Electronic circular dichroism (ECD) and electronic absorption calculations

The calculation of Electronic Circular Dichroism (ECD) is invoked by the keyword .ECD in the ABACUS input module. However, it is also necessary to specify the number of electronic excitations in each symmetry. As ECD only is observed for chiral molecules, such calculations will in general not employ any symmetry, a complete input for a molecule without symmetry will thus look like:

**DALTON INPUT
.RUN PROPERTIES
**WAVE FUNCTIONS
.HF
**PROPERTIES
.ECD
*EXCITA
.NEXCIT
    3
**END OF DALTON INPUT

In this run we will calculate the rotatory strength corresponding to the three lowest electronic excitations (the .NEXCIT keyword) using London atomic orbitals. If rotatory strengths obtained without London atomic orbitals is also wanted, this is easily accomplished by adding the keyword .ROTVEL in the *EXCITA input module.

There are only a few studies of Electronic Circular Dichroism using London atomic orbitals [79,85], and the results of these investigation indicate that the aug-cc-pVDZ or the d-aug-cc-pVDZ basis set, which is supplied with the DALTON basis set library, is reasonable for such calculations, the double augmentation being important in the case of diffuse/Rydberg-like excited states.

Another property that may often be of interest is the oscillatory strength. This property can be calculated by an input similar to the one for ECD calculation, and for a molecule with C$_{2v}$ symmetry an input would look like:

**DALTON INPUT
.RUN PROPERTIES
**WAVE FUNCTIONS
.HF
**PROPERTIES
.EXCITA
*EXCITA
.DIPSTR
.NEXCIT
    3    2    1    0
**END OF DALTON INPUT

This input will calculate the dipole strength ( .DIPSTR) of the 6 lowest electronic excitations distributed in a total of 4 irreducible representations (as in C$_{2v}$). The dipole strength will be calculated both in length and velocity forms. It is expected that the same requirements for basis set quality applies to this property as for ECD.

For a SOPPA or SOPPA(CCSD) calculation of the oscillator strength the additional keywords .SOPPA or .SOPPA(CCSD) have to be specified in the **PROPERTIES input module. For SOPPA an MP2 calculation has to be requested by the keyword .MP2 in the **WAVE FUNCTIONS input module, whereas for SOPPA(CCSD) a CCSD calculation has to be requested by the keyword .CC in the **WAVE FUNCTIONS input module with the *CC INPUT option .SOPPA(CCSD).

The two properties may of course be combined in a single run with an input that would then look like (where we also request the rotatory strength to be calculated without the use of London orbitals):

**DALTON INPUT
.RUN PROPERITES
**WAVE FUNCTIONS
.HF
**PROPERTIES
.ECD
.EXCITA
*EXCITA
.DIPSTR
.ROTVEL
.NEXCIT
    3
**END OF DALTON INPUT

We also note that excitation energies also can be obtained using the RESPONSE program (see Chapter 12). For a more detailed control of the individual parts of the calculation of properties related to electronic excitation energies, we refer to the input modules affecting the different parts of such calculations:

*EXCITA

Controls the calculation of electronic excitation energies and the evaluation of all terms contributing to for instance dipole strength or electronic circular dichroism.

*GETSGY

Controls the setup of the necessary right-hand sides.