LA MÚSICA COMO RECURSO PARA LA CONSECUCIÓN DE LAS CC.BB (LOE Y LOMCE)

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Spectroscopy has been the most powerful tool to study and investigate the interaction of electro-magnetic radiation with the three states of matter (gas, liquid and solid) for more than a century. The interaction can be absorption, emission or scattering of the electromagnetic radiation by the atoms or molecules of the sample matter. These interactions lead to different types of spectroscopy that have been classified based on the spectral region of the electromagnetic radiation i.e. gamma-ray, X-ray, UV, Vis, microwave, infrared…etc. In absorption spectroscopy, the type of the involved transition between energy levels in the studied sample can define the frequency range of the electromagnetic radiation. For example, if the absorption is associated with a transition from one molecular rotational level to another, then the radiation belongs to the microwave region of the EM spectrum and the technique is known as microwave spectroscopy. While in ultraviolet-visible or electronic absorption spectroscopy, the involved transition takes place among the valence electrons in atoms or molecules. But if the transition is from one vibrational level to another level, then the radiation belongs to the infrared region and the technique is called infrared spectroscopy.

Infrared spectroscopy has a long history, but it has been a well established and effectively used technique since the 1930’s. Infrared spectroscopy is the most common and popular spectroscopic technique used mainly by chemists to study a broad band of atomic and molecular species. It yields a great deal of information on substance and compound identification and the determination of various characteristics of their structures. The versatility of infrared spectroscopy along with the development of a wide variety of new laser techniques encouraged the researchers to use IR spectroscopy to study the molecular complexes produced by supersonic molecular beam techniques.

Early infrared studies of molecular complexes started back in the beginning of the 1980’s where a long path cell cooled down to low temperatures was used (126), whereas the first set of rotationally resolved infrared studies of molecular complexes in molecular beams appeared in the late 1980’s (127 -131).

The Van der Waals molecular complexes have been of considerable interest both experimentally and theoretically for a long time. Therefore, in the last two decades this technique (IR) is continued to be used by an increasing number of research groups to investigate a variety of Van der Waals molecular complexes. The rare-gas Van der Waals molecular complexes involving symmetric, asymmetric and spherical top molecules are of great interest in the field of molecular spectroscopy because these complexes play an important role in understanding the anisotropic behavior of the Van der Waals interactions. Methane is a spherical top molecule which exists in huge quantities and different forms on earth; it is also an active constituent of the atmospheres of earth and the outer planets of the solar system. The methane Van der Waal complexes have a relatively simple structure. Therefore, the methane related phenomena can be accurately monitored by studying and investigating the spectroscopic and collisional processes of all possible methane complexes. These studies are highly desirable to produce improved models which can be extended to more complicated molecular systems.

The spectroscopic studies of Van der Waals complexes allows one to determine the geometrical structure of the complex, the characteristic of the internal motion of the molecule relative to the atom inside the complex, and to develop an accurate intermolecular potential energy surface from which various chemical and physical properties of the molecular system can be extracted. The potential energy surfaces of these complexes are far from isotropic; i.e. different mutual orientations result in minima, maxima, saddle points and other features which are essential to their

structural and dynamical properties.Over more than two decades great experimental

and theoretical progress has been made in the understanding of the properties of Van der Waals complexes. The work on methane Van der Waals complexes started first by investigating the methane-argon complex using conventional techniques. There has been a considerable amount of experimental work and measurements on both the bulk and transport properties of the system (viscosities (132-134), diffusion coefficients (135 -

137)

, second virial coefficients (138 - 145), and thermal diffusion factors (136, 137, 146 - 150). These data are not sensitive enough to provide the detailed information of the features of the multidimensional potential. The data always showed simple isotropic potential. After the advent of modern spectroscopic techniques a large number of experimental studies have been devoted to examine the collisional processes involving methane and argon systems (151-158). The experiments were mainly concerned with the studies of rotational relaxation processes and integral and differential cross sections of rotational excitation (151, 159). In the late seventies Buck et al, (153) measured the total differential cross-sections in a crossed molecular beam experiment. The results were used to develop an empirical potential that showed a cross-sectional rainbow structure sensitive to the depth of the potential. In another study Nesbitt et al, (160) measured the state-to-state integral cross-sections for rotational excitation of CH4 in collision with

Ar atoms using crossed molecular beams. The agreement with the empirical potential developed by Buck et al is quite reasonable.

