptions: Rotational component of wave function ONLY depends on BLAHHH A. S. Petit and A. B. Mc. Coy, J. Phys. Chem. A. , 113, 12706 (2009).

+? ? ? Why H Our Rotational 3 DMC Ansatz Two Key Assumptions: Rotational component of wave function ONLY depends on BLAHHH A. S. Petit and A. B. Mc. Coy, J. Phys. Chem. A. , 113, 12706 (2009).

+? ? ? Why H Our Rotational 3 DMC Ansatz Two Key Assumptions: Rotational component of wave function ONLY depends on BLAHHH M=0 nodal surfaces given by: A. S. Petit and A. B. Mc. Coy, J. Phys. Chem. A. , 113, 12706 (2009).

Energy (cm-1) +? ? ? Why H Is Our Ansatz Reasonable? ? ? 3 EJ=10, K − Fit to E 10, K=A+BK 2 K A. Aguado, O. Concero, C. Tablero, C. Sanz, and M. Paniagua, J. Chem. Phys. , 112, 1240 (2000).

EJ=10, K − Fit to E 10, K=A+BK 2 Residual of Fit (cm-1) Energy (cm-1) +? ? ? Why H Is Our Ansatz Reasonable? ? ? 3 K A. Aguado, O. Concero, C. Tablero, C. Sanz, and M. Paniagua, J. Chem. Phys. , 112, 1240 (2000).

Why. J=1 H 3+? ? ? Rotationally Excited State ZPE DMC Energy (cm-1) 4361. 7 ± 1. 7 Literature (cm-1) 4362. 1 DMC Error (cm-1) 0. 4 |1, 0, 0> |1, 1, 0>+ 88. 3 ± 2. 0 64. 3 ± 2. 3 87. 0 64. 1 1. 3 0. 2 A. Aguado, O. Concero, C. Tablero, C. Sanz, and M. Paniagua, J. Chem. Phys. , 112, 1240 (2000). B. M. Dinelli, L. Neale, O. L. Polyansky, and J. Tennyson, J. Mol. Spect. , 181, 142 (1997).

Why. J=1 H 3+? ? ? Rotationally Excited State ZPE DMC Energy (cm-1) 4361. 7 ± 1. 7 Literature (cm-1) 4362. 1 DMC Error (cm-1) 0. 4 |1, 0, 0> |1, 1, 0>+ 88. 3 ± 2. 0 64. 3 ± 2. 3 87. 0 64. 1 1. 3 0. 2 |1, 0, 0> |1, 1, 0>+ A. Aguado, O. Concero, C. Tablero, C. Sanz, and M. Paniagua, J. Chem. Phys. , 112, 1240 (2000). B. M. Dinelli, L. Neale, O. L. Polyansky, and J. Tennyson, J. Mol. Spect. , 181, 142 (1997).

+? ? ? Why H Moving on to 3 Higher J + + + + + A. Aguado, O. Concero, C. Tablero, C. Sanz, and M. Paniagua, J. Chem. Phys. , 112, 1240 (2000). B. M. Dinelli, L. Neale, O. L. Polyansky, and J. Tennyson, J. Mol. Spect. , 181, 142 (1997). +

+? ? ? Why H Moving on to 3 Higher J + + + + + A. Aguado, O. Concero, C. Tablero, C. Sanz, and M. Paniagua, J. Chem. Phys. , 112, 1240 (2000). B. M. Dinelli, L. Neale, O. L. Polyansky, and J. Tennyson, J. Mol. Spect. , 181, 142 (1997). +

+? ? ? Why H Moving on to 3 Higher J

+? ? ? Why H Moving on to 3 Higher J

+? ? ? Why H Moving on to 3 Higher J + + + + + A. Aguado, O. Concero, C. Tablero, C. Sanz, and M. Paniagua, J. Chem. Phys. , 112, 1240 (2000). B. M. Dinelli, L. Neale, O. L. Polyansky, and J. Tennyson, J. Mol. Spect. , 181, 142 (1997). +

+? ? ? Why H Moving on to 3 Higher J

+? ? ? Why H Moving on to 3 Higher J

+? ? ? Why H Moving on to 3 Higher J

+? ? ? Why H Moving on to 3 Higher J

+? ? ? Why H Moving on to 3 Higher J

+? ? ? Why H Rotation-Vibration Coupling 3 + + Å +

+? ? ? Why H Rotation-Vibration Coupling 3 + + Θ (°) +

+? ? ? Why H Rotation-Vibration Coupling 3 + + Å + + State E 10, |K| (cm-1) E 10, |K|-E 10, |K|+1 (cm-1) |10, 1, 0>+ 4348. 8 51. 7 |10, 2, 0>+ 4297. 0 81. 3 |10, 3, 0>+ 4215. 7 |10, 4, 0>+ 4086. 8 128. 8+ 160. 3 |10, 5, 0>+ 3926. 6 199. 6 |10, 6, 0>+ 3726. 9 241. 8 |10, 7, 0>+ 3485. 1 287. 9 |10, 8, 0>+ 3197. 2 340. 2 |10, 9, 0>+ 2857. 0 405. 2 |10, 0> 2451. 8 + Θ (°) A. Aguado, O. Concero, C. Tablero, C. Sanz, and M. Paniagua, J. Chem. Phys. , 112, 1240 (2000).

+? ? ? Why H Future 3 Work Understand the cause of the breakdown of the methodology at high J

+? ? ? Why H Future 3 Work Understand the cause of the breakdown of the methodology at high J H 5+

+? ? ? Why H Future 3 Work Understand the cause of the breakdown of the methodology at high J H 5+ Use DMC to map out the minimized energy pathways for the formation of H 5+

+? ? ? Why H Acknowledgements 3 Dr. Anne B. Mc. Coy (TJ 02) Bethany A. Wellen Dr. Sara E. Ray Annie L. Lesiak Dr. Samantha Horvath Andrew S. Dr. Charlotte Petit E. Hinkle (RI 10) (RI 02)

+? ? ? Why H Acknowledgements 3 Dr. Anne B. Mc. Coy (TJ 02) Bethany A. Wellen Dr. Sara E. Ray Annie L. Lesiak Dr. Samantha Horvath Andrew S. Dr. Charlotte Petit E. Hinkle (RI 10) (RI 02)

+? ? ? Why H QUESTIONS? ? ? 3