High resolution spectroscopy of the ν3 band of the van der Waals complex Ar—DCOOH

The vibrational-rotational spectrum of the van der Waals complex Ar-DCOOH has been recorded in the spectral region of the carbonyl stretch band. This work represents the first rotationally resolved vibrational spectrum for this complex. A full set of molecular constants could be deduced by fitting 105 lines with a standard S-reduced Watson Hamiltonian. The band origin was determined to be 1725.8440(1)cm^?1 which corresponds to a small red shift of 0.0309cm^?1 compared to the monomer band. The rotational constants deviate only slightly from the rotational constants in the ground state, as determined by microwave spectroscopy (I. I. Ioannou and R. L. Kuczkowski, 1993, J. phys. Chem., 98, 2231).     

Vibrational and Rotational Motions Model of Nucleus(Ⅰ) Cranking Bohr-Mottelson Hamiltonian and Analyses of the Rotational Bands of Even-Even Nuclei

Starting from cranking shell model,a collective vibrational and rotational Hamiltonian(cranking Bohr-Mottelson Hamiltonian CBMH)is derived,in which the rotational frequency is not quantized.Introducing a reasonable collective potential,the formula for the rotational spectrum can be obtained.The formula is applied to analyze the rotational bands of even-even nuclei with satisfactory results.     

原子核振动与转动模型（Ⅰ）推转玻尔─莫特逊哈密顿量和偶偶核正常转动谱分析

从推转壳模型出发，导出了转动频率未量子化的集体振动－转动哈密顿量，称为推转玻尔－莫特逊哈密顿量（ＣＢＭＨ）．引入合理的集体运动位势，由ＣＢＭＨ可以得到解析形式的转动谱公式．应用这一振动－转动模型，对偶偶变形核的正常转动能谱进行了分析，取得了满意的结果．     

On the absorption saturation in the vibrational-rotational bands of molecules

Analytical expressions describing saturation of the stationary absorption coefficient in a vibrational-rotational band in the spectrum of a molecular gas are obtained taking into account that many other bands are involved in the absorption process as well. The formulas are derived for an arbitrary spectral composition of the pumping radiation with an allowance for a difference between the rotational and vibrational relaxation rates and between the relaxation rates of the lower and upper vibrational levels. The influence of saturation on the appearance of the partial inversion and the negative absorption effects is considered. The general formulas are simplified and the vibrational and rotational contributions to the saturation are separated within the frame-work of the local Elsasser model for the rotational band structure. Explicit relationships between the dimensionless parameters describing the vibrational and rotational saturation mechanisms are obtained and analyzed, and conditions under which one of these mechanisms is dominating are determined. Particular calculations were performed for the (000)–(010) and (000)–(001) absorption bands of the O₃ molecule and features of the saturation effect in these bands were established.     

Partial inversion in small molecules: New potentialities for the spectroscopic diagnostics of gases

The formation of vibrational-rotational absorption spectra of small molecules in vibrationally non-equilibrium conditions, with the possibility of manifestation of partial population inversion of levels and negative absorption, is studied. Specific features of the partial inversion in linear and top molecules are analyzed. It is shown that water vapor is the best object among atmospheric gases for the realization of this effect. Formulas for the integrated line intensities and the absorption coefficient of two-and three-level nonequilibrium vibrational systems with a rotational structure are obtained. It is shown that the partial-inversion effect can be used to study weak vibrational-rotational transitions. Concrete calculations for the (000)-(010)-(020) bands of water molecules at different temperatures are made. The frequencies are determined for which negative absorption is the strongest.     

Lifetimes of the electronic-vibrational-rotational states of hydrogen molecule (Review)

Data on the lifetimes of the vibrational-rotational levels of the excited electronic states of hydrogen molecule (including H₂, D₂, HD, DT, and T₂ isotopomers) are reviewed. All data on the rotational sublevels of the lowest vibrational levels of various electronic states are presented, which were available before June 2001. A comparative analysis of the data obtained by various researchers using different methods (experimental, semi-empirical, and non-empirical) is performed for the first time. The influence of non-adiabatic intramolecular interactions on the dependence of lifetimes of the rovibronic levels of hydrogen molecule on the vibrational and rotational quantum numbers is discussed. A set of reliable data is selected which can be recommended for use in various applications.     