The Rg-CH4 complex has also been the subject of several high resolution

spectroscopic studies aiming to provide a better understanding about the nature of internal motions of methane in the complex (161 - 163). The first high resolution studies are the infrared spectra of Ar-CH4, Kr-CH4 and Ne-CH4 that were recorded by

McKellar et al (161) using a Fourier transform infrared spectrometer with a long path glass cell cooled down to low temperatures. Strong transitions correlated to the R(0) transition of the triply degenerate ν3 stretching vibrational band of the CH4 monomer

were measured for the Ar-CH4 and Kr-CH4, while weak features were observed for

Ne-CH4. Jet spectra for the same spectral region of Ar-CH4 at lower temperature were

also recorded by Lovejoy and Nesbitt et al (163) using a diode laser spectrometer system along with supersonic slit expansion. Further lower temperature spectra for Ar-CH4 were detected by Block and Miller et al (162), and Howard with co workers (164)

. Although the spectra showed partially resolved rotational structures it was not possible to securely assign the spectra because of the limited resolution in the McKellar measurements (0.01 cm-1) and the line broadening due to the fast predissociation in the other measurements. However the large spacing between the sub-bands in the spectra indicated that the methane molecule is freely rotating within the complex. The spectra were assigned a few years later using an ab initio dynamical calculation where infrared spectra have been calculated and a potential energy surface

has been also developed for this system (165-167). The calculated spectra showed a good qualitative agreement with the recorded ones and contributed in the assignment of the most other transitions. In more recent spectroscopic studies, the infrared spectra of Ar-CH4, Kr-CH4 and Ne-CH4 complexes in the 7µm region correlating to the ν4 triply

degenerate bending mode of the methane monomer have been measured by Pak et al

(168-170, 236)

using a diode laser spectrometer system. The spectra were later reassigned as P, Q, and R branches corresponding to the R (0) transition of the methane monomer employing a model initiated first by Randall et al and developed later by Brook et al

(171)

for the Ne-SiH4 complex. A Coriolis term is introduced in the Hamiltonian model

to be able to fit the recoded spectra.

Despite a lot of interest, a limited number of ab initio studies have been reported so far on Rg-CH4 complexes. In the first study, Fowler et al (172) calculated the long

range dispersion coefficients of Ar-CH4. In a recent work, Szczesniak et al, (173)

reported a few cuts through the interaction potential of Ar-CH4 using MP2 calculation

methods with a relatively small basis set. The calculation predicted an equilibrium structure with a face configuration where the rare gas atom sits on one of the C3 axes

of CH4 monomer and approaches the face of the CH4 tetrahedron. The position and

the depth of the minimum were determined to be 7.5 bohr and -113 cm-1 respectively. They also stated that the minimum is overestimated by 0.5 bohr while the depth is underestimated by 25% respectively due to the applied low level theory and small basis set. In the most recent study, Hijmann et al, (174) employed the symmetry adapted perturbation theory (SAPT) to compute enough data points on the surface to determine the ab initio intermolecular potential energy surface of the Ar-CH4

complex. This potential is in a good agreement with the previous theoretical study

(175)

, it also displays a face configuration but with a well depth of -144.3 cm-1 and a position of 7 bohr. The SAPT potential is shown to reproduce most of the experimentally observed data. It is also used to calculate the IR spectrum which assisted in assigning most the of other transitions; it is probably the best available potential for the Ar-CH4 complex.

