Semirigid Bender Hamiltonian Research Articles

Equilibrium Structure and HCC Bending Potential Energy Function of 3A‘‘ HCCN

The molecular parameters of the ground triplet state of cyanocarbene, 3A‘‘ HCCN, have been determined in large-scale ab initio calculations using the coupled-cluster method, RCCSD(T), and basis sets of double-through-quintuple-ζ quality. The equilibrium structure of the molecule was found to be planar and bent, with the trans conformation of the HCCN chain and the parameters re(HC) = 1.069 A, re(CC) = 1.328 A, re(CN) = 1.186 A, ∠e(HCC) = 144.9°, and ∠e(CCN) = 175.4°. The potential energy function for the HCC bending motion (v5 mode) was determined to be strongly anharmonic, with the barrier to linearity of 286 cm-1. Influence of various electron-correlation effects on the shape of the HCC bending potential energy function is discussed. The rotation−bending energy levels of the HCCN and DCCN molecules were then calculated using a semirigid-bender Hamiltonian. For both molecules, the predicted patterns of rotational transitions in the excited ν5 states agree favorably with the experimental data.

Ab Initio Study on the Equilibrium Structure and CCN Bending Energy Levels of Cyanofulminate (NCCNO)

The molecular parameters of cyanofulminate, NCCNO, have been determined in large-scale ab initio calculations using the coupled-cluster method, CCSD(T), and basis sets of double- through quadruple-ζ quality. The equilibrium structure of the molecule was found to be linear, with a strongly anharmonic potential energy function of the CCN bending motion (ν7 mode). The rotation−bending energy levels were then calculated using a semirigid-bender Hamiltonian. The vibrational energy levels and effective rotational constants determined for various ν7 states were found to be in good agreement with the experimental data.

An ab initio study on the equilibrium structure and CCC bending energy levels of carbon suboxide

The molecular parameters of carbon suboxide, C 3O 2, have been determined in large-scale ab initio calculations using the coupled-cluster method, CCSD(T), and basis sets of double- through quadruple-zeta quality. The potential energy function for the large-amplitude CCC bending motion (the ν 7 mode) was determined to be strongly anharmonic. The equilibrium structure of the molecule was found to be bent, with a barrier to linearity of only 18 cm −1. The rotation-bending energy levels were then calculated using a semirigid-bender Hamiltonian. The vibrational energy levels and effective rotational constants determined for various ν 7 states were found to be in good agreement with the experimental data.

Amino groups in nucleic acid bases, aniline, aminopyridines, and aminotriazine are nonplanar: Results of correlated ab initio quantum chemical calculations and anharmonic analysis of the aniline inversion motion

The amino group nonplanarity in nucleic acid bases, aniline, aminopyridines, and aminotriazine was investigated by ab initio methods with and without inclusion of correlation energy utilizing medium and extended basis sets. For all the systems studied, the amino group was found to be nonplanar and the coupled cluster method [CCSD(T)] ‘‘nonplanarities’’ and inversion barriers slightly higher than their second-order many-body perturbation-theory (MP2) counterparts. To assess the reliability of the calculations, inversion splittings for aniline and aniline-ND2 were evaluated by solving a two-dimensional vibrational Schrödinger equation for the large-amplitude inversion and torsion motions, while respecting the role of small-amplitude C–N stretching and H–N–H bending motions. Because a large number of points is required for the description of the aniline potential energy surface, the Hartree–Fock (HF) method with 6-31G* basis set was utilized. The vibrational calculations were performed within the framework of the semirigid bender Hamiltonian of Landsberg and Bunker. Excellent agreement between experimental and theoretical inversion-torsion frequencies for fundamental, overtone, and combination modes was found, which gives strong evidence for the adequacy of the theoretical model used in general, and potential energy surface in particular. Similarity between the HF, MP2, and CCSD(T) aniline inversion barriers and amino group nonplanarities gives us confidence that the MP2 and CCSD(T) inversion barriers and amino group nonplanarities of the DNA bases, aminopyridine, and aminotriazine, are close to the actual values which are still experimentally unknown.

