Pau̧l Geerlings

Quantum-chemical study of the Fukui function as a reactivity index : probing the acidity of bridging hydroxyls in zeolite-type model systems

Abstract The Fukui function, ƒ+, was studied for a series of compounds which proved to be adequate model structures for zeolite systems containing bridging hydroxyls. The structures were derived from the basic structure H3SiOAlH3 in which the hydrogen atoms on Si and Al are gradually replaced by fluorine atoms, thus mimicking changes in the average framework electronegativity upon variation of the Si/Al ratio. A basis-set study of the condensed Fukui function for a series of small molecules (H2CO, NH3 and H2O) indicated that, at least for the larger systems, the 3–21G basis may be expected to yield an optimal quality/cost ratio. Calculations on NH3 show that highly diffuse functions should not be introduced in the evaluation of ƒ+ in order to cope with the anionic metastability problem. The condensed Fukui function, ƒH+ , correlates well with the experimentally observed increase in acidity upon increasing framework electronegativity. Moreover, the function is found to be a more sensitive probe for the acidity of the OH group than is the previously calculated isolated molecule OH group properties, including the dipole-moment derivative. The trends in ƒ+H are duplicated in the contour plots of ƒ+ in the OH region indicating that the “probing” capacity of ƒ+ is not lost by the highly approximate integration performed when condensing ƒ+ via a Mulliken population analysis. A study of ƒ+ along the OH bond axis reveals that its sensitivity, being more difficult to extract than that of the condensed function, is of comparable magnitude to that of ƒH+.

The influence of electrical and mechanical anharmonicity on the vibrational transition moments of diatomic and polyatomic molecules

Abstract Double contact-transformation theory up to the second order is used to derive general expressions for the vibrational transition matrix elements ( v | P | v ′)( v ′ = v + 1, v + 2, v + 3) of diatomic and polyatomic molecules. An analysis of the magnitude of the different terms contributing to the fundamental transition and the second overtone, starting from experimental data for five well-documented diatomics (CO and HX; X = F, Cl, Br and I) illustrates the importance of the purely mechanical anharmonic terms. From the general expressions for polyatomic molecules it can be concluded that these terms may be of even greater importance in polyatomic molecules than in diatomics.

Reactivity of 2-t-butyl-4,5-didehydropyrimidine and electronic structure of the parent hetaryne

Abstract 2-t-Butyl-4,5-didehydropyrimidine, generated by oxidation of 3-amino-5-t-butyl-3H-v-triazolo[4,5-d] pyrimidine, was allowed to react with a variety of reagents. Trapping experiments with furan and two tetracyclones gave the expected adducts in low to moderate yields. On treatment with anthracene and 1,3-cyclohexadiene, complex mixtures were obtained from which the adducts could not be isolated. Cycloaddition of phenyl azide to the intermediate yielded 3-phenyl-5-t-butyl-3H-v-triazolo[4,5-d]pyrimidine as the major product together with the unexpected 2-t-butyl-9H-pyrimido[4,5-b]indole in lesser amount. The structure of these two compounds was established by comparison with authentic specimens whose synthesis is described. Cycloaddition also occurred with 2,3,5-tri-O-benzoyl-β-D-ribofuranosyl azide to give an 8-azanucleoside in low yield. Oxidation of the precursor in ethanol gave solely 4-ethoxy-2-t-butylpyrimidine. Oxidation in the presence of iodine, in dichloromethane or benzene, afforded products arising from attack on the solvent, i.e. 4-chloro-5-iodo-2-t-butylpyrimidine and 5-iodo-4-phenyl-2-t-butylpyrimidine respectively. In addition, 5-iodo-2-t-butyl-4(3H)-pyrimidinone was obtained in both cases. Mechanisms for these reactions are proposed. The electronic structure of 4,5-didehydropyrimidine has been calculated by an ab initio 3-21G quantum chemical method. Both the Molecular Electrostatic Potential and the Fukui function give a very reasonable account of the strong orientation effects observed in the additions to 2-t-butyl-4,5-didehydropyrimidine.

A CDOE/INDO LMO study of the nuclear spin-spin coupling constants between directly bonded C-H and C-C atoms

Müller-Pritchard (MP) type relations are used to study1JCH and1JCC coupling constants in a series of unsubstituted as well as in heterosubstituted hydrocarbons. In the case of the coupling constant between two atoms connected by a multiple bond, a generalised MP-type relation is derived.

