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Intramolecular anharmonic force constants expressed in Wilson’s valence coordinates (bond stretches, angle bands, wagging deformation and torsional angles) have linear dependence on Cartesian displacements and are consequently mass-dependent due to Eckart conditions. True mass-independent internal coordinates are defined in a purely geometric way; the potential energy surface defined with through them is also mass-independent. In practice multi-dimensional intramolecular potential energy surfaces (PES) are often defined directly in the normal mode representation which is also mass dependent. In this work, we have defined normal coordinate anharmonic PES for C2H4, C2H2D2-cis, C2H2D2-cis, C2H2D2-cis, C2H3D, and C2HD3 molecules using MP2/cc-pVTZ quantum-mechanical model. In this case, aforementioned six isotopologues of ethylene are considered as different molecules. An accuracy of these different ab initio PES have been accessed by comparing them after transformation to mass-independent curvilinear coordinate representations. The latter set of parameters is calibrated by the modern experimental infrared data for the C2H4, C2H2D2-cis, C2H2D2-cis, C2H2D2-cis, C2H3D, and C2HD3.
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