Equilibrium structure in the presence of internal rotation: A case study of cis-methyl formate

The Born-Oppenheimer (BO) equilibrium molecular structure () of cis-methyl formate has been determined at the CCSD(T) level of electronic structure theory using Gaussian basis sets of at least quadruple-ζ quality and a core correlation correction. The quadratic, cubic and semi-diagonal quartic force field in normal coordinates has also been computed at the MP2 level employing a basis set of triple-ζ quality. A semi-experimental equilibrium structure () has been derived from experimental ground-state rotational constants and the lowest-order rovibrational interaction parameters calculated from the ab initio cubic force field. To determine structures, it is important to start from accurate ground-state rotational constants. Different spectroscopic methods, applicable in the presence of internal rotation and used in the literature to obtain “unperturbed” rotational constants from the analysis and fitting of the spectrum, are reviewed and compared. They are shown to be compatible though their precision may be different. The and structures are in good agreement showing that, in the particular case of cis-methyl formate, the methyl torsion can still be treated as a small-amplitude vibration. The best equilibrium structure obtained for cis-methyl formate is: r(C_m-O) = 1.434 Å, r(O-C_c) = 1.335 Å, r(C_m-H_s) = 1.083 Å, r(C_m-H_a) = 1.087 Å, r(C_c-H) = 1.093 Å, r(CO) = 1.201 Å, ∠(COC) = 114.4°, ∠(CCH_s) = 105.6°, ∠(CCH_a) = 110.2°, ∠(OCH) = 109.6°, ∠(OCO) = 125.5°, and τ(H_aCOC) = 60.3°. The accuracy is believed to be about 0.001 Å for the bond lengths and 0.1° for the angles.     

Experimental and theoretical studies on X-ray induced secondary electron yields in Ti and TiO2

Generation of X-ray induced secondary electrons in Ti and TiO₂ was studied from both experimental and theoretical approaches, using X-ray photoelectron spectroscopy (XPS) attached to a synchrotron radiation facility and Monte Carlo simulation, respectively.The experiment revealed that the yields of secondary electrons induced by X-rays (electrons/photon) at photon energies to 4950 and 5000 eV for Ti and TiO₂ are δ_Ti(4950 eV) = 0.002 and δ_Ti(5000 eV) = 0.014 while those for TiO₂ are δTiO₂(4950 eV)=0.003 and δTiO₂(5000 eV)=0.018.A novel approach to obtain the escape depth of secondary electrons has been proposed and applied to Ti and TiO₂. The approach agreed very well with the experimental data reported so far. The Monte Carlo simulation predicted; and while and .An experimental examination on the contribution of X-ray induced secondary electrons to photocatalysis in TiO₂ has also been proposed.     

The v6 = 1 and v6 = 2 vibrational states of DCF3

The high-resolution infrared spectra of DCF₃ were reinvestigated in the ν₆ fundamental band region near 500 cm⁻¹ and around 1000 cm⁻¹ with the aim to assign and analyze the overtone level of the asymmetric CF₃ bending vibration v₆ = 2.The present paper reports on the first study of both its sublevels (A₁ and E corresponding to l = 0 and ±2, respectively) through the high-resolution analysis of the overtone band and the hot and bands.The well-known “loop method”, applied to and , yielded ground state energy differences Δ(K, J) = E₀(K, J) − E₀(K − 3,J) for the range of K = 6 to 30.In the final fitting of molecular parameters, we used the strategy of fitting all upper state data together with the ground state rotational transitions.This is equivalent to that calculating separately the and coefficients of the K-dependent part of the ground state energy terms from the combination loops.All rotational constants of the ground state up to sextic order could be refined in the calculation.This led to a very accurate determination of C₀ = 0.18924413(25) cm⁻¹, , and also .In the course of analyzing simultaneously the overtone band together with the and ν₆ bands, the original assignment of the fundamental ν₆ band [Bürger et al., J. Mol. Spectrosc. 182 (1997) 34-49] was found to be incompatible with the present one. Assignments of the (k + 1, l₆ = +1)/(k − 1,l₆ = −1) levels had to be interchanged, which changed the value of Cζ₆ = −0.14198768(26) cm⁻¹ and the sign of the combination of constants C − B − Cζ in the v₆ = 1 level to a negative value.     

