On the calculation of force constants using isotopic frequencies by parametric method: Application to systems of (3×3) order

A method is proposed for the determination of angle parameters for ONF, ONCl and ONBr, utilising the isotopic frequencies of two isotopically substituted molecules. The force constants, Coriolis coupling constants, inertia defect, mean amplitudes of vibration and rotational distortion constants were also calculated and compared with literature values.     

The vibrational spectrum of thiazole between 600 and 1400 cm revisited: A combined high-resolution infrared and theoretical study

The Fourier transform infrared gas-phase spectrum of thiazole, C₃H₃NS, has been recorded in the 600-1400 cm⁻¹ wavenumber region with a resolution around 0.0030 cm⁻¹. Nine fundamental bands (ν₅(A′) to ν₁₁(A′), ν₁₅(A″), and ν₁₆(A″)) are analysed employing the Watson model. Ground-state rotational and quartic centrifugal distortion constants as well as upper state spectroscopic constants have been obtained from the fits. A detailed analysis of perturbations identified in the ν₁₁(A′) band at 866.5 cm⁻¹ enables a definitive location of the very weak ν₁₀(A′) and ν₁₄(A″) bands at 879.3 and 888.7 cm⁻¹, respectively. The three levels are analysed simultaneously by a model including Coriolis resonance using an ab initio predicted first order c-Coriolis coupling constant; second and higher order Coriolis parameters are determined. Qualitative explanations in terms of Coriolis resonances are given for a number of crossings observed in ν₅(A′), ν₆(A′), and ν₇(A′) at 1383.7, 1325.8, and 1240.5 cm⁻¹, respectively. The rotational constants, anharmonic frequencies, and vibration-rotation constants (alphas, ) calculated by quantum chemical calculations using a cc-pVTZ and TZ2P basis with B3LYP methodology, have been compared with the present experimental data. The rotation constant differences for each vibrational state, from the ground state values, are closer to experiment from the TZ2P calculations relative to those using cc-pVTZ. The values for Δ_J, Δ_JK, Δ_K, δ_J, and δ_K are close to experiment with both basis sets.     

Vibrational Parameters of Some Mixed Tetracoordinate Halogenomercurate(II) Complexes

Abstract

The normal coordinate analysis has been performed for the mercury(II) halogeno complexes HgX₃Y²? (X≠Y=C1, Br, I) using latest Raman spectral data for the first time. The general quadratic valence force field has been used in this study. The results in turn are utilized to investigate the useful vibrational parameters such as compliance constants and mean amplitudes of vibration. The trends among the vibrational parameters are discussed and the bond properties of the mercury(II) and related complexes are examined.     

High-resolution infrared and theoretical study of gaseous oxazole in the 600-1400 cm region

The Fourier transform gas-phase IR spectrum of oxazole, C₃H₃NO, has been recorded with a resolution of ca. 0.0030 cm⁻¹ in the wavenumber region 600-1400 cm⁻¹. The rotational structures of 10 fundamental bands (four of a-type, three of b-type and three of c-type) have been analysed using the Watson model. Ground state rotational and quartic centrifugal distortion constants as well as upper state spectroscopic constants have been obtained from the fits. A number of perturbations have been identified in the bands. From a local crossing observed in ν₁₅ we located the very weak ν₁₄ band at 858.19(1) cm⁻¹. Also ν₁₃ is definitively located at 899.3 cm⁻¹. The three global c-Coriolis interacting dyads ν₉/ν₁₀, ν₁₀/ν₁₁, and ν₁₂/ν₁₃ have each been analysed by a model including first and second order Coriolis resonance using ab initio predicted first order Coriolis coupling constants; second order Coriolis interaction parameters are determined. The rotational constants, harmonic and anharmonic frequencies, intensities, and vibration-rotation constants (alphas, ) have been predicted by quantum chemical calculations using a cc-pVTZ basis at the MP2 and B3LYP methodology levels, and compared with the present experimental data. Both the rotational constants and frequencies are marginally closer to experiment from the B3LYP calculations. In order to make more significant comparisons between theory and experiment for the alphas, we take differences between ground and vibronic state values; under these circumstances, the B3LYP definitely have a closer fit to experiment.     

