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While CIS excitation energies are relatively inaccurate, with errors of the
order of 1 eV, CIS excited state properties, such as structures and
frequencies, are much more useful. This is very similar to the manner in
which ground state Hartree-Fock (HF) structures and frequencies are much
more accurate than HF relative energies. Generally speaking, for low-lying
excited states, it is expected that CIS vibrational frequencies will be
systematically 10% higher or so relative to
experiment.^{903, 1121, 303} If the excited states are of
pure valence character, then basis set requirements are generally similar to
the ground state. Excited states with partial Rydberg character require the
addition of one or preferably two sets of diffuse functions.

Q-Chem includes efficient analytical first and second derivatives of the CIS
energy,^{641, 642} to yield analytical gradients, excited
state vibrational frequencies, force constants, polarizabilities, and infrared
intensities. Analytical gradients can be evaluated for any job where the CIS
excitation energy calculation itself is feasible, so that efficient
excited-state geometry optimizations and vibrational frequency calculations are
possible at the CIS level. In such cases, it is necessary to specify on which
Born-Oppenheimer potential energy surface the optimization should proceed, and
care must be taken to ensure that the optimization remains on the excited state
of interest, as state crossings may occur. (A “state-tracking” algorithm, as
discussed in Section 9.7.5, can aid with this.)

Sometimes it is precisely the crossings between Born-Oppenheimer potential
energy surfaces (*i.e.*, conical intersections) that are of interest, as these
intersections provide pathways for non-adiabatic transitions between electronic
states.^{638, 377} A feature of Q-Chem that is not
otherwise widely available in an analytic implementation (for both CIS and
TDDFT) of the non-adiabatic couplings that define the topology around conical
intersections.^{252, 1100, 1101, 717} Due to the
analytic implementation, these couplings can be evaluated at a cost that is not
significantly greater than the cost of a CIS or TDDFT analytic gradient
calculation, and the availability of these couplings allows for much more
efficient optimization of minimum-energy crossing points along seams of conical
intersection, as compared to when only analytic gradients are
available.^{1100} These features, including a brief overview of the
theory of conical intersections, can be found in
Section 9.7.1.

For CIS vibrational frequencies, a semi-direct algorithm similar to that used
for ground-state Hartree-Fock frequencies is available, whose computer time
scales as approximately $\mathcal{O}({N}^{3})$ for large molecules.^{640}
The main complication associated with analytical CIS frequency calculations is
ensuring that Q-Chem has sufficient memory to perform the calculations.
Default settings are adequate for many purposes but if a large calculation
fails due to a memory limitation, then the following additional information may
be useful.

The memory requirements for CIS (and HF) analytic frequencies primarily come from dynamic memory, defined as

dynamic memory = MEM_TOTAL $-$ MEM_STATIC .

This quantity must be large enough to contain several arrays whose size is $3{N}_{\mathrm{atoms}}{N}_{\mathrm{basis}}^{2}$. Meanwhile the value of the *$rem* variable
MEM_STATIC, which obviously reduces the available dynamic memory,
must be sufficiently large to permit integral evaluation, else the job may
fail. For most purposes, setting MEM_STATIC to about 80 MB is
sufficient, and by default MEM_TOTAL is set to a larger value that
what is available on most computers, so that the user need not guess or
experiment about an appropriate value of MEM_TOTAL for low-memory
jobs. However, a memory allocation error will occur if the calculation demands
more memory than available.

Note: Unlike Q-Chem’s MP2 frequency code, the analytic CIS second derivative code currently does not support frozen core or virtual orbitals. These approximations do not lead to large savings at the CIS level, as all computationally-expensive steps are performed in the atomic orbital basis.

$molecule 0 1 C O 1 CO H 1 CH 2 A H 1 CH 2 A 3 D CO = 1.2 CH = 1.0 A = 120.0 D = 150.0 $end $rem JOBTYPE = opt EXCHANGE = hf BASIS = 6-31+G* CIS_STATE_DERIV = 1 Optimize state 1 CIS_N_ROOTS = 3 Do 3 states CIS_SINGLETS = true Do do singlets CIS_TRIPLETS = false Don’t do Triplets $end @@@ $molecule read $end $rem JOBTYPE = freq EXCHANGE = hf BASIS = 6-31+G* CIS_STATE_DERIV = 1 Focus on state 1 CIS_N_ROOTS = 3 Do 3 states CIS_SINGLETS = true Do do singlets CIS_TRIPLETS = false Don’t do Triplets $end