Adam Mackenzie Flowers

Presented in this work is a thorough determination of the transition states between the different isomers of cyclic tetra-atomic silicon carbide, germanium carbide, and germanium silicide clusters. Through use of density functional theory (B3LYP-D3BJ, M06-2X, ωB97X-D4, and B2GP-PLYP) in conjunction with the aug-cc-pVTZ basis set, transition state structures and their barrier heights are determined for the interconversions between the various isomers for the family of tetra-atomic SiC, GeC, and GeSi compounds. SiC dust grains are known to be prevalent in interstellar dust, and among this group, so far only diamond-shaped (d-)SiC₃ has been detected in the interstellar medium (ISM). Determining which other structures might be detectable not only depends on their intrinsic spectroscopic features, but whether or not they are likely to exist as isomers in interstellar environments. By examining the energy barrier heights for transitions between isomers, we determined that many of these structures are unlikely to exhibit interconversion in the ISM, outside of hotter circumstellar environments. Although Boltzmann population ratios at approximate circumstellar temperatures suggest the presence of higher energy minima, it is likely that once interconversion happens, as molecules travel away from a star and cool, they will get kinetically trapped in the potential energy well they inhabit, making how the ratios freeze out dependent on the time and pathways the molecules take to cool down. As such, many of these higher energy minima may still be good candidates for detection including (rhomboidal) r-SiC₃, r-GeC₃, r-GeSi₃, (trapezoidal) t-Si₂C₂, r-Ge₂C₂, and d-Si₃C.

An extensive, high-level theoretical study on tetra-atomic germanium carbide/silicide clusters is presented. Accurate harmonic and anharmonic vibrational frequencies and rotational constants are calculated at the CCSD(T)-F12a(b)/cc-pVT(Q)Z-F12 levels of theory. With growing capabilities to discern more of the chemical composition of the interstellar medium (ISM), an accurate database of reference material is required. The presence of carbon is ubiquitous in the ISM, and silicon is known to be present in interstellar dust grains; however, germanium-containing molecules remain elusive. To begin understanding the presence and role of germanium in the ISM, we present this study of the vibrational and rotational spectroscopic properties of various germanium-containing molecules to aid in their potential identification in the ISM with modern observational tools such as the James Webb Space Telescope. Structures studied herein include rhomboidal (r-), diamond (d-), and trapezoidal (t-) tetra-atomic molecules of the form GexC4-x and GexSi4-x, where x = 0-4. The most promising structure for detection is r-Ge2C2 via the nu(4) mode with a frequency of 802.7 cm(-1) (12.5 mu m) and an intensity of 307.2 km mol(-1). Other molecules that are potentially detectable, i.e., through vibrational modes or rotational transitions, include r-Ge3C, r-GeSi3, d-GeC3, r-GeC3, and t-Ge2C2.

Presented in this work is a thorough determination of the transition states between the different isomers of cyclic tetra-atomic silicon-carbide, germanium-carbide, and germanium-silicide clusters. Through use of density functional theory (B3LYP-D3BJ, M06-2X, ωB97X-D4, and B2GP-PLYP) in conjunction with the aug-cc-pVTZ basis set, transition state structures and their barrier heights are determined for the interconversions between the various isomers for the family of tetra-atomic SiC, GeC, and GeSi compounds. SiC dust grains are known to be prevalent in interstellar dust, and among this group, so far only diamond-shaped (d-)SiC(3) has been detected in the interstellar medium (ISM). Determining which other structures might be detectable not only depends on their intrinsic spectroscopic features, but whether or not they are likely to exist as isomers in interstellar environments. By examining the energy barrier heights for transitions between isomers, we determined that many of these structures are unlikely to exhibit interconversion in the ISM, outside of hotter circumstellar environments. Although Boltzmann population ratios at approximate circumstellar temperatures suggest the presence of higher energy minima, it is likely that once interconversion happens, as molecules travel away from a star and cool, they will get kinetically trapped in the potential energy well they inhabit, making how the ratios freeze out dependent on the time and pathways the molecules take to cool down. As such, many of these higher energy minima may still be good candidates for detection including (rhomboidal) r-SiC(3), r-GeC(3), r-GeSi(3), (trapezoidal) t-Si(2)C(2), r-Ge(2)C(2), and d-Si(3)C.

An extensive, high-level theoretical study on tetra-atomic germanium carbide/silicide clusters is presented. Accurate harmonic and anharmonic vibrational frequencies and rotational constants are calculated at the CCSD(T)-F12a(b)/cc-pVT(Q)Z-F12 levels of theory. With growing capabilities to discern more of the chemical composition of the interstellar medium (ISM), an accurate database of reference material is required. The presence of carbon is ubiquitous in the ISM, and silicon is known to be present in interstellar dust grains, however germanium-containing molecules remain elusive. To begin understanding the presence and role of germanium in the ISM, we present this study of the vibrational and rotational spectroscopic properties of various germanium- containing molecules to aid in their potential identification in the ISM with modern observational tools such as the James Webb Space Telescope. Structures studied herein include rhomboidal (r-), diamond (d-), and trapezoidal (t-) tetra-atomic molecules of the form Ge(x)C(4−x) and Ge(x)Si(4−x) , where x=0-4. The most promising structure for detection is r-Ge(2)C(2) via the ν4 mode with a frequency of 802.7 cm−1 (12.5 μm) and an intensity of 307.2 km mol−1. Other molecules potentially detectable, i.e., through vibrational modes or rotational transitions, include r-Ge(3)C, r-GeSi(3), d-GeC(3), r-GeC(3), and t-Ge(2)C(2).

We demonstrate that a Δ-density functional theory (Δ-DFT) approach based on atom-centered potentials (ACPs) represents a computationally inexpensive and accurate method for representing potential energy surfaces (PESs) for the HONO and HFCO molecules and vibrational frequencies derived therefrom. Using as few as 100 CCSD(T)-F12a reference energies, ACPs developed for use with B3LYP/def2-TZVPP are shown to produce PESs for HONO and HFCO with mean absolute errors of 27.7 and 5.8 cm^-1, respectively. Application of the multiconfigurational time-dependent Hartree (MCTDH) method with ACP-corrected B3LYP/def2-TZVPP PESs produces vibrational frequencies for cis- and trans-HONO with mean absolute percent errors (MAPEs) of 0.8 and 1.1, compared to 0.8 obtained for the two isomers with CCSD(T)-F12a/cc-pVTZ-F12/MCTDH. For HFCO, the vibrational frequencies obtained using the present (Δ-DFT)/MCTDH approach give a MAPE of 0.1, which is the error obtained with CCSD(T)-F12a/cc-pVTZ-F12/MCTDH. The ACP approach is therefore successful in representing a PES calculated at a high level of theory (CCSD(T)-F12a) and a promising method for the development of a general protocol for the representation of accurate molecular PESs and the calculation of molecular properties from them.