Chapter 8
A Refined Quartic Potential Surface for S 0
Formaldehyde
Svetoslav Rashev and David C. Moule
Abstract We present an improved quartic potential energy surface for S 0 formaldehyde. The field was refined starting from the original Martin, Lee, Taylor ab initio
field (Martin et al. in J. Mol. Spectrosc. 160:105, 1993). In the calculations we have
been using our recently developed variational vibrational calculation method. During the refinement procedure, all (80) harmonic, cubic and quartic force constants
of the original field have been varied sequentially in groups of ten, until the best
possible fit between the calculated and experimentally measured results has been
obtained for a set of carefully selected 29 frequencies (of A 1 symmetry), extending
up to ∼6000 cm −1 of excess vibrational energy.
8.1 Introduction
Formaldehyde is a benchmark polyatomic molecule that has been thoroughly studied spectroscopically [1–6] and has frequently served as a model for large scale
vibrational calculations [7–19]. To the present day, 276 vibrational levels in the
ground electronic state (up to 12500 cm −1 ) have been experimentally observed
and assigned [3–6]. There have been a number of ab initio determinations of the
S 0 ground electronic state molecular force field and equilibrium geometry parameters [20–24], of steadily improving quality. The first exact variational calculation of vibrational levels in formaldehyde, using an exact analytical expression
for the kinetic energy [25] and the Martin, Lee, Taylor (MLT) quartic field [22],
was carried out by Carter, Pinnavaia and Handy [11]. There have been numerous adjustments and refinements of the MLT quartic force field based on extensive vibrational calculations [11–14]. Burleigh et al. [14] performed a calculation
and adjustment to experimental data of 138 vibrational levels in formaldehyde, using 4th and 6th order canonical Van Vleck perturbation theory [6, 14]. Lee and
Light [18] applied their iterative solutions/energy selected bases variational method
S. Rashev (B)
Institute of Solid State Physics, Bulgarian Academy of Sciences, Tsarigradsko chaussee 72,
1784 Sofia, Bulgaria
e-mail: rashev@issp.bas.bg
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_8,
© Springer International Publishing Switzerland 2013
141
A Refined Quartic Potential Surface for S 0
Formaldehyde
Svetoslav Rashev and David C. Moule
Abstract We present an improved quartic potential energy surface for S 0 formaldehyde. The field was refined starting from the original Martin, Lee, Taylor ab initio
field (Martin et al. in J. Mol. Spectrosc. 160:105, 1993). In the calculations we have
been using our recently developed variational vibrational calculation method. During the refinement procedure, all (80) harmonic, cubic and quartic force constants
of the original field have been varied sequentially in groups of ten, until the best
possible fit between the calculated and experimentally measured results has been
obtained for a set of carefully selected 29 frequencies (of A 1 symmetry), extending
up to ∼6000 cm −1 of excess vibrational energy.
8.1 Introduction
Formaldehyde is a benchmark polyatomic molecule that has been thoroughly studied spectroscopically [1–6] and has frequently served as a model for large scale
vibrational calculations [7–19]. To the present day, 276 vibrational levels in the
ground electronic state (up to 12500 cm −1 ) have been experimentally observed
and assigned [3–6]. There have been a number of ab initio determinations of the
S 0 ground electronic state molecular force field and equilibrium geometry parameters [20–24], of steadily improving quality. The first exact variational calculation of vibrational levels in formaldehyde, using an exact analytical expression
for the kinetic energy [25] and the Martin, Lee, Taylor (MLT) quartic field [22],
was carried out by Carter, Pinnavaia and Handy [11]. There have been numerous adjustments and refinements of the MLT quartic force field based on extensive vibrational calculations [11–14]. Burleigh et al. [14] performed a calculation
and adjustment to experimental data of 138 vibrational levels in formaldehyde, using 4th and 6th order canonical Van Vleck perturbation theory [6, 14]. Lee and
Light [18] applied their iterative solutions/energy selected bases variational method
S. Rashev (B)
Institute of Solid State Physics, Bulgarian Academy of Sciences, Tsarigradsko chaussee 72,
1784 Sofia, Bulgaria
e-mail: rashev@issp.bas.bg
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_8,
© Springer International Publishing Switzerland 2013
141