Variational calculations on the hydrogen molecular ion

We present high-precision non-relativistic variational calculations of bound vibrational—rotational state energies for the H⁺ ₂ and D⁺ ₂ molecular ions in each of the lowest electronic states of Σ _g , Σ _u , and Π _u symmetry. The calculations are carried out including coupling between Σ and Π states but without using the Born—Oppenheimer or any adiabatic approximation. Convergence studies are presented which indicate that the resulting energies for low-lying levels are accurate to about 10^?13. Our procedure accounts naturally for the lambda-doubling of the Π _u state.     

Millimeter-wave spectroscopy of the internal rotation hot band (j=2-1) of the Ar-HCN complex

Millimeter-wave absorption spectroscopy combined with a pulsed jet expansion technique was applied to measure the internal rotation j=2-1 hot band of the Ar-HCN complex in the frequency region of 147-287 GHz. In total 153 rovibrational lines, split into hyperfine components due to the nitrogen nucleus, were assigned to the Σ₂-Σ₁, Σ₂-Π₁, Π₂-Σ₁, Π₂-Π₁, Δ₂-Σ₁, and Δ₂-Π₁ subbands. A set of molecular constants for the Σ₂, Π₂, and Δ₂ internal rotation substates, including subband origins, rotational constants, nuclear quadrupole coupling constants, and Coriolis interaction constants, was determined. The internal rotation energy for the Σ₂ state, 412.8949 GHz, is higher than those for the Π₂ and Δ₂ states, 392.3974 and 355.9570 GHz, by 20.498 and 56.938 GHz, respectively, in contrast to the Σ₁ state located by 17.094 GHz lower than the Π₁ state, the anisotropy of potential energy surface affecting the j=2 and j=1 states differently. The rotational and quadrupole coupling constants in the j=2 excited state are quite different from those in the ground state, indicating drastic change in the average structure in the j=2 state from the ground state. The determined molecular constants were compared with those calculated from the potential energy surface computed at the CCSD(T) level.     

Optical potential study of Σ nuclear states

Single-particle energies and widths of Σ hypernuclear states are calculated in light systems (A ≤ 40) as energy eigenvalues of the Schrödinger equation for a complex optical potential that fits level shifts and widths of Σ^? atoms. The interpretation and significance of Σ (normalizable) bound states embedded in the Λ hypernuclear (as well as, sometimes, in the Σ hypernuclear) continuum are discussed and their properties are studied, primarily in order to identify relatively narrow (Γ ? 10 MeV) states. The connection between these calculations and the recently observed Σ hypernuclear states suggests that bound states embedded in the Σ continuum, rather than (nonnormalizable) Gamow resonant states, are produced in (K^?, π) nuclear reactions.     

The calculation of valence shell ionization potentials by the ΔSCF method

Valence shell ionization potentials for several small molecules (HF, H₂O, CH₄, CO, H₂S, PH₃, SiH₄, SO₂ and F₂CO) are calculated by means of ab initio ΔSCF calculations on all the valence hole states of each molecule. The results are compared with the experimental low energy photoelectron spectra. In the case of the higher energy ion states, particular attention is paid to finding practical means for obtaining convergence of the ΔSCF iterations, and numerical evidence is presented, indicating that the ΔSCF procedure provides upper bounds to the energy of such states, at least for the cases studied herein. A new procedure, the ‘ combined ΔSCF ’ method, for the determination of a common set of molecular orbitals for use in the construction of wavefunctions for a number of ion states is described.     

Ab initio prediction of the infrared absorption spectrum of the C2Br radical

The first three electronic states of the C₂Br radical, correlating at linear geometries with ²Σ⁺ and ²Π states, have been studied ab initio, using Multi Reference Configuration Interaction techniques. The electronic ground state is found to have a bent equilibrium geometry, RCC=1.2621Å, R _CBr=1.7967Å, ∠ CCBr=156.1°, with a very low barrier to linearity. Similarly to the valence isoelectronic radicals C₂F and C₂Cl, this anomalous behaviour is attributed to a strong three-state non-adiabatic electronic interaction. The Σ ,Π_1/2,Π_3/2 vibronic energy levels and their absolute infrared absorption intensities at a temperature of 5 K have been calculated for the ¹² C¹² C⁷⁹Br isotopomer, to an upper limit of 2000 cm^?1, using ab initio diabatic potential energy and dipole moment surfaces and a recently developed variational method.     

