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1.
《Journal of Molecular Spectroscopy》1986,118(1):50-63
We have written a new computer program for diagonalizing the nonrigid bender Hamiltonian, and have based the program entirely on the theory as reviewed by P. Jensen [Comp. Phys. Rep. 1, 1–56 (1983)] and P. Jensen and P. R. Bunker [J. Mol. Spectrosc. 118, 18–39 (1986)]. Using this program we can calculate the rotation-vibration energy levels of a triatomic molecule from the potential energy function. The program is an improvement over an earlier version, particularly in the systematic treatment of all singular terms, and in the allowance made for the dependence of all perturbation energy denominators on the bending quantum number v2 and rotation quantum number K. The new program can be used for symmetric and unsymmetric triatomic molecules. In the present paper we test the program by applying it to the calculation of the rotation-vibration energy levels of C3 from an ab initio potential surface, and of H2O from ab initio and experimental potential surfaces. 相似文献
2.
Ch.V.S. Ramachandra Rao 《Journal of Molecular Spectroscopy》1981,89(1):197-213
Self-Consistent Field (SCF) and Configuration Interaction (CI) studies are performed on the bending mode of the water molecule using a double zeta plus polarization basis set. The ab initio points are fitted to a three-parameter double minimum potential consisting of a quadratic plus Lorentzian terms. The vibration-rotation energies are then evaluated using the large amplitude Hamiltonian developed by P. R. Bunker and co-workers at various levels of approximations. It is found that the calculated frequencies improve significantly as one proceeds from approximate Hb00(ρ) to rigid bender Hb0(ρ) [P. R. Bunker and J. M. R. Stone, J. Mol. Spectrosc.41, 310–332 (1972)] to semirigid bender Hb0(r, ρ) [P. R. Bunker and P. M. Landsberg, J. Mol. Spectrosc.67, 374–385 (1977)] Hamiltonian. With Hb0(r, ρ), the ab initio calculated bending frequency ν2 differs from the observed value (1595 cm?1) by 30 cm?1 and the barrier height is 12 229 cm?1. It is also shown that ν2 and its first four overtones are better calculated by 45–98 cm?1 when the ab initio potential is used directly instead of the three-parameter analytic potential fitted to ab initio data. Finally, rotation bending energy levels are calculated for v2 ≤ 3 and J ≤ 10 on the basis of a nonrigid bender Hamiltonian of A. R. Hoy and P. R. Bunker [J. Mol. Spectrosc.74, 1–8 (1979)], using the ab initio quadratic force field of P. Hennig, W. P. Kraemer, G. H. F. Diercksen, and G. Strey, [Theor. Chim. Acta47, 233–248 (1978)]. These results show that the accuracy of calculated force constants and frequencies is critically dependent not only on the size of the basis set but also on the number and spacing of the ab initio points used to derive the force field. 相似文献
3.
The rotation-vibration-electronic Hamiltonian of a triatomic molecule has been derived in a manner similar to that used by J. T. Hougen, P. R. Bunker, and J. W. C. Johns [J. Mol. Spectrosc.34, 136 (1970)] in deriving the rotation-vibration Hamiltonian. An effective rotation-vibration Hamiltonian for the ground electronic state has been obtained from this, by using the perturbation technique of P. R. Bunker and R. E. Moss [Mol. Phys.33, 417 (1977)], in order to account for the effect of the breakdown of the Born-Oppenheimer approximation to second order. The same form of effective rotation-vibration Hamiltonian, in which the breakdown of the Born-Oppenheimer approximation is allowed for, will be obtained for any molecule. This Hamiltonian contains effective moments of inertia (these involve rotation g-factor corrections) and effective nuclear masses (likely to be close to the atomic masses). Following the procedure of A. R. Hoy and P. R. Bunker [J. Mol. Spectrosc.74, 1 (1979)] the effective rotation-bending Hamiltonian is derived from the effective rotation-vibration Hamiltonian, and this could be used to fit the rotation-bending energy levels. 相似文献
4.
5.
Per Jensen 《Journal of Molecular Spectroscopy》1984,104(1):59-71
The semirigid bender Hamiltonian for carbon su?ide C3O2 [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 ν7 CCC bending mode) superimposed on a high-frequency vibrational state involving excited quanta of the CCO bending modes ν5 and ν6. The extended model is used to fit CCC bending and rotation energy level separations for12C316O2 superimposed on the ν5 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 ν5 state, but estimates of the potential energy parameters are obtained by determining them in two limiting cases. 相似文献
6.
