3. Ab Initio Calculations 2543 C. Dynamics 2550 1. Group Theory 2551 2. H-Bond Network Rearrangement (HBNR) 2552 3. Intramolecular Vibrations 2557 4. Intermolecular Vibrations 2558 III. Experimental Data 2558 A. Condensed-Phase Environments 2560 1. Matrix-Isolation Spectroscopy 2560 2. Inorganic Host Complexes 2561 3. Water Trimer in Liquid Helium Droplets 2561 B. Gas-Phase Spectroscopy of the Free Water Trimer 2561

The water trimer.

The conformation and dynamical behavior of molecular systems is very often advantageously described in terms of physically well-adapted curvilinear coordinates. It is rather easy to show that the numerous analytical expressions of the kinetic energy operator of a molecular system described in terms of n curvilinear coordinates can all be transformed into the following more usable expression: (T) over cap=Sigma(ij)f(2)(ij)(q)partial derivative(2)/partial derivativeq(i)partial derivativeq(j)+Sigma(i)f(1)(i)(q)partial derivative/partial derivativeq(i)+nu(q), where f(2)(ij)(q), f(1)(i)(q), and nu(q) are functions of the curvilinear coordinates q=(...,q(i),...). If the advantages of curvilinear coordinates are unquestionable, they do have a major drawback: the sometimes awful complexity of the analytical expression of the kinetic operator (T) over cap for molecular systems with more than five atoms. Therefore, we develop an algorithm for computing (T) over cap for a given value of the n curvilinear coordinates q. The calculation of the functions f(2)(ij)(q), f(1)(i)(q), and nu(q) only requires the knowledge of the Cartesian coordinates and their derivatives in terms of the n curvilinear coordinates. This coordinate transformation (curvilinear-->Cartesian) is very easy to perform and is widely used in quantum chemistry codes resorting to a Z-matrix to define the curvilinear coordinates. Thus, the functions f(2)(ij)(q), f(1)(i)(q), and nu(q) can be evaluated numerically and exactly for a given value of q, which makes it possible to propagate wavepackets or to simulate the spectra of rather complex systems (constrained Hamiltonian). The accuracy of this numerical procedure is tested by comparing two calculations of the bending spectrum of HCN: the first one, performed by using the present numerical kinetic operator procedure, the second one, obtained in previous studies, by using an analytical kinetic operator. Finally, the ab initio computation of the internal rotation spectrum and wave functions of 2-methylpropanal by means of dimensionality reduction, is given as an original application. (C) 2002 American Institute of Physics.

Exact numerical computation of a kinetic energy operator in curvilinear coordinates

The microwave spectrum of tetrahydrofuran has been studied. Nine complete rotational spectra have been observed. These arise from the ground and eight excited states. All of these states are less than 200 cm−1 from the ground state. The rotational constants and dipole moments exhibit a strong nonlinear dependence on the quantum number of the excited state. Vibration–rotation interaction is strong and the spectra of the first four states deviate from that of rigid rotor spectra. These deviations permit the determination of two energy separations: Δ01 = 0.67 cm−1 and Δ23 = 1.5 cm−1. All of the results are interpreted in terms of a model of restricted pseudorotation with a potential function of [30(1‐cos2φ) / 2] + [40(1‐cos4φ) / 2] cm−1, where φ is the angle of pseudorotation. The dipole moment varies from 1.52 to 1.76 D depending upon the pseudorotation state. The details of this variation indicate that the twisted configuration is at lower energy than the bent configuration.

Ring Puckering in Five‐Membered Rings. II. The Microwave Spectrum, Dipole Moment, and Barrier to Pseudorotation in Tetrahydrofuran

Far-infrared spectra of ring compounds: A semi-rigid model for the ring-puckering vibration in some pseudo-four-membered ring molecules☆

Microwave spectra of cyclopentanone and 2‐d‐cyclopentanone are reported. Eight vibrational satellites have been assigned for cyclopentanone, and two conformers have been observed for 2‐d‐cyclopentanone. The rotational constants of the ground states are: 6621, 3351.54, and 2410.40 MHz for the normal isotopic species of cyclopentanone; 6309, 3322.55, and 2382.82 MHz; and 6258, 3344.54, and 2361.96 MHz for the two conformers of the 2‐deutero isotopic species. It was found that the nature of the ring‐puckering potential is such that the ring is permanently twisted and undergoing bending and twisting vibration quite independently. The lower limit to the height of barrier‐hindering pseudorotation was set about 400 cm−1. The structural parameters, r;(C1–C2), r;(C2–C3), ∠(C2–C1–C5), and the twist angle τ, were calculated by the iterative procedure of the weighed least‐squares analysis. They are 1.504 ± 0.01 A, 1.557 ± 0.007 A, 110.5 ± 0.7°, and 23.6 ± 0.4°. The components of dipole moments were determined by the ...

Ring Puckering in Five‐Membered Rings. III. The Microwave Spectrum, Dipole Moment, and Structure of Cyclopentanone

As a general introduction to a subsequent series of papers on pseudorotation and five‐membered rings, the two‐ring puckering modes of a five‐membered ring are discussed in general terms. Five cases are separated depending upon the nature of the potential function for each mode. Correlation diagrams connecting the various cases are given. Consistent with our basic policy, we have gone directly from fundamental theory to an arithmetical development using large digital computers. The classical section of this development is outlined. The quantum‐mechanical section is developed in the following paper.

Chadwick A. Tolman

Papers

Ring Puckering in Five‐Membered Rings. I. General Theory