Comparison of Calculated Normal Mode Molecular Vibrations with Experimental Gas-Phase Infrared Spectroscopy
Computational vibrational spectroscopy serves as an important tool in the interpretation of experimental infrared (IR) spectra. Analysis of computational results provides a perspective over broader wavelength ranges and at higher precision. Although there are issues regarding accuracy, this can be approximated by using a scaling factor. High-resolution gas-phase FTIR spectroscopy at a resolution of 0.125 cm-1 can partially resolve rovibrational transitions in the P, Q, and R bands and therefore identify fundamental frequencies with approximately 1 cm-1 precision. This research has compared high-resolution gas-phase FTIR absorption peaks to calculated vibrational frequencies. In the calculation of normal mode frequencies, reliability, feasibility, and ease of interpretation are still a matter of concern due to the interplay of several factors (time, accuracy, and memory requirement of computer hardware). Calculations were performed using different methods (theories and basis sets), such as, B3LYP-D/cc-pVDZ, MP2-cc-pVDZ, CCSD/cc-pVDZ, CCSD(T)/aug-cc-pVDZ, CCSD(T)/aug-cc-pVTZ, CCSD/cc-pVDZ and CCSD/cc-pVTZ on different diatomic and polyatomic molecules using the ab initio computational software package, Psi4. H2, C2, HCl and CO required 15-20 minutes to get the output file with ± 0 to 8 cm-1 variations compared to experimental values. Couple cluster theory (CC) yields quite accurate calculations for diatomic molecules. Whereas, with polyatomic H2O, CH4 and CH2O required a time of 45 minutes to 1 hour with variation of ± 0 to 20 cm-1. For H2O couple cluster theory is best. For CH4 and CH2O density functional theory (DFT) provides the nearly similar number to experimental frequencies. The molecules, CH2O2, CH3COOH and C3H6O, required up to 48 hours due to the number of electrons (N) in each molecule and the number of calculations needed for a particular theory, for example MP2 scales as O(N5) and CCSD(T) scales as O(N7). Vibrational frequencies were calculated using only B3LYP-D/cc-pVDZ as a computational method and basis set for polyatomic molecules, since it requires less computational power as compared to other methods and basis sets. In addition, a slightly larger molecule, cyclohexane (C6H12), was used to evaluate the effectiveness of B3LYP-D/cc-pVDZ. Larger molecular systems have the conflict between accuracy and computational cost in terms of time, accuracy, and memory requirement of the hardware. In contrast, the smaller molecules consume less time to calculate and make it possible to use a high level of theory that gives accurate results. The initial goal of this research was to find the best theoretical method and basis set for diatomic molecules such as HCl. The HCl calculated vibrational frequency is 2999 cm-1, while experimental frequency is 2991 cm-1 with an 8 cm-1 difference in comparing experimental values with the CCSD(T)/cc-pVTZ method. For C3H6O using B3LYP-D/cc-pVDZ, the observed Psi4 frequency of the CH3 degenerate stretching (d-str) vibrational mode is 1425 cm-1, while the experimental value is 1426 cm-1 and demonstrates very small difference of 1 cm-1. Density functional theory proved accurate for polyatomic molecules, while for diatomic molecules couple cluster theory performed well. CCSD(T)/cc-pVTZ required less than 500 megabytes for diatomic molecules. To calculate energy, Psi4 needed 8 s while optimization was 1 m 59 s and frequency was 2 m 35 s for HCl. To calculate energy Psi4 needed 1 h 5 m, while optimization 54 m 19 s and frequency took 1 h 54 m for calculation for acetone. High-resolution FTIR gas-phase spectra of molecules were collected and compared to calculated molecular vibrational frequencies. This study revealed that couple cluster theory is the best approach for diatomic molecules, and density functional theory is more accurate for polyatomic molecules.
FTIR, Coupled cluster theory, Psi4, Density functional theory, Vibrational normal modes, Physical Chemistry
City University of New York - City College
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