Vibrational analysis of the fullerene family using Tersoff potential

Using Tersoff bond order potential, a vibrational analysis of the spherical fullerene family, namely C₆₀, C₈₀, C₁₈₀, C₂₄₀, C₂₆₀, C₃₂₀, C₅₀₀, and C₇₂₀ was performed. To evaluate the validity of our results, we have compared our simulation results with available experimental data and also with DFT B3LYP/6-31G(d) calculations. In general, molecular stiffness tends to decrease with increasing size, but its variation is limited in cases where mostly the tension-compression interaction sites are active such as the breathing mode. Furthermore, the bond length of each molecule is derived and compared with experimental and theoretical values calculated for graphene. Finally, vibrational frequencies are plotted in a histogram to reveal the common frequency gap and concentration points of the frequency distribution.     

The high-resolution infrared spectrum of pyrrole between 900 and 1500 cm revisited

The Fourier transform gas-phase infrared spectrum of pyrrole, C₄H₅N, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the 900-1500 cm⁻¹ spectral region. Four fundamental bands, ν₈(A₁; 1016.9 cm⁻¹), ν₂₃(B₂; 1049.1 cm⁻¹), ν₇(A₁; 1074.6 cm⁻¹), ν₂₀(B₂; 1424.4 cm⁻¹) and the overtone band 2ν₁₆(A₁; 962.7 cm⁻¹) have been analysed using the Watson model. The ν₈ and 2ν₁₆ bands are unperturbed; the ν₇ and ν₂₃ bands are locally perturbed, while the ν₂₀ band is globally perturbed by weak c-Coriolis resonance. Upper state vibrational term values, and rotational and centrifugal distortion constants, have been obtained from fits using S-reduction and I^r-representation as well as A-reduction and III^r-representation. A set of ground state rotational and centrifugal distortion constants using A-reduction was obtained from a simultaneous fit of ground state combination differences from all five bands and previous microwave and millimetre-wave data.     

Comparison Between the IR Spectra and the Structure of the Two Conformations of a Diazabicyclanol

Abstract

In the two stable conformations of the diazabicyclanol 3, 7-dimethyl-3, 7-diazabicyclo[3. 3. 1]nonan-9-ol, chair-chair (Va) and chair-boat (Vb), the infrared spectra (200–4000 cm^?1) were recorded, compared and their vibrations analysed. Using the AMI senlempirical method, the geometry was fully optimized in both forms, and the theoretical Infrared spectra were calculated and compared. In the (Vb) conformation, the IR spectra were recorded in CCl₃D, CCl₄ and S₂C solvents. Some correlations were established.     

A high-resolution infrared study of five bands of 1,2,5-thiadiazole in the range 750-1250 cm, together with ab initio and DFT studies

The Fourier transform gas-phase IR spectrum of 1,2,5-thiadiazole, C₂H₂N₂S, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the wavenumber region 750-1250 cm⁻¹. Five fundamental bands in this region, ν₄ (A₁), ν₅ (A₁), ν₁₁ (B₁), ν₁₃ (B₁), and ν₁₄ (B₂), have been analysed by the Watson Hamiltonian model to yield ground-state rotational and quartic centrifugal distortion constants as well as upper-state spectroscopic constants. A global perturbation of the ν₄ level is explained by Fermi resonance with the 2ν₁₅ level which has been located from its resonance effect. Rotational constants, harmonic and anharmonic frequencies have been calculated using a cc-pVTZ basis, at the MP2 and B3LYP methodology levels, and compared with the experimental data.     

Vibrational Analysis and Geometry Optimization of a Local Anesthetic by Means of the Am1 Semiempirical Method

The semiempirical method AM1 was used to optimize the geometric parameters: bond lengths, bond angles and torsional angles in the local anesthetic benzocaine hydrochloride. The frequencies and intensities of the normal modes were computed. These results were compared with the infrared and Raman spectroscopic data. A theoretical spectrum using several scale coefficients was plotted. Electron density maps in two and three dimensions were drawn. Several calculated thermodynamic parameters are discussed.     

