Ar HCl Research Articles

Rotational spectra of the ∑ bend states of Ar–H/DCl and the ∑ stretch of Ar–HCl

Rotational transitions of excited van der Waals states of Ar–H/DCl have been observed using the Balle–Flygare pulsed nozzle, Fourier transform, microwave spectrometer. Rotational constants and hyperfine interactions have been determined for the 35Cl/37Cl isotopes of both Ar–HCl and Ar–DCl in the lowest ∑ bending state. The HCl results are in good agreement with previous tunable far-infrared work [J. Chem. Phys. 89, 1268 (1988)]. For Ar–D35Cl and Ar–D37Cl, the rotational constants B and D and the quadrupole interaction χaa(Cl) were determined to be 1727.9887(1) MHz, 39.505(1) kHz, and −28.246(9) MHz, respectively, and 1686.4892(2) MHz, 39.167(4) kHz, and −22.344(10) MHz. χaa(D) for the Ar–D35Cl was found to be 132(7) kHz. Analysis of the 35Cl/37Cl isotope effects shows that the H(D) in H(D)Cl is pointed predominately away from the Ar. Measurement of the J=0→1 to J=4→5 transitions and their hyperfine structure for the ∑-stretch state of Ar–H35Cl give the rotational constants B, D, H, L, and the quadrupole interaction χaa(Cl) to be 1562.876(1) MHz, −67.2(1) kHz, −415(7) Hz, 1.6(1) Hz, and −20.774(7) MHz, respectively. The negative D centrifugal distortion constant and the large H and L constants suggest that this state is strongly perturbed by Coriolis interaction with the π bending state.

Rainbow scattering and time of flight spectra for ArHCl

We have measured an angular distribution and time of flight spectra of HCl scattered from Ar at a collision energy of 85 meV. QCT simulations of the time of flight spectra based on the M5 potential with Hutson and Howard's parameters deviate significantly from the data. To remedy this discrepancy without deteriorating the properties of the M5 potential precisely known from spectroscopic data we had to revise those parameters which are responsible for the anisotropy of the well depth. We find a lower rotational barrier between the two collinear conformations and further indication for the existence of a secondary potential energy minimum.

Determination of the bound and quasibound states of Ar–HCl van der Waals complex: Discrete variable representation method

The ArHCl (HCl; ν=0) van der Waals (vdW) molecule has a large number of bound and rotationally predissociative (resonance) states for total angular momentum in the range of 0≤J≤60. Using the Jacobi coordinates and the total angular momentum representation in the body-fixed reference frame, the Hamiltonian is evaluated in the discrete variable representation (DVR) of the stretch and bend internal vibrational basis and a basis of parity adapted rotation functions. The facile and effective application of the DVR is greatly enhanced by an appropriate choice of the basis set. The sequential diagonalization and truncation of the Hamiltonian permit accurate and efficient determination of eigenstates. Using Hutson’s H6 potential energy surface, the energies and wave functions of all bound and resonance states are computed for selected J’s up to J=60. A novel flux projection technique facilitates semiquantitative evaluation of the lifetimes of all states and, in particular, the simple identification of the resonance states in the ℒ 2 eigenvector basis.

An adapted form of the collocation method for calculating energy levels of rotating atom–diatom complexes

A method is presented for calculating energy levels of atom–rigid-diatom systems for various values of the total angular momentum (J) of the complex. The technique is based upon the collocation method for the vibrational motions of the system and the Galerkin approach for the total rotation. Unlike the Rayleigh–Ritz variational principle, the method does not require the evaluation of integrals over the Hamiltonian and so is very simple to implement. An important feature of the method is that the wave function is obtained in an analytic form and so it is a simple matter to calculate many quantities of spectroscopic interest such as rotational constants and spectral intensities. It is also shown that contracted basis sets can be used in conjunction with the collocation method to enhance the efficiency of the calculation. The method is demonstrated by calculating rovibrational levels of the van der Waals complex Ar–HCl for J up to 10.

The collocation method for calculating vibrational bound states of molecular systems—with application to Ar–HCl

The ability of the collocation method to calculate vibrational bound states of molecules is investigated. The technique is simpler to implement than conventional variational methods; no integration over the basis functions is involved. We apply the method to the weakly bound complex Ar–HCl, a real multidimensional system of considerable physical interest, and find the procedure to be of equivalent accuracy to the corresponding variational approach at all times. This confirms the conclusions of our previous studies on one-dimensional test problems [W. Yang and A. C. Peet, Chem. Phys. Lett. (in press)]. Both low lying and highly excited states are examined and the conclusions hold even for levels very close to the dissociation limit. A test of the wave functions obtained also finds these to be of good accuracy and very similar to the ones given by the variational procedure.

A theoretical study of the Ar2HCl van der Waals cluster

A theoretical method for treating the dynamics of polymeric van der Waals clusters is developed, based on an adiabatic separation of the heavy atom motions. The method is applied to the calculation of spectroscopic parameters for the complex Ar2HCl, and the results are compared with experimental data from high-resolution microwave studies. Potentials based on pairwise additivity and the known Ar–HCl pair potential are used. Small discrepancies between experiment and theory are observed, and it seems likely that these are attributable to the effects of three-body forces rather than to deficiencies of the pair potentials used. High-resolution spectroscopy of van der Waals clusters shows great promise as a tool for investigating nonadditive intermolecular forces.

