Elisabetta Cané

Experimental and theoretical anharmonicity for benzene using density functional theory

The anharmonic force field of benzene has been calculated using a finite difference method by means of density functional theory (DFT) with the B3LYP functional and a TZ2P atomic orbitals basis set, and compared to the field calculated by Maslen et al. [J. Chem. Phys. 97, 4233 (1992)]. The vapor phase infrared (IR) spectra of benzene (natural isotopic mixture) and of 12C-benzene have been recorded from 450 to 6000 cm−1, at resolutions varying from 0.05 to 0.008 cm−1, and at various path lengths (0.18/42 m). The parallel bands ν11, ν4+ν12, ν5+ν12, ν2+ν11, and ν7+ν16, using the Wilson numbering, with their accompanying hot bands, have been analyzed and their origins determined to test our computed anharmonic force field. The Raman spectra of gas-phase benzene have been also recorded at medium resolution (∼0.7 cm−1) using an argon laser (line at 514.5 nm) with a power of 0.8 W and a multipass cell. In this work we compare the experimental and the theoretical frequencies and band profiles of the parallel ν1, ...

The gas-phase infrared spectra of anthracene-h10 and anthracene-d10

The IR spectra of anthracene-h10 and -d10 have been recorded for the first time in the gas phase from 450 to 3200 cm−1 with a resolution of 0.2 cm−1, using a multipass cell heated to 100°C. For the assignment of vibrational bands we have evaluated the theoretical spectrum using density functional theory (DFT) and scaled self consistent field force fields. We found that both methods reproduce the sequence of the experimental frequencies to a good accuracy, allowing in most cases consistent and unambiguous assignments. The relative intensities of C14H10 and C14D10 have also been measured and compared to theory.

Gas-phase infrared spectrum of indazole. Scaled quantum mechanical force field and complete spectrum assignment

The gas-phase IR spectrum of indazole has been recorded from 100 to 4000 cm–1, using a multipass cell heated to 120 °C, and completely assigned using theoretical predictions based on the scaled quantum mechanical (SQM) method. The single-crystal IR spectrum of this molecule, previously reported, has been compared with our data and partially reassigned. The harmonic force field of indazole, evaluated at the HF-SCF level using 6-31G** orbitals, is corrected by scaling the force field over a convenient set of internal coordinates. Scaling factors were determined by least-squares fitting of the theoretical to the experimental frequencies of two parent molecules, benzene and pyrazole and their perdeuteriated isotopomers. Our final prediction gives frequencies for indazole which, on average, differ from experiment by 24 cm–1. We confirm the validity of the SQM method as a practical tool for a complete analysis of vibrational spectra, even for molecules of this complexity.

Gas-phase IR spectrum of 7-azaindole. Scaled quantum mechanical force field and complete spectrum assignment

The gas-phase IR spectrum of 7-azaindole has been recorded from 100 to 4000 cm–1, using a multipass cell heated to ca. 110 °C, and completely assigned using theoretical predictions based on the scaled quantum mechanical (SQM) method. The harmonic force field of 7-azaindole, evaluated at the HF-SCF level using 6-31G** orbitals, is corrected by scaling the force field over a convenient set of internal coordinates. Scaling factors were determined by least-squares fitting of the theoretical to the experimental frequencies of the two parent molecules, pyridine and pyrrole, and their perdeuteriated isotopomers. Our final prediction gives frequencies for 7-azaindole which on average differ from experiment by 18 cm–1.

Microwave spectrum and ab initio calculations of indazole

Abstract The microwave spectrum of indazole and its ND isotopomer has been investigated at 70°C. The tautomer with the NH group closer to the phenyl ring is found to be the more stable both by the analysis of the rotational spectrum and ab initio calculations. The second tautomer is calculated at HF/4–21G level of theory to be 2800 cm −1 higher in energy. Information on the dipole moment and the low energy vibrational excited states has also been obtained.

Microwave spectrum of benzimidazole

Abstract The microwave spectra of benzimidazole and of its N-D monodeuterated isotopic species, obtained at 120°C, show the full planarity of the molecule. Information on the lower energy vibrational excited states, and on the dipole moment have also been obtained.

The infrared spectrum of 12C2HD: the bending states up to υ4 +υ5 =3

The infrared spectrum of 12C2HD has been recorded at high resolution between 450 and 2100 cm−1 by Fourier transform spectroscopy. The ν4 and ν5 bending fundamental bands together with overtones, combination bands and associated hot bands involving modes up to υtot = υ4 + υ5 = 3 have been identified. Altogether, 43 vibrational bands have been analysed, leading to the spectroscopic characterization of the ground state and of 18 vibrationally excited states. They include all the components of the vibrational manifolds up to υtot = 3, with the exception of the υ4 = 3, ℓ = ±3 state. A simultaneous fit of all the assigned transitions has been performed. The adopted model includes vibration and rotation ℓ-type interaction resonances. The determined spectroscopic parameters reproduce the assigned wavenumber transitions with RMS values close to the estimated experimental uncertainties.

