# ROOT=n

In a configuration interaction calculation, a specific state can be requested by specifying the state name and the quantum number of that state.  The lowest state of each type has the quantum number 1, the next is 2 and so on.  To see the quantum numbers and state names, run a 1SCF calculation for the desired configuration interaction.  The normal way to define the C.I. is to use the keywords C.I.=n. and MECI (to print out the state information). Two ways of defining the desired state are provided: ROOT=n, where n is an integer, and ROOT=n<text>, where n is an integer and <text> is a text string.

ROOT=n

The n'th root of a C.I. calculation is to be used in the calculation. If a keyword specifying the spin-state is also present, e.g. SINGLET or TRIPLET, then the n'th root of that state will be selected. Thus ROOT=3 and SINGLET will select the third singlet root. If ROOT=3 is used on its own, then the third root will be used, regardless of the states' name.  This might be a triplet, the third singlet, or the second singlet (the second root might be a triplet). If the state selected is degenerate, all components of that state will be selected.

ROOT=n<text>

The n'th root of a C.I. calculation that has the symmetry <text> is to be used in the calculation.  If a keyword specifying the spin-state is also present, e.g. SINGLET or TRIPLET, then the n'th root of that state that has the symmetry <text> will be selected. Thus, in an octahedral system, ROOT=3T2g and SINGLET will select the third singlet T2g root. If ROOT=3T2g is used without any spin-state being specified, then the third T2g root will be used, regardless of spin. If the state selected is degenerate, all components of that state will be selected.

See also C.I.=n .

To see how these different forms behave, consider the following states of a d6 transition metal complex:
 STATE Q.N. Spin Symmetry 1 1 TRIPLET T2g 4 1 SINGLET A1g 5 1 SINGLET T2g 8 1 TRIPLET T1g 11 1 QUINTET T1g 14 1 SEPTET A1g 15 1 QUINTET T2g 18 2 TRIPLET T1g 21 3 TRIPLET T1g 24 2 SINGLET T2g 27 2 TRIPLET T2g 30 1 TRIPLET A2g 31 1 SINGLET T1g 34 3 TRIPLET T2g 37 4 TRIPLET T1g 40 1 TRIPLET Eg 42 2 SINGLET T1g 45 1 SINGLET Eg 47 1 QUINTET Eg

ROOT=14 would select the 14th state, the 17A1g state. No spin being specified, ROOT applies to the STATE column.

ROOT=7 and QUINTET would select the 47th and 48th states, the 15Eg  state. This is the 7th quintet state, the states 1-6 being T1g, T1g, T1g, T2g, T2g, and T2g. That these states are degenerate is not important, because ROOT=n specifies the n'th state, without regard to symmetry.

ROOT=2T2g and TRIPLET would select the 27th, 28th, and 29th states, the 23T2g state. This is the preferred method of specifying states. When ROOT=n<text> is used then the state specified will not change if the state moves up or down the list of states. If the system has no symmetry, ROOT=nA can be used.

When a geometry is to be optimized, symmetry should be used, if present.  This is particularly important in octahedral transition metal complexes. If the state has orbital degeneracy, e.g. if it is of type E, T, G, or H, then Jahn-Teller effects might cause a loss of symmetry. High symmetry is automatically detected, so, if present, it will be conserved. However, during a normal unconstrained geometry optimization, minor excursions from high symmetry are allowed, and these might confuse the high-symmetry detector.  To prevent this, use symmetry.  In the case of a simple octahedral complex, MX6, the data set might look like this:

ROOT=1T2g QUINTET  OPEN(5,5) MECI  SYMMETRY
Generic octahedral complex

M 0.0 0   0 0   0 0 0 0 0
X 2.0 1   0 0   0 0 1 0 0
X 2.0 0  90 0   0 0 1 2 0
X 2.0 0  90 0  90 0 1 2 3
X 2.0 0  90 0 180 0 1 2 3
X 2.0 0  90 0 -90 0 1 2 3
X 2.0 0 180 0   0 0 1 2 3

2 1 3 4 5 6 7