R-matrix propagation study of He scattering from NaCl(001) and its Kr overlayer

Heidinger, Linda

doi:10.1016/s0039-6028(99)00924-3

Cited by 2 publications

(2 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…11 Variational principles do exist, for example, several varieties of the Kohn variational principle (KVP), 12 particularly the S matrix KVP. 10, [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] Using the KVP requires finding a stationary point (a saddle point) of a functional of the wave function, and this typically means a (slow) matrix inversion. There are also instabilities associated with this approach, for example, spurious resonances.…”

Section: Introductionmentioning

confidence: 99%

“…No strict minimum principle is known for scattering states particularly the S matrix KVP. ,− Using the KVP requires finding a stationary point (a saddle point) of a functional of the wave function, and this typically means a (slow) matrix inversion. There are also instabilities associated with this approach, for example, spurious resonances. − …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Inelastic Scattering with Chebyshev Polynomials and Preconditioned Conjugate Gradient Minimization

2008

View full text Add to dashboard Cite

We describe and test an implementation, using a basis set of Chebyshev polynomials, of a variational method for solving scattering problems in quantum mechanics. This minimum error method (MEM) determines the wave function Psi by minimizing the least-squares error in the function (H Psi - E Psi), where E is the desired scattering energy. We compare the MEM to an alternative, the Kohn variational principle (KVP), by solving the Secrest-Johnson model of two-dimensional inelastic scattering, which has been studied previously using the KVP and for which other numerical solutions are available. We use a conjugate gradient (CG) method to minimize the error, and by preconditioning the CG search, we are able to greatly reduce the number of iterations necessary; the method is thus faster and more stable than a matrix inversion, as is required in the KVP. Also, we avoid errors due to scattering off of the boundaries, which presents substantial problems for other methods, by matching the wave function in the interaction region to the correct asymptotic states at the specified energy; the use of Chebyshev polynomials allows this boundary condition to be implemented accurately. The use of Chebyshev polynomials allows for a rapid and accurate evaluation of the kinetic energy. This basis set is as efficient as plane waves but does not impose an artificial periodicity on the system. There are problems in surface science and molecular electronics which cannot be solved if periodicity is imposed, and the Chebyshev basis set is a good alternative in such situations.

show abstract