Symmetry Species Research Articles

ChemInform Abstract: High-Resolution Spectrum of the C-O Stretch Overtone Band in Methyl Alcohol

The Fourier‐transform spectrum of the CH3OH overtone C–O stretching band (vCO=2←0) has been recorded in the range 1950–2060 cm−1, at a resolution of 0.004 cm−1. The spectrum is resolved into J multiplets, each displaying complicated substructure due to strong torsion–vibration–rotation effects. Within this structure, it has been possible so far to identify R and P branch transitions for K=0 and K=1 for both A and E torsional symmetry species for J≤24. The assignments are supported by combination differences derived from known ground‐state frequencies. The identified branches have been analyzed in terms of effective state‐dependent series‐expansion parameters, and the leading terms in the torsion–rotation Hamiltonian have been derived for the second excited C–O stretching state. The vCO=2 torsional barrier height is obtained as 395.5±0.2 cm−1, and the effective B value as 23 671.9±1.3 MHz. In addition, the 34.946 cm−1 far‐infrared laser line pumped by the 10R(48) CO2 laser line has been tentatively identif...

ChemInform Abstract: Electronic Structure of Vinylthio Radical (CH2CHS): A Theoretical Study.

A predictive ab initio MO calculation was performed for the thus far undetected sulfur analog of the vinoxy radical. Multiconfigurational self‐consistent field (MCSCF) and symmetry adapted cluster expansion–configuration interaction (SAC–CI) wave functions were used to describe the electronic structure of the radical. The symmetry species of the ground state was found to be 2A‘ as in the case of the vinoxy radical. The crucial difference between the two radicals is that the thio‐radical is more or less characterized as a sulfur‐centered radical, CH2=CH–S⋅ whereas the oxy‐radical is regarded as a carbon centered ⋅CH2–CH=O in their ground state. Excitation energies, normal modes, Franck–Condon factors, hyperfine coupling parameters, and electron affinity were predicted.

Performance of multireference and equation-of-motion coupled-cluster methods for potential energy surfaces of low-lying excited states: Symmetric and asymmetric dissociation of water

Multireference (MR), general-model-space (GMS), state-universal (SU) coupled-cluster (CC) method that considers singly (S) and doubly (D) excited cluster amplitudes relative to the reference configurations spanning the model space (GMS SU CCSD), as well as its externally corrected (ec) version (N,M)-CCSD that employs N-reference MR CISD as an external source of higher-than-pair cluster amplitudes in a M-reference GMS CCSD, are employed to investigate low-lying states of the water molecule. The emphasis is on a generation of several low lying states belonging to the same symmetry species. Cuts of the potential energy surface (PES) corresponding to the breaking of a single OH bond and leading to the OH+H fragments, as well as the simultaneous breaking of both bonds into the O+2H are considered. Relying on a simple ab initio model that enables a comparison with the exact full configuration interaction energies, the performance of the GMS-based methods is assessed in the whole relevant range of internuclear separations. It is shown that the ec (N,M)-CCSD version provides best results for both the singlet and the triplet states considered. The same cuts of the PES are then explored using a realistic aug-cc-pVTZ basis set. For triplets, the use of high-spin (M(S)=1) references is to be preferred.

On the Physical Reasons for the Extension of Symmetry Groups in Molecular Spectroscopy

Several situations of general interest, in which the symmetry groups usually applied to spectroscopy problems need to be extended, are reviewed. It is emphasized that any symmetry group of geometrical operations to be used in Molecular Spectroscopy should be extended for completeness by considering the time reversal operator, as far as the Hamiltonian is invariant with respect to the inversion of the direction of motion. This can explain the degeneracy of pairs of vibrational and rotational states spanning the so-called separably degenerate irreducible representations, in symmetric tops of low symmetry, and Kramers degeneracy in odd electron molecules in the absence of magnetic fields. An extension with account of time reversal is also useful to determine relative phase conventions on vibration-rotation wavefunctions, which render all vibration-rotation matrix elements real. An extension of a molecular symmetry group may be required for molecules which can attain different geometries by large amplitude periodical motions, if such motions are hindered and are not completely free. Special cases involving the internal rotation are discussed in detail. It is observed that the symmetry classification of vibrational modes involving displacements normal to the internal rotation axis is not univocal, but can be done in several ways, which actually correspond to different conventions on the separation of vibration and internal rotation in the adopted basis functions. The symmetry species of the separate vibrational and torsional factors of these functions depend on the adopted convention.

