Volume 97, Issue 5, 01 September 1992
Index of content:

Autoionizing‐resonance enhanced preferential photodissociation of CO_{2} in superexcited states
View Description Hide DescriptionFluorescence excitation spectra of CO_{2} ^{+}(Ã ^{2}Π_{ u }→X̃ ^{2}Π_{ g }), (B̃ ^{2}∑_{ u } ^{+}→X̃ ^{2}Π_{ g }), and CO(A ^{1}Π→X ^{1}Σ) emissions produced in the photoionization and neutral photodissociation of CO_{2} have been obtained in the 30–92 nm region. A strong competition between autoionization and neutral dissociation observed in the region near the ionization thresholds to form CO_{2} ^{+}(Ã ^{2}Π_{ u }) and CO_{2} ^{+}(B̃ ^{2}Σ_{ u } ^{+}) states clearly shows the preferential enhancement of the neutral dissociation, which is explained mainly by the intrinsic autoionization rate of the individual superexcited Rydberg states. A drastic step‐down decrease in a fluorescence excitation spectrum in the vacuum ultraviolet region at the thresholds has been ascribed to a dramatic density dilution of the superexcited states into the continuum.

High resolution threshold photoelectron spectroscopy of aniline and aniline van der Waals complexes
View Description Hide DescriptionZero electron kinetic energy threshold photoelectron spectroscopy is applied to jet cooled aniline and the van der Waals molecules aniline–Ar, aniline–(Ar)_{2}, and aniline–CH_{4}. The monomer cation spectrum is assigned and more precise values of the vibrational frequencies are determined. The spectra of the cation complexes reveal significant vibronic activity indicative of a significant change in complex geometry upon ionization. The change in complex binding energy upon ionization is obtained from a determination of the complex ionization potentials. For the first time zero electron kinetic energy is used to probe van der Waals complex predissociation on the S _{1} electronic surface. Both reactants (complex) and products (monomer) of the reaction are observed in the photoelectron spectrum. Details of the mechanism of the zero electron kinetic energy threshold photoionization process and its impact on the observation of van der Waals molecules are discussed.

Water in weak interactions: The structure of the water–nitrous oxide complex
View Description Hide DescriptionThe rotational spectra of H_{2}O–N_{2}O, D_{2}O–N_{2}O, and HDO–N_{2}O have been observed using molecular beam electric resonance techniques at both zero and nonzero electric fields. H_{2}O–N_{2}O is nonrigid with respect to internal rotation of the water subunit. Rotational constants in MHz for the spatially antisymmetric tunneling state are A=12 605.001(77), B=4437.978(32), and C=3264.302(32). Rotational constants for the spatially symmetric tunneling state are A=12 622.595(203), B=4437.422(47), C=3264.962(47). These together with the rotational constants of the other isotopomers are consistent with a planar, T‐shaped arrangement of the heavy atoms of the complex, with the distance between the centers of mass of the two subunits, R _{c.m}., equal to 2.91(2) Å or a distance of 2.97(2) Å from the H_{2}O oxygen to the central nitrogen of N_{2}O. The measureddipole moments of the two tunneling isomers are identical; μ_{ a } = 1.480(2) and μ_{ b } = 0.31(2) D. The values of these dipole moment components indicate an in‐plane equilibrium tilt of about 20° between the C _{2v } axis of water and the N–O weak bond. This tilt suggests a second interaction may exist between a hydrogen on water and the N_{2}O subunit. The rotational constants suggest that the N_{2}O unit is tilted by about 9° from perpendicular to the N–O weak bond. The barrier for the tunneling interchange of the water protons is estimated to be 235(10) cm^{−1}. Quadrupole coupling constants eqQ _{ aa } for the outer and inner nitrogen of N_{2}O are 0.371(130) and 0.128(45) MHz, respectively. Electrostatic models applied to water–N_{2}O and water–CO_{2} predict hydrogen bonded structures rather than the experimentally observed Lewis base structures.