The intermolecular potential of Ar–HCl: Determination from high-resolution spectroscopy

Two new intermolecular potentials for Ar–HCl are obtained by least-squares fitting to molecular beam microwave and far-infrared laser spectra of the Ar–HCl van der Waals complex. In agreement with previous potentials, the equilibrium geometry is found to be linear Ar–H–Cl, with a well depth around 175 cm−1. However, the far-infrared spectra allow the potential in the region of the linear Ar–Cl–H geometry to be determined as well, and a secondary minimum is found at this geometry, with a depth around 140 cm−1. The secondary minimum arises because the Ar atom can approach closer to the Cl atom at the linear geometry than at a T-shaped geometry. The fitted potential is used to calculate additional bound states of the Ar–HCl van der Waals complex, which have not yet been observed spectroscopically.

An extended study of the lowest Π bending vibration–rotation spectrum of Ar–HCl by intracavity far infrared laser/microwave double resonance spectroscopy

The lowest Π bending state in Ar–HCl has been more completely characterized through the use of far infrared laser/microwave double resonance spectroscopy. This extended analysis includes a partial reassignment of the far infrared spectra of Ar–H35Cl previously reported by Ray et al. and by Marshall et al., as well as an analysis of the ArH37 Cl spectra. Improved molecular constants have been determined. The value of the rotational constant is now in good agreement with that calculated by Hutson from the M5 double minimum potential surface. Along with the recently reported spectrum of the Σ bending vibration, this extended analysis provides strong evidence for the existence of two minima character in the intermolecular potential surface of Ar–HCl.

The high-resolution far infrared spectrum of a van der Waals stretching vibration: The ν3 band of Ar–HCl

The first high-resolution measurement of a van der Waals stretching vibration is reported. The ν3 fundamental stretching vibration in Ar–HCl has been measured by intracavity far infrared laser/microwave double resonance spectroscopy of a supersonic free jet. Coupling between the stretching state and the nearby bending states gives the spectrum an intensity which is greater than predicted. The molecular constants for the stretching state are in close agreement with calculations by Hutson for the M5 potential surface.

The augmented secular equation method for calculating spectra of van der Waals complexes. Application to the infrared spectrum of Ar–HCl

The recently proposed secular equation–perturbation theory (SEPT) procedure for calculating spectra of van der Waals molecules is tested on the strongly anisotropic system Ar–HCl. It is found to be more accurate than other available approximate schemes, but the convergence with respect to basis set size is slow. An alternative method, which uses the perturbation correction from a SEPT calculation to augment the original secular equation basis set, is then proposed and tested, and is found to converge considerably faster. This method is then used to calculated spectroscopic properties for various excited states of Ar–HCl, and the results are compared with the recent experimental data of Marshall et al.(J. Chem. Phys., 1985, 83, 4924) and Ray et al.(J. Chem. Phys., 1986, 84, 1171).

Characterization of the lowest-lying Π bending state of Ar–HCl by far infrared laser–Stark spectroscopy and molecular beam electric resonance

Far infrared laser–Stark spectroscopy is used to populate an excited vibrational state in the van der Waals molecule, ArHCl, in a molecular beam. Microwave–far infrared double resonance allows the identification of this state as the first excited bending state of Π symmetry. Subsequent radio frequency electric resonance of the vibrationally excited molecule combined with far infrared–radio frequency two photon experiments gives the following spectroscopic constants: ν0−B′=33.9248(7) (cm−1), B′=1695.(20) (MHz), μ=0.265(3) (D), eqQaa=12.(7) (MHz), eqQbb−eqQcc=−73.927(23) (MHz), q1=−49.583(2) (MHz). These constants are compared with theoretical predictions obtained using previously suggested potential energy surfaces and are related to the presence of other nearby vibrational states.

Rotational predissociation and libration in the infrared spectrum of ArHCl

Fully resolved rotational structure in the high-frequency vibrational region of the ArHCl van der Waals complex has been recorded under thermal equilibrium conditions at T=127 K with a tunable difference-frequency laser. Both the fundamental HCl stretch and its combination with the low-frequency large-amplitude bend (libration) have been observed with comparable intensities. An abrupt cutoff of the spectrum at high J due to rotational predissociation yields a measure of the binding energy of the complex. The band centre shifts and rotational and distortion constants provide much information about the interaction potential surface and its vibrational dependence and about perturbations from other low-frequency modes not directly observed.

