Theoretical study of the spin-orbit coupling in the X2Π state of OH

The spin-orbit coupling constant, A(r), as a function of internuclear distance (r) was computed for the X²Π state of OH, using the microscopic spin-orbit Hamiltonian, extended basis sets, and extensive configuration-interaction wavefunctions. Our best theoretical results are in excellent agreement with the “experimental” A(r) functions deduced from an inversion of the observed A_v. Our calculated first-order contributions to A_v, v ≤ 10, obtained by vibrationally averaging our theoretical A(r) function using the X²Π RKR potential, differ from experiment by less than 0.12%. A minimum occurs in the A_v at v = 7 in agreement with experiment, reflecting the local minimum in A(r) near 2.8 bohr. The second-order contributions to A_v are only about 0.1% for v ≤ 10. They arise mainly from the A²Σ⁺ state for the lower vibrational levels, but each of the A²Σ⁺, B²Σ⁺, (1)²Σ^?, (1)⁴Σ^?, and (1)²Δ states contributes significantly for higher vibrational levels. Spin-orbit centrifugal distortion parameters, A_Dv and a_Dv, are reported for v ≤ 6. The theoretical A_Dv are also in excellent agreement with experiment when the “experimental” A(r) function has the same slope at the equilibrium separation as that obtained from the effective spin-rotation constants of OH, OD, and OT.     

How chaotic is a state of a quantum system?

A concept related to the entropy is studied. Let A and B be two density matrices, with eigenvalues a₁, a₂,… and b₁, b₂,…, arranged in decreasing order and repeated according to multiplicity. Then A is said to be “more mixed”, or “more chaotic”, than B, if a₁?b₁, a₁+a₂?b₁+b₂,…,a₁+…+a_m?b₁+…+b_m,…; It turns out that if A is more mixed than B, then the entropy of A is larger than the entropy of B. However, more generally, let v be an arbitrary concave function, ?0, and vanishing at 0. Then, if A is more mixed than B, trv(A)?trv(B). It is shown that also the converse is true. Furthermore, a variety of other characterizations of the relation “A is more mixed than B” is obtained, and several applications to quantum statistical mechanics are given.     

Amino wagging and inversion in hydrazines: RR branch of the antisymmetric wagging band of NH2NH2

Infrared absorption spectrum of undeuterated hydrazine in the gaseous state has been observed with a resolving power better than 0.06 cm^?1 in the 1024 ～ 961 cm^?1 region, where the ^RR- and ^RQ-branch lines of the antisymmetric wagging band (v_a = 1 ← 0) appear. It has been found that every line belonging to the ^RR branch as well as every ^RQ peak of the band splits into four components, a, b, c, and d. This is explained by considering that the v_a = 0 state splits into A_I, E, and B₂ substates and the v_a = 1 state into B₁, E, and A₂ substates, because of the four equivalent potential minima (D₄) of the hydrazine molecule which are reached by inversions of the two amino groups. From the observed wave numbers of the ^RR lines, effective values of the rotational constants of the B₁, E, and A₂ sublevels of the v_a = 1 state were obtained. On the basis of these values and the ones for the A₁, E, and B₂ sublevels of the ground vibrational state, obtained from a previous microwave study, a discussion of the antisymmetric wagging-inversion coordinate is given.     

Studies of vibrational surface modes in ionic crystals: III. Vibrational contributions to the surface thermodynamic functions for the (001) face of LiF,MgO, NaF,NaCl, Nal,RbF, and RbCl

