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0242291480
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An overview of the configuration interaction method can be found in Chap. 4 of Ref. 20
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An overview of the configuration interaction method can be found in Chap. 4 of Ref. 20
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42
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0242323125
-
-
note
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12 cannot, of course, be represented as a direct product of single-electron operators: interactions between the electrons will not be diagonal in a one-electron basis.
-
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43
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0242323127
-
-
note
-
Because the Coulomb interaction does not affect the spin of an electron, spin flips can only be induced by terms in the electron-solvent Hamiltonians (e.g., by magnetic fields induced by moving charges in the solvent) or by direct spin-spin interactions. In this work, we will neglect such spin interactions, but we note that the extension to such cases is straightfor-ward.
-
-
-
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45
-
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0242291479
-
-
note
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ij results from the symmetry of the cubic lattice.
-
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46
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0242291482
-
-
note
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-8, therefore, we can use our tabulated values to compute ø between cubes within 16 grid points of each other, approximating all other values of ø by 1/r.
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49
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J. J. Sakurai, Modern Quantum Mechanics, revised ed. (Addison-Wesley, Reading, MA, 1994), Chap. 2.
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Sakurai, J.J.1
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62
-
-
0242291474
-
-
note
-
We define energy conservation by requiring any long-term drift in the total energy to be within the rms fluctuation over the course of a 2 ps run. The rms energy fluctuation is 0.08 eV for △t = 1.0 and 0.02 eV for △t = 0.5fs.
-
-
-
-
63
-
-
0242291476
-
-
note
-
update= 4 fs criterion is actually overly generous.
-
-
-
-
65
-
-
0242354480
-
-
note
-
A simple uncertainty-principle argument shows that the kinetic energy reduction associated with going from a cavity 4.0 Å in diameter to one 4. 8 Å in diameter is less than ∼0.1 eV.
-
-
-
-
66
-
-
0242354483
-
-
note
-
This change of shape from an "s-like" symmetry to a "p-like" symmetry is similar to what happens when a single hydrated electron is excited (see Refs. 9, 11, and 23), so it is not suprising that the time scale and mechanism of the Stokes shift are similar for the hydrated electron and the singlet dielectron.
-
-
-
-
67
-
-
0242323121
-
-
note
-
The two cavities of the excited state dielectron cannot properly be thought of as two separated single electrons because the exchange energy of ∼0.5 eV indicates that each one-electron basis state has amplitude in both holes.
-
-
-
-
68
-
-
0242385977
-
-
note
-
i). At first glance, the latter term appears quite similar to the Pulay force (Ref. 51) that corrects the Hellmann-Feynman force when the basis functions used to describe the quantum system vary with, e.g., nuclear postion. A difference between the adiabatic and nonadiabatic cases, however, is that this nonadiabatic "Pulay-type" term comes from changes in the adiabatic expansion coefficients rather than from changes in the basis. Unlike the Pulay force, therefore, the time dependence of the CI expansion coefficients is physically meaningful, and does not vanish in the limit that the basis set (here |nm〉±) is complete.
-
-
-
-
69
-
-
0242385975
-
-
note
-
i〉) = 0, applying the product rule for derivatives and integrating by parts once.
-
-
-
-
70
-
-
0242323120
-
-
edited by H. F. Schaefer III (Plenum, New York)
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P. Pulay, in Applications of Electronic Structure Theory, edited by H. F. Schaefer III (Plenum, New York, 1977); M. Di Ventra and S. T. Pantelides, Phys. Rev. B 61, 16207 (2000).
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P. Pulay, in Applications of Electronic Structure Theory, edited by H. F. Schaefer III (Plenum, New York, 1977); M. Di Ventra and S. T. Pantelides, Phys. Rev. B 61, 16207 (2000).
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Di Ventra, M.1
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0242354482
-
-
note
-
One difference between the usual single-electron force and that for our CI case is that the CI expansion coefficients change in time. This change gives rise to a correction to the HF force, the Pulay force, Ref. 51, whenever a finite CI basis set is used (as will always be the case in practice). The specific form of the Pulay force for CI wave functions is straightfor-ward, though tedious, to derive using first-order perturbation theory and the approach of Di Ventra and Pantelides (Ref. 51). We have examined the Pulay force for the hydrated dielectron system discussed in Sec. IV and found it to be negligible in comparison to the HF forces themselves, so we do not bother to explicitly display it here.
-
-
-
-
73
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0000577528
-
-
C. C. Huang, G. S. Couch, E. F. Pettersen, and T. E. Ferrin, in Proceedings of the Pacific Symposium on Biocomputing, 1996, Vol. 1, p. 724. The CHIMERA code is freely available on the worldwide web at http://www.cgl.ucsf.edu/chimera
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