Predicting DNA–intercalator binding: the development of an arene–arene stacking parameter from SAPT analysis of benzene‐substituted benzene complexes

A series of substituted naphthalimides were synthesized and intercalated into the DNA sequence d(GCGCGCGC)₂, and an experimental ΔT_m value was obtained. Two‐parameter QSAR analyses were performed to generate a theoretical ΔT_m value. Although by no means exhaustive in terms of parameter selection, the correlations did not yield statistics that indicated the models met the threshold for significance at the 95% confidence level. Rather than continue with an exhaustive search of all possible QSAR parameters, a one‐parameter QSAR analysis was performed utilizing a novel arene–arene stacking parameter, designated Π^π, developed from Symmetry‐Adapted Perturbation Theory (SAPT) energy decomposition studies of calculated benzene‐substituted benzene dimer binding energies. The QSAR analysis using the Π^π stacking parameter yielded statistics suggesting the model was significant at the 95% confidence level. The approach of developing a novel QSAR parameter via SAPT calculations, rather than exhaustively searching all traditional QSAR parameters, is presented both as a new approach for QSAR studies and as a unique application of SAPT. Copyright © 2013 John Wiley & Sons, Ltd.     

The coadsorption of carbon monoxide and deuterium on potassium predosed Ni(100)

The effect of potassium on the coadsorption of carbon monoxide and deuterium on Ni(100), with particular attention given to the low temperature Σ-CO and Σ-D₂ desorption states, has been studied by thermal desorption spectroscopy. Potassium shifts the Σ state peak temperatures to higher values and attenuates their intensities. The effects of potassium on the higher temperature carbon monoxide and deuterium desorption states are similar to the effects observed when one or the other is absorbed alone. A model is presented for the conversion of carbide to graphite on transition metal surfaces and for a possible role which potassium may play.     

Effect of the atomic composition of the surface on the electron surface states in topological insulators A<Stack><Subscript>2</Subscript><Superscript>V</Superscript></Stack>B<Stack><Subscript>3</Subscript><Superscript>VI</Superscript></Stack>

The results of the theoretical investigation of the surface electronic structure of A₂^VB₃^VI compounds containing topologically protected surface states are reported. The ideal Bi₂Te₃, Bi₂Se₃, and Sb₂Te₃ surfaces and surfaces with an absent external layer of chalcogen atoms, which were observed experimentally as monolayer terraces, have been considered. It has been shown that the discrepancy between the calculated Fermi level and the value measured in the photoemission experiments can be attributed to the presence of the “dangling bond” states on the surface of the terraces formed by semimetal atoms. The fraction of such terraces on the surface has been estimated.     

Helium scattering and work function investigation of co adsorption on Pt(111) and vicinal surfaces

CO adsorption on Pt(111) and vicinal Pt(111) surfaces has been studied by means of work function variation and He scattering measurements. AES and LEED were used mainly for correlations with other work. Special attention has been paid to the low coverage regime (θ_co < 0.1) with emphasis on surface structural dependencies. The minimum of the work function versus CO exposure curve occurs at a coverage less than 11% on “kink-free” surfaces. This is much lower than the hitherto commonly accepted value of 33%, and does not relate to any observed LEED superstructure. The value of Δφ_min depends strongly on the surface structure. For an “ideal” Pt(111) surface with a step density less than 10^?3 at a temperature of 300 K, Δφ_min = ?240 meV. The scattering cross section Σ of CO adsorbed on Pt(111) for 63 meV He is typically > 250 Ų, i.e. much larger than expected from the Van der Waals radii of He and CO. For two nominal Pt(111) surfaces with step densities of 10^?2 and less than 10^?3, respectively, the measured Σ values varied by a factor of three. This can be explained by preferential CO occupation of defect sites, which are already not “seen” by thermal helium. By comparing results on a stepped (997) and a kinked (12 11 9) Pt surface with similar defect densities, the kinks are proven to play a decisive role. They probably form saddles in the recently proposed activation barrier for migration between terrace and step sites.     