The temperature dependence of the vibrational contributions to surface specific heat, surface entropy, surface energy, and surface Helmholtz free energy have been calculated for the (001) face of seven crystals having the rocksalt structure. The calculations assume a perfect, unrelaxed surface and make use of shell models fitted to bulk phonon spectra determined from inelastic neutron scattering. In terms of the bulk zero-temperature Debye temperature θ₀, the surface specific heat C_v^s exhibits an effective power law behavior, T^α, from at least T = 0.02 θ₀ up to 0.05 θ₀ in most cases (and up to 0.07 θ₀ for NaF), with α ≈ 2.5 in most cases — in contrast with the result of α = 2 in a Debye-like model. (Below 0.02 θ₀, results derived for our 15-layer films depart significantly from intrinsic surface effects because of the finite thickness.) C_v^s attains a maximum at a temperature T(C_max^s) ranging from 0.14 θ₀ to 0.20 θ₀, in contrast with the result T(C_max^s) = 0.21 θ₀ for the Debye-like model. The peak value C_max^s ranges from 0.34 k_BA_SUC to 0.41 k_BA_SUC, where A_SUC is the area of the surface unit cell. The shap the peak in C_v^s differs characteristically between that class of crystals in which there is some overlap of the acoustical and optical bulk bands and that class in which there is an appreciable absolute gap between the acoustical and optical bulk bands; in the latter class the peak is flattened on the low side of the maximum, with the maximum pushed to somewhat higher temperature. On those points of comparison with the rather sparse existing data for surface-excess heat capacity in which the value of specific surface area is not required (e.g., the value of T(C^s_max)), the agreement ranges from encouraging to equivocal. On those comparisons which require the surface area of the experimental samples (e.g., the magnitude of C^s_max) the agreement ranges from only fair to bad. Further experimental work is needed, and great care in surface area determinations is necessary.     

Adatom mobility on the surface planes of a simple metal

An approach using the Density Functional Approximation, which had in an earlier paper been applied to the binding of an adatom to a jellium metal (r_s = 4a₀), has been extended to a partially structured metal surface by introducing a layer of surface atoms to replace an equivalent layer of jellium. The model has been used to estimate the adatom motion energies over several quite close packed planes for a simple surface. An important preliminary step was to determine the general electron density contours for each surface by a simple variational method. The ensuing shielding charge distributions have an important bearing on the adatom motion energy. Adatom energies were calculated at three positions: (1) A above a surface atom, (2) B above a bridge position between two surface atoms and (3) C above a central position between three or four neighboring atoms. The motion energy was taken to be E_B ? E_C. As might have been expected this quantity was larger for the less closely packed planes, although it was always quite small due to the nature of the metal — large r_S, small ion core and typical s-p binding. To a rather surprising degree the strength of the shielding charge, the energies and the positions of the adatoms proved to be quite smooth functions of a parameter chosen to measure the close packing of the surface, namely the square of the interplanar distance divided by the surface area per atom.     

High vibrational levels of the X state of ICl,and the electronic-coriolis coupling of the X and A states

Ro-vibrational levels of the ground state of ICl have been measured in the range v_x = 35–73 and J_x < 55 using three-stage polarization-labeling spectroscopy. When merged with established microwave and fluorescence data for the lower levels, these results lead to a self-consistent set of spectroscopic constants G_v, B_v, D_v and H_v for all levels v_x ≤ 73. The highest G_v and G_v + F_J term values recorded are, respectively, 52.7 and 1.37 cm^?1 below the dissociation limit. Coefficients of the long-range interaction I + Cl are determined by analysis of the outer wings of the RKR potentials for the X(0⁺) and A′(2) states. Electronic rotational interaction between X and the well-known A(1) state of ICl is shown to account for at least a major part of the $\text{Ω-doubling}$ splitting observed in A: the electronic matrix element characterizing this interaction is shown to be strongly r-dependent, and reasons for this are reviewed.     

