共查询到20条相似文献,搜索用时 20 毫秒
1.
The transformation of the effective rotational Hamiltonian H of nonrigid X 2 Y molecules to the form having a minimum number of diagonals in the basis of rotational functions of a symmetric top is discussed. Such a transformation is a generalization of the reduction transformation performed for the polynomial effective Hamiltonian H. It is shown that in the general case the transformation substantially changes the form of the initial Hamiltonian, which restricts the region of applicability (J<J*) of the reduced Hamiltonian represented in a class of elementary functions in terms of angular momentum operators. The values of the rotational quantum number J* are estimated for the (000) ground and (010) vibrational states of the H2O molecule. 相似文献
2.
《Journal of Molecular Spectroscopy》1987,124(2):272-284
A mixed matrix-operator form of the effective rotational Hamiltonian has been discussed for the degenerate vibrational states of symmetric top molecules. In this scheme, a rotational contact transformation can be applied to the effective Hamiltonian such that the operators of the “2, +2,” “2, −2,” and “2, −1” l-type interactions as well as the operators of the Δk = ±3 and ±4 interactions are eliminated from the first-order terms of the expansion of the rotational Hamiltonian in terms of the small parameter λ. The results have been used to discuss the correlation between various interaction parameters in the effective rotational Hamiltonian for the doubly degenerate fundamental vibrational levels of semirigid symmetric top molecules. For example, for C3v or D3 molecules, the parameter of the “2, −1” interaction is correlated with other parameters and cannot be determined separately by fitting the experimental data (unless there are certain accidental resonances between vibrational-rotational levels). 相似文献
3.
V. I. Starikov 《Optics and Spectroscopy》2001,91(4):600-603
Using the method of generating functions for the effective rotational Hamiltonian of H2X molecules, an expression for estimating the critical value J c of the rotational quantum number is obtained, starting with which the formation of four-level clusters in a molecule is possible. The analysis made in the harmonic approximation for rotational operators and for a particular form of generating functions showed the impossibility of clusterization for nonrigid H2X molecules with strong centrifugal effects. 相似文献
4.
Domagoj Kuić 《International Journal of Theoretical Physics》2013,52(4):1221-1239
Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G,H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J 2, J z and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry. 相似文献
5.
A Hamiltonian taking explicitly into account both Fermi and Coriolis interactions has been set up for triatomic molecules of symmetry Cs and used to reproduce, very satisfactorily, the available rotational energy levels of the {(100), (020)} interacting states of HDO, providing us with realistic wavefunctions as well as precise rotational constants and vibrational energies. Then, to calculate line intensities, these wavefunctions were used together with suitably chosen transition moment operators expanded up to degree 2 in and having the correct symmetry in the Cs group, leading to hybrid bands of both A and B type., Using this formalism, it has been possible to determine, from the fit of the existing experimental intensities, the coefficients appearing in the expansions of the transition moment operators of the 2ν2 and ν1 bands of HDO. In this way, we have improved upon the F-factor formalism which needs much more parameters to reproduce the line intensities with the same precision. Finally, using the transition moments as well as the wavefunctions and energy levels deduced from the diagonalization of the Hamiltonian matrix, we have calculated the whole spectrum of the ν1 and 2ν2 bands of HDO. 相似文献
6.
Relations are found for the calculation of eigenvalues and eigenfunctions of the Hamiltonian of internal rotational motion in molecules in the basis of plane waves. The dependences of kinematic coefficient F(φ) and potential V(φ) on dihedral angle φ are represented by Fourier series for both symmetric and asymmetric functions, as well as for general periodic functions. If a molecule has symmetry elements, the found solution transforms to that previously known. 相似文献
7.
H. A. Naqvi C. Bahri D. Troltenier J. P. Draayer A. Faessler 《Zeitschrift für Physik A Hadrons and Nuclei》1995,351(3):259-270
An algebraic realization of the quantum rotor for non-zero spin values (integer as well as half-integer) is established by constructing a model Hamiltonian out of rotationally invariant functions of the generators ofSU(3). The eigenvalues of this Hamiltonian in the leading normal-SU(3) symmetry for25Mg and the so-called leading pseudo-SU(3) symmetries for159Dy and165Er are compared with the corresponding rotor results. For spinfree systems the internal symmetry group of the rotor and itsSU(3) realization are known to be D2, the Vierergruppe. This symmetry extends to integral spin values, while for half-integer spins the rotor and itsSU (3) realization are shown to display an internal quaternion group symmetry. The theory points to a microscopic (many-particle shell-model) picture of nuclear rotational motion with spin degrees of freedom taken fully into account. An algebraic realization of the many-particle Nilsson model for odd-A nuclei, with the orbit-orbit and spin-orbit terms included, is given and applied to23Na. 相似文献
8.