The semirigid bender model (P. R. Bunker and D. J. Howe, J. Mol. Spectrosc.83, 288–303 (1980)) has been developed to fit the observed vibrational energy levels of the ground electronic state of and allowing for the complete bending (internal rotation) of HCN into CNH and of DCN into CND. From the fit we have been able to determine the bending potential function and the contribution to the bending potential that arises from the effect of averaging over the two stretching vibrations. The results are compared with ab initio calculations. 相似文献
7.
Ch.V.S. Ramachandra Rao 《Journal of Molecular Spectroscopy》1982,95(2):239-253
The semirigid bender Hamiltonian [Bunker and Landsberg, J. Mol. Spectrosc.67, 374–385 (1977)] was used to fit the rotation-inversion energy level separations in the excited state of formaldehyde. We fix the r0(CH) bond length and allow the R(CO) bond length and (H?H) bond angle to vary with the inversion angle ρ. The fit to 64 rotation-inversion energies (with v4 and J < 4) is significantly better with a standard deviation of 0.199 cm?1 than when the rigid bender [Bunker and Stone, J. Mol. Spectrosc.41, 310–332 (1972)] is used. The barrier height to planarity is 358 cm?1 and the equilibrium ρe = 34.7°. The CO bond length is found to decrease by 0.034 from 1.3670 Å and the H?H angle by about 6 from 122.4° as the molecular configuration changes from planar to pyramidal. The rigid bender model developed earlier by Moule and Rao for formaldehyde [J. Mol. Spectrosc.45, 120–141 (1973)] is then used to fit the 32 rotation-(out-of-plane) bending energy levels (with v4 = 0 and 1) of the ground electronic state of H2CO. For this, a simple potential consisting of quadratic and quartic terms is used and the standard deviation of the fit is 0.148 cm?1. 相似文献
8.
《Journal of Molecular Spectroscopy》1988,128(1):24-61
The nonrigid (effective) rotation-large-amplitude internal motion Hamiltonian (NRLH) of the general molecule with one or more large-amplitude vibrations has been derived to the order of magnitude κ2TVIB. The derivation takes advantage of the idea of a nonrigid reference configuration and uses the contact transformation method as a mathematical tool. The NRLH has a form fairly similar to that of the effective rotation Hamiltonian of semirigid (i.e., normal) molecules. From a careful examination of the Eckart-Sayvetz conditions and of the Taylor expansions of the potential energy surface in terms of curvilinear displacement coordinates, three types of large-amplitude internal coordinates of different physical meaning (effective large-amplitude internal coordinates, real large-amplitude internal coordinates, and reaction path coordinates) are described. To test the ideas and the formulas the effective bending potential function of the C3 molecule in its ground electronic and ground stretching vibrational state is calculated from the ab initio potential energy surface given by W. P. Kraemer, P. R. Bunker, and M. Yoshimine (J. Mol. Spectrosc. 107, 191–207 (1984)). The calculations were carried out by using either the effective or the real large-amplitude bending coordinate of C3. The NRLH theory is compared to the nonrigid bender theory at a theoretical level as well as through the results of the test calculations. 相似文献
9.
In this paper we report the results of improving the non-rigid bender formulation of the rotation-vibration Hamiltonian of a triatomic molecule [see A. R. Hoy and P. R. Bunker, J. Mol. Spectrosc., 52, 439 (1974)]. This improved Hamiltonian can be diagonalized as before by a combination of numerical integration and matrix diagonalization and it yields rotation-bending energies to high values of the rotational quantum numbers. We have calculated all the rotational energy levels up to J = 10 for the (v1, v2, v3) states (0, 0, 0) and (0, 1, 0) for both H2O and D2O. By least squares fitting to the observations varying seven parameters we have refined the equilibrium structure and force field of the water molecule and have obtained a fit to the 375 experimental energies used with a root mean square deviation of 0.05 cm?1. The equilibrium bond angle and bond length are determined to be 104.48° and 0.9578 Å respectively. We have also calculated these energy levels using the ab initio equilibrium geometry and force constants of Rosenberg, Ermler and Shavitt [J. Chem. Phys., 65, 4072 (1976)] and this is then the first complete ab initio calculation of rotation-vibration energy levels of high J in a polyatomic molecule to this precision. the rms fit of these ab initio energies to the experimental energies for the H2O molecule is 2.65 cm?1. 相似文献
10.