The methane-water complex (CH4-H2O) is another example of the Van der Waal

methane complexes which has attracted special research interest. The specialty of this complex comes from the fact that methane hydrates are a combination of a methane

molecule locked in a cavity of hydrogen bonded water molecules. Therefore the ability to develop a modeling technique that can predict the behavior of methane hydrates would be very important for the development of production and transmission operation of conventional methane hydrates. On the other hand, a proper determination of the intermolecular interaction potential of the complex is also essential for both computing the thermodynamic properties and performing classical simulation of the kinetic phenomena of hydrates such as formation and dissociation. The primary modeling efforts started by applying the Van der Waals and Platteeuw statistical mechanical model with Lennard-Jones and Devonshire LJD potential approximation (176, 177 ). This approximation was shown later to be inadequate (178, 179). The inadequacy is based on the fact that the potential parameters calculated from the hydrate phase data by this approximation don’t match the calculated parameters from other experimental data (179, 180, 141).

The alternative approach used to derive the potential energy of the complex is the ab initio calculation methods. This approach provides a direct route to determine the intermolecular potential that can be corroborated using experimental data. The early ab initio calculations on the CH4 - H2O complex were aimed to study and characterize

the C-H…O interaction energy (181 - 190). These studies pointed out that CH4 - H2O is

bound with predicted binding energies ranging from 0.5-2.3 kcal/mol depending on the employed basis sets, but because of the low flexibility of the used basis sets the interaction energies were not corrected for the basis set superposition error (BSSE). More ab initio studies on the CH4-H2O complex have been carried out later on but

with serious discrepancies among the results. In his study, Novoa et al, performed ab initio calculations on the methane-water complex at the self-consistent-field molecular orbital (SCF-MO) and MP2 level with various basis sets along with the near Hartree- Fock limit (191). His calculations provided the first reliable interaction potential for the C-H…O contact with an estimated binding energy to be 0.59 +/- 0.05 kcal. In another study, Woon et al (190), reported a shallower minimum of 0.5 kcal for the same configuration, he also stated that the C-H...O contact is more stable than the C...H-O contact. Few years later Szczesniak et al explored more possible configurations in methane-water complexes using fourth-order Moller-Plesset perturbation theory with 6-31++G(2d2p) basis set (192). They found that the global minimum occurs at the C…H-O geometry which is inconsistent with the Novoa et al results.

Very limited experimental work has been done on the methane-water complex. The first high resolution spectra of the CH4 - H2O complex have been recorded by using

tunable far-infrared (FIR) laser technique combined with a cw supersonic jet expansion (193). Thirteen VRT bands have been measured and rotationally assigned in the spectral region from 18 to 35.5 cm-1. In the same work, an approximate ab initio calculation using the site-site potential energy surface of Woon et al, have been carried out to find the bending VRT levels of the complex. A comparison between the theoretical and experimental results showed that the eigenvalues have almost the same pattern compared to the observed spectra but are not in quantitative agreement. This indicates that either a less approximate method or a more reliable potential or both will be required to obtain a quantitative agreement between theory and experiment. The second spectroscopic study was almost accomplished in the same time as the first one using Fourier transform microwave spectrometer technique (194). The observed data in this study are in a good agreement with and support the bands assignment in the first study. However, the authors in reference (195) stated that the relation of the observed spectra and the intermolecular potential is still not clear and represents a challenging task for future studies.

The above studies on the methane-water (CH4 - H2O) complex show that the potential

energy surface of this complex has not been properly described yet and there is a need for a full characterization of this potential.

In a series of studies, Legon and co-workers investigated the rotational spectra of CH4-HX (X=CN, Cl, Br, and F) using Fourier transform microwave technique (196 - 199)

. The recorded spectra of these complexes are complicated by the motion of methane within the complex and also showed different patterns for different complexes. These studies indicated that methane acts as a proton acceptor. Few more studies appeared on other methane complexes in the microwave region for CH4-O3 (200)

and in the infrared region for CH4-para H2 and CH4-CO (201, 202). The spectra of

these complexes showed more complications.

