DFT/B3LYP calculations are used to analyse the occurrence of reverse isotope shift ratios (ISR) in H/D substitution of the free-base tetrapyrroles, in situations where the frequency ratio νH/νD is less than 1. The reverse ISR effect is found to be most evident in the out-of-plane bending modes (b2g and b3u symmetry) involving some N–H motion for the four molecules studied, viz., porphine (H2P), tetraaza-porphine (H2TAP), tetrabenzo-porphine (H2TBP), and phthalocyanine (H2Pc). It was analysed by following the evolution of the normal mode frequencies with incremental variation of the H atom masses from 1 to 2 amu. This method allows direct, unambiguous mode correlations to be established between the light and the heavy isotopologues. When the NH(D) motion is predominant, the H to D frequency evolution decreases in a continuous manner for a particular normal mode. In the case of two modes of the same symmetry and whose frequencies are similar, their frequency evolutions could cross, depending on the extent of NH(D) motion involved in them. The evolution diagrams may show avoided crossings of various extents, which thereby reflects the degree of the NH(D) motion in the modes. The reverse ISR effect is directly correlated to these avoided crossings. Because the isotope shifts are quite small (<10 cm–1) and occur in the congested 1500–500 cm–1 spectral region, high-resolution methods yielding narrow line transitions are required for experimental analysis. The matrix isolation technique is particularly well suited for this work and is proposed for use in a search for this effect.
DYNAMIC ANALYSIS OF PIPELINES BY MEANS OF NORMAL MODE SHAPES TAKING INTO ACCOUNT INTERACTION WITH THE ENVIRONMENT
