Absolute shielding scale for 31P from gas-phase NMR studies

Methods for the determination of the frequency dependent hyperpolarizabilities, β(−2ω;ω,ω), β(−ω;ω,0), and β(0;ω,−ω) at the self‐consistent field (SCF) level of theory are discussed and compared. Two efficient alternatives are proposed; one involves determination of appropriate response vectors which arise in first‐order perturbation theory at frequency ω, and the other involves solving first‐order perturbation theory equations at frequency 0 (static), ω and 2ω. Neither approach involves solution of the second‐order perturbation theory equations. The method is illustrated with application to formaldehyde and methyl fluoride using large one‐particle basis sets. The basis set requirement for convergence of this property at the SCF level of theory is investigated. Basis sets including up to d functions on first row atoms and p functions on hydrogen incorporating diffuse functions appear to be adequate. The effect of electron correlation on the static hyperpolarizability is estimated using second‐order Mo/ller–Plesset theory. Comparison is made with experimental values where available.

Frequency dependent hyperpolarizabilities with application to formaldehyde and methyl fluoride

31 P
 NMR chemical shifts for the phosphorus compounds PX3 (X=H, F, Cl, CH3, iC3H7 and OCH3), OPX3
 (X=CH3
 and OCH3), Si(PH2)4, Cr(CO5)(PH3), PX4+ (X=H, CH3), PF6−, P4 and PN have been calculated with various
 density functional methods as well as at the Hartree–Fock and MP2 level, using both the IGLO and GIAO
 variants of introducing distributed gauge origins except for MP2 (only GIAO available) and the new method proposed recently by Wilson, Amos and Handy (WAH, GIAO not available). Except for PCl3
 and PN, all density
 functional approaches achieve comparable accuracy, better than Hartree–Fock and similar to MP2. For PCl3 and PN, the WAH method leads to a substantial improvement. The GIAO and IGLO results are of
 comparable accuracy. Numerical benchmark values for the absolute magnetic shielding of PN at its experimental
 equilibrium value are presented and compared with literature data. A theoretical
 analysis reveals that the approximation used
 by WAH makes their method lose gauge invariance.

A comparison of density functional methods for the calculation of phosphorus-31 NMR chemical shifts

Laser–microwave double resonance (LMDR) with high electric field was applied to the OCS molecule. Stark Lamb‐dip spectra due to the infrared transitions of the 2ν2(0200–0000, 9.6 μm), 2ν1 (2000–0000, 5.8 μm), and ν1+2ν2 (1200–0000, 5.3 μm) bands were observed with the CO2 and CO lasers. The spectra due to the corresponding hot bands; 0310–0110, 0400–0200, 1200–1000, 1310–1110; 2110–0110, 3000–1000; 1400–0200, 1420–0220, 1510–0310, 2200–1000; and a few bands of OC34S and O13CS were also identified. Associated with these infrared transitions, more than 90 LMDR signals were detected and assigned to rotational transitions in the 11 vibrational states 0000, 1000, 2000, 0110, 0200, 0220, 0310, 0400, 1200, 1420, and 2200 of the normal species, and in the two vibrational states 0000 and 0200 of both OC34S and O13CS. Dipole moments were determined with accuracies (2.5σ) better than 2×10−5 D for all these vibrational states. Polarizability anisotropies were also obtained for some states. The data for the ground ν1 ...

CO2 and CO laser microwave double resonance spectroscopy of OCS: Precise measurement of dipole moment and polarizability anisotropy

A theoretical approach to study ro-vibrational molecular states from a full nuclear Hamiltonian expressed in terms of normal-mode irreducible tensor operators is presented for the first time. Each term of the Hamiltonian expansion can thus be cast in the tensor form in a systematic way using the formalism of ladder operators. Pyramidal XY3 molecules appear to be good candidates to validate this approach which allows taking advantage of the symmetry properties when doubly degenerate vibrational modes are considered. Examples of applications will be given for PH3 where variational calculations have been carried out from our recent potential energy surface [Nikitin et al., J. Chem. Phys. 130, 244312 (2009)].

Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing energy levels from potential energy surfaces for symmetric-top molecules

Rotational analyses of the four fundamental bands, equilibrium structure, and general quadratic force field of PD3

A spectrometer for infrared microwave double resonance with an intense Stark field is described that is useful for accurate determination of dipole moments and other electric properties of molecules. High precision and sensitivity are attained by the use of gold‐coated glass optical‐flat Stark plates, a white‐type multiple reflection optical path, and microwave frequency stabilization. The spectrometer was tested by observing double resonances in H2CO with a CO laser as an infrared light source, and was shown to be adequate for measurement of dipole moments to better than ±10−4D.

Infrared laser microwave double‐resonance spectrometer with a high‐precision multipass stark cell

CO laser-microwave double-resonance spectroscopy of H2CO with intense Stark field. Precise measurement of dipole moment in the ground and ν2 vibrational states

Kazuhiro Kijima

Papers

Rotational analyses of the four fundamental bands, equilibrium structure, and general quadratic force field of PD3

Infrared laser microwave double‐resonance spectrometer with a high‐precision multipass stark cell

CO laser-microwave double-resonance spectroscopy of H2CO with intense Stark field. Precise measurement of dipole moment in the ground and ν2 vibrational states