On the relation between the energy level classification of a nonrigid molecule and the symmetry of its equilibrium configurations

The problem of changes in the energy level classification of a nonrigid molecule upon a change in its equilibrium configurations, in the case in which different possible geometries of such configurations correspond to different point groups, is considered for the example of the nonrigid dimethylacetylene molecule CH₃C₂CH₃ in the ground electronic state.     

Symmetry coordinates of nonrigid molecules

Motivated by Altmann’s definition of symmetry groups of nonrigid molecules, Wigner’s method of obtaining the symmetry coordinates of a molecule is extended to nonrigid molecules with free internal rotations. The molecule BF₂ CH₃ is exemplified.     

Classification of energy levels of the isopropanol molecule

Using the methods of a symmetry group chain, an energy level classification is constructed for the nonrigid isopropanol molecule (CH₃)₂CHOH in the ground electronic state with an allowance for the internal motion of hydroxyl and two methyl tops.     

On the normal vibrations of nonrigid molecule B(CH3)3

Treating the symmetry operations as transformations in higher dimensional space, it is shown that Wigner’s method can be straightaway extended to study the vibrations of nonrigid molecules exhibiting free or nearly free internal rotations. The molecule B(CH₃)₃ is illustrated.     

The inversion potential and rotation-inversion energy levels of H3O+ and CH3−

The rotation-inversion-vibration energy levels of H₃O⁺ and CH₃^? using the ab initio potential surfaces and the nonrigid bender Hamiltonian are calculated. It is hoped that these results will be of use in the search for the spectra of these ions.     

Geometry of the internal dynamics of the 12C13CH 3 + carbocation

The internal dynamics of the ¹²C¹³CH₃⁺ isotopomer of the simplest carbocation is considered to be a distorted dynamics of its symmetric C₂H₃⁺ isotopomer. By using the group-chain methods and assuming quite naturally that the carbocation equilibrium structures continue to be planar and the nonrigid motion occurring between them is retained upon this isotopic substitution, a simple algebraic model is constructed to describe the spectrum of the ¹²C¹³CH₃⁺ isotopomer. The correctness of the model is limited only by that of the adopted geometrical symmetry of internal dynamics of the C₂H₃⁺ isotopomer.     

从头计算研究CH3C(O)OSSOC(O)CH3的构型和能量

采用从头计算B3LYP,MP3和MP4方法结合Aug-cc-pVDZ基组研究了CH₃C(O)OSSOC(O)CH₃最稳定的五种构象及其阳离子构型.理论计算了五种稳定构象的转动常数和偶极矩;运用电子传播子理论P3近似方法计算稳定构象外价壳层轨道的电离能,计算结果与光电子能谱实验结果符合的较好.根据构象的相对能量以及理论模拟电离能谱和实验光电子能谱之间的比较,说明在气相光电子能谱实验中至少存在两种构象.与中性构型相比,电离后的五种阳离子构型均发生了明显的结构弛豫,尤 关键词： 构象 电离能 相对能量 光电子能谱     

The potential function and rotation-vibration energy levels of the methyl radical CH3

The equilibrium bond length and the shape of the complete potential energy curve for the methyl radical CH₃ are determined. This is done by fitting the experimental data [mainly from C. Yamada, E. Hirota, and K. Kawaguchi, J. Chem. Phys.75, 5256–5264 (1981)] using the nonrigid invertor Hamiltonian and a model anharmonic potential function. As a result the v₂ (out-of-plane bending) dependence of the rotational constants is explained and the v₂ dependence of the spin-rotation coupling constants is modeled. In addition, some of the vibrational energies and rotational, centrifugal distortion, and spin-rotation constants are predicted for the ¹³CH₃, ¹²CD₃, and ¹²CT₃ isotopes.     

Adsorption and co-adsorption of CH<Subscript>3</Subscript> and H on flat and defective nickel (111) surfaces

We use a periodic density functional theory (DFT) code to study the adsorption of CH₃ and H, as well as their co-adsorption on a Ni(111) surface with and without Ni ad-atom, at a surface coverage of 0.25 monolayer (ML). We systematically investigate the site preference for CH₃ and H. Then we combine CH₃ and H in many co-adsorbed configurations on both surfaces. Methyl and hydrogen adsorption on a flat Ni(111) surface favours the hollow site over the top site. The presence of a Ni ad-atom stabilizes the adsorption of CH₃ better than a flat surface, while hydrogen is more stable on a flat Ni(111) surface. When H and CH₃ are co-adsorbed at nearest Ni neighbours on the (111) surface, their interaction is always repulsive. However, the dissociative adsorption of CH₄ is stabilised when the fragments are infinitely separated. For the co-adsorbed fragments CH₃ and H, in the presence of an ad-atom, the repulsive interaction is lowered, so that the dissociative form of CH₄ is locally stable.     

Non-stationary states in molecular spectroscopy: The Hanle effect in NO2

The excited state NO₂ molecule is described as a nonrigid molecule capable of changing between two asymmetric equilibrium configurations. The tunnelling motion introduces a narrow level splitting in this molecule and causes the optically prepared states to be non-stationary states. This explains the different lifetimes obtained from radiative decay measurements and from Hanle effect measurements on NO₂.     

A rigorous description of the energy spectrum of the ammonia dimer. II. Taking into account the inversional motion

Using the group chain methods, a rigorous algebraic model for describing the energy spectrum of the ammonia dimer (NH₃)₂ is constructed with an allowance for both the most important torsional and exchange nonrigid motions and the inversional nonrigid motion also taken into account. The model is rigorous in the sense that its correctness is limited only by the correctness of the chosen symmetry of internal dynamics of the dimer.     

