Marginal electron density and density-difference functions

Summary For visual analysis of the density reorganization and distortion, the one-dimensional cut (x, y₀,z₀) and the two-dimensional cut (x, y, z₀) of the three-dimensional electron density difference function (x, y, z) are frequently employed. However, these cut functions do not satisfy any sum rules in contrast to the original difference function (x, y, z). To avoid this difficulty, the use of the marginal electron density functions _x(x) and _xy(x, y) and their difference functions _x(x) and _xy(x, y) is proposed. The marginal densities are condensation of the three-dimensional density onto a particular plane or line of our interest, and they satisfy the sum rule (i.e., the conservation of the number of electrons) exactly. Some basic properties of the marginal electron density are clarified for typical diatomic molecular orbitals. An illustrative application is given for the bonding and antibonding processes in the H₂ system.