Kinetic Isotope Effect Provides Insight into the Vibrational Relaxation Mechanism of Aromatic Molecules: Application to Cyano-phenylalanine

Varying the reduced mass of an oscillator via isotopic substitution provides a convenient means to alter its vibrational frequency and hence has found wide applications. Herein, we show that this method can also help delineate the vibrational relaxation mechanism, using four isotopomers of the unnatural amino acid p-cyano-phenylalanine (Phe-CN) as models. In water, the nitrile stretching frequencies of these isotopomers, Phe-¹²C¹⁴N (1), Phe-¹²C¹⁵N (2), Phe-¹³C¹⁴N (3), and Phe-¹³C¹⁵N (4), are found to be equally separated by ∼27 cm^-1, whereas their vibrational lifetimes are determined to be 4.0 ± 0.2 (1), 2.2 ± 0.1 (2), 3.4 ± 0.2 (3), and 7.9 ± 0.5 ps (4), respectively. We find that an empirical relationship that considers the effective reduced mass of CN can accurately account for the observed frequency gaps, while the vibrational lifetime distribution, which suggests an intramolecular relaxation mechanism, can be rationalized by the order-specific density of states near the CN stretching frequency.