Structures of proton solvates in the HCl-H2O-(CH3)2NCHO system as determined by IR spectroscopy and quantum-chemical calculations

The structures of proton solvates in the HCl-H₂O-(CH₃)₂NCHO (DMFA) system at H₂O: DMFA ratios ranging from 1: 1 to 21: 1 are studied by the IR spectroscopy method. It is demonstrated that H₂O?H⁺?OH₂ ions and (CH₃)₂NCHO?H⁺?OH₂ mixed solvates with a strong quasi-symmetrical hydrogen bond are formed in solutions. With an increase in the DMFA concentration, the fraction of H₅O ₂ ⁺ ions decreases. At HCl: H₂O ≥ 1: 3 and arbitrary DMFA concentrations, only mixed proton solvates are formed. The continuous absorption coefficients for the (CH₃)₂NCHO?H⁺?OH₂ ions are determined. The results obtained are compared with the results of quantum-chemical calculations of the structure and relative stability of the (DMFA) _m H⁺(H₂O) _n (m = 0–2, n = 0–3) positively charged complexes which were performed by the B3LYP/6-31++G(d,p) DFT method. We identified 19 stable configurations with chain, cyclic, and branched structures. Most of these configurations contain the (CH₃)₂NCHO?H⁺?OH₂ fragment. The parameters of the O?H⁺?O bridge show that some configurations have a strong quasi-symmetrical hydrogen bond. In some cases, the proton is located between two DMFA molecules. The H₂O?H⁺?OH₂ bridge is observed in none of the stable configurations of the (DMFA) _m H⁺(H₂O) _n (m ≠ 0) complexes.     

Classification of energy levels of the ammonia dimer

Using the methods of a symmetry-group chain, the total classification of energy levels of the ammonia dimer (NH₃)₂ is constructed with the torsional, exchange, and inversional nonrigid motions taken into account.     

Derivation of the nonrigid rotation-large-amplitude internal motion Hamiltonian of the general molecule

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 κ²T_VIB. 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.     

Adsorption and decomposition of methyl iso-cyanide on Pt(111)

CH₃NC adsorption and thermal decomposition on a Pt(111) surface has been studied by high resolution EEL and TD spectroscopies. At 90 K, CH₃NC adsorbs initially in a terminal-bonded configuration characterized by a blue-shifted iso-cyanide stretch at 2265-2240 cm^?1. At higher coverages this form co-exists with a second form characterized by an imine-like stretch at 1600–1770 cm^?1, increasing with coverage. This form is associated with bridge bonding to adjacent surface platinum atoms. Adsorption is irreversible and. except for multilayer desorption at 135 K, only reaction-limited H₂ (T_p = 440–460 K) andHCN (T_p = 420–610 K) desorption and. at high coverages, isomerization to CH₃CN (T_p = 430 K) was seen. EEL spectra recorded after heating the adsorbed layer indicated that at lower coverages, the molecular integrity of the adsorbed CH₃NC was completely lost before dehydrogenation occurred. On the other hand, at saturation structural changes in the adsorbed layer corresponded firstly to the onset of dehydrogenation and then. at higher temperatures, to HCN evolution. No spectroscopic evidence for an η²-bonding configuration was found either at low temperatures or during thermal decomposition. The terminal- and bridged-bonded configurations adopted by CH₃NC have been compared and contrasted with those found with the isoelectronic CO and the isomeric CH₃CN by reference to the chemically important frontier orbitals of these ligand molecules.     

Reduction of the effective rotational Hamiltonian for pyramidal XY3 molecules with a large-amplitude inversion motion

The previously described reduction of the effective rotational Hamiltonian for semirigid molecules of C_3v 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, J_z]₊ 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.     

Geometry of the internal dynamics of C<Subscript>2</Subscript>H<Stack><Subscript>3</Subscript><Superscript>+</Superscript></Stack> carbocation

Using the symmetry group chain methods, the internal dynamics of the simplest carbocation, C₂H ₃ ⁺ , is analyzed under the traditional assumptions that the equilibrium structures of the carbocation are planar and that the nonrigid motion between them is in-plane. This geometry of the internal dynamics is shown to agree with the data of the microwave spectroscopy on the splittings of rotational energy levels caused by the nonrigid motion. Previously, this statement was based on the model that violated the requirement of self-adjointness of operators of physical quantities.     

The photoelectron spectra of the tetrafluoro and tetramethyl compounds of the group IV elements

The photoelectron spectra of CF₄, SiF₄, GeF₄, C(CH₃)₄, Si(CH₃)₄, Ge(CH₃)₄, Sn(CH₃)₄, and Pb(CH₃)₄ h     

Vibrational anharmonicity and the inversion potential function of NH3

The nonrigid bender formulation of the vibration-inversion-rotation Hamiltonian for an XY₃ pyramidal molecule (V. ?pirko, J. M. R. Stone, and D. Papou?ek, J. Mol. Spectrosc.60, 159 (1976)) is improved by allowing for anharmonicity in all the vibrations. To model the anharmonic potential function of an XY₃ molecule with a low barrier to inversion a Plíva-type empirical potential (J. Plíva, Collect. Czech. Chem. Commun.23, 777 (1958)) is used. A fitting procedure that involves the numerical integration of the effective inversion Schrödinger equation (the nonrigid bender equation) and diagonalization of some resonance matrices is used to determine the equilibrium structure and the anharmonic potential function of the ammonia molecule.