Interactions between methane molecules can also result in additional products of Van der Waals methane complexes like methane dimers, trimers, tetramers, pentamers. These complexes have been the subject of interest for many researchers in different branches of chemistry. As this work here is concerned with the IR spectra of methane

dimer, I will concentrate on giving a brief introduction about both experimental and theoretical efforts that have been achieved on this complex. Experimentally, the growing interest in reaching an exact description of methane-methane interaction led to number of spectroscopic studies from which they tried to develop a proper intermolecular potential for this complex (203-205). These studies were mainly based on a large body of experimental data on the bulk and transport properties of methane such as (spectroscopic measurements, second virial coefficients, molecular-beam scattering data, viscosities …etc) often measured at a narrow range of interaction energies. These measurements normally lead to a semi-empirical isotropic potential that can only predict one or at most two of the interaction properties of the methane- methane complex. The results of these studies are consequently not consistent.

On the other hand, theoretical efforts on methane dimer started only about two decades ago. Various methods of ab initio calculation have been used in many studies to develop a potential energy surface for methane dimer. In one study, Szczesniak et al (206), applied the newly proposed combination of intermolecular Moller-Plesset perturbation theory (IMPPT) with the super-molecular Moller-Plesset perturbation theory (SMPPT) to generate a potential energy surface for (CH4)2. This coupling

potential consists of two major interaction components: the repulsive Heilter-London (HL) exchange energy and the dispersion attractive force. The former contribution is responsible for the main anisotropy in the potential surface, while the dispersion energy represents the dominating attractive force in the complex. Both contributions show orientation dependence of the hydrogen atoms on both methane monomers. These results are almost in a good agreement with the early attempts of ab initio studies on methane dimer using SCF methods (207). Novoa et al (208), also used the ab initio MPn (n = 2-4) method with small and moderate size basis sets to determine the

dissociation energies and the equilibrium distances of all possible CH…HC contacts within the several orientations of two methane molecules. Although a previous study

(209)

showed that the methane dimer (CH4)2 is not bound, Novoa et al (208) found that

the methane dimer (CH4)2 is bound in all possible orientations of the two methane

monomers with all used basis sets, and the arrangements with more than one CH…CH contact give more stabilization than the arrangement of one CH…CH contact. This method along with 6-311G (2d, 2p) basis set shows a quantitative agreement with the experimentally deduced isotropic potential. In another study,

Ferguson et al (210), used three molecular mechanics and three semi-empirical parameter sets along with 6-311G (2d,2p) basis set at MP2 level to examine the interaction energies for four different orientations of the methane-methane complex. The results indicated that the molecular mechanics models are consistent with the ab initio calculations while the semi-empirical models produced a diversity of results. The atomic probe approach has been employed by Hill et al (211), to show that it can be used to derive a reliable intermolecular potential based on ab initio calculations. He calculated the ab initio Counterpoise-corrected CPC interaction energies for different orientations of Ne-CH4 using aug-cc-PVTZ basis set at the MP2 level in order to

produce the Lennard-Jones LJ type of analytical potential. The ab initio CPC interaction energies have been also calculated for Ne-C, Ne-H, and Ne-Ne using the LJ type parameters. The potential parameters were in a good agreement with the empirical values and properties in MD calculations. This model (atomic probe) has been extended by Stone et al (212) to study methane dimer in a trail to give an accurate anisotropic potential in terms of atomic parameters. The results demonstrated that the atom probe model, when used for two pairs of molecules, can be useful in exploring some functional forms of the intermolecular potential, but at the same time does not produce a good fit for the real potential and has to be refined with more calculations. In a relatively recent study, Rowley et al (213), used the Counterpoise-corrected (CPC) ab initio model with a 6-311G (2d f,2pd) basis set to compute the interaction energies of eleven orientations of two methane molecules as a function of C-C separation distance. These energies were then used to derive an analytical site-site potential consistent with the models from the MD simulation. The C-C, C-H, and H-H interactions were directly extracted from the calculated ab initio potential energies. This model suggests that the C-H interaction energies are the dominant energy