High-resolution infrared and theoretical study of gaseous 1,2,5-selenadiazole in the 600-1400 cm range

The Fourier transform gas-phase IR spectrum of natural isotopic 1,2,5-selenadiazole, C₂H₂N₂Se, has been recorded with a resolution of ca. 0.0025 cm⁻¹ in the wavenumber region 600-1400 cm⁻¹. The three a-type bands, ν₂ (A₁), ν₄ (A₁), ν₅ (A₁), the two b-type bands ν₁₁ (B₁), ν₁₂ (B₁), and the c-type band ν₁₄ (B₂) for each of the isotopologues C₂H₂N₂⁸⁰Se and C₂H₂N₂⁷⁸Se have been analyzed using the Watson model. Ground state rotational and quartic centrifugal distortion constants as well as upper state spectroscopic constants have been obtained from the fits. The rotational constants, harmonic and anharmonic frequencies, and vibration-rotation constants (alphas, ) have been predicted by quantum chemical calculations using a cc-pVTZ basis at the MP2 and B3LYP methodology levels, and compared with the present experimental data. Although the rotation constants are marginally closer to experiment from the MP2 calculations, in general the B3LYP frequencies and alphas are closer to experiment.     

High-resolution infrared and theoretical study of four fundamental bands of gaseous 1,3,4-oxadiazole between 800 and 1600 cm

The Fourier transform infrared spectrum of gaseous 1,3,4-oxadiazole, C₂H₂N₂O, has been recorded in the 800–1600 cm⁻¹ wavenumber region with a resolution around 0.0030 cm⁻¹. The four fundamental bands ν₉(B₁; 852.5 cm⁻¹), ν₁₄(B₂; 1078.5 cm⁻¹), ν₄(A₁; 1092.6 cm⁻¹), and ν₂(A₁; 1534.9 cm⁻¹) are analyzed by the standard Watson model. Ground state rotational and quartic centrifugal distortion constants are obtained from a simultaneous fit of ground state combination differences from three of these bands and previous microwave transitions. Upper state spectroscopic constants are obtained for all four bands from single band fits using the Watson model. The ν₄ and ν₁₄ bands form a c-Coriolis interacting dyad, and the two bands are analyzed simultaneously by a model including first and second order Coriolis resonance using the ab initio predicted Coriolis coupling constant . An extended local resonance in ν₂ is explained as higher order b-Coriolis type resonance with ν₆ + ν₁₀, which is further perturbed globally by the ν₁₅ + ν₁₀ level. A fit of selected low-J transitions to a triad model including ν₂(A₁), ν₆ + ν₁₀(B₁), and ν₁₅ + ν₁₀(A₂) using an ab initio calculated Coriolis coupling constant is performed.The rotational constants, ground state quartic centrifugal distortion constants, anharmonic frequencies, and vibration–rotational constants (α-constants) predicted by quantum chemical calculations using a cc-pVTZ and TZ2P basis with B3LYP methodology, are compared with the present experimental data, where there is generally good agreement. A complete set of anharmonic frequencies and α-constants for all fundamental levels of the molecule is given.     

Vibrational Spectra of Cd(NH3)2Cl2 with 2H Isotopic Substitution

The infrared and Raman spectra of the cadmium diammindichloride complexes with ²H isotopic substitution, have been measured. A normal coordinate analysis for the isotopic compounds has been carried out based on a Local Symmetry Force Field (LSFF). The results sup port the experimental assignments.     

Vibrational Spectra of Cd(NH3)2Br2 with 2H Isotopic Substitution and Local Symmetry Force Field

The infrared and Raman spectra of the cadmiumdiammindibromide with ²H - isotopic substitution, have been measured. In order to examine the transferabilities of the skeletal and -NH₃, ligand force constants, a normal coordinate analysis was carried out based on a Local Symmetry Force Field (LSFF). The results support the experimental assignments.     

Relationship Between 1H-1H and 19F-19F Inter-Ring Coupling Constants in Fused Aza-Aromatic Systems

A complete analysis of the proton magnetic resonance spectra of quinoline¹ and isoquinoline^2,3 allowed to obtain signs and accurate magnitudes of the ¹H-¹H inter-ring coupling constants (HIRC). Since corresponding ¹⁹F-¹⁹F inter-ring coupling constants (FIRC) in perfluoro-quinoline⁴ and -isoquinoline⁵ are available it was worthwhile to consider whether a correlation could be established between HIRC and FIRC. A correlation of this kind would be of obvious interest to a better understanding of the transmission mechanism of long-range ¹⁹F-¹⁹F couplings.     

Vibrational Spectra and Normal Coordinate Analysis of Diamminediiodidezinc(II) with 15N and 2H Isotopic Substitution.

