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DOE OSTI2024

A new computational framework for spinor-based relativistic exact two-component calculations using contracted basis functions

Here, a new computational framework for spinor-based relativistic exact two-component (X2C) calculations is developed using contracted basis sets with a spin–orbit contraction scheme. Generally contracted, j-adapted basis sets of p-block elements using primitive functions in the correlation-consistent basis sets are constructed for the X2C Hamiltonian with atomic mean-field spin–orbit integrals (the X2CAMF scheme). The contraction coefficients are taken from atomic X2CAMF Hartree–Fock spinors, thereby following the simple concept of a linear combination of atomic orbitals. Benchmark calculations of spin–orbit splittings, equilibrium bond lengths, and harmonic vibrational frequencies demonstrate the accuracy and efficacy of the j-adapted spin–orbit contraction scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1983

Supplemental basis functions for the second transition row elements

It is noted that for molecular calculations, the basis sets presented by Huzinaga (1977) need to be augmented by (1) 5p functions to describe the 5s - 5p near degeneracy; (2) a diffuse 4d function to provide for a balanced description of the 5s2 4dn, 5s1 4d(n+1), and 4d(n+2) states of the atom; and (3) a set of 4f functions to correlate the 4d functions. Here, the diffuse 4d function is similar in function to the diffuse 3d function for the first transition row elements recommended by Hay (1977). A table is included giving the optimized values for the diffuse 4d, the 5p, and 4f (STO exponent) functions. The diffuse 4d function and the 5p functions are optimized at the SCF level on the basis of the 5s1 4d(n+1) state (except for Pd, which is optimized for the 4d10 state) and the 5s1 5p1 4dn state, respectively. The table also gives the energies and the atomic symmetries for each of the SCF calculations.

Walch, S. P.↗

NASA NTRS2007

Zernike-like Orthogonal Basis Functions for Wavefront Characterization over Sampled, Irregular Apertures

For optical systems with circular apertures, wavefronts are often analyzed using Zernike polynomials, and individual Zernike functions are associated with familiar optical aberrations. For systems with noncircular apertures, or in practical situations in which wavefronts are measured at a limited number of points in the aperture, the Zernike polynomials are no longer an orthogonal basis for the measured data. Although there are an endless number of ways to create a basis for such measured data, a "Zernike-like" basis is useful to connect with our experience with the usual optical aberrations. In this paper, the steps required to identify a Zernike-like basis for wavefronts over sampled, irregular apertures are presented, based on the Gram-Schmidt orthogonalization technique. The benefits of analyzing optical wavefronts using an orthogonal basis specific to an optical system's aperture shape and wavefront sampling, instead of using the traditional Zernike polynomials, are detailed in two examples, from image-based wavefront sensing on a segmented-aperture telescope (the James Webb Space Telescope Testbed Telescope at Ball Aerospace) and from interferometer characterization for surface metrology of a hexagonal mirror segment.

Aronstein, David L.↗

DOE OSTI2024

2D temperature field reconstruction using optimized Gaussian radial basis function networks

Not provided.

Engineering↗

DOE OSTI2024