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and references contained therein
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4143072375
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note
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Our dielectron trajectories were assembled by concatenating several shorter runs, and at the beginning of each of these runs, the coordinates were shifted so as to place the dielectron at the center of the simulation box. By keeping track of these shifts, we can convert our simulated positions (all of which are inside the box) into global coordinates and thus calculate the diffusion constant, D.
-
-
-
-
42
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4143061249
-
-
note
-
As was discussed in detail in ref 16, the approximations made in the CI-with-important-states algorithm lead to a small drift in the total energy of ∼0.1 eV/ps. Although temperature is relatively constant despite this drift, to reduce fluctuations of temperature, we have rescaled the magnitudes (but not the directions) of the classical velocities every 2 ps, so as to maintain a constant average temperature.
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44
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0031251820
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(b) Bergman, D. L.; Laaksonen, L.; Laaksonen, A. J. Mol. Graph. Modell. 1997, 75, 301.
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49
-
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4143108913
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-
note
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We have defined the Coulomb and exchange energies (ref 16) such that if the two-electron state consists of a single product basis state with both electrons in the same single-electron state, a will be one.
-
-
-
-
50
-
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4143127602
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-
note
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The sphericity order parameters, n reported in ref 24 are ∼0.1 and ∼0.2 for the "compact" and "dumbbell" dielectrons, respectively. These values compare favorably to the values of our singlet and triplet dielectrons, as reported in Table 1.
-
-
-
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51
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4143116586
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-
note
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The standard deviations in Table 1 were calculated by computing the root-mean-square deviation and dividing by the square root of the number of independent samples, which was taken to be the length of the run divided by the decorrelation time of the listed property (typical decorrelation times were ∼0.2-1 ps for dielectrons and ∼2 ps for the single electron).
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-
-
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52
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0038115241
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The pseudopotential we use produces a much more spherically symmetric single-electron charge density than has been reported in the recent ab initio density-functional calculations of Parinello et al., Phys. Rev. Lett. 2003, 90, 226403-1. The moments of inertia that they report for their (single) electron correspond to n = 0.27, which is much larger than we find (Table 1). We do note, however, that the density-functional calculations of Kaukonen et al., ref 24, used a different electron-water pseudopotential than the one we use, and they report values of n for the "compact" dielectron very similar to those reported here for the singlet dielectron.
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Phys. Rev. Lett.
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Parinello1
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53
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4143114429
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note
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3, after forcing the vector at each time to have the maximum overlap with the vector at the previous time.
-
-
-
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54
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4143106701
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-
note
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The average root-mean-squared fluctuation for the two angles that describe the orientation in spherical coordinates is less than 30°.
-
-
-
-
56
-
-
4143086929
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-
note
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2/5, and the results in Table 1 imply that a = 2.5 Å and c = 5.8 Å for this model of the triplet dielectron.
-
-
-
-
58
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4143057949
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note
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n are the single-electron eigenenergies involved in the transition.
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-
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63
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0242291481
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