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PdSb is Tungsten Carbide-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Pd2+ is bonded to six equivalent Sb2- atoms to form a mixture of face, edge, and corner-sharing PdSb6 octahedra. The corner-sharing octahedral tilt angles are 51°. All Pd–Sb bond lengths are 2.78 Å. Sb2- is bonded in a 6-coordinate geometry to six equivalent Pd2+ atoms.
EuPd2Sb2 crystallizes in the tetragonal P4/nmm space group. The structure is three-dimensional. Eu2+ is bonded in a 8-coordinate geometry to eight Sb3- atoms. There are four shorter (3.52 Å) and four longer (3.63 Å) Eu–Sb bond lengths. There are two inequivalent Pd2+ sites. In the first Pd2+ site, Pd2+ is bonded to four equivalent Sb3- atoms to form a mixture of edge and corner-sharing PdSb4 tetrahedra. All Pd–Sb bond lengths are 2.70 Å. In the second Pd2+ site, Pd2+ is bonded in a 5-coordinate geometry to five Sb3- atoms. There are one shorter (2.62 Å) and four longer (2.71 Å) Pd–Sb bond lengths. There are two inequivalent Sb3- sites. In the first Sb3- site, Sb3- is bonded in a 4-coordinate geometry to four equivalent Eu2+ and four equivalent Pd2+ atoms. In the second Sb3- site, Sb3- is bonded in a 9-coordinate geometry to four equivalent Eu2+ and five Pd2+ atoms.
Sr(PdSb)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Sr2+ is bonded in a distorted body-centered cubic geometry to eight equivalent Sb3- atoms. All Sr–Sb bond lengths are 3.63 Å. Pd2+ is bonded to four equivalent Sb3- atoms to form a mixture of edge and corner-sharing PdSb4 tetrahedra. All Pd–Sb bond lengths are 2.68 Å. Sb3- is bonded in a 9-coordinate geometry to four equivalent Sr2+, four equivalent Pd2+, and one Sb3- atom. The Sb–Sb bond length is 2.93 Å.
BaPd2Sb2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Ba2+ is bonded in a distorted body-centered cubic geometry to eight equivalent Sb3- atoms. All Ba–Sb bond lengths are 3.71 Å. Pd2+ is bonded to four equivalent Sb3- atoms to form a mixture of corner and edge-sharing PdSb4 tetrahedra. All Pd–Sb bond lengths are 2.71 Å. Sb3- is bonded in a 9-coordinate geometry to four equivalent Ba2+, four equivalent Pd2+, and one Sb3- atom. The Sb–Sb bond length is 3.06 Å.
Sr(PdSb)2 crystallizes in the tetragonal P4/nmm space group. The structure is three-dimensional. Sr2+ is bonded in a 8-coordinate geometry to eight Sb3- atoms. There are four shorter (3.56 Å) and four longer (3.66 Å) Sr–Sb bond lengths. There are two inequivalent Pd2+ sites. In the first Pd2+ site, Pd2+ is bonded to four equivalent Sb3- atoms to form a mixture of edge and corner-sharing PdSb4 tetrahedra. All Pd–Sb bond lengths are 2.72 Å. In the second Pd2+ site, Pd2+ is bonded in a 5-coordinate geometry to five Sb3- atoms. There are one shorter (2.65 Å) and four longer (2.74 Å) Pd–Sb bond lengths. There are two inequivalent Sb3- sites. In the first Sb3- site, Sb3- is bonded in a 4-coordinate geometry to four equivalent Sr2+ and four equivalent Pd2+ atoms. In the second Sb3- site, Sb3- is bonded in a 9-coordinate geometry to four equivalent Sr2+ and five Pd2+ atoms.
Vibrational sum frequency generation (SFG) spectroscopy has been extensively used for obtaining structural information of molecular functional groups at two-dimensional (2D) interfaces buried in the gas or liquid medium. Although the SFG experiment can be done elegantly, interpreting the measured intensity in terms of molecular orientation with respect to the lab coordinate is quite complicated. One of the main reasons is the difficulty of determining the hyperpolarizability tensors of even simple molecules that govern their SFG responses. The single-bond polarizability derivative (SBPD) model has been proposed to estimate the relative magnitude of SFG-active hyperpolarizability by assuming that the perturbation associated to each vibration is negligible. In this study, density functional theory (DFT) was used to calculate the polarizability and dipole derivative tensors of the CH 3 stretch mode of CH 3 I, CH 3 CH 2 I, CH 3 OH, CH 3 CH 2 OH. Then, the hyperpolarizability tensors of symmetric and asymmetric vibration modes were calculated considering the Boltzmann distribution of representative conformers, which allowed theoretical calculation of their SFG intensities at all polarization combinations as a function of the tilt angle of the CH 3 group with respect to the surface normal direction. Then the ratios of the calculated SFG intensities for the CH 3 peaks used in experimental studies for the CH 3 tilt angle determination were compared. This comparison clearly showed the effect of vibrational coupling among neighboring functional groups. As a result, this study presents new parameters that can be used in determining the average tilt angle of the CH 3 group at the 2D interface with SFG measurements as well as limitations of the method.