Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing energy levels from potential energy surfaces for symmetric-top molecules

A theoretical approach to study ro-vibrational molecular states from a full nuclear Hamiltonian expressed in terms of normal-mode irreducible tensor operators is presented for the first time. Each term of the Hamiltonian expansion can thus be cast in the tensor form in a systematic way using the formalism of ladder operators. Pyramidal XY₃ molecules appear to be good candidates to validate this approach which allows taking advantage of the symmetry properties when doubly degenerate vibrational modes are considered. Examples of applications will be given for PH₃ where variational calculations have been carried out from our recent potential energy surface [Nikitin et al., J. Chem. Phys. 130, 244312 (2009)].     

H2S和H2S+的振动光谱和电子能谱计算

本文基于MOLPRO软件包使用从头算方法计算了星际分子H₂S及其阳离子H₂S⁺的势能面及光电子能谱.首先,在(U)CCSD/cc-pVQZ理论水平下获取了H₂S沿法线坐标展开的势能面,势能面直观描述了不同振动模式耦合对分子能量变化的影响,S-H键的非对称伸缩振动和面内弯曲振动共同作用使得系统势能变化范围明显变大.振动多组态相互作用方法被用来计算非谐振动频率和振动光谱,计算结果显示,倍频和组合频之间出现了强烈的费米共振,使得相应波段处的红外强度显著增强.最后,使用拉曼波函数和收缩不变Krylov子空间方法首次计算了H₂SΧ¹A₁→H₂S⁺ X²B₁的光电子能谱.此项研究有助于进一步理解星际分子的内部结构,并为实验研究及星际观测提供参考.     

苯胺分子S_1态振动光谱及ab initio计算(英文)

利用紫外激光,结合超声速脉冲分子技术和飞行时间质谱仪,在287～296 nm波长范围内实验研究了苯胺分子的共振双光子电离光谱(R2PI).实验中观测到对应S_1←S_0跃迁的0-0带出现在293.86nm(3.4029 cm~(-1))处,并测得对应S_1态的若干振动模和来自S_0态的热带.为了对S_1态的振动模进行标定,分别在HF/6-31+G(d,p)和CIS/6-31+G(d,p)基组水平上对苯胺在S_0态的构型进行优化和在S_1态对其振动频率进行分析计算.另外,利用自然键轨道分析(NBO)讨论了电子激发过程.结果显示,来自氨基氮原子上的一个电子从对应的孤对电子轨道激发到苯环的π反键轨道上,恰好对应的是S_1←S_0跃迁.     

The co-adsorption of H2 and CO on Ni(110)

The effect of co-adsorption of hydrogen and CO on Ni(110) has been examined with HREELS. In the mixed adlayer at low CO and hydrogen coverage, the spectra indicate that no strong interaction between H_(a) and CO_(a) occurs. At high hydrogen coverage the surface reconstructs and consequently the adsorption site for the CO is modified. The reconstruction and site modification is reversible and depends on the hydrogen coverage.     

Scalar–tensor representation of f(R) gravity and Birkhoff's theorem

Birkhoff's theorem is discussed in the frame of f(R) gravity by using its scalar–tensor representation. Modified gravity has become very popular in recent times as it is able to reproduce the unification of inflation and late‐time acceleration with no need of a dark energy component or an inflation field. Here, another aspect of modified f(R) gravity is studied, specifically the range of validity of Birkhoff's theorem, compared with another alternative to general relativity, the well‐known Brans–Dicke theory. As a novelty, here both theories are studied using a conformal transformation and writing the actions in the Einstein frame, where spherically symmetric solutions are studied using perturbation techniques. The differences between both theories are analyzed as well as the validity of the theorem within the Jordan and Einstein frames, where interesting results are obtained.     

