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1.
《Journal of Molecular Spectroscopy》1986,118(1):18-39
The derivation of the nonrigid bender Hamiltonian for the calculation of the rotation-vibration energies of a triatomic molecule was completed by P. Jensen and P. R. Bunker [J. Mol. Spectrosc. 99, 348–356 (1983)] using Van Vleck perturbation theory. This perturbation technique assumes that the bending vibration frequency is much less than the stretching vibration frequencies (such as in the ground electronic state of C3). For molecules such as H2O, for which this is not the case, an alternative formulation of the theory is possible in which allowance is made for the dependence of the perturbation theory energy denominators on the bending vibration quantum number v2 and on the rotational quantum number K. This was pointed out by A. R. Hoy and P. R. Bunker [J. Mol. Spectrosc. 74, 1–8 (1979)], and some of the corrections were made by them. We now develop the perturbation theory expressions allowing for the dependence of all the energy denominators on v2 and K. 相似文献
2.
《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
3.
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
4.
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
5.
Sergey V. Petrov 《Journal of Molecular Spectroscopy》2007,243(2):245-252
We report and substantiate a method for constructing the rotational energy surface (RES) of a molecule as a pure classical object. For an arbitrary molecule we start from the potential energy surface rather than from a conventional “effective Hamiltonian”. The method is used for constructing the RES of the PH3 molecule in its ground vibrational state. We have used an ab initio potential energy surface [D. Wang, Q. Shi, Q.-S. Zhu, J. Chem. Phys. 112 (2000) 9624-9631; S.N. Yurchenko, M. Carvajal, P. Jensen, F. Herregodts, T.R. Huet, Chem. Phys. 290 (2003) 59-67.]. The shape of the RES is shown not to change for J from 0 to 120. The procedure of quasiclassical quantization of the RES was also undertaken, yielding a set of quasiclassical critical values of the angular momentum. The results explain the structure of quantum rotational energy levels obtained by variational calculations [S.N. Yurchenko, W. Thiel, S. Patchkovskii, P. Jensen, Phys. Chem. Chem. Phys. 7 (2005) 573-582]. 相似文献
6.
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
7.
We report an ab initio calculation, at the MR-SDCI + Q + Erel/[Roos ANO (Fe), aug-cc-pVQZ (C, N)] level of theory, of the potential energy surface for 6Δi FeNC. From the ab initio results, we have computed values for the standard spectroscopic parameters of FeN12C and FeN13C. Analytical representations of the potential energy surfaces have been fitted through the ab initio points, and the resulting functions have been used for directly solving the rotation-vibration Schrödinger equation by means of the MORBID program and by means of an adiabatic-separation method. For 6Δi FeNC, our ab initio calculations show that the equilibrium structure is linear with re (Fe-N) = 1.9354 Å and re (N-C) = 1.1823 Å. We find that the bending potential is very shallow, and the MORBID calculations show that the zero-point averaged structure is bent with the expectation values 〈r (Fe-N)〉 = 1.9672 Å, 〈r(N-C)〉 = 1.1866 Å, and . The experimentally derived bond length r0 (N-C) = 1.03(8) Å reported for 6Δi FeNC by Lie and Dagdigian [J. Chem. Phys. 114 (2001) 2137-2143] is much shorter than the corresponding ab initio re-value and the averaged value from MORBID. Our calculations suggest that this discrepancy is caused by the inadequate treatment of the large-amplitude bending motion of 6Δi FeNC. It would appear that for floppy triatomic molecules such as FeNC, r0-values have little physical meaning, at least when they are determined with the effects of the large-amplitude bending motion being ignored, i.e., under the assumption that the r0 structure is linear. 相似文献
8.
