The lanthanides comprise a group of 15 elements with atomic numbers 57 through 71 that include the following in order of atomic number (atomic symbol): lanthanum (La), cerium (Ce), praseodymium (Pr), neodymium (Nd), promethium (Pm), samarium (Sm), europium (Eu), gadolinium (Gd), terbium (Tb), dysprosium (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb), and lutetium (Lu).
The rare earths are often described as being a "light-group rare-earth element" (LREE) or "heavy-group rare-earth element" (HREE). The definition of a LREE and HREE is based on the electron configuration of each rare-earth element. The LREE are defined as lanthanum, atomic number 57 through gadolinium, atomic number 64. This is based on the fact that starting with lanthanum, which has no 4f shell electrons, clockwise spinning electrons are added for each lanthanide through gadolinium. Gadolinium has seven clockwise spinning 4f electrons, which creates a very stable, half-filled electron shell. The LREE also have in common increasing unpaired electrons, from 0 to 7. The HREE are defined as terbium, atomic number 65 through lutetium, atomic number 71, and also yttrium, atomic number 39. This is based on the fact that starting with terbium, counter-clockwise spinning electrons are added for each lanthanide through lutetium. All of the HREE therefore differ from the first eight lanthanides in that they have “paired” electrons (a clockwise and counter-clockwise spinning election). The LREE have no paired electrons. Yttrium is included in the HREE group based on its similar ionic radius and similar chemical properties. In its trivalent state, which is similar to the other REE, yttrium has an ionic radius of 90 picometers, while holmium has an ionic radius of 90.1 picometers. Scandium is also trivalent; however, its other properties are not similar enough to classify it as either a LREE or HREE.
The differences in electronic configuration are critical to the individual properties the rare-earth elements exhibit and how they interact with other elements and compounds.
The definition of LREE and HREE given above is definitive and used by the U.S. Government’s U.S. Department of the Interior-U.S. Geological Survey and the U.S. Department of Energy, including the National Laboratories. Based on electronic configuration there is no "middle-group rare-earth elements" and any such grouping should be referred to as the mid-atomic numbered rare-earth elements and should include only those elements from atomic numbers 63 to 68, inclusive. /...3