CO2 laser CVD of a-Si:H: in situ gas analysis and model calculations

4 and disilane Si₂H₆ induced by continuous wave CO₂ laser irradiation has been investigated under the conditions of chemical vapor deposition (CVD) of amorphous hydrogenated silicon a-Si:H. At the very position of depositing the thin film the stationary chemical composition of the processing gas is probed in situ by an effusive molecular beam which passes through a differential pumping stage into a quadrupole mass spectrometer (QMS). With SiH₄ as educt and SF₆ as a sensitizer, SiH₄ and Si₂H₆ are found in the processing gas while Si₃H₈ or higher silanes are lacking. Si₂H₆ and SF₆ lead to SiH₄, Si₂H₆, and Si₃H₈, but higher silanes are missing. The experimentally determined composition of the processing gas is semi-quantitatively reproduced by model calculations based on the assumption of stationary local equilibrium conditions and applying thermodynamic and spectroscopic data (molecular statistics). The mass balance of the processing gas entering and leaving the CVD chamber states an atomic ratio Si:H of 1:2 for the gas phase species forming the solid deposit on the reactor walls. This finding together with theoretical considerations indicates the intermediate Si₂H₄ to be the dominating gas phase species forming the a-Si:H thin films. Received: 17 July 1998/Accepted: 20 July 1998     

The Mössbauer spectrum of synthetic hureaulite: Fe5 2+(H2O)4(PO4H)2(PO4)2

The crystal structure of synthetic ferrous hureaulite, Fe₅ ²⁺ (H₂O)₄(PO₄H)₂(PO₄)₂, was refined from single-crystal X-ray data. It is monoclinic, space group C2/c, with a=17.487(4), b=9.017(2), c=9.338(2) Å, β=96.27(3)°, V=1463.6(6) Å³, Z=4 and D _calc=3.327 g/cm³. This end member of the hureaulite series was crystallized under distinctly acidic conditions, by a method that gives perfect crystals, large enough for X-ray single crystal studies. The main feature of the hureaulite structure is that it has an equal number of normal (PO₄)³⁺ and acid (PO₄H)²⁺ tetradentate groups. These are centered on Fe²⁺ atoms and share corners with edge-linked octahedra, forming pentamer units. The five Fe²⁺ atoms are distributed on three distinct sites in these units. This can be directly observed in the Mössbauer spectrum at 295 K, which contains three doublets whose relative intensities correspond to the 1:2:2 distributions of crystallographic sites.     

Cluster and band structure ab initio calculations on the adsorption of CO on acid sites of the TiO2(110) surface

The interaction of CO with the cationic sites of the TiO₂(110) surface has been investigated with cluster models and band structure calculations. The analysis of Hartree-Fock and correlated wavefunctions has shown that CO adsorbs at a distance of 4.4–4.5 bohr and a binding energy of 0.7–0.8 eV at low coverage. The bond strength is determined by the CO polarization and the CO б-donation to the surface while the electrostatic attraction is almost exactly cancelled by the Pauli repulsion. The adsorption is accompanied by two important measurable features, a considerable blue shift of the CO vibrational frequency and an increase of the CO 5б ionization potential. Both these effects have been analyzed in detail. We found that the CO ω shift is largely due to a combination of the electrostatic Stark effect and of the repulsion occurring when the CO molecule stretches in the presence of the rigid surface. The change in the 1π–5б binding energies, on the other hand, has an entirely electrostatic origin. Neither the ω shift nor the 5б binding energy shift are determined by the б-donation mechanism. Nevertheless, the occurrence of a charge transfer from CO to the empty levels of the Ti centers is well documented by (a) the energy and dipole moment change associated to this mechanism, (b) the expectation value of a projection operator which measures the charge associated with a given orbital, and (c) the CO dynamic dipole moment. The same analyses also rule out the occurrence of a Ti-to-CO back donation.     

Adsorption and diffusion behaviors of H2, H2S,NH3, CO and H2O gases molecules on MoO3 monolayer: A DFT study

Molybdenum trioxide (MoO₃) with α-phase is a promising material for gas sensing because of its high sensitivity, fast response and thermodynamic stability. To probe the mechanism of superior gas detection ability of MoO₃ monolayer, the adsorption and diffusion of H₂, H₂S, NH₃, CO and H₂O molecules on two-dimensional (2D) MoO₃ layer are studied via density functional theory (DFT) calculations. Based on calculated adsorption energies, density of states, charge transfer, diffusion barriers and diffusion coefficient, MoO₃ shows a superior sensitive and fast response to H₂ and H₂S than CO, NH₃, H₂O, which is consistent with experimental conclusions. Moreover, the response of MoO₃ to H₂S and H₂ will be obviously enhanced at high gas concentration, and the incorporation of H₂ and H₂S results in an obvious increasing in DOS near Fermi level. Our analysis provides a conceptual foundation for future design of MoO₃-based gas sensing materials.     