Vibrational relaxation of diatomic hydrides in inert gases. Rate constant calculations

Systematic calculations of thermal rate constants of vibrational relaxation of diatomic hydrides (HX) in inert gases (A) have been carried out for all available potential of such pairs. The method of calculation is based on a static approximation with respect to relative motion and includes a numerical calculation of Fourier harmonics of the perturbation during rotational motion of the molecule in the potential of the pair AHX. For all systems AHX, A = He, Ne, Ar, Xe, X = HCl, HF, OH, DCl, etc. the theoretical rate constants obtained with the power-type potentials (by Lennard-Jones, or Howard and Hutson) are significantly larger than experimental data. For available exponential-type potentials of ArHCl or the ab initio potentials of Ar, He + HF there is reasonable agreement between calculated and experimental data. The mechanism of VR relaxation is specified: the large contribution of trajectories with quasi-free molecule rotation passing through the linear configuration AHX has been established. Estimates of the rate constants as a function of initial rotational energy permit us to discuss the role of VR processes in recently observed laser effects on the rotational transition of hydrides.

Vibrational predissociation and infrared spectrum of the Ar–HCl van der Waals molecule

The energies and lifetimes of bound and vibrationally predissociating states of Ar–HCl are calculated, using accurate close coupling calculations on the best available potential energy surface, and the selection rules governing the infrared spectrum are described. The vibrational predissociation lifetimes are of the order of microseconds; thus the resulting spectroscopic lines will be sharp (width <1 MHz), but the excited states will not survive to travel far down a molecular beam. The dominant predissociation product is found to be HCl in the highest accessible rotational level ( j=15). Perturbation theory calculations of the lifetimes and product state distributions are drastically in error.

Ab initio calculations on weakly bonded systems

Large-basis CI calculations are performed on the van der Waals complexes Ar–HCl and (H2O)2. It is shown that a reasonable estimate of the CI basis-set superposition error is obtained from a ghost calculation involving the orbitals of the monomer and only the virtual orbitals of the ghost.Both basis-set superposition error corrections and size-consistency corrections are of vital importance to obtain a reliable potential-energy surface.For Ar–HCl the minima of the potential are predicted within 50 µhartree of the experimental surface, viz. –804 µhartree for the Ar–HCl orientation and –565 µhartree for the HCl–Ar geometry.The water dimer van der Waals minimum is estimated to be –4.9 kcal mol–1, which is less deep then experimentally derived minimum of –5.4 kcal mol–1, but just within the experimental error limit.

Classical path sudden approximations for atom—rigid rotor collisions

The classical path sudden approximation has been used to calculate cross sections for rotational excitation in atom—molecule collisions. Three different decoupling approximations for the angular momentum of the molecule are used: one effective potential approach and two different coupled states approaches, all in their semiclassical versions. Numerical results are presented and discussed for the systems ArN 2, ArLi 2, ArLiH, HeCO and ArHCl assumming intermolecular potentials of P 1 symmetry, P 2 symmetry and combinations.

Exact calculation of the rotational–vibrational energy levels of triatomic species

A recently proposed method for calculating the bound rotational-vibrational energy levels of triatomic molecules is applied to the Ar—HCl van der Waals complex and to the water molecule. For Ar—HCl energy levels, rotational constants and centrifugal distortion constants for several different potential-energy functions are calculated. The accuracy of the calculations is critically examined and is found to be very high. It is demonstrated that the method may be used to calculate the higher lying rotational–vibrational energy levels of the complex without either a significant loss of accuracy or any large increase in computational effort. The complete set of rotational–vibrational energy levels is calculated for two different Ar—HCl potentials and for several different values of the total angular momentum. The coupled states or p-helicity decoupling approximation, which has been used previously in the context of molecular scattering theory, is examined and shown to yield very reliable results. This approximation greatly reduces the computational effort required to perform calculations, especially for higher values of the total angular momentum. In the case of the water molecule we examine the use of a “hindered-rotor” basis set, and show that we are able to obtain a faster rate of convergence and greater accuracy for the low-lying energy levels of water with this type of basis.

Quasiclassical close-coupling approximation: Comparison with experimental Ar–HCl differential cross section

Total differential cross section for Ar–HCl collisions are calculated using the Neilsen–Gordon potential surface within the quasiclassical close coupling approximation (QCCA). Comparison is made with the experimental results of Farrar and Lee.

HCl rotational excitation by Ar impact: Quasiclassical close coupling approximation for atom–diatomic molecule scattering

We apply quasiclassical approximations for the relation motion degree of freedom to full quantum mechanical space fixed close coupling equations. This approximation is carried through in the context of atom–diatomic molecule rotational excitation collisions. Criteria for the validity of these approximations are described. We apply the method to treat Ar HCl collisions using previously suggested potential energy surfaces. The importance of diffraction, rotational inelasticity, and various features of the potential energy surface for state to state differential and integral cross sections are discussed.

Determination of potential energy surfaces for Ar–HCl and Kr–HCl from rotational linebroadening data

Using recent rotational linebroadening data at different temperatures of HCl–Ar and HCl–Kr mixtures, an attempt is made to determine anisotropic intermolecular potential surfaces for both systems. The parameters characterizing the anisotropic part of the potential were determined from numerical fitting of computed linebroadening cross sections using the model of Smith, Giraud, and Cooper. The potential for HCl–Ar obtained that way is found to be rather different from potential surfaces that have been put forward in the literature. A comparison between the different potentials is made. In the HCl–Kr case no other ’’experimental’’ potential surfaces are available for comparison.