9.1. BDF Example

BDF (Beijing Density Functional) is an independent and complete quantum chemistry calculation software package with complete independent intellectual property rights. It is also the first program based on modern density functional theory that can accurately calculate the total ground state energy of molecular systems with complete relativistic density functional (early similar programs could not accurately calculate total energy due to poor numerical integration accuracy).

BDF Official User Manual Website: https://bdf-manual.readthedocs.io/zh_CN/latest/index.html

BDF Development Team Information:

• International Quantum Molecular Science Academy Academician Wenjian Liu’s Research Team.

• Hongzhiwei Development Team, Service Team.

fig. 9.1 BDF Software Features Diagram

BDF Software Features:

1. High-precision relativistic methods.

2. Arbitrary point group symmetry.

3. Bottom-up self-consistent field methods.

4. Efficient orbital localization.

5. Sub-linear scaling time-dependent density functional methods.

6. Sub-linear scaling chemical shift calculation methods.

7. Spin-matched open-shell time-dependent density functional methods.

8. Ground state and excited state spin-orbit coupling calculations.

9. Ground state-excited state and excited state-excited state non-adiabatic coupling matrix elements.

10. Chemical structure and reaction path optimization.

Taking ground state molecule CH2S sf-X2C/TDDFT-SOC spin-orbit coupling calculation as an example to describe BDF application in Device Studio in detail.

9.1.1. BDF Development History

BDF development began in 1993 and was officially named in 1997. The initial idea was to perform high-precision calculations on small molecular systems such as rare earths, actinides, transition metals, and superheavy elements, examining relativistic effects in these systems, therefore initially adopting complete relativistic density functional theory (4C-DFT) based on Dirac operators and nearly complete basis functions “numerical basis + STO” (Slater-type orbital). Because of this, BDF’s calculation results for rare earths, actinides, and superheavy elements have been used as benchmarks for testing other approximate relativistic methods. BDF’s calculation results for electronic and molecular structures of heavy element systems have been verified by more than 20 subsequent experiments.

In 2009, analytical integration based on Gaussian basis was introduced, and BDF entered a new development stage.

Needless to say, BDF was initially positioned as a platform for developing new theories, new methods, and new algorithms, therefore it is a “research software”. Theories and methods developed based on BDF include: relativistic time-dependent density functional theory (4C/ZORA/X2C-TDDFT), exact two-component (X2C) relativistic theory, quasi-four-component (Q4C) relativistic theory, spin-separated X2C relativistic theory (sf-X2C+so-DKHn), many-body effective quantum electrodynamics (eQED), relativistic nuclear magnetic theory (4C/X2C-NMR), relativistic nuclear spin-rotation theory (4C-NSR), relativistic band theory (X2C-PBC), X2C analytical gradients and Hessian; excited state HF/KS methods (mom); orbital localization scheme (FLMO) based on the idea of “synthesizing molecules from molecular fragments” (F2M), sub-linear scaling time-dependent density functional theory (FLMO-TDDFT), sub-linear scaling NMR methods (FLMO-NMR), iterative orbital interaction “bottom-up” self-consistent field methods (iOI); spin-matched open-shell time-dependent density functional theory (SA-TDDFT), spin-flip time-dependent density functional theory (SF-TDDFT), ground state/excited state-excited state non-adiabatic coupling time-dependent density functional theory (NAC-TDDFT), time-dependent density functional theory analytical energy gradients, arbitrary single-value/double-value point group symmetrization, etc.

Besides the above relativistic/non-relativistic density functional and time-dependent density functional theory, BDF also has wave function electron correlation methods based on the idea of “static then dynamic then static” (SDS), including SDSPT2SDSCI, iCI, iCIPT2, iCAS, iCISCF, SOC-iCI, iCI-SOC, and the iVI method for directly solving large matrix internal eigenstates, etc.

Given BDF’s current status, the first commercial version will focus on fluorescence/phosphorescence material luminescence mechanism and material design as the main application targets, therefore it does not include 4C/X2C relativity, wave function electron correlation, solid band/nuclear magnetic methods, etc. That is, the first commercialized BDF will mainly focus on DFT and TDDFT, including ground state and excited state KS, QM/MM, FLMO-TDDFT, SF-TDDFT, NAC-TDDFT, sf-X2C-SA-TDDFT/SOC, SA-TDDFT analytical energy gradients and numerical Hessian, stable structure and transition state optimization, reaction path optimization, implicit solvation models, FLMO-NMR, based on localized orbitals (FLMO) property calculations and analysis, and other special features.

9.1.2. BDF Calculation Process

The BDF calculation process in Device Studio is shown in fig. 9.2.

fig. 9.2 BDF Calculation Process

9.1.3. Creating a BDF Project

Double-click the Device Studio icon shortcut, log in and launch Device Studio. In the create or open project interface (Graphical interface for selecting to create or open a project after starting the software), according to the interface prompts, select to create a new project ( Create a new Project ) or open an existing project ( Open an existing Project ) button, then click the OK button in the interface. If you choose to create a new project, users can name the project as needed, such as naming this project BDF, or use the software’s default project name.

