Content overview: Using traditional methods to analyze the interaction between chemical systems and external fields has the disadvantages of low efficiency and high cost. Jiang Bin's research group at the University of Science and Technology of China introduced field correlation features into the description of the atomic environment, developed FIREANN, and used machine learning to describe the field correlation of the system well.
Keywords: Chemical Physics Molecular Dynamics External Field
Author | Xuecai
Editor | Li Baozhu
The interaction between chemical systems and external fields is crucial in physical, chemical and biological processes. External fields, mainly electric fields, can interact with atoms, molecules and condensed matter, causing electron or spin polarization, or changing the spatial orientation of the system.
Density functional theory (DFT) and ab initio molecular dynamics (AIMD) have been used to study complex periodic and nonperiodic systems under applied electric fields. However, the application of AIMD is very demanding especially in systems where nuclear quantum effects (NQEs) are important.
Empirical force field analysis is efficient but has limited accuracy, while accurate field-dependent quantum scattering calculations are only suitable for very small systems.
Meanwhile,machine learning (ML) has achieved impressive results in solving high-dimensional chemical problems. However, most machine learning models treat the potential energy and the system's response to the electric field separately, ignoring the field dependence of the system.
To this end, Jiang Bin’s research group at the University of Science and Technology of China introduced field-related features into the description of the atomic environment and developed the Field-Induced Recursive Embedding Atomic Neural Network (FIREANN) ) . FIREANN can not only accurately describe the changing trend of system energy when the external field intensity and direction change, but can also predict the system response of any order. This result has been published in "Nature Communication".
This result has been published in "Nature Communication"
Paper link:
https://www.nature.com/articles/s41467-023-42148-y
FIREANN model link:
https://github.com/zhangylch/FIREANN
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FIREANN: REANN + pseudo-atom field vector
FIREANN is based on the REANN model, which describes the atomic environment through embedded atomic densities (EADs). When an external field is applied, the electron density will be redistributed and the rotational invariance of the system will be destroyed. The interaction between the system and the external field is obviously affected by the strength and direction of the electric field.
FIREANN'S ARCHITECTURE
FIREANN will assign each atom a pseudo-atom field vector that simulates the behavior of real atoms, and then the two are combined to obtain the field-related embedded atom density, which is used as the input of the neural network. Finally, Output physical quantities such as atomic force, dipole moment, and polarizability.
The pseudo-atom field vector of each atom can be expressed as:
Subsequently, combines field-dependent orbitals and Gaussian orbitals (GTOs) into field-induced EADs (FI-EAD) vectors:
Here, the applied field to each atom is represented by the position vector of the pseudoatom relative to that atom. FI-EAD can then be rewritten in terms of interatomic distances and closed angles:
Experimental verification
Toy Model:Accurate prediction and extrapolation of water molecules
The researchers first used water molecules as a toy model (Toy System) to verify FIREANN's prediction of system-external field interaction. There is a water molecule on the yz plane and an electric field with a strength of 0.1 V/Å in the x direction.
Since the external field and the plane of the molecule are always orthogonal, the potential energy of the molecule does not change. FIREANN accurately predicted this outcome.
Meanwhile,FIREANN accurately predicts the dipole-electric field interaction as the molecule rotates along the y-axis.
FIREANN's prediction of the influence of external electric field on water molecules on the yz surface
a: Water molecules rotate along the x-axis;
b: Water molecules rotate along the y-axis;
c: Prediction results of DFT, FIREANN and FieldSchNet when the electric field intensity changes.
FIREANN also has strong extrapolation capabilities. Using only a single training data, it can infer the molecular potential energy when the electric field intensity is -0.2-0.2 V/Å. Variety. This is something that the traditional FieldSchNet model cannot do.
NMA:Accurate prediction of IR spectra
A typical feature of FIREANN is thatit can predict the energy and response characteristics of chemical systems in the presence or absence of external fields in one step.
The researchers tested it on N-methylacetamide (NMA). When the external electric field changes between 0.0-0.4 V/Å, FIREANN can effectively predict the energy, dipole moment and polarizability of NMA molecules. The root mean square errors (RMSEs) are respectively 0.0053 eV, 0.028 Debye and 0.51 a.u.
Plot of predicted correlations between FIREANN and DFT for energy (a), dipole moment (b) and polarizability © of NMA
FIREANN also made predictions of molecular spectra within the field. The change in the C–O stretching band is most pronounced when the electric field strength is gradually increased from 0.0 to 0.4 V/Å in steps of 0.1 V/Å. As the electric field intensity increases, the P/R branch of the C-O stretching band gradually disappears and the absorption peak becomes sharper.
