scholarly journals Hydrogen Intramolecular Stretch Redshift in the Electrostatic Environment of Type II Clathrate Hydrates from Schrödinger Equation Treatment

2020 ◽  
Vol 10 (23) ◽  
pp. 8504
Author(s):  
Christian J. Burnham ◽  
Zdenek Futera ◽  
Zlatko Bacic ◽  
Niall J. English

The one-dimensional Schrödinger equation, applied to the H2 intramolecular stretch coordinate in singly to quadruply occupied large cages in extended Type II (sII) hydrogen clathrate hydrate, was solved numerically herein via potential-energy scans from classical molecular dynamics (MD), employing bespoke force-matched H2–water potential. For both occupation cases, the resultant H–H stretch spectra were redshifted by ~350 cm−1 vis-à-vis their classically sampled counterparts, yielding semi-quantitative agreement with experimental Raman spectra. In addition, ab initio MD was carried out systematically for different cage occupations in the extended sII hydrate to assess the effect of differing intra-cage intrinsic electric field milieux on H–H stretch frequencies; we suggest that spatial heterogeneity of the electrostatic environment is responsible for some degree of peak splitting.

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.


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