The 2ν4 overtone bands of FClO3

The high resolution infrared spectrum of the mono-isotopic species F³⁵Cl¹⁶O₃ has been studied in the region of the 2ν₄ overtone, from 2560 to 2680 cm⁻¹. The perpendicular component is strong and clearly observed while the parallel component is very weak and almost completely hidden by the perpendicular one. Their origins differ by 12.6 cm⁻¹, the being located at higher wavenumbers. The band is perturbed by the anharmonic interaction between the v₄ = 2, l₄ = ?2 and v₂ = v₄ = v₅ = 1, l₄ = l₅ = ±1 excited states, both of E symmetry. In total 3157 transitions have been assigned, 83% of these to , 12% to , and 5% to . The three bands have been analyzed simultaneously, taking into account the Fermi resonance effective between the excited states of E symmetry. The ro-vibration parameters of the excited states have been obtained, including the deperturbed band origins of and , at 2628.5890(4) and 2619.3342(5) cm⁻¹, respectively. The W₂₄₅ anharmonic constant is equal to 4.0161(4) cm⁻¹. The x₄₄+g₄₄ and x₂₄+x₄₅+g₄₅ anharmonicity constants have been derived from the obtained band origins and those of ν₄ and ν₂ + ν₅.     

FTIR and diode laser spectroscopy of isobutylene: Analysis of the rotational structure in the v28 fundamental band

Rotational structure in the fundamental band of isobutylene has been examined at room temperature using a combination of FTIR and Pb-salt diode laser instruments. The highest spectral resolution for the FTIR measurements was 0.125 cm⁻¹. Even at this resolution however, rotational structure for the band could be observed and appeared to possess a very regular pattern. A preliminary spectral assignment was obtained using the Watson/Gora asymptotic approximation for a rigid oblate asymmetric rotor. Within this approximation, the band origin was determined to be 890.937 (4) cm⁻¹. Excited state rotational constants, without the inclusion of centrifugal distortions terms, are A = 0.3033(16), B = 0.2801(12) and C = 0.15362 (8) cm⁻¹ respectively. Finally, a full set of spectroscopic constants, including quartic centrifugal distortion constants, were obtained for the band by including the high resolution Pb-salt spectra.     

Temperature and pressure effects on the spin state of ferric ions in the [Fe(sal2-trien)][Ni(dmit)2] spin crossover complex

Thermal and pressure effects have been investigated on the [Fe(sal₂-trien)][Ni(dmit)₂] spin crossover complex by means of Mössbauer spectroscopic, calorimetric, X-ray diffraction and magnetic susceptibility measurements. The complex displays a complete thermal spin transition between the and spin states of Fe^III near 245 K with a hysteresis loop of ca. 30 K. This transition is characterised by a change of the enthalpy, ΔH_HL=7 kJ/mol, entropy, ΔS_HL=29 J/Kmol, and the unit cell volume, ΔV_HL=15.4 Å³. Under hydrostatic pressures up to 5.7 kbar the thermal transition shifts to higher temperatures by ca. 16 K/kbar. Interestingly, at a low applied pressure of 500 bar the hysteresis loop becomes wider (ca. 61 K) and the transition is blocked at ∼50% upon cooling, indicating a possible (irreversible) structural phase transition under pressure.     

The 2ν5 overtone bands of perchloryl fluoride

The high-resolution infrared spectra of the monoisotopic species F³⁵Cl¹⁶O₃, F³⁷Cl¹⁶O₃, F³⁵Cl¹⁸O₃ and F³⁷Cl¹⁸O₃ have been studied in the region of the 2ν₅ overtones, from 1100 to 1200 cm⁻¹. Both the parallel and the perpendicular components are clearly observed in the spectra, their origins differing by about 0.4 cm⁻¹. In each spectrum about 2000 transitions have been assigned, 35% of them belonging to . The parallel and perpendicular bands in each manifold have been analyzed separately since no evidence of perturbations has been observed. The rovibration parameters of the v₅ = 2, l₅ = 0 and v₅ = 2, l₅=?2 excited states have been obtained. For the four species combining the and band origins with those of the ν₅ fundamentals the harmonic wavenumbers, , and the x₅₅ and g₅₅ anharmonicity constants have also been derived.     

