V. Špirko

Coriolis and l-type interactions in the ν2, 2ν2, and ν4 states of 14NH3

High-resolution infrared spectra have been remeasured for the ..nu../sub 2/, 2..nu../sub 2/, and ..nu../sub 4/ bands of /sup 14/NH/sub 3/ using a vacuum grating infrared spectrometer and a diode laser spectrometer. Far-infrared spectra of /sup 14/NH/sub 3/ have been measured with microwave accuracy in the 700 to 1100 GHz region by employing a submillimeter wave spectrometer (RAD) with acoustic detection. The pure inversion and inversion-rotation transition frequencies in the ..nu../sub 2/ excited state of /sup 14/NH/sub 3/ have been determined for the first time. The vibration-inversion-rotation Hamiltonian of ammonia reported by Spirko, Stone, and Papousek has been used for a precise parameterization of the energy levels of ammonia. The ground state rotational and centrifugal constants of /sup 14/NH/sub 3/ have been determined using a modified method of combination differences. Coriolis and l-type interactions between ..nu../sub 2/, ..nu../sub 4/, 2..nu../sub 2/, ..nu../sub 2/ + ..nu../sub 4/, and 3..nu../sub 2/ states have been analyzed and the band parameters have been obtained which reproduce the transition frequencies within the accuracy of the experimental data.

A simultaneous analysis of the microwave, submillimeterwave, far infrared, and infrared-microwave two-photon transitions between the ground and ν2 inversion-rotation levels of 14NH3

Abstract Fourier transform infrared spectra of the inversion-rotation transitions have been measured with 0.010-cm −1 resolution between 40 and 300 cm −1 in the ground state and ν 2 excited states of 14 NH 3 . Submillimeterwave spectra of the inversion and inversion-rotation transitions in the ν 2 state of 14 NH 3 , including a few Δ k = ±3 “perturbation-allowed” transitions, have been measured with microwave accuracy between 540 and 770 GHz. A simultaneous least-squares analysis of these data, the microwave ground-state transition frequencies, and the ν 2 infrared-microwave two-photon transition frequencies has been carried out. A theory of the Δ k = ±3 n interactions in the ground and ν 2 excited states of ammonia (S. P. Belov, L. I. Gershtein, A. F. Krupnov, A. V. Maslovskij, S. Urban, V. Spirko, and D. Papousek, J. Mol. Spectrosc. 84 , 288–304 (1980)) has been used in the analysis. A set of the ground- and ν 2 -state molecular parameters has been obtained which describes the experimental data within the precision of the experiment. The “smoothed” values of transition frequencies can be used for calibration purposes with a precision better than 3 × 10 −5 cm −1 in the submillimeterwave region, better than 10 −3 cm −1 in the far-infrared region, and better than 1.5 × 10 −3 cm −1 in the region 700 – 1200 cm −1 .

Frequency‐dependent polarizabilities and first hyperpolarizabilities of H2O

Static and frequency‐dependent dipole polarizabilities α and first hyperpolarizabilities β are calculated for H2O using self‐consistent field (SCF) and multiconfigurational self‐consistent‐ field (MCSCF) linear and quadratic response theory. With an active orbital space where one correlating orbital is included for each occupied valence orbital excellent agreement is obtained with the experimental hyperpolarizability. Basis set dependency has been investigated and a detailed vibrational analysis has been carried out.

Vibration-inversion-rotation spectra of ammonia. A vibration-inversion-rotation Hamiltonian for NH3☆

Abstract A new model Hamiltonian has been developed to study the vibration-inversion-rotation energy levels of ammonia. In this model the inversion motion is removed from the vibrational problem by allowing the molecular reference configuration to be a function of the large amplitude motion coordinate. The treatment follows closely that developed by Hougen, Bunker, and Johns for the study of triatomic molecules. The numerical methods that have been used to solve the zeroth-order Hamiltonian describing the inversion-rotation energy levels of NH 3 and ND 3 in the ground vibrational state are discussed. Certain group-theoretical problems concerning the symmetry classification of the states of ammonia are also discussed.

Anharmonic potential function and effective geometries for the NH3 molecule

Abstract An accurate analytic anharmonic potential function for NH3 is determined by fitting to experimental rovibrational transition data of the 14NH3, 15NH3, 14ND3, 15ND3, and 14NT3 isotopic species using the nonrigid invertor Hamiltonian method [V. Spirko, J. Mol. Spectrosc.101, 30–47 (1983).]. Information from ab initio potential energy calculations is used to obtain a numerically stable and physically meaningful solution to the fitting procedure. From the potential function determined in this study effective geometries are evaluated for the low lying roinversional states of 14NH3 and 14ND3. To allow for a quantitative analysis of the inversional dependence of other molecular constants, the roinversional matrix elements 〈ψv2,J,k(ϱ)|sin2nϑ|ψ′v2,J,k(ϱ)〉 ( ϑ = ϱ − π 2 , ϱ being the inversion angle, and n an integer number) are evaluated for spectroscopically important values of the inversion (v2) and rotation (J, k) quantum numbers.