Sergei V. Shirin Oleg L. Polyansky Nikolai F. Zobov Roman I. Ovsyannikov Jonathan Tennyson 《Journal of Molecular Spectroscopy》2006,236(2):216-223
Adiabatic potential energy surfaces (PESs) for three major isotopologues of water, H216O, H217O, and H218O, are constructed by fitting to observed vibration-rotation energy levels of the system using the nuclear motion program DVR3D employing an exact kinetic energy operator. Extensive tests show that the mass-dependent ab initio surfaces due to Polyansky et al. [O.L. Polyansky, A.G. Császár, S.V. Shirin, N.F. Zobov, P. Barletta, J. Tennyson, D.W. Schwenke, P.J. Knowles, Science 299 (2003) 539-542.] provide an excellent starting point for the fits. The refinements are performed using a mass-independent morphing function, which smoothly distorts the original adiabatic ab initio PESs. The best overall fit is based on 1788 experimental energy levels with the rotational quantum number J = 0, 2, and 5. It reproduces these levels with a standard deviation of 0.079 cm−1 and gives, when explicit allowance is made for nonadiabatic rotational effects, excellent predictions for levels up to J = 40. Theoretical linelists for all three isotopologues of water involved in the PES construction were calculated up to 26 000 cm−1 with energy levels up to J = 10. These linelists should make an excellent starting point for spectroscopic modelling and analysis. 相似文献
9.
The potential energy surface for the electronic ground state of the hydrogen selenide molecule has been determined previously by Jensen and Kozin [J. Mol. Spectrosc. 160 (1993) 39] in a fitting to experimental data by means of the MORBID computer program. We report here a further refinement of this surface, also made with the MORBID program. With the refined potential surface, we can make predictions of rotation-vibration transition wavenumbers for H2Se, D2Se, and HDSe, and with these predictions we can assign weak spectra of these molecules. We assign here two very weak bands of HD80Se, ν1+ν2+ν3 and 2ν1+ν3. The refinement of the potential energy surface was made possible because (1) the number of vibrational states characterized experimentally for various isotopomers of H2Se has approximately doubled since 1993, and (2) we now have access to larger computers with which we can fit energy spacings of states with J?8, whereas Jensen and Kozin could only use J?5. In the present work, we fitted rotation-vibration energy spacings associated with 24 vibrational states of H280Se with v1?6, v2?3, and v3?2; 11 vibrational states of D280Se with v1?2, v2?3, and v3?2, and 17 vibrational states of HD80Se with v1?3, v2?3, and v3?3. The input data set comprised 3611 energy spacings. In the fitting, we could usefully vary 29 potential energy parameters. The standard deviation of the fitting was 0.12 cm−1 and the root-mean-square deviation for 49 vibrational term values was 0.59 cm−1. 相似文献
10.
11.
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
12.
I. I. Bubukina N. F. Zobov O. L. Polyansky S. V. Shirin S. N. Yurchenko 《Optics and Spectroscopy》2011,110(2):160-166
A semiempirical potential energy surface is obtained for the major isotopologue of the water molecule H2
16O that allows the vibration-rotation energy levels in the range of 0–26000 cm−1 to be calculated with an accuracy almost equal to the average experimental accuracy of measurements in the infrared and visible
ranges. Variational calculations using this potential energy surface reproduce the experimental energy values of more than
1500 vibration-rotation levels of H2
16O with the total angular momentum quantum number J = 0, 2, and 5 in the indicated range with a standard deviation of 0.022 cm−1. The potential was obtained by optimizing a starting ab initio surface using a combination of two approaches, i.e., (1) the
multiplication of the starting ab initio surface by a morphing function whose parameters were optimized and (2) the optimization
of parameters of the ab initio surface using both the experimental values of energy levels and the results of quantum-chemical
electronic structure calculations. 相似文献
13.
《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
14.
Yu-Zhi Song Yong-Qing Li Shou-Bao Gao Qing-Tian Meng 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2014,68(1):1-8
A globally accurate potential energy surface is reported for the electronic ground-state HLi2 by fitting ab initio energies to double many-body expansion formalism. The total 3726 ab initio energies used to map the HLi2 potential energy surface are calculated using the multi-reference configuration interaction method, with their dynamical correlation being semiempirically corrected by the double many-body expansion-scaled external correlation method. The current potential energy surface generates an excellent fit of the ab initio energies, showing a small root-mean squared derivation of 0.636 ? kcal ? mol-1. The topographical features of the HLi2 potential energy surface are examined in detail, which concludes that the H + Li2(X ? 1 Σ g ) → Li + LiH(X ? 1 Σ) reaction is essentially barrierless and the exothermicity is calculated to be 33.668 ? kcal ? mol-1, thus corroborates the available experimental and theoretical results. 相似文献
15.