Optical properties of Tl3SbS3 acousto-optic crystals

Optical properties of acousto-optical material Tl₃SbS₃ were investigated at the fundamental absorption edge. The basic (n = 1) and excited (n = 2, 3) exciton states were obtained from the λ-modulated reflection spectra for polarizations E⊥c at 10 K. Taking into account the spatial dispersion we determined the parameters of excitons by calculating the spectra shapes of λ-modulated reflection of line n = 1 and estimated values of the zone-translation masse and the reduced effective masse of excitons, the effective masse of electrons , heavy and light holes.     

Electro-optic behavior of lithium niobate at cryogenic temperatures

The unclamped relative permittivity, , and the Pockels coefficient, , of congruent lithium niobate at a frequency f = 5760 Hz have been determined at low temperatures (7 K < T < 300 K). A He cryostat setup mounted to one arm of an electronically phase-stabilized Michelson interferometer was utilized for the measurement of . A continuous decrease in both parameters was observed as T → 0 K with limiting values of and , respectively.     

High-resolution infrared and subterahertz spectroscopy of the v2 = 1, v5 = 1, and v3 = 2 levels of CH3Cl

High-resolution Fourier-transform infrared spectra between 1235 and 1680 cm⁻¹ and subterahertz spectra between 250 and 630 GHz of monoisotopic ¹³CH₃³⁵Cl have been recorded and analyzed simultaneously, with all Coriolis, α-resonance, and l-type interactions in the polyad of the v₂ = 1, v₅ = 1, and v₃ = 2 levels taken into account. Several α-resonances (Δk = ±2, Δl = ?1) generating perturbation-allowed transitions have been assigned in the rovibrational spectra. These resonances enabled us to determine accurately and independently the ground state rotational and centrifugal distortion parameters A₀ = 5.205 746 9 (55) cm⁻¹ and . Even , which is, however, correlated to higher-order α-resonance terms, was determined. With 51 upper state parameters varied, about 5800 rovibrational wavenumbers and more than 550 rotational frequencies pertaining to the excited vibrational states were fitted within their experimental accuracy.     

Quantum amplitudes in black-hole evaporation: Spins 1 and 2

Quantum amplitudes for s = 1 Maxwell fields and for s = 2 linearised gravitational-wave perturbations of a spherically symmetric Einstein/massless scalar background, describing gravitational collapse to a black hole, are treated by analogy with the previous treatment of s = 0 scalar-field perturbations of gravitational collapse at late times. Both the spin-1 and the spin-2 perturbations split into parts with odd and even parity. Their detailed angular behaviour is analysed, as well as their behaviour under infinitesimal coordinate transformations and their linearised field equations. In general, we work in the Regge-Wheeler gauge, except that, at a certain point, it becomes necessary to make a gauge transformation to an asymptotically flat gauge, such that the metric perturbations have the expected fall-off behaviour at large radii. In both the s = 1 and s = 2 cases, we isolate suitable ‘coordinate’ variables which can be taken as boundary data on a final space-like hypersurface Σ_F. (For simplicity of exposition, we take the data on the initial surface Σ_I to be exactly spherically symmetric.) The (large) Lorentzian proper-time interval between Σ_I and Σ_F, measured at spatial infinity, is denoted by T. We then consider the classical boundary-value problem and calculate the second-variation classical Lorentzian action , on the assumption that the time interval T has been rotated into the complex: T → |T| exp (−iθ), for 0 < θ ? π/2. This complexified classical boundary-value problem is expected to be well-posed, in contrast to the boundary-value problem in the Lorentzian-signature case (θ = 0), which is badly posed, since it refers to hyperbolic or wave-like field equations. Following Feynman, we recover the Lorentzian quantum amplitude by taking the limit as θ → 0₊ of the semi-classical amplitude . The boundary data for s = 1 involve the (Maxwell) magnetic field, while the data for s = 2 involve the magnetic part of the Weyl curvature tensor. These relations are also investigated, using 2-component spinor language, in terms of the Maxwell field strength ?_AB = ?_(AB) and the Weyl spinor Ψ_ABCD = Ψ_(ABCD). The magnetic boundary conditions are related to each other and to the natural boundary conditions by supersymmetry.     

