scholarly journals Towards theoretical spectroscopy with error bars: systematic quantification of the structural sensitivity of calculated spectra

2020 ◽  
Vol 11 (7) ◽  
pp. 1862-1877 ◽  
Author(s):  
Tobias G. Bergmann ◽  
Michael O. Welzel ◽  
Christoph R. Jacob
Keyword(s):  
Uncertainty Quantification ◽  
Structural Sensitivity ◽  
Theoretical Spectroscopy ◽  
Error Bars

Uncertainty quantification is applied in theoretical spectroscopy to obtain error bars accounting for the structural sensitivity of calculated spectra.

Towards Theoretical Spectroscopy with Error Bars: Systematic Quantification of the Structural Sensitivity of Calculated Spectra

2019 ◽  
Author(s):  
Tobias G. Bergmann ◽  
Michael O. Welzel ◽  
Christoph R. Jacob
Keyword(s):  
Molecular Structure ◽  
Emission Spectra ◽  
Principal Component ◽  
Molecular Spectra ◽  
Calculated Spectrum ◽  
Carbonyl Complexes ◽  
Chemical Methods ◽  
Theoretical Spectroscopy ◽  
Quantum Chemical Methods ◽  
Error Bars

Molecular spectra calculated with quantum-chemical methods are subject to a number of uncertainties (e.g., errors introduced by the computational methodology) that hamper the direct comparison of experiment and computation. Judging these uncertainties is crucial for drawing reliable conclusions from the interplay of experimental and theoretical spectroscopy, but largely relies on subjective judgment. Here, we explore the application of methods from uncertainty quantification to theoretical spectroscopy, with the ultimate goal of providing systematic error bars for calculated spectra. As a first target, we consider distortions of the underlying molecular structure as one important source of uncertainty. We show that by performing a principal component analysis, the most influential collective distortions can be identified, which allows for the construction of surrogate models that are amenable to a statistical analysis of the propagation of uncertainties in the molecular structure to uncertainties in the calculated spectrum. This is applied to the calculation of X-ray emission spectra of iron carbonyl complexes, of the electronic excitation spectrum of a coumarin dye, and of the infrared spectrum of alanine. We show that with our approach it becomes possible to obtain error bars for calculated spectra that account for uncertainties in the molecular structure. This is an important first step towards systematically quantifying other relevant sources of uncertainty in theoretical spectroscopy.

Towards Theoretical Spectroscopy with Error Bars: Systematic Quantification of the Structural Sensitivity of Calculated Spectra

2019 ◽  
Author(s):  
Tobias G. Bergmann ◽  
Michael O. Welzel ◽  
Christoph R. Jacob
Keyword(s):  
Molecular Structure ◽  
Emission Spectra ◽  
Principal Component ◽  
Molecular Spectra ◽  
Calculated Spectrum ◽  
Carbonyl Complexes ◽  
Chemical Methods ◽  
Theoretical Spectroscopy ◽  
Quantum Chemical Methods ◽  
Error Bars

Molecular spectra calculated with quantum-chemical methods are subject to a number of uncertainties (e.g., errors introduced by the computational methodology) that hamper the direct comparison of experiment and computation. Judging these uncertainties is crucial for drawing reliable conclusions from the interplay of experimental and theoretical spectroscopy, but largely relies on subjective judgment. Here, we explore the application of methods from uncertainty quantification to theoretical spectroscopy, with the ultimate goal of providing systematic error bars for calculated spectra. As a first target, we consider distortions of the underlying molecular structure as one important source of uncertainty. We show that by performing a principal component analysis, the most influential collective distortions can be identified, which allows for the construction of surrogate models that are amenable to a statistical analysis of the propagation of uncertainties in the molecular structure to uncertainties in the calculated spectrum. This is applied to the calculation of X-ray emission spectra of iron carbonyl complexes, of the electronic excitation spectrum of a coumarin dye, and of the infrared spectrum of alanine. We show that with our approach it becomes possible to obtain error bars for calculated spectra that account for uncertainties in the molecular structure. This is an important first step towards systematically quantifying other relevant sources of uncertainty in theoretical spectroscopy.

scholarly journals Towards Theoretical Spectroscopy with Error Bars: Systematic Quantification of the Structural Sensitivity of Calculated Spectra

2019 ◽  
Author(s):  
Tobias G. Bergmann ◽  
Michael O. Welzel ◽  
Christoph R. Jacob
Keyword(s):  
Molecular Structure ◽  
Emission Spectra ◽  
Principal Component ◽  
Molecular Spectra ◽  
Calculated Spectrum ◽  
Carbonyl Complexes ◽  
Chemical Methods ◽  
Theoretical Spectroscopy ◽  
Quantum Chemical Methods ◽  
Error Bars

Molecular spectra calculated with quantum-chemical methods are subject to a number of uncertainties (e.g., errors introduced by the computational methodology) that hamper the direct comparison of experiment and computation. Judging these uncertainties is crucial for drawing reliable conclusions from the interplay of experimental and theoretical spectroscopy, but largely relies on subjective judgment. Here, we explore the application of methods from uncertainty quantification to theoretical spectroscopy, with the ultimate goal of providing systematic error bars for calculated spectra. As a first target, we consider distortions of the underlying molecular structure as one important source of uncertainty. We show that by performing a principal component analysis, the most influential collective distortions can be identified, which allows for the construction of surrogate models that are amenable to a statistical analysis of the propagation of uncertainties in the molecular structure to uncertainties in the calculated spectrum. This is applied to the calculation of X-ray emission spectra of iron carbonyl complexes, of the electronic excitation spectrum of a coumarin dye, and of the infrared spectrum of alanine. We show that with our approach it becomes possible to obtain error bars for calculated spectra that account for uncertainties in the molecular structure. This is an important first step towards systematically quantifying other relevant sources of uncertainty in theoretical spectroscopy.

INVERSE UNCERTAINTY QUANTIFICATION OF A CELL MODEL USING A GAUSSIAN PROCESS METAMODEL

2020 ◽  
Vol 10 (4) ◽  
pp. 333-349
Author(s):  
Kevin de Vries ◽  
Anna Nikishova ◽  
Benjamin Czaja ◽  
Gábor Závodszky ◽  
Alfons G. Hoekstra
Keyword(s):  
Gaussian Process ◽  
Uncertainty Quantification ◽  
Cell Model ◽  
A Cell
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