Contact transformational and quantum chemical calculations of the integrated intensities of fundamental, first and second overtone, binary combination and difference infrared absorption bands of the water molecule

Abstract Double contact transformation theory, considering both mechanical and electrical anharmonicity effects up to the same (2nd) order in perturbation (inclusion of quartic terms in the energy expansion and cubic terms in the dipole moment function) is used to calculate the integrated intensities of fundamentals and of first and second overtones and binary combination and difference bands in H 2 O. It is shown that the simplicity and the symmetry of the H 2 O molecule reduces the general, sometimes rather complicated expressions, both for the transition moments and the intensities, to the simpler working equations actually used. In the numerical calculations, use was made of large basis ab initio calculated energy and dipole moment function expansion coefficients. The intensities of 15 bands have been calculated, for which in 13 cases an experimental value is available. The order of magnitude of the experimental values and the observed sequence is in most cases correctly reproduced, not only within one group of bands but also throughout the whole series. In nine cases the ratio between the theoretical and experimental transition moments is smaller than 1.4. For the fundamental transitions the influence of the inclusion of anharmonicity is small: only for the low intensity ν 1 mode does the effect become important and amounts to 15% of the value obtained in the double harmonic approximation. The transition moments for the first overtone are analysed in detail in order to estimate the relative importance of mechanical and electrical anharmonicity: in the stretching modes mechanical anharmonicity dominates whereas in the bending mode the largest contribution arises from the electrical one. The calculations for the second overtones show that the 3ν 3 band whose intensity has been quoted as “medium” should by far be the most intense mainly due to an effect of mechanical anharmonicity. The purely anharmonic bands with the highest intensity are the binary combination bands ν 1 + ν 3 and ν 2 + ν 3 . The origin of their relatively large intensity is shown to be different: whereas in the ν 1 + ν 3 case it is the mechanical anharmonicity which gives the largest contribution, in the ν 2 + ν 3 case the electrical anharmonicity dominates. In the case of the difference bands, the relative order of magnitude of ν 1 −ν 2 and ν 3 −ν 1 is reproduced, the lower intensity of ν 3 −ν 1 being essentially due to the statistical factor appearing in the final formula for the integrated intensity. The intensity of the ν 3 −ν 2 band however is not correctly reproduced and at present no explanation can be offered for this discrepancy. The temperature effect on all the calculated intensities is examined in detail. Up to 500 K all bands, except the difference bands, are hardly affected (less than 1%) indicating that the statistical factor in the intensity formulae may be taken equal to 1 in the cases considered up to this temperature.

Ab initio and LMO studies of integrated intensities of infrared absorption bands of polyatomic molecules. Part 1.—Method, application to cyanoacetylene and comparison with semi-empirical “all-valence” theories

A general scheme is described for a non-empirical quantum chemical interpretation of the integrated intensities of infrared absorption bands. The localized molecular orbital (LMO) technique is used to calculate bond moment derivatives with respect to the normal coordinates. A second general decomposition scheme of (ab initio) calculated molecular dipole moments, into point charge, hybridization and homopolar terms, is also presented.The theory is applied to the stretching modes of cyanoacetylene. The calculations are performed with three fundamentally different types of SCF-wavefunctions (INDO, INDO/D and STO-NG). The canonical molecular orbitals are localized with an INDO approximate charge density localization technique. Two different force fields were used in the calculation of the normal coordinates.As opposed to the STO-NG functions, neither INDO, nor INDO/D functions yield satisfactory results for the calculated intensities. The influence of the force field on the calculated intensity seems to be of minor importance compared with the influence of the wavefunction.Quantum chemical evidence is presented for the failure of the classical bond moment hypothesis for stretching modes. The dipole moment decomposition scheme provides sound evidence for the importance of the hybridization and homopolar terms in ab initio calculated intensities. LMO-analysis of the (∂µ/∂Qi)0 values led to an understanding of the combined effect of vibrational and electronic factors on the integrated intensity.

