The atomic characteristics, which govern changes in bonding properties due to relativistic effects in heavy atoms, are identified from a scattering theoretic standpoint. It is shown that within an all-electron calculation scalar relativistic corrections to valence orbitals relevant to atomic bonding properties can be made via a local pseudopotential for all elements. The present approach reproduces molecular geometries and vibrational frequencies excellently for a test set of relatively simple molecules, where good experimental data are available. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 423–433, 1998

A scattering theoretic approach to scalar relativistic corrections on bonding

The fundamental role of Eckart vectors and Eckart frames is demonstrated in the theort of the vibration--rotation Hamiltonian for a polyatomic molecule. (AIP)

Eckart vectors, Eckart frames, and polyatomic molecules

Every design problem begins with an effort to achieve fitness between two entities: the form in question and its context. The form is the solution to the problem; the context defines the problem. We want to put the context and the form into effortless contact or frictionless coexistence, i.e., we want to find a good fit. For a good fit to occur in practice, one vital condition must be satisfied. It must have time to happen. In slow-changing, traditional, unselfconscious cultures, a form is adjusted soon after each slight misfit occurs. If there was good fit at some stage in the past, no matter how removed, it will have persisted, because there is an active stability at work. Tradition and taboo dampen and control the rate of change in an unselfconscious culture's designs. It is important to understand that the individual person in an unselfconscious culture needs no creative strength. He does not need to be able to improve the form, only to make some sort of change when he notices a failure. The changes may not always be for the better; but it is not necessary that they should be, since the operation of the process allows only the improvements to persist. Unselfconscious design is a process of slow adaptation and error reduction. In the unselfconscious process there is no possibility of misconstruing the situation. Nobody makes a picture of the context, so the picture cannot be wrong. But the modern, selfconscious designer works entirely from a picture in his mind - a conceptualization of the forces at work and their interrelationships - and this picture is almost always wrong. To achieve in a few hours at the drawing board what once took centuries of adaptation and development, to invent a form suddenly which clearly fits its context - the extent of invention necessary is beyond the individual designer. A designer who sets out to achieve an adaptive good fit in a single leap is not unlike the child who shakes his glass-topped puzzle fretfully, expecting at one shake to arrange the bits inside correctly. The designer's attempt is hardly as random as the child's is; but the difficulties are the same. His chances of success are small because the number of factors which must fall simultaneously into place is so enormous. The process of design, even when it has become selfconscious, remains a process of error-reduction. No complex system will succeed in adapting in a reasonable amount of time or effort unless the adaptation can proceed component by component, each component relatively independent of the others. The search for the right components, and the right way to build the form up from these components, is the greatest challenge faced by the modern, selfconscious designer. The culmination of the modern designer's task is to make every unit of design both a component and a system. As a component it will fit into the hierarchy of larger components that are above it; as a system it will specify the hierarchy of smaller components of which it itself is made.

Notes on the Synthesis of Form. By Christopher Alexander. Pp. 191. 54s. 1964. (Harvard University Press.)

A rotational analog of the vibrational potential energy surface is introduced for describing the rotational fine structure of polyatomic molecules. Classical trajectories on rotational energy (RE) surfaces are related to quantum rotational eigenvalue structure. Interpretation of RE surfaces shows how very different types of molecules may undergo dynamical symmetry breaking and a corresponding clustering of rotational energy sublevels for high angular momentum (J>10). Cluster splitting and spacing are calculated using semiclassical quantization methods. Some consequences of dynamical symmetry breaking such as mixing of nuclear spin species are discussed qualitatively.

Rotational energy surfaces and high‐J eigenvalue structure of polyatomic molecules

Excitation of polyatomic molecules by radiation

The infrared-active combination bands of SF/sub 6/ gas were remeasured and the band origins estimated. These data were combined with the Raman frequencies of Bosworth et al., and with the spectrum of SF/sub 6/ in cryogenic liquid oxygen solutions reported by Bertsev et al., to obtain estimates for the 21 anharmonicity constants X/sub ij/. The resulting harmonic vibrational frequencies were used in a calculation of the general quadratic harmonic force field of SF/sub 6/. The most useful constraint in the F/sub 1//sub u/ symmetry block was the Coriolis constant zeta/sub 3/ = 0.693 +- 0.004 obtained from an analysis of ..nu../sub 3/ resolved with tunable diode lasers; but zeta/sub 4/ estimated from a similar analysis of ..nu../sub 4/, and the /sup 32/S--/sup 34/S isotope frequency shifts reported by Brunet and Perez for these fundamentals, are all in general agreement. The more important valence force constants are f/sub r/ = 5.45 +- 0.03, f/sub rr/(cis interaction) = 0.36 +- 0.01, f/sub rr'/ (trans interaction) = -0.02 +- 0.03, and f/sub ..cap alpha../ approximately 0.83, all in mdyn/A. From the absolute band intensities of Schatz and Hornig and the present force field, the S--F bond moment and its derivative are estimated tomore » be ..mu../sub 0/ = 2.44 +- 0.12 D and delta ..mu../delta r = 4.2 +- 0.3 D/A.« less

Vibrational constants and force field of sulfur hexafluoride

Octahedral fine-structure splittings in ν3 of SF6☆

High‐resolution spectra of the infrared‐active stretching fundamental ν3 of 238UF6 have been obtained between 620.6 and 633.5 cm−1 using tunable semiconductor diode lasers. Interference from hot bands was suppressed by cooling the UF6 in a supersonic expansion, and useful monomer concentrations were produced with effective temperatures of <100 K. Portions of the band from P(77) to R(66) are illustrated. All transitions from the vibrational ground state have been assigned, and the Q branch has been fully analyzed. A total of 43 line frequencies and 110 frequency differences extending in J to P(77), Q(91), and R(67) has been used to fit seven spectroscopic constants. The ground‐ and excited‐state values of the rotational constant B could be individually determined, and the U–F bond length in the ground vibrational state is r0=1.9962±0.0007 A. The Q branch of 235UF6 has also been analyzed and the 235UF6–238UF6 ν3 isotope shift measured to be 0.603 79±0.000 17 cm−1. The isotope shift and the Coriolis constant...

Measurement and analysis of the infrared‐active stretching fundamental (ν3) of UF6

High-resolution spectroscopy of the 16-μm bending fundamental of CF4☆

The ν3 bands of 187Os16O4, 189Os16O4, and 192Os16O4 have been recorded using both a Michelson interferometer (resolution 0.06 cm−1) and a tunable semiconductor diode laser (resolution limited by the Doppler width, ∼0.0007 cm−1). The rotational fine structure differs from that of most other spherical‐top molecules, for only rotational levels of A symmetry exist. A total of 112 individual vibration–rotation lines in the P and R branches of the three isotopic species were calibrated against stimulated emission lines from a high‐voltage CO2 gain cell, and were used to determine three scalar and two tensor spectroscopic constants for each species; an additional scalar constant was obtained from an analysis of the Q branch of 192OsO4. The strength of P (11) A2 0 was measured for 192OsO4 and yields a vibrational transition moment for ν3 of 0.17±0.02 D. Transitions of all isotopic species that are expected to fall near CO2 laser lines in the region 949–972 cm−1 are tabulated as an aid in the interpreation of satu...

J. P. Aldridge

Papers

Vibrational constants and force field of sulfur hexafluoride

Octahedral fine-structure splittings in ν3 of SF6☆

Measurement and analysis of the infrared‐active stretching fundamental (ν3) of UF6

High-resolution spectroscopy of the 16-μm bending fundamental of CF4☆

High resolution spectroscopy of the OsO4 stretching fundamental at 961 cm−1