Momentum and velocity autocorrelation functions of a diatomic molecule are not necessarily proportional to each other

We present a computation of the classical momentum and velocity correlation functions of Br2 considered as an idealized molecular wire connecting dissipated lead atoms at each end of the dimer. It is demonstrated that coupling of the diatomic relative momentum to the leads may result in momenta that are not equal to the mass-weighted velocity. These differences show up in numerical simulations of both the average value and time correlations of the bond momentum and velocity. These observations are supported by analytical predictions for the average temperature of the diatomic. They imply that the "standard recipes" for modeling the system with a generalized Langevin equation are insufficient.     

Electron momentum distributions from valence-bond wave functions

Momentum densities obtained from the Heitler-London (HL) wave functions for diatomic molecules and those from the corresponding valence-bond (VB) wave functions including ionic terms are compared. In each case they shown maxima in the direction perpendicular to the bond. However, the dependence of momentum densities on mutual orientations of the two electronic momenta is quite complex in the latter case. The improvement in the Compton profile on including the ionic terms is illustrated with the example of H₂. The momentum denmsities obtained from the VB wave function constructed from orthogonalized atomic orbitals (OAO) have also been examined. The HL wave function with OAOS leads to the same momentum distribution as the repulsive state HL wave function constructed from overlapping AOS.     

Bond critical points in the electronic structures of the main group diatomic hydrides of lithium through bromine

The bond critical points and associated electronic properties of the diatomic hydrides of the twenty-one main group elements from lithium to bromine have been calculated with large basis sets. As part of a systematic study of the polarity of chemical bonds, the position of the bond critical point, the charge density at the bond critical point, the Laplacian of the charge density at the bond critical point, and the molecular dipole moment of each molecule have been calculated. Particular attention has been paid to the effect of bond length elongation and contraction on the electronic properties. Variation of the bond length reveals that with atoms of low electronegativity, the bond critical point of AH tends to follow atom A, whereas with atoms of high electronegativity, the bond critical point tends to follow the hydrogen atom as the bond lengthens. Furthermore, it is shown that some properties of the diatomic hydrides vary monotonically within each row of the periodic table, while others effect a classification according to the character of the bond.     

Bond lengths of diatomic molecules periodically driven by light: the p-LAMB scheme

A laser scheme using a periodically changing frequency is used to induce oscillations of the internuclear motion, which are quantum analogs of classical vibrations in diatomic molecules. This is what we call the periodic laser adiabatic manipulation of the bond, or p-LAMB scheme. In p-LAMB, the carrier frequency of the laser must vary periodically from the blue to the red of a photodissociation band and backwards, following for instance a cosine-dependent frequency of period τ(c). In the adiabatic regime the dynamics is fully time-reversible. The amplitude of the internuclear oscillation is controlled by the pulse frequency ω(t), while τ(c) determines the duration (or period) of the bond oscillation. In the presence of efficient dipole coupling, the bandwidth of the pulse is the main constraint to the maximum bond stretch that can be obtained. Before the onset of the adiabatic regime the dynamics are more complex, showing dispersion of the vibrational wave packet and anharmonic deformation of the bond. However, the nonadiabatic effects are mostly canceled and full revivals are observed at certain multiples of τ(c).     

氮氧自由基的研究(Ⅱ)——哌啶类氮氧自由基的溶剂效应及其分子结构的研究

对4-氧-2,2,6,6-四甲基哌啶-1-氧自由基在26种不同溶剂中的顺磁共振谱进行了测定,发现超精细分裂常数A_N随溶剂极性的增加而上升,而g值却呈现微小的下降趋势。A_N与ReichardtE_T、KosowerZ值之间有线性关系,而与ε、μ却不呈现线性关系。由于E_T、Z为模型反应的溶剂微观极性效应参数,而ε、μ为非模型反应的溶剂宏观极性效应参数,所以A_N可以作为一种新的非模型反应的溶剂微观极性效应参数。     

Alternating charge densities,peierls distortion,and charge-conjugation symmetry in correlated one-dimensional diatomic systems

The full-optimized-APSG approach based on the MC SCF technique is developed and applied to study ground-state properties of one-dimensional correlated systems. The effects of electron–electron interactions and bond relaxation are considered for the conjugated diatomic polymer; charge distribution and bond relaxation are calculated for the N = 50 chain within a wide range of site energy and e–e integral modulation involving the case of alternancy symmetry for diatomic systems. With relation to the results obtained, the problem of the neutral–ionic transition in mixed-stack crystals is discussed. © 1994 John Wiley & Sons, Inc.     

