Quantum chemical studies of carbon-13 equilibrium fractionation in ion–molecule reactions

Ab initio computational quantum chemical methods are used to calculate reduced partition function ratios for all isotopomers of CO, HCO+,HCO+, and HOC+HOC+ involving the nuclides 1H,1H, 2H2H (D), 12C,12C, 13C,13C, 16O,16O, and 18O.18O. The ratios are used to calculate equilibrium constants for the reaction pairs HCO+/CO,HCO+/CO, HOC+/CO,HOC+/CO, and C+/CO.C+/CO. Both simple proton transfers and more complex isotopic variants involving the breaking and reforming of CO bonds are considered. The probable pathways for the HCO+/COHCO+/CO and C+/COC+/CO exchange reactions are explored in detail using high-accuracy quantum chemical calculations. It appears most likely that the HCO+/COHCO+/CO reaction proceeds through exothermic formation of the linear adduct OCHCO+OCHCO+ with D∞hD∞h symmetry. Similarly, the C+/COC+/CO reaction proceeds along a spin-allowed pathway with exothermic formation of the linear adduct COC+COC+ with D∞hD∞h symmetry. An alternate but higher energy spin-allowed pathway for the C+/COC+/CO reaction passes through a transition state with only CsCs symmetry and a locally stable intermediate with C2vC2v symmetry. In the ISM these reactions may proceed by these direct pathways or indirectly through coupled exothermic reaction pairs involving other species to achieve 13C/12C13C/12C isotope exchange. © 1998 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70679/2/JCPSA6-108-19-8012-1.pd

Simple Model of the Dynamic Jahn‐Teller Effect in Six‐Coordinated Copper(II) Complexes

A model potential is assumed for describing the vibrational degrees of freedom associated with the Jahn‐Teller effect in six‐coordinated copper (II) complexes. The pseudorotational limit is characterized by a potential that is constant in the region between two concentric cylinders, but becomes infinite elsewhere. The energy spectrum is obtained for both angular and radial excitations. A square‐well periodic angular potential is applied as a perturbation, yielding a localization of states. The results are used to describe the temperature dependence of the electron spin resonance spectra of copper (II) complexes with emphasis on the system NaCl:Cu(II) containing the hexachlorocuprate (II) complex.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70781/2/JCPSA6-57-2-702-1.pd

Rotational energy dispersions for van der Waals molecular clusters: Analytic descriptions for Rg3, Rg4, and Rg6

We have obtained analytic expressions, parametric in centrifugal displacement coordinates, which provide exact classical descriptions of the rotational energy dispersions, that is, the dependence of the combined rotational and ‘‘electronic’’ (vibrational potential) energies on the rotational angular momenta, for small molecular clusters bound by van der Waals interactions modeled by pairwise additive Lennard‐Jones 6–12 potential energies. The clusters considered consist of three (equilateral triangle), four (tetrahedron), and six (octahedron) units and serve as models for small clusters of rare‐gas atoms such as argon. This work represents an extension of our recently published study of analytic rotational energy dispersions for diatomic molecules bound by harmonic oscillator, Morse, or Lennard‐Jones potentials [J. Mol. Spectrosc. 155, 205 (1992)]. A parallel set of studies were made using an angular momentum‐conserving simulation program. The physical properties of the clusters that are addressed using our results include calculation of quartic and higher‐order spectroscopic constants, location of rotational instabilities, and characterization of the ‘‘cubic’’ anisotropies for the spherical top clusters A4 and A6. Of particular interest is the result that for each of these cluster types the preferred direction of the rotational angular momentum is parallel to a molecular fourfold axis, leading to reduced symmetries of D2d for tetrahedral A4 and D4h for octahedral A6.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70411/2/JCPSA6-99-9-6369-1.pd

Ab initio synthesis of the ozone ultraviolet continuum

Potential energy surfaces for the ground and excited electronic states responsible for the Hartley continuum of ozone are used to obtain quadratic, cubic, and quartic force constants. Vibrational dependence of rotational constants to sixth order is calculated by perturbation theory. The spectroscopic constants enable computation of rovibronic energy levels. Overlap of ground state and excited state perturbed vibrational wave functions yield Franck–Condon factors. Electric dipole allowed rovibronic transitions are generated under the Ir representation. The entire set of results generate the ultraviolet absorption spectrum. It is shown that inclusion of anharmonic terms in the vibrational Hamiltonian has a small effect upon the final spectrum, whereas rotational broadening plays a greater role in achieving agreement with experiment.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69598/2/JCPSA6-86-10-5329-1.pd

Erratum: Crystal‐field model study of the xenon hexafluoride molecule. I. Energy levels and molecular geometry

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70482/2/JCPSA6-62-5-2013-1.pd

