First-Principles Calculations

First-principles calculations are computational methods based on the fundamental principles of quantum mechanics. They do not require any empirical parameters, relying solely on fundamental physical constants (such as electron mass, Planck's constant, etc.) and atomic numbers. By solving the Schrödinger equation, they predict and simulate the electronic structure, as well as the physical and chemical properties of molecules or solid materials.

DFT is the most mainstream and core method within first-principles calculations. Strictly solving the Schrödinger equation for multi-electron systems is extremely difficult. DFT ingeniously transforms the complex many-body wavefunction problem into a calculation of electron density, drastically reducing the computational workload. Therefore, DFT is widely recognized as the "gold standard" for balancing computational accuracy and cost.

The core principles of the two are different. First-principles calculations (like DFT) start at the electronic level, offering extremely high accuracy, but due to computational constraints, they can typically only handle small systems of a few hundred atoms. Conventional molecular dynamics, on the other hand, relies on artificially fitted empirical force fields to simulate atomic motion without considering electronic behavior. Consequently, its accuracy is relatively lower, but it can handle large-scale systems containing tens of thousands or even millions of atoms.

Conventional Local Density Approximation (LDA) or Generalized Gradient Approximation (GGA) suffers from "self-interaction error" (where an electron erroneously repels itself), which typically leads to an underestimation of the bandgaps of semiconductors or insulators. Solutions include: introducing the Hubbard parameter via the DFT+U method, using hybrid functionals (such as HSE06 or B3LYP), or employing higher-accuracy GW approximation methods.

• VASP: Based on plane-wave basis sets and pseudopotentials, it is the absolute benchmark software for solid-state physics, surface science, and periodic material systems.

• Gaussian: Based on linear combinations of atomic orbitals, it holds a dominant position in isolated systems, small molecule catalysis, organic chemistry, and spectroscopic predictions (such as NMR and IR).

• Other open-source/commercial software: Quantum ESPRESSO (plane-wave, open-source), CP2K (suitable for large-scale systems), CASTEP, etc.

It can comprehensively predict the microscopic characteristics of materials, mainly including:

• Structural properties: Lattice constants, atomic relaxation, and defect formation energies.

• Electronic properties: Band structure, density of states (DOS), charge transfer, and work function.

• Optical and magnetic properties: Dielectric functions, absorption spectra, and magnetic moment distributions.

• Dynamic properties: Phonon spectra (to determine structural stability) and ion diffusion pathways (such as Nudged Elastic Band (NEB) calculations for battery materials).

The biggest bottleneck is that the computational cost increases sharply with the system size (typically scaling as $O(N^3)$). For conventional computing power, standard high-accuracy DFT calculations are usually limited to systems of a few hundred atoms. Although linear-scaling algorithms ($O(N)$) are developing, the computational overhead remains astronomically high for complex strongly correlated systems involving thousands of atoms.

It can "reconstruct" the entire process of a chemical reaction from the microscopic electronic level. In practical applications, it is primarily used to precisely locate the transition states (TS) of chemical reactions, calculate activation energies (to determine the difficulty of a reaction occurring), and accurately predict various spectroscopic features of molecules (such as NMR and IR spectra). This provides direct theoretical guidance for efficient catalyst design and novel drug molecule synthesis, effectively avoiding blind experimental trial and error.