In addition, FIREANN predicts that an external electric field will reduce the strength of the chemical bond, causing the stretching vibration of CO to be red-shifted by a distance proportional to the electric field strength.
FIREANN prediction results of NMA under different electric fields at 300 K
Liquid water:High agreement with the periodic system
To verify the ability of the FIREANN model to predict the response of periodic systems to external electric fields, the researchers conducted tests in liquid water. Unlike molecular systems, the polarization intensity (dipole moment per unit volume) of a periodic system is a multi-valued quantity, resulting in the existence of multiple parallel branches, causing sudden changes in the dipole moment.
In the AIMD prediction, we can clearly see the discontinuity in the results caused by the mutation of the dipole moment. After an external electric field is applied, such mutations will be more frequent, which brings challenges to traditional machine learning algorithms.
AIMD, modified AIMD and FIREANN analysis of dipole moment of liquid water without field (a) and with field (b)
In the FIREANN framework, since the model is only trained on atomic forces in the presence of an electric field, the energy gradient of the system is not actually affected, so this problem can be easily bypassed.
To this end, the researchers constructed a model containing 64 water molecules, an electric field strength of 0.6 V/Å in the x direction, and atomic forces as the only prediction object, called FIREANN-wF. The model's predictions of atomic forces are highly consistent with experiments, with a root mean square error of only 39.4 meV/Å.
FIREANN-wF's predictions of field-free radial distribution functions (RDFs) of liquid water are also in good agreement with DFT and experimental results.
FIREANN predictions of radial distribution functions for O-O (a), O-H (b) and H-H ©, and comparison with experimental results
The dipole moment has an important influence on the IR spectrum. Since the FIREANN-wF model analyzes nuclear quantum effects,it can correctly predict the potential energy surface (PES) and dipole moment surface, which is consistent with the results of DFT< a i=2>.
Subsequently, FIREANN-wF was used to predict the IR spectrum after adding 0.4 V/Å. As the electric field reduces the strength of the O-H bond and simultaneously induces the reorientation of water molecules parallel to the electric field, there is a clear red shift in the O-H stretching band in the spectrum.
FIREANN's spectral predictions of liquid water without field (a) and with field (b) and comparison with experimental results
Comparison REANN:Extrapolation ability and high-speed training
Although there have been previous models similar to FIREANN-wF in training methods, they process external fields in completely different ways. As a result, these models cannot predict high-order interactions. .
In FIREANN, after introducing field-related atomic orbitals, the model can capture the response of electron density to external fields through the interaction between orbitals.
The difference between FIREANN and FieldSchNet in water molecules has been compared before, and this difference still exists in periodic systems.
The researchers established a test system using water molecules and an electric field in the x direction. The prediction root mean square errors of FIREANN and FieldSchNet are 54.5 meV/Å and 245.4 meV/Å, respectively. Similar to previous results, FIREANN can extrapolate predictions to ±2 V/Å, whereas FieldSchNet does notthis capability.
Extrapolation results of liquid water system energy when electric field changes by DFT, FIREANN and FieldSchNet
In terms of training time, on the A100 with a single video memory of 80 GB, FieldSchNet's single epoch is 7.6 minutes, while FIREANN only takes 2.4 minutes.
Molecular-Field Interactions: A Remote Control for Microscopic Systems
The interaction between chemical systems and external fields provides a window for people to study microscopic systems and provides a powerful tool for the manipulation of microscopic systems. By regulating the external electric field, we can change the chemical structure of substances, promote electron transfer, control phase transitions of substances and conformational changes of biomolecules, adjust the selectivity of catalysts, and even affect the quantum dynamics of cold chemical reactions.
Applying an electric field between the tip of a scanning tunneling microscope and the metal surface can reversibly trans-cis isomerize the azobenzene derivatives on the metal surface.
Trans-cis isomerization of gold(111) surface azobenzene
Likewise, changing the orientation of the electric field can change the mixing patterns of molecules at the nanometer scale.
Mixing modes of 1,3,5-tris(4-carboxyphenyl)benzene and trimosilicic acid at different voltages
It can be said that the interaction between molecules and external fields is the remote control of microscopic systems. Understanding this interaction is of great significance for scientific research at the microscale. FIREANN can accurately analyze the interaction between periodic and non-periodic systems and external fields, and predict the system response of any order, providing a new method for microscopic research.
Reference links:
[1]https://pubs.acs.org/doi/full/10.1021/ja065449s
[2]https://pubs.acs.org/doi/full/10.1021/acsnano.7b04610
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