Calculation of the rotational energies of the H2O molecule from a force field

The rotational energy levels up to J,K?10 are calculated for the lowest vibrational state of the water molecule. A rapidly convergent model of the effective rotational Hamiltonian is used.     

A new modification of the method of investigation of vibration-rotation interactions in molecules

The superoperator generalization of contact transformations has been used. New forms are presented for derivation of an effective rotational Hamiltonian and for investigation of rotational structure of vibrational bands (symmetric rotors).     

Forbidden vibrational-rotational transitions and Herman-Wallis factors in fundamental IR bands of symmetric-top molecules

Within the theory of coupled schemes of ordering of vibrational-rotational interactions, the operator of the effective dipole moment of single-quantum vibrational transitions is represented in the form of an infinite series in vibrational (normal coordinates and conjugate momenta) or rotational variables (components of the total angular momentum). Mechanisms of activation of infrared-inactive totally symmetric vibrations in molecules of the D _2a , D _3h , C _3h , D _n (n ≥ 3), S ₄, T, T _a , and O symmetries and forbidden vibrational-rotational transitions in IR bands of active vibrations have been studied. The group-theoretic analysis of tensor parameters in higher-order effective dipole moments of single-quantum vibrational transitions in axially symmetric molecules has been performed. The strengths of allowed transitions and forbidden transitions in fundamental and hot IR bands of axially symmetric molecules are calculated with allowance for the Herman-Wallis factors. For effective dipole moments of multiquantum transitions in molecules, models are developed in the form of infinite series in rotational variables and in the form of Padé approximants.     

Transformation of the effective rotational Hamiltonian of nonrigid X 2 Y molecules

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.     

Effective theory for deformed nuclei

Techniques from effective field theory are applied to nuclear rotation. This approach exploits the spontaneous breaking of rotational symmetry and the separation of scale between low-energy Nambu–Goldstone rotational modes and high-energy vibrational and nucleonic degrees of freedom. A power counting is established and the Hamiltonian is constructed at next-to-leading order.     

The interacting states (020), (100), and (001) of H217O and H218O

A fit of about 350 rotational levels of the (020), (100), and (001) vibrational states has been performed for H₂¹⁷O as well as for H₂¹⁸O leading to the determination of 51 rotational and coupling constants for each isotopic species. The Fermi-type interaction and the two Coriolis-type interactions have been taken into account by appropriate rotation-vibration operators and the v-diagonal part of the Hamiltonian is, for each vibrational state, a Watson-type Hamiltonian. The results are very satisfactory since 87% of the experimental levels are reproduced within 15 × 10^?3 cm^?1.     

Semiempirical study of perturbations of the Landé g factors of the electronic-vibrational-rotational levels of hydrogen: I. Theory

Theoretical analysis of perturbations of the Landé g factors of the electronic-vibrational-rotational levels of a diatomic molecule is performed for the case of interactions between electronic states whose number is arbitrary finite and that are not limited by the smallness of the parameter describing these interactions, with regard for the interaction of rovibrational states with an arbitrary finite number of vibrational-rotational levels of individual perturbing electronic states. The spin-multiplet interaction between rovibrational states was disregarded. As a result of general consideration, formulas are obtained for the g factors of rovibrational levels for the following cases: (i) mutual perturbation of a pair of levels; (ii) an nl complex of terms; and (iii) the interaction between an arbitrary number of vibrational-rotational levels of electronic states (whose number is also not limited) considered in the first order of the perturbation theory. The formulas obtained are given in the form of dependences on differences in observed (perturbed) values of rovibrational terms and matrix elements of vibrational wave functions dependent on the internuclear distance, which, in turn, are matrix elements of the electron wave functions of different operators that take into account the interaction between the electrons and nuclei of a molecule. The possibilities of using the obtained expressions in semiempirical study of perturbations and of determining the absolute dependences of the g factors of rovibrational levels of the electronic states of diatomic molecules (in particular, the hydrogen molecule) on the vibrational and rotational quantum numbers are analyzed.     

