Calculation of Vibrational Isotope Effect in Polyatomic Molecules by a Perturbation Method

1934 ◽  
Vol 45 (6) ◽  
pp. 427-427 ◽  
Author(s):  
E. Bright Wilson
Keyword(s):  
Perturbation Method ◽  
Isotope Effect ◽  
Polyatomic Molecules ◽  
Vibrational Isotope Effect

scholarly journals The absorption spectrum of bromine in the near infra-red

1937 ◽  
Vol 159 (896) ◽  
pp. 93-109 ◽  
Keyword(s):  
Absorption Spectrum ◽  
Isotope Effect ◽  
Numerical Data ◽  
Lower State ◽  
Rotational Constants ◽  
Dissociation Energies ◽  
Main System ◽  
Infra Red ◽  
True Quantum ◽  
Vibrational Isotope Effect

Vibrational analyses of the absorption spectrum of bromine were first published in 1926 by Kuhn (1926) and by Nakamura (1926). Kuhn’s measurements covered the range 5117-6722 A except for the region 5280- 5550 A., where the band-heads were too indefinite for measurement. As a result of this gap an error of 5 units in K uhn’s v' numeration was subsequently shown to have arisen (Birge 1929). Nakam ura’s observations extended from 5130 to 7586 A but did not fit a v ', v " table satisfactorily. Neither observer recorded isotope band-head measurements. In 1931 Browne stablished the existence of two absorption systems in the range 5113- 7605 A; one, referred to as the main system, consisting of six v ' progressions between 5113 and 6590 A, and the other, an extreme red system, consisting of five v ' progressions between 6448 and 7605 A. These systems are attributed to the transitions 3 Π 0+ u ← 1Σ + g and 3 Π 1+ u ← 1Σ + g respectively. Observations of the vibrational isotope effect in the main system due to the existence of two isotopes enabled him to determine the true quantum numeration in the upper state of this system. The assignment thus made was later confirmed by him (Brown 1932) from his analysis of the fine structure of bands of this system. The vibrational and rotational constants and the dissociation energies associated with the lower and upper states of the main system are now known fairly completely and accurately. The numerical data are consistent with the view that dissociation of the lower state leads to two normal 2 P 3/2 atoms, whilst dissociation of the upper state yields a normal 2P | atom and an excited 2 P 1/2 atom. The lower state of the extreme red system is identical with that of the main system, but as no measurement of the vibrational isotope effect and no rotational analysis for the extreme red system has been reported so far, the true quantum numeration, the vibrational and rotational constants and the dissociation energy of the upper state are not known accurately. From observations of the bands in each progression for which the heads are sharpest and the assumption that these are the points where the isotope effect changes sign, Brown was led to suggest that his arbitrary numeration should be increased by 4 ± 2 units. When the Morse potential energy curves are drawn assuming the provisional numeration to be correct (Jevons 1932; Sponer 1935), calculating r'e from the approximate empirical rule

Collective hyperspherical coordinates for polyatomic molecules and clusters

2000 ◽  
Vol 98 (21) ◽  
pp. 1763-1770 ◽  
Author(s):  
Vincenzo Aquilanti, Andrea Beddoni, Simonett
Keyword(s):  
Polyatomic Molecules ◽  
Hyperspherical Coordinates
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