High-resolution Fourier spectrometry of 14N2 infrared emission spectrum: Extensive analysis of the B3Πg-A3Σu+ system

The B³Π_g-A³Σ_u⁺ system of N₂ excited in a microwave discharge was recorded between 3 000 and 18 000 cm^?1 with a high-resolution Fourier spectrometer. There are no observed irregularities in the levels of the A³Σ_u⁺ and B³Π_g states at least for the values of v and J considered here, except the predissociation in the B³Π_g state for v = 12 and J higher than 33. This predissociation will be checked with more complete data in another article. Thirty three bands of the first positive system with 0 ≤ v′ ≤ 12 and 0 ≤ v″ ≤ 8 are analyzed. The molecular parameters of the B³Π_g and A³Σ_u⁺ are obtained by a complete fitting procedure. Derived values of equilibrium constants are deduced; RKR potential energy curves for the two states are constructed, and the Franck-Condon factors calculated for the A-B system.     

Stoichiometry invariants for ternary and quatenary solid solutions with two nearly perfect sublattices

We consider a quatenary semiconductor compound, (A_1?uB_u)_1?y(C_1?vD_v)_y, in which the A and B atoms occupy sites in one sublattice. the C and D atoms occupy sites in a second sublattice, and for which y is always near $\text{1}\text{2}$. A statistical thermodynamic analysis for a specific defect model gives three independent “stoichiometry invariants” for the chemical potentials, e.g. μ_B + μ_D, μ_A ? μ_B, and μ_C ? μ_D, which are independent of approximation for small ratios of defect to site concentration. This result is independent of the specific defects chosen, but is obtained under the assumptions that the distribution of the A and B atoms among themselves and that of C and D atoms among themselves are random. A more general analysis that removes these assumptions still yields the same stoichiometry invariants. These invariants provide simple, model-independent relations among the chemical potentials that are extremely useful and to some extent already employed. They also provide the basis for a check on internal self-consistency when all the chemical potentials are measured. The analogous results for a ternary compound are readily extracted as a special case.     

Study of the torsion-rotation Hamiltonian for symmetric tops using the millimeter wave spectrum of methyl silane

The torsion-rotation Hamiltonian for symmetric tops has been tested in methyl silane by combining recent anticrossing molecular beam measurements in the ground torsional state (v = 0) with pure rotational spectra taken for v as high as 4. The earlier microwave data set which consisted of J = 1 ← 0 and 2 ← 1 has been greatly extended by studying millimeter transitions for J = 4 ← 3, 5 ← 4, and 13 ← 12. An analysis of the 72 rotational frequencies for v ≤ 2 and the 15 anticrossing data for v = 0 yielded an excellent fit using 14 rotational, torsional, and distortion constants including the effective values for the A rotational constant and the barrier height V₃. No satisfactory fit could be obtained when the data set was extended to include measurements for (v = 3) or (v = 4). For each of these higher torsional levels, the difference between the observed frequencies and the predictions based on the best (v ≤ 2) constants can be expressed in terms of a shift δB_v in the B rotational constant, where δB_v is a smooth function of the torsional energy. This disagreement is of particular interest because it may result from the fact that the molecule passes from hindered to free rotation as v is increased from 2 to 4. The possibility of perturbation by a low-lying vibrational level is considered briefly. The information contained in the different types of spectra is discussed; the redundancy relations are treated and a Fourier expansion of the diagonal torsional matrix elements is introduced. For ¹²CH₃²⁹SiH₃, ¹²CH₃³⁰SiH₃, and ¹³CH₃²⁸SiH₃ pure rotational spectra for v = 0 were studied briefly in natural abundance. The results were combined with existing data for two deuterated symmetric rotors to obtain a structure based only on symmetric top rotational constants.     