Ab initio calculations of the Raman intensities of fundamental vibrations of polyatomic molecules using the improved virtual orbital technique

Abstract The SOS-IVO method previously successfully applied to the calculation of molecular dipole polarizabilities at equilibrium geometry is used, in conjunction with the finite difference approach for the evaluation of polarizability derivatives, to calculate scattering coefficients and depolarization ratios of vibrational Raman bands. A large basis set, based on Dunnings double and triple zeta s-p basis, is used in which polarization and diffuse functions are introduced ([DTZ/DPP]). Use is also made, in view of its success in equilibrium polarizability calculations, of a reduced basis ([DTZ/DP]) in which only a limited number of polarization functions, simulated by spherical Gaussian orbitals, are included based on symmetry considerations about the polarizability tensor components. The theory is applied to a series of molecules belonging to the C 2v (H 2 O, H 2 CO), C 3v (NH 3 , CH 3 CN), C ∞v and D ∞h (HF and N 2 ) point groups, for which experimental gas phase intensity data are available and for which, in most cases, calculations using more demanding methods (finite field perturbation theory, analytical gradient method) were already available in the literature. Except for shortcomings in the cases of vibrational modes involving the elongation of a triple bond, a satisfactory agreement between theoretical and experimental intensities is obtained, indicating an average deviation factor of about 1.4 between theoretical and experimental polarizability derivative tensor components. The reduced basis performs well, except in the case of some very weak bending modes where recently an extremely high basis set sensitivity has been noticed.

Origin of the saturation of the third-order optical nonlinear response of one-dimensional conjugated systems

Abstract The coupled quantum oscillator model is applied to the evaluation of conformational effects in thiophene and polyene oligomers. Thermochromism measurements on heptathiophene are presented and modeled. The effect of conformation is also studied in recently published nonlinear optical experiments on polyene oligomers. It is shown that the model accounts for a masterplot which summarizes the length dependence of the optical properties of conjugated molecules.

Reactivity and electronic structure of a 4,5-didehydropyrimidine

The reaction of 2-t-butyl-4,5-didehydropyrimidine (2) with 1,3-dienes, two 1,3-dipoles (azides), an electrophile (iodine) and a nucleophile (ethanol) has been investigated. The results are correlated with the electronic structure of 4,5-didehydropyrimidine calculated by an ab initio quantum chemical method.

An ab initio “3.1” quantum chemical investigation and LMO interpretation of the integrated intensities of infrared absorption bands in NH3, PH3, NF3 AND PF3

Abstract Ab initio quantum chemical calculations are performed, within the Double Harmonic Approximation, on the integrated intensities of infrared absorption bands associated with the fundamental transitions in the pyramidal AX3-type molecules: NH3, PH3, NF3 and PF3. The (∂μ/∂Qi)0 values needed were calculated using a finite difference method employing the (3.1) basis published by Maroulis et al. [27] which can be considered as a compromise between quality and cost. When comparing these theoretical values with experimental intensity values, a substantial improvement is obtained in comparison to the results of previous calculations employing a Double Zeta basis; the average ratio between theoretical and experimental derivatives decreasing from 2.08 to 1.52. The (3.1) results are close to those obtained using a much larger (DTZP) basis, previously used in the case of the simplest molecule NH3 [22]. The experimental intensity sequences (a) for various modes within a given molecule, and (b) for a given mode throughout the series NH3, PH3, NF3 and PF3 are correctly reproduced at the (3.1) level. An analysis of the combined influence of purely vibrational and electronic factors on the calculated intensities is performed, showing, for example, that the A1 sequence (NH3 NF3) is due to electronic effects. An analysis of the dipole moment derivatives (∂μ/∂Qi)0 in terms of contributions from Localized Molecular Orbitals [18] is performed with special attention being paid to the symmetric bending mode Q2 in view of its high vibrational purity and the possible importance of an (incomplete) orbital following effect with molecular distortions along this normal coordinate. The results of a study of the behaviour of the lone pair on the A atom upon deformation of the molecule along Q2 can be considered as a non-empirical support for the McKean and Schatz model [23a], based upon classical geometry-hybridization relationships, and relating the moment of the lone pair to the XAX angle, α, for a given molecule. It is shown how the complete series of molecules considered can be fitted into this scheme. Inspection of the behaviour of the AX bond LMOs following molecular deformation along Q2 gives a clear insight into the phenomenon of incomplete orbital following and its influence on the ν2 intensity.