Vibration–rotation-tunneling states of the benzene dimer: an ab initio study

An improved intermolecular potential surface for the benzene dimer is constructed from interaction energies computed by symmetry-adapted perturbation theory, SAPT(DFT), with the inclusion of third-order contributions. Twelve characteristic points on the surface have been investigated also using the coupled-cluster method with single, double, and perturbative triple excitations, CCSD(T), and triple-zeta quality basis sets with midbond functions. The SAPT and CCSD(T) results are in close agreement and provide the best representation of these points to date. The potential was used in calculations of vibration-rotation-tunneling (VRT) levels of the dimer by a method appropriate for large amplitude intermolecular motions and tunneling between multiple equivalent minima in the potential. The resulting VRT levels were analyzed with the use of the permutation-inversion full cluster tunneling (FCT) group G(576) and a chain of subgroups that starts from the molecular symmetry group C(s)(M) of the rigid dimer at its equilibrium C(s) geometry and leads to G(576) if all possible intermolecular tunneling mechanisms are feasible. Further information was extracted from the calculated wave functions. It was found, in agreement with the experimental data, that for all of the 54 G(576) symmetry species (with different nuclear spin statistical weights) the lower VRT states have a tilted T-shape (TT) structure; states with the parallel-displaced structure are higher in energy than the ground state of A symmetry by at least 30 cm(-1). The dissociation energy D(0) equals 870 cm(-1), while the depth D(e) of the TT minimum in the potential is 975 cm(-1). Hindered rotation of the cap in the TT structure and tilt tunneling lead to level splittings on the order of 1 cm(-1). Also intermolecular vibrations with excitation energies starting at a few cm(-1) were identified. A further small, but probably significant, level splitting was assigned to cap turnover, although in scans of the potential surface we could not find a plausible 'reaction path' for this process. Rotational constants were extracted from energy levels calculated for total angular momentum J = 0 and 1, and from expectation values of the inertia tensor. Although the end-over-end rotational constant B + C agrees well with the measured microwave spectra, there is disagreement with the measurements concerning the (a)symmetric rotor character of the benzene dimer. It is concluded from calculations for the 54 nuclear spin species that the microwave spectrum should show overlapping contributions from many different species. Another interesting conclusion regards the role of the quantum number K, for a prolate near-symmetric rotor the projection of the total angular momentum on the prolate axis. For the benzene dimer, K has a substantial effect on the energy levels associated with the intermolecular motions of the complex.

VIBRATE!A program to compute irreducible representations for atomic vibrations in crystals

VIBRATE!is a computer program that uses group theory to carry out factor group analysis of a crystal structure. The symmetry species of the normal modes of vibration are derived, together with information relating to the symmetry-adapted vectors. The program is simple to use, relying on input mainly from a crystallographic information file. The output is presented in a form that should be familiar not only to crystallographers but also to others such as chemical spectroscopists.

Vibrational and electronic optical activity of the chiral disulphide group: Implications for disulphide bridge conformation

