No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Gauge invariance, current conservation, and GIAO's
1.See, for example, W. Pauli, Rev. Mod. Phys. 13, 203 (1941).
2.GIAO’s were first introduced by F. London, J. Phys. Rad. 8, 307 (1937).
2.The recent paper by R. Ditchfield, J. Chem. Phys. 56, 5688 (1972), contains an extensive bibliography.
3.J. O. Hirschfelder, J. Chem. Phys. 33, 1762 (1960).
4.One can of course consider more general unitary transformations. For example, at the other extreme, with Λ an arbitrary function of all coordinates, one is led to and hence where J is the N‐electron current.
5.S. T. Epstein and J. O. Hirschfelder, Phys. Rev. 123, 1495 (1961).
6.S. T. Epstein, J. Chem. Phys. 42, 2896 (1965).
7.One uses the same set of trial functions‐the set of all Slater determinants‐in any gauge, and this set is invariant to all gauge transformations (see Ref. 6).
8.Our statement of course refers to total current. The individual orbital currents are not in general conserved.
9.The work reported in this section stems in part from a conversation with Professor R. McWeeny in which he raised the question of current conservation in variational calculations.
10.Strictly speaking, these symmetry restrictions on and are irrelevant for the questions we are considering. Also irrelevant is the question whether or not α, and are determined variationally, so we will treat them as given.
11.R. McWeeny, Chem. Phys. Lett. 9, 341 (1971), has discussed some aspects of the question of invariance to choice of coordinates (rotating or translating the coordinate system of course also involves unitary transformations). We will not enter into a discussion of such matters here except to note that similar considerations apply as in the case of gauge invariance.
12.As derived in Ref. 5 these conditions are only sufficient conditions. However, in practice they, and others like them, seem usually to be necessary unless symmetry and reality considerations intervene.
13.A. C. Hurley, Proc. Roy. Soc. A226, 179 (1954).
14.They might therefore be better called gauge variant atomic orbitals.
15.Unless the set of atomic orbitals is essentially complete, but in such a case the use of the gauge factors become irrelevant anyway.
16.That is, with the gauge origin at the center, the eigenfunctions of the one electron problem are unchanged through first order in B (more precisely they are the zero field eigenfunctions whose orbital angular momenta are quantized along B).
17.For the purpose of invariance of the set, it would already suffice to use with ϱ as a variational parameter.
18.E. F. Hayes and R. G. Parr, J. Chem. Phys. 43, 1831 (1961).
19.S. T. Epstein, J. Chem. Phys. 45, 385 (1966);
19.S. T. Epstein and R. E. Johnson, J. Chem. Phys. 51, 188 (1969).
Article metrics loading...
Full text loading...
Most read this month
Most cited this month