Vertical Excitation and CD Spectra

The calculation of excited states within the TDHF(RPA)/TDDFT approach is enabled by

$scfinstab rpas

for closed-shell singlet excitations,

$scfinstab rpat

for closed-shell triplet excitations, and

$scfinstab urpa

for excitations out of spin-unrestricted reference states.

If it is intended to use the TDA instead, specify

$scfinstab ciss

for closed-shell singlet excitations,

$scfinstab cist

for closed-shell triplet excitations, and

$scfinstab ucis

for excitations out of spin-unrestricted reference states.

Next, the IRREPs of the excitations need to be defined, which is again accomplished using $soes. For example, to calculate the 17 lowest excitations in IRREP b1g, the 23 lowest excitations in IRREP eu, and all excitations in IRREP t2g, use

$soes
b1g  17
eu   23
t2g  all

and run ESCF.

Note that $soes specifies the IRREP of the excitation vector which is not necessarily identical to the IRREP of the excited state(s) involved. In general, the IRREP(s) of the excitation(s) from the ground to an excited state is given by the direct product of the IRREPs of the tow states. For example, to calculate the first $A_2$ mathend000# state in a $C_{2v}$ mathend000#-symmetric molecule with a $B_2$ mathend000# (open-shell) ground state, it is necessary to specify

$soes
b1   1

The number of excitations that have to be calculated in order to cover a certain spectral range is often difficult to determine in advance. The total number of excitations within each IRREP as provided by the DEFINE ex menu may give some hint. A good strategy is to start with a smaller number of excitations and, if necessary, perform a second ESCF run on a larger number of states using the already converged excitation vectors as input.

To compute absorption and CD spectra, it is often sufficient to include optically allowed transitions only. This leads to substantial reduction of computational effort for molecules with higher symmetry. For example, in the UV-VIS spectrum of an $O_h$ mathend000# symmetric molecule, only $t_{1u}$ mathend000# excitations are optically allowed. The IRREPs of the electric and magnetic dipole moments as well as of the electric quadrupole moment are displayed automatically in the DEFINE ex menu.

If a large number of states is to be calculated, it is highly recommended to provide extra memory by specifying

$rpacor m

the integer m being the core memory size in megabytes (default is 20). The larger m, the more vectors can be processed simultaneously without re-calculation of integrals. As a rule of thumb, m should be ca. 90% of the available main memory. If RI-$J$ mathend000# is used ($ridft), it is recommended to set $ricore to a small value and $rpacor to a large value if the number of states is large, and vice versa if it is small.

By specifying

$spectrum unit

        and/or

$cdspectrum unit

        

a list of excitation energies and oscillator and/or rotatory strengths of the optically allowed transitions is written onto file spectrum and/or cdspectrum. As above, unit specifies the energy unit and may be ev, nm, 1/cm, or a.u. (default). The files spectrum and cdspectrum may conveniently be used for further processing, e.g., using a plotting program such as Gnuplot.