Vibrational Excitation of N2(B,C) and N+2(B) States in N2 and N2 – H2 Flowing Microwave Discharges

The ro‐vibrational spectra of N₂ microwave discharges have been analysed by emission spectroscopy. It is deduced the rotational and vibrational temperatures of N₂ states. The characteristic of vibrational temperature Θ₁ of the N₂ (X, v) ground state has been specifically determined.It has been found that the N₂ (C, B, v') and N⁺₂ (B, v') radiative states are directly excited by electron collisions on the N₂ (X,v) ground state at a N₂ gas pressure of 0.1 Torr (discharge tube of 5 mm I.D, microwave power 100 Watt) with a Θ₁ value near 10⁴ K. At higher gas pressure up to 5 Torr, the N₂ (C, v') states remain alone to be mainly excited by electron collisions on N₂ (X, v). It is considered the excitations of the N₂ (B, v') states by collisions of electrons and N₂ (X,v > 4) vibrational molecules on the N₂ (A) metastable states.With x < 9% H₂ into N₂, it is observed an increase of N₂, 2^nd pos intensity, resulting of an increase of high energy electrons. Inversely, the N₂, 1^st pos intensity decreased, partly following the decrease of low energy electrons (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

具有D4h对称性构型的C42+分子的Jahn-Teller效应与能级分裂

依据量子理论与配位场理论,利用群论和对称性分析的方法探讨了C42+分子在具有D4h对称性构型时,E(b1g+b2g)系统的Jahn-Teller效应中的相关问题.研究了C42+分子的电子态与声子态的对称性及其活跃声子态,讨论了系统声子间的耦合与CG系数,构建了E(b1g+b2g)系统的电声耦合哈密顿量,利用幺正平移变换将系统变换到了无声子激发的空间中,由此计算出了系统无声子激发的基态与激发态及其能级,结果表明由于系统的电声耦合作用缘故,在系统的势能面上形成了四个对称性势阱.无论系统处在哪一个势阱中,在Jahn-Teller畸变之后,系统的二重简并的能级都将发生分裂,分裂后系统电子态的简并性完全被消除.文中利用群论又进一步探讨了系统的Jahn-Teller畸变方向及其基态对称性,发现系统将沿着D4h→D2h方向发生畸变.畸变后C24+分子的基态具有D2h群下的B1u对称性.     

Deposition of iron on MgO(100): Reaction of CO and H2

Ultraviolet photoelectron spectroscopy (UPS), electron energy loss spectroscopy (EELS) and surface extended energy loss fine structure (SEELFS) were used to study the deposition of Fe on MgO(100) and to identify the surface compounds formed after reaction of CO/H₂ (1:1). The clean MgO(100) surface was characterized using the above techniques and the effect of argon ion bombardment damage to the surface was investigated. With the deposition of iron, metallic characteristics appear in the photoemission spectrum; the electron energy loss peaks of the MgO(100) substrate diminish in intensity with no significant shifts in loss energies. Fine structure analysis of the oxygen K-edge of the MgO(100) surface with less than 2 monolayers (ML) of iron suggests that the iron atoms bond with the oxygen at the surface of the MgO(100) lattice. For less than 4 ML of iron, the EEL spectra show that the deposited iron is oxidized after reaction of CO/H₂. Higher iron coverages result in carburization of the surface. Carbon deposition was observed with CO for all Fe coverages. Measurement of the fine structure above the carbon K-edge suggests that the types of carbide formed depend on the iron coverage; one carbide has a short CFe distance of 1.78 Å and the other a distance of 2.06 Å (high metal coverage).     

Adsorption and desorption of CO and H2 on Rh(111): Laser-induced desorption

Isosteric heats of adsorption ΔH_ad of CO and sticking coefficients S for CO and H₂ on Rh(111) are determined by laser-induced thermal desorption (LITD) in which a pulsed laser beam is focused onto the surface, and rapid local heating yields a desorption signal that is proportional to the adsorbate coverage θ. ΔH_ad for CO falls from 32.0±2 kcal/mol at low coverage to 14 kcal/mol at saturation, and the desorption pre-exponential factor v_d decreases from 10^14±0.5 to 10¹⁰ s^-1. ΔH_ad, v_d, and S of CO all decline sharply above θ = 0.2, corresponding to the occupation of a second binding state. Sticking coefficients for CO and hydrogen indicate precursor intermediates in adsorption.     

