## Current Research Topics

### First-Principles Equation of State (FPEOS)

For ICF and HED applications, we have been using *ab initio* quantum molecular-dynamics (QMD) and path-integral Monte Carlo (PIMC) methods to study
the equation-of-state of materials under high pressures. Comparing the generated FPEOS tables with traditional EOS models, we can identify what
important physics is determining the EOS property of materials, in particular in the warm-dense-matter (WDM) regime. **These FPEOS studies have covered
DT [1,2], CH [3,4], Be [5], and Si [6,7] for the past several years.** Implementing these
FPEOS tables into our ICF/HED hydrocodes helps to redefine reliable 1-D target designs. We are currently improving the QMD method by implementing the
temperature dependent xc-functionals for more-accurate and mid-/high-*Z* materials. Some examples of our recent results are given:

- [1] S. X. Hu
*et al.*, Phys. Rev. Lett.**104**, 235003 (2010). - [2] S. X. Hu
*et al.*, Phys. Rev. B**84**, 224109 (2011). - [3] S. X. Hu, T. R. Boehly, and L. A. Collins, Phys. Rev. E
**89**, 063104 (2014). - [4] S. X. Hu
*et al.*, Phys. Rev. E**92**, 043104 (2015). - [5] Y. H. Ding and S. X. Hu, Phys. Plasmas
**24**, 062702 (2017). - [6] S. X. Hu
*et al.*, Phys. Rev. B**94**, 094109 (2016). - [7] S. X. Hu
*et al.*, Phys. Rev. E**95**, 043210 (2016).

### First-Principles Opacity Table (FPOT) of Warm Dense Matter

**Opacity/emissivity** determines how much x-ray radiation is absorbed/emitted in systems. Once materials are highly compressed and heated, atoms and ions in such HED
systems can no longer be viewed as individual entities. The surrounding plasma environment will significantly alter the opacity and emissivity in such HED systems. For ICF and HED applications,
we have been using the *ab initio* quantum-molecular-dynamics (QMD) method, based on density-functional theory, to study the **first-principles optical properties** of materials under high pressures.
**These FPOT studies have covered DT [1], C [2], and CH [3] so far.** Implementing FPOT in our ICF/HED hydrocodes also redefines reliable 1-D target designs. We are currently developing the QMD method,
by writing a real-space discrete-variable-representation, all-electron, TD-DFT code for studying the optical properties of mid-/high-*Z* materials. Some examples of our recent results show
that traditional continuum-lowering models can be wrong for strongly coupled and degenerate plasmas:

- [1] S. X. Hu
*et al.*, Phys. Rev. E**90**, 033111 (2014). - [2] S. X. Hu, Phys. Rev. Lett.
**119**, 065001 (2017). - [3] S. X. Hu
*et al.*, "Optical Properties of Highly-Compressed Polystyrene (CH): An*Ab Initio*Study," submitted to Physical Review B.

*Ab initio* Studies of Transport Properties in HED Plasmas

**Transport properties,** including thermal/electrical conductivity, diffusivity, viscosity, and stopping-power, are important quantities to know for ICF and HED experiment
simulations. These properties essentially determine both energy and mass transport in such systems. For the past few years, we have been using quantum molecular-dynamics (QMD) method,
based on density-functional theory, to study the **first-principles transport properties** of materials under high pressures. These studies have covered the thermal conductivity and
ionization of **DT [1] and CH [2] and their effects on ICF simulations [3]**. Currently, we are developing a TD-DFT code for extending our calculations of the transport properties of HED plasmas
to high-temperature regimes. Some examples of our recent results show that traditional thermal-conduction models can be wrong for strongly coupled and degenerate plasmas:

- [1] S. X. Hu
*et al.*, Phys. Rev. E**89**, 043105 (2014). - [2] S. X. Hu
*et al.*, Phys. Plasmas**23**, 042704 (2016). - [3] S. X. Hu
*et al.*, Phys. Plasmas**22**, 056304 (2015).

### Developing Accurate Density-Functional-Theory (DFT) Methods

The accuracy and efficiency of the modern DFT method really depends on the advancement in finding the best exchange-correlation functionals. To that end, we have put effort on **developing an accurate presentation for
the free-energy functional** over a wide range of state conditions [1]. In addition, improving the orbital-free DFT simulations for high-temperature plasmas is one of our current focuses, through introducing
temperature-dependent xc-functional [2]. We wish to continue this works to accurately simulate warm dense matter.

Deuterium electronic pressure as a function of *T* for the finite-*T* GGA ("KDT16") and ground-state PBE XC functionals, as well as PIMC reference results. *Ab initio*
MD simulations, Γ-point only, for 128 atoms (8500 steps, *T* ≤ 40 kK) or for 64 atoms (4500 steps *T* ≤ 62.5 kK)

- [1] V. V. Karasiev, J. W. Dufty, and S. B. Trickey, "Non-Empirical Semi-Local Free-Energy Density Functional for Matter Under Extreme Conditions," submitted to Physical Review Letters.
- [2] V. V. Karasiev
*et al.*, Phys. Rev. Lett.**112**, 076403 (2014).

### Combing QMD-CMD for Simulations of HED dynamics

In collaboration with Profs. Chuang Ren and Niaz Abdolrahim from ME at the University of Rochester, we are planning to combine the QMD method with classical molecular-dynamics (CMD) simulations to tackle dynamical problems in HED sciences. Basically, QMD can give the ion–ion interaction potentials in an HED system, while the CMD method can use such first-principles potentials to simulate the dynamics of large systems consisting of thousands or even up to millions of atoms. The goals are to answer many fundamental questions, such as:

- How quick phase-transition happens under dynamic loading?
- What are the transient states behind shocks?
- How fast thermal equilibrium among species occurs in a shocked mixture?