@article {109721,
	title = {Lagrangian formulation with dissipation of Born-​Oppenheimer molecular dynamics using the density-​functional tight-​binding method},
	journal = {J. Chem. Phys.},
	volume = {135},
	year = {2011},
	pages = {044122/1-044122/17},
	abstract = {An important element detg. the time requirements of Born-​Oppenheimer mol. dynamics (BOMD) is the convergence rate of the self-​consistent soln. of Roothaan equations (SCF)​.  We show here that improved convergence and dynamics stability can be achieved by use of a Lagrangian formalism of BOMD with dissipation (DXL-​BOMD)​.  In the DXL-​BOMD algorithm, an auxiliary electronic variable (e.g., the electron d. or Fock matrix) is propagated and a dissipative force is added in the propagation to maintain the stability of the dynamics.  Implementation of the approach in the self-​consistent charge d. functional tight-​binding method makes possible simulations that are several hundred picoseconds in lengths, in contrast to earlier DFT-​based BOMD calcns., which have been limited to tens of picoseconds or less.  The increase in the simulation time results in a more meaningful evaluation of the DXL-​BOMD method.  A comparison is made of the no. of iterations (and time) required for convergence of the SCF with DXL-​BOMD and a std. method (starting with a zero charge guess for all atoms at each step)​, which gives accurate propagation with reasonable SCF convergence criteria.  From tests using NVE simulations of C2F4 and 20 neutral amino acid mols. in the gas phase, it is found that DXL-​BOMD can improve SCF convergence by up to a factor of two over the std. method.  Corresponding results are obtained in simulations of 32 water mols. in a periodic box.  Linear response theory is used to analyze the relationship between the energy drift and the correlation of geometry propagation errors. },
	author = {Guishan Zheng and Anders M. N. Niklasson and Martin Karplus}
}