Using dihydrogendisulphide (H(2)S(2)), dimethyl- ((CH(3))(2)S(2)), and diethyldisulphide ((CH(3)CH(2))(2)S(2))as model molecules, theoretical ECD, VCD, and ROA spectra of nonplanar disulphides were calculated by DFT methods. Most of the calculated electronic and vibrational chiroptical features suffer an equivocal relation between calculatedsigns of ECD, VCD, or ROA and the sense of disulphide nonplanarity as noted earlier for low-lying ECD bands. This is a consequence of local C(2) symmetry of a disulphide group causing most electronic and vibrational transitions to occur as pairs falling to alternative A, B symmetry species, which become degenerate and switch their succession (and consequently the observed chiroptical sign pattern) at the energetically most favorable perpendicular conformation. According to present calculations, the key to resolving this ambiguity may involve the S-S stretching vibrational mode at approximately 500 cm(-1). The relation of signs of the relevant VCD and ROA features to sense of disulphide chirality seems simpler and less ambiguous. The right-handed arrangement of the S-S group (0 < chi(S-S) < 180 degrees) results in mostly negative VCD signals. Although relation to ROA still suffers some ambiguity, it gets clearer along the series H(2)S(2)-(CH(3))(2)S(2)-(CH(3)CH(2))(2)S(2). ROA is also attractive for the analysis of disulphide-containing peptides and proteins, because applying it to aqueous solutions is not problematic.

The role of symmetry in representing reduced density operators and reduced transition density operators: General formulation with specific application to atomic systems

The p-particle reduced transition (density) matrix between a properly chosen given member of one degenerate manifold and a properly chosen given member of a (possibly) different manifold of eigenstates of a nonrelativistic atomic Hamiltonian contains sufficient information to construct the p-particle reduced transition (density) matrix between any member of the first manifold and any member of the second manifold. A synthetic procedure for this construction is presented in this article and is completely spelled out for p = 1. Application of these ideas to the more general symmetries of a molecular system or of an atom in a crystal field is outlined. This procedure is particularly useful when one has made a calculation of the reduced density matrix of the state belonging to one symmetry species within a degenerate manifold and desires the reduced density matrix of another state [or the reduced transition (density) matrix between two states] within the same manifold.

VIBRATIONAL SPECTRUM AND THERMODYNAMIC PROPERTIES OF PYRIDAZINE

Vibrational spectrum of pyridazine was recorded. Assignment of frequencies to normal vibrations was made. Tellr-Redlich product rule was applied for symmetry species A1, A2, B1 and B2. Thermodynamic functions were calculated from spectroscopic data.

Strategies for advanced applications of permutation–inversion groups to the microwave spectra of molecules with large amplitude motions

This article presents permutation–inversion group-theoretical strategies and recipes aimed at helping a high-resolution molecular spectroscopist use the existing pedagogical literature to carry out their own treatment of the basic symmetry questions in rotating molecules with large-amplitude vibrational motions. Topics addressed include: determination of the feasible permutation-inversion group and its symmetry species and character table; a general equation defining coordinates that can describe translation, overall rotation, large-amplitude vibrations and small-amplitude vibrations for a large class of floppy molecules; and the determination of symmetry species for basis functions and selection rules for operators written in these coordinates. The article is intended to be more advanced than existing pedagogical works, but it still leaves many important topics untreated.

Analysis and fit of the high-resolution spectrum of the Ã1A u– [formula omitted]1A g LIF spectrum of the two-equivalent-top molecule biacetyl

The jet-cooled laser-induced visible fluorescence excitation spectrum of the à 1 A u (S 1)– X ˜ 1 A g ( S 0) transition in biacetyl (CH 3 C( O) C( O) CH 3) exhibits a long progression in the torsional vibrations of the two equivalent methyl tops in this molecule, whose structure has previously been described and qualitatively understood using local mode ideas applied to the two equivalent methyl rotor torsions together with the G 36 symmetry species A 1, A 2, A 3, A 4, E 1, E 2, E 3, E 4, and G. In the present rotational analysis, we have assigned a G 36 symmetry species, two local-mode torsional quantum numbers, and the usual three asymmetric rotor quantum numbers J KaKc to the upper and lower torsion–rotation levels involved in the observed transitions, relying heavily on comparison of quantum-beat patterns to determine transitions with a common upper state. These torsion–rotation transitions were then globally fit using a two-equivalent-top computer program, which was written in the principal axis system of the molecule and which uses a free-rotor basis set for each top, a symmetric-top basis set for the rotational functions, and a single-step diagonalization procedure. We can fit 411 lines involving 16 torsional sublevels from states with zero to three quanta of torsional excitation in the excited electronic state, using 24 parameters to obtain a standard deviation of 0.0045 cm −1, which is quite satisfactory, but inclusion in the fit of 440 transitions from all 17 rotationally assigned torsional levels increases the standard deviation by some 25%. The present fit gives a value of V 3 = 238 cm −1 for the threefold barrier height in the excited electronic state, in reasonable agreement with earlier studies.