The effect of solvation on molecular Rydberg states: Dioxane clustered with nonpolar solvents
View Description Hide DescriptionOne color 2+1 mass resolved excitation spectroscopy is employed to obtain molecular Rydberg 3s←n transition spectra of 1,4‐dioxane clustered in a molecular beam with nine nonpolar solvents. The solvents are Ar, Kr, CH_{4}, CD_{4}, CF_{4}, SiH_{4}, Si(CH_{3})_{4}, ethane, n‐propane, cyclohexane‐h _{12}, and cyclohexane‐d _{12}. Spectral results are interpreted in terms of cluster size, isotope effects, and model calculations. A Lennard‐Jones–Coulomb 6‐12‐1 potential is used to model the intermolecular interactions and predict minimum energy cluster geometries, cluster binding energies, and intermolecular force constants which are used to calculate van der Waals vibrational frequencies. The results show that for simple solvents (i.e., Ar, CH_{4}) the calculations offer a simple interpretation of the observed spectra in terms of multiple cluster geometries with distinct transition energies; however, as the solvent becomes more complex, the cluster spectra also become more complex, and the number of calculated minimum energy cluster geometries increases. Complex spectra are interpreted as a distribution of cluster geometries with similar transition energies. For all of the clusters, the electronic origins are blue shifted with respect to the bare 1,4‐dioxane origin. This observation is consistent with a model in which the excited state intermolecular potential becomes more repulsive due to the increased radial distribution of a nonbonding electron upon excitation into the 3sRydberg state.

Rydberg∼valence perturbations in matrix‐isolated NO
View Description Hide DescriptionThe absorptionspectrum of NO in rare gas matrices has been reinvestigated. The valence B ^{2}Π(v’,0) bands which, in the gas phase, show perturbations for v’≥7 due to homogeneous configuration mixing with the RydbergC ^{2}Π state, appear unperturbed up to v’=10 in Xe, 12 in Kr, 14 in Ar, and 19 in Ne matrices. The perturbations are shifted to higher energies due to the large blue matrix shifts experienced by the Rydberg states. They appear as irregular vibrational spacings, anomalous intensities, as well as modifications of the B ^{2}Π(v’,0) band profiles. The intensity patterns are qualitatively explained in terms of quantum‐mechanical interference effects. When resonant with a multiphonon Rydberg band, Fano line shapes appear in place of the sharp B(v’,0) valence lines. The line shapes have been simulated by means of the Fano theory assuming that only part of the Rydberg multiphonon quasicontinuum interferes with the sharp valence band. Good agreement is obtained with the experimental spectrum and the fitted Fano indices lie close to the calculated ones.

Rotational line strengths for the photoionization of diatomic molecules
View Description Hide DescriptionWe derive an expression for the probability that a diatomic molecule AB(n,v,N) in the electronic state n, vibrational statev, and rotational level N yields upon photoionizationAB ^{+}(n ^{+},v ^{+},N ^{+}), where we assume Hund’s case (b) coupling. Our result is formally equivalent to the previous work of Buckingham, Orr, and Sichel [Phil. Trans. Roy. Soc. London, Ser. A 268, 147 (1970)] but differs substantially in that we use spherical tensor methods, which provide insight into the photoionization dynamics in terms of the contribution of different multipole moments. The total interaction term is given by the tensor product of the electric dipole moment operator T(1,μ_{0}) and the multipole moment tensorT(l,m) describing the photoelectron in the lth partial wave. The interaction term is further simplified into a sum of reduced multipole moments T(k,p), where k=l±1 and p=μ_{0}+m. For an isotropic distribution of initial states, the transition probability is given by P(N,N ^{+})=1/3∑_{ k } S ^{ k }(N,N ^{+})‖μ̄(k,q)‖^{2}, where the factor of 1/3 arises from the use of a beam of polarized light, S ^{ k }(N,N ^{+}) is a generalized rotational line strength factor, and ‖μ̄(k,q)‖^{2}=‖μ_{ l=k+1}(k,q) ‖^{2}+‖μ_{ l=k−1}(k,q)‖^{2} is the sum of the squares of reduced multipole moment matrix elements.
The summation over k is restricted to even values for a (±)↔(±) transition and to odd values for a (±)↔(∓) transition. Thus, for an unpolarized molecular sample, the integrated photoelectron intensity associated with an N→N ^{+} transition is the incoherent sum of the multipole moments that contribute to this transition, and each such contribution is an incoherent sum over l=k+1 and l=k−1. If the molecular sample is polarized (aligned and/or oriented), then the expression for the N→N ^{+} integrated photoelectron intensity becomes a coherent sum over different k values with the same l value. Moreover, if the photoelectron distribution is angle resolved, then the expression for the N→N ^{+} transition probability is a coherent sum over l values with the same k value when the molecular sample is unpolarized and cannot be separated into incoherent parts when the molecular sample is polarized. The expression for P(N,N ^{+}) has been used to fit the results of the photoionization of H_{2} and NO. In both cases, the fit obtained, which required only one or two adjustable parameters, respectively, agrees well with the experimental data. This treatment may be readily extended to photoionization of polyatomic molecules and to molecules that follow different angular momentum coupling cases.

