## Barrier potentials, molecular structure, force filed calculations and quantum chemical studies of some bipyridine di-carboxylic acids using the experimental and theoretical using (DFT, IVP) approach

FT-IR and FT-Raman spectra of 2,2′-bipyridine-3,3′-dicarboxylic acid (B3DA), 2,2′-bipyridine-4,4′-dicarboxylic acid (B4DA) and 2,2′-bipyridine-5,5′-dicarboxylic acid (B5DA) were recorded and analysed. The quantum chemical calculations of the title compounds begin with barrier potentials at different rotation angles around the C–C′ and C–Cα bonds in order to arrive conformation of lowest energy using DFT employing B3LYP functional with 6-311++G(d,p) basis set. This confirmation was further optimised to get the global minimum geometry. The vibrational frequencies along with IR, Raman intensities were computed, the rms error between observed and calculated frequencies were 11.2 cm^{−1}, 10.2 cm^{−1} and 12.2 cm^{−1} for B3DA, B4DA, and B5DA. An 87-element modified valence force field is derived by solving the inverse vibrational problem using Wilson’s GF matrix method. This force field is refined using 163 observed fundamentals employing in overlay least-squares technique. The average error between computed and experimental frequencies was found as 12.85 cm^{−1} using potential energy distribution (PED) and eigenvectors. By using the gauge-independent atomic orbital (GIAO) method calculate the ^{1}H and ^{13}C NMR chemical shifts of the molecules and compared with experimental results. The first-order hyperpolarisability, HOMO and LUMO energies, molecular electrostatic potential (MESP) and natural orbital analysis (NBO) of titled compounds were evaluated using DFT.