Autoionization of O2 by photoelectron spectroscopy

Photoelectron spectra of molecular oxygen have been studied at photon wavelengths of 736, 744 and 584 Å, respectively. The reported strong perturbation at 736 Å leading to changes in the normal vibrational intensifies of the X² Π_g and a⁴Π_u states is ascribed to autoionization from a very wide, near-repulsive state of the neutral molecule. The values measured for the relative vibrational intensifies of the ionic states are compared with the latest experimental results available in the literature.     

Static hyperon properties in a linearizedSU(3)-Chiral Bag model

We use a linearized Chiral Bag model to describe the strange octet and decuplet baryons. The approach is canonically extended to spontaneously broken chiral SU(3)_L × SU(3)_R, and the corresponding Goldstone Bosons are identified with the pseudoscalar meson octet. We include explicit symmetry breaking corrections both for baryons and mesons. The linearized quark-meson intraction is applied in a self-consistent calculation of the masses and, for Δ, Σ^* and Ξ^*, of the decay widths. Our special interest is in the influence of theK- andη-cloud (in addition to theπ) on hyperon static properties. We show results for radii, masses, decay widths and renormalization constants as obtained by a fit to the experimental hyperon spectra. The effects of theK- andη-mesons are found to be non-negligible, although supressed by symmetry breaking effects. The effective gluon coupling α is reduced in comparison to the SU(2)_L × SU(2)_R case. In addition, we discuss the dependence on the bag constantB. It turns out that the lightest hyperon states, Λ and Σ are well described and stable for B^1/4 < 130 MeV. The heavier strange baryons have stable solutions also for larger values ofB. The bag radii determined at the minimal energies are R₀?1.15 fm for the octet and R₀?1.25 fm for the decuplet baryons.     

A skew ray tracing approach for the error analysis of optical elements with paraboloidal boundary surfaces

Using the error analysis methodology developed by the current author in previous studies for optical systems comprising elements with flat boundary surfaces, this study examines the errors induced in a light ray's path as it is reflected or refracted at a paraboloidal boundary surface. In analyzing the light path, two principal sources of error are considered, namely (1) translational errors (Δx_i, Δy_i and Δz_i) and rotational errors (ΔΓ_i, ΔΨ_i and ΔΦ_i), which collectively determine the deviation of the light path at each boundary surface, and (2) the differential changes induced in the incident point position and unit directional vector of the refracted/reflected ray as a result of differential changes in the position and unit directional vector of the light source. The validity of the proposed approach is verified using a generic parabaloidal boundary surface for illustration purposes. Overall, the results show that the proposed error analysis methodology provides a straightforward means of analyzing the performance of optical systems characterized by paraboloidal boundary surfaces such as headlight reflectors, optical telescope mirrors, flashlights and so forth.     

Numerical study of overpopulation density for laser oscillation in recombining hydrogen plasmas

Overpopulation densities Δn_itij, which are defined as the differences between the population densities per unit statistical weight of the upper and lower excited levels i and j, are calculated as a function of the electron density n_e for various electron temperatures T_e in recombining hydrogen plasmas. Calculation have been made for line pairs with principal quantum numbers (2 ,3), (3, 4) and (4, 5). The effect of the ground-level population density n₁ on Δn_ij is calculated. In this calculation, the atom-atom collision and the self-absorption of the resonance lines are taken into account. The n₁-dependence of Δn_ij remains almost constant until the self-absorption becomes significant. The threshold condition for laser oscillation is discussed in relation to the calculated Δn_ij. Laser oscillation is possible for the line pair (2, 3) at an electron density and temperature higher than for the other pairs (3, 4) and (4, 5) when self-absorption is negligible.     