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
16.
The variational method of calculating vibrational energy levels for triatomic molecules has been extended to determine the lowest 22 levels for H2O, using an analytic form for the potential surface developed by Sorbie and Murrell. In addition, complete ab initio calculations of the fundamental frequencies for H2O have been carried out using extensive configuration interaction forms for the potential. They are predicted to be 3720, 1629, and 3807 cm?1, to be compared with experimental values of 3656, 1597, and 3754 cm?1. Also discussed is how the variational method may be extended to allow the calculation of vibrational energy levels for larger molecules. 相似文献
17.
The absolute radiative transition probabilities are calculated for previously observed spontaneous emission from A1Σu+ (v′,J′) → X1Σg+ (v″, J″ = J′ ± 1) reported in the preceding paper and by Woerdman (Chem. Phys. Lett.53, 219 (1978)). The calculations employ accurate hybrid potential energy curves, based on Rydberg-Klein-Rees (RKR), ab initio and long-range results, and a hybrid transition moment function, based on ab initio calculations. These calculated probabilities are compared with the various experimental results; while overall agreement is reasonable, detailed differences do occur. 相似文献
18.
《Journal of Molecular Spectroscopy》1986,118(1):88-95
Ninety-three points on the potential energy surface of the ground electronic state of the phosphine molecule (with energies up to 12 000 cm−1 above equilibrium) have been calculated ab initio using second-order many-body perturbation theory. A polynomial potential function (quartic in the in-plane coordinates and containing up to 12th-order terms in the out-of-plane coordinate) has been fitted to these points using the reduced inversion potential and standard polynomials. Using the nonrigid invertor Hamiltonian with this function, rotation-vibration energies have been calculated and found in reasonable agreement with experiment. The results are believed to be helpful in the determination of a realistic experimental potential function of the phosphine molecule over a wide range of values for the out-of-plane motion coordinate. 相似文献
19.
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 ν0(J = 1?0) rotational transition frequency of the DOC+ isotope is predicted to be 76 200 ± 40 MHz. 相似文献
20.
Tsuneo HiranoKeisaku Ishii Tina Erica Odaka Per Jensen 《Journal of Molecular Spectroscopy》2002,215(1):42-57
The MgNC radical was the first Mg-containing species to be observed in interstellar space. This fact has stimulated considerable spectroscopic interest in this molecule, and in its isomer MgCN, but nevertheless the only rotationally resolved spectroscopic data presently available for X?2Σ+ MgNC comprise the rotational spectrum (K. Kawaguchi et al., 1993, Astrophys. J.406, L39-L42; K. Ishii et al., 1993, Astrophys. J.410, L43-L44; M. A. Anderson and L. M. Ziurys, 1994, Chem. Phys. Lett.231, 164-170; E. Kagi et al., 1996, J. Chem. Phys.104, 1263-1267; E. Kagi and K. Kawaguchi, J. Mol. Spectrosc. 2000, 199, 309-310) together with a few vibronic bands, all originating in the vibronic ground state and belonging to the Ã2Π←X?2Σ+ electronic transition (R. R. Wright and T. A. Miller, 1999, J. Mol. Spectrosc.194, 219-228). For MgCN, only the rotational spectrum in the vibrational ground state is known (M. A. Anderson, T. C. Steimle, and L. M. Ziurys, 1994, Astrophys. J.429, L41-L44). We report here potential energy surfaces calculated by the Averaged Coupled-Pair Functional (ACPF) method with TZ3P+f (Mg), TZ2P+f(N,C) basis sets including core-valence correlation due to the Mg 2s and 2p electrons. The ab initio results are used for determining the standard spectroscopic constants of X?2Σ+ MgNC and MgCN. Also, we report variational calculations of the rotation-vibration energies, and variational simulations of the lowest rotation-vibration bands, carried out with the MORBID program system (P. Jensen, 1988, J. Mol. Spectrosc.128, 478-501). We hope that our theoretical results will encourage and facilitate further characterization of X?2Σ+ MgNC and MgCN by high-resolution spectroscopy. 相似文献