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The errors associated with truncating the long-range Coulomb interactions in our simulation were somewhat reduced by adopting a group-based cutoff scheme so that the longest ranged interactions were charge-dipole interactions. Although there exist better methods to treat long-range interactions in MD simulations, e.g., the Ewald summation (Ref.) we decided to use this simpler cutoff approach to allow for direct comparison to the 1EM sodide (Ref.) and dielectron simulations (Ref.), which also used the simple truncation scheme.
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The experimental electron affinity of a sodium cation is 0.188 857 6 hartree [CRC Handbook of Chemistry and Physics, 88th ed., edited by, D. R. Lide, (CRC/Taylor and Francis, Boca Raton, 2008)] the difference between this value and the negative of the frozen-core HF eigenvalue is due mainly to electron correlation between the valence and core electrons being neglected in the frozen core approximation [see W. Müller, J. Flesch, and W. Meyer, J. Chem. Phys. 0021-9606 10.1063/1.447083 80, 3297 (1984)].
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The reason for our choice of single-electron adiabatic states over other possible bases, e.g., HF orbitals, is that these adiabatic states are easy to generate by diagonalizing a one-electron Hamiltonian: No self-consistent iterations are required. Furthermore, the excited-state HF orbitals (virtuals) are often unbound and are thus a poor representation of the lowest-lying many-electron excited-state wave functions, so that a large number of these states are required to form an adequate product basis. Our choice of the single-electron adiabatic product basis gives many bound higher-lying basis states, providing greater flexibility to simultaneously represent both the many-electron ground and lowest excited states.
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The reason for our choice of single-electron adiabatic states over other possible bases, e.g., HF orbitals, is that these adiabatic states are easy to generate by diagonalizing a one-electron Hamiltonian: No self-consistent iterations are required. Furthermore, the excited-state HF orbitals (virtuals) are often unbound and are thus a poor representation of the lowest-lying many-electron excited-state wave functions, so that a large number of these states are required to form an adequate product basis. Our choice of the single-electron adiabatic product basis gives many bound higher-lying basis states, providing greater flexibility to simultaneously represent both the many-electron ground and lowest excited states.
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The mean potential energy of the dielectron-water interaction was calculated from the mean values of the dielectron total and kinetic energy and the electron-electron interaction energy as reported in Ref., which is why the uncertainty in this value is unknown.
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The mean potential energy of the dielectron-water interaction was calculated from the mean values of the dielectron total and kinetic energy and the electron-electron interaction energy as reported in Ref., which is why the uncertainty in this value is unknown.
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We note that the lower states also could have substantial many-electron character in the form of radial correlation, although we have not probed this in our analysis.
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We note that the lower states also could have substantial many-electron character in the form of radial correlation, although we have not probed this in our analysis.
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A gas-phase calculation of sodide's electronic structure with our two-electron model reveals that the ground state has 9% pcharacter.
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A gas-phase calculation of sodide's electronic structure with our two-electron model reveals that the ground state has 9% pp character.
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The dipole moment of a charged species depends on the origin of the coordinate system, which for sodide we took to be r Na+.
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-
An empirical estimate of the solution-phase polarizability of sodide has been previously reported as 430 a03 by Pyper and Edwards (Ref.). This estimate is considerably larger than our calculated polarizability of 169±4 a03, and is based on the assumption that changes in sodide's polarizability between different phases are the same as for the iodide ion. We believe that this assumption is not valid given the very different electronic structure of iodide and sodide.
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We chose to integrate the charge density up to 3.6 Å since we found empirically that this gave the most contrast between instances when both electrons were attached to the sodium core (Z≈-1) and when one electron was detached (Z≈0).
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The standard deviations in Table 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 estimated decorrelation time of the listed property (roughly 0.2 ps).
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The standard deviations in Table 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 estimated decorrelation time of the listed property (roughly 0.2 ps).
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