Trace correcting density matrix extrapolation in self-consistent geometry optimization.

A linear scaling trace correcting density matrix extrapolation method is proposed for accelerated self-consistency convergence in geometry optimization. The technique is based on nonorthogonal trace correcting purification and perturbation theory. Compared with alternative schemes, extrapolated total energies are often an order of magnitude closer to the self-consistent solution. For insulators, the computational cost is low and it scales linearly with the size of the perturbed region affected by the modified geometry, O(N(pert)). For local perturbations, the computational cost is therefore independent of the total size of the system and scales as O(1).

[1]  Michele Benzi,et al.  A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method , 1996, SIAM J. Sci. Comput..

[2]  Nonorthogonal density-matrix perturbation theory. , 2005, The Journal of chemical physics.

[3]  P. Ordejón.  Linear Scaling ab initio Calculations in Nanoscale Materials with SIESTA , 2000 .

[4]  Li,et al.  Density-matrix electronic-structure method with linear system-size scaling. , 1993, Physical review. B, Condensed matter.

[5]  Matt Challacombe,et al.  Density matrix perturbation theory. , 2003, Physical review letters.

[6]  David E. Manolopoulos,et al.  Canonical purification of the density matrix in electronic-structure theory , 1998 .

[7]  P. Mezey.  Electron density extrapolation along reaction paths , 2005 .

[8]  G. M. Stocks,et al.  Order-N multiple scattering approach to electronic structure calculations. , 1995, Physical review letters.

[9]  Gustavo E. Scuseria,et al.  Linear Scaling Density Functional Calculations with Gaussian Orbitals , 1999 .

[10]  Guanhua Chen,et al.  Linear-scaling time-dependent density-functional theory , 2003 .

[11]  Daniel Sánchez-Portal,et al.  Density‐functional method for very large systems with LCAO basis sets , 1997 .

[12]  Evert Jan Baerends,et al.  Towards an order , 1998 .

[13]  A. Holas.  Transforms for idempotency purification of density matrices in linear-scaling electronic-structure calculations , 2001 .

[14]  P. Mezey,et al.  Diagonalization-free initial guess to SCF calculations for large molecules , 2006 .

[15]  P. Mezey.  Charge-conserving electron density averaging for a set of nuclear configurations , 2008 .

[16]  Martin,et al.  Unconstrained minimization approach for electronic computations that scales linearly with system size. , 1993, Physical review. B, Condensed matter.

[17]  Chakram S. Jayanthi,et al.  Order-/N methodologies and their applications , 2002 .

[18]  S. Goedecker.  Linear scaling electronic structure methods , 1999 .

[19]  R. Mcweeny,et al.  The density matrix in self-consistent field theory I. Iterative construction of the density matrix , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[20]  Johansson,et al.  Order-N Green's function technique for local environment effects in alloys. , 1996, Physical review letters.

[21]  Emilio Artacho,et al.  LINEAR-SCALING AB-INITIO CALCULATIONS FOR LARGE AND COMPLEX SYSTEMS , 1999 .

[22]  Colombo,et al.  Efficient linear scaling algorithm for tight-binding molecular dynamics. , 1994, Physical review letters.

[23]  Valéry Weber,et al.  Ab initio linear scaling response theory: electric polarizability by perturbed projection. , 2004, Physical review letters.

[24]  Anders M.N. Niklasson.  Implicit purification for temperature-dependent density matrices , 2003 .

[25]  Gustavo E. Scuseria,et al.  What is the Best Alternative to Diagonalization of the Hamiltonian in Large Scale Semiempirical Calculations , 1999 .

[26]  Car,et al.  Orbital formulation for electronic-structure calculations with linear system-size scaling. , 1993, Physical review. B, Condensed matter.

[27]  Valéry Weber,et al.  Linear scaling density matrix perturbation theory for basis-set-dependent quantum response calculations: an orthogonal formulation. , 2007, The Journal of chemical physics.

[28]  Satoshi Yokojima,et al.  Time domain localized-density-matrix method , 1998 .

[29]  Giulia Galli,et al.  Linear scaling methods for electronic structure calculations and quantum molecular dynamics simulations , 1996 .

[30]  Yang,et al.  Direct calculation of electron density in density-functional theory. , 1991, Physical review letters.

[31]  A. Niklasson.  Iterative refinement method for the approximate factorization of a matrix inverse , 2004 .

[32]  Galli,et al.  Large scale electronic structure calculations. , 1992, Physical review letters.

[33]  Anders M.N. Niklasson.  Expansion algorithm for the density matrix , 2002 .

[34]  David A Mazziotti.  Towards idempotent reduced density matrices via particle-hole duality: McWeeny's purification and beyond. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  P. Pulay.  Convergence acceleration of iterative sequences. the case of scf iteration , 1980 .

[36]  Károly Németh,et al.  The quasi-independent curvilinear coordinate approximation for geometry optimization. , 2004, The Journal of chemical physics.

[37]  David A Mazziotti,et al.  Comparison of two genres for linear scaling in density functional theory: purification and density matrix minimization methods. , 2005, The Journal of chemical physics.

[38]  Matt Challacombe,et al.  A simplified density matrix minimization for linear scaling self-consistent field theory , 1999 .

[39]  R. Mcweeny.  Some Recent Advances in Density Matrix Theory , 1960 .

[40]  Kim,et al.  Total-energy global optimizations using nonorthogonal localized orbitals. , 1995, Physical review. B, Condensed matter.

[41]  Paul G. Mezey,et al.  Quantum similarity measures and Löwdin's transform for approximate density matrices and macromolecular forces , 1997 .

[42]  Anders M. N. Niklasson,et al.  Trace resetting density matrix purification in O(N) self-consistent-field theory , 2003 .

[43]  Kohn,et al.  Density functional and density matrix method scaling linearly with the number of atoms. , 1996, Physical review letters.

[44]  R. Baer,et al.  Electronic structure of large systems: Coping with small gaps using the energy renormalization group method , 1998 .

[45]  Jon Baker,et al.  Techniques for geometry optimization: A comparison of cartesian and natural internal coordinates , 1993, J. Comput. Chem..

[46]  D. Pettifor,et al.  A comparison of linear scaling tight-binding methods , 1997 .

[47]  Paul G. Mezey,et al.  Comparison of nonlinear transformation methods for electron density approximation , 2002 .

[48]  P. Löwdin.  On the Non‐Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals , 1950 .

[49]  Williams,et al.  N-scaling algorithm for density-functional calculations of metals and insulators. , 1994, Physical review. B, Condensed matter.