In this article, we will talk about Density Functional Theory covering the introduction, lectures, overview, and thesis. Machine learning is an increasingly popular method to search the structure and information behind data. many efforts have been made on combining ML (Machine Learning) techniques with (QM) quantum mechanics. Most articles in ML (Machine Learning), and QM (quantum mechanics) predict quantum properties from geometries, trained on the data produced by (DFT) density functional theory. using ML(Machine learning) to find density functional approximation will be a more applied physics problem.

It is essential to understand the mechanism of the ML (Machine Learning) model and how it works. In this essay, two detailed technical reports will be presented. 1st we explore KRR (kernel ridge regression) on a simple function with only one variable. All randomness is removed and the analysis is extremely thorough and careful. The basic relationship between underfitting, optimal, and overfitting regions with hyperparameters discover that ML (machine learning) a density functional shares similar characteristically behaviors with learning a simple function. The detailed explanation of ML (Machine Learning) approximation of KE of non-interacting fermions in a one-dimensional box. Several important concepts and steps of ML (machine learning) in DFT (density functional theory) are explained and tested.

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The performance of different methods and kernels of cross-validation are explored. The local PCA (principal component analysis) reconstructs the density manifold and a modified Euler-Lagrange constrained minimization of the ML (machine learning) total energy can give accurate constrained optimal densities. The development of ML (Machine learning) algorithms in DFT (Deficiency functional theory) includes 1d and 3d. In 1d, we model an interacting quantum system trained on raw fact and figure from density matrix renormalization group calculations.

A set of atomic centers was developed to represent density in 1d (1 deminstinal) by PCA and Hirshfeld partitioning. The Hohenberg-Kohn universal functions are learned bypassing the need for a Kohn-Sham scheme. This methodology approach is applied to a wide range of 1d (1 dimensional) systems, from diatomic to thermodynamic limit.

ML (machine learning) can help with data set fitting. The function is created by fitting to certain data sets it would be beneficial if ML (machine learning) is introduced. The protocol is a well-defined practice in ML (machine learning) that can be applied without controversy.

The following term can be predicted accurately using DFT (density functional theory), especially for metal alloy and composite design. Metal alloys are most important, especially for various mechanical applications. The tuning of mechanical properties is following.

- bulk modulus
- elastic
- stiffness constants

## Advantages Of Density Theory:

The most significant advantage of DFT (density functional theory) methods is a significant increase in computational accuracy without the additional increase in computing time. DFT (density functional theory) methods such as B3LYP/6-31G(d) are oftentimes considered to be a standard model pysics and chemistry for many applications.

## Conclusion

DFT (Density functional theory) is currently the most popular approach for calculating the electronic structure of molecules and extended materials. (1âˆ’3) Although DFT (density functional theory) is formally exact.

## FAQs

### What is density functional theory?

DFT (Density functional theory) is a (QM) quantum-mechanical method used in chemistry and physics to calculate the electronic structure of atoms and molecules and solids. It has been very popular in computational solid-state physics since the 1970s. ), QM (quantum mechanics) predicts quantum properties from geometries, trained on the data produced by (DFT) density functional theory. using ML(Machine learning) to find density functional approximation will be a more applied physics problem.

### What Is b3lyp Density Functional Theory?

B3LYP is a hybrid functional developed in 80s. It turns out that DFT (density functional theory) and Hartree-Fock-based methods are basically trying to do the same thing and recover electron correlation. they have different difficulties, Hartree-Fock methods exactly treat exchange-correlation but have difficulties recovering dynamic electron correlation while DFT (density functional theory) has an exact form for dynamic electron correlation but since DFT (density functional theory) is not quantum mechanical, it must approximate exchange-correlation.