Dynamical inhomogeneous broadening and lattice‐assisted intramolecular energy transfer in the fundamental A _{1} vibrations of liquid chloroform Cl‐35
View Description Hide DescriptionThis report gives extensive isotropic Raman spectral data and their numerical Fourier transformation into the time domain (∼0–20 ps) for the three A _{1} vibrational fundamentals of Cl‐35 isotopically pure chloroform. It was found that the vibrational amplitude correlation decay of the ν_{1} mode (C–H stretch) at 300 K follows a rapid vibrational dephasing process (inhomogeneous broadening with motional narrowing) that is 1.7 times faster than the concomitant intramolecular energy transfer to the overtone of the C–H bending mode. From the temperature dependence (213 K, 300 K) of the amplitude correlation decay of the ν_{3} mode (C–Cl deformation) we deduce that it relaxes essentially only by vibrational dephasing and in such a fast modulation regime that the ν_{3}oscillator is effectively decoupled from the local lattice anisotropies. From the temperature dependence of the amplitude correlation decay of the ν_{2} mode (C–Cl stretch) we infer a simultaneous vibrational dephasing and lattice‐assisted intramolecular energy transfer process, the latter possibly to the overtone of ν_{3}. This paper concludes with some general remarks on the predictability of relative contributions of various types of vibrational relaxation processes to vibrational amplitude correlation decay in molecular liquids and, in an Appendix, gives estimates on the rates of excess phonon depopulation into the lattice as governed by a permanent dipole–transition dipole coupling process for modes ν_{6}, ν_{3}, ν_{2}, and ν_{5} of liquid chloroform.

Molecular beam optical Stark spectroscopy of calcium monocyanide
View Description Hide DescriptionThe 617.7 and 614.7 nm bands of calcium monocyanide, CaNC/CaCN, have been recorded at high resolution by laser‐induced fluorescence using a supersonic molecular beam. The two bands consist of twelve branches that are assigned to a case a transition. A reduction of the data to an effective Hamiltonian model produced the spectroscopic parameters It is proposed that the anomalous values of the excited state parameters arise because of Renner–Teller interactions. The magnitude of the permanent electric dipoles, were also determined and are 5.949(1) and 6.895(9) The large value of is consistent with an isocyanide structure, CaNC. A comparison with theoretical predictions is presented.

Cation vibrational spectroscopy of trans and gauche n‐propylbenzene rotational isomers. Two‐color threshold photoelectron study and ab initio calculations
View Description Hide DescriptionIn this paper, a full account of an earlier report [Takahashi, Okuyama, and Kimura, J. Mol. Struct. 249, 47 (1991)] on the cation vibrational spectra of trans and gauche n‐propylbenzene, which were obtained by means of a two‐color (1+1’) multiphoton ionization threshold photoelectron technique is presented. The trans and gauche cations were separately produced by (1+1’) multiphoton ionization resonant through the S _{1} vibronic levels of n‐propylbenzene in supersonic free jets in which both the trans and gauche isomers exist. From the observed threshold photoelectron spectra, adiabatic ionization energies are determined as I _{ a }(trans)=70 278 cm^{−1} (8.7134 eV) and I _{ a }(gauche)=70 420 cm^{−1} (8.7311 eV) with an accuracy of ±8 cm^{−1} (±1 meV). Furthermore, four benzene ring modes (6b ^{+}, 1^{+}, 12^{+}, and 18a ^{+}) as well as several low‐frequency torsional and bending modes have been identified which are sensitive to the relative conformations of the n‐propyl group with respect to the benzene ring [(trans)^{+}: 82, 212, and 300 cm^{−1}; (gauche)^{+}: 46, 73, 207, and 252 cm^{−1}]. The present vibrational assignments of the trans and gauche cations are based on a normal modeanalysis performed for the trans cation by ab initio calculations. In the present work, this technique is demonstrated to be quite powerful for distinguishing the vibrational spectra of different cation isomers.