Ab initio potential energy curves and vibrational levels for the c, l, and i states of the hydrogen molecule

Potential energy curves for the hydrogen molecule in the c³Π_u, I¹Π_g, and i³Π_g state have been calculated in the Born-Oppenheimer approximation. Highly flexible wavefunctions have been used, and for each state the calculations have been carried out for 40 different internuclear distances in the region 1 ≤ R ≤ 12 a.u. For the Π_g states the wavefunctions are known to change their character around R = 5 a.u. The effect of this change on various components of the energy has been analyzed. The vibrational Schrödinger equation for all states has been solved for H₂, HD, and D₂. For H₂ the resulting energies are compared with the experimental values and it is shown that the adiabatic effects are likely to be responsible for the existing discrepancy between the theoretical and experimental values.     

Three-dimensional ab initio dipole moment surfaces and stretching vibrational band intensities of the XH3 molecules

Stretching vibrational band intensities of XH₃ (X=N, Sb) molecules are investigated employing three-dimensional dipole moment surfaces combined with the local mode Hamiltonian model.The dipole moment surfaces of NH₃ and SbH₃ are calculated with the density functional theory and at the correlated MP2 level,respectively. The calculated band intensities are in good agreement with the available experimental data. The contribution to the band intensities from the different terms in the polynomial expansion of the dipole moments of four group V hydrides (NH₃, PH₃,AsH₃ and SbH₃) are discussed. It is concluded that the breakdown of the bond dipole approximation must be considered. The intensity “borrowing” effect due to the wave function mixing among the stretching vibrational states is found to be less significant for the molecules that reach the local mode limit.     

Rotational spectrum of ONCl in the (0, 0, 1) and (0, 1, 0) vibrational states and “b” type spectrum in the ground state. Comparison of force field obtained by different combinations of experimental data

From the rotational spectrum of ONCl in (0, 0, 1) and (0, 1, 0) excited vibrational states the inertia defects in these states have been determined. The “b” type rotational spectrum in the ground state has also been measured allowing the determination of Δ⁰ and of all the first-order centrifugal distortion constants.It is shown that by using differences of inertia defects Δ₂ and Δ₃ together with centrifugal distortion constants which do not involve the planarity relations and with harmonic vibrational frequencies of two isotopic species, the harmonic vibrational frequencies of two other isotopic species can be satisfactorily predicted.By using only inertia defects differences Δ₂ and Δ₃ as extra data, a definite choice can be made among the three sets of force constants which equally well reproduce the harmonic frequencies of four isotopic species.     

二个强飞秒延时激光脉冲对Na2+光解离的控制

本文报告Na₂⁺离子的最低四个Σ态(1²Σ_g、1²Σ_u、2²Σ_g、2²Σ_u)在二个光脉冲作用下的解离动量谱和解离率的定量计算结果。激光波长为680nm,各脉冲功率1×10¹²W/cm²,脉宽50fs,第二个脉冲的延时取0、50、100、…350fs.计算结果用三维图表出。在这些图中看到,沿相对动量坐标有单光子、双光子、三光子激发的对应的解离峰及峰值随延时的显着变化情况。各通道的解离率和总解离率列出在表中。结果表明分子解离率分支比的二脉冲延时控制有着很高的效率.     