The spin-rotational Hamiltonian for an asymmetric-top molecule in a given vibrational level of an open-shell electronic state may contain more parameters than can be determined from the observed energy levels. This paper describes the reduction of the Hamiltonian by means of a unitary transformation to a form suitable for fitting to observed energies. It is shown that, for molecules of lower than orthorhombic symmetry, there are fewer determinable quadratic spin-rotation parameters than have been used previously. For example, for a molecule belonging to the group C8, there are four, not five, determinable spin-rotation constants, ?αβ. Similar indeterminacies exist among the quartic terms of the spin-rotation Hamiltonian. The case of a molecule of orthorhombic symmetry, for which there are six determinable quartic parameters, is considered in detail. The results are applied to the experimental data available on the spin-rotation splittings of the HO2 and NH2 radicals in their ground vibrational and electronic states. 相似文献
9.
《Journal of Molecular Spectroscopy》1987,126(2):329-340
A fourth-order effective Hamiltonian has been derived for the torsion-rotation problem of a methanol-type molecule, i.e., for a C3v top attached to a Cs frame. First, symmetry considerations based on a frame-fixed axis system are used to determine allowed terms in the Hamiltonian. These terms are then subjected to a contact transformation to remove the indeterminate ones. This procedure is essentially an extension of Watson's method for semirigid molecules to the torsion-rotation problem. It is demonstrated that the Hamiltonian derived in the present work is capable of improving the fittings of the millimeter and submillimeter absorption frequencies of CH3OH and CH3SH. 相似文献
10.
11.
Line frequencies and intensities in the ν3 fundamental band of molecules with an octahedral symmetry
Frequencies and lines intensities in the υ3 band of molecules with an octahedral symmetry have been calculated by the use of second-order perturbation theory, according to the model of clusters. The calculations are developed by the use of the Hamiltonian of Hecht and the special properties of these molecules. Comparisons are made between the present theoretical calculations and other theoretical and experimental works. 相似文献
12.
J.K Lawson 《Reports on Mathematical Physics》2004,53(1):19-37
We construct momentum mappings for covariant Hamiltonian field theories using a generalization of symplectic geometry to the bundle LVY of vertically adapted linear frames over the bundle of field configurations Y. Field momentum observables are vector-valued momentum mappings generated from automorphisms of Y, using the (n + k)-symplectic geometry of LVY. These momentum observables on LVY generalize those in covariant multisymplectic geometry and produce conserved field quantities along flows. Three examples illustrate the utility of these momentum mappings: orthogonal symmetry of a Kaluza-Klein theory generates the conservation of field angular momentum, affine reparametrization symmetry in time-evolution mechanics produces a version of the parallel axis theorem of rotational dynamics, and time reparametrization symmetry in time-evolution mechanics gives us an improvement upon a parallel transport law. 相似文献
13.
The jet-cooled Fourier-transform microwave spectrum of N-methylacetamide (CH3NHC(O)CH3), a molecule containing two methyl tops with relatively low barriers to internal rotation, has been recorded and fit to nearly experimental uncertainty. Measurements were carried out between 10 and 26 GHz, with the nitrogen quadrupole splittings resolved for many transitions. The permutation-inversion group for this molecule is G18 (not isomorphic to any point group), with irreducible representations A1, A2, E1, E2, E3, and E4. One of these symmetry species and the usual three asymmetric rotor quantum numbers JKaKc were assigned to each torsion-rotation level involved in the observed transitions. F values were assigned to hyperfine components, where . Transitions involving levels of A1 and A2 species could be fit to an asymmetric rotor Hamiltonian. The other transitions were first fit separately for each symmetry species using a Pickett-like effective rotational Hamiltonian. Constants from these fits show a number of additive properties which can be correlated with sums and differences of effects involving the two tops. A final global fit to 48 molecular parameters for 839 hyperfine components of 216 torsion-rotation transitions involving 152 torsion-rotation levels was carried out using a newly written two-top computer program, giving a root-mean-square deviation of observed-minus-calculated residuals of 4 kHz. This program was written in the principal axis system of the molecule and uses a free-rotor basis set for each top, a symmetric-top basis set for the rotational functions, and a single-step diagonalization procedure. Such an approach requires quite long computation times, but it is much less prone to subtle programming errors (a consideration felt to be important since checking the new program against precise fits of low-barrier two-top molecules in the literature was not possible). The two internal rotation angles in this molecule correspond to the Ramachandran angles ψ and φ often defined to describe polypeptide folding. Barriers to internal rotation about these two angles were found to be 73 and 79 cm−1, respectively. Top-top coupling in both the kinetic and potential energy part of the Hamiltonian is relatively small in this molecule. 相似文献
14.
