tcal: Program for the calculation of transfer integral

Requirements

• Python 3.7 or newer
• NumPy
• Gaussian 09 or 16

Important notice

• The two monomers must be the same molecule.
• The path of the Gaussian must be set.

Options

Short	Long	Explanation
-a	--apta	Perform atomic pair transfer analysis.
-c	--cube	Generate cube files.
-g	--g09	Use Gaussian 09. (default is Gaussian 16)
-h	--help	Show options description.
-l	--lumo	Perform atomic pair transfer analysis of LUMO.
-m	--matrix	Print MO coefficients, overlap matrix and Fock matrix.
-o	--output	Output csv file on the result of apta.
-r	--read	Read log files without executing Gaussian.
-x	--xyz	Convert xyz file to gjf file.

How to use

1. Create gjf file

First of all, create a gaussian input file as follows:
ex: xxx.gjf

The xxx part is an arbitrary string.

Description of link commands

pop=full: Required to output coefficients of basis functions, overlap matrix, and Fock matrix.
iop(3/33=4,5/33=3): Required to output coefficients of basis functions, overlap matrix, and Fock matrix.

How to create a gjf using Mercury

1. Open cif file in Mercury.
2. Display the dimer you want to calculate.
   
3. Save in mol file or mol2 file.
4. Open a mol file or mol2 file in GaussView and save it in gjf format.

2. Execute tcal.py

Suppose the directory structure is as follows.

yyy
├── tcal.py
└── xxx.gjf

1. Open a terminal.
2. Go to the directory where the files is located.

cd yyy

3. Execute the following command.

python tcal.py -a xxx.gjf

3. Visualization of molecular orbitals

1. Execute the following command.

python tcal.py -cr xxx.gjf

2. Open xxx.fchk in GaussView.
3. [Results] → [Surfaces/Contours...]
   
4. [Cube Actions] → [Load Cube]
5. Open xxx_m1_HOMO.cube and xxx_m2_HOMO.cube.
   
6. Visualize by operating [Surface Actions] → [New Surface].
   
   

Interatomic transfer integral

For calculating the transfer integral between molecule A and molecule B, DFT calculations were performed for monomer A, monomer B, and the dimer AB. The monomer molecular orbitals $\ket{A}$ and $\ket{B}$ were obtained from the monomer calculations. Fock matrix F and overlap matrix S were calculated in the dimer system. Finally the intermolecular transfer integral $t^{[1]}$ was calculated by using the following equation:

$$t = \frac{\braket{A|F|B} - \frac{1}{2} (\epsilon_{A}+\epsilon_{B})\braket{A|S|B}}{1 - \braket{A|S|B}^2},$$

where $\epsilon_A \equiv \braket{A|F|A}$ and $\epsilon_B \equiv \braket{B|F|B}$.

In addition to the intermolecular transfer integral in general use, we developed an interatomic transfer integral for further analysis $^{[2]}$. By grouping the basis functions $\ket{i}$ and $\ket{j}$ for each atom, the molecular orbitals can be expressed as

$$\ket{A} = \sum^A_{\alpha} \sum^{\alpha}_i a_i \ket{i},$$

$$\ket{B} = \sum^B_{\beta} \sum^{\beta}_j b_j \ket{j},$$

where $\alpha$ and $\beta$ are the indices of atoms, $i$ and $j$ are indices of basis functions, and $a_i$ and $b_j$ are the coefficients of basis functions. Substituting this formula into aforementioned equation gives

$$t = \sum^A_{\alpha} \sum^B_{\beta} \sum^{\alpha}_i \sum^{\beta}_j a^*_i b_j \frac{\braket{i|F|j} - \frac{1}{2} (\epsilon_A + \epsilon_B) \braket{i|S|j}}{1 - \braket{A|S|B}^2}$$

Here we define the interatomic transfer integral $u_{\alpha\beta}$ as:

$$u_{\alpha \beta} \equiv \sum^{\alpha}_i \sum^{\beta}_j a^*_i b_j \frac{\braket{i|F|j} - \frac{1}{2} (\epsilon_A + \epsilon_B) \braket{i|S|j}}{1 - \braket{A|S|B}^2}$$

References

[1] Veaceslav Coropceanu et al., Charge Transport in Organic Semiconductors, Chem. Rev. 2007, 107, 926-952.
[2] Satoru Inoue et al., Regioisomeric control of layered crystallinity in solution-processable organic semiconductors, Chem. Sci. 2020, 11, 12493-12505.

Example of using tcal

1. Satoru Inoue et al., Regioisomeric control of layered crystallinity in solution-processable organic semiconductors, Chem. Sci. 2020, 11, 12493-12505.
2. Toshiki Higashino et al., Architecting Layered Crystalline Organic Semiconductors Based on Unsymmetric π-Extended Thienoacenes, Chem. Mater. 2021, 33, 18, 7379–7385.

Authors

Matsui Laboratory, Research Center for Organic Electronics (ROEL), Yamagata University
Hiroyuki Matsui, Koki Ozawa
Email: h-matsui[at]yz.yamagata-u.ac.jp
Please replace [at] with @

Acknowledgements

This work was supported by JST, CREST, Grand Number JPMJCR18J2.