For atoms, the arrangement of valence electrons on the periodic table of elements is the ground state, and electrons are excited from the lower energy orbit to the higher energy orbit, which is the excited state. The energy absorbed in this process is called excitation energy. There are two forms of excitation for molecules in the ground state which are adiabatic excitation energy and vertical excitation energy. The transition dipole moment or transition moment, usually denoted for a transition between an initial stat and a final state, is the electric dipole moment associated with the transition between the two states. In general, the transition dipole moment is a complex vector quantity that includes the phase factors associated with the two states.

### Excitation energy calculation

Vertical excitation energy and adiabatic excitation energy are two common forms of excitation energy. At Alfa Chemistry, we generally study the calculation of excitation energy in the following four transition modes using time-dependent density functional theory (TDDFT) methods:

- Vertical absorption

The electron absorbs photons from the ground state and is excited to the excited state, and the structure maintains the minimal point structure of the ground state.

The calculation of vertical absorption energy consists of the following two steps:

1. Optimize the ground state geometry.

2. Calculate the excitation energy from the ground state to the excited state on the basis of the optimized structure.

- Vertical emission

The electrons emit photons from the excited state and de-excited to the ground state, and the structure maintains the minimal point structure of the excited state.

The calculation of vertical emission energy includes the following two steps:

1. Optimize the geometric structure of the excited state using the structure of the ground state with the minimum energy.

2. Calculate the excitation energy from the ground state to the excited state on the basis of the optimized structure, which is the energy emitted vertically from the excited state to the ground state.

- Adiabatic absorption

The electron is excited from the ground state to the excited state, and the structure also changes from the ground state with the minimum energy to the excited state with the minimum energy.

The calculation of adiabatic absorption energy consists of the following three steps:

1. Optimize the geometric structure of the ground state, and obtain the ground state with the minimum energy in the last step.

2. Optimize the geometric structure of the excited state, and obtain the excited state with the minimum energy in the last step.

3. Calculate the difference between the energy obtained in the second step and the energy obtained in the first step.

- Adiabatic emission

The adiabatic emission process is the reverse process of adiabatic absorption, and the transition energy is the same.

Figure 1. Energy level diagram of S0 f S1 electronic excitation (oscillator strength of 0.7445) of the R6G molecule calculated at the TD-B3LYP/6-311++G(*d*,*p*) level. The corresponding frontier Kohn-Sham orbitals (φ117, φ118, φ119, φ121, and φ121) of the R6G ground state are depicted. (Watanabe, H.; *et al*. 2005)

### Transition Dipole Moment (TDM) Calculation

- Process

Step 1: Optimize the ground state structure and frequency.

Step 2: Calculate the excited state

Step 3: Find the excited state that needs to be calculated from the step 2, and further optimize the structure and frequency.

Step 4: Find the last dipole moment from the result of the step 1, and the corresponding value is used as the ground state dipole moment.

Step 5: Find the last dipole moment from the result of step 3, and the corresponding value is used as the excited state dipole moment.

Step 6: Find the ground to excited state transition electric dipole moments from the result of step 3.

Step 7: The value corresponding to the excited state in the step 3 is used as the transition dipole moment.

*Ab initio*method

1. We introduce our *ab initio* potentials for the excited states which can be used to identify the complex behavior of the transition dipole moment.

2. *Ab initio* potential energy curves have been calculated using the multi-reference configuration interaction method with large active space and basis sets.

- Density functional theory (DFT)

1. We use hybrid configuration interactions (CIS)-DFT method to study excited states structure under external electric field.

2. Our teams can also apply time-dependent Hartree-Fock calculations (TDHF) to calculate the transition probability and energy of the ground state to the excited state.

3. Alfa Chemistry supports the application of TDDFT to obtain the transition dipole moment and rotation strength.

4. We are capable of performing TDA-DFT to calculate the transition dipole moment from the ground state to the excited state.

Figure 2. DFT optimized molecular structure, calculated relative magnitude and orientation of permanent dipole moment μ (blue arrows) for all phosphorescent emitter molecules investigated here. All dipole moments originate at the center of charge. (Graf, A.; *et al*. 2014)

### Our Advantages

- Our groups apply the obtained transition dipole moment data to calculate the (super) polarizability using sum-over-states (SOS) method.
- At Alfa Chemistry, we can also use transient absorption spectroscopy to calculate the absorption spectrum from excited state to excited state.

Excitation energy and transition dipole moment calculation provides an effective way to optimize the chemical process. Our excitation energy and transition dipole moment calculation services remarkably reduce the cost, promote further experiments, and enhance the understanding of chemical process for customers worldwide. Our personalized and all-around services will satisfy your innovative study demands. If you are interested in our services, please don't hesitate to contact us. We are glad to cooperate with you and witness your success!

References

- Watanabe, H.;
*et al*. DFT vibrational calculations of rhodamine 6G adsorbed on silver: analysis of tip-enhanced Raman spectroscopy.*Journal of Physical Chemistry B*. 2005, 109(11): 5012-5020. - Graf, A.;
*et al*. Correlating the transition dipole moment orientation of phosphorescent emitter molecules in OLEDs with basic material properties.*Journal of Materials Chemistry C*. 2014, 2(48): 10298-10304.