Pure absorption‐mode chemical exchange nuclear magnetic resonance spectroscopy with suppression of spinning sidebands in a slowly rotating solid
View Description Hide DescriptionA new technique is presented for studying chemical exchange in solids under conditions of magic angle spinning (MAS); it is based on the original two‐dimensional exchange experiment but uses the combination of a TOSS (total suppression of sidebands) sequence with its time‐reversed counterpart in the first dimension to effect evolution under the isotropic chemical shift alone. Pure absorption‐mode spectra can then be obtained in the usual way. One version of this experiment also uses TOSS at the start of acquisition, producing an exchange spectrum that has isotropic chemical shifts in both frequency dimensions. This is useful for isotropic powder samples with anisotropies that are too large to be averaged completely by sample spinning but are still within the regime where TOSS can be applied. A second experiment allows free MAS evolution during acquisition, giving a spectrum with isotropic shifts in the first dimension and both shifts and sidebands in the second dimension. This version has two important features: (i) it does not suffer from the intensity losses normally inherent in TOSS when the anisotropy is large compared to the spinning speed; and (ii) it is applicable even to samples that have an anisotropic distribution of crystallites. The tautomeric hydrogen shift in solid tropolone is used to illustrate how chemical exchange can be readily monitored, irrespective of the number of spinning sidebands present in the one‐dimensional MAS spectrum. This method of obtaining ‘‘isotropic evolution’’ can be used in any two‐ or three‐dimensional MAS experiment and provides a practical alternative to high‐speed MAS.

Determining potential‐energy surfaces from spectra: An iterative approach
View Description Hide DescriptionA general method for iteratively fitting the coefficients of a Taylor‐series expansion of the potential‐energy surface for a polyatomic molecule to the observed transition frequencies and rotational constants is presented. This approach utilizes the efficiency of fourth‐order Van Vleck perturbation theory for calculating these properties, scaled to the results of converged variational calculations. Three fits to the transition frequencies and rotational constants obtained from absorption and stimulated emission pumping spectra of HCN are presented. Comparison of these potentials sheds light on the uniqueness of fit potential surfaces, given this set of observables. We fit the vibrational energies for 71 states with a mean absolute deviation of 0.69 cm^{−1}.

Spectral diffusion in liquids
View Description Hide DescriptionSpectraldiffusion of an electronic transition of solute chromophores in liquid solutions is investigated experimentally and theoretically through its influence on electronic excited‐state transfer (EET). Observation of dispersive EET in liquids (the EET rate depends on the excitation wavelength) demonstrates that absorption lines are inhomogeneously broadened on a nanosecond time scale in the systems studied although the time scale for homogeneous dephasing is tens of femtoseconds. A theory is developed that relates the rate of spectraldiffusion to the wavelength dependence and temperature dependence of EET. Time‐resolved fluorescence depolarization measurements are used to measure EET in the systems rhodamine B (RB) in glycerol and propylene glycol as a function of wavelength and temperature from room temperature (298 K) to 200 K. Comparison with theory permits the rates of the solvent fluctuations responsible for spectraldiffusion to be determined for the two solvents at several temperatures. Measurements are also made of the rates of solvent relaxation about the excited RB and of RB orientational relaxation. The results demonstrate that the mechanism for spectraldiffusion is solvent orientational relaxation which causes the initial (time of optical excitation) dipolar field, produced by the solvent at the chromophore, to randomize.

Infrared diode laser spectroscopy of the allyl radical. The ν_{11} band
View Description Hide DescriptionAllyl radicals were generated by the photolysis of 1,5‐hexadiene at 193 nm and were detected by observing the ν_{11}, i.e., CH_{2} symmetric wagging band by infrared diode laser kinetic spectroscopy. The observed spectrum showed clearly the effect of nuclear‐spin statistical weights, establishing the presence of a C ^{ b } _{2} axis in the molecule. The spin–rotation splitting was not resolved; only some high‐K _{ a } lines were found broader than others, placing an upper limit for the ε_{ aa } constant at about 200 MHz or less. The rotational constants derived from the observed spectrum indicate that the molecule is essentially planar. The C–C bond length and the CCC bond angle were calculated from the ground‐state rotational constants to be 1.3869 Å and 123.96°, respectively, where structural parameters involving hydrogens were fixed to those of ab initio values.

