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We taper the electron-water interactions smoothly to zero instead of applying Ewald summation for the electron-water interaction because it is not clear how to apply Ewald summation when solving for the quantum electronic eigenstates without having to solve for the electronic eigenstates iteratively. Our neglect of the Ewald summation will lead to incorrect absolute energies (see, e.g., Peter, C.; van Gunsteren, W. F.; Hunenberger, P. H. J. Chem. Phys. 2003, 119, 12205), but we do not expect much effect on either the calculated energy gaps or dynamics. Since the two electrons share a single cavity at all times in our calculations, they should not see periodic images of each other, so we also do not need to use Ewald summation for the direct electron-electron interaction.
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84906403274
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note
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We note that using 10 single-electron basis states gives energy-conserving dynamics in the ground state, but that energy conservation is significantly worse in the excited states. Using 12 basis states restores energy conservation over long times, but because most runs spend less than 1 ps in the excited state, we used only 10 states in order to speed up the calculation. Over short times (less than ∼200 fs), the adiabatic dielectron states were found to have the same dynamics whether we used 10 or 12 single-electron basis states.
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48
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84906373542
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note
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j/∂t〉.
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50
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84906402316
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note
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As individual trajectories reach the ground state they are removed from the ensemble, so that long-time data has much poorer statistics than short-time data.
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51
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84906373543
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note
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2 = 0.996.
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52
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0033737139
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Aherne, D.; Tran, V.; Schwartz, B. J. J. Phys. Chem. B 2000, 104, 5382.
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Aherne, D.1
Tran, V.2
Schwartz, B.J.3
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53
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84906359159
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note
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We define the exchange energy as in ref 18, such that a two-electron wave function with both electrons in the same state splits the total electron-electron interaction into half Coulomb and half exchange energy. This definition means that when the two separated single electron cavities have precisely degenerate energies, the Coulomb energy drops by a factor of 2 and the exchange energy increases by the amount of the decrease; the total interaction is continuous.
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54
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84906390539
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note
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To conserve energy over several picoseconds with the singlet dielectron fixed to be in the first excited state, we found it necessary to use 12 single-electron states in the CI calculation and to update the important states every 2 ps instead of every 3 ps: see Note 31.
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55
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84906390540
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note
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A similar configuration of perpendicular charge densities and a rapid transition to the ground state was also seen in ref 18 when the triplet dielectron was excited directly to its first excited state.
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56
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84906359160
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Bedard-Hearn, M. J.; Larsen, R. E.; Schwartz, B. J., in preparation.
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Bedard-Hearn, M.J.1
Larsen, R.E.2
Schwartz, B.J.3
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59
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84906359161
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note
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The averaging in Figures 7 and 8 is performed using only those trajectories that are still in an excited state at each time, cf. Figures 2c and 5b.
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60
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0345802848
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Bedard-Hearn, M. J.; Larsen, R. E.; Schwartz, B. J. J. Phys. Chem. B 2003, 107, 14464.
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Larsen, R.E.2
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0000577528
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Huang, C. C.; Couch, G. S.; Pettersen, E. F.; Ferrin, T. E. Pacific Symposium on Biocomputing 1996, 1, 724. The Chimera code is freely available on the worldwide web at http://www.cgl.ucsf.edu/chimera.
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Huang, C.C.1
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Ferrin, T.E.4
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