Determination of Vibrational and Electronic Parameters From an Electronic Spectrum of I2 and a Birge-Sponer Plot

Using an electronic spectrum of I2, Deslanders table and Birge-Sponer plots, vibrational and electronic parameters were calculated. The vibrational frequency, anharmonicity constant, dissociation energy and the equilibrium dissociation energy for the ground state were found to be 221.103 cm, 0.0119 cm, 12189 cm and 12300.2 cm, respectively. The vibrational frequency, anharmonicity constant, dissociation energy and the equilibrium dissociation energy for the excited state were calculated to be 132.21 cm, 0.00771 cm, 4351.29 cm and 4284.93 cm, respectively. The convergence limit, electronic energy of the B state and the energy of the excited iodine atom were calculated to be 19903.3 cm, 15440.8 cm and 10174.89 cm, respectively. The calculated parameters for the excited state were in good agreement to tabulated values. It was concluded that the excited state follows a harmonic oscillator better than the ground state and that the bond length in the excited state was longer than the ground state. Introduction Upon heating, the excited vibrational levels of the ground state of I2 become populated. The vibronic spectrum that may be obtained by monitoring these excitations provides vibrational constants and dissociation energies of each electronic state. The electronic transitions observed in the spectrum are the transitions between the lower levels, XΣ (v”=0), and various excited vibrational levels of the BΠ (v’) electronic state. In this investigation, transitions from v”=0,1 and 2 states to v’=13, 14, 15, ...,47 are investigated using an electronic spectrum of I2 and a Birge-Sponer plot. Experimental A prepared 1 cm cuvette containing iodine crystals was heated until I2(g) was visible. The cuvette was placed into a Cary UV-Visible spectrophotometer and I2(g) was scanned from 500-600 nm. The settings on the spectrophotometer included an average time of 1 sec, average data interval of 0.1 nm, a band width of 0.2 nm and a double beam mode. The resulting spectrum was analyzed yielding the vibrational and electronic parameters ' ~ *, , ' , ' , ' ~ , ' ~ , " , " , " ~ , " ~ 0 0 e e e e e e e T E D D x D D x ν ν and E(I*). These parameters were calculated using Equations 1-5 and a Birge-Sponer plot. ) 1 ' ( ' ~ ' ~ 2 ~ ) ' ( ~ + − = Δ v x v e e e ν ν ν Equation 1 45 ... ) 2 ' ( ~ ) 1 ' ( ~ ) 0 ' ( ~ ' 0 + = Δ + = Δ + = Δ = v v v D ν ν ν = A Equation 2 e e e vib e x D v E D D ~ ' ~ 4 1 ' ~ 2 1 ' ) 0 ' ( ' ' 0 0 ν ν − + = = + = Equation 3 *) ( ' ' ) ' ( ~ * I E D A b v v E o + = + = = Equation 4 ' *) ( " ' ~ e e e D I E D T − + = Equation 5 In these equations, ν~ is the vibrational frequency, e x ~ is the anharmonicity constant, ' is the dissociation energy, A is the area under the Birge-Sponer plot, is the equilibrium dissociation energy, E* is the convergence limit, is the energy of the excited iodine atom, 0 D 50 ' D *) (I E e ' e T is the electronic energy of the B state, v’=b at the last transitions state before the bands become continuous and A’ is the area under the Birge-Sponer plot from v’=b to the convergence point. A Birge-Sponer plot of (v’+1) vs. ν~ Δ (v’) was constructed to yield desired values in Equations 1-5. A two-point plot of (v”+1) vs. 55 ν~ Δ (v”) was constructed to compare a calculated value of E(I*) to the tabulated value of 7603.15 cm used in Equation 4.