Semirigid Bender Determination of the Quasilinear Bending Potential Energy Function of HNCS from the Ground State Rotational Spectra

The semirigid bender Hamiltonian of Bunker and Landsberg ( J. Mol. Spectrosc. 67, 374-385, 1977) is used to study the ground state microwave, millimeter-wave, and far-infrared spectroscopic data for HNCS and its isotopomers. The results of the nonlinear least-squares fitting include a determination of the geometry of the molecule and of the in-plane HNC bending potential energy function. The fitted barrier to linearity is found to be approximately 990 cm −1, while consideration of the rotation structure of the v 4 = 1 state implies that the barrier lies near 900 cm −1. With an estimated uncertainty of about 200 cm −1 these values are in reasonable agreement.

Torsional-Rotational Dynamics of Carbodiimide, HNCNH: A Semirigid Bender Approach

A one-dimensional semirigid bender Hamiltonian was developed for the description of the torsional motion of carbodiimide, HNCNH. The interaction of torsion with the other vibrational degrees of freedom is described by the variation of molecular geometry along the minimum energy torsional tunneling path. The large changes of the ∠HNC angles during torsion generate rotationally dependent contributions to the effective torsional potential function, which explain qualitatively the observed decrease of the torsional splittings as a function of Ka in the rotational spectrum of the ground torsional state. The parameters of the minimum energy torsional path were optimized with respect to the available experimental splittings and rotational constants and used for predictions of rotational constants and torsional splittings of the first excited torsional state of HNCNH as well as the ground and first excited torsional states of DNCND.

Vibrational Frequencies from Microwave Data: Semirigid Bender Prediction of the ν11 Bending Fundamental of HC5N

A suitably extended version of the semirigid bender Hamiltonian of Bunker and Landsberg (J. Mol. Spectrosc.34, 59-7 5 (1983)) is applied to the available microwave data for HC5N, including satellite transitions involving the low frequency ν11 bending vibration. The resulting nonlinear least-squares fitting of the semirigid bender Hamiltonian allows a prediction for the ν11 vibrational energy. The result of fitting two models for this vibration is that the νl11: 11 ← 00 transition is predicted to lie at approximately 102 cm−1. This is significantly higher than previous predictions of about 75 cm−1. Experience with other molecules suggests that the current prediction should be within about 10% of the actual vibrational frequency.

The watson U( ρ) term in the one-dimensional Semirigid Bender Hamiltonian for the HF dimer

We have recalculated the minimum energy path for the trans-bending tunneling motion of the HF dimer using mass-scaled Cartesian coordinates, and have set up the appropriate Semirigid Bender wave equation. Using Hougen-Bunker-Johns axes that keep I xρ; = 0, we can calculate the full Watson U( ρ) term as a function of the tunneling coordinate ρ. The rapid change in the magnitude of R ab (the distance between the centers of mass of the two HF fragments), along the minimum energy trans-tunneling path, causes U( ρ) to become very large in the vicinity of the equilibrium structure. For the calculation of the K-type rotation and trans-tunneling energies it is possible to set up a one-dimensional model Hamiltonian, as we did previously, by neglecting the variation of R ab with ρ. We do this in an optimization of the minimum energy path to the currently available term values in order to obtain an effective minimum energy path and predicted term values.

