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# Fourier Grid Hamiltonian 1D Program Errors

FGH Errors

There are several ways to get bad answers when using the FGH1D program. Two of the more common are using too few basis functions (not enough points), and not having the range go beyond the edge of a well far enough (Poor range choice).

Not enough points

This is usually obvious from the display of the eigenvectors. When there are too few basis functions the eigenvectors tend to consist of just one peak near a potential wall. This can be demonstrated using the default Morse potential parameters but changing the range to be 0.5 to 3.0 and using only 18 points. (It should be noted that in general as the number of points (basis functions) is increased the eigenvalues converge to good values faster than the eigenvectors converge to nice looking curves.)

Poor Range Choice

Because of the periodic boundary conditions of the FGH method as the top of a barrier is reached the wavefunction goes over to free rotor wavefunctions. This is useful for torsional potentials, but unwanted for other potentials. This can usually be checked by examining the eigenvectors. The amplitude of the eigenvectors should go to zero beyond a sufficiently high barrier. This can be illustrated with the double well potential, using

C2 = 500 cm-1, C4 and others all set to 0.

range set to -1.8 to 1.8 Å

points set to 40.

The v=5 eigenvector just barely goes to zero at the edges, and higher eigenvectors do not. For this harmonic potential the effect is also apparent in the energy spacing of the eigenvalues, which should be constant. The energy spacing starts to deviate significantly from 182.9 cm-1 at v=4 as shown in the Eigenvalues Frame.

Contact

General Information:
Russ Johnson
301-975-2513 Telephone
russell.johnson@nist.gov

100 Bureau Drive, M/S 8320
Gaithersburg, MD 20899-8320