Vibrational frequencies and structural determination of 2,2 '-biquinoline

We present a detailed analysis of the structure and infrared spectra of 2,2'-biquinoline. The vibrational frequencies of the 2,2'-biquinoline molecule have been analyzed using standard quantum chemical techniques. Frequencies have been calculated with HF, and DFT (BLYP, B3LYP and B3PW91) theory, using the standard 6-311G* as the basis set. The assignments of the observed bands corresponding to 2,2'-biquinoline were made on the basis of such calculations and the comparison with related molecules

Molecular structure and vibrational spectra of 4-tert-butylpyridine by density functional theory and ab initio Hartree-Fock calculations

The molecular geometry and vibrational frequencies of 4-tert-butylpyridine(4-tbpy) in the ground state have been calculated by using the Hartree-Fock and density functional methods (B3LYP and BLYP) with 6-31G (d) as the basis set. The optimized geometric bond lengths obtained by using B3LYP and bond angles obtained by BLYP show the best agreement with the experimental values. Comparison of the observed fundamental vibrational frequencies of 4-tbpy and calculated results by density functional B3LYP, BLYP and Hartree-Fock methods indicates that B3LYP is superior to the scaled Hartree-Fock and BLYP approach for molecular vibrational problems

DFT studies and vibrational spectra of trans 1,2-bis(4-pyridyl)ethylene and its zinc(II)halide complexes

The geometry, frequency and intensity of the vibrational bands of trans 1,2-bis(4-pyridyl)ethylene (which is abbreviated as bpe) were obtained using the density functional theory (DFT) with the BLYP, B3LYP, B3PW91 functionals and 6-311G* basis set

HF and DFT studies and vibrational spectra of 1,2-bis(2-pyridyl) ethylene and its zinc (II) halide complexes

Ab initio restricted Hartree-Fock and density function theory calculations using BLYP, B3LYP and B3PW91 functionals were carried out to study molecular structure and vibrational spectrum of 1,2-bis(2-pyridyl)ethylene (which is abbreviated as bpe). Comparison of calculated and experimental results indicates the density functional B3LYP and BLYP/6-311G* methods are more accurate in predicting fundamental vibrational frequencies than the scaled other approaches. On the basis of calculated results, assignment of fundamental vibrational modes of bpe was proposed. Complexes of the type Zn(bpe)X-2 [where X = Cl, Br, I] have been studied in the 4000-400 cm(-1) region, and assignments of all the observed bands were made. The analysis of the infrared spectra indicates that there is some structure-spectra correlations

Frechet-Hilbert spaces and the property SCBS

In this note, we obtain that all separable Frechet-Hilbert spaces have the property of smallness up to a complemented Banach subspace (SCBS). Djakov, Terzioglu, Yurdakul, and Zahariuta proved that a bounded perturbation of an automorphism on Frechet spaces with the SCBS property is stable up to a complemented Banach subspace. Considering Frechet-Hilbert spaces we show that the bounded perturbation of an automorphism on a separable Frechet-Hilbert space still takes place up to a complemented Hilbert subspace. Moreover, the strong dual of a real Frechet-Hilbert space has the SCBS property

The property of smallness up to a complemented Banach subspace

This article investigates locally convex spaces which satisfy the property of smallness up to a complemented Banach subspace, the SCBS property, which was introduced by Djakov, Terzioglu, Yurdakul and Zahariuta. It is proved that a bounded perturbation of an automorphism on a complete barrelled locally convex, space with the SCBS is stable up to a Banach subspace. New examples are given, and the relation of the SCBS with the quasinormability is analyzed. It is proved that the Frechet space l(p+) does not satisfy the SCBS, therefore this property is not inherited by subspaces or separated quotients

A remark on a paper of P. B. Djakov and M. S. Ramanujan

Let l be a Banach sequence space with a monotone norm in which the canonical system (e(n)) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between l-Kothe spaces, then there exists a continuous unbounded quasidiagonal operator between them. Using this result, we study the corresponding Kothe matrices when every continuous linear operator between l-Kothe spaces is bounded. As an application, we observe that the existence of an unbounded operator between l-Kothe spaces, under a splitting condition, causes the existence of a common basic subspace

A NOTE ON TRIANGULAR OPERATORS ON SMOOTH SEQUENCE SPACES

For a scalar sequence (theta(n))(n is an element of N), let C be the matrix defined by c(n)(k) = theta(n-k+1) if n >= k, c(n)(k) = 0 if n < k. The map between Kothe spaces lambda(A) and lambda(B) is called a Cauchy Product map if it is determined by the triangular matrix C. In this note we introduced some necessary and sufficient conditions for a Cauchy Product map on a nuclear Kothe space lambda(A) to nuclear G(1) - space lambda(B) to be linear and continuous. Its transpose is also considered