An a b i n i t i o calculation of the stretching energies for the HF dimer

For the HF dimer we calculate the fundamental HF stretching vibration frequencies, and the fundamental and overtone frequencies of the intermolecular (HF–HF) stretching vibration, using an ab initio potential energy surface and the previously developed semirigid bender Hamiltonian. The ab initio surface used involves the addition of 459 nuclear geometry points to the 1061 reported in our earlier work. These extra points have been chosen to give more information on those parts of the surface that involve distortions of the HF bond lengths. We have fitted these 1520 points to an analytic expression, slightly modified from our previous work, that involves 39 adjustable parameters and one constrained parameter; the weighted standard deviation of the fit is 29.3 cm−1. To calculate the vibrational frequencies, and the tunneling splittings in these vibrationally excited states, we use the semirigid bender Hamiltonian to average over the trans-tunneling path. We also calculate from the ab initio surface the effect of the adiabatic corrections, for the HF stretching states, that arise from the separation of the tunneling mode. In the adiabatically corrected calculation we obtain ν1=3926 cm−1, and ν2=3875 cm−1, which are in good agreement with the experimental results (3930.9 and 3868.1 cm−1, respectively). We also predict ν4=146 cm−1, 2ν4=280 cm−1, and 3ν4=405 cm−1. The value obtained for ν4 enables us to explain the observed perturbation of the lower tunneling component of the K=4 ground state level as being due to interaction with the lower tunneling component of the ν4=1, K=3 level.

Ab initio rotational energy levels and internal rotation splittings in protonated acetylene C 2H 3+

The C 2H 3 + ion has an unusual internal-rotation tunneling degree of freedom in which the three protons rotate around the C 2 core with the molecule remaining planar. We have used our semirigid bender Hamiltonian (R. Escribano and P.R. Bunker, J. Mol. Spectry. 122 (1987) 325), with the results of an ab initio calculation of this tunneling potential (R. Lindh et al., Chem. Phys. Letters 139 (1987) 407), to calculate the rotational energy levels and internal-rotation splittings.

Ab initio rotation-vibration energies of HOC+ calculated using the nonrigid bender Hamiltonian

Abstract In a previous paper [W. P. Kraemer and P. R. Bunker, J. Mol. Spectrosc. 101, 379–394 (1983)] the results of configuration interaction calculations, performed in order to investigate the bending potential of the molecular ion HOC+, were reported. In the present paper we give the results of such calculations including additional points on the potential surface chosen mainly in order to study the HO and OC stretching potentials at longer bond lengths. We have determined the rotation-vibration energies from this extended potential surface using a newly written computer program that diagonalizes the nonrigid bender Hamiltonian. We compare the results with those obtained using the second-order rotation-vibration perturbation Hamiltonian, the rigid bender Hamiltonian, and the semirigid bender Hamiltonian.

C 3O 2 as a semirigid bender: The degenerate ν5 state

The semirigid bender Hamiltonian for carbon su☐ide C 3O 2 [ P. R. Bunker, J. Mol. Spectrosc. 80, 422–437 (1980) ] is extended in a manner similar to the extension previously described for HCNO [ P. Jensen, J. Mol. Spectrosc. 101, 422–439 (1983) ]. The extended Hamiltonian describes the manifold of large-amplitude vibrational states (due to the ν 7 CCC bending mode) superimposed on a high-frequency vibrational state involving excited quanta of the CCO bending modes ν 5 and ν 6. The extended model is used to fit CCC bending and rotation energy level separations for 12C 3 16O 2 superimposed on the ν 5 fundamental level. Due to the severely limited experimental data it is not possible to unambiguously determine the effective CCC bending potential energy function in the ν 5 state, but estimates of the potential energy parameters are obtained by determining them in two limiting cases.

An extended ab initio study of the rotation-vibration spectrum of HOC +

Configuration interaction calculations have been performed in order to investigate the bending potential of the molecular ion HOC + in detail. It is found that the bending potential has its minimum at the linear configuration and that it is very shallow. The ab initio points on the electronic ground state surface of HOC + were combined with previously calculated points to determine an improved force field. This force field was used in the second-order rotation-vibration perturbation Hamiltonian, as well as in the semirigid bender Hamiltonian, to evaluate rotation and vibration frequencies of HOC + and of some of its isotopes. The ν 0( J = 1−0) rotational transition frequency of the DOC + isotope is predicted to be 76 200 ± 40 MHz.

