The authors present a first-principles prediction of the energies of the eight lowest-lying anharmonic vibrational states of CO(2), including the fundamental symmetric stretching mode and the first overtone of the fundamental bending mode, which undergo a strong coupling known as Fermi resonance. They employ coupled-cluster singles, doubles, and (perturbative) triples [CCSD(T) and CCSDT] in conjunction with a range of Gaussian basis sets (up to cc-pV5Z, aug-cc-pVQZ, and aug-cc-pCVTZ) to calculate the potential energy surfaces (PESs) of the molecule, with the errors arising from the finite basis-set sizes eliminated by extrapolation. The resulting vibrational many-body problem is solved by the vibrational self-consistent-field and vibrational configuration-interaction (VCI) methods with the PESs represented by a fourth-order Taylor expansion or by numerical values on a Gauss-Hermite quadrature grid. With the VCI, the best theoretical estimates of the anharmonic energy levels agree excellently with experimental values within 3.5 cm(-1) (the mean absolute deviation). The theoretical (experimental) anharmonic frequencies of the Fermi doublet are 1288.9 (1285.4) and 1389.3 (1388.2) cm(-1).
Franck-Condon (FC) integrals of polyatomic molecules are computed on the basis of vibrational self-consistent-field (VSCF) or configuration-interaction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the Gauss-Hermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys. 104, 33 (2006)]. These methods in conjunction with the VCI and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the X 2B1 photoelectron band of H2O with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The X 2B2 photoelectron band of H2CO is less accurately reproduced by this method, likely because of the inability of CCSD(T)/cc-pVTZ to describe the potential energy surface of open-shell H2CO+ with the same high accuracy as in H2O+.
One-pot reactions of sulfinic acid salts (produced from organometallic reagents with SO2) with N-chlorobenzotriazole gave the corresponding N-alkane-, N-arene-, and N-heteroenesulfonylbenzotriazoles 3a-j in 41-93% yields. Reagents 3a-j are efficient sulfonylating agents, reacting at 20-80 degrees C with various primary and secondary aliphatic amines to yield the corresponding sulfonamides in 64-100% yields.
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