High resolution spectroscopy of 1,2‐difluoroethane in a molecular beam: A case study of vibrational mode‐coupling
View Description Hide DescriptionThe high resolution infrared spectrum of 1,2‐difluoroethane (DFE) in a molecular beam has been obtained over the 2978–2996 cm^{−1}spectral region. This region corresponds to the symmetric combination of asymmetric C–H stretches in DFE. Observed rotational fine structure indicates that this C–H stretch is undergoing vibrational mode coupling to a single dark mode. The dark mode is split by approximately 19 cm^{−1} due to tunneling between the two identical gauche conformers. The mechanism of the coupling is largely anharmonic with a minor component of B/C plane Coriolis coupling. Effects of centrifugal distortion along the molecular A‐axis are also observed. Analysis of the fine structure identifies the dark state as being composed of C–C torsion, CCF bend, and CH_{2} rock. Coupling between the C–H stretches and the C–C torsion is of particular interest because DFE has been observed to undergo vibrationally induced isomerization from the gauche to trans conformer upon excitation of the C–H stretch.

Photoabsorption, fluorescence excitation, and lifetimes of the excited states of Br_{2} at 116–170 nm
View Description Hide DescriptionThe photoabsorption and fluorescence excitation of Br_{2} have been investigated in the wavelength region 116–170 nm. The fluorescence lifetimes of some Rydbergexcited states were measured. Perturbations in the excited states are discussed based on the comparison of the absorption and the excitation spectra.

Laser vaporization generation of the diatomic radicals PdB, ^{105}PdB, PdAl, and ^{105}PdAl: Electron spin resonance investigation in neon matrices at 4 K
View Description Hide DescriptionThe new diatomic radicals PdB and PdAl have been generated by depositing the products produced from the pulsed laservaporization of the elemental mixtures into neon matrices at 4 K. ESR(electron spin resonance) studies of these matrix isolated radicals, including an analysis of the ^{105}Pd(I=5/2), ^{27}Al(I=5/2), and ^{11}B(I=3/2) nuclear hyperfineinteractions, show that both have X ^{2}Σ electronic ground states. These new results are compared with previous ESR measurements for PdH, PdCH_{3}, YPd, ScPd, and PdH_{2} ^{+} to reveal electronic structure information and bonding trends as the complexity of the ligand increases 1s, 2p, 3p, 3d, and 4d. Ab initio UHF (unrestricted Hartree–Fock) theoretical calculations were also conducted on four of these small palladium radicals as part of this experimental investigation. A simple interpretation of the ^{105}Pd hyperfineinteractions and molecular g tensors based on the degree of charge transfer to palladium is presented. The observed magnetic parameters (MHz) for ^{105}Pd^{11}B in a neon matrix at 4 K are g _{∥}=2.009(2), g _{⊥}=2.042(2), A _{∥}=−1483(15), and A _{⊥}=−1483(2) for ^{105}Pd, and A _{∥}=197(4) and A _{⊥}=140(1) for ^{11}B. The parameters for ^{105}Pd^{27}Al are g _{∥}=2.010(1), g _{⊥}=2.0343(5), A _{∥}=−1283(10) and A _{⊥}=−1268(2) for ^{105}Pd, and A _{∥}=182(2) and A _{⊥}=84.6(5) for ^{27}Al.

Microwave spectrum of benzene⋅SO_{2}: Barrier to internal rotation, structure, and dipole moment
View Description Hide DescriptionThe microwave spectrum of the benzene⋅SO_{2} complex was observed with a pulsed beam Fourier‐transform microwave spectrometer. The spectrum was characteristic of an asymmetric‐top with a‐ and c‐dipole selection rules. In addition to the rigid‐rotor spectrum, many other transitions were observed. The existence of a rich spectrum arose from torsional–rotation interactions from nearly free internal rotation of benzene about its C _{6} axis. Transitions from torsional states up to m=±5 were observed. The principal‐axis method (PAM) internal rotation Hamiltonian with centrifugal distortion was used to assign the spectrum. Assuming six‐fold symmetry for the internal rotation potential, the barrier height was determined as V _{6}=0.277(2) cm^{−1}. The spectrum of C_{6}D_{6}⋅SO_{2} was also assigned. Analysis of the moments of inertia indicated that the complex has a stacked structure. The distance R _{cm} separating the centers of mass of benzene and SO_{2}, as well as the tilt angles of the benzene and SO_{2} planes relative to R _{cm} were determined. The values obtained were R _{cm}=3.485(1) Å, θ_{C6H6 }=±12(1)° and θ_{SO2 }=44(6)°. While SO_{2} is certainly tilted with the sulfur end towards benzene, the sign of the benzene tilt angle could not be unambiguously determined. The dipole moment of C_{6}H_{6}⋅SO_{2} was determined as μ_{ a }=1.691(2) D, μ_{ c }=1.179(2) D, and μ_{ T }=2.061(2) D.