HCNO as a semirigid bender: The degenerate ν4 state

The semirigid bender Hamiltonian for fulminic acid HCNO (Bunker, Landsberg, and Winnewisser, J. Mol. Spectrosc. 74, 9–25 (1979)) is extended. The extended Hamiltonian describes the manifold of large amplitude vibrational states (due to the ν 5 HCN bending mode) superimposed on a high frequency vibrational state involving excited quanta of the ν 4 CNO bending mode. Such high frequency vibrational states may be degenerate when the large amplitude coordinate is zero, and the semirigid bender Hamiltonian is modified to account for the ν 4 vibrational angular momentum around the molecular axis in the linear limit, and for l-doubling effects. The extended Hamiltonian is used to fit HCN bending and rotation energy level separations for HCNO superimposed in the ν 4 fundamental level. It is found that the effective HCN bending potential in the ν 4 state is very similar to that in the high frequency vibrational ground state. The results obtained confirm the conclusion reached by Bunker, Landsberg, and Winnewisser: HCNO is linear at equilibrium.

The rotational spectrum of the CD2 radical studied by far infrared laser magnetic resonance spectroscopya)

We report the detection of 17 pure rotation transitions in the ground vibronic state of the CD2 radical using far infrared laser magnetic resonance spectroscopy. Fitting the data using an effective rotational Hamiltonian yields values for the three rotational constants, seven centrifugal distortion constants, the three electronic spin-rotation, and two electronic spin–spin parameters. We also fit this data, and CD2 ν2 band data (published separately), using the semirigid bender Hamiltonian and obtain the effective bending potential function for CD2. Combining this with previous CH2 results enables us to predict the rotation bending energy levels of CHD. We also report here the detection of two further rotational transitions in the ν1 excited vibrational state of CH2.

The laser magnetic resonance spectrum of the ν2 band of the methylene radical CH2

Ten rotation–vibration transitions in the ν2 (bending) fundamental band of CH2 in its 3B1 ground electronic state have been measured and assigned using the technique of intracavity CO2 laser magnetic resonance (LMR) spectroscopy in the region 880–1090 cm−1. Using the present data, and the microwave and far-infrared LMR measurements of pure rotational transitions, an effective bending potential energy curve has been derived for CH2 using the semirigid bender Hamiltonian. The bending frequency of CH2 is determined to be ν2=963.0987(4) cm−1, which is considerably lower than previous theoretical and experimental estimates.

The rigid bender and semirigid bender models for the rotation-vibration Hamiltonian

The rigid bender Hamiltonian used by Bunker and Stone ( J. Mol. Spectrosc., 41, 310 (1972)) is reviewed and applied to fit the recently obtained rotation-bending energy levels of the H 2O molecule. This rotation-bending Hamiltonian treats a triatomic molecule as bending with fixed bond lengths. A simple improvement is made by allowing the bond lengths to vary with the bond angle and the new Hamiltonian is called the semirigib bender Hamiltonian. This Hamiltonian allows for all the important stretch-bend interaction terms from the potential energy and rotation-bending interaction terms from the kinetic energy. As a result the variation of the rotational constants with bending vibrational state is treated better than by the rigid bender. The model is used to fit the rotation-bending energy levels of the H 2O molecule. While not as good as the nonrigid bender Hamiltonian of Hoy and Bunker ( J. Mol. Spectrosc., 52, 439 (1974)) the semirigid bender Hamiltonian is easier to apply to a larger molecule, and this is the reason for introducing it. At the end of the paper the rigid bender model is compared to a more approximate model in which the variation of the bending reduced mass with bending angle is ignored. The approximate model can introduce serious errors but since we know how the bending reduced mass varies with bond angle in the rigid bender model the approximation of the simpler model is unnecessary.