Coherent and incoherent orientation and alignment of ICN photoproducts

We report extended measurements of the rotational polarization and correlated angular distribution of CN photofragments from ICN photodissociation, with a particular emphasis on the creation and detection of molecular orientation with circularly-polarized light. Doppler profiles of the nascent photoproducts are measured by Frequency-Modulated (FM) transient absorption, and the resulting high signal-to-noise data are valuable for verifying the form of the angular correlations between the recoil velocity, the photofragment rotational angular momentum, and the space-fixed frame defined by the dissociation polarization. A space-fixed bipolar moment notation can be used for an unambiguous characterization of the maximal set of polarization properties that can be created with one-photon excitation and detected with one-photon Doppler-resolved absorption spectroscopy. Relating the observed polarization moments to the various coherent and incoherent, adiabatic and non-adiabatic mechanisms, that have been derived and verified extensively in the case of diatomic photodissociation to polarized atomic fragments, is not unambiguous in the case of diatomic fragments from triatomic precursors. Constraints among various polarization moments confirmed in the case of diatomic dissociation are not confirmed in this triatomic case, where the perpendicular transitions to non-degenerate A' and A' components of a linear Omega = 1 state are qualitatively different from excitation to degenerate Omega = +/-1 states in a diatomic molecule.     

An energy criterion for determiningd orbital contribution to adsorbate bonding to a transition metal: CO/Fe12

Summary A new criterion is presented for determining the contribution of a particular class or group of orbitals to a chemical bond. The new criterion is the diatomic energy contribution of particular orbitals to a bond. In neglect to differential overlap methods the total energy may be decomposed entirely into monoatomic and diatomic terms. The contribution of the electrons ind orbitals to the diatomic energy terms, which are responsible for holding a molecule together, have been calculated for an Fe-Fe bond of Fe₁₂ and for the Fe-C bond of CO absorbed at an on-top site of an Fe₁₂ cluster. This direct measure of thed electron contribution to the total energy indicates that thed orbitals are responsible for only a small contribution to the Fe-Fe binding energy and to the binding energy for absorbed CO. This occurs, despite there being larged orbital attractive diatomic energy terms, because a careful analysis indicates repulsive terms balance the attractive terms.     

Computations and application of classical phase space integrals in reactive molecular collisions

Classical treatment of the evaluation of prior distribution functions (PDF) of product state and recoil energy distributions in reactive collisions is presented. It is shown that for any diatomic potential a single one dimensional numerical (or often analytical) integration suffices to determine the relevant PDF. The conservation of total angular momentum leads to an explicit dependence of the resulting distributions on the maximal total angular momentum of the reactants. The evaluation of prior cross section and branching ratios in collision induced dissociation necessitates the estimation of the radius of the interaction zone. A method for the estimation of the interaction radius and the evaluation of the priors is presented.     

Experimental and calculated momentum densities for the valence orbitals of carbon tetrafluoride

Carbon tetraflouoride has been investigated by binary (e,2e) spectroscopy at 1200 eV impact energy. Binding energy spectra (10–60 eV) at azimuthal angles of 0° and 8° are reported and are found to be in quantitative agreement with a previous Green's function calculated spectrum. Momentum distributions corresponding to individual orbitals are also reported and compared with theoretical momentum distributions evaluated using double-zeta quality SCF wavefunctions. Excellent agreement between experimental and theories is found for the strongly bonding 3t₂ orbital and the antibonding 4a₁ orbital but agreement is less good for the outermost non-bonding orbitals. Intense structure due to molecular density (bond) oscillation is observed experimentally in the region above 1.0 a_o^?1 in the case of the non-bonding 4t₂ orbital. It is also notable that the measured 4a₁ momentum distribution exhibits an extremely well-defined “p” character with clear separation between the s and p components. Contour maps of the position-space and momentum-space orbital densities in the F-C-F plane of the molecule are used to provide a qualitative interpretation of the features observed in the momentum distribution. In order to further extend momentum-space chemical concepts to three-dimensional systems, constant density surface plots are also used to give a more comprehensive view of the density functions of the CF₈ molecule.     

Valence bond study of hyperfine interactions and structure of Kr2F

A semi-empirical valence bond method for calculating isotropic and anisotropic hyperfine interaction constants in diatomic halogen anions and noble gas monohalides has been extended to the linear triatomic KrFKr. Comparison with the experimental values yields estimates for the KrF bond distance and the electron charge distribution in Kr₂F.     

