`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 and MS=n.m.

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 1⁷A_1g state. No spin being specified, ROOT applies to the STATE column.

ROOT=7 and QUINTET would select the 47th and 48th states, the 1⁵E_g 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 2³T_2g 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