立方对称晶场中6S(3d5)态离子的磁相互作用及其自旋哈密顿参量的微观起源

基于完全对角化方法(complete diagonalization method, CDM), 研究了⁶S(3d⁵)态离子在立方对称晶场中的磁相互作用,分析了自旋哈密顿参量(a, g,Δg)的微观起源.研究中除了考虑研究者通常考虑的SO(spin-orbit)磁相互作用外,同时考虑了SS(spin-spin),SOO(spin-other-orbit),OO(orbit-orbit)磁相互作用.研究表明：⁶S(3d⁵)态离子在立方对称晶场中的自旋哈密顿参量起源于五种机理,即SO机理,SS机理,SOO机理,OO机理以及SO-SS-SOO-OO联合作用机理.文中研究了五种机理的相对重要性,结果表明：SO机理与SO-SS-SOO-OO联合作用机理在五种机理中最为重要.尽管SS,SOO,OO磁相互作用单独作用时对自旋哈密顿参量的贡献很小,但它们的联合作用SO-SS-SOO-OO机理对自旋哈密顿参量的贡献非常可观.此外研究表明：零场分裂参量a主要来自纯自旋四重态及自旋二重态与自旋四重态联合作用的贡献,而Zeemang(或者Δg)因子主要来自纯自旋四重态的贡献.纯自旋二重态对自旋哈密顿参量a与g(或者Δg)的贡献为零.在我们所选择的晶场区域,发现下列关系始终成立：a>0,a(-|Dq|)<a(|Dq|),g(-Dq)=g(Dq),a(-Dq,-ξ_d,B,C)=a(Dq,ξ_d, B,C),Δg(-Dq,-ξ_d, B, C)=Δg(Dq,ξ_d, B, C).作为本文理论的应用,研究了四种典型的Mn²⁺掺杂晶体材料,即Mn²⁺:KZnF₃,Mn²⁺: RbCdF₃,Mn²⁺: MgO,Mn²⁺: CaO,理论与实验测量符合很好. 关键词： 自旋哈密顿参量 6S(3d⁵)态离子')" href="#">⁶S(3d⁵)态离子 磁相互作用 完全对角化方法(CDM)     

H2SiCl2 中 SiH 伸缩振动的泛频光谱

在2000 ～ 9000 波数 、 12000 ～12900 波数的光谱区间记录了室温下H2SiCl2气体分子的振动泛频光谱，所用的仪器分别是高分辨傅立叶变换光谱仪和高灵敏激光腔内吸收光谱仪。用局域模模型和包含达林－丹尼生共振的简正模模型，归属了SiH伸缩振动的基频和泛频，振动量子数的改变△VSiH=1, 2, 3, 4 and 6。通过对实验能级的非线性拟合，得到SiH伸缩振动的谐振频率ωm、非谐性常数χm、键间耦合系数λ、莫尔斯振子参数 De、α 和相互作用力常数 。实验发现，随着振动能量的增加，振动簇（manifold，两个SiH键的伸缩振动量子数m+n=常数 ）中能量最低的两个能级的间距逐渐减小。当△VSiH≥4时，在实验误差范围内这两个最低的振动态能级简并。这种简并的能级结构类似双原子莫尔斯振子，符合Birge-Sponer 关系。双原子莫尔斯振子直接描述了H2SiCl2分子中SiH 的高泛频伸缩振动，表明在高振动情况下振动能量已经集中到单个SiH键上。     

Microwave optical double resonance used as an assignment tool in optical spectroscopy

Microwave transitions between excited rovibronic states were used to assign transitions in the optical spectrum of NH₂ using microwave optical double-resonance spectroscopy. The microwave frequency was set so as to pump one particular hyperfine component of the previously observed 1₁₀, $\text{J =}\text{1}\text{2}$, Π(0, 10, 0), $\text{A}\text{?}{}^2\text{A}{}_1\text{? u}$, F₂ transition around 6.3 GHz, the frequency of the dye laser was then tuned over a wide spectral range. Double-resonance signals occurred in four level systems whenever the optically excited level was collisionally coupled to either of the microwave pumped levels. This method, when used in conjunction with the results of a conventional absorption spectrum of the molecule, yields information on perturbing states around the Π(0, 10, 0) region. In addition it has proved possible to detect further levels of similar vibronic character to the u state, in particular the spin rotation partners of u and u′. Some discussion on a possible vibronic assignment for these levels is included.