Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules

1951 ◽  
Vol 19 (6) ◽  
pp. 390-391 ◽  
Author(s):  
Gerhard Herzberg ◽  
S. Mrozowski
Keyword(s):  
Molecular Structure ◽  
Diatomic Molecules ◽  
Molecular Spectra

A qp-DEFORMED ANHARMONIC OSCILLATOR WITH THE Uqp(U2) ⊃ Uqp(O2) SYMMETRY AND ITS APPLICATION TO VIBRATIONAL MOLECULAR SPECTRA

1995 ◽  
Vol 09 (17) ◽  
pp. 1053-1057 ◽  
Author(s):  
HUAN-QIANG ZHOU ◽  
XIN-MING ZHANG ◽  
JING-SONG HE
Keyword(s):  
Vibrational Spectra ◽  
Anharmonic Oscillator ◽  
Diatomic Molecules ◽  
The State ◽  
Molecular Spectra ◽  
State Formula ◽  
Energy Formula

A qp-deformed anharmonic oscillator with the Uqp(U2) ⊃ Uqp(O2) symmetry is presented for describing vibrational spectra of diatomic molecules. The energy formula is tested on the vibrational spectra in the state [Formula: see text] of H2 obtained through the Rydberg-Klein-Rees (RKR) method.

scholarly journals The structure and activation of the phosgene molecule. Part I.—General introduction—Predissociation of molecules

1930 ◽  
Vol 128 (807) ◽  
pp. 178-189 ◽  
Keyword(s):  
Diatomic Molecules ◽  
Molecular Spectra ◽  
Wave Mechanics ◽  
General Introduction ◽  
Atomic Spectra ◽  
Different Types ◽  
Experimental Researches ◽  
Number Of Authors

The study of diatomic molecules is already very advanced. By applying the principles of wave mechanics a number of authors, especially Hund, Heitler, London, Mulliken, Herzberg, Wigner and Witmer, have developed the theory of the conditions of formation, of electronic activation, and of different types of dissociation of diatomic molecules. They have also established relations between the electronic terms of atoms and those of related molecules, and have thus succeeded in arranging the terms of molecular spectra in a manner analogous to that for atomic spectra. The experimental researches during recent years of Mulliken, Mecke, Hund, Diecke, Franck and his school, Hulthen, Birge, Hopfield, Richardson, Curtis, Johnson, Herzberg and many others have established a very exact knowledge of the structure of spectra of diatomic molecules.

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.

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