Rotational-vibrational polarizability operator for nonlinear X<Subscript>2</Subscript>Y molecules: Application to the calculation of the Raman spectrum of the H<Subscript>2</Subscript>O molecule

For nonlinear X₂Y molecules, an expression for the transformed polarizability operator is obtained with an accuracy of up to the second order of the theory of perturbation. This operator is applied to the calculation of the intensities of Raman lines of the H₂O molecule. The corrections to the polarizability of the molecule associated with the vibrational-rotational interaction are shown to considerably change the integral intensity of a pure rotational band. The dependence of the average polarizability of the molecule on the vibrational quantum number V ₂, describing deformation vibrations, is estimated.     

High-Lying Rotational Levels of Water: An Analysis of the Energy Levels of the Five First Vibrational States

As a continuation of the work carried out on the ground and (010) vibrational states of water (R. Lanquetin, L. H. Coudert, and C. Camy-Peyret, 1999, J. Mol. Spectrosc. 195, 54-57), rotational energy levels for these two states are revisited here and new accurate rotational energy levels are considered for the three next vibrational states, that is, the (020), (100), and (001) states. Experimental rotational energies, along with their uncertainties, are retrieved through analyses of already published data sets and of discharge and flame emission spectra. The maximum value of J for the obtained levels is 25 for the ground state, 21 for the (010) state, and 20 for the three next states. Based on the bending-rotation Hamiltonian approach (L. H. Coudert, 1997, J. Mol. Spectrosc. 181, 246-273), a new theoretical approach is proposed to calculate rotational energies in the five interacting vibrational states under consideration and is used to carry out an analysis of the experimental energies. Comparisons with other existing energy level data sets are also presented. Copyright 2001 Academic Press.     

Analysis of the "Unusual" Vibrational Components of Triply Degenerate Vibrational Mode nu(6) of Mo(CO)(6) Based on the Classical Interpretation of the Effective Rotation-Vibration Hamiltonian

Rotational structure of the triply degenerate vibrational state nu(6)(F(1u)) of the octahedral molecule Mo(CO)(6) is analyzed qualitatively on the basis of classical mechanics. We show that the energy level redistribution between the vibrational components of nu(6)(F(1u)) occurs due to rotational excitation and is related to the formation of singular points of classical rotational energy surfaces. The singularity is stable under small variations of parameters of the effective rovibrational Hamiltonian. Parameters responsible for the persistence of this phenomenon are specified. Comparison with quantum calculations demonstrates the high qualitative and quantitative accuracy of our classical analysis. Copyright 2000 Academic Press.     

Irreducible tensor operators and operations over them in the theory of molecular spectra

The explicit shape of symmetrized powers of three-dimensional representations of the groups Td and Oh is found in general form. Equations are obtained for calculating the vibrational commutators and matrix elements of irreducible tensor operators. Programs have been developed (in the C and FORTRAN languages) to remove the multiple-valued property of the vibrational-rotational Hamiltonian of spherical top molecules (CH₄, SiH₄, GeH₄, SF₆, and so on).Institute of Atmospheric Optics, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 16–25, March, 1993.     

计算7Li2振动能级煌振动-转动能级的辛格式矩阵法

利用辛格式矩阵法计算了双原子分子⁷Li₂在A¹Σ_u⁺态的振动能级和振动-转动能级,并与Ley-Koo等的计算结果作了比较.结果显示,辛格式矩阵法是收敛的和可靠的,是计算双原子分子的振动能级和振动-转动能级的合理的数值方法.     

Submillimeter measurements of isotopes of nitric acid

The ground and low-lying vibrational states of nitric acid are observable with current instrumentation in the Earth’s thermal submillimeter atmospheric emission. Remote sensing continues to improve to higher sensitivity and future missions will allow these measurements with minimal integration time. Sensing of weaker spectral features will require signal averaging, and choices of spectral windows for these features will require knowledge of the higher vibrational states and rare isotopes of the strongly emitting species. Nearly comprehensive information on vibrational states and isotopically substituted species is now available from wide bandwidth scans of natural and isotopically enriched nitric acid. In this work, ground state rotational spectra of five isotopically substituted species of nitric acid are analyzed in the submillimeter spectral range. We present the Hamiltonian parameters necessary for prediction and identification of isotopic features across the nitric acid ground state rotational spectrum.