The Raman and IR. spectra of solid diamminediiodidezinc (II) with ¹⁵N and ²H isotopic substitution have been measured. The spectra have been interpreted assuming C_2v symmetry for the Zn(NH₃)₂I₂ complex structure. The skeletal stretching metal-ligand modes v_s(ZnN), v_as(ZnN), v_s(ZnI), v_as(ZnI) as well as the three bending modes δ(NZnN), δ(IZnI) and δ(IZnN) were assigned by comparison with the spectra of Zn(NH₃)₂C1₂ and Zn(NH₃)₂Br₂, and by the observed isotopic shifts of the frequencies. A normal coordinate analysis for the whole complex was carried out using the Local Symmetry Force Field Model.     

Geometric curvature and phase of the Rabi model

We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to measure in the qubit–cavity system. We also calculate the geometric phase beyond the RWA and find an anomalous sudden change, which implies the breakdown of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution are ill-defined near the anti-crossing point in the spectrum.     

Vibrational Spectroscopic Studies of Molecules with Biochemical Interest: The Cysteine Zwitterion

Abstract

The L-cysteine zwitterions in the orthorhombic crystal structure and in aqueous solution, including the deuterated isotopologues HSCD₂CH(NH₃ ⁺)COO^?, DSCH₂CH(ND₃ ⁺)COO^?, and DSCD₂CH(ND₃ ⁺)COO^?, have been studied by mid-infrared, far-infrared, and Raman spectroscopy. Density functional theory (DFT) calculations were performed for an equilibrium molecular geometry of the cysteine zwitterion to obtain vibrational frequencies of fundamental modes, infrared (IR) and Raman intensities, and the depolarization ratio of the Raman bands and combined with normal coordinate force field analyses. The force field obtained for dissolved (in H₂O and D₂O) cysteine, based on the 4 × 36 experimental fundamental modes of the four isotopologues, was successfully transferred to the two conformers in the solid state. The experimentally observed multiple bands (generally doublets) of L-cysteine and its deuterated isotopologues in the solid state were interpreted based on the coexistence of two conformers in the unit cell. The calculated frequencies were used for full assignments of the fundamental IR and Raman vibrational transitions, including an attempt to interpret all low-frequency vibrations (below 400 cm^?1) of the zwitterion also in the solid state. In particular, the hydrogen bonding effects on conformation, bond lengths, and force constants were studied, including those of the distorted NH₃ ⁺ amino group. The –S-H and -S-D stretching vibrations were found to be local modes, not sensitive to deuterium substitution of the -CH₂ and -NH₃ ⁺ groups in the molecule or to the H(D)-S-C-C torsional angle. The two major -S-H or -S-D stretching bands observed in the solid state correspond to different S-H/D bond lengths and resulted in the force constants K _SH = 3.618 N·cm^?1 and 3.657 N·cm^?1 for the SH^… S and SH^… O hydrogen-bonded interactions. A remarkable result was that the S(H)^… O interaction was weaker than the S(H)^… S interaction in the solid state and even weaker in aqueous solution, K _SH = 3.715 N·cm^?1, possibly due to intramolecular interactions between the thiol and amino groups. A general correlation between the S-H/D bond length and vibrational frequency was developed, allowing the bond length to be estimated for sulfhydryl groups in, for example, proteins. The C-S stretching modes were fitted with different C-S stretching force constants, K _CS = 3.213 and 2.713 N·cm^?1, consistent with the different CS bond lengths for the two solid-state conformers.     

Dispersed fluorescence spectroscopy of S0 vibrational levels in formaldehyde-d

High resolution dispersed fluorescence (DF) spectra of excited vibrational levels in S₀ HDCO up to 10 000 cm⁻¹ energy were recorded in a free-jet expansion. Excitation to the 0₀₀ rotational level in 4⁰ and 4¹ S₁ HDCO yielded pure vibrational spectra that are free from rotational congestion. The 162 transitions (133 unique vibrational levels) assigned in these spectra have been fit to a multiresonant Hamiltonian model, which includes harmonic frequencies , anharmonic constants (x_ij), and resonance constants (K). The assigned vibrational states were fit to the model with a standard deviation of 4.02 cm⁻¹. Extensive vibrational mixing is observed throughout the spectra. Six harmonic constants, eight anharmonic constants, and four resonance constants (K_44,1, K_66,1, K_44,66, and K_33,5) were determined experimentally. The 18 experimentally determined spectroscopic constants, with the exception of and K_66,1, were found to agree within 6 cm⁻¹ of ab initio calculated values.