TY - JOUR
T1 - Error bounds for molecular Hamiltonians inverted from experimental data
AU - Geremia, J. M.
AU - Rabitz, Herschel
PY - 2003/1/1
Y1 - 2003/1/1
N2 - Inverting experimental data provides a powerful technique for obtaining information about molecular Hamiltonians. However, rigorously quantifying how laboratory error propagates through the inversion algorithm has always presented a challenge. In this paper, we develop an inversion algorithm that realistically treats experimental error. It propagates the distribution of observed laboratory measurements into a family of Hamiltonians that are statistically consistent with the distribution of the data. This algorithm is built upon the formalism of map-facilitated inversion to alleviate computational expense and permit the use of powerful nonlinear optimization algorithms. Its capabilities are demonstrated by identifying inversion families for the [Formula Presented] and [Formula Presented] states of [Formula Presented] that are consistent with the laboratory data.
AB - Inverting experimental data provides a powerful technique for obtaining information about molecular Hamiltonians. However, rigorously quantifying how laboratory error propagates through the inversion algorithm has always presented a challenge. In this paper, we develop an inversion algorithm that realistically treats experimental error. It propagates the distribution of observed laboratory measurements into a family of Hamiltonians that are statistically consistent with the distribution of the data. This algorithm is built upon the formalism of map-facilitated inversion to alleviate computational expense and permit the use of powerful nonlinear optimization algorithms. Its capabilities are demonstrated by identifying inversion families for the [Formula Presented] and [Formula Presented] states of [Formula Presented] that are consistent with the laboratory data.
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U2 - 10.1103/PhysRevA.67.022711
DO - 10.1103/PhysRevA.67.022711
M3 - Article
AN - SCOPUS:85037253804
SN - 1050-2947
VL - 67
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 2
ER -