Inversion and inversion-rotation spectrum of 14NH3 in the ν2 excited state

Using the vibration-inversion-rotation Hamiltonian for ammonia [V. Spirko, J. M. R. Stone, and D. Papousek, J. Mol. Spectrosc. 60, 159–178 (1976)], a modified theory is worked out for the Δk = ±3n interactions between the inversion-rotation energy levels of NH3 which takes into account the large amplitude inversion motion. Eighty frequencies of inversion and inversion-rotation transitions and two perturbation-allowed transitions in the ν2 state of 14NH3 are measured in the far-infrared region around 1 THz (≈33 cm−1), mostly with the microwave accuracy, by the radiofrequency spectrometer with acoustic detector. By a least-squares fit of these data and the data of the infrared-microwave two-photon and infrared heterodyne measurements of the ν2 band, a set of molecular constants for the ν2 state of 14NH3 is obtained which reproduces the submillimeterwave data with the accuracy of the experiment.

Vibration-inversion-rotation spectra of ammonia: Centrifugal distortion, Coriolis interactions, and force field in 14NH3, 15NH3, 14ND3, and 14NT3☆

Abstract An effective inversion-rotation Hamiltonian has been developed for NH 3 which avoids the necessity of having to include high powers of the inversion motion coordinate in the Taylor expansions of the potential energy and the inverse moment of inertia tensor. This nonrigid bender Hamiltonian describes the centrifugal distortion and the Coriolis interactions in the ground and excited inversion states. It also describes the inversion doublings in the ground and excited vibration-inversion states of ammonia. A least-squares procedure that includes the numerical integration of the Schrodinger wave equation has been used to determine the harmonic force field and the double-minimum inversion potential function for ( 14 NH 3 , 15 NH 3 ) and for ( 14 ND 3 and 14 NT 3 ). The anomalous rotational dependence of the inversion doublings in the (± l ) components of the ∥ v 4 = 1〉 state of 14 NH 3 has been explained by the Coriolis interactions between ∥ v 2 =1〉, ∥ v 4 = 1〉, ∥ v 2 = 2〉, ∥ v 2 = 1, v 4 = 1〉, and ∥ v 2 = 3〉 vibration-inversion states.

Propargylene: A C3H2 isomer with unusual bonding

Propargylene was identified in a matrix as a product of photolysis of cyclopropenylidene and diazopropyne. The molecule is a triplet. The optimum geometry predicted by ab initio calculations corresponds to a structure HC≡C–CH. The transition structure in the interconversion HC≡C–CH⇄HĊ=C=ĊH⇄HC–C≡CH is very low in energy and close to the energy of the vibrational ground state. Owing to this nonrigidity, computed infrared (IR) frequencies based on a harmonic treatment do not match the experimental spectrum. When this nonrigidity is taken into account by using a nonharmonic approximation calculated UMP2/6‐31G** IR spectra are in good agreement with the observed spectra of HCCCH and DCCCD.

The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H3+

Abstract The rotation-vibration Hamiltonian for an equilateral triangular X 3 molecule is derived in terms of the three curvilinear stretching coordinates Δ r i , and expanded in the form of a power series in the variables y i = 1 − exp(- a Δ r i ), where a is a molecular parameter obtained from the potential function. The reason for the use of the variable y i is twofold: Stretching potentials exhibit a much stronger convergence in the y i than in the Δ r i , and a Hamiltonian expressed in the y i can be diagonalized in a straightforward fashion using a Morse-oscillator basis set as we do here. Using a published ab initio potential surface we have expanded it as a polynomial in the y i , and have calculated variationally the rotation-vibration energies of H 3 + and D 3 + using a symmetry-adapted Morse-oscillator-rigid symmetric top basis set. The results indicate that an expansion of the potential function to quartic terms in the y i might be adequate, and that satisfactorily converged energies can be obtained with a relatively small basis set. The molecule H 3 + is the simplest polyatomic molecule. Inspection of the Appendix of this paper shows that the rotation-vibration Hamiltonian used here is one of the more complicated ones.

Abinitio calculations on the energy of activation and tunneling in the automerization of cyclobutadiene

Results of ab initio two‐configuration CI‐SD/[3s2p1d/2s], MBPT(4), CCSD+T(CCSD), and CCSDT‐1 calculations are reported for the rectangular D2h equilibrium and square D4h transition structures of cyclobutadiene. The latter is a classic example of a multireference correlated method. The optimum CC and CH bond lengths found for the D4h transition structure are 1.448 and 1.093 A, respectively. The activation barrier for the automerization is 9.0 kcal/mol at the two‐reference GVB‐CISD level while the single reference CCSD gives 19.9, 14.4 for CCSD+T(CCSD) and finally a dramatic change to 9.5 at the highest CCSDT‐1 level. The importance of triples in overcoming the multireference character at the transition state is apparent. On the other hand, GVB‐CISD is simpler than CCSDT‐1 which attests to the importance of a qualitatively correct multireference starting point for this example. A less sophisticated computational method, GVB/4‐31G, which also gives a reasonable barrier of 10.2 kcal/mol was used for the const...