9.1.4. Importing BDF Structure

In the Device Studio graphical interface, click File → Import → Import Local, which will pop up the interface for importing BDF structure files. According to the interface prompts, find the location of the CH2S.hzw structure file, select the CH2S.hzw structure file, click the Open button, and the Device Studio interface after importing the CH2S.hzw structure is shown in fig. 9.3. Other methods for importing structures in Device Studio are not explained in detail here, users can refer to the Import Structure section content.

fig. 9.3 Device Studio graphical interface after importing the CH2S.hzw structure

9.1.5. Generating BDF Input Files

In the interface shown in fig. 9.3, select Simulator → BDF → BDF, which will pop up the BDF parameter settings interface BDF Job Setup as shown in fig. 9.4.

Taking the generation of input files for ground state molecule CH2S sf-X2C/TDDFT-SOC spin-orbit coupling calculation as an example, in the BDF Job Setup interface shown in fig. 9.3, according to calculation needs, select Basic Settings, SCF Settings, TDDFT Settings and Preview Script respectively, set parameters as shown in fig. 9.4, fig. 9.5, fig. 9.6 and fig. 9.7 respectively, then click the Generate files button in the interface to generate the input file bdf.inp.

fig. 9.4 Basic Settings parameter settings interface

fig. 9.5 SCF Settings parameter settings interface

fig. 9.6 TDDFT Settings parameter settings interface

fig. 9.7 Preview Script parameter settings interface

The Device Studio interface for generating the input file bdf.inp for ground state molecule CH2S sf-X2C/TDDFT-SOC spin-orbit coupling calculation is shown in fig. 9.8.

fig. 9.8 Device Studio interface for generating input files for ground state molecule CH2S sf-X2C/TDDFT-SOC spin-orbit coupling calculation

9.1.6. BDF Calculation

Before performing the ground state molecule CH2S sf-X2C/TDDFT-SOC spin-orbit coupling calculation, you need to connect to a server with BDF installed. The specific connection process is not explained in detail here, users can refer to the Nanodcal Connect to Server section content. After connecting to the server with BDF installed, before performing the calculation, users can open the input file and check if the parameter settings in the file are reasonable according to their needs. If not reasonable, they can choose to edit directly in the file or regenerate, and finally perform the BDF calculation (here BDF calculation refers to ground state molecule CH2S sf-X2C/TDDFT-SOC spin-orbit coupling calculation). For example, to open the bdf.inp file, in the Device Studio’s Project Explorer area, select bdf.inp → right-click → Open with to view the bdf.inp file as shown below.

$compass
Title
  CH2S
Geometry
C 0.00000000 0.00000000 -1.03983899
S 0.00000000 0.00000000 0.59328400
H 0.00000000 0.93261200 -1.62675900
H 0.00000000 -0.93261200 -1.62675900
End Geometry
Basis
  cc-pVDZ-DK
Skeleton
Group
  C(2v)
$end

$xuanyuan
Heff
  21
Hsoc
  2
Direct
$end

$scf
RKS
Charge
  0
SpinMulti
  1
DFT
  PBE0
D3
MPEC+COSX
Molden
$end

$tddft
Imethod
  1
Isf
  0
Idiag
  1
Iroot
  6
MPEC+COSX
Istore
  1
$end

$tddft
Imethod
  1
Isf
  1
Idiag
  1
Iroot
  6
MPEC+COSX
Istore
  2
$end

$tddft
Isoc
  2
Nfiles
  2
Imatsoc
  -1
Imatrsf
  -1
Imatrso
  -1
$end

note

During actual calculations, users can refer to the BDF User Manual to understand the detailed meaning of each parameter and set them appropriately according to calculation needs. To learn more about BDF, click on the corresponding purple or blue software name, or send an email to support@hzwtech.com for consultation.

In the interface shown in fig. 9.3, in the Device Studio’s Project Explorer area, select bdf.inp → right-click → Run, which will pop up the Run interface. In the Run interface, click the Run button to perform the BDF calculation. Users can observe the BDF calculation status in the Job Manager area. When the BDF calculation task is in the queue, in progress, or completed, Status is Queued, Running, Finished respectively. After the calculation is completed, click the Actions button in the Job Manager area, which will pop up the Qsftp Explorer interface. In this interface, find the calculation result file, click the Download button to download the calculation result file from the server to the local, and the downloaded result file can be viewed in the Device Studio’s Project Explorer area.

9.1.7. BDF results visualization

Currently, there is no visualization analysis function for BDF calculation results in Device Studio. Users can analyze them themselves. The specific analysis process can refer to the BDF user manual. The visualization analysis function of BDF will be integrated into the Device Studio in subsequent version updates.