Simulated annealing with floating Gaussians: Hellmann-Feynman forces without corrections
An all-electron density-functional-based molecular-dynamical algorithm for static and dynamic studies of atomic clusters is formulated and discussed. A time-dependent fictitious Lagrangian that depends on both the classical nuclear positions as well as the quantum-mechanical electronic variational parameters is introduced. By integrating the resulting equations of motion, the static ground state of a many-electron and -nuclei system may be found. A floating Gaussian formulation is introduced, and we demonstrate that, by allowing the nonlinear Gaussian parameters and positions to vary so as to minimize the total energy, the Pulay corrections to the Hellmann-Feynman force vanish. Further advantages of this method over conventional diagonalization schemes are that it allows for a compact self-optimizing basis set and that the algorithm is not susceptible to numerical instabilities when nearly, or exact, linear dependencies are encountered. By expanding the electronic wave functions in terms of floating s-type Gaussian orbitals, the method is illustrated with applications to the Li/sub 2/ molecule and the Ne atom. Results are in excellent agreement with other theoretical results and experiments.
- Research Organization:
- Condensed Matter Physics Branch, Naval Research Laboratory, Washington, D.C. 20375-5000
- OSTI ID:
- 6852685
- Journal Information:
- Phys. Rev. B: Condens. Matter; (United States), Vol. 38:6
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
SOLID CLUSTERS
ANNEALING
ALGORITHMS
ATOMS
DENSITY
EQUATIONS OF MOTION
FUNCTIONALS
GROUND STATES
LAGRANGIAN FUNCTION
LITHIUM
MOLECULES
NEON
SIMULATION
VARIATIONAL METHODS
WAVE FUNCTIONS
ALKALI METALS
DIFFERENTIAL EQUATIONS
ELEMENTS
ENERGY LEVELS
EQUATIONS
FLUIDS
FUNCTIONS
GASES
HEAT TREATMENTS
MATHEMATICAL LOGIC
METALS
NONMETALS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
RARE GASES
656002* - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-)