Interference of resonance luminescence of exciton polaritons in CuGaS2 crystals

The nonmodulated and wavelength-modulated reflection spectra of CuGaS₂ crystals for the polarization EIIc of 10 K are studied. The states n = 1, 2 and 3 of the excitons Γ₄ (A-excitons) and n = 1, n = 2 of B- and C-excitons are found. The nonmodulated absorption spectra for the polarization E⊥c at 10 K have been studied. The states n = 1, 2 and 3 of Γ₅ excitons are found. The main parameters of the A (Γ₄, Γ₅) and B, C exciton series at the energies of the longitudinal and transverse excitons Γ₄ for the states n = 1 and n = 2, the effective masses of electrons and holes are determined. The photoluminescence peaks were observed at n = 3 and n = 4 of the excitons Γ₅ in the luminescence spectra excited by the line 4880 Å of Ar⁺ laser. In the luminescence spectra the interference is found.     

Infrared laser magnetic resonance spectroscopy of the ν3 fundamental and associated hot bands of the NCO free radical

The v₃ = 1 ← 0 (out-of-phase stretching vibration) transition wavenumbers of gas-phase NCO have been measured, in many cases with sub-Doppler resolution, by mid-infrared laser magnetic resonance (LMR) spectroscopy. In addition to the fundamental transition from the ²Π ground vibronic state, hot bands from the v₂ = 1 ²Σ and ²Δ and from the v₂ = 2 ²Φ vibronic states were detected and analyzed. The ²Σ vibronic level, with a spin-orbit coupling only partly quenched by the Renner-Teller effect, is characterised by complex and rapid tuning of energies in the magnetic field. This is the first successful analysis of magnetic resonance spectra for non-unique Renner-Teller vibronic states. The new LMR transitions were combined with data from previous studies and analysed, using an effective Hamiltonian in a 40-parameter fit to 660 transitions and combination differences. Several new coupling parameters are required, having magnitudes generally consistent with predictions from standard vibration-rotation theory.     

Magnetic ordering and low-temperature thermodynamic properties of ErFe2Ge2

Polycrystalline sample of ErFe₂Ge₂ was investigated by means of magnetic susceptibility, heat capacity and electrical resistivity measurements, as well as by powder neutron diffraction. All these experiments yielded an evidence of magnetic ordering setting at about 3 K. The low-temperature neutron data revealed the formation of a sine-modulated commensurate antiferromagnetic structure characterized by the propagation vector k=(0, 0, ). The erbium magnetic moment is aligned parallel to the crystallographic a-axis. At T=1.55 K it is equal to 7.06(5) μ_B.     

Laser excitation spectrum of C3 in the region 26 000-30 700 cm

The vibrational structure of the electronic state of C₃ in the region 26 000-30 775 cm⁻¹ has been re-examined, using laser excitation spectra of jet-cooled molecules. Rotational constants and vibrational energies have been determined for over 60 previously-unreported vibronic levels; a number of other levels have been re-assigned. The vibrational structure is complicated by interactions between levels of the upper and lower Born-Oppenheimer components of the state, and by the effects of the double minimum potential in the Q₃ coordinate, recognized by Izuha and Yamanouchi [16]. The present work shows that there is also strong anharmonic resonance between the overtones of the ν₁ and ν₃ vibrations. For instance, the levels 2 1⁺ 1 and 0 1 ⁺ 3 are nearly degenerate in zero order, but as a result of the resonance they give rise to two levels 139 cm⁻¹ apart, centered about the expected position of the 2 1⁺ 1 level. With these irregularities recognized, every observed vibrational level up to 30 000 cm⁻¹ (a vibrational energy of over 5000 cm⁻¹) can now be assigned. A vibronic level at 30181.4 cm⁻¹, which has a much lower B′ rotational constant than nearby levels of the state, possibly represents the onset of vibronic perturbations by the electronic state; this state is so far unknown, but is predicted by the ab initio calculations of Ahmed et al. [36].