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EXTREME-SCALE QUANTUM SIMULATIONS

### Software: QXMD

#### Introduction

QXMD is a Quantum Molecular Dynamics (QMD) simulation software with various eXtensions.
QMD follows the trajectories of all atoms while computing interatomic forces quantum mechanically
in the framework of density functional theory (DFT)
[P. Hohenberg & W. Kohn, *Phys. Rev.* **136**, B864 (1964);
W. Kohn & L. J. Sham, *Phys. Rev.* **140**, A1133 (1965)].
The QXMD software has been developed by Fuyuki Shimojo since 1994 [1]. Since 1999, various extensions have been developed in collaboration with
Rajiv Kalia, Aiichiro Nakano and Priya Vashishta [2].

The basic QXMD code is based on a plane-wave basis to represent electronic wave functions and pseudopotential (PP) methods to describe electron-ion interaction.
Supported PPs include norm-conserving PP
[N. Troullier & J. L. Martins, *Phys. Rev. B* **41**, 1993 (1991)]
and ultrasoft PP
[D. Vanderbilt, *Phys. Rev. B* **41**, 7892 (1991)],
as well as an all-electron projector augmented-wave (PAW) method
[P. E. Blochl, *Phys Rev B* **50**, 17953 (1994)].
Electron-electron interaction beyond the mean-field Hartree approximation is included using various exchange-correlation functionals,
with and without spin polarization:
generalized gradient approximation (GGA)
[J. P. Perdew, K. Burke & M. Ernzerhof, *Phys. Rev. Lett.* **77**, 3865 (1996)],
DFT+U method for transition metals
[A. I. Liechtenstein, V. I. Anisimov & J. Zaanen, *Phys. Rev. B* **52**, R5467 (1995)],
van der Waals (vDW) functional for molecular crystals and layered materials
[S. Grimme, *J. Comput. Chem.* **25**, 1463 (2004)],
nonlocal correlation functional
[M. Dion et al., *Phys. Rev. Lett.* **92**, 246401 (2004)],
and range-separated exact-exchange functional
[J. Heyd, G. E. Scuseria & M. Ernzerhof, *J. Chem. Phys.* **118**, 8207 (2003)].

Various extensions included in the QXMD code are described in Ref. [2]:
- Linear-scaling DFT algorithms [3,4,5]
- Scalable algorithms on massively parallel computers [6,7]
- Nonadiabatic quantum molecular dynamics (NAQMD) to describe excitation dynamics [8]
- Omni-directional multiscale shock technique (OD-MSST) to study anisotropic shock response of materials [9]

#### References

1. "First-principles molecular-dynamics simulation of expanded liquid rubidium,"
F. Shimojo, Y. Zempo, K. Hoshino & M. Watabe,
* Phys. Rev. B*, **52**, 9320 (1995)

2. "A divide-conquer-recombine algorithmic paradigm for large spatiotemporal quantum molecular dynamics simulations,"
F. Shimojo, S. Hattori, R. K. Kalia, M. Kunaseth, W. Mou, A. Nakano, K. Nomura, S. Ohmura, P. Rajak, K. Shimamura & P. Vashishta
*J. Chem. Phys.* **140**, 18A529 (2014)

3. "Linear-scaling density-functional-theory calculations of electronic structure based on real-space grids: design, analysis, and scalability test of parallel algorithms,"
F. Shimojo, R. K. Kalia, A. Nakano & P. Vashishta
*Comput. Phys. Commun.* **140**, 303 (2001)

4. "Embedded divide-and-conquer algorithm on hierarchical real-space grids: parallel molecular dynamics simulation based on linear-scaling density functional theory,"
F. Shimojo, R. K. Kalia, A. Nakano & P. Vashishta,
*Comput. Phys. Commun.* **167**, 151 (2005)

5. "Divide-and-conquer density functional theory on hierarchical real-space grids: parallel implementation and applications,"
F. Shimojo, R. K. Kalia, A. Nakano & P. Vashishta,
*Phys. Rev.* **B** 77, 085103 (2008)

6. "Scalable atomistic simulation algorithms for materials research,"
A. Nakano, R. K. Kalia, P. Vashishta, T. J. Campbell, S. Ogata, F. Shimojo & S. Saini
*Proc. Supercomputing, SC01* (ACM/IEEE, 2001)

7. "Metascalable quantum molecular dynamics simulations of hydrogen-on-demand,"
K. Nomura, R. K. Kalia, A. Nakano, P. Vashishta, K. Shimamura, F. Shimojo, M. Kunaseth, P. C. Messina& N. A. Romero
*Proc. Supercomputing, SC14* (IEEE/ACM, 2014)

8. "Large nonadiabatic quantum molecular dynamics simulations on parallel computer,"
F. Shimojo, S. Ohmura, W. Mou, R. K. Kalia, A. Nakano & P. Vashishta
*Comput. Phys. Commun.* **184**, 1 (2013)

9."Crystalline anisotropy of shock-induced phenomena: omni-directional multiscale shock technique,"
K. Shimamura, M. Misawa, S. Ohmura, F. Shimojo, R. K. Kalia, A. Nakano & P. Vashishta
*Appl. Phys. Lett.* **108**, 071901 (2016)

#### Software

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