Fine structure of the close-lying A 2Π and B 2Σ+ states of BaH and BaD

Molecular parameters for the close-lying and strongly interacting A ²Π and B ²Σ states of BaH and BaD have been re-evaluated by means of a numerical matrix diagonalization procedure. The results obtained according to this exact method deviate considerably from the effective ones of previous investigations, particularly with respect to the A ²Π-B ²Σ⁺ interaction matrix elements which describe the large Λ-doubling and spin-splitting. The new values of the Λ-doubling and spin-splitting parameters are in excellent agreement with pure precession values for L = 2, and thus the present results form an interesting extension of the pure precession model which so far has been found applicable in a number of cases for which L equals one. The pure precession result L = 2 indicates that the outermost electron of the A ²Π and B ²Σ⁺ states must be a d-electron, and this requires a re-assignment of the configuration quantum numbers of these states. Strong local perturbations are observed in the rotational levels of the A ²Π state of both BaH and BaD, and the result L = 2 now yields a further confirmation of the previous assumption that a ²Δ state causes these perturbations. In the case of BaD the electronic + vibrational energy and the rotational constants (B_v , D_v ) of the perturbing level could be determined from the perturbed A ²Π term values, and in particular the value of the interaction matrix element leads to the conclusion that there is a A ²Π, v = 0 - ²Δ, v = 2 interaction. Finally the influence of the A ²Π - ²Δ, Δv = 0 interaction on the A ²Π and B ²Σ⁺ molecular parameters was investigated.     

Spectral properties of chlorines and electron transfer with their participation in the photosynthetic reaction center of photosystem II

Structural factors that provide localization of excited states and determine the properties of primary donor and acceptor of electron in the reaction center of photosystem II (PSII RC) are studied. The results of calculations using stationary and time-dependent density functional theory indicate an important role of protein environments of chlorophylls P_A, P_B, B_A, and B_B and pheophytins H_A and H_B in the area with a radius of no greater than ≤10 Å in the formation of excitonic states of PSII RC. When the neighboring elements are taken into account, the wavelength of long-wavelength Q _y transition of chlorophyll molecules is varied by about 10 nm. The effect is less developed for pheophytin molecules (Δλ ? 2 nm). The following elements strongly affect energy of the transition: His^A198 and His^D197 amino-acid residues that serve as ligands of magnesium atoms affect P_A and P_B, respectively; Met^A183 affects P_A; Met^A172 and Met^D198 affect B_A; water molecules that are located above the planes of the B_A and B_B macrocycles form H bonds with carbonyl groups; and phytol chains of P_A and P_B affect B_A, B_B, H_A, and H_B. The analysis of excitonic states, mutual positions of molecular orbitals of electron donors and acceptors, and matrix elements of electron transfer reaction shows that (i) charge separation between B_A and H_A and P_B and B_A is possible in the active A branch of cofactors of PSII RC and (ii) electron transfer is blocked at the B_B - H_B fragment in inactive B branch of PSII RC.     

Franck-Condon factors and absolute transition probabilities for the if (B3Π0+-X1Σ+) transition

Improved spectroscopic constants have been used to calculate Rydberg-Klein-Rees (RKR) potentials and Franck-Condon factors for the IF(B³Π₀₊-X¹Σ⁺) transition. The Franck-Condon factors are generally in good agreement with previously calculated values, but differ by as much as 30% for transitions from higher levels of the B-state. Several experimentally measured relative transition moment functions have been evaluated and the best scaled, so that the total transition probability calculated for each B-state vibrational level, A(v'), matched measured values. The scaled function was then used to calculate individual transition probabilities, A(v',v), for the vibronic transitions.     

Atomistic modeling of β-Sn surface energies and adatom diffusivity

Energies for low number Miller index surfaces of β-Sn (b.c.t. structure) were computed and the (1 0 0) plane was found to have the lowest un-relaxed energy of 0.0497 eV/Ų. We then used the Dimer method to find mechanisms and corresponding activation energies, E_A, for a Sn adatom moving on a β-Sn (1 0 0) surface. After extensive dimer searches and comparison to long molecular dynamics simulations, we conclude that two simple hopping mechanisms dominate transitions on this surface. For each, we determined hopping rates of the adatom using transition state theory and computed its tracer diffusivity. A hop of the adatom in the lattice c-direction gives D_300 K = 1.893 × 10⁻⁰⁶ cm²/s (E_A = 0.1493 eV), while in the lattice a-direction D_300 K = 3.994 × 10⁻⁰⁶ cm²/s (E_A = 0.1138 eV). When compared to studies on the existence of low energy multi-atom adatom diffusion on Cu and Al (1 0 0), we assert that β-Sn's successive (2 0 0) plane layering in the [1 0 0] direction provides for significantly lower activation energies and may contribute to the inability to locate any concerted atomic motion mechanisms.     