Hydrogen storage of Mg1-xMxH2 (M=Ti, V, Fe) studied using first-principles calculations

In this work, the hydrogen storage properties of the Mg-based hydrides, i.e., Mg_1-xM_xH₂ (M=Ti, V, Fe, 0 ≤ x ≤ 0.1), are studied using the Korringa-Kohn-Rostoker (KKR) calculation with the coherent potential approximation (CPA) approximation. In particular, the nature and the concentrations of the alloying elements and their effects are studied. Moreover, the material's stability and hydrogen storage thermodynamic properties are discussed. In particular, we find that the stability and the temperature of desorption decrease without significantly affecting the storage capacities.     

Vibrational and reorientational dynamics,crystal structure and solid–solid phase transition studies in [Ca(H2O)6]Cl2 supported by theoretical (DFT) calculations

[Ca(H₂O)₆]Cl₂ between 93 and 300 K possesses two solid phases. One phase transition (PT) of the first‐order type at = 218.0 K (on heating) and = 208.0 K (on cooling) was determined by differential scanning calorimetry. Thermal hysteresis of this PT (10 K), as well as the heat flow anomaly sharpness, suggests that the detected PT is a first‐order one. The entropy change value [ΔS ≈ 8.5 J mol⁻¹ K⁻¹ ≈ Rln(2.8)] associated with the observed PT suggests a moderate degree of molecular dynamical disorder of the high‐temperature phase. The temperature dependencies of the full width at half maximum values of the infrared band are due to ρ(H₂O)A₂ mode (at 205 cm⁻¹), and two Raman bands are arising from τ(H₂O)E and τ(H₂O)A₁ modes (at ca. 410 and 682 cm⁻¹, respectively), suggesting that the observed PT is associated with a sudden change of speed of the H₂O reorientational motions. The estimated mean value of activation energy for the reorientation of the H₂O ligands in the high‐temperature phase is ca. 11.4 kJ mol⁻¹ from Raman spectroscopy and 11.9 kJ mol⁻¹ from infrared spectroscopy. X‐ray single‐crystal diffraction measurement and spectroscopic studies (infrared, Raman and inelastic neutron scattering) also confirm that [Ca(H₂O)₆]Cl₂ includes two sets of differently bonded H₂O molecules. Ab initio calculations of the complete unit cell of one molecule of calcium chloride with a different number of water molecules (2, 4 and 6) have also been carried out. A comparison of Fourier Transform Infrared (FT‐IR), Fourier Transform Raman Scattering (FT‐RS) and inelastic neutron scattering spectroscopies results with periodic density functional theory calculations was used to provide a complete assignment of the vibrational spectra of [Ca(H₂O)₆]Cl₂. Copyright © 2016 John Wiley & Sons, Ltd.     

Dissociations of O2 molecules on ultrathin Pb(111) films: first-principles plane wave calculations

Using first-principles calculations, we systematically study the dissociations of O₂ molecules on different ultrathin Pb(111) films. According to our previous work revealing the molecular adsorption precursor states for O₂, we further explore why there are two nearly degenerate adsorption states on Pb(111) ultrathin films, but no precursor adsorption states existing at all on Mg(0001) and Al(111) surfaces. The reason is concluded to be the different surface electronic structures. For the O₂ dissociation, we consider both the reaction channels from gas-like and molecularly adsorbed O₂ molecules. We find that the energy barrier for O₂ dissociation from the molecular adsorption precursor states is always smaller than that from O₂ gas. The most energetically favorable dissociation process is found to be the same on different Pb(111) films, and the energy barriers are found to be influenced by the quantum size effects of Pb(111) films.     