A theoretical study of the optical absorption band shape for xenon hexafluoride

The classical Franck–Condon approximation is used together with the Monte Carlo integration technique to calculate the optical absorption band shape arising in xenon hexafluoride from the pseudo‐Jahn–Teller active t1u bending mode. The potential energy function for this mode has the Devonshire form for the hindered rotational motion of a diatomic molecule in a cubic site and is characterized by three parameters. Results are presented using values of these parameters as determined by Pitzer and Bernstein for the 1A1g electronic ground state and as estimated by us from the crystal‐field model of Wang and Lohr for the 1T1u and 3T1u electronic excited states.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71170/2/JCPSA6-67-5-1935-1.pd

Crystal‐field model study of the xenon hexafluoride molecule. II. Comparisons with other hexavalent xenon molecules

The two‐electron crystal‐field model previously used to describe in detail the energy levels of XeF6 is applied to other hexavalent xenon systems, namely the XeOF4, XeO2F2, and XeO3 molecules and the XeF82−XeF82− ion. Comparisons of the calculated excited state energies of these three molecules at their observed geometries are made to those calculated for various geometries of XeF6. The strong low symmetry fields in XeOF4, XeO2F2, and XeO3 result in very high excitation energies, which may also be taken to represent greater energy stabilization for the lone electron pair relative to that for XeF6. The ground state energy of XeF82−XeF82− is explored as a function of geometry, and within the two‐space considered, the results match the structure observed in solid (NO)2XeF8.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70286/2/JCPSA6-60-10-3916-1.pd

Crystal‐field model study of the xenon hexafluoride molecule. III. Electronic transitions and band shapes

The application of a two‐electron crystal‐field model to the electronic structure of xenon hexafluoride is extended to include the calculation of oscillator strengths for absorption transitions to the largely spin singlet and the largely spin triplet excited states. Band shapes are calculated in terms of their spectral moments by obtaining vibrational energies and wavefunctions for the mixed quadratic‐quartic potential energy functions calculated from the crystal‐field model. The key experimental features of the absorption spectrum of the vapor are reproduced, namely the pronounced red shift and the increased bandwidth with rising temperature. The over‐all similarity of the vapor spectrum to that of the isovalent hexahalotellurate (IV) complexes in solids in noted. It is concluded that the experimental data of Claassen, Goodman, and Kim are compatible with the pseudo‐Jahn‐Teller model of Gillespie as developed by Bartell and Gavin and by Wang and Lohr, and that the data do not require the use of the electronic isomers model of Goodman, although the latter model is not excluded.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70287/2/JCPSA6-61-10-4110-1.pd

Thermal relaxation of electron spin motion in a thermal equilibrium ensemble: Relation to paramagnetic nuclear magnetic resonance relaxation

The electron spin relaxation times measured in ESR spectroscopy are physically distinct from the electron spin relaxation times which appear in the theory of NMR Paramagnetic Relaxation Enhancement (NMR-PRE). ESR involves decay of a perturbed spin density matrix toward thermal equilibrium, while in NMR-PRE measurements, the electron spin density matrix remains at thermal equilibrium throughout the NMR experiment. The pertinent spin relaxation involves the thermal decay of the time correlation functions, Gr(τ) ≡ 〈Sr(0)⋅Sr(τ)〉 (r = x,y,z),Gr(τ)≡〈Sr(0)⋅Sr(τ)〉(r=x,y,z), of the spin components, quantities which describe the persistence in microscopic correlation of the spin motion in the thermal equilibrium sample. The decay of the Gr(τ)Gr(τ) is shown to be level-specific; i.e., Gr(τ)Gr(τ) is composed of a sum of contribution associated with individual eigenstates, each of which decays exponentially via a process that is uncoupled to the decay in other eigenstates. This behavior differs markedly from the decay of the nonequilibrium parts of a perturbed density matrix, which involves coupled degree of freedom of the electron spin system. An expression for the level-specific relaxation times has been derived in terms of Redfield matrix elements. This expression is valid for any S⩾1 when the static spin Hamiltonian consists of Zeeman and zfs contributions of arbitrary magnitude. Simple closed-form expressions are given for level-specific relaxation times in the cylindrical and orthorhombic zfs limits for S=1 and S=3/2. The theory is used to interpret electron and nuclear spin relaxation for S=3/2 with specific reference to high-spin Co(II), for which the zfs splittings are typically large. For this spin system, the presence of orthorhombic terms in the zfs tensor causes profound shortening of the electron spin relaxation times relative to the reference cylindrical zfs case and, in consequence, a comparably large rhombicity-induced depression of the NMR relaxation efficiency. © 2001 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70242/2/JCPSA6-115-11-5005-1.pd

Rotational energy dispersions: Analytic descriptions

Closed-form analytic expressions parametric in the centrifugal displacement are presented for the dependence of the classical rotational energy of a harmonic oscillator (HO), Morse oscillator (MO), and Lennard-Jones 6-12 oscillator (LJO) upon the rotational angular momentum. Powerseries expansions of the energy in terms of the angular momentum are used to construct Pade approximants for the rotational energy dispersion which approximate well the exact parametric solutions and which may be used for fitting experimental spectroscopic data.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30323/1/0000725.pd