Stress-optical studies of VI B transition metal dichalcogenides

The effect of a uniaxial stress on the excitonic optical spectra are studied for MoS₂, WS₂, MoSe₂ and WSe₂. Stress dichroism appears in the A′, B′ excitons in diselenides, while it is absent in the A, B excitons in the four compounds. The A′, B′ excitons shift oppositely to the A, B excitons, indicating that A, B and A′, B′ are not pair excitons split by interlayer interaction.     

The spectrum of allene near 5 μm

The infrared bands of allene between 1920 and 2028 cm^?1 were measured on a large grating spectrometer with effective resolution of 0.006–0.007 cm^?1 after deconvolution. The main band in this region is the antisymmetric CC stretching fundamental ν₆ of symmetry B₂, accompanied on the high-frequency side by the overtone band 2ν₉ of the degenerate CH₂ rocking vibration. The overtone has three components of species B₂, B₁, and A₁, of which B₂ is in Fermi resonance with ν₆, B₁ has second-order Coriolis interaction with ν₆, while A₁ is in l-type interaction with the B₁ and B₂ components. Additional perturbations by other unobserved states were detected in the spectrum. The observed transitions were analyzed with the aid of a general computer program system SYMTOP designed for analysis of symmetric-top spectra. The main program effects a least-squares refinement of the spectroscopic constants for a set of bands whose upper states interact through arbitrary matrix elements. Two sets of spectroscopic constants for the ν₆, 2ν₉ states were calculated. One, based only on those lines which appear to be unperturbed by unknown and unobserved states, and a second, obtained after inclusion in the H matrix of two perturbing states designed to simulate the effect of the perturbations on all of the data. Comparison indicates that the lower-order constants based merely on the “unperturbed” data are quite satisfactory. Molecular constants for the ν₉ vibration of C₃H₄ are reported.     

Rotational analyses and vibrational assignments of the 463- and 474-nm bands of NO2

The excitation spectrum of NO₂ was investigated in the blue region by using a Nd:YAG laser-pumped dye laser. The 463- and 474-nm bands of the ²B₂-²A₁ system were identified and analyzed using the simplification that occurs if the excitation spectrum is monitored at particular wavelengths. Band origins and rotational constants were obtained. Vibrational assignments have been given to these bands by comparing the Franck-Condon Factors calculated for the ²B₂-²A₁ system with the fluorescence intensities of bands going to different vibrational levels of the ground state. The vibrational assignments and molecular constants obtained in this work are (v′₁, v′₂, v′₃) = (3, 11, 0)ν₀(K′ = 0) = 21584.1, $\text{B}\text{= 0.405}$, and $\text{∥}\text{?}\text{′∥ = 0.05}\text{cm}{}^{\mathrm{?1}}$ for the 463-nm band; and (v′₁, v′₂, v′₃) = (2, 12, 0), ν₀(K′ = 1) = 21104.9, $\text{B}\text{= 0.408}$, and $\text{∥}\text{?}\text{′∥ = 0.03}\text{cm}{}^{\mathrm{?1}}$ for the 474-nm band.     

