Hubert P. Figeys

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.

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 calculations of static dipole polarizabilities using improved virtual orbitals and symmetry adapted polarization functions

The method previously described by the present authors [1] for the calculation of molecular static electric dipole polarizabilities is applied to a series of saturated and unsaturated compounds. The method is based on the use of improved virtual orbitals within a sum over states (SOS) formalism. The basis sets used are a large basis of double and triple zeta quality including diffuse functions and two sets of polarization functions ([DTZ/DPP]) and a reduced version of it in which only those polarization functions which are needed by symmetry are included. The construction of this basis set which is obviously symmetry dependent is described for the molecules studied. The use of improved virtual orbitals considerably improves the results for the ten-electron molecules HF, NH3 and CH4, in line with the H2O case study in [1]. The results obtained with the largest basis are comparable with those obtained by more elaborate, beyond Hartree-Fock, Finite Field calculations. The reduced basis performs almost equally well and forms an interesting alternative when the large [DTZ/DPP] basis becomes untractable. For unsaturated systems (C2H4, H2CO, CH3CN, N2, CO2, HCN and C2H2) the component parallel to the double or triple bond is overestimated in the IVO technique. Fair agreement with experiment is however obtained for the perpendicular component(s). The deviation from experiment increases with increasing polarity, and degree of unsaturation. In the case of linear molecules considerable improvement can be obtained via the introduction of symmetry breaking spherical gaussian orbitals or by slightly bending the molecule.

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.

Ab initio and LMO studies on the integrated intensities of infrared absorption bands of polyatomic molecules. Part III. NH3

Abstract Minimal basis set (STO-3G) ab initio calculations are performed for the integrated intensities of the four fundamental infrared absorption bands in NH3. The agreement between experimental and theoretical values is excellent except for the asymmetric bending. The results are interpreted via analysis of the dipole moment derivatives into (a) molecular contributions (point-charge, hybridization and homopolar terms), and (b) bond-dipole contributions obtained using a Localized Molecular Orbital (LMO) method. The large difference between the symmetrical stretching and bending intensities is essentially due to hybridization effects. At the LMO level, these effects can be localized in the NH bonds. The unexpectedly low contribution of the nitrogen lone pair to the bending intensity results from a cancellation between the hybridization and homopolar terms. In the asymmetric vibrations, the contribution of the hybridization terms turns out to be appreciably lower for the bending mode, as compared to the stretching vibration. The influence on the intensity difference between the symmetric stretching and bending vibrations of “incomplete orbital following” in the NH bonds is analyzed in detail. This effect is also detectable in the asymmetric modes, although less easily visualized.

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.

Ab initio and localised molecular orbital studies of the integrated intensities of infrared absorption bands of polyatomic molecules. Part 5.—Minimal- and extended-basis-set results for the pyramidal AX3 series (A = N, P; X = H, F)

Ab initio SCF-GTO type calculations on the dipole-moment derivatives with respect to the normal coordinates of vibration (∂µ/∂Qi)0 for pyramidal AX3 molecules (A = N, P; X = H, F) are reported. A comparison between theoretical and experimental infrared intensity values Ai shows that double-zeta (DZ) values are generally worse than those obtained with a minimal (STO-3G) basis set, which may be qualified as satisfactory. For NH3 and PH3 calculations with more extended basis sets, including polarization functions, (DZ + P) were also performed. Finally, diffuse functions were included in the calculations for NH3; this leads to a substantial improvement of the DZ or “DZ + P” results. A “DTZPD” basis for NH3(double-zeta for N, triple-zeta for H, including polarization and diffuse functions) was set up; this gives (∂µ/∂Qi)0 values which are close to recently published near-Hartree–Fock results. The sign instability of the stretching derivatives upon change of atomic basis is discussed in terms of derivatives with respect to symmetry coordinates. The “DTZPD” signs for the (∂µ/∂Qi)0 in NH3 are identical to those obtained in the STO-3G case, except for Q3.The STO-3G dipole-moment derivative calculations reproduce the experimental sequence for the A1, A2 and A3 integrated intensities along the AX3 series; this sequence is interpreted via a combined investigation of vibrational and electronic factors. The smaller A1 value for NH3 as compared with NF3 is vibrational in origin, whereas the smaller A1 intensity of NF3 as compared with PF3 is essentially due to electronic factors. The A2 sequence is analysed in terms of the N or P lone-pair behaviour during the bending mode; the lone pairs of the fluorine atoms present in the molecule are seen to have a drastic influence on the intensities; incomplete orbital following of the AX bonds is described. The NH3 LMO results in the minimal basis for (∂µ/∂Q1)0 and (∂µ/∂Q2)0 are quite comparable with those obtained with the larger “DTZPD” basis set. For the asymmetric stretching vibration (Q3), the higher calculated (and experimental) intensity in PF3 as compared with NH3 again mainly resides in an important contribution of the fluorine lone pairs to the intensity of this mode, but also in an inversion of sign in the contributions of the corresponding P—F and N—H bonds.

Some Aspects of the Quantumchemical Interpretation of Integrated Intensities of Infrared Absorption Bands

Integrated Intensities of Infrared Absorption Bands corresponding with fundamental transitions, calculated in the Double Harmonic Approximation and with single determinantal wavefunctions can be analyzed in various ways in order to obtain an insight into the various electronic and vibrational factors determining the intensities. The computational strategy for obtaining dipole moment derivatives, with respect to the normal coordinates governing these intensities, is discussed together with the decomposition in non-local and LMO contributions.