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(June 30, 2021)

Analysis of the leading wave function amplitudes is always necessary for
determining the character of the state (*e.g.*, $\mathrm{HOMO}\to \mathrm{LUMO}$
excitation, open-shell diradical, *etc.*). The CCMAN module print out leading
EOM/CI amplitudes using its internal orbital numbering scheme, which is
printed in the beginning. The typical CCMAN EOM-CCSD output looks like:

Root 1 Conv-d yes Tot Ene= -113.722767530 hartree (Ex Ene 7.9548 eV), U1^2=0.858795, U2^2=0.141205 ||Res||=4.4E-07 Right U1: Value i -> a 0.5358 7( B2 ) B -> 17( B2 ) B 0.5358 7( B2 ) A -> 17( B2 ) A -0.2278 7( B2 ) B -> 18( B2 ) B -0.2278 7( B2 ) A -> 18( B2 ) A

This means that this state is derived by excitation from occupied orbital #7 (which has ${b}_{2}$ symmetry) to virtual orbital #17 (which is also of ${b}_{2}$ symmetry). The two leading amplitudes correspond to $\beta \to \beta $ and $\alpha \to \alpha $ excitation (the spin part is denoted by $A$ or $B$). The orbital numbering for this job is defined by the following map:

The orbitals are ordered and numbered as follows: Alpha orbitals: Number Energy Type Symmetry ANLMAN number Total number: 0 -20.613 AOCC A1 1A1 1 1 -11.367 AOCC A1 2A1 2 2 -1.324 AOCC A1 3A1 3 3 -0.944 AOCC A1 4A1 4 4 -0.600 AOCC A1 5A1 5 5 -0.720 AOCC B1 1B1 6 6 -0.473 AOCC B1 2B1 7 7 -0.473 AOCC B2 1B2 8 0 0.071 AVIRT A1 6A1 9 1 0.100 AVIRT A1 7A1 10 2 0.290 AVIRT A1 8A1 11 3 0.327 AVIRT A1 9A1 12 4 0.367 AVIRT A1 10A1 13 5 0.454 AVIRT A1 11A1 14 6 0.808 AVIRT A1 12A1 15 7 1.196 AVIRT A1 13A1 16 8 1.295 AVIRT A1 14A1 17 9 1.562 AVIRT A1 15A1 18 10 2.003 AVIRT A1 16A1 19 11 0.100 AVIRT B1 3B1 20 12 0.319 AVIRT B1 4B1 21 13 0.395 AVIRT B1 5B1 22 14 0.881 AVIRT B1 6B1 23 15 1.291 AVIRT B1 7B1 24 16 1.550 AVIRT B1 8B1 25 17 0.040 AVIRT B2 2B2 26 18 0.137 AVIRT B2 3B2 27 19 0.330 AVIRT B2 4B2 28 20 0.853 AVIRT B2 5B2 29 21 1.491 AVIRT B2 6B2 30

The first column is CCMAN’s internal numbering (*e.g.*, 7 and 17 from the
example above). This is followed by the orbital energy, orbital type (frozen,
restricted, active, occupied, virtual), and orbital symmetry. Note that the
orbitals are blocked by symmetries and then ordered by energy within each
symmetry block, (*i.e.*, first all occupied ${a}_{1}$, then all ${a}_{2}$, *etc.*), and
numbered starting from 0. The occupied and virtual orbitals are numbered
separately, and frozen orbitals are excluded from CCMAN numbering. The two
last columns give numbering in terms of the final ANLMAN printout (starting
from 1), *e.g.*, our occupied orbital #7 will be numbered as 1${B}_{2}$ in the
final printout. The last column gives the absolute orbital number (all
occupied and all virtuals together, starting from 1), which is often used by
external visualization routines.

CCMAN2 numbers orbitals by their energy within each irrep keeping the same numbering for occupied and virtual orbitals. This numbering is exactly the same as in the final printout of the SCF wave function analysis. Orbital energies are printed next to the respective amplitudes. For example, a typical CCMAN2 EOM-CCSD output will look like that:

EOMEE-CCSD transition 2/A1 Total energy = -75.87450159 a.u. Excitation energy = 11.2971 eV. R1^2 = 0.9396 R2^2 = 0.0604 Res^2 = 9.51e-08 Amplitude Orbitals with energies 0.6486 1 (B2) A -> 2 (B2) A -0.5101 0.1729 0.6486 1 (B2) B -> 2 (B2) B -0.5101 0.1729 -0.1268 3 (A1) A -> 4 (A1) A -0.5863 0.0404 -0.1268 3 (A1) B -> 4 (A1) B -0.5863 0.0404

which means that for this state, the leading EOM amplitude corresponds to the transition from the first b${}_{2}$ orbital (orbital energy $-0.5101$) to the second b${}_{2}$ orbital (orbital energy 0.1729).

The most complete analysis of EOM-CC calculations is afforded by deploying a general wave-function analysis tool contained in the libwfa module and described in Section 10.2.6. The EOM-CC state analysis is activated by setting STATE_ANALYSIS = TRUE. In addition, keywords controlling calculations of state and interstate properties should be set up accordingly.

Note: Wave function analysis is only available for CCMAN2.

$molecule 0 1 He He 1 R1 He 2 R1 1 A R1 = 1.236447 A = 180.00 $end $rem METHOD = EOM-CCSD BASIS = 6-31G IP_STATES = [1,0,0,0,0,1,0,0] CC_EOM_PROP = true Analyze state properties (state OPDM) CC_STATE_TO_OPT = [1,1] Compute transition properties wrt 1st EOM state of 1st irrep CC_TRANS_PROP = true Analyze transitions (transition OPDM) STATE_ANALYSIS = true MOLDEN_FORMAT = true NTO_PAIRS = 2 $end