无定形靶中离子注入的R,Rp,△Rp的理论计算

本文在Thomas-Fermi势能基础上,导出了全射程R的解析解:R=2/a[E^1/2-A₁(arctg(2E^1/2-f)/△^1/2+arctg f/△^1/2)+B₁ln((E^1/2-f)²)/(E-fE^1/2+d) ·d/f²],其中A₁,B₁,f,d和△均为与离子及靶的质量、原子序数有关的常数。结合导出的η=R/(R_p)(R_p指投影射程)比值的双曲线函数关系 η=F(μ)[A₂(μ)+(B₂(μ))/(ε^1/2+C)],和ω=R_p/△R_p(△R_p指投影射程的标准偏差)比值的线性关系ω=A₃(μ)ε^1/21/2+B₃(μ),可简便而又准确地计算R,△R_p,R_p.这里F(μ),A₂(μ),B₂(μ), B₃(μ)和A₃(μ)为μ的代数函数,μ为离子与靶的质量比,C是经验常数.并对η等关系式的物理意义作了讨论。上述公式的计算结果与Gibbons的数值解结果及有关实验结果作了比较,表明可用于元素半导体如Si、二元化合物如GaAs以及三元化合物如SiO₂等;既对较轻离子适用,也对重离子适用,具有一定的普适范围。     

Rotational analysis of the A2Πu-X2Πg Second Negative band system of O2+

Existing high-resolution data for the $\text{O}{}_2{}^{\mathrm{+}}\text{A}{}^2\text{Π}{}_{\mathrm{u}}\text{- X}{}^2\text{Π}{}_{\mathrm{g}}$ Second Negative band system have been analyzed using a nonlinear least-squares fit that employs numerically diagonalized Hamiltonians. Values for the full set of molecular constants of the A²Π_u and X²Π_g states are obtained for the first time. In addition to values for ν₀(v′, v″), B_v, and D_v, the values for the spin-orbit coupling constants A_v are determined for both states. For the X²Π_g state, which is near Hund's case (a), the agreement between these A_v″ values and those predicted by theory is good. However, for the A²Π_u state, which is much nearer to case (b), these A_v′ values and theory disagree both in magnitude and in variation with vibrational level. The A²Π_u state is an inverted state for vibrational levels v′ ≤ 5 and is a regular state for levels v′ = 6–8 (the upper limit of present high-resolution data). Λ-doubling parameters are determined for the X²Π_g state, the only state where Λ-doubling is statistically significant. Spin-rotation interaction is not statistically significant for either state. Dunham Y_i0 and Y_i1 expansion coefficients are determined for each state. Theoretical D_v values calculated from RKR potentials are used to improve the B_v values in the reduction of the data.     

The theoretical and experimental study of the ionization processes during the low energy ion sputtering

The process by which atoms are ionized as they are sputtered from a metal surface has been analyzed both theoretically and experimentally. In the theoretical part the expressions for ionization coefficient R⁺ of atoms having the ionization energy much larger than the metal work function have been derived using a molecular orbital method. The effect of the level crossing was estimated in an approximate way. In the experimental part the SIMS experiments on clean Ni and Al surfaces and on Ni surface covered with a submonolayer of adsorbed K, Na and Al are reported. It has been found and it is for the first time reported that the energy distribution of ions sputtered from a submonolayer of adatoms is independent of energy (200–2500 eV) and mass (Ar⁺ Xe⁺ of incident ions and depends only upon the adsorption energy of the adatom. The energy distribution of ions sputtered from bulk samples has been found dependent on the primary ion energy. The measurement of the absolute value of R⁺ has shown that there is a strong correlation between the number of the adatom valence d-electrons and the value of R⁺, the value of R⁺ being smaller for atoms with more d-electrons. These experimental data have been compared with the theoretical expressions and the important role of the mechanism which takes into account the bending of the adatom energy level has been assessed.     

The structure and the analytical potential energy function of NH2 （X^2B1）

This paper reports that the equilibrium structure of NH2 has been optimized at the QCISD/6-311＋＋G （3df, 3pd） level. The ground-state NH2 has a bent （C2v, X^2B1） structure with an angle of 103.0582°. The geometrical structure is in good agreement with the other calculational and experimental results. The harmonic frequencies and the force constants have also been calculated. Based on the group theory and the principle of microscopic reversibility, the dissociation limits of NH2（C2v, X^2B1） have been derived. The potential energy surface of NH2（X^2B1） is reasonable. The contour lines are constructed, the structure and energy of NH2 reappear on the potential energy surface.