Hartree–Fock and density functional theory study of remote substituent effects on heterolytic Fe―C bond energies of p‐G‐C6H4CH2Fe(CO)2(η5‐C5H5) and p‐G‐C6H4(H)(CN)CFe(CO)2(η5‐C5H5)

Knowledge of the strength of the metal–ligand bond breaking and formation is fundamental for an understanding of the thermodynamics underlying many important stoichiometric and catalytic organometallic reactions. Quantum chemical calculations at different levels of theory have been used to investigate heterolytic Fe―C bond energies of para‐substituted benzyldicarbonyl(η⁵‐cyclopentadienyl)iron, p‐G‐C₆H₄CH₂Fp [1, G = NO₂, CN, COMe, CO₂Me, CF₃, Br, Cl, F, H, Me, MeO, NMe₂; Fp = (η⁵‐C₅H₅)(CO)₂Fe], and para‐substituted α‐cyanobenzyldicarbonyl(η⁵‐cyclopentadienyl)iron, p‐G‐PANFp [2, PAN = C₆H₄CH(CN)]. The results show that BP86 and TPSSTPSS can provide the best price/performance ratio and more accurate predictions in the study of ΔH_het(Fe―C)'s. The good linear correlations [r = 0.98 (g, 1a), 0.99 (g, 2b)] between the substituent effects of heterolytic Fe―C bond energies [ΔΔH_het(Fe―C)'s] of series 1 and 2 and the differences of acidic dissociation constants (ΔpK_a) of C―H bonds of p‐G‐C₆H₄CH₃ and p‐G‐C₆H₄CH₂CN imply that the governing structural factors for these bond scissions are similar. And the excellent linear correlations [r = ?1.00 (g, 1c), ?0.99 (g, 2d)] between ΔΔH_het(Fe―C)'s and the substituent σ_p^? constants show that these correlations are in accordance with Hammett linear free energy relationships. The polar effects of these substituents and the basis set effects influence the accuracy of ΔH_het(Fe―C)'s. ΔΔH_het(Fe―C)'s(1, 2) follow the Capto‐dative Principle. The detailed knowledge of the factors that determine the Fp―C bond strengths would greatly aid in understanding reactivity patterns in many processes. Copyright © 2011 John Wiley & Sons, Ltd.     

Mn5(PO3(OH))2(PO4)2(H2O)4的水热合成和光谱研究

在水热反应条件下合成出具有红磷锰矿结构的Mn5(PO3(OH) ) 2 (PO4 ) 2 (H2 O) 4单晶 ,在X ray单晶结构分析的基础上 ,对其固体紫外可见漫反射光谱、红外光谱、荧光光谱和热重光谱进行了研究。结果表明 ,构成该化合物的PO4 四面体及MnO6 八面体通过共顶点或共棱方式相连接 ,与P ,Mn配位的氧分为 3类 :即端基氧 (Od)、二桥氧 (Ob)和三桥氧 (Oc)。因而在 2 10和 2 5 0nm左右出现了Od→Mn和Ob ,c→Mn的荷移跃迁吸收谱带 ;在 10 0 0～ 110 0cm- 1 处 ,P—O的伸缩振动峰分裂为 3个 ;70 0～ 980cm- 1 处存在 3类Mn—O的伸缩振动。对标题化合物分别采用 2 18和 310nm的光激发 ,分别在 35 4和 4 13nm产生强而尖锐的荧光光谱发射峰 ,表现了很强的光学效应。热重分析表明该化合物在 2 70℃以下结构保持稳定 ,在 2 70～36 0℃范围内失去配位水。量化计算得单点能为 - 4 5 5 8 6 5 95 5 5 1a u ;前线轨道能量HOMO(Alpha) =- 0 2 80 80a u ,LOMO(Alpha) =0 0 15 2 7a u ,能隙为 0 2 96 0 7a u ;HOMO(Beta) =- 0 2 5 919a u ,LOMO(Beta)=0 0 0 10 8a u ,能隙为 0 2 6 0 72a u ;偶极矩为 4 2 0 82Debye。     

MgF2：V^2＋晶体能级和振动结构的DV—Xa研究

首次用DV-X_a方法计算了终端声子激光晶体MgF_2:V~(2+)的电子能级和振动结构,给出的晶场能级与实验值相当接近.使用晶格振动的“呼吸”模型,得到了基态~4B_(1g)和第一激发态~4B_(2g)的振动势能曲线.在简谐振动近似下,它们分别具有454cm~(-1)和460cm~(-1)的声子能量,与实验值399cm~(-1)符合很好.另外,还获得晶体振动的黄昆参数,激活能,和Franck—Condon交距等参数.计算了四种温度(0K,2K,77K和300K)下的振动线形,并与2K的实验吸收谱作了比较.