We use the RENNER program system (see, for example, P. Jensen, G. Osmann, and P. R. Bunker, in “Computational Molecular Spectroscopy” (P. Jensen and P. R. Bunker, Eds.), Wiley, Chichester, 2000, and references therein) to make a detailed calculation of the rovibronic energies in the first excited electronic state, Ã2Π, of the MgNC radical. This calculation is based on ab initio data (supplemented here with points for larger bending displacements from linearity) calculated at the level of MR-SDCI(+Q)/[TZ3P+f(Mg), aug-cc-pVQZ (N and C)] by T. E. Odaka, T. Taketsugu, T. Hirano, and U. Nagashima (J. Chem. Phys.115, 1349-1354 (2001)). These authors employed ab initio derived spectroscopic constants to calculate vibronic energies using perturbation expressions (J. T. Hougen and J. P. Jesson, J. Chem. Phys.38, 1524-1525 (1963)), and their results suggested that an observed vibronic band belonging to the Ã2Π←X?2Σ+ electronic transition (R. R. Wright and T. A. Miller, J. Mol. Spectrosc.194, 219-228 (1999)) should be reassigned. The present work confirms this conclusion, which is further substantiated by the rotational structures calculated in the vibronic states and by Franck-Condon theory predicting relative intensities. 相似文献
11.
Per Jensen 《Journal of Molecular Spectroscopy》1983,101(2):422-439
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 ν5 HCN bending mode) superimposed on a high frequency vibrational state involving excited quanta of the ν4 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 ν4 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 ν4 fundamental level. It is found that the effective HCN bending potential in the ν4 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. 相似文献
12.
《Journal of Molecular Spectroscopy》1986,118(1):208-231
In two recent publications [V. Špirko, P. Jensen, P. R. Bunker, and A. Čejchan, J. Mol. Spectrosc. 112, 183–202 (1985); P. Jensen, V. Špirko, and P. R. Bunker, J. Mol. Spectrosc. 115, 269–293 (1986)], we have described the development of Morse oscillator adapted rotation-vibration Hamiltonians for equilateral triangular X3 and Y2X molecules, and we have used these Hamiltonians to calculate the rotation-vibration energies for H3+ and its X3+ and Y2X+ isotopes from ab initio potential energy functions. The present paper presents a method for calculating rotation-vibration line strengths of H3+ and its isotopes using an ab initio dipole moment function [G. D. Carney and R. N. Porter, J. Chem. Phys. 60, 4251–4264 (1974)] together with the energies and wave-functions obtained by diagonalization of the Morse oscillator adapted Hamiltonians. We use this method for calculating the vibrational transition moments involving the lowest vibrational states of H3+, D3+, H2D+, and D2H+. Further, we calculate the line strengths of the low-J transitions in the rotational spectra of H3+ in the vibrational ground state and in the ν1 and ν2 states. We hope that the calculations presented will facilitate the search for further rotation-vibration transitions of H3+ and its isotopes. 相似文献
13.
The reduction of the effective Hamiltonian has been derived for C3v symmetric top molecules in the vtequals;1 state with extension to nuclear quadrupole coupling. The theory has been applied to the hyperfine structures of rotational transitions observed for AsF3 (v4equals;1) [H. Bürger, J. Demaison, P. Dréan, C. Gerke, L. Halonen, H. Harder, H. Mäder, J. Radtke, and H. Ruland, J. Mol. Spectrosc.180, 85-99 (1996)]. The data have been analyzed using two reduced forms of the effective Hamiltonian which follow the reductions Q and D [E. I. Lobodenko, O. N. Sulakshina, V. I. Perevalov, and Vl. G. Tyuterev, J. Mol. Spectrosc.126, 159-170 (1987)] in the pure rovibrational case. The unitary equivalence of the derived parameter sets has been demonstrated. 相似文献
14.
The stretch-bender model, developed originally to describe the effects of stretch-bend interactions and Renner-Teller coupling in symmetrical triatomic molecules, has been extended to incorporate the effects of spin-orbit interaction and of overall rotation. A comparison is made between the treatment of spin-orbit interaction and of overall rotation in our model and in the MORBID approach of P. Jensen, M. Brumm, W. P. Kraemer, and P. R. Bunker (J. Mol. Spectrosc.171, 31-57 (1995)). 相似文献
15.
《Journal of Molecular Spectroscopy》1986,120(1):169-174
The rotational spectra in the v10 = 4 vibrational state of propyne have been determined in the frequency range 17–52 GHz. Molecular constants for this vibrationally excited state have been determined from more than 16 observed rotational transitions. Agreement between experimentally measured frequencies are presented and compared with those calculated using the results of basic perturbation theory. Matrix elements for the diagonal and nondiagonal terms were obtained from a previous paper by A. Bauer, G. Tarrago, and A. Remy. [J. Mol. Spectrosc. 58, 111–124 (1975)]. 相似文献
16.
