Appendix¶

Optimization calculation on ground state (\(S_0\))¶

After constructing the initial geometry, we have to find the optimized \(S_0\) geometry. The route section is set as #p opt b3lyp/6-31g*, which indicates an optimization calculation at B3LYP/6-31G* level.

When the calculation is completed, find the last line with “SCF Done” in the output *.log file in order to find single point energy at the optimized \(S_0\) geometry. In this example, the last line with “SCF Done” is the following:

SCF Done: E(RB3LYP) = -849.172438992 A.U.

Complete results can be found in directory examples/DSB/opt_and_frequency.

Frequency calculation at the optimized \(S_0\) geometry¶

After finding the optimized \(S_0\) geometry, we need to verify the optimization result and calculate its force constant matrix via frequency calculation. The route section is set as #p freq b3lyp/6-31g*, which runs a frequency calculation at B3LYP/6-31G* level. You have to define the location of *.chk file in Link 0 Commands as well.

Use Gaussian built-in command formchk to generate a *.fchk file based on output

*.chk. The *.fchk file contains readable force constant matrix information that is needed in evc calculation.

Complete results can be found in directory examples/DSB/opt_and_frequency.

In this example, the route section is set as #p opt freq b3lyp/6-31g*, which means we run optimization and frequency calculations at the same time. But we recommend separating them into two types of calculation in order to avoid any possible mistakes.

Transition dipole moment (absorption) at the optimized \(S_0\) geometry¶

After finding the optimized \(S_0\) geometry, we can calculate transition dipole moment (absorption) and vertical excitation energy at this geometry. The route section is set as #p td b3lyp/6-31g*, which runs a calculation at B3LYP/6-31G* level using TDDFT method.

When the calculation is completed, find the relative information about “Excited State 1” in the output *.log file in order to find vertical excitation energy and transition dipole moment (absorption) at the optimized \(S_0\) geometry. In this example, the information is listed below:

Ground to excited state transition electric dipole moments (Au):
      state          X           Y           Z       Dip. S.     Osc.
        1        -4.6693     -0.0118      0.0112     21.8029    1.7826


Excited State   1:      Singlet-A   3.3372 eV   371.52 nm   f=1.7826  <S**2>=0.000
     75 -> 76         0.70728
This state for optimization and/or second-order correction.
Total Energy, E(TD-HF/TD-KS) =  -848.655200149

Hence, vertical excitation energy at the optimized \(S_0\) geometry is 3.3372 eV, and transition dipole moment (absorption) can be obtained using Dip. S.:

Optimization calculation on lowest singlet excited state (\(S_1\))¶

With the optimized \(S_0\) geometry, we can start optimizing \(S_1\) geometry using the optimized \(S_0\) geometry as the initial structure. The route section is set as #p td opt b3lyp/6-31g*, which indicates an optimization calculation at B3LYP/6-31G* level using TDDFT method.

When the calculation is completed, find the last line with “SCF Done” in the output *.log file in order to find single point energy at the optimized \(S_0\) geometry. In this example, the last line with “SCF Done” is the following:

SCF Done:   E(RB3LYP) = -849.165742659  A.U.

Complete results can be found in directory examples/DSB/opt_and_frequency.

Frequency calculation at the optimized \(S_1\) geometry¶

After finding the optimized \(S_1\) geometry, we need to verify the optimization result and calculate its force constant matrix via frequency calculation. The route section is set as #p td freq b3lyp/6-31g*, which runs a frequency calculation at B3LYP/6-31G* level using TDDFT method. You have to define the location of *.chk file in Link 0 Commands as well.

Use Gaussian built-in command formchk to generate a *.fchk file based on output *.chk. The *.fchk file contains readable force constant matrix information that is needed in evc calculation.

Complete results can be found in directory examples/DSB/opt_and_frequency.

Transition dipole moment (emission) at the optimized \(S_1\) geometry¶

Transition dipole moment (emission) and vertical excitation energy at the optimized \(S_1\) geometry are also given when the calculation in section 7.4 is completed. Find the relative information about “Excited State 1” in the output *.log file in order to find vertical excitation energy and transition dipole moment (emission) at the optimized \(S_1\) geometry. In this example, the information is listed below:

Ground to excited state transition electric dipole moments (Au):
      state          X           Y           Z       Dip. S.     Osc.
        1        -5.3165     -0.0242      0.0000     28.2653    1.9597


Excited State   1:      Singlet-?Sym    2.8300 eV   438.11 nm   f=1.9597  <S**2>=0.000
     75 -> 76         0.71066
This state for optimization and/or second-order correction.
Total Energy, E(TD-HF/TD-KS) =  -849.061743778

Hence, vertical excitation energy at the optimized \(S_1\) geometry is 2.8300 eV, and transition dipole moment (emission) can be obtained using Dip. S.:

and transition dipole moment (absorption) can be obtained using Dip. S.:

Complete results can be found in directory examples/DSB/opt_and_frequency.

Adiabatic energy difference between \(S_0\) and \(S_1\) states¶

The adiabatic energy difference between \(S_0\) and \(S_1\) states can be calculated using single point energy results from sections 7.1 and 7.4.

In this example, the adiabatic energy difference is:

Transition electric field and NACME at the optimized \(S_1\) geometry¶

After finding the optimized \(S_1\) geometry, we can calculate transition electric field at this geometry. Then it’s possible to run a evc calculation with NACME option toggled on.

The route section is set as the following line:

#p td b3lyp/6-31g(d) prop=(fitcharge,field) iop(6/22=-4, 6/29=1, 6/30=0, 6/17=2)

When the calculation is completed, copy two output *.log files into a new directory. One is transition electric field *.log file, which is obtained in this section. The other is frequency calculation at the optimized \(S_0\) geometry *.log file, which is obtained in section 7.2. Then use get-nacme to start calculating NACME.

Complete results can be found in directory examples/DSB/nacme.