Empirical physical models rely on parameters from experiments, and so induce various inaccuracies. However, a quantum mechanical model can offer independent data. Also, QM is able to predict everything theoretically. But QM has properties not easily addressed, which depends on complexities at larger length scales over heterogeneities. And, there is no universal QM method appropriate for all materials and phenomena.

Ab initio post-Hartree-Fock quantum chemistry and quantum Monte Carlo simulation are the most accurate. They make no other physical approximations and can get accurate ground and excited state properties. However, the main drawback of such methods is computational expense. Therefore, more common methods for QM modeling uses or builds upon density functional theory(DFT). It is much simpler and less costly. DFT is a formally exact ground state theory in which the material's energy is expressed as a fun of the electron density alone. The primary disadvantage of current DFT methods is the approximate XC functional. However, for most ground state properties, the generalized gradient approximation(GGA) XC functionals provide sufficient accuracy. Hybrid XC DFT-GGA techniques are developed, such as DFT+U, include some exact HF exchange, and are suitable for description of mid-to-late first row transition metal oxides and sulfides, but not appropriate for metals. TD-DFT can be used to calculate electronic or optical spectra of materials and GW method can be used to obtain ionization energies and electron affinities. BSE takes DFT and GW data as input and accounts for electron -hole interactions. With these methods in mind, we can use the appropriate method to predict a given property for a given materials class as a function of accuracy and expense.

Amorphous structures are difficult to model with QM because the usual 3D periodic boundary conditions introduce correlation length artifacts and it is certain that a random amorphous structure generated. Heterogeneous mixtures offer the most severe challenge for future materials modeling. Multiscale modeling aims to bridge length and time scales to make overarching predictions of materials behavior. Major unsolved issues in this area include how to transfer heat and mass across all scales and etc.

Now the typical simulation still starts with guidance from experiment regarding approximate initial structure and composition, but given such guidance, QM can provide sight to how properties change when composition and structure change, thereby furthering atomic-scale manipulation of material design.

Reference: Emily A. Carter, Science, 321, 800, 2008