In this study the asymptotic behavior of rotational energies of simple rigid molecules of X2Y-type is considered. This behavior is obtained using various forms of an effective rotational Hamiltonian. The results of calculations for highly excited rotational energies of the molecules H2O and CH2 are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 9–12, January, 1990. 相似文献
15.
The previously described reduction of the effective rotational Hamiltonian for semirigid molecules of C3v or D3 point group symmetry [M. R. Aliev and V. T. Aleksanyan, Opt. Spectrosc.24, 201–206 (1968)] has been extended to nonrigid molecules with a significant inversion splitting of the energy levels (e.g., NH3, H3O+, CH3?, or SiH3 molecules). Although for semirigid molecules like PH3 or AsH3, the parameters α and η′3 which appear in the terms α[J+3 + J?3, Jz]+ and η′3(J+6 + J?6) are almost completely correlated, the effects of the inversion splitting and the accidental resonance which can occur between the interacting rotational levels in nonrigid molecules make it possible to determine α and η′3 separately. The results of fitting the experimental data for 14NH3 and 15NH3 [?. Urban, Romola D'Cunha, K. Narahari Rao, and D. Papou?ek, Canad. J. Phys.62, 1775–1791 (1984); Romola D'Cunha, ?. Urban, K. Narahari Rao, L. Henry, and A. Valentin, J. Mol. Spectrosc.111, 352–360 (1985)] are in agreement with this conclusion. The possibility of the determination of the sign of η3 from a simultaneous analysis of the allowed and Δk = ±3 forbidden transitions in semirigid XY3 molecules has been discussed. 相似文献
16.
The theory of irreducible tensor systems is used to obtain general formulas for the dependence of the matrix elements of the transformed vibrational—rotational dipole moment on the rotational quantum numbers. The relations obtained are valid for molecules of arbitrary symmetry and can take into account all possible intramolecular effects and interactions (resonances, vibration—rotation interactions, splitting, etc.). As illustrations we consider molecules of the type XY4 (symmetry Td) and XY2 (symmetry C2v).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 8, pp. 3–10, August, 1987. 相似文献
17.
A. M. Shirokov N. A. Smirnova Yu. F. Smirnov O. Castaños A. Frank 《Physics of Atomic Nuclei》2000,63(4):695-699
It is shown that the set of transformations of the s and d boson operators that maintain the IBM-like form of the Hamiltonian comprises a discrete point symmetry group D 2′. The transformations manifest themselves as a parameter symmetry of the IBM-1 Hamiltonian. The transformations considered are also necessary for constructing the most general IBM-2 Hamiltonian. The properties of the potential energy surfaces arising in connection with these transformations are discussed. 相似文献
18.
Two lowest eigenvalues of the Hamiltonian for the hydrogen molecule corresponding to the 1Πu symmetry have been calculated in the Born-Oppenheimer approximation. They represent the C and D states, respectively. Different highly flexible wavefunctions were used for both states and the calculations were performed for a wide range of internuclear distances: 1 ≤ R ≤ 12 a.u. for the C state, and 1 ≤ R ≤ 25 a.u. for the D state. The calculated potential energy curves are more accurate than any previous ab initio results for the above states. The vibrational Schrödinger equation for both states has been solved for H2, HD, and D2 using the Numerov method. The resulting energies and rotational constants are compared with the experimental values. 相似文献
19.
Microwave measurements in the interval from 6 to 133 GHz, consisting of 444 rotational transitions in the vibrational ground state of hydrazine with J ≤ 31 and Ka ≤ 6 were fit to an effective rotational Hamiltonian containing 9 asymmetric rotor constants, 14 NH2 inversion parameters, and 1 internal rotation parameter, with an overall standard deviation of the fit of 0.40 MHz. This set of parameters contains: (i) the three rotational constants; (ii) tunneling splitting constants for NH2 inversion at one end of the molecule, for NH2 inversion at both ends of the molecule, and for internal rotation through the trans barrier; (iii) two K-type doubling constants affecting the K = 1 levels; (iv) an a-type Coriolis interaction with matrix elements linear in K; and (v) various centrifugal distortion corrections to the above parameters. A consistent group theoretical formalism was used to label the energy levels and to select terms in the phenomenological rotational Hamiltonian. The Hamiltonian matrix, which is set up in a tunneling basis set, is of dimension 16×16 and contains only ΔKa = 0 matrix elements, asymmetric rotor effects being taken into account on the diagonal by terms from a Polo expansion in bn. Hyperfine splittings and barrier heights are not discussed. 相似文献