The gas-phase infrared spectra of phenanthrene-h10 and phenanthrene-d10

Abstract The IR spectra of phenanthrene-h10 and -d10 have been recorded in the vapour phase from 200 to 3200 cm−1 with a resolution of 0.2 cm−1, using a multipass cell heated at 90°C. The assignment of the vibrational bands has been performed by comparison with the theoretical spectra, evaluated using Density Functional Theory and Scaled Quantum Mechanical (SQM) force fields. We found that both methods reproduce the sequence of the experimental frequencies to a good accuracy, allowing in most cases consistent and unambiguous assignments. The relative intensities have also been measured and compared with theory.

The v2, v3 and 2v10 Raman bands of ethylene (12C2H4)

Abstract The Raman spectrum of 12C2H4 has been recorded in the 1343–1347cm−1, 1617–1626cm−1 and 1651–1664cm−1 regions using an inverse Raman technique with an instrumental resolution of about 3×10−3cm−1. The Q branches of V3 (CH2 bending, Ag) at 1343.31 cm−1, V2 (CC stretching, A g ) at 1626.17 cm−1 and 2v10 (overtone of CH bending in plane, A g ) at 1664.16 cm−1, were observed and analysed. The recorded bands are of type A, and the selection rules for the transitions are ΔJ=0, ΔK a =0 and ΔK C =0 since only Q branches are strong enough to be observed. The v 2 and 2v10 bands are perturbed owing to a Fermi interaction between the V 2 =1 and v10=2 states, the latter being in turn perturbed by the v 7 =v 10=1 state, at about 1780 cm−1, through a z(a)-type Coriolis interaction. The V3 band has been analysed taking into account the y(c)-type Coriolis interaction between the v3=1 and V 6 =1 levels. Although the v6 fundamental and v 7 +v 10 combination bands have not been detected, their origins and rotational c...Doubly stochastic, magic square, and alternating sign matrices are matrices of order n over the set of real positive numbers , the set of nonnegative numbers , and the set of integers {−1,0,1}, respectively, having fixed row and columns sums of 1, an arbitrary positive integer N, and 1. Each can be expressed as a sum over permutation matrices of order n with coefficients that belong to , to the positive integers , and to , respectively. Mathematically, these objects are basic in combinatorics; physically, they arise in several contexts that are briefly reviewed. Little has been developed on their expansions in terms of permutation matrices, and little is known about counting formulas for them, except for alternating sign matrices where a closed formula for arbitrary n was recently obtained through the work of Zeilberger. Expansions of these matrices in terms of permutation matrices can be used to investigate and develop their properties. Such an expansion is called a representation of the magic square. Representations are, however, not unique, and the problem arises of enumerating the number of distinct representations of one and the same magic square. The present investigation addresses this problem in the context of primitive magic squares, which are defined as the class of magic squares of order n having a unique representation in which each permutation matrix occurs exactly once in the expansion, and such that this uniqueness is destroyed by the addition of another permutation matrix not already in the representation, a property called completeness. The set of primitive magic squares has a rich structure that is invariant under the action of a group G that is isomorphic to the dihedral group. The group G is definitive in unveiling the general structure of primitive magic squares by providing a complete labelling scheme that utilizes the (n − 4)-fold direct product group of G and a binary tree that specifies a path that shows how the elements in the direct product group are to be selected. Based on this structure, a recurrence relation is derived that generates all inequivalent primitive magic squares. The recurrence relation itself shows a hidden structure of more basic magic squares, called universal kernels, that underlie the structural form of all primitive magic squares. The recurrence relation for primitive magic squares is thus shifted to a recurrence relation for the universal kernels that is simpler in form, which is also derived. These recurrence relations produce one and the same primitive magic square in multiple ways, and the sorting out of the distinct magic squares thus generated remains a problem that is not yet solved.

The harmonic vibrational frequencies and the geometry of the 12C6H6

Abstract The harmonic frequencies ω est of 12 C 6 H 6 calculated by combining the anharmonic constants from a DFT quartic force field with the experimental fundamentals, are compared with harmonic frequencies, ω calc , obtained with different theoretical methods. One set of ω calc was derived by Martin, Taylor and Lee by ab initio CCSD(T) theory, the others have been calculated by us by means of the density funcional theory DFT with B3LYP, B3PW91, B3P86 and mPW1PW hybrid functionals. The mean absolute deviation between ab initio ω calc and ω est is 6.8 cm −1 while between DFT ω calc and ω est is between 8.6 and 10.5 cm −1 . Moreover the DFT ω calc show a small systematic underestimation of the CH stretching vibrations.