The semirigid bender Hamiltonian [Bunker and Landsberg, J. Mol. Spectrosc., 67, 374–385 (1977)] is used to fit the rotation-vibration energy level separations in the fulminic acid (HCNO) molecule. The allowance made in the model for the variation of the CH and CN bond lengths with the HCN bending angle proves to be very important, and as well as achieving a good fit we are able to make a detailed investigation of the shape of the HCN bending potential function.From the results we conclude that the equilibrium structure of HCNO is linear but that excitation of the ν1 or ν2 stretching vibrations gives rise to an effective HCN bending potential function having its minimum at a nonlinear configuration. Even in the ground state the zeropoint vibrational contributions from ν1 and ν2 to the effective HCN bending potential give a small barrier (11.5 cm?1) to linearity, and we determine that the zero-point HCN bending vibrational amplitude is ±34°. 相似文献
17.
V. Špirko 《Journal of Molecular Spectroscopy》1979,74(3):456-464
This paper is concerned with the determination of the shape of the electric dipole moment function of a pyramidal XY3 molecule with a low barrier to inversion over a wide range of values for the inversion coordinate. The effective inversion-rotation Hamiltonian [V. ?pirko, J. M. R. Stone, and D. Papou?ek, J. Mol. Spectrosc.60, 159–178 (1976)] is used to explain the anomalous vibrational dependence of the electric dipole moment of 14NH3 [F. Shimizu, J. Chem. Phys.52, 3572–3576 (1970)], and of 15NH3 [B. J. Orr and Takeshi Oka, J. Mol. Spectrosc.66, 302–313 (1977)]. The experimental data of Orr and Oka are used to fit the μz component of the total dipole moment function and the fitted function is used to predict the transition moments in the nν2 inversion sequence of 14NH3 and 15NH3. To illustrate the measure of the rotational dependence of the transition moments, two examples, involving ground and excited (v2 = 1) states, are also presented. 相似文献
18.
《Journal of Molecular Spectroscopy》1996,177(1):124-133
The microwave and submillimeter wave spectra of propyne between 17 and 358 GHz were measured and the rotational transitions in thev8= 1 excited vibrational state of the CH3rocking vibration were assigned. About 1050 wavenumbers of the ν8vibration–rotation fundamental band and about 600 wavenumbers of the ν5fundamental band of the[formula]stretching vibration were assigned from the infrared spectrum between 910 and 1130 cm−1which was used previously (G. Graneret al., J. Mol. Spectrosc.161,80–101 (1993)) in the analysis of the combinationv9=v10= 1 and thev10= 3 overtone levels (ν9being the[formula]bending and ν10the[formula]bending vibrations). The rovibrational and rotational data corresponding to the two fundamental levels were analyzed simultaneously in least-squares fits using a model which treats together all the vibrational levels in the region around 1000 cm−1with their strong anharmonic and vibration–rotation resonances. The refined parameters reproduce the infrared and submillimeter wave data of thev5= 1 level with standard deviations of 0.32 × 10−3cm−1and 59 kHz, respectively, while for thev8= 1 level the standard deviations were 0.41 × 10−3cm and 290 kHz. The refined parameters of the combination and overtone levels provide reliable predictions for future submillimeter wave studies. 相似文献
19.
Measurements of line center positions of H218O in the 2900 to 3400 cm?1 region have been made at high resolution. This region contains absorptions of the (020) band and P-branch absorptions of the (100) and (001) bands of H218O. Values of the energy levels of the (020) state were determined in which ground state energy levels derived by Fraley, Rao, and Jones [J. Mol. Spectrosc.29, 312 (1969)] and Williamson, Rao, and Jones [J. Mol. Spectrosc.40, 372 (1971)] were used in the analysis. A new set of ground state levels was obtained by an iterative procedure. 相似文献
20.
《Journal of Molecular Spectroscopy》1987,124(2):306-316
The pure rotational spectrum in the vibrational ground state [J. Bendtsen and F. M. Nicolaisen, J. Mol. Spectrosc. 119, 456–466 (1986)] and the infrared spectrum of the fundamental bands ν5 and ν6 [J. Bendtsen, F. Hegelund, and F. M. Nicolaisen, J. Mol. Spectrosc. 118, 121–131 (1986)] of HN3 have been simultaneously analyzed using a three-level model taking into account resonance between the ground state and ν5 due to centrifugal distortion [K. Yamada, J. Mol. Spectrosc. 81, 139–151 (1980)] and a- and b-Coriolis interactions between ν5 and ν6. A set of ground- and upper-state constants have been obtained and values for the centrifugal distortion parameter C5ab and the Coriolis coupling constant ζ5,6b are derived. A complete set of ground-state energies for J ≦ 50 and Ka ≦ 10 is tabulated. 相似文献