Frequency modulated spectroscopy as a probe of molecular collision dynamics

We describe the application of frequency modulated spectroscopy (FMS) with an external cavity tuneable diode laser to the study of the scalar and vector properties of inelastic collisions. CN X(2)Sigma(+) radicals are produced by polarized photodissociation of ICN at 266 nm, with a sharp velocity and rotational angular momentum distribution. The collisional evolution of the distribution is observed via sub-Doppler FMS on the A(2)Pi-X(2)Sigma(+) (2,0) band. He, Ar, N(2), O(2) and CO(2) were studied as collider gases. Doppler profiles were acquired in different experimental geometries of photolysis and probe laser propagation and polarization, and on different spectroscopic branches. These were combined to give composite Doppler profiles from which the speed distributions and specific speed-dependent vector correlations could be determined. The angular scattering dynamics with species other than He are found to be very similar, dominated by backward scattering which accompanies transfer of energy between rotation and translation. The kinematics of collisions with He are not conducive to the determination of differential scattering and angular momentum polarization correlations. Angular momentum correlations show interesting differences between reactive and non-reactive colliders. We propose that this reflects differences in the potential energy surfaces, in particular, the nature and depth of attractive potential wells.     

Diatomic interactions in momentum space. The effect of polarization and floating functions

The method of momentum density for interatomic interactions is used to investigate the pictures and roles of the polarization and floating functions in momentum (p-) space. Referring to the previous results from the minimal LCAO (Finkelstein-Horowitz) momentum density, we quantitatively discuss the effect of these functions for the bonding process in the ground state of H ₂ ⁺ system. The essence of the polarization and floating effects is found to be a modulation of the oscillation in the two-center part of the momentum density. The polarization function introduces a term with a phase and the floating function enlarges the period of the oscillation. An increased migration of the density from the one-center to the two-center part is also important. As a result, both the functions contribute to emphasize the contraction and expansion of momentum density observed previously. However, the floating function disturbs the density distribution in high momentum region, reflecting the destruction of cusps in position (r-) space. We point out an error in the pioneer work of Duncanson.     

Analytical solutions of Schr?dinger equation for the diatomic molecular potentials with any angular momentum

Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also considered. Algebraic method is used in the calculations.     

Vibration-rotation spectroscopy of molecules trapped inside C60

A simple model is developed to treat the energy levels and spectroscopy of diatomic molecules inside C 60. The C 60 cage is treated as spherically symmetric, and the coupling to the C 60 vibrations is ignored. The remaining six degrees of freedom correspond to the vibrations and rotations of the diatomic molecule and the rattling vibration of the molecule inside the cage. By using conservation of angular momentum, we can remove two of these motions and simplify the calculations. The resulting energy levels are simple and can be labeled by a set of quantum numbers. The IR and Raman spectra look like those of gas-phase diatomic molecules at low temperatures. At higher temperatures, hot bands due to the low-frequency rattling mode appear, and the spectrum becomes congested, looking like a solution spectrum.     

Atomic polarization in the photodissociation of diatomic molecules

The angular momentum polarization of atomic photofragments provides a detailed insight into the dynamics of the photodissociation process. In this article, the origins of electronic angular momentum polarization are introduced and experimental and theoretical methods for the measurement or calculation of atomic orientation and alignment parameters described. Many diatomic photodissociation systems are surveyed, in order to provide an overview both of the historical development of the field and of the most state-of-the-art contemporary studies.     

Semiclassical theory of predissociation induced by rotational (Coriolis) coupling

The dynamical-state representation and the multichannel quantum-defect theory of predissociation are used to formulate a semiclassical theory of predissociation of a diatomic molecule induced by Coriolis coupling. It is demonstrated that the simple perturbation theory becomes invalid when the rotational angular momentum quantum number is large, and that the non-perturbative formula developed in this paper should be employed.     

On the origin of the redshift of the OH stretch in Ice Ih: evidence from the momentum distribution of the protons and the infrared spectral density

Recent measurements of the momentum distribution in water and ice have shown that the proton is in a considerably softer potential in ice Ih than in water or the free monomer. This is broadly consistent with the large red shift observed in the vibrational spectrum. We show that existing water models, which treat the intramolecular potential as unchanged by the hydrogen bonding are unable to reproduce the momentum distribution. In addition, even if they can substantially explain the red shift they are unable to explain the large increase in intensity observed in the infrared spectrum in going from the monomer to ice Ih. We show that the inclusion of a bond dipole derivative term is essential to explain the observed intensities in the infrared spectrum. Though this term is partially responsible for the softening of the effective potential of the proton we show that best agreement with the observed momentum distribution requires a further softening of the harmonic component of the intramolecular potential. We introduce an efficient normal-mode molecular dynamics algorithm for calculating the momentum distribution with path-integrals.     

Study of molecular orbitals in momentum space

Molecular orbitals are presented in configuration and momentum representations. We propose to minimize large oscillations present in calculated momentum wavefunctions by cancelling position factor phases. We illustrate the distortion introduced by different electron translation factors and show continuum states and dynamical wavefunctions in momentum coordinates. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001