Knowledge Bank

An empirical approach to estimate the harmonic from the experimental fundamental vibrational frequencies is presented. It is based on a partitioning of the eigenvectors of each normal mode into intenal motion components involving bond stretching, $BS$, bond angle bending, $AS$, torsional, $TS$, and out-of-plane, $Os$, motion. These normalized components. $BS+AS+TS+OS=1$, are used in an empirical formula, $fS=(1200BS+2000AS+1300TS+1600OS)10-8cm$, which relates fundamental to harmonic frequencies with $vS=\omega S(1-2xS)=\omega S(1-fS\omega S)$ when the anharmonic states follow a Morse expression. $vsn=\omega S(n+1/2)-\omega SxS(n+1/2)2$, where $n=0,1.2\dots$. denotes the vibrational states of mode s. This formula is tested with the available experimental data for $vs\exp$ and $\omega s\exp$. It allows one to estimate harmonic frequencies, $\omega s$. from experimental fundamental frequencies, $vs\exp$ In a self consistent procedure in cases where $\omega s\exp$ are not known. Experimental data is available for approximately 20 molecules (and isotopes) including diatomics. $CO2,HCN,O3,H2O,H2S,NH3,CH2O,C2H2,CH4$ and $C3H8$. The method, calibrated with these molecules, yields results which suggest that harmonic frequencies can be predicted accurately from experimental anharmonic frequencies. Therefore the empirical harmonic frequencies obtained from $vs\exp =\omega semp(-fs\omega semp)$ can be used to adjust the force constants in Molecular Mechanics calculations until the theoretical eigenvalues, $\omega sth$, agree with the emprical harmonic frequencies, $\omega semp$.