Raman‐ultraviolet double resonance in acetylene: Rovibrational state preparation and spectroscopy
View Description Hide DescriptionWe report time‐resolved optical double resonancespectroscopic experiments in which gas‐phase acetylene molecules are selectively prepared and monitored in discrete rotational states of the v _{2}=1 (C≡C stretch, 1974 cm^{−1}) vibrational level. This is achieved by pulsed coherent Raman excitation and laser‐induced fluorescence detection. State‐selective spectra of single rovibrational states are presented under effectively collision‐free conditions. Several new rovibronic bands in the Ã←X̃ absorption system of acetylene are identified in this way, owing to the enhanced sensitivity and spectral simplification of our Raman‐optical double resonance technique. Investigations of C_{2}H_{2}(g) concentrate on rotationally resolved vibronic bands of the form 2_{1} ^{0}3_{0} ^{ x } (where x=1,2,3,...), exploring spectroscopic subtleties such as axis switching. The method has also been extended to the 2_{1} ^{0}3_{0} ^{ x }4_{1} ^{0} vibronic bands of C_{2}H_{2}(g), by Raman excitation in the (ν_{2}+ν_{4}−ν_{4}) hot band, and to studies of the deuterated isotopomers, C_{2}HD(g) and C_{2}D_{2}(g). Two distinct experimental strategies are demonstrated, in terms of their utility for spectroscopic assignment and energy transfer applications. One such approach comprises a rovibronic fluorescence excitation spectrum, recorded with fixed Raman excitation frequency. The alternative approach yields state‐selected Raman spectra, with the Raman excitation frequency varied and the rovibronic excitation wavelength fixed.

The structures of small methyl fluoride clusters from infrared dissociation experiments
View Description Hide DescriptionMolecular beam depletion spectroscopy has been employed to study the dissociation of small methyl fluoride clusters upon excitation of the ν_{3} C–F stretch vibration at 1048.6 cm^{−1}. Size selection has been achieved by dispersing the (CH_{3}F)_{ n } cluster beam by a secondary rare gas beam. For the methyl fluoride dimer only very weak dissociation signals could be observed. The corresponding spectrum features a single, 13.4 cm^{−1} broad absorption line. This observation is explained with a symmetric dimer structure, in which both monomer units reside at equivalent positions, and an inefficient coupling of the molecular vibration to the intermolecular bond. For the trimer and tetramer very strong dissociation yields are observed. Whereas the trimer shows a complicated spectrum which is attributed to its nonsymmetric structure, the tetramer spectrum is again characterized by a single peak. In order to obtain supplementary information, dissociationspectra have also been measured for small methyl fluoride clusters residing inside or on the surface of large Ar_{ x } host clusters. These matrixlike spectra are consistent with the free gas‐phase cluster data. Finally, in a computational approach, the structures of the methyl fluoride dimer, trimer, and tetramer have been determined by total energy minimization. The theoretical results are in perfect agreement with the experimental findings.

The discrete variable representation of a triatomic Hamiltonian in bond length–bond angle coordinates
View Description Hide DescriptionThe discrete variable representation (DVR) is used to calculate vibrational energy levels of H_{2}O and SO_{2}. The Hamiltonian is written in terms of bond length–bond angle coordinates and their conjugate momenta. It is shown that although these coordinates are not orthogonal and the appropriate kinetic energy operator is complicated, the discrete variable representation is quite simple and facilitates the calculation of vibrational energy levels. The DVR enables one to use an internal coordinate Hamiltonian without expanding the coordinate dependence of the kinetic energy or evaluating matrix elements numerically. The accuracy of previous internal coordinate calculations is assessed.