Multispectrum analysis of 12CH 4 in the ν4 band: I. : Air-broadened half widths, pressure-induced shifts, temperature dependences and line mixing

Lorentz air-broadened half widths, pressure-induced shifts and their temperature dependences have been measured for over 430 transitions (allowed and forbidden) in the ν 4 band of 12CH 4 over the temperature range 210–314 K. A multispectrum non linear least squares fitting technique was used to simultaneously fit a large number of high-resolution (0.006–0.01 cm −1) absorption spectra of pure methane and mixtures of methane diluted with dry air. Line mixing was detected for pairs of A-, E-, and F-species transitions in the P- and R-branch manifolds and quantified using the off-diagonal relaxation matrix elements formalism. The measured parameters are compared to air- and N 2-broadened values reported in the literature for the ν 4 and other bands. The dependence of the various spectral line parameters upon the tetrahedral symmetry species and rotational quantum numbers of the transitions is discussed. All data used in the present work were recorded using the McMath–Pierce Fourier transform spectrometer located at the National Solar Observatory on Kitt Peak.

The effective Hamiltonian for the coupling between inversion–torsion states in methylamine

The Hougen’s formalism of group-theoretical effective Hamiltonian has been extended to include the resonances between the wagging, ν 9, and third or fourth excited torsional, 3 ν 15 and 4 ν 15, states in methylamine. The presented Hamiltonian treats explicitly these couplings. For each of these bands the rovibrational sublevels belong to all symmetry species of the G 12 group of methylamine. On the other hand the vibrational states for ν 9 and 4 ν 15 are symmetric with respect to reflection in the symmetry plane of the NH 2 group, and antisymmetric for 3 ν 15. We have shown that the coupling terms between the ν 9 and 3 ν 15 states are limited to Coriolis-like coupling, and no Fermi-type interactions are allowed. For the coupling between the ν 9 and 4 ν 15 states all kind of interaction terms are possible.

Conformational symmetry and vibrational dynamics of polymers

Abstract Polymers are an important class of materials, and their conformation dictates their dynamical, thermodynamical, and hydrodynamical behavior. Several spectroscopic and other techniques have been employed to characterize their conformation. However, little use has been made of group-theoretical techniques except in the classification of symmetry species. In the present review, an attempt has been made to correlate normal modes and their dispersion profiles with the conformation of the polymeric systems. This has been attempted in the case of 2-, 3-, 4-fold and α-helical polymers.

Accurate determination of the anisotropy factors and the phase differences of Ramanpolarizabilities in some uniaxial crystals: the case of lithium niobate

The present study highlights self-consistently helpful improvements dedicated toovercoming the difficulty resulting from the fitting procedure of integrated Ramanintensities recorded according to the rotation crystal method described earlier. Tothis end, the anisotropy factors of Raman polarizabilities and the correspondingrelative phases are determined within the framework of the exact mathematicalderivation of the phase factors. These are the relevant parameters of the Ramanefficiency relations which are numerically difficult to obtain from the fitting of theintegrated areas. The present theoretical approach is then applied to the modes of theA1 and Ey symmetry species of the lithium niobate (LN) crystal point group.All the expressions of the Raman absolute intensities of theA1 and Ey irreducible representations initially imply three parameters to be determined from thefitting computations. However, from the derived analytical expressions of the phasedifferences, the number of parameters involved in the fitting procedure is reduced from 3 to2, thus improving the statistics of the numerical treatment.

High resolution IR spectrum of the ν8 band of CH2DF: analysis of the interactions with the near vibrational levels

The IR spectrum of the ν8 band of monodeutero methyl fluoride has been recorded with a resolution of 0.004 cm−1 using a Fourier transform spectrometer. The ν8 vibration, of A′′ symmetry species, gives rise to a pure c-type envelope centred at 1298.58 cm−1, resembling a perpendicular band of a prolate symmetric rotor. From the spectral analysis it has been found that ν8 is coupled with ν4 for the low Ka sublevels while for the higher ones other vibrational states, directly or indirectly, are also interacting. For satisfactory reproduction of the rovibrational data of ν8, the Watson's Hamiltonian in the Ir representation has been implemented with interaction parameters, which included first- and second-order a-, b-type and c-type Coriolis couplings with ν4 and ν9, respectively. Being these states also interacting with other levels, the effective spectroscopic parameters of the analysed band up to fourth order have been obtained from a data set formed by the six fundamentals located below 1500 cm−1.

Negative thermal expansion change of different stoichiometric proportions calcium-doped strontium barium niobate crystals

The polarization Raman spectra were measured for the calcium-doped strontium barium niobate crystals ((Ca 0.28Ba 0.75) x(Sr 0.60Ba 0.40) 1 − x Nb 2O 6 ( x = 0.25,0.50 or 0.75, CSBN) to determine the negative thermal expansion(NTE) change induced by different stoichiometric proportions calcium-doped concentration. The different count-intensity (CI) of Raman peaks with the scattering geometry Z( XY) Z­, corresponding to the symmetry species B 2, are attributed to the different vacancy rate(VR) in A2 sites of tetragonal tungsten bronze-type structure, which can result in the change of the short-range molecular force (SRMF) between ions filled in A2 sites and Nb–O octahedron. Since the thermal properties of materials direct responding to the vibration of crystal lattices, the NTE change of CSBN crystals are considered as arising due to the geometry change for the different calcium-doped concentration.

FTIR spectra and rovibrational analysis of the ν11 band of trans-ClHC [dbnd]CHF and ν10 of trans-ClHC [dbnd]CDF

High-resolution Fourier transform infrared spectra of natural trans-ClHC CHF and of its isotopologue trans-ClHC CDF have been recorded in the region between 700 and 1150 cm −1 with the purpose to analyze the ν 11 fundamental of the main species and the ν 10 of its deuterated compound. Both bands, of symmetry species A″, present c-type envelope absorptions. Beside the expected features, the K structure of the P( J), Q( J), and R( J) manifolds was resolved and identified; the assignment of the rovibrational transitions was extended up to J = 92 and K a = 13 for the trans- 35ClHC CHF and up to J = 86 and K a = 10 for trans- 35ClHC CDF. More than 2900 and 2700 lines for the main and deuterated species, respectively, were analyzed by a least-squares procedure and reliable spectroscopic molecular parameters were determined for both isotopologues.

Calculation of optical polarizability of atoms with two open shells in the Hartree-Fock approximation

Time-dependent Hartree-Fock equations (the Huzinaga method) in terms of density functionals have been obtained for a multielectronic system with two open shells of different symmetry species subjected to a time-dependent external perturbation. Based on these, the equations of time-dependent “bound” perturbation theory have been written in the orbital representation. The dynamic dipole polarizability of a number of atoms with two open shells with s1pn-configurations has been calculated using an optimized basis set of Slater-type atomic orbitals.

The symmetric amino-wagging band of hydrazine: Assignment and analysis

For the first time a weak fundamental symmetric amino-wagging band, ν 6, was assigned in the high-resolution Fourier-transform infrared spectrum of hydrazine. The analysis of the Fermi-type resonance between the ν 6 and the third excited torsional state, 3 ν 7, is presented. A global fitting was carried out taking into account 3392 lines of the ν 6 band (for K′ from 0 to 10 and for all symmetry species) and 428 lines of the 3 ν 7 band (for K′ from 3 to 9 and only for the symmetry species in resonance). For all 3820 rovibrational transitions the overall standard deviation of the fit of 0.019 cm −1 was obtained. The band centers of the symmetric wagging state and the third torsional were determined at 795.137 and 860.138 cm −1, respectively. Individual fits were also carried out for K′ from 3 to 8 for all symmetry species with much improved standard